optical fibers- properties, measurement, and applications Ori - PowerPoint PPT Presentation

Nonlinear interference noise in optical fibers- properties, measurement, and applications Ori Golani

What is NLIN? Nonlinear Interference Noise Tx Rx Tx Rx Tx Rx Tx Rx Tx Rx IC IC COI IC IC frequency 2

What is NLIN? Nonlinear Interference Noise 3

Channel model 𝑥 𝑜 𝑡 𝑜 ⊕ 𝑏 𝑜 User of interest demux Fiber link mux 𝑐 𝑜,IC 1 … Interfering users 𝑐 𝑜,IC 𝑂 ∗ 𝑏 𝑚 𝑡 𝑜 = 𝑏 𝑜 + 𝑥 𝑜 + ෍ ෍ 𝑗𝛿𝑌 ℎ,𝑙,𝑚 𝑐 ℎ 𝑐 𝑙 𝐽𝐷 ℎ,𝑙,𝑚 Received Transmitted signal AWGN Nonlinear interference symbol 4

Treating NLIN- interference as noise ∗ 𝑏 𝑚 𝑡 𝑜 = 𝑏 𝑜 + 𝑥 𝑜 + ෍ ෍ 𝑗𝛿𝑌 ℎ,𝑙,𝑚 𝑐 ℎ 𝑐 𝑙 𝐽𝐷 ℎ,𝑙,𝑚 = 𝑏 𝑜 + 𝑥 𝑜 + 𝑤 𝑜 Approximately Gaussian, 2 = 𝛽𝑄 3 𝜏 𝑤 Treatment as AWGN 5

Stochastic ISI model of NLIN Total NLIN contribution: ∗ 𝑏 𝑚 NLIN = ෍ ෍ 𝑗𝛿𝑌 ℎ,𝑙,𝑚 𝑐 ℎ 𝑐 𝑙 𝐽𝐷 ℎ,𝑙,𝑚 ∗ 𝑏 𝑜−𝑚 = ෍ (𝑜) 𝑏 𝑜−𝑚 = ෍ ෍ ෍ 𝑗𝛿𝑌 ℎ,𝑙,𝑚 𝑐 ℎ 𝑐 𝑙 𝑆 𝑚 𝑚 𝐽𝐷 ℎ,𝑙 𝑚 Sum on unknown ICs 6

What is this model good for? (𝑜) 𝑏 𝑜−𝑚 ∗ 𝑏 𝑚 Δ𝑏 𝑜 = ෍ 𝑆 𝑚 Δ𝑏 𝑜 = ෍ ෍ 𝑗𝛿𝑌 ℎ,𝑙,𝑚 𝑐 ℎ 𝑐 𝑙 𝑚 𝐽𝐷 ℎ,𝑙,𝑚 Linear Time varying Nonlinear problem • NLIN behaves like a doubly-selective linear channel- we can use tools from RF communication (𝑜) , change slow enough, we can track them and mitigate • If the ISI coefficients, 𝑆 𝑚 their effect 7

Characterization of time-varying ISI model (𝑜) Characterizing the statistics of the ISI coefficients 𝑆 𝑚 • Temporal auto-correlation functions (how do they change over time) • Cross-correlation between different elements Analytical approach - solve a lot of integrals Experimental approach - get the statistics from a transmission experiment 8

Characterization: analytical approach The channel coefficients are unknown, but we can describe their statistics (𝑜) = ෍ ∗ 𝑆 𝑚 ෍ 𝑗𝛿𝑌 ℎ,𝑙,𝑚 𝑐 ℎ 𝑐 𝑙 𝐽𝐷 ℎ,𝑙 Autocorrelation function: 𝑜 𝑆 𝑚 𝑜+Δ𝑜 ∗ ACF Δ𝑜 = 𝔽 𝑆 𝑚 ∗ ] ∗ ∗ 𝑐 ℎ ′ 𝑐 𝑙 ′ = ෍ ෍ 𝑗𝛿𝑌 ℎ,𝑙,𝑚 𝑌 ℎ ′ +Δ𝑜,𝑙 ′ +Δ𝑜,𝑚 𝔽[𝑐 ℎ 𝑐 𝑙 𝐽𝐷 ℎ,𝑙 Surprisingly, we can find these functions analytically (with some numeric integration … ) - Dependent on: link structure, bandwidth & frequency of ICs, modulation format … 9

Characterization: analytical approach 500km link with distributed amp, 32GBuad 5x100km link, 32GBuad 2 2 𝑜 ′ ∗ − 𝔽 𝑆 𝑚 𝑜 ′ ∗ − 𝔽 𝑆 𝑚 l=0 (𝑜) 𝑆 𝑚 (𝑜) 𝑆 𝑚 𝔽 𝑆 𝑚 𝔽 𝑆 𝑚 Symbol delay Δ𝑜 Symbol delay Δ𝑜 Dots= SSFM results, lines= model predictions Golani et al, “ Correlations and phase noise in NLIN- modelling and system implications, ” OFC 2016 10

Characterization: experimental approach (𝑜) 𝑏 𝑜 + 𝑗𝑆 1 (𝑜) 𝑏 𝑜−1 + 𝑗𝑆 2 (𝑜) 𝑏 𝑜−2 … + 𝑥 𝑜 𝑡 𝑜 = 𝑏 𝑜 + 𝑗𝑆 0 𝑡 𝑜 − 𝑏 𝑜 (𝑜) + 𝑠𝑓𝑡𝑗𝑒𝑣𝑏𝑚 Measuring ISI coefficient: = 𝑗𝑆 𝑀 𝑏 𝑜−𝑀 11

Characterization: experimental approach First-order: Third-order: Second-order: Zero-order (phase noise): 𝑡 𝑜 − 𝑏 𝑜 𝑡 𝑜 − 𝑏 𝑜 𝑡 𝑜 − 𝑏 𝑜 𝑡 𝑜 − 𝑏 𝑜 𝑏 𝑜−1 𝑏 𝑜−2 𝑏 𝑜−3 𝑏 𝑜 The summation is infinite, but the variance of coefficients drops rapidly 20x101km link, 7 WDM channels, 40GBuad 12

Experimental setup Recirculating loop experiment: • 64-QAM, dual polarization • 40GBaud • 101km spans • 42.5GHz channel spacing Joint work with UCL, Golani et al, “ Experimental characterization of the time correlation properties of nonlinear interference noise, ” ECOC 2017 13

Results- measuring the ACFs 0 th order 1 st order Effect of 2 nd order transmission 3 rd order distance: *7 WDM channels Effect of number Can also find cross of ICs: correlations and other moments from these *2000km link measurements 14

Applications of time-varying ISI model Simulation and performance estimation  “ Virtual lab ” tool- a fast alternative to split-step simulations  Predict system performance in the presence of nonlinearity, including interaction between NLIN and the receiver ’ s DSP 15

Channel model 𝑥 𝑜 𝑡 𝑜 ⊕ 𝑏 𝑜 Channel of interest demux Fiber link mux 𝑐 𝑜,IC 1 … Interfering channels 𝑐 𝑜,IC 𝑂 ∗ 𝑏 𝑚 𝑡 𝑜 = 𝑏 𝑜 + 𝑥 𝑜 + ෍ ෍ 𝑗𝛿𝑌 ℎ,𝑙,𝑚 𝑐 ℎ 𝑐 𝑙 𝐽𝐷 ℎ,𝑙,𝑚 Received Transmitted signal AWGN Nonlinear interference symbol 16

Simplified channel model 𝑥 𝑜 𝑏 𝑜 𝑡 𝑜 ⊕ ⊕ ⊗ ෨ ෍ 𝑆 𝑜 𝑏 𝑜 𝑚 ෨ 𝑆 𝑜 Elements ෨ 𝑆 𝑜 are created artificially If the statistics of the artificial ෨ 𝑆 𝑜 are the same as those of 𝑆 𝑜 , the simplified channel model will behave like the original model O. Golani at Al, “ Modeling the Bit-Error-Rate Performance of Nonlinear Fiber-Optic System, ” JLT (2016) O. Golani at Al, “ Correlations and phase noise in NLIN- modelling and system implications, ” OFC (2016) 17

A virtual lab for performance assessment Distributed Variance based model Bit-error-rate Lumped 0.5 dB in Q Virtual Lab 0 20 40 60 80 Number of channels Performed with 11 WDM channels, 500km link Dots= SSFM results, solid lines= model predictions, dashed lines= AWGN model 18

Applications of time-varying ISI model Design algorithms for nonlinearity mitigation  Use explicit knowledge of the statistics of NLIN to design equalizers tailored for nonlinearity mitigation 19

NLIN mitigation using equalization We can use explicit knowledge of ISI statistics to design better equalizers. The equalizer evaluates the ISI coefficients, and attempts to cancel their effect. |ො 𝑏 𝑜 ۧ ۧ |𝑡 𝑜 Viterbi algorithm ෡ Survivor sequences 𝑺 𝑚 symbol estimations Kalman filter |ො 𝑏 𝑜+𝑀 … ۧ |ො 𝑏 𝑜−𝑀 ۧ Filter uses the statistics of NLIN O. Golani at Al., “ Kalman-MLSE equalization of nonlinear noise, ” OFC (2017) O. Golani at Al., “ Equalization Methods for NLIN Mitigation, ” submitted to JLT 20

Application of statistical characterization: NLIN mitigation No adaptive equalizer 1 tap 3 taps 5 taps RLS 1 tap RLS 3 taps 5 taps 5 tap filter requires to measure the ISI coefficients 𝑆 −2 … 𝑆 2 21

Conclusions • The time varying-ISI model: a powerful tool to treat fiber nonlinearity • Key idea: converting a nonlinear problem into a linear-time varying model • Can use this model to import techniques from RF communication to optical communication Thanks for listening! 22