Deep learning based digital backpropagation demonstrating SNR gain at low complexity in a 1200†km transmission link.

A deep learning (DL) based digital backpropagation (DBP) method with a 1 dB SNR gain over a conventional 1 step per span DBP is demonstrated in a 32 GBd 16QAM transmission across 1200 km. The new DL-DPB is shown to require 6 times less computational power over the conventional DBP scheme. The achievement is possible due to a novel training method in which the DL-DBP is blind to timing error, state of polarization rotation, frequency offset and phase offset. An analysis of the underlying mechanism is given. The applied method first undoes the dispersion, compensates for nonlinear effects in a distributed fashion and reduces the out of band nonlinear modulation due to compensation of the nonlinearities by having a low pass characteristic. We also show that it is sufficient to update the elements of the DL network using a signal with high nonlinearity when dispersion or nonlinearity conditions changes. Lastly, simulation results indicate that the proposed scheme is suitable to deal with impairments from transmission over longer distances.

Performance of carrier phase recovery for electronically dispersion compensated coherent systems.

An analytical approach taking into account carrier phase estimation (CPE) is presented to predict performance of quadrature phase shift-keying (QPSK) systems using coherent detection. Using this approach, system performance is found as a function of symbol rate, local oscillator (LO) linewidth, chromatic dispersion (CD) and signal-to-noise ratio (SNR). A new expression is derived for the covariance matrix of the conditional probability density function (pdf) of the decision statistic. This pdf is used to find bit error rate (BER) semi-analytically. Our analytical derivation assumes perfect removal of data modulation which corresponds to an ideal decision feedback (DF) carrier recovery. The validity of the analytical pdf for predicting BER is verified for a wide range of system parameters of interest in long haul systems. In addition, our semi-analytical BER provides a lower bound for the Viterbi-Viterbi (VV) BER, while showing the analytical BER previously proposed in the literature shows an overly pessimistic prediction of VV BER performance. We show that inaccuracy in previous analysis stems from overly simple model for the CPE when compensating large accumulated dispersion electronically. Finally, we study extension of our results to quadrature amplitude modulation (QAM). Preliminary simulation results are promising but the accuracy of our semi-analytical approach for predicting BER should be investigated further.