We introduce for the first time the utilization of Long short-term memory (LSTM) neural network architectures for the compensation of fiber nonlinearities in digital coherent systems. We conduct numerical simulations considering either C-band or O-band transmission systems for single channel and multi-channel 16-QAM modulation format with polarization multiplexing. A detailed analysis regarding the effect of the number of hidden units and the length of the word of symbols that trains the LSTM algorithm and corresponds to the considered channel memory is conducted in order to reveal the limits of LSTM based receiver with respect to performance and complexity. The numerical results show that LSTM Neural Networks can be very efficient as post processors of optical receivers which classify data that have undergone non-linear impairments in fiber and provide superior performance compared to digital back propagation, especially in the multi-channel transmission scenario. The complexity analysis shows that LSTM becomes more complex as the number of hidden units and the channel memory increase, however LSTM can be less complex than Digital Back Propagation in long distances (> 1000 km).

We investigate the complexity and performance of recurrent neural network (RNN) models as post-processing units for the compensation of fibre nonlinearities in digital coherent systems carrying polarization multiplexed 16-QAM and 32-QAM signals. We evaluate three bi-directional RNN models, namely the bi-LSTM, bi-GRU and bi-Vanilla-RNN and show that all of them are promising nonlinearity compensators especially in dispersion unmanaged systems. Αs far as inference is concerned, οur simulations show that the three models provide similar compensation performance, therefore, in real-life systems, the simplest scheme based on Vanilla-RNN units should be preferred. We compare bi-Vanilla-RNN in its many-to-many form with Volterra nonlinear equalizers and exhibit its superiority both in terms of performance and complexity, thus highlighting that RNN processing is a very promising pathway for the upgrade of long-haul optical communication systems utilizing coherent detection.

We introduce the use of Fabry-Perot (FP) lasers as potential neuromorphic computing machines with parallel processing capabilities. With the use of optical injection between a master FP laser and a slave FP laser under feedback we demonstrate the potential for scaling up the processing power at longitudinal mode granularity and perform real-time processing for signal equalization in 25 Gbaud intensity modulation direct detection optical communication systems. We demonstrate the improvement of classification performance as the number of modes multiplies the number of virtual nodes and offers the capability of simultaneous processing of arbitrary data streams. Extensive numerical simulations show that up to 8 longitudinal modes in typical Fabry-Perot lasers can be leveraged to enhance classification performance.

Kerr nonlinearity in the form of self- and cross-phase modulation imposes a fundamental limitation to the capacity of wavelength division multiplexed (WDM) optical communication systems. Digital back-propagation (DBP) is a widely adopted technique for the mitigation of impairments induced by Kerr nonlinearity. However, multi-channel DBP is too complex to be implemented commercially in WDM systems. Recurrent neural networks (RNNs) have been recently exploited for nonlinear signal processing in the context of optical communications. In this work, we propose multi-channel equalization through a bidirectional vanilla recurrent neural network (bi-VRNN) in order to improve the performance of the single-channel bi-VRNN algorithm in the transmission of WDM polarization multiplexed signals. We compare the proposed digital algorithm to full-field DBP and to the single channel bi-RNN in order to reveal its merits with respect to both performance and complexity. We finally provide experimental verification in QPSK transmission, showcasing over 2.5 dB optical signal-to-noise ratio (OSNR) gain and a significant reduction in bit-error-rate (BER) by an order of magnitude compared to single channel equalization. Moreover, a complexity reduction of up to 43% was achieved compared to the single-channel RNN, and up to 550% compared to the single channel DBP in the case of 24-span long haul transmission.

The transition to the edge-cloud era makes ultra-high data rate signals indispensable for covering the immense and increasing traffic demands created. This ecosystem also seeks for power efficient optical modules that will deliver this enormous data load. Optical communication systems and their continuous evolution have responded to the upward trend of capacity needs in all different network ecosystems, scaling from short-reach links serving data center, fiber-to-the-home and 5G/B5G services to metro and long-haul transoceanic cables. Kerr induced non-linearities at long haul and dispersion induced power fading at short reach remain intractable problems that vastly affect high symbol rate systems. So, they must be addressed in a power efficient way in order to cope with the ever-increasing traffic requirements. In this paper, we review our recent work in machine learning and neuromorphic processing in the optical domain for the mitigation of transmission impairments at very high symbol rates. Post-detection techniques based on bidirectional recurrent neural networks for non-linearity compensation and neuromorphic recurrent optical spectrum slicers for power fading mitigation and self-coherent detection emerge as promising solutions for mid-term deployment in long-haul and short-reach communication systems respectively. The current work provides new results in both fields focusing on multi-channel detection in the coherent long-haul domain and on a cost/consumption/performance assessment of neuromorphic photonic processing based on recurrent spectrum slicing in comparison to the state-of-the-art. A thorough analysis of other state-of-the-art techniques in both domains is also provided revealing the merits and shortcomings of recurrent neural networks and neuromorphic photonic processing in high-speed optical communication systems.

Coherent technology supporting higher order modulation formats is indispensable for fulfilling the ever-increasing need for higher capacity. However, coherent receivers require heavy digital signal processing (DSP) which increases the power envelope of coherent puggables well above the Intensity Modulation and Direct Detection (IM/DD) counterparts. Although self-coherent or phase retrieval methods have gained significant attention, they still lack in efficiency and suffer from multiple drawbacks in comparison with the standard coherent receiver. Here, we propose and numerically simulate a neuromorphic receiver based on recurrent optical spectrum slicing (ROSS) for detection and equalization of coherent modulation formats, utilizing minimal DSP and low bandwidth components. Through spectral slicing, the receiver can support up to 800 Gb/s/λ net data rate in single polarization configuration for short reach scenarios. © 2022 The Authors.