Robust Transmission over Fast Fading Channels on the - Cost 289

COST289 Final Workshop - Gothenburg, Sweden

April 11-12, 2007

Robust Transmission over Fast Fading Channelson the Basis of OFDM-MFSK

Matthias Wetz, Ivan Perisa, Werner G. Teich, Jurgen Lindner

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[email protected]

http://it.e-technik.uni-ulm.de

Matthias Wetz Robust Transmission over Fast Fading Channels on the Basis of OFDM-MFSK

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Information Technology · University of Ulm 2

Outline

u Motivation

u A Robust Transmission Scheme – OFDM-MFSK

u Increasing the Bandwidth Efficiency using Hybrid Modulation

u BER Simulation Results

u The PAPR Problem

u PAPR Reduction Methods

u Conclusions


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Motivation

u Scenario: Communication with high speed trains

u Speed up to 600 km/h causes fast changing channels

u Channel estimation is very difficult

u Security relevant control data requires robusttransmission

u Additional services for passengers like internet accessrequire high data rates

u FSK schemes are very robust and are currently in use

Goal: Robust transmission scheme based on OFDM with high data rate


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A Robust Transmission Scheme – OFDM-MFSK

f00 01 10 00 01 11 1011

∆f

group n group n + 1

u Subcarriers are grouped into groups of M and MFSK modulation is applied toeach group

u Alternative: Multitone FSK (N out of M subcarriers occupied)

u No CSI is needed for noncoherent detection

u Very robust against time variant channels

u Low bandwidth efficiency (uncoded OFDM-4FSK: 0.5 bit/subcarrier)


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A Robust Transmission Scheme – OFDM-MFSK

Noncoherent detection

u Subcarrier phase of transmit symbols is arbitrary

This degree of freedom can be exploited

u Use phases to increase bandwidth efficiency by transmitting additional data

u Phases can be used for PAPR reduction

u Noncoherent detection of OFDM-MFSK is not influenced


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Hybrid Modulation Scheme

11 10

0 1

OFDM subcarriers

occupied subcarrier

4FSK bits:

2DPSK bits:

01

u Additional differential encoding of phases of occupied subcarriers

u Encoding in frequency or time direction

u Noncoherent detection, no CSI needed


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Channel Coding

u Separate encoding of MFSK and DPSK component

u Detection and decoding of MFSK component first to determine occupiedsubcarriers

u Afterwards detection and decoding of DPSK component

Advantages:

u Different level of protection for both components using different codes

u Coded OFDM-MFSK transmission is not affected by DPSK component

Convolutional code: rate 1/2, memory 6, generator polynomial [133,171],soft decision detection


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Simulation Results – AWGN

0 1 2 3 4 5 6 7 8 9

10−4

10−3

10−2

10−1

100

Eb/N0 [dB]

BE

R

4FSK4FSK−2DPSK4FSK−4DPSKBPSK

η=0.25 bit/(sHz)

η=0.375 bit/(sHz)

η=0.5 bit/(sHz)

Hybrid Modulation SchemeOverall BER for coded transmission:

u Separate coding for 4FSK andDPSK component using the sameconvolutional code

u BER is dominated by 4FSK errorsfor AWGN

u Codes can be adapted


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Worst Case Channel Model

v

u Reflection at tunnel entrance or bridge

u Two paths with equal attenuation

u Maximum Doppler spread 2fd = 2fcvc due to opposite direction of arrival

carrier frequency fc = 38 GHz subcarrier separation ∆f = 312.5 kHzFFT length Nf = 256 cyclic extension Tg = Ng∆t = 0.8 µsno. of used subcarriers Nfused = 160 symbol duration Ts = (Ng + Nf) ∆t = 4 µs


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Simulation Results

4 5 6 7 8 9 10 11 12 13 14

10−4

10−3

10−2

10−1

100

Eb/N0 [dB]

BE

R

v = 600 km/hv = 300 km/hv = 0 km/h

OFDM-4FSK

BER for coded OFDM-4FSK:

u Path delay td = 0.75 µs

u Strong frequency selectivity

u Very robust against frequency se-lectivity

u Very robust against high velocity


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Simulation Results

0 2 4 6 8 10 12 14 16

10−4

10−3

10−2

10−1

100

Eb/N0 [dB]

BE

R

4FSK4FSK−4DPSK (t

d=0.075µs)

4FSK−4DPSK (td=0.03µs)

Hybrid Modulation Scheme (4FSK-4DPSK)

Overall BER for coded transmission:

u DPSK component encoded in fre-quency direction

u Speed v = 600 km/h

u Very robust against high velocity

u DPSK component very sensitiveagainst frequency selectivity (largedistance between used subcarriers)


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The PAPR Problem

Definition of the PAPR:

PAPR =(maxt|s(t)|)2

1TS

∫ Ts

0|s(t)|2dt

u Unfavourable superposition of subcarriers in OFDM may lead to high PAPR

u Problem: Transmit amplifier has saturation limit

8 Nonlinear distortion (out of band radiation)

8 High backoff necessary (amplifier inefficient)

u Noncoherently detected OFDM-MFSK:

8 Subcarrier phases can be chosen arbitrarily so that PAPR is reduced

8 No side information necessary


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The PAPR Problem

Goal: Find optimum subcarrier phases for each OFDM symbol, so that PAPRis minimum

Problem: N = 256 and OFDM-4FSK:

u 2128 possible OFDM symbols

u 264 possibilities to assign the phase if only two phases for eachsubcarrier are considered

⇒Exhaustive search is impossible

Worst case: All subcarrier phases are the same

u Subcarriers add coherently

u PAPR = NM = 256

4= 18 dB


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PAPR Distribution – Random Phases

5 6 7 8 9 10 11

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

z=PAPR[dB]

CD

F(z)

random continuous phases [0,2π)

random discrete phases 0 or π

Cumulative Distribution FunctionFirst Approach:

u Use random phases

u Allow only binary phases

u No additional complexity


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PAPR Distribution - Selected Mapping

5 6 7 8 9 10 11

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

z=PAPR[dB]

CD

F(z)

random continuous phases [0,2π)

"Selected Mapping": best of 10 symbols with discrete random phases (0 or π) is chosen

random discrete phases 0 or π

"Selected Mapping": best of 2 symbols

"Selected Mapping": best of 4 symbols

Cumulative Distribution Function

Selected Mapping:

u Introduced by Bauml, Huber andFischer (’96)

u Assign random phases to each sym-bol several times

u Select OFDM symbol with lowestPAPR for transmission

u For noncoherently detectedOFDM-MFSK no side informationis needed


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Time-Frequency Domain Swapping

?

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6

6

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FFTIFFT

Amplitude clipping in time domain

Random startingphases ϕn

Build spectrum withfixed amplitudes andvariable ϕn

determine newphases ϕn

u Introduced by Ouderaa et al. (’88)

u Swapping between time and fre-quency domain

u Iterative reduction of PAPR

u Stop when PAPR is not decreasingany more

u Parameter: time domain clippinglevel CL


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PAPR Distribution - Swapping Algorithm

3 4 5 6 7 8 9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

z=PAPR[dB]

CD

F(z)

time−frequency domain swapping algorithm

CL=0.95

random phases 0 or π

CL=0.9 CL=0.8

selected mapping best of 10 symbols

Cumulative Distribution Functionu Good performance

u Very high complexity: up to severalhundred iterations per symbol


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Sequential Algorithm

IFFT

IFFT

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? ?

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PAPR evaluation

noyes

random phases for all subcarriers

flip ϕn

discard changes

PAPRnew < PAPR ?

PAPR = PAPRnew

accept ϕn

next subcarrier n

u Subcarrier phases are systematicallychanged to reduce PAPR

u Subcarrier phases are flipped sequentially

u Complexity: one extra IFFT per occupiedsubcarrier

u Complexity can be reduced by exploitinglinearity of DFT


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PAPR Distribution - Sequential Algorithm

3 4 5 6 7 8 9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

z=PAPR[dB]

CD

F(z)

swap algorithmCL = 0.9

sequential algorithm

random phases 0/π

selected mappingbest of 10

selected mappingbest of 65

Cumulative Distribution Functionu Better performance than selected

mapping

u Lower complexity than swapping al-gorithm

Good complexity/performance tradeoff


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Conclusions

u Noncoherently detected OFDM-MFSK is a robust transmission scheme in fastfading environments

u Subcarrier phases can be used for PAPR reduction or transmission of additionaldata

u Hybrid modulation does not affect the underlying MFSK transmission but offersadditional data rate for moderate channels

u no CSI necessary

u PAPR reduction methods do not affect the noncoherent MFSK detection butreduce the PAPR

u In general: the better the performance of PAPR reduction methods the higherthe complexity


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CDF - QPSK vs. BPSK

Assumption:all subcarries occupied, QPSK modulation (or random phases ϕn ∈ [0, 2π)), nooversampling

All Nf time domain samples are Gaussian distributed and uncorrelated:

P (PAPR ≤ z) = CDF (z) = (1 − e−z)Nf (1)

On the other hand, if we allow only ϕn ∈ {0, π}, i.e. the OFDM symbols in thefrequency domain are real-valued, some of the time domain samples will be correlated:

P (PAPR ≤ z) = (1 − erfc(

√

z/2)

)2(1 − e−z)Nf−2

2 (2)

Robust Transmission over Fast Fading Channels on the - Cost 289

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