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  • Investigation of the Nonlinear Characteristic of Costas Loop based Carrier Recovery Systems

    Semjon Schaefer

    International Workshop on

    Optical Phase-locked-Loop Techniques

    16.06.2015

    Kiel

    Lehrstuhl fr Nachrichten- und bertragungstechnikTechnische Fakultt

    Christian-Albrechts-Universitt zu Kiel

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    for Communications

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    Nachrichten- und bertragungstechnik

    Semjon Schaefer, PLL-Workshop, 16.06.2015

    Motivation

    Main focus:

    1) Carrier recovery system nonlinear OPLL characteristic

    2) Influence of the carrier recovery (OPLL) on the data recovery

    TransmitterChannel Coherent

    Receiver

    Carrier

    Recovery(=PLL)

    Data

    Recovery

    Receiver

    ..010110.. ..010110..

    Data Data

    e.g.

    Fiber

    Free-space

    Atmosphere

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    Semjon Schaefer, PLL-Workshop, 16.06.2015

    Content

    1. Introduction

    2. Optical Phase-Locked Loop

    3. Nonlinear OPLL Characteristic

    4. Noise Sources & Cycle Slip Phenomena

    5. Conclusion

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    Semjon Schaefer, PLL-Workshop, 16.06.2015

    Content

    1. Introduction

    2. Optical Phase-Locked Loop

    3. Nonlinear OPLL Characteristic

    4. Noise Sources & Cycle Slip Phenomena

    5. Conclusion

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    Semjon Schaefer, PLL-Workshop, 16.06.2015

    Introduction

    Why coherent detection?

    Pros:

    Full amplitude and phase recovery

    High flexibility

    Cons:

    Requires local oscillator with same

    carrier frequency as transmitter

    High complexity

    Carrier recovery structures:

    Digital carrier frequency estimation (D. Clausen)

    Phase-locked loop techniques

    University of Kiel: Optical PLL based on Costas-loop in optical intersatellite links

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    Semjon Schaefer, PLL-Workshop, 16.06.2015

    Optical Intersatellite Link (OISL)

    Current RF Scenario: OISL Scenario:

    LEO GEO GS:

    High data rate (LEO GEO)

    Long time window (GEO GS)

    LEO GS:

    Low data rate

    Short time window

    LEO: Low-Earth Orbit

    GEO: Geostationary Orbit

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    Semjon Schaefer, PLL-Workshop, 16.06.2015

    OISL Transmission System

    Typical Laser Communication Terminal (LCT) Setup:

    Data modulation:

    Binary phase shift keying (BPSK)

    Phase of the laser is switched: Bit 1 180

    Bit 0 0

    Frequency mismatch between LO and input signal due to

    Natural frequency drift

    Phase noise

    Doppler shift

    PM: Phase modulator

    YDFA: Ytterbium-doped fiber amplifier

    OPLL: Optical phase-locked loop

    LO: Local oscillator

    Transmitter

    Receiver

    Optical

    Electrical

    Digital

    OPLL

    I

    QData Recov.Diff. Decod.

    OPLLElectronic

    CoherentReceiver

    Fast Tuneable LO(VCO)

    Data

    1064 nm YDFA

    Free-spaceChannel

    Tx/Rx Antenna

    PM

    Diff.Encoding

    PulseShaper

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    Caused by the relative velocity between the satellites

    Maximum frequency offset of approx. 7 GHz

    Coarse compensation by using satellite trajectory data

    Fine compensation by optical phase-locked loop (OPLL)

    Residual Doppler shift, natural frequency drift and phase noise

    Doppler Frequency Shift

    2

    21

    1 cos

    v

    c

    Tx vc

    Rxf f

    : Transmitted frequency

    : Received frequency

    : Speed of light in vacuum

    : Relative velocity

    Tx

    Rx

    f

    f

    c

    v

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    Content

    1. Introduction

    2. Optical Phase-Locked Loop

    3. Nonlinear OPLL Characteristic

    4. Noise Sources & Cycle Slip Phenomena

    5. Conclusion

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    Optical PLL based on Costas loop

    Fundamentals of Costas PLL

    with

    1 2

    ( ) ( ) ( )

    ~ sin 2 ( ) ( )

    I Qt I t I t

    t t

    Error signal:

    1 1 0 1

    2 2 0 2

    sin ( )

    sin ( )

    s t s t t

    s t s t t

    1 2,0( )t t

    Frequency offset

    Phase offset

    2,0

    1 2

    1 21 2 0 1 2

    1 21 2 0 1 2

    cos ( ) ( ) cos 2 ( ) ( )

    2

    sin ( ) ( ) sin 2 ( ) ( )

    2

    I

    Q

    I t s t s t

    s st t t t t

    s sI t t t t t t

    LP Filter

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    Optical Phase-Locked Loop

    Optical phase-locked loop for BPSK transmission based on Costas loop

    1 2

    1 2

    ( ) ~ cos ( ) ( ) ( )

    ( ) ~ sin ( ) ( ) ( )

    I M

    Q M

    U t t t t

    U t t t t

    AGC: Automatic gain control

    TIA: Transimpedance amplifier

    LO: Local oscillator

    ( ) 0,M t

    Demodulated data signal after coherent detection:

    BPSK modulation:

    1 2

    ( ) ( ) ( )

    ~ sin 2 ( ) ( )

    I Qt U t U t

    t t

    Phase error

    Coherent Receiver

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    Frequency Acquisition

    Example: Residual frequency offset of 5 MHz

    Error Signal Frequency Error( )t

    0.7

    2 6.5 MHzn

    D

    Damping:

    Natural Frequency:

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    Content

    1. Introduction

    2. Optical Phase-Locked Loop

    3. Nonlinear OPLL Characteristic

    4. Noise Sources & Cycle Slip Phenomena

    5. Conclusion

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    Mathematical description of Costas-PLL

    Error signal:

    Loop filter: e.g. passive PI filter (lag-lead)

    Phase error:

    Nonlinear differential equation system:

    0 02 1 2

    1 12 cos 2 sin 2D D

    d

    dt

    dK K m K K m

    dt T T T

    ( ) sin 2Dt K

    1

    1 1 1

    2 2

    1 1( )( ) , with

    ( ) 1 1T

    m

    sT sT TX sF s m

    E s sT Ts

    1 2 1 0

    1

    0

    ( ) ( ) ( ) ( ) ( )

    1( )

    t t t t K x t dt

    ddx t

    K dt dt

    No analytical solutions exist

    Numerical approximation

    Phase plane

    2 1

    1 1( ) ( )

    d dx t t m

    dt T dt T

    KD: Phase discriminator gain [V/rad]

    K0: LO (VCO) gain [MHz/V]

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    Phase Plane Diagram

    Each solution of the NLDE system is represented by a trajectory in the phase plane

    All trajectories end in

    a stable point P

    L :

    H Hold-in range

    Lock-in rangeL

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    Phase Plane Diagram

    Each solution of the NLDE system is represented by a trajectory in the phase plane

    Not all trajectories end

    in a stable point P

    A stable periodic state

    exists

    L H :

    H Hold-in range

    Lock-in rangeL

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    Phase Plane Diagram

    Each solution of the NLDE system is represented by a trajectory in the phase plane

    No trajectories end in

    a stable point P but in

    the stable periodic state

    H :

    H Hold-in range

    Lock-in rangeL

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    Content

    1. Introduction

    2. Optical Phase-Locked Loop

    3. Nonlinear OPLL Characteristic

    4. Noise Sources & Cycle Slip Phenomena

    5. Conclusion

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    Noise Sources

    Shot noise

    Results from transformation of optical power into photo current

    Phase noise

    Due to laser linewidth (Tx and LO laser)

    Main focus: noise influence on the phase error (i.e. carrier frequency offset)

    noise distortion affects directly the carrier recovery1 2

    (Ideal) (Measurement)

    Laser spectrum:

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    Semjon Schaefer, PL