Machine learning (ML) has disrupted a wide range of science and engineering disciplines in recent years. ML applications in optical communications and networking are also gaining more attention, particularly in the areas of nonlinear transmission systems, optical performance monitoring, and cross-layer network optimizations for software-defined networks. However, the extent to which ML techniques can benefit optical communications and networking is not clear and this is partly due to an insufficient understanding of the nature of ML concepts. This paper aims to describe the mathematical foundations of basic ML techniques from communication theory and signal processing perspectives, which in turn will shed light on the types of problems in optical communications and networking that naturally warrant ML use. This will be followed by an overview of ongoing ML research in optical communications and networking with a focus on physical layer issues.

An Optical Communication's Perspective on Machine Learning and Its Applications

Orthogonal frequency division multiplexing (OFDM) is a modulation technique which is now used in most new and emerging broadband wired and wireless communication systems because it is an effective solution to intersymbol interference caused by a dispersive channel. Very recently a number of researchers have shown that OFDM is also a promising technology for optical communications. This paper gives a tutorial overview of OFDM highlighting the aspects that are likely to be important in optical applications. To achieve good performance in optical systems OFDM must be adapted in various ways. The constraints imposed by single mode optical fiber, multimode optical fiber and optical wireless are discussed and the new forms of optical OFDM which have been developed are outlined. The main drawbacks of OFDM are its high peak to average power ratio and its sensitivity to phase noise and frequency offset. The impairments that these cause are described and their implications for optical systems discussed.

OFDM for Optical Communications

Optical communication systems represent the backbone of modern communication networks. Since their deployment, different fiber technologies have been used to deal with optical fiber impairments such as dispersion-shifted fibers and dispersion-compensation fibers. In recent years, thanks to the introduction of coherent detection based systems, fiber impairments can be mitigated using digital signal processing (DSP) algorithms. Coherent systems are used in the current 100 Gb/s wavelength-division multiplexing (WDM) standard technology. They allow the increase of spectral efficiency by using multilevel modulation formats, and are combined with DSP techniques to combat linear fiber distortions. In addition to linear impairments, the next generation 400 Gb/s and 1 Tb/s WDM systems are also more affected by the fiber nonlinearity due to the Kerr effect. At high input powers, fiber nonlinear effects become more important and their compensation is required to improve the transmission performance. Several approaches have been proposed to deal with the fiber nonlinearity. In this paper, after a brief description of the Kerr-induced nonlinear effects, a survey on fiber nonlinearity compensation (NLC) techniques is provided. We focus on the well-known NLC techniques and discuss their performance, as well as their implementation and complexity. An extension of the inter-subcarrier nonlinear interference canceler approach is also proposed. A performance evaluation of the well-known NLC techniques and the proposed approach is provided in the context of Nyquist and super-Nyquist superchannel systems.

A Survey on Fiber Nonlinearity Compensation for 400 Gb/s and Beyond Optical Communication Systems

In this work, we proposed two k-means-clustering-based algorithms to mitigate the fiber nonlinearity for 64-quadrature amplitude modulation (64-QAM) signal, the training-sequence assisted k-means algorithm and the blind k-means algorithm. We experimentally demonstrated the proposed k-means-clustering-based fiber nonlinearity mitigation techniques in 75-Gb/s 64-QAM coherent optical communication system. The proposed algorithms have reduced clustering complexity and low data redundancy and they are able to quickly find appropriate initial centroids and select correctly the centroids of the clusters to obtain the global optimal solutions for large k value. We measured the bit-error-ratio (BER) performance of 64-QAM signal with different launched powers into the 50-km single mode fiber and the proposed techniques can greatly mitigate the signal impairments caused by the amplified spontaneous emission noise and the fiber Kerr nonlinearity and improve the BER performance.

K-means-clustering-based fiber nonlinearity equalization techniques for 64-QAM coherent optical communication system.

We investigate the application of dynamic deep neural networks for nonlinear equalization in long haul transmission systems. Through extensive numerical analysis we identify their optimum dimensions and calculate their computational complexity as a function of system length. Performing comparison with traditional back-propagation based nonlinear compensation of 2 steps-per-span and 2 samples-per-symbol, we demonstrate equivalent mitigation performance at significantly lower computational cost.

Equalization performance and complexity analysis of dynamic deep neural networks in long haul transmission systems

A support vector machine (SVM)-based classification nonlinear equalizer (NLE) is demonstrated, for the first time, in coherent optical orthogonal frequency-division multiplexing (CO-OFDM). For a 40-Gb/s 16 quadrature amplitude modulated (16QAM) CO-OFDM system at 400 km of transmission, SVM-NLE reduces the fiber-induced nonlinearity penalty by about 1 dB in comparison to the benchmark artificial-neural-network (ANN)-based and inverse-Volterra-series-transfer-function-based NLEs.

Fiber Nonlinearity Equalizer Based on Support Vector Classification for Coherent Optical OFDM

In this paper, we show the remarkable timing error (TE) and residual chromatic dispersion (CD) tolerance improvements of the filter bank multicarrier (FBMC) over orthogonal frequency division multiplexing (OFDM) for high-baudrate spectral slicing transmitter and single coherent receiver transmissions. For a 512 Gb/s 16 quadrature amplitude modulated (16QAM) spectrum slicing system at 1600 km of fiber transmission, the FBMC-based system reduces TE and residual CD penalties by more than 1.5 dB and 3 dB, in comparison to the OFDM-based system, respectively.

Multicarrier Approaches for High-Baudrate Optical-Fiber Transmission Systems With a Single Coherent Receiver

We propose a cost-efficient scheme called pseudo-pilot coding based phase noise estimation (PC-PNE) to compensate laser phase noises for filter-bank multicarrier (FBMC) transmission systems. The performance of the proposed PC-PNE with rectangular quadratic-amplitude modulation (QAM) is evaluated and compared with the state-of-the-art modified blind phase search (M-BPS) approach via extensive Monte Carlo simulations. Under 200 kHz combined laser linewidth, 32 Gbaud 256-subcarriers FBMC optical transmission equipped with PC-PNE provides a comparable performance with the complicated M-BPS method for QPSK, 16QAM and 64QAM. Moreover, a significant reduction in computational complexity (up to 50 times) is obtained with PC-PNE in comparison with M-BPS method at the cost of 3.1% spectral efficiency loss.

Pseudo-Pilot Coding Based Phase Noise Estimation for Coherent Optical FBMC-OQAM Transmissions

In this paper, we show the remarkable timing error (TE) and residual chromatic dispersion (CD) tolerance improvements of the filte bank multicarrier (FBMC) over orthogonal frequency division multiplexing (OFDM) for high-baudrate spectral slicing transmitter and single coherent receiver transmissions. For a 512 Gb/s 16 quadrature amplitude modulated (16QAM) spectrum slicing system at 1600 km of fibe transmission, the FBMC-based system reduces TE and residual CD penalties by more than 1.5 dB and 3 dB, in comparison to the OFDM-based system, respectively.

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Ludo Van Compernolle

Papers

Fiber Nonlinearity Equalizer Based on Support Vector Classification for Coherent Optical OFDM

Multicarrier Approaches for High-Baudrate Optical-Fiber Transmission Systems With a Single Coherent Receiver

Pseudo-Pilot Coding Based Phase Noise Estimation for Coherent Optical FBMC-OQAM Transmissions

Multicarrier approaches for high-baudrate optical-fiber transmission systems with a single coherent receiver