Investigation of the Nonlinear Characteristic of Costas ... · Investigation of the Nonlinear...

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 für Nachrichten- und ÜbertragungstechnikTechnische Fakultät

Christian-Albrechts-Universität zu Kiel

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Lehrstuhl für

Nachrichten- und Übertragungstechnik

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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Content

1. Introduction

2. Optical Phase-Locked Loop

3. Nonlinear OPLL Characteristic

4. Noise Sources & Cycle Slip Phenomena

5. Conclusion

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Content

1. Introduction




5. Conclusion

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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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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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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




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

ˆ sin ( )

ˆ 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

ˆ ˆcos ( ) ( ) cos 2 ( ) ( )

2

ˆ ˆsin ( ) ( ) 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




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 0

2 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


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


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




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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Equivalent mathematical block diagram

Both noise sources influence the phase error

Phase error variance

PLL bandwidth BL influences the noise performance:

• Variance due to shot noise increases with BL

• Variance due to phase noise decreases with BL

Optimum bandwidth exists

2 L

L Rx

Phase noise Shot noise

Ba b

B P

a,b const.

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Cycle Slip phenomena

High phase errors may drive the PLL

in the nonlinear regime

OPLL unlocks from stable point P and

relocks after several jumps

Caused by nonlinear OPLL characteristic:

( ) sin(2 )t

OPLL may lose lock

without relock

sin(2 ) 2

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Noise Influence

Cycle slips will impair data demodulation

Phase jumps in will flip the data

Bit errors!

Solution:

Observe relative changes of bits

and not absolute values

Differential Encoding

T1<T2<T3

T: Observing time per simulation

n: No. of simulations

( ) ~ cos ( ) ( )

( ) ~ sin ( ) ( )

I M

Q M

U t t t

U t t t

( )t

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Conclusions

Coherent detection requires carrier frequency recovery

OPLL as carrier recovery in optical communication systems

Investigation of the nonlinear characteristic

Shot and phase noise impair the (nonlinear) OPLL performance

Cycle slips influence the communication system and data recovery

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Thank you!

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