A novel technique estimating ASE and non-linear SNR is presented. Our method
is evaluated by simulations obtaining a std error of 0.23 dB for both ASE and non-linear SNR

Ives, David

O'Sullivan, Maurice

Savory, Seb

Vaquero Caballero, FJ

Zhuge, Qunbi

English

Apollo (Cambridge)

Joint Estimation of Linear and Non-linearSignal-to-Noise Ratio based on Neural NetworksF.J. Vaquero Caballero(1), David Ives(1), Qunbi Zhuge(2), Maurice O’Sullivan(2),Seb J. Savory(1)(1) University of Cambridge, 9 JJ Thomson Avenue, Cambridge, CB3 0FA, U.K.(2) Ciena Corporation, Ottawa, ON, CanadaEmail: fjv24@cam.ac.ukAbstract: A novel technique estimating ASE and non-linear SNR is presented. Our methodis evaluated by simulations obtaining a std error of 0.23 dB for both ASE and non-linear SNR.OCIS codes: (060.4510) Optical communications; (120.3940) Metrology.1. IntroductionTraffic demand is growing, increasing the pressure on operators to maximize the capacity over the deployed networks.Flexible Optical Networking and Impairment Aware Networking will heavily rely on signal quality information forrouting decisions, which will be required to be estimated a posteriori due to the heterogeneity and complexity ofnetworks. Optical Performance Monitoring (OPM) is the research field aiming to characterize the impairments sufferedover transmission from the received signal.Optical communication links comprise of several spans of optical fibre followed by noisy Erbium doped fibreamplifiers (EDFA), compensating for signal loss. During transmission, the received signal is affected by different im-pairments: inter-symbol interference (ISI) from the induced chromatic dispersion (CD), state-of-polarization rotation(SOPR), amplified spontaneous emission noise (ASE) and non-linear interference noise (NLI). The origins of ASEand NLI are fundamentally different: while ASE is produced by spontaneous emission by EDFAs and is independentof the signal, NLI is caused by the interaction of electromagnetic fields in silica glass and is proportional to the cubeof the signal power (p) multiplied by a non-linear efficiency factor ηNL [1].CD and SOPR are compensated at the receiver by the equalizer in the Digital Signal Processing (DSP) blockincurring insignificant penalties [2]; ASE cannot be similarly compensated and in-band NLI can be compensatedby perturbation-based precompensation [3] or digital back-propagation [4], with both algorithms expensive in termsof computations. Thus, ASE and NLI limit the symbol rate, reach, and modulation format of the signal. The signal-to-noise ratio (SNR) dictates the overall maximum achievable capacity of a given link and is the de facto figure of meritof any communication system:SNR−1 =ASEp+ηNLp3p= SNR−1ASE +SNR−1NLI (1)Current research focuses on different definitions of the amplitude noise covariance to estimate the NLI based onlinear regressions [5] or Neural Networks (NN) [6]. Others jointly estimate both ASE and NLI, by performing a fittingbetween the transmitted power and the received SNR requiring varying the power of the transmitted signal [1] and sodoing compromising the quality of the transmitted signal.This paper presents a novel technique capable of simultaneously estimating NLI and ASE, with similar complexityto previous approaches. The proposed technique is transparent to transmitter and receiver: without relying on powervariations or requiring special training sequences. We evaluated our method with extensive computer simulations andwe observed it is capable of estimating both the ASE and NLI with a standard deviation (std) error of 0.23 dB for bothSNRNLI and SNRASE .2. The proposed techniqueA typical 16-QAM noisy signal constellation is illustrated in Figure 1 with the 3 constellation rings attributed todifferent power levels. The noise for each constellation symbol can be decomposed in its tangential, t, and normal, n,components. Its noise components are approximately constant for each symbol within a ring but varies from ring toring. ASE produces symmetric Gaussian noise with tangential and angular components independent of the symbol. Onthe other hand, NLI is power dependent and, for advance modulation formats, a large contribution can be characterizedas non-linear phase noise [7], manifesting as correlated noise and producing non-circular variations along the differentt and n components. Averages of the t and the n components are calculated for each ring, resulting in Thr and Nhr ;∀ h = {1,2,3}. Figure 2 shows the behaviour of the proposed metrics in simulations and experiments for 800km ofTrue-Wave Classic fibre (TWC). By incrementing the transmitted power, NLI is also increased and the contributionsof T2r and T3r have a more pronounced growth than the rest of contributions. The normal components also show adifferent evolution by varying the transmitted power: N3r component experiments a steeper growth than N1r and N2r .The described evolution of the noise components takes place even after carrier-phase estimation (CPE), indispensablefor processing the included experimental data.Based on [7], we do not expect the resultant NLI to be circularly symmetric Gaussian for 16-QAM with 16-QAMinterfering channels, in contrast to QPSK signals with QPSK interfering channels, where NLI is expected to be almostcircularly symmetric Gaussian. In this paper we also show that in the scenarios considered for 16-QAM, NLI is farfrom having a circular symmetric Gaussian distribution.The other metrics used in this paper are the amplitude noise covariance (ANC) and its accumulative logarithmicANC (ALANC). The amplitude noise of an x-polarization symbol-k (∆sk,x) is the difference between expected andreceived symbols for the x-polarization: |sk,x|-|sˆk,x|, the amplitude noise correlation of y-polarization (∆sk,y) is definedaccordingly. The introduced metrics are calculated as:ANCi j(m) = cov(∆sk,i,∆sk+m, j), ALANCi j = 10log10(1/6∑i=1|ANCi j(i)|), i, j ∈ {x,y} (2)The presented metrics: Thr , Nhr , ALANCxx and ALANCxy, in combination with ACD and number of WDM channels(nWDM), are used as input of a NN, consisting of 1 hidden layer and 7 neurons (Figure 3). The NN network uses anhyperbolic tangent sigmoid as non-linear function, g(x), and is trained by the 70/15/15 rule for the train/dev/test withearly stopping over the dev.Figure 4 plots the ALANC metric, Thr , and Nhr against SNRNLI illustrating the need of a NN as an estimator of theirnon-linear relationship. Table 1 summarizes the 2160 cases considered for the training and validation of our algorithm.The 35 Gbaud, DP-16QAM with a 0.14 roll-off factor was transmitted over different WDM configurations, fibrestypes, and lengths. The 50 GHz spaced WDM system was simulated as noise-free, while ASE was loaded into thereceiver according to several ASE-to-NLI power ratios (ANR), comprising the optimum operation point, ANR = 2,and another 4 cases: 0.5, 1, 4 and 8.IQtntntnring 1ring 2 ring 3Fig. 1: 16-QAM signal and tand n components.-6 -5 -4 -3 -2 -1 0Power [dBm]0.040.060.080.10.12T rh and Nrh  [a.u.]ExperimentTr3Tr2Tr1Nr3Nr2Nr1-6 -5 -4 -3 -2 -1 0Power [dBm]0.040.060.080.10.12SimulationTr3Tr2Tr1Nr3Nr2Nr1Fig. 2: Thr and N1:3r for 11xDWDMover 800km of TWC.g(a11)T 1:3r g(a12) a21N1:3r ...ACD,nWDM ...ALANCxx,xy g(a16) a22g(a17)SNRASESNRNLIW11,1:3W11,9:10W 21,1W 17,9:10W2 1,7W22,71. IntroductionFig. 3: Structure of the implemented NN (biases areomitted).14 16 18 20 22 24 26 28 30 32SNRNLI [dB]2530354045ALANC [a.u.]00.0050.010.0150.020.0250.03Nr, T r  [a.u.]ALANCTr3Tr2Tr1Nr3Nr2Nr1Fig. 4: Evolution of ALANC and T hr and Nhr for all thesimulation data.Fibre types NDSF TWC ELEAF NDSF & TWC NDSF & ELEAF ELEAF & TWCChannel launch power [dBm] 0.5 -2.5 -1 -1 -0.5 -2Distance [km] 320, 400, 480, 560, 640, 720, 800, 880, 960, 1040, 1120, 1200WDM channel 1, 3, 5, 7, 11, 21ASE-to-NLI ratio 0.5, 1, 2, 4, 8Table 1: Scenarios considered for the proposed technique10 15 20 25 30 35 505101520253035Est. SNRASE [dB]5 10 15 20 25 30 35True SNRASE  [dB]-2-1012 SNR [dB]Fig. 5: True vs estimated SNRASE .10 15 20 25 30 35 505101520253035Est. SNRNLI [dB]5 10 15 20 25 30 35True SNRNLI [dB]-2-1012 SNR [dB]Fig. 6: True vs estimated SNRNLI .3. ResultsFigure 5 and 6 shows the true vs estimated SNRASE and SNRNLI , respectively. Good agreement between expected andestimated values is observed corresponding to a std error of 0.23 dB. Several iterations are performed over the NNwith different initializations of the weights. The possibility of over-fitting was minimized by evaluating the error ofthe three data sets and ensuring that the solution does not suffer from bias or variance errors. Although solutions inwhich one of the estimates can have a smaller estimation error at expense of the other are possible, we aimed forsolutions with approximately same performance for both estimates. We evaluated the performance under CPE, byloading phase noise equivalent of 200 kHz of linewidth over the simulated data and recovering the resultant signalwith a modified Viterbi&Viterbi, the NN was then trained with the metrics influenced by residual phase noise and wascapable of estimating SNRASE and SNRNLI with a std of 0.31 dB. The CPE analysis was limited to an SNR >10 dB,suppressing 106 signals, corresponding to the cases where the pre-FEC bit error rate exceeded 6%. Finally, we testedthe performance of the NN trained without Thr , or Nhr , obtaining a std error 0.39 and 0.25 dB, respectively.4. Conclusion and future workWe developed and evaluated a novel technique for jointly estimating SNRASE and SNRNLI with std error of 0.23dB over a wide range of fibres, ASE-to-NLI ratios, WDM channels, and distances. The proposed metric is simple,requiring the extraction of basic features of the post-DSP signal and a small Neural Network suitable for itsimplementation in receivers. Its performance was also validated under the influence of CPE and phase noise. Futurework will include the experimental evaluation of the proposed technique.Acknowledgements: FJVC, DI, and SJS thank Ciena and UK EPSRC (through the project INSIGHT EP/L026155/2)for funding and support.References1. D.J. Ives, et al., ”Single Channel Probe Utilizing the EGN Model to Estimate Link Parameters for Network Abstraction,” Proc. ECOC 17,P2.SC6.13 (2017)2. Seb J. Savory, ”Digital filters for coherent optical receivers,” Opt. Express 16, 804-817 (2008)3. Y. Gao, et al., ”Reducing the complexity of perturbation based nonlinearity pre-compensation using symmetric EDC and pulse shaping,”Opt. Express 22, 1209-1219 (2014)4. C.B. Czegledi, et al., ”Digital backpropagation accounting for polarization-mode dispersion,” Opt. Express 25, 1903-1915 (2017)5. Z. Dong, et al.,”OSNR monitoring for QPSK and 16-QAM systems in presence of fiber nonlinearities for digital coherent receivers,” Opt.Express 20, 19520-19534 (2012)6. A.S. Kashi, et al., ”Fiber Nonlinear Noise-to-Signal Ratio Monitoring Using Artificial Neural Networks,” Proc. ECOC 17, M.2.F.2 (2017)7. R. Dar, et al., ”Properties of nonlinear noise in long, dispersion-uncompensated fiber links,” Opt. Express 21, 25685-25699 (2013)

Joint Estimation of Linear and Non-linear Signal-to-Noise Ratio based on Neural Networks

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Joint Estimation of Linear and Non-linear Signal-to-Noise Ratio based on Neural Networks

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