Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing S. Civelli, E. Forestieri, and M. Secondini

Nonlinear Fourier Transform in Optical Communications th Florence, February 21 , 2018

Introduction Nonlinear Fourier transform (NFT)-based transmission schemes for optical fibre communications to overcome limitation imposed by nonlinearty ● NFT defines a nonlinear spectrum that evolves trivially and linearly along the optical fibre ● Nonlinear Frequency-Division Multiplexing (NFDM) encodes information on the nonlinear spectrum ●

It is not clear yet whether NFDM can outperform conventional systems Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

Nonlinear inverse synthesis (NIS) Digitally diagonalized and linearized channel Transmitted message

Encoder Nonlinear spectrum

Received message

Detector

BNFT

DAC

Time-domain samples

FNFT

Minimum Euclidean distance detection optimal at low powers

Waveform

Channel

Le et al., Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers, Optics express 2014

ADC

Burst transmission to ● NFT boundary conditions ● Avoid burst-burst interaction during propagation

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

Nonlinear inverse synthesis (NIS) Digitally diagonalized and linearized channel Transmitted message

Encoder Nonlinear spectrum

Received message

Detector

BNFT

DAC

Time-domain samples

FNFT

Minimum Euclidean distance detection optimal at low powers

Waveform

Channel

ADC

Burst transmission to ● NFT boundary conditions ● Avoid burst-burst interaction during propagation

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

Nonlinear inverse synthesis (NIS) Digitally diagonalized and linearized channel

Encoder Nonlinear spectrum

Received message

Detector

BNFT

DAC

Time-domain samples

FNFT

Minimum Euclidean distance detection optimal at low powers

Waveform

35 ADC 30 Q-factor (dB)

Transmitted message

25

Channel

Nb=8 ( =1%) Nb=16 ( =2%) Nb=32 ( =4%) Nb=64 ( =7%) Nb=128 ( =14%) Nb=256 ( =24%) Nb=512 ( =39%) Nb=1024 ( =56%)

simulations (fiber link) simulations (AWGN) theory

Burst transmission to 15 ● NFT boundary conditions 10 ● 5 Avoid burst-burst interaction during propagation 0 -20 -15 -10 -5 0 5 10 20

Civelli et al., IEEE Photon. Technol. Lett. 2017

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

Power (dBm)

Nonlinear inverse synthesis (NIS) Digitally diagonalized and linearized channel

Encoder Nonlinear spectrum

Received message

Detector

BNFT

DAC

Time-domain samples

FNFT

Minimum Euclidean distance detection optimal at low powers

Waveform

35 ADC 30 Q-factor (dB)

Transmitted message

25

Channel

Nb=8 ( =1%) Nb=16 ( =2%) Nb=32 ( =4%) Nb=64 ( =7%) Nb=128 ( =14%) Nb=256 ( =24%) Nb=512 ( =39%) Nb=1024 ( =56%)

simulations (fiber link) simulations (AWGN) theory

Burst transmission to 15 ● NFT boundary conditions 10 ● 5 Avoid burst-burst interaction during propagation 0 -20 -15 -10 -5 0 5 10 20

Civelli et al., IEEE Photon. Technol. Lett. 2017

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

Power (dBm)

Alternative detection Digitally diagonalized and linearized channel Transmitted message

Encoder Nonlinear spectrum

Received message

Detector

BNFT

DAC

Time-domain samples

FNFT

Waveform

Channel

ADC

Minimum Euclidean distance detection optimal at low powers

Compare the received signal with all possible received noiseless waveforms

Civelli et al., IEEE Photon. Technol. Lett. 2017

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

NFT causality property

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

Decision-Feedback BNFT detection

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

1.5

Received signal

1

Decision-Feedback BNFT detection Rer(t)

0.5

0 -0.5 -1 -1.5

t0

t3 t4

Time

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

DF-BNFT performance Nb Nb Nb

Nb Nb Nb

Ps

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

DF-BNFT suboptimality ●

AWGN channel assumption

●

DF-BNFT detection It does not account for the information received after its time window It is affected by error propagation

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

Impact of fiber propagation Without phase compensation With phase compensation AWGN channel

Nb

Nb Nb Nb

Ps

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

Impact of error propagation

Q2 (dB)

15

Nb=128 ( =6%) Nb=256 ( =11%) Nb=512 ( =20%)

Nb=1024 ( =34%) Nb=2048 ( =51%) Nb=4096 ( =67%)

10 5 Actual Error-prop. free

0 -5 -25

-20

-15

-10 Ps

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

-5

0

Conclusions Novel detection strategy for NFT-based systems: minimize the Euclidean distance in the time domain. ● Performance improvement up to 6.2dB ● Semianalytical approximation and bounds given ● Performance decay remains ●

Future work ● ● ●

Implementation of the optimum detection strategy Computational complexity reduction Extension to dual-polarization case

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

Thank you for your attention! Stella Civelli [email protected] arXiv preprint arXiv:1801.05338

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

Performance Vs rate efficiency 25 20

DF-BNFT NFDM FNFT NFDM

Q2 (dB)

15

EDC DBP

10 continuous transmission

5 0 -5

0

10

20

30

40

50

60

70

Rate efficiency η [%]

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

80

90

100

BER estimation and bounds Assuming AWGN channel and correct previous decision, the probability of error of a given sequence is and

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

BER estimation and bounds (a)

Ps

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

BER estimation and bounds (b)

Ps

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

BER estimation and bounds

Decision-Feedback Detection Strategy for Nonlinear Frequency-Division Multiplexing

Decision-Feedback Detection Strategy for Nonlinear ...

Feb 21, 2018 - Nonlinear Frequency-Division Multiplexing. Encoder. Channel. DAC. Transmitted message. Detector. ADC. Received message. Nonlinear. Time-domain spectrum samples. Waveform. Digitally diagonalized and linearized channel. BNFT. FNFT. Minimum Euclidean distance detection optimal at low powers.
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