School of Multiple Access Engineering - MyWWW ZHAWrumc/MSEwirecom/0_basics/MSEwirecom MAC… ·...
35
School of Engineering Kontakt: ZHAW Zürcher Hochschule für angewandte Wissenschaften Prof. Dr. M. Rupf ZSN Zentrum für Signalverarbeitung und Nachrichtentechnik Technikumstrasse 9, TB 409 CH-8401 Winterthur Tel: ++41 (0)58 934 7129 Mail: [email protected] Web: http://www.zsn.zhaw.ch Literature [1] Christian Lüders, „Mobilfunksysteme“, Grundlagen, Funktionsweise, Planungsaspekte, Vogel Buchverlag, 2001. see Chapter 4 and 7 partly. [2] Jean-Frédéric Wagen, „Mobile & Wireless Networks and Services“, 2009. see Chapter 2. [3] Jochen Schiller, „Mobile Communications“, 2. Edition, Addision-Wesley, 2003. [4] Ke-Lin Du, M.N.S. Swamy, "Wireless Communication Systems", Cambridge, 2010. Multiple Access MSE-WCom, MAC, 1
Transcript of School of Multiple Access Engineering - MyWWW ZHAWrumc/MSEwirecom/0_basics/MSEwirecom MAC… ·...
School of
Engineering
Kontakt
ZHAW Zuumlrcher Hochschule fuumlr angewandte Wissenschaften
Prof Dr M Rupf
ZSN Zentrum fuumlr Signalverarbeitung und Nachrichtentechnik
Technikumstrasse 9 TB 409
CH-8401 Winterthur
Tel ++41 (0)58 934 7129
Mail marcelrupfzhawch
Web httpwwwzsnzhawch
Literature
[1] Christian Luumlders bdquoMobilfunksystemeldquo Grundlagen Funktionsweise
Planungsaspekte Vogel Buchverlag 2001
see Chapter 4 and 7 partly
[2] Jean-Freacutedeacuteric Wagen bdquoMobile amp Wireless Networks and Servicesldquo 2009
see Chapter 2
[3] Jochen Schiller bdquoMobile Communicationsldquo 2 Edition Addision-Wesley 2003
[4] Ke-Lin Du MNS Swamy Wireless Communication Systems Cambridge 2010
Multiple Access MSE-WCom MAC 1
School of
Engineering Multiple Access
time
frequency
code T
B
0
1
2
space
Radio channel assignment
dedicated frequency bands assigned to mobile radio standards
efficient radio channel assignment to active mobile subscribers
as many connections as possible at the bdquosameldquo time
Multiplex techniques
space - Space Division Multiple Access (SDMA)
time - Time Division Multiple Access (TDMA)
frequency - Frequency Division Multiple Access (FDMA)
code - Code Division Multiple Access (CDMA)
MSE-WCom MAC 2
School of
Engineering FDMA Frequency Division Multiple Access
f 1 2 3 hellip N
Uplink-Carriers Downlink-Carriers
1 2 3 hellip N
Carrier distance
B0 ~ 1Tsym
Example GSM900
UL 890-915 MHz
N=124 channels
channel separation B0 = 200 kHz
(bit period Tsym = 37 us)
P
Frequency-Duplex-Separation
(Frequency Division Duplexing FDD)
Example GSM900
DL 935-960 MHz
N=124 channels
B0 = 200 kHz
duplex separation = 45 MHz
neighbouring
channel
interference
Gu
ard
Ba
nd
Gu
ard
Ba
nd
Gu
ard
Ba
nd
Gu
ard
Ba
nd
User-separation in frequency
the user permanently transmit but only on a part of the bandwidth Btot
MSE-WCom MAC 3
School of
Engineering
0 1 2 3 hellip N-1 0 1 2 3 hellip i hellip N-1 0
TDMA-frame
GSM-frame = 46 ms with N = 8 time-slots
time slot i
(GSM time slot = 0577 ms)
User-separation in time
the user transmit for short periods only but on the whole bandwidth Btot
synchronisation is required (or big guard periods)
higher data rates by assigning more than one time slot
also dynamic and asymmetric partition of time-slots for data services
guard period (against overlap caused by
different propagation delays)
t
data bursts of same
connection
TDMA Time Division Multiple Access
time slot 0
guard time Multipath
Burst C 0 burst Burst
time slot 2
MSE-WCom MAC 4
School of
Engineering Example FDMA-TDMA-System GSM [3] p106
FDMA
FDD
(Tbit = 37 us 270 kbs)
small due to time advance
4 TS TDD
for channel estimation
(equalization of 4 bit ISI)
FDMA
MSE-WCom MAC 5
School of
Engineering
MSE-WCom MAC 6
SDMA Space Division Multiple Access
Spatial user-separation
SDMA is used in mobile radio to reuse radio channels in different
spatially separated cells
Example The same radio channels can be reused in the cells with the same laquocolorraquo
(because spatial separation is large enough to prevent co-channel interference)
in the following we consider the concept of cellular radio coverage more thoroughly
School of
Engineering SDMA MIMO
N M
hNM
Multiple-In-Multiple-Out- systems
bull use of several signal paths between Tx and Rx
by using several Rx- and Tx-antennas
bull most important implementations
ndash Spatial-Diversity mostly with SIMO-configuration
improvement of SNR or reliability in a fading-environment
ndash Spatial-Multiplexing (SDMA)
use of several signal paths in a multipath-environment as
independent data channels to improve data throughput
MSE-WCom MAC 7
School of
Engineering
Coverage of a larger area with many radio cells
contrary requirements
1 reuse of the same channel as often as possible
2 co-channel-interference (Gleichkanalstoumlrung) as small as possible
Spatial decoupling of two co-channel-transmitters (SDMA)
co-channel interference no longer bdquonoticeableldquo
co-channel
distance D
cell radius R
D D
D
equilateral
co-channel
triangle
further BS
required
Hexagon circular coverage
with overlaping areas as small as possible
Concept of cellular radio coverage MSE-WCom MAC 8
School of
Engineering
R
D1 D2
D3
D4 D5
D6
Co-channel minimum distance D is dependent of the desired CI
user at cell border
carrier power C ~ R-γ
γ propagation parameter
(typical 35 4 in urban mobile radio)
interference from 6
co-channel neighbouring cells
carrier-to-interference-ratio CI asymp R-γ (6D-γ)
depends on modulation type FEC etc
interference-limited operation (ne thermal noise limited)
Normalized frequency reuse distance q = DR asymp (6middotCI)1γ
6-γ -γ
k
k=1
I = D 6 D D
Frequency reuse distance MSE-WCom MAC 9
School of
Engineering
Homogeneous hexagonal radio network
ij-coordinates with 600 disposed axis
unit length ei=ej=radic3∙R corresponds edge length of elementary triangle
Tx with coordinates (i1j1) has distance d = radic(i12+i1j1+j1
2) to origin
Co-channel diamond is a basic component for area-wide network
area diamond AR = radic3∙D2 2 hexagonal cell area AZ = 6∙radic3∙R2 4
Cluster size N is a function of the (normalized) reuse distance
number of cells in the diamond N ge AR AZ = D2 (3R2) = q23
q = radic(3N)
i-axis
j-axis
ei
ej
D
D
diamond
Cluster with N=4
Cluster size MSE-WCom MAC 10
School of
Engineering
Example
Assume a required CI =18 dB for acceptable service quality
GSM CI ge 9 dB typical ge 12 dB
Assume a radio propagation parameter γ=4
=gt frequency reuse distance q = DR = (6∙1018)14 = 4411
=gt cluster size N ge q23 = 64857 =gt N=7
radio network with two clusters of N=7 cells
R D
channelcarrier groups
0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
cell 0
0 0
1
1
2
2 3 3
4
4
5
5
6 6
Concept of cellular radio coverage MSE-WCom MAC 11
School of
Engineering
Cluster-size N = I2+IJ+J2 IgeJ
I J N q=radic(3N) CI asymp 10middotlog10(q46)
1 0 1 173 174 dB
1 1 3 300 1130 dB
2 0 4 346 1378 dB
2 1 7 458 1865 dB
3 0 9 520 2086 dB
2 2 12 600 2335 dB
3 1 13 624 2403 dB
4 0 16 693 2585 dB
Concept of cellular radio coverage
co-channel BS
cluster 4 cluster 7
BS
serving cell
CI
cell boarder
The smaller the cluster size N
=gt the larger the interference I
(the Rx has to cope with)
=gt the larger the capacity ie
number of carriers cell
= total carriers N
distance
C I I
MSE-WCom MAC 12
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering Multiple Access
time
frequency
code T
B
0
1
2
space
Radio channel assignment
dedicated frequency bands assigned to mobile radio standards
efficient radio channel assignment to active mobile subscribers
as many connections as possible at the bdquosameldquo time
Multiplex techniques
space - Space Division Multiple Access (SDMA)
time - Time Division Multiple Access (TDMA)
frequency - Frequency Division Multiple Access (FDMA)
code - Code Division Multiple Access (CDMA)
MSE-WCom MAC 2
School of
Engineering FDMA Frequency Division Multiple Access
f 1 2 3 hellip N
Uplink-Carriers Downlink-Carriers
1 2 3 hellip N
Carrier distance
B0 ~ 1Tsym
Example GSM900
UL 890-915 MHz
N=124 channels
channel separation B0 = 200 kHz
(bit period Tsym = 37 us)
P
Frequency-Duplex-Separation
(Frequency Division Duplexing FDD)
Example GSM900
DL 935-960 MHz
N=124 channels
B0 = 200 kHz
duplex separation = 45 MHz
neighbouring
channel
interference
Gu
ard
Ba
nd
Gu
ard
Ba
nd
Gu
ard
Ba
nd
Gu
ard
Ba
nd
User-separation in frequency
the user permanently transmit but only on a part of the bandwidth Btot
MSE-WCom MAC 3
School of
Engineering
0 1 2 3 hellip N-1 0 1 2 3 hellip i hellip N-1 0
TDMA-frame
GSM-frame = 46 ms with N = 8 time-slots
time slot i
(GSM time slot = 0577 ms)
User-separation in time
the user transmit for short periods only but on the whole bandwidth Btot
synchronisation is required (or big guard periods)
higher data rates by assigning more than one time slot
also dynamic and asymmetric partition of time-slots for data services
guard period (against overlap caused by
different propagation delays)
t
data bursts of same
connection
TDMA Time Division Multiple Access
time slot 0
guard time Multipath
Burst C 0 burst Burst
time slot 2
MSE-WCom MAC 4
School of
Engineering Example FDMA-TDMA-System GSM [3] p106
FDMA
FDD
(Tbit = 37 us 270 kbs)
small due to time advance
4 TS TDD
for channel estimation
(equalization of 4 bit ISI)
FDMA
MSE-WCom MAC 5
School of
Engineering
MSE-WCom MAC 6
SDMA Space Division Multiple Access
Spatial user-separation
SDMA is used in mobile radio to reuse radio channels in different
spatially separated cells
Example The same radio channels can be reused in the cells with the same laquocolorraquo
(because spatial separation is large enough to prevent co-channel interference)
in the following we consider the concept of cellular radio coverage more thoroughly
School of
Engineering SDMA MIMO
N M
hNM
Multiple-In-Multiple-Out- systems
bull use of several signal paths between Tx and Rx
by using several Rx- and Tx-antennas
bull most important implementations
ndash Spatial-Diversity mostly with SIMO-configuration
improvement of SNR or reliability in a fading-environment
ndash Spatial-Multiplexing (SDMA)
use of several signal paths in a multipath-environment as
independent data channels to improve data throughput
MSE-WCom MAC 7
School of
Engineering
Coverage of a larger area with many radio cells
contrary requirements
1 reuse of the same channel as often as possible
2 co-channel-interference (Gleichkanalstoumlrung) as small as possible
Spatial decoupling of two co-channel-transmitters (SDMA)
co-channel interference no longer bdquonoticeableldquo
co-channel
distance D
cell radius R
D D
D
equilateral
co-channel
triangle
further BS
required
Hexagon circular coverage
with overlaping areas as small as possible
Concept of cellular radio coverage MSE-WCom MAC 8
School of
Engineering
R
D1 D2
D3
D4 D5
D6
Co-channel minimum distance D is dependent of the desired CI
user at cell border
carrier power C ~ R-γ
γ propagation parameter
(typical 35 4 in urban mobile radio)
interference from 6
co-channel neighbouring cells
carrier-to-interference-ratio CI asymp R-γ (6D-γ)
depends on modulation type FEC etc
interference-limited operation (ne thermal noise limited)
Normalized frequency reuse distance q = DR asymp (6middotCI)1γ
6-γ -γ
k
k=1
I = D 6 D D
Frequency reuse distance MSE-WCom MAC 9
School of
Engineering
Homogeneous hexagonal radio network
ij-coordinates with 600 disposed axis
unit length ei=ej=radic3∙R corresponds edge length of elementary triangle
Tx with coordinates (i1j1) has distance d = radic(i12+i1j1+j1
2) to origin
Co-channel diamond is a basic component for area-wide network
area diamond AR = radic3∙D2 2 hexagonal cell area AZ = 6∙radic3∙R2 4
Cluster size N is a function of the (normalized) reuse distance
number of cells in the diamond N ge AR AZ = D2 (3R2) = q23
q = radic(3N)
i-axis
j-axis
ei
ej
D
D
diamond
Cluster with N=4
Cluster size MSE-WCom MAC 10
School of
Engineering
Example
Assume a required CI =18 dB for acceptable service quality
GSM CI ge 9 dB typical ge 12 dB
Assume a radio propagation parameter γ=4
=gt frequency reuse distance q = DR = (6∙1018)14 = 4411
=gt cluster size N ge q23 = 64857 =gt N=7
radio network with two clusters of N=7 cells
R D
channelcarrier groups
0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
cell 0
0 0
1
1
2
2 3 3
4
4
5
5
6 6
Concept of cellular radio coverage MSE-WCom MAC 11
School of
Engineering
Cluster-size N = I2+IJ+J2 IgeJ
I J N q=radic(3N) CI asymp 10middotlog10(q46)
1 0 1 173 174 dB
1 1 3 300 1130 dB
2 0 4 346 1378 dB
2 1 7 458 1865 dB
3 0 9 520 2086 dB
2 2 12 600 2335 dB
3 1 13 624 2403 dB
4 0 16 693 2585 dB
Concept of cellular radio coverage
co-channel BS
cluster 4 cluster 7
BS
serving cell
CI
cell boarder
The smaller the cluster size N
=gt the larger the interference I
(the Rx has to cope with)
=gt the larger the capacity ie
number of carriers cell
= total carriers N
distance
C I I
MSE-WCom MAC 12
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering FDMA Frequency Division Multiple Access
f 1 2 3 hellip N
Uplink-Carriers Downlink-Carriers
1 2 3 hellip N
Carrier distance
B0 ~ 1Tsym
Example GSM900
UL 890-915 MHz
N=124 channels
channel separation B0 = 200 kHz
(bit period Tsym = 37 us)
P
Frequency-Duplex-Separation
(Frequency Division Duplexing FDD)
Example GSM900
DL 935-960 MHz
N=124 channels
B0 = 200 kHz
duplex separation = 45 MHz
neighbouring
channel
interference
Gu
ard
Ba
nd
Gu
ard
Ba
nd
Gu
ard
Ba
nd
Gu
ard
Ba
nd
User-separation in frequency
the user permanently transmit but only on a part of the bandwidth Btot
MSE-WCom MAC 3
School of
Engineering
0 1 2 3 hellip N-1 0 1 2 3 hellip i hellip N-1 0
TDMA-frame
GSM-frame = 46 ms with N = 8 time-slots
time slot i
(GSM time slot = 0577 ms)
User-separation in time
the user transmit for short periods only but on the whole bandwidth Btot
synchronisation is required (or big guard periods)
higher data rates by assigning more than one time slot
also dynamic and asymmetric partition of time-slots for data services
guard period (against overlap caused by
different propagation delays)
t
data bursts of same
connection
TDMA Time Division Multiple Access
time slot 0
guard time Multipath
Burst C 0 burst Burst
time slot 2
MSE-WCom MAC 4
School of
Engineering Example FDMA-TDMA-System GSM [3] p106
FDMA
FDD
(Tbit = 37 us 270 kbs)
small due to time advance
4 TS TDD
for channel estimation
(equalization of 4 bit ISI)
FDMA
MSE-WCom MAC 5
School of
Engineering
MSE-WCom MAC 6
SDMA Space Division Multiple Access
Spatial user-separation
SDMA is used in mobile radio to reuse radio channels in different
spatially separated cells
Example The same radio channels can be reused in the cells with the same laquocolorraquo
(because spatial separation is large enough to prevent co-channel interference)
in the following we consider the concept of cellular radio coverage more thoroughly
School of
Engineering SDMA MIMO
N M
hNM
Multiple-In-Multiple-Out- systems
bull use of several signal paths between Tx and Rx
by using several Rx- and Tx-antennas
bull most important implementations
ndash Spatial-Diversity mostly with SIMO-configuration
improvement of SNR or reliability in a fading-environment
ndash Spatial-Multiplexing (SDMA)
use of several signal paths in a multipath-environment as
independent data channels to improve data throughput
MSE-WCom MAC 7
School of
Engineering
Coverage of a larger area with many radio cells
contrary requirements
1 reuse of the same channel as often as possible
2 co-channel-interference (Gleichkanalstoumlrung) as small as possible
Spatial decoupling of two co-channel-transmitters (SDMA)
co-channel interference no longer bdquonoticeableldquo
co-channel
distance D
cell radius R
D D
D
equilateral
co-channel
triangle
further BS
required
Hexagon circular coverage
with overlaping areas as small as possible
Concept of cellular radio coverage MSE-WCom MAC 8
School of
Engineering
R
D1 D2
D3
D4 D5
D6
Co-channel minimum distance D is dependent of the desired CI
user at cell border
carrier power C ~ R-γ
γ propagation parameter
(typical 35 4 in urban mobile radio)
interference from 6
co-channel neighbouring cells
carrier-to-interference-ratio CI asymp R-γ (6D-γ)
depends on modulation type FEC etc
interference-limited operation (ne thermal noise limited)
Normalized frequency reuse distance q = DR asymp (6middotCI)1γ
6-γ -γ
k
k=1
I = D 6 D D
Frequency reuse distance MSE-WCom MAC 9
School of
Engineering
Homogeneous hexagonal radio network
ij-coordinates with 600 disposed axis
unit length ei=ej=radic3∙R corresponds edge length of elementary triangle
Tx with coordinates (i1j1) has distance d = radic(i12+i1j1+j1
2) to origin
Co-channel diamond is a basic component for area-wide network
area diamond AR = radic3∙D2 2 hexagonal cell area AZ = 6∙radic3∙R2 4
Cluster size N is a function of the (normalized) reuse distance
number of cells in the diamond N ge AR AZ = D2 (3R2) = q23
q = radic(3N)
i-axis
j-axis
ei
ej
D
D
diamond
Cluster with N=4
Cluster size MSE-WCom MAC 10
School of
Engineering
Example
Assume a required CI =18 dB for acceptable service quality
GSM CI ge 9 dB typical ge 12 dB
Assume a radio propagation parameter γ=4
=gt frequency reuse distance q = DR = (6∙1018)14 = 4411
=gt cluster size N ge q23 = 64857 =gt N=7
radio network with two clusters of N=7 cells
R D
channelcarrier groups
0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
cell 0
0 0
1
1
2
2 3 3
4
4
5
5
6 6
Concept of cellular radio coverage MSE-WCom MAC 11
School of
Engineering
Cluster-size N = I2+IJ+J2 IgeJ
I J N q=radic(3N) CI asymp 10middotlog10(q46)
1 0 1 173 174 dB
1 1 3 300 1130 dB
2 0 4 346 1378 dB
2 1 7 458 1865 dB
3 0 9 520 2086 dB
2 2 12 600 2335 dB
3 1 13 624 2403 dB
4 0 16 693 2585 dB
Concept of cellular radio coverage
co-channel BS
cluster 4 cluster 7
BS
serving cell
CI
cell boarder
The smaller the cluster size N
=gt the larger the interference I
(the Rx has to cope with)
=gt the larger the capacity ie
number of carriers cell
= total carriers N
distance
C I I
MSE-WCom MAC 12
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
0 1 2 3 hellip N-1 0 1 2 3 hellip i hellip N-1 0
TDMA-frame
GSM-frame = 46 ms with N = 8 time-slots
time slot i
(GSM time slot = 0577 ms)
User-separation in time
the user transmit for short periods only but on the whole bandwidth Btot
synchronisation is required (or big guard periods)
higher data rates by assigning more than one time slot
also dynamic and asymmetric partition of time-slots for data services
guard period (against overlap caused by
different propagation delays)
t
data bursts of same
connection
TDMA Time Division Multiple Access
time slot 0
guard time Multipath
Burst C 0 burst Burst
time slot 2
MSE-WCom MAC 4
School of
Engineering Example FDMA-TDMA-System GSM [3] p106
FDMA
FDD
(Tbit = 37 us 270 kbs)
small due to time advance
4 TS TDD
for channel estimation
(equalization of 4 bit ISI)
FDMA
MSE-WCom MAC 5
School of
Engineering
MSE-WCom MAC 6
SDMA Space Division Multiple Access
Spatial user-separation
SDMA is used in mobile radio to reuse radio channels in different
spatially separated cells
Example The same radio channels can be reused in the cells with the same laquocolorraquo
(because spatial separation is large enough to prevent co-channel interference)
in the following we consider the concept of cellular radio coverage more thoroughly
School of
Engineering SDMA MIMO
N M
hNM
Multiple-In-Multiple-Out- systems
bull use of several signal paths between Tx and Rx
by using several Rx- and Tx-antennas
bull most important implementations
ndash Spatial-Diversity mostly with SIMO-configuration
improvement of SNR or reliability in a fading-environment
ndash Spatial-Multiplexing (SDMA)
use of several signal paths in a multipath-environment as
independent data channels to improve data throughput
MSE-WCom MAC 7
School of
Engineering
Coverage of a larger area with many radio cells
contrary requirements
1 reuse of the same channel as often as possible
2 co-channel-interference (Gleichkanalstoumlrung) as small as possible
Spatial decoupling of two co-channel-transmitters (SDMA)
co-channel interference no longer bdquonoticeableldquo
co-channel
distance D
cell radius R
D D
D
equilateral
co-channel
triangle
further BS
required
Hexagon circular coverage
with overlaping areas as small as possible
Concept of cellular radio coverage MSE-WCom MAC 8
School of
Engineering
R
D1 D2
D3
D4 D5
D6
Co-channel minimum distance D is dependent of the desired CI
user at cell border
carrier power C ~ R-γ
γ propagation parameter
(typical 35 4 in urban mobile radio)
interference from 6
co-channel neighbouring cells
carrier-to-interference-ratio CI asymp R-γ (6D-γ)
depends on modulation type FEC etc
interference-limited operation (ne thermal noise limited)
Normalized frequency reuse distance q = DR asymp (6middotCI)1γ
6-γ -γ
k
k=1
I = D 6 D D
Frequency reuse distance MSE-WCom MAC 9
School of
Engineering
Homogeneous hexagonal radio network
ij-coordinates with 600 disposed axis
unit length ei=ej=radic3∙R corresponds edge length of elementary triangle
Tx with coordinates (i1j1) has distance d = radic(i12+i1j1+j1
2) to origin
Co-channel diamond is a basic component for area-wide network
area diamond AR = radic3∙D2 2 hexagonal cell area AZ = 6∙radic3∙R2 4
Cluster size N is a function of the (normalized) reuse distance
number of cells in the diamond N ge AR AZ = D2 (3R2) = q23
q = radic(3N)
i-axis
j-axis
ei
ej
D
D
diamond
Cluster with N=4
Cluster size MSE-WCom MAC 10
School of
Engineering
Example
Assume a required CI =18 dB for acceptable service quality
GSM CI ge 9 dB typical ge 12 dB
Assume a radio propagation parameter γ=4
=gt frequency reuse distance q = DR = (6∙1018)14 = 4411
=gt cluster size N ge q23 = 64857 =gt N=7
radio network with two clusters of N=7 cells
R D
channelcarrier groups
0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
cell 0
0 0
1
1
2
2 3 3
4
4
5
5
6 6
Concept of cellular radio coverage MSE-WCom MAC 11
School of
Engineering
Cluster-size N = I2+IJ+J2 IgeJ
I J N q=radic(3N) CI asymp 10middotlog10(q46)
1 0 1 173 174 dB
1 1 3 300 1130 dB
2 0 4 346 1378 dB
2 1 7 458 1865 dB
3 0 9 520 2086 dB
2 2 12 600 2335 dB
3 1 13 624 2403 dB
4 0 16 693 2585 dB
Concept of cellular radio coverage
co-channel BS
cluster 4 cluster 7
BS
serving cell
CI
cell boarder
The smaller the cluster size N
=gt the larger the interference I
(the Rx has to cope with)
=gt the larger the capacity ie
number of carriers cell
= total carriers N
distance
C I I
MSE-WCom MAC 12
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering Example FDMA-TDMA-System GSM [3] p106
FDMA
FDD
(Tbit = 37 us 270 kbs)
small due to time advance
4 TS TDD
for channel estimation
(equalization of 4 bit ISI)
FDMA
MSE-WCom MAC 5
School of
Engineering
MSE-WCom MAC 6
SDMA Space Division Multiple Access
Spatial user-separation
SDMA is used in mobile radio to reuse radio channels in different
spatially separated cells
Example The same radio channels can be reused in the cells with the same laquocolorraquo
(because spatial separation is large enough to prevent co-channel interference)
in the following we consider the concept of cellular radio coverage more thoroughly
School of
Engineering SDMA MIMO
N M
hNM
Multiple-In-Multiple-Out- systems
bull use of several signal paths between Tx and Rx
by using several Rx- and Tx-antennas
bull most important implementations
ndash Spatial-Diversity mostly with SIMO-configuration
improvement of SNR or reliability in a fading-environment
ndash Spatial-Multiplexing (SDMA)
use of several signal paths in a multipath-environment as
independent data channels to improve data throughput
MSE-WCom MAC 7
School of
Engineering
Coverage of a larger area with many radio cells
contrary requirements
1 reuse of the same channel as often as possible
2 co-channel-interference (Gleichkanalstoumlrung) as small as possible
Spatial decoupling of two co-channel-transmitters (SDMA)
co-channel interference no longer bdquonoticeableldquo
co-channel
distance D
cell radius R
D D
D
equilateral
co-channel
triangle
further BS
required
Hexagon circular coverage
with overlaping areas as small as possible
Concept of cellular radio coverage MSE-WCom MAC 8
School of
Engineering
R
D1 D2
D3
D4 D5
D6
Co-channel minimum distance D is dependent of the desired CI
user at cell border
carrier power C ~ R-γ
γ propagation parameter
(typical 35 4 in urban mobile radio)
interference from 6
co-channel neighbouring cells
carrier-to-interference-ratio CI asymp R-γ (6D-γ)
depends on modulation type FEC etc
interference-limited operation (ne thermal noise limited)
Normalized frequency reuse distance q = DR asymp (6middotCI)1γ
6-γ -γ
k
k=1
I = D 6 D D
Frequency reuse distance MSE-WCom MAC 9
School of
Engineering
Homogeneous hexagonal radio network
ij-coordinates with 600 disposed axis
unit length ei=ej=radic3∙R corresponds edge length of elementary triangle
Tx with coordinates (i1j1) has distance d = radic(i12+i1j1+j1
2) to origin
Co-channel diamond is a basic component for area-wide network
area diamond AR = radic3∙D2 2 hexagonal cell area AZ = 6∙radic3∙R2 4
Cluster size N is a function of the (normalized) reuse distance
number of cells in the diamond N ge AR AZ = D2 (3R2) = q23
q = radic(3N)
i-axis
j-axis
ei
ej
D
D
diamond
Cluster with N=4
Cluster size MSE-WCom MAC 10
School of
Engineering
Example
Assume a required CI =18 dB for acceptable service quality
GSM CI ge 9 dB typical ge 12 dB
Assume a radio propagation parameter γ=4
=gt frequency reuse distance q = DR = (6∙1018)14 = 4411
=gt cluster size N ge q23 = 64857 =gt N=7
radio network with two clusters of N=7 cells
R D
channelcarrier groups
0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
cell 0
0 0
1
1
2
2 3 3
4
4
5
5
6 6
Concept of cellular radio coverage MSE-WCom MAC 11
School of
Engineering
Cluster-size N = I2+IJ+J2 IgeJ
I J N q=radic(3N) CI asymp 10middotlog10(q46)
1 0 1 173 174 dB
1 1 3 300 1130 dB
2 0 4 346 1378 dB
2 1 7 458 1865 dB
3 0 9 520 2086 dB
2 2 12 600 2335 dB
3 1 13 624 2403 dB
4 0 16 693 2585 dB
Concept of cellular radio coverage
co-channel BS
cluster 4 cluster 7
BS
serving cell
CI
cell boarder
The smaller the cluster size N
=gt the larger the interference I
(the Rx has to cope with)
=gt the larger the capacity ie
number of carriers cell
= total carriers N
distance
C I I
MSE-WCom MAC 12
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
MSE-WCom MAC 6
SDMA Space Division Multiple Access
Spatial user-separation
SDMA is used in mobile radio to reuse radio channels in different
spatially separated cells
Example The same radio channels can be reused in the cells with the same laquocolorraquo
(because spatial separation is large enough to prevent co-channel interference)
in the following we consider the concept of cellular radio coverage more thoroughly
School of
Engineering SDMA MIMO
N M
hNM
Multiple-In-Multiple-Out- systems
bull use of several signal paths between Tx and Rx
by using several Rx- and Tx-antennas
bull most important implementations
ndash Spatial-Diversity mostly with SIMO-configuration
improvement of SNR or reliability in a fading-environment
ndash Spatial-Multiplexing (SDMA)
use of several signal paths in a multipath-environment as
independent data channels to improve data throughput
MSE-WCom MAC 7
School of
Engineering
Coverage of a larger area with many radio cells
contrary requirements
1 reuse of the same channel as often as possible
2 co-channel-interference (Gleichkanalstoumlrung) as small as possible
Spatial decoupling of two co-channel-transmitters (SDMA)
co-channel interference no longer bdquonoticeableldquo
co-channel
distance D
cell radius R
D D
D
equilateral
co-channel
triangle
further BS
required
Hexagon circular coverage
with overlaping areas as small as possible
Concept of cellular radio coverage MSE-WCom MAC 8
School of
Engineering
R
D1 D2
D3
D4 D5
D6
Co-channel minimum distance D is dependent of the desired CI
user at cell border
carrier power C ~ R-γ
γ propagation parameter
(typical 35 4 in urban mobile radio)
interference from 6
co-channel neighbouring cells
carrier-to-interference-ratio CI asymp R-γ (6D-γ)
depends on modulation type FEC etc
interference-limited operation (ne thermal noise limited)
Normalized frequency reuse distance q = DR asymp (6middotCI)1γ
6-γ -γ
k
k=1
I = D 6 D D
Frequency reuse distance MSE-WCom MAC 9
School of
Engineering
Homogeneous hexagonal radio network
ij-coordinates with 600 disposed axis
unit length ei=ej=radic3∙R corresponds edge length of elementary triangle
Tx with coordinates (i1j1) has distance d = radic(i12+i1j1+j1
2) to origin
Co-channel diamond is a basic component for area-wide network
area diamond AR = radic3∙D2 2 hexagonal cell area AZ = 6∙radic3∙R2 4
Cluster size N is a function of the (normalized) reuse distance
number of cells in the diamond N ge AR AZ = D2 (3R2) = q23
q = radic(3N)
i-axis
j-axis
ei
ej
D
D
diamond
Cluster with N=4
Cluster size MSE-WCom MAC 10
School of
Engineering
Example
Assume a required CI =18 dB for acceptable service quality
GSM CI ge 9 dB typical ge 12 dB
Assume a radio propagation parameter γ=4
=gt frequency reuse distance q = DR = (6∙1018)14 = 4411
=gt cluster size N ge q23 = 64857 =gt N=7
radio network with two clusters of N=7 cells
R D
channelcarrier groups
0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
cell 0
0 0
1
1
2
2 3 3
4
4
5
5
6 6
Concept of cellular radio coverage MSE-WCom MAC 11
School of
Engineering
Cluster-size N = I2+IJ+J2 IgeJ
I J N q=radic(3N) CI asymp 10middotlog10(q46)
1 0 1 173 174 dB
1 1 3 300 1130 dB
2 0 4 346 1378 dB
2 1 7 458 1865 dB
3 0 9 520 2086 dB
2 2 12 600 2335 dB
3 1 13 624 2403 dB
4 0 16 693 2585 dB
Concept of cellular radio coverage
co-channel BS
cluster 4 cluster 7
BS
serving cell
CI
cell boarder
The smaller the cluster size N
=gt the larger the interference I
(the Rx has to cope with)
=gt the larger the capacity ie
number of carriers cell
= total carriers N
distance
C I I
MSE-WCom MAC 12
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering SDMA MIMO
N M
hNM
Multiple-In-Multiple-Out- systems
bull use of several signal paths between Tx and Rx
by using several Rx- and Tx-antennas
bull most important implementations
ndash Spatial-Diversity mostly with SIMO-configuration
improvement of SNR or reliability in a fading-environment
ndash Spatial-Multiplexing (SDMA)
use of several signal paths in a multipath-environment as
independent data channels to improve data throughput
MSE-WCom MAC 7
School of
Engineering
Coverage of a larger area with many radio cells
contrary requirements
1 reuse of the same channel as often as possible
2 co-channel-interference (Gleichkanalstoumlrung) as small as possible
Spatial decoupling of two co-channel-transmitters (SDMA)
co-channel interference no longer bdquonoticeableldquo
co-channel
distance D
cell radius R
D D
D
equilateral
co-channel
triangle
further BS
required
Hexagon circular coverage
with overlaping areas as small as possible
Concept of cellular radio coverage MSE-WCom MAC 8
School of
Engineering
R
D1 D2
D3
D4 D5
D6
Co-channel minimum distance D is dependent of the desired CI
user at cell border
carrier power C ~ R-γ
γ propagation parameter
(typical 35 4 in urban mobile radio)
interference from 6
co-channel neighbouring cells
carrier-to-interference-ratio CI asymp R-γ (6D-γ)
depends on modulation type FEC etc
interference-limited operation (ne thermal noise limited)
Normalized frequency reuse distance q = DR asymp (6middotCI)1γ
6-γ -γ
k
k=1
I = D 6 D D
Frequency reuse distance MSE-WCom MAC 9
School of
Engineering
Homogeneous hexagonal radio network
ij-coordinates with 600 disposed axis
unit length ei=ej=radic3∙R corresponds edge length of elementary triangle
Tx with coordinates (i1j1) has distance d = radic(i12+i1j1+j1
2) to origin
Co-channel diamond is a basic component for area-wide network
area diamond AR = radic3∙D2 2 hexagonal cell area AZ = 6∙radic3∙R2 4
Cluster size N is a function of the (normalized) reuse distance
number of cells in the diamond N ge AR AZ = D2 (3R2) = q23
q = radic(3N)
i-axis
j-axis
ei
ej
D
D
diamond
Cluster with N=4
Cluster size MSE-WCom MAC 10
School of
Engineering
Example
Assume a required CI =18 dB for acceptable service quality
GSM CI ge 9 dB typical ge 12 dB
Assume a radio propagation parameter γ=4
=gt frequency reuse distance q = DR = (6∙1018)14 = 4411
=gt cluster size N ge q23 = 64857 =gt N=7
radio network with two clusters of N=7 cells
R D
channelcarrier groups
0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
cell 0
0 0
1
1
2
2 3 3
4
4
5
5
6 6
Concept of cellular radio coverage MSE-WCom MAC 11
School of
Engineering
Cluster-size N = I2+IJ+J2 IgeJ
I J N q=radic(3N) CI asymp 10middotlog10(q46)
1 0 1 173 174 dB
1 1 3 300 1130 dB
2 0 4 346 1378 dB
2 1 7 458 1865 dB
3 0 9 520 2086 dB
2 2 12 600 2335 dB
3 1 13 624 2403 dB
4 0 16 693 2585 dB
Concept of cellular radio coverage
co-channel BS
cluster 4 cluster 7
BS
serving cell
CI
cell boarder
The smaller the cluster size N
=gt the larger the interference I
(the Rx has to cope with)
=gt the larger the capacity ie
number of carriers cell
= total carriers N
distance
C I I
MSE-WCom MAC 12
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
Coverage of a larger area with many radio cells
contrary requirements
1 reuse of the same channel as often as possible
2 co-channel-interference (Gleichkanalstoumlrung) as small as possible
Spatial decoupling of two co-channel-transmitters (SDMA)
co-channel interference no longer bdquonoticeableldquo
co-channel
distance D
cell radius R
D D
D
equilateral
co-channel
triangle
further BS
required
Hexagon circular coverage
with overlaping areas as small as possible
Concept of cellular radio coverage MSE-WCom MAC 8
School of
Engineering
R
D1 D2
D3
D4 D5
D6
Co-channel minimum distance D is dependent of the desired CI
user at cell border
carrier power C ~ R-γ
γ propagation parameter
(typical 35 4 in urban mobile radio)
interference from 6
co-channel neighbouring cells
carrier-to-interference-ratio CI asymp R-γ (6D-γ)
depends on modulation type FEC etc
interference-limited operation (ne thermal noise limited)
Normalized frequency reuse distance q = DR asymp (6middotCI)1γ
6-γ -γ
k
k=1
I = D 6 D D
Frequency reuse distance MSE-WCom MAC 9
School of
Engineering
Homogeneous hexagonal radio network
ij-coordinates with 600 disposed axis
unit length ei=ej=radic3∙R corresponds edge length of elementary triangle
Tx with coordinates (i1j1) has distance d = radic(i12+i1j1+j1
2) to origin
Co-channel diamond is a basic component for area-wide network
area diamond AR = radic3∙D2 2 hexagonal cell area AZ = 6∙radic3∙R2 4
Cluster size N is a function of the (normalized) reuse distance
number of cells in the diamond N ge AR AZ = D2 (3R2) = q23
q = radic(3N)
i-axis
j-axis
ei
ej
D
D
diamond
Cluster with N=4
Cluster size MSE-WCom MAC 10
School of
Engineering
Example
Assume a required CI =18 dB for acceptable service quality
GSM CI ge 9 dB typical ge 12 dB
Assume a radio propagation parameter γ=4
=gt frequency reuse distance q = DR = (6∙1018)14 = 4411
=gt cluster size N ge q23 = 64857 =gt N=7
radio network with two clusters of N=7 cells
R D
channelcarrier groups
0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
cell 0
0 0
1
1
2
2 3 3
4
4
5
5
6 6
Concept of cellular radio coverage MSE-WCom MAC 11
School of
Engineering
Cluster-size N = I2+IJ+J2 IgeJ
I J N q=radic(3N) CI asymp 10middotlog10(q46)
1 0 1 173 174 dB
1 1 3 300 1130 dB
2 0 4 346 1378 dB
2 1 7 458 1865 dB
3 0 9 520 2086 dB
2 2 12 600 2335 dB
3 1 13 624 2403 dB
4 0 16 693 2585 dB
Concept of cellular radio coverage
co-channel BS
cluster 4 cluster 7
BS
serving cell
CI
cell boarder
The smaller the cluster size N
=gt the larger the interference I
(the Rx has to cope with)
=gt the larger the capacity ie
number of carriers cell
= total carriers N
distance
C I I
MSE-WCom MAC 12
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
R
D1 D2
D3
D4 D5
D6
Co-channel minimum distance D is dependent of the desired CI
user at cell border
carrier power C ~ R-γ
γ propagation parameter
(typical 35 4 in urban mobile radio)
interference from 6
co-channel neighbouring cells
carrier-to-interference-ratio CI asymp R-γ (6D-γ)
depends on modulation type FEC etc
interference-limited operation (ne thermal noise limited)
Normalized frequency reuse distance q = DR asymp (6middotCI)1γ
6-γ -γ
k
k=1
I = D 6 D D
Frequency reuse distance MSE-WCom MAC 9
School of
Engineering
Homogeneous hexagonal radio network
ij-coordinates with 600 disposed axis
unit length ei=ej=radic3∙R corresponds edge length of elementary triangle
Tx with coordinates (i1j1) has distance d = radic(i12+i1j1+j1
2) to origin
Co-channel diamond is a basic component for area-wide network
area diamond AR = radic3∙D2 2 hexagonal cell area AZ = 6∙radic3∙R2 4
Cluster size N is a function of the (normalized) reuse distance
number of cells in the diamond N ge AR AZ = D2 (3R2) = q23
q = radic(3N)
i-axis
j-axis
ei
ej
D
D
diamond
Cluster with N=4
Cluster size MSE-WCom MAC 10
School of
Engineering
Example
Assume a required CI =18 dB for acceptable service quality
GSM CI ge 9 dB typical ge 12 dB
Assume a radio propagation parameter γ=4
=gt frequency reuse distance q = DR = (6∙1018)14 = 4411
=gt cluster size N ge q23 = 64857 =gt N=7
radio network with two clusters of N=7 cells
R D
channelcarrier groups
0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
cell 0
0 0
1
1
2
2 3 3
4
4
5
5
6 6
Concept of cellular radio coverage MSE-WCom MAC 11
School of
Engineering
Cluster-size N = I2+IJ+J2 IgeJ
I J N q=radic(3N) CI asymp 10middotlog10(q46)
1 0 1 173 174 dB
1 1 3 300 1130 dB
2 0 4 346 1378 dB
2 1 7 458 1865 dB
3 0 9 520 2086 dB
2 2 12 600 2335 dB
3 1 13 624 2403 dB
4 0 16 693 2585 dB
Concept of cellular radio coverage
co-channel BS
cluster 4 cluster 7
BS
serving cell
CI
cell boarder
The smaller the cluster size N
=gt the larger the interference I
(the Rx has to cope with)
=gt the larger the capacity ie
number of carriers cell
= total carriers N
distance
C I I
MSE-WCom MAC 12
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
Homogeneous hexagonal radio network
ij-coordinates with 600 disposed axis
unit length ei=ej=radic3∙R corresponds edge length of elementary triangle
Tx with coordinates (i1j1) has distance d = radic(i12+i1j1+j1
2) to origin
Co-channel diamond is a basic component for area-wide network
area diamond AR = radic3∙D2 2 hexagonal cell area AZ = 6∙radic3∙R2 4
Cluster size N is a function of the (normalized) reuse distance
number of cells in the diamond N ge AR AZ = D2 (3R2) = q23
q = radic(3N)
i-axis
j-axis
ei
ej
D
D
diamond
Cluster with N=4
Cluster size MSE-WCom MAC 10
School of
Engineering
Example
Assume a required CI =18 dB for acceptable service quality
GSM CI ge 9 dB typical ge 12 dB
Assume a radio propagation parameter γ=4
=gt frequency reuse distance q = DR = (6∙1018)14 = 4411
=gt cluster size N ge q23 = 64857 =gt N=7
radio network with two clusters of N=7 cells
R D
channelcarrier groups
0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
cell 0
0 0
1
1
2
2 3 3
4
4
5
5
6 6
Concept of cellular radio coverage MSE-WCom MAC 11
School of
Engineering
Cluster-size N = I2+IJ+J2 IgeJ
I J N q=radic(3N) CI asymp 10middotlog10(q46)
1 0 1 173 174 dB
1 1 3 300 1130 dB
2 0 4 346 1378 dB
2 1 7 458 1865 dB
3 0 9 520 2086 dB
2 2 12 600 2335 dB
3 1 13 624 2403 dB
4 0 16 693 2585 dB
Concept of cellular radio coverage
co-channel BS
cluster 4 cluster 7
BS
serving cell
CI
cell boarder
The smaller the cluster size N
=gt the larger the interference I
(the Rx has to cope with)
=gt the larger the capacity ie
number of carriers cell
= total carriers N
distance
C I I
MSE-WCom MAC 12
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
Example
Assume a required CI =18 dB for acceptable service quality
GSM CI ge 9 dB typical ge 12 dB
Assume a radio propagation parameter γ=4
=gt frequency reuse distance q = DR = (6∙1018)14 = 4411
=gt cluster size N ge q23 = 64857 =gt N=7
radio network with two clusters of N=7 cells
R D
channelcarrier groups
0 1 2 3 4 5 6
7 8 9 10 11 12 13
14 15 16 17 18 19 20
cell 0
0 0
1
1
2
2 3 3
4
4
5
5
6 6
Concept of cellular radio coverage MSE-WCom MAC 11
School of
Engineering
Cluster-size N = I2+IJ+J2 IgeJ
I J N q=radic(3N) CI asymp 10middotlog10(q46)
1 0 1 173 174 dB
1 1 3 300 1130 dB
2 0 4 346 1378 dB
2 1 7 458 1865 dB
3 0 9 520 2086 dB
2 2 12 600 2335 dB
3 1 13 624 2403 dB
4 0 16 693 2585 dB
Concept of cellular radio coverage
co-channel BS
cluster 4 cluster 7
BS
serving cell
CI
cell boarder
The smaller the cluster size N
=gt the larger the interference I
(the Rx has to cope with)
=gt the larger the capacity ie
number of carriers cell
= total carriers N
distance
C I I
MSE-WCom MAC 12
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
Cluster-size N = I2+IJ+J2 IgeJ
I J N q=radic(3N) CI asymp 10middotlog10(q46)
1 0 1 173 174 dB
1 1 3 300 1130 dB
2 0 4 346 1378 dB
2 1 7 458 1865 dB
3 0 9 520 2086 dB
2 2 12 600 2335 dB
3 1 13 624 2403 dB
4 0 16 693 2585 dB
Concept of cellular radio coverage
co-channel BS
cluster 4 cluster 7
BS
serving cell
CI
cell boarder
The smaller the cluster size N
=gt the larger the interference I
(the Rx has to cope with)
=gt the larger the capacity ie
number of carriers cell
= total carriers N
distance
C I I
MSE-WCom MAC 12
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
Multiple-Access-Systems
use the bdquomediumldquo manyfold
serve many users bdquoat the same timeldquo but how many
consider a MA-system with 2 traffic channels
channel 1
channel 2
requests
t
t
t
=gt both channels are occupied
=gt blocking probability PB
=gt grade of service (GoS)
busy channel
Traffic calculation MSE-WCom MAC 13
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering Erlang B formula
Assumptions
connection requests are independent (no worst-case scenario)
number of requests per time is Poisson distributed
blocked requests are lost
there are many more users than traffic channels
Computation of PB with Erlang B formula
K
B K n
n=0
A KP =
A n PB blocking probability
K available traffic channels
A bdquoAngebotldquo A = bdquoarrival rate λldquo times bdquomean connection timeldquo
V traffic = Amiddot(1-PB) asymp A if PBltlt1 in Erlang (to honour AK Erlang)
The Erlang-B-formula gives the traffic V that can be managed with K
traffic channels if the grade of service is GoS = PB
MSE-WCom MAC 14
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering Traffic calculation
Example 1
500 users producing 25 mE traffic each (90s busy per hour [3600s])
generate a total traffic of V = 125 Erlang
grade of service GoS blocking probability PB = 2
=gt The number of traffic channels K ge 20
Example 2
GSM cell with 1 2 4 and 6 carriers agrave 200 kHz or equivalently
K = 7 15 30 45 traffic channels
GoS PB=2
bdquoAngebotldquo A asymp traffic V = 294 901 2193 and 3561 Erlang
=gt 117 360 877 and 1424 users with 25 mE traffic can be served
bundling effect
the traffic increases over-proportional with the number of traffic channels K
MSE-WCom MAC 15
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering CDMA Code Division Multiple Access MSE-WCom MAC 16
Direct-Sequence-Spread-Spectrum (DSSS-) in time domain
bullinstead of data-bit d[n] = plusmn1 spreaded data-bit d[n]∙s(t-nTbit) is sent
bulls(t) is the spreding-sequence or the code with N (antipodal) chips
1 ∙ [ 1 1 -1 1 -1 -1 -1 ]
Tbit = N∙Tchip
d[1] = -1
t
BPSK-
Modulator
cos(ωct)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
(-1) ∙ [ 1 1 -1 1 -1 -1 -1 ]
d[0] = 1
Tchip
1
-1
1
-1
t
s(t) Multiplikator
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
MSE-WCom MAC 17
DSSS-modulation in frequency domain
bull multiplication with chip sequence causes frequency spreading
frequency
power density [WHz]
Bun-spreaded = Rbit
Bspreaded = Rchip
N Spreading-Factor
N = Tbit Tchip
( = Rchip Rbit = Bspreaded Bun-spreaded )
same power
=gt blue area = red area Spreading Factor N
Spreading Gain in dB
(after despreading)
Gspreading = 10∙log10(N)
Rbit = 1Tbit Rchip = 1Tchip
CDMA Code Division Multiple Access
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
MSE-WCom MAC 18
CDMA Code Division Multiple Access
Despreading in time domain
bull reconstruction of the narrowband data signal by
multiplication with s(t) (in the right moment) =gt s(t)middots(t) = 1
Data demodulation
bull averaging over Tbit and algebraic-sign- or bit-decision (matched-filtering)
d[0] ∙ s(t) d[1] ∙ s(t-Tbit)
t
d[n]
s(t)
t Tchip Tbit
r(t)
τp
s(t-τp-nTbit) propagation time
bull there are several τp in a multipath environment =gt several correlators in parallel
(Rake-receiver uses multiple-transmissions no Intersymbol-Interferenz ISI)
bitTbitT
1sign()
correlation
Tbit
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
Despreading in frequency domain
before despreading after despreading
Rchip
f
power density [WHz]
Rchip
f
power density [WHz]
interference is uncorrelated with
code s(t) and remains wideband
interference signal interference
Signal
signal-power remains constant
but bandwidth N times smaller
bull Processing Gain SNR after despreading = N ∙ SNR before despreading
bull in dB SNR after desp = Gspreading + SNR before desp
Spreading Factor N
Spreading Gain in dB
Gspreading = 10∙log10(N)
MSE-WCom MAC 19
CDMA Code Division Multiple Access
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
B asymp Rchip = NmiddotRbit
f
power density
f
WHz
interference noise
signal 1
DSSS-connection with s2(t)
DSSS-connection with sK(t)
interference noise
DSSS-connection with s1(t)
several DSSS-connections at the same time
bull before despreading after despreading
f
signal 1
interference noise
0dt(t)s(t)sT
1
bitT
k1
bit
ideal orthogonal codes
kne1
in reality crosscorrelations ne 0
=gt (intracell-) interference
0ssT
k1 or kne1
MSE-WCom MAC 20
CDMA Code Division Multiple Access
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering CDMA Code Division Multiple Access
d1[n]
s1 = [1 1 -1 1 -1 -1 -1]
dK[n]
sK = [-1 -1 -1 1 -1 1 1]
s1
sum Tbit
sK
sum Tbit
Noise dlsquo1[n]
dlsquoK[n]
r[n]
[6 -8 8]
[6 8 -8]
[1 -1 1]
[1 1 -1]
1 1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1 -1
-1 -1 -1 1 -1 1 1 1 1 1 -1 1 -1 -1
d1[0] = -1 d1[-1] = 1 d1[1] = 1
dK[-1] = 1 dK[1] = -1
-1 -1 -1 1 -1 1 1
r[n] 0 0 -2 2 -2 0 0 -2 -2 0 0 0 2 2 2 2 0 0 0 -2 -2
1 1 -1 1 -1 -1 -1
dK[0] = 1
[1 -1 1]
[1 1 -1]
Chip sequences
spreading 1 Bit to N chip
W asymp Nmiddot(1Tbit)
Tbit
Tx
Rx
despreading (correlation) data bits
of user 1
estimated data bits
of user 1
Correlator for user 1
data bits
of user K
0 2Tbit
MSE-WCom MAC 21
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
Alice 0 1 0 1
0 1 1 1
Carol
Bob 0 1 0 1
0 1 1 1
Dave
sA
dA
dAmiddotsA
dC
sC
dCmiddotsC
r
sA
rmiddotsA
sC
rmiddotsC
CDMA Principle
sA= [1 1 -1 -1]
sC= [1 -1 1 -1]
MSE-WCom MAC 22
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
A
0
D 0 C 0
B 0
CDMA
A 0
B 0
C 0
D 0
symbol 0 symbol 1 symbol 2 A 1
B 1
C 1
D 1
A 0
B 0
C 0
D 0
A 2
B 2
C 2
D 2
A 0
D 1 D 2 C 1 C 2
B 1 B 2 A 1 A 2
TDMA
B
0
C
0
D
0
A
1
B
1
C
1
D
1
A
2
B
2
C
2
D
2
f
t
f
t
f
t
f
t middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot middotmiddotmiddot
middotmiddotmiddot middotmiddotmiddot
T0
B0
B0 T0 1
B
B
asymp1Tc
B
Single Channel FDMA
CDMA vs FDMA and TDMA
CDMA users permanently transmit on B = NmiddotB0
(N is the spreading factor)
code
interference (limited)
MSE-WCom MAC 23
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering CDMA Sequence Design
OVSF-Codes are well suited at perfect synchronisation (eg DL in UMTS)
orthogonal variable spreading factor N (Walsh-Hadamard codes)
N=1 N=2 N=4 hellip
1
1 1
1 -1
1 1 1 1
1 1 -1 -1
1 -1 1 -1
1 -1 -1 1
1 -1 1 -1
1 1
1 -1
-1 1 -1 1
1 -1 1 1
1 1 1 1 -1 -1 hellip
hellip
user service 1 with N=2
(data rate = 2R)
user service 2 with N=4
(data rate = R)
user service 1
user service 2
orthogonal
Example with
different data rates
but same bandwidth
B asymp 1Tchip
do not select a code in this subtree
concatenation of parent code
and (inverted) parent code
MSE-WCom MAC 24
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
Chiprate CA-Code = 1023 kChips =gt bandwidth asymp 1 MHz
Gold codes are bdquonearldquo-orthogonal in asynchronous case
generation with 2 Linear Feedback Shift Registers (LFSR)
GPS-satellites use Gold-sequences of length N=1023
CDMA Sequence Design MSE-WCom MAC 25
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
user k
radicEchipdk[n]
sk[m]
bipolar bdquorandomldquo chip
sum Tb
sk[m]
AWGN-approximation of K-1 interferer
(mean = 0 variance = I0 = (K-1)Echip)
SNR = Eb I0 = NEc (K-1)Ec = N (K-1) =gt K asymp N SNR
with SNR = 3 dB follows K asymp N 2
CDMA Sequence Design random codes
Spreading every data bit with another bdquorandomldquo sequence
averaging over good and bad correlation values
use of different N-bit-patterns of a very long PN- (LFSR-) sequence
AWGN-interference model
assumptions perfect power control no intercell interference
no voice activity no thermal noise no antenna sectorization
MSE-WCom MAC 26
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
1 Frequency reuse distance = 1
use of the same frequency band in every cell
=gt good for spectral efficiency [BitHz] bdquonoldquo frequency planing
fast and exact power control required because of near-far-problem
2 robust broadband-communication in multipath environment
frequency diversity
Rake-receiver combines constructively multipath-signals
=gt time resolution Tchip = 1 Btot
IHch(f
)I
f
Btot
t
y(t
)
correlator phase estimation delay
Matched Filter
Finger
Σ
IQ IQ
Arguments for CDMA in mobile radio MSE-WCom MAC 27
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
3 variable bit rates
rate-R1-user produces R1R2-times more interference than rate-R2-user
4 soft(er) Handover
t
t
0 1R1
1R2 0
Tc
R1 gt R2 but energy per bit Eb1 = Eb2
f P
Frame
R1-user
R2-user t
RNC
Arguments for CDMA in mobile radio MSE-WCom MAC 28
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering OFDM Orthogonal Frequency Division Multiplexing
t
f
QAM
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
QAM
QAM
QAM
QAM
Pilot
QAM
QAM
Tsym asymp 1Bc
subchan N-1
subchan 0
data fromto 1hellipK users services
on N parallel narrow-band (low-
rate) flat-fading subchannels
(=gt no costly equalizer)
Btot asymp NTsym
Δ
hellip
t
Δ
Tsym
NLOS-Pfad
LOS-Pfad
Tsym
cyclic prefix
Signal spectrum of subchannels overlap but are still orthogonal
Guard interval Δ = 132 hellip 14 Tsym with cyclic prefix
bull Δ gt max channel delay (to avoid ISI and thus Inter-Channel-Interference)
MSE-WCom MAC 29
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering OFDM-ModulationDemodulation Source httpdewikipediaorgwikiOFDM
Nlsquo-point
Nlsquo-point
(I)FFT-length = Nlsquo gt N (some spectral values are not used for Tx)
(I)FFT-frequency-resolution = fsNlsquo = subchannel separation
unused
unused
MSE-WCom MAC 30
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
FIC Fast Information Channel (3 OFDM-symbols)
MSC Main Service Channel (72 OFDM-symbols)
OFDM Example DAB
DAB-networks with 1712 MHz VHF-channels in 200 MHz band
DAB transmission mode I
bull N = 1536 subchannels (Nrsquo = 2048 point (I)FFT)
1 kHz subchannel spacing DQPSK-modulation
bull OFDM-symbol period Tsym = 1 ms (carries 3072 bits)
plus guard interval Δ = 246 micros (=gt path distance lt 738 km)
bull DAB frame lasts 96 ms contains DAB ensemble (gt20 radio programs)
MSE-WCom MAC 31
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering Random Access Slotted ALOHA
Basic idea (N Abramson 1970 University of Hawaii)
unnumbered bdquousersldquo transmit data in an uncoordinated way
eg connection requests RFID-ACKsIDs etc
occasional collisions destroy whole data packets (CRC-failure)
transmitter gets feedback about success failure
repeats transmission after random waiting time
Slotted Aloha protocol
station 1
station 2
station 3 x
x
x
random selection
of a slot in the
backoff-interval
double
backoff-interval
success collision idle collision idle success idle
MSE-WCom MAC 32
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering Random Access Slotted ALOHA
Stabilization eg with bdquobinary exponential backoffldquo
known from Ethernet
after i failures select randomly 1 of the next 2i slots for next attempt
Throughput-versus-Delay for stabilised slotted Aloha
delay
throuput
[successful slot total slots] 1e
Backoff-interval (i=1) backoff-interval (i=2)
1
TDMA
maximum throughput = 1e = 37
(37 idle slots 37 successful slots 26 slots with collision)
MSE-WCom MAC 33
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering Random Access Slotted ALOHA
Probability of n packets per slot
where G is the mean number of packets per slot (ie the traffic) G
n
n en
G(G)P
37
P(bdquosuccessldquo)
P(bdquocollisionldquo) P(bdquoidleldquo)
optimum throughput
with a total traffic of
1 packet per slot on
the average
MSE-WCom MAC 34
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
School of
Engineering
EPC Gen2 UHF RFID uses slotted Aloha based anti-collision-procedure
Reader sends Query with parameter Q
start of an inventory-round with max 2Q slots
Tags randomly choose a slot-number in the range of 0hellip2Q-1
and answer in the chosen slot
if just 1 Tag answers in a slot =gt success (after identification)
if no Tag (idle) or gt1 Tags (collision) answer in a slot
Reader starts with the next slot to laquounblockraquo the medium
Reader starts with a new inventory round (Query)
Q-parameter (ie frame length) is chosen to maximize success-rate
frame length asymp unidentified Tags (can be estimated)
Random Access Example (simplified)
query (Q=2) query (Q=1)
Tag 3
Reader
Tag(s)
slot 0 slot 1 slot 2
Tags 1amp2
slot 3
t
t
idle idle success collision
MSE-WCom MAC 35
