Carrier Recovery Algorithms and Real-time DSP ......Title: Carrier Recovery Algorithms and Real-time...

T. Pfau, OFC’14, W4K.1 March 12, 2014

1 COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.

COPYRIGHT © 2014 ALCATEL-LUCENT. ALL RIGHTS RESERVED.

2

Timo PfauW4K.1 – March 12, 2014

Carrier Recovery Algorithms and Real-time DSP Implementation for Coherent Receivers

3


1. Origins of phase noise

2. History of carrier recovery

3. Blind carrier recovery

4. Pilot-based carrier recovery

5. Semi-blind carrier recovery

6. Summary

AGENDA

W4K.1.pdf OFC 2014 © OSA 2014

978-1-55752-993-0/14/$31.00 ©2014 Optical Society of America



4


There are two main sources of phase noise in coherent optical transmission systems:

• Laser phase noise

- Signal laser

- Local oscillator

• Nonlinear phase noise

- Self phase modulation (SPM)

- Cross phase modulation (XPM) in WDM systems

• The two types have different statistical properties.

Why do we need a carrier recovery?

5


• Spontaneous emission in lasers causes a “random walk” of the optical phase.

• This causes a finite laser linewidth.

• The linewidth describes the “sharpness” of the optical spectrum (assuming a Lorentzian shape).

Origins of phase noiseLaser phase noise

0 2000 4000 6000 8000 10000-25

-20

-15

-10

-5

0

5

Discrete time index: kDiscrete time index: kDiscrete time index: kDiscrete time index: k

ψψ ψψkk kk [

rad

] [

rad

] [

rad

] [

rad

]

∆f3dB

TS=10-4

∆f3dB

TS=10-3

∆f3dB

TS=10-2

-0.04 -0.03 -0.02 -0.01 0 0.01 0.02 0.03 0.04-50

-40

-30

-20

-10

0

10

Normalized frequency Normalized frequency Normalized frequency Normalized frequency ∆∆∆∆ fTfTfTfTSSSS

Po

we

r [d

B]

Po

we

r [d

B]

Po

we

r [d

B]

Po

we

r [d

B]

∆f3dB

TS=10-4

∆f3dB

TS=10-3

∆f3dB

TS=10-2

W4K.1.pdf OFC 2014 © OSA 2014



6


• The refractive index of fibers is changing in proportion to the intensity or power of the electromagnetic field (Kerr effect).

• Self phase modulation (SPM): Phase shift induced by the intensity variations of the transmitted signal itself.

• Cross phase modulation (XPM):Phase shift induced by the intensity variations of the neighboring channels in a WDM system.

• SPM can be partially compensated before carrier recovery, e.g. through digital back propagation.

Origins of phase noiseNonlinear phase noise

7


• Main research focus:Homodyne receivers with OPLL (optical phase locked loop)

• Challenges:

- Stringent requirements on laser linewidth

- Alignment of SOP (state of polarization) of signal and LO.

Analog approach to compensate phase noiseCoherent receiver research in the 1980s

[1] L. G. Kazovsky et al., JLT, vol. 8, no. 9, pp. 1414–1425, Sep. 1990.

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The race between optical baud rates and CMOSLightwave fiber capacity trends

Data rate per channel (Gb/s)

0.1

1

10

100

1000

0.01 0.1 1 10 100 1000

Nu

mb

er

of

ch

an

ne

ls

'80 '83 '86 '87

'89

'91

'93

'95

'95

'96

'98

'98

'02

10Gb/s100Gb/s

1Tb/s

10Tb/s

Total

Capacity

'01

'01

'05 40λ, 5.94λ, 5.94λ, 5.94λ, 5.94Tbps PDM, DQPSK, 1.56 b/s/Hz

100Tb/s

Electronics

Op

tics

'02 256λ, 42.7λ, 42.7λ, 42.7λ, 42.7Gbps PDM VSB 1.28b/s/Hz

‘11 112λλλλ , , , , 11.211.211.211.2Tbps

PDM-DQPSK25GBaud3.2b/s/Hz

9


• Traditionally, there has been a lag between analog/mixed and digital ICs.

• SoC’s required that this gap had to close.� Increased rate of early node adoption for ADCs.

The race between optical baud rates and CMOSADC performance evolution – CMOS node adoption

[2] B. E. Jonsson, “ADC research trends: CMOS node adoption,” Converter Passion, July 4, 2012, Available: http://converterpassion.wordpress.com

W4K.1.pdf OFC 2014 © OSA 2014



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• From year 2000 to present day, significant advances were made above 10 GS/s.

• By the mid 2000s ADC sampling rate has caught up to optical baud rates.

The race between optical baud rates and CMOSADC performance evolution – Sampling rate & ENOB

199020002010

[3] B. E. Jonsson, “ADC performance evolution: Sampling rate and resolution,” Converter Passion, Aug. 16, 2012, Available: http://converterpassion.wordpress.com

11


• Faster analog-to-digital converters enabled the implementation of DSP-based intradyne coherent receivers

• Free-running signal and local oscillator lasers

• Laser frequency offsets are compensated by DSP

DSP-based intradyne coherent receiversPossibility of digital carrier recovery

LO

ADC

ADC

ADC

ADC

DS

PU

Dig

ital S

ign

al P

roce

ssin

g U

nit

Localoscillator

90 hybrid

90 hybrid

I1

Q1

I2

Q2

TX

single chipor

modular system

W4K.1.pdf OFC 2014 © OSA 2014



12


• Traditionally used in wireless data transmission.

BUT

• DSP clock frequency often higher the transmission data rate.

• Serial signal processing is possible.

Decision-directed carrier recoveryBlind carrier recovery

ψk

decisioncircuit

+

-

exp{-j( )}

arg( )

arg( )

W(z)

Yk

^

FF

Xk^

filter function

1ˆ −− kje

ψ

13


DSP implementation in coherent optical receiversParallelization & pipelining

……… …

1:m demux

ADC

1:m demux

ADC

1:m demux

ADC

1:m demux

ADC

memory or flip-flops

processing block

……… …



processing block


I1 Q1 I2 Q2

me

mo

ryo

rflip

-flo

ps

memory orflip-flops

pro

ce

ssi

ng

blo

ck

T-spaced sampling:fIN = 1/TS

T/2-spaced sampling:

fIN = 2/TS

fDIV = fIN/m

feedbackpath

m:1 mux

m:1 mux

m:1 mux

m:1 mux fOUT = 1/TS

• Data rate and ADC sampling frequency >> DSP clock frequency

�

• Parallel processing required.

• Complex receiver algorithms

�

• Buffering of intermediate results = pipelining.

W4K.1.pdf OFC 2014 © OSA 2014



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• Example: 5 pipelining stages × 64 parallel channels = 320 samples feedback delay

• Phase noise tolerance is significantly reduced.

Decision-directed carrier recoveryParallel and pipelined implementation

W(z)

exp{-j( )}FF

Decisioncircuit

+

-arg( )

arg( )

FF

FF

FFFFDecision

circuit+

-arg( )

arg( )

FF

FF

FFFFDecisioncircuit

+

-arg( )

arg( )

FF

FF

FFFFdecisioncircuit

+

-arg( )

arg( )

FF

FF

FFFF

FF

FF

Yk

Yk-m+1

Xk-2m^

Xk-3m+1^

ψk-4m^mkj

e 5ˆ −− ψ

15


• Data can be processed in a serial fashion.

• Conversion requires a large memory block � increased latency and power

• Discontinuities at the beginning/end of each block� Frame based data structure required, e.g. with training symbols at the beginning of each frame.

Decision-directed carrier recoveryParallel to serial conversion

Serial data stream

After demultiplexer

Parallel to serial conversion

1NN+12N

1N

N+12N

1N

N+

12N

W4K.1.pdf OFC 2014 © OSA 2014



16


Feed-forward carrier recovery exploits geometric properties of the used constellation to remove the modulation from the signal.

Advantages:

• Can be easily parallelized.

• Can use preceding and trailing symbols for phase estimation

Disadvantages:

• Modulation format specific

• Higher computational effort than decision-directed carrier recovery

• Cannot resolve rotational symmetries of the constellation(as this property is usually used to remove the modulation)

Feed-forward carrier recoveryBlind carrier recovery

17


QPSK carrier recoveryViterbi & Viterbi algorithm

(n·π/2+ π/4+ϕ)·4

Re

Im

Re

Im |ϕ(i)-ϕ(i-1)|

nj(i)=0

nj(i)=±145°

n·π/2+ π/4+ϕ

ϕ

= π+4ϕ

……

Uk

Uk-NCR

Uk+NCR

| · |u

arg{·}

p

exp{j(·)}

Yk∑

+12

1

CRNkIF ,ψ̂arg{·}

1/p

[4] A. Viterbi et al., IEEE Trans. Inf. Theory, vol. 29, no. 4, July 1983, pp. 591-598.

W4K.1.pdf OFC 2014 © OSA 2014



18


QPSK carrier recoveryBarycenter algorithm

(·)modπ2arg(·)Yk kϕ̂

Inherent weightingdue to multiple use

of inputs

Re

Im

Each filter cell performs pairwise

averaging along the shortest path.

[5] S. Hoffmann et al., IEEE PTL, vol. 21, no. 3, Feb. 1, 2009, pp. 137-139

19


The optimal carrier recovery filter length balances two opposing goals:

• The longer the filter, the better AWGN is removed from the filter

• The shorter the filter, the better fast changes of the phase can be tracked

Most commonly used filters are

• Rectangular filter – simplest and hardware efficient, but poor approximation of the optimal filter

• Wiener filter – optimal filter, but expensive to implement in hardware

• Triangular filter – good compromise between hardware efficiency and approximation of the optimal filter

Optimal carrier recovery filterWiener filter

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20


• Block processing

- One phase estimate is calculated for a block of data samples

- Block length equals filter width

- Hardware efficient implementation, but up to 1dB penalty compared to sliding window.

• Sliding window processing

- One phase estimate per data sample

- More complex implementation, but optimum performance

• Hybrid between sliding window and block processing (sliding block)

- One phase estimate is calculated for a block of data samples

- Block length is smaller than filter width

- Compromise between hardware efficiency and performance.

Sliding window vs. block processingHardware efficiency vs. performance

21


• The Viterbi & Viterbi and barycenter algorithm exploit a constant phase offset between constellation points to remove the modulation

• Square QAM constellations don’t have this feature.

• Alternative algorithms are required:

- QPSK reduction ([6] M. Seimetz, Proc. OFC/NFOEC’08, OTuM2, Feb. 24-28, 2008, San Diego, CA, USA)

- QPSK partitioning ([7] I. Fatadin et al., IEEE PTL, vol. 22, no. 9, May 1, 2010, pp. 631-633)

- Blind phase search ([8] T. Pfau et al., JLT, vol. 27, no. 8, April 15, 2009)

Carrier recovery for quadrature amplitude modulationRemoving modulation gets tricky…

W4K.1.pdf OFC 2014 © OSA 2014



22


QPSK reduction

• Only use symbols that match a QPSK constellation (●).

• For larger QAM constellations the number of useable constellation points reduces � large performance penalty.

Carrier recovery for quadrature amplitude modulationQPSK reduction & partitioning

QPSK partitioning

• 2-stage approach:

• First stage: QPSK reduction

• Second stage: Compensate phase offset of remaining symbols based on first stage result and recalculate phase estimate.

• Only practical up to 16-QAM.[6] M. Seimetz, Proc. OFC’08, OTuM2, Feb. 24-28, 2008, San Diego, CA, USA[7] I. Fatadin et al., IEEE PTL, vol. 22, no. 9, May 1, 2010, pp. 631-633

23


Carrier recovery for quadrature amplitude modulationBlind phase search

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5 Modulation cannot be removed through nonlinear operations.

Instead of extracting the carrier phase from the signal,

we can just try different angles.-5 -4 -3 -2 -1 0 1 2 3 4 5

-5

-4

-3

-2

-1

0

1

2

3

4

5

φk

[8] T. Pfau et al., JLT, vol. 27, no. 8, April 15, 2009

W4K.1.pdf OFC 2014 © OSA 2014



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Carrier recovery for quadrature amplitude modulationBlind phase search

-5 -4 -3 -2 -1 0 1 2 3 4 5-5

-4

-3

-2

-1

0

1

2

3

4

5 Yk

16exp

πj

−

4exp

πj

−

16exp

πj

4exp

πj… …

Squared. distance to const.-

point


point


point


point


point

… …

∑2NCR+1

∑2NCR+1

∑2NCR+1

∑2NCR+1

∑2NCR+1

Choose carrier phase with lowest sum

… …

kϕ̂

φk

[8] T. Pfau et al., JLT, vol. 27, no. 8, April 15, 2009

27


0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

20

b

sb

4-QAM4-QAM4-QAM4-QAM

NCR

=0

NCR

=1

NCR

=2

NCR

=3

NCR

=4

NCR

=5

NCR

=6

NCR

=7

NCR

=8

NCR

=9

0 5 10 15 20 25 300

2

4

6

8

10

12

14

16

18

20

b

sb


NCR

=0

NCR

=1

NCR

=2

NCR

=3

NCR

=4

NCR

=5

NCR

=6

NCR

=7

NCR

=8

NCR

=9

0 10 20 30 40 50 600

2

4

6

8

10

12

14

16

18

20

b

sb


NCR

=0

NCR

=1

NCR

=2

NCR

=3

NCR

=4

NCR

=5

NCR

=6

NCR

=7

NCR

=8

NCR

=9

0 10 20 30 40 50 600

2

4

6

8

10

12

14

16

18

20

b

sb


NCR

=0

NCR

=1

NCR

=2

NCR

=3

NCR

=4

NCR

=5

NCR

=6

NCR

=7

NCR

=8

NCR

=9

• Minimum distance notch becomes steeper for higher constellations. � Higher angle resolutions for phase search are required.

Blind phase searchExamples of minimum distance distribution

W4K.1.pdf OFC 2014 © OSA 2014



28


Disadvantages of blind carrier recoveryHigh computational complexity

• Blind carrier recovery for beyond 16-QAM requires the use of the blind phase search (BPS) algorithm.

• In order to achieve sufficient accuracy, ≥64 test angles are required.� Computational complexity might be prohibitive.

• Investigation of options to reduce computational complexity.

29


• Several dual-stage algorithms have been proposed.

• General idea for all proposals:

- Calculate a coarse phase estimate using the BPS algorithm.

- A second stage increases the accuracy.

• Different options for second stage:

- A second BPS stage with smaller search interval but higher resolution[9] J. Li et al., JTL, Vol. 29, No. 16, Aug. 15, 2011, pp. 2358-2364

- Decision-directed feed-forward carrier recovery[10] X. Zhou, IEEE PTL, Vol. 22, No. 14, July 15, 2010, pp. 1051-1053

Dual-stage carrier recoveryBlind phase search

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30


Two BPS stagesWhat resolution is required for the first stage?

• First stage must guarantee to find or be close to the global minimum.

• According to [1], two stages with 8 test angles each achieve same performance as single stage with 64 test angles.

BUT

• Neighboring symbols can have differentphase estimate.� Sliding window filtering is not possible.

[9] J. Li et al., JTL, Vol. 29, No. 16, Aug. 15, 2011, pp. 2358-2364

31


Decision-directed second stageML phase recovery

• First stage can be reduced to 16 test angles � hardware reduction by factor of 4.

• ML stage adds additional hardware � total savings approx. factor of 3.

[10] X. Zhou, IEEE PTL, Vol. 22, No. 14, July 15, 2010, pp. 1051-1053

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33


• Blind carrier recovery algorithms cannot resolve rotational symmetries.

• Phase slips can cause catastrophic errors.

• Differential coding is required to make the system tolerant to phase slips.� This causes a BER penalty!

• Differential coding penalty for square QAM:

Disadvantages of blind carrier recoveryDifferential coding

Re

Im

00

11

00

11

11

00

11

00

0011 01

1001

10

10

01

10

01

01

10

Constellation Bits per symbol Differential coding penalty

4-QAM 2 2.00 (3.0 dB)

16-QAM 4 1.67 (2.2 dB)

64-QAM 6 1.43 (1.5 dB)

256-QAM 8 1.27 (1.0 dB)

( )( )12

log1 2

−+=

M

MF

34


• On the transmitter side symbols known to the receiver (pilot symbols) are inserted into the data stream.

• The receivers detects the pilot symbols and uses them to calculate the carrier phase.

• Advantages:

- Absolute phase detection is possible. � No differential coding required.

- Hardware implementation is very efficient compared to blind carrier recovery.

- Compatible with any kind of constellation.

• Disadvantages:

- Additional overhead � Less overhead available for other functions (e.g. FEC).

Pilot-based carrier recovery

W4K.1.pdf OFC 2014 © OSA 2014



35


• Two-stage approach, similar to dual-stage blind carrier recovery.

• First stage uses pilot-based carrier recovery instead of BPS.

• Second stage can use V&V, decision-directed FF carrier recovery…[11] M. Magarini et al., IEEE PTL, Vol. 24, No. 9, May 1, 2012, pp. 739-741[12] F. Zhang et al., IEEE PTL, Vol. 24, No. 18, Sept. 15, 2012, pp. 1577-1579

• No phase unwrapping for blind 2nd stage algorithms

• Advantages:

- Reduced overhead compared to pilot-based carrier recovery.

- No differential coding required.

• Disadvantages:

- Higher computational complexity

- Still requires small overhead � Less overhead for FEC

- Possibility of burst errors

Semi-blind carrier recoveryThe best from both worlds?

36


• As the second stage algorithm does not use phase unwrapping, the pilot-based first stage must have an accuracy of <±pi/4.

• If pilot rate is not sufficient for the amount of phase noise present in the system, burst errors can occur.

• Burst error free operation cannot be guaranteed.

�

Challenging FEC design!

Semi-blind carrier recoveryExample of burst errors

6.92 6.94 6.96 6.98 7 7.02 7.04 7.06

x 104

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

sample #

phase [

rad]

Actual and recovered carrier phase (square)

true phase

recovered phase

pilot phase

phase error

W4K.1.pdf OFC 2014 © OSA 2014



37


• Phase noise is the most dynamic distortion in coherent optical transmission systems.

• In the development of carrier recovery algorithms hardware implementation constraints have to be taken into account.

• The choice between blind and pilot-based carrier recovery is not obvious.

- Blind carrier recovery requires no overhead and achieves maximum phase noise tolerance, but requires differential coding and complex processing.

- Pilot-based carrier recovery enables absolute phase detection and simple processing at the cost of additional signal overhead.

• The optimal choice can be different depending on system constraints, e.g. long-haul vs. metro, power consumption vs. performance…

Summary

38


Acknowledgements

Noriaki Kaneda Reinhold Noé

Young-Kai Chen Ulrich Rückert

Jeffrey Lee Xiang Liu

Giancarlo Gavioli Chandrasekhar Sethumadhavan

Maurizio Magarini Sebastian Randel

Carlo Constantini Peter Winzer

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