Design of APSK Constellations for Coherent Optical Channels with Nonlinear Phase Noise

We study the design of amplitude phase-shift keying (APSK) constellations for a coherent fiber-optical communication system where nonlinear phase noise (NLPN) is the main system impairment. APSK constellations can be regarded as a union of phase-shift keying (PSK) signal sets with different amplitude levels. A practical two-stage (TS) detection scheme is analyzed, which performs close to optimal detection for high enough input power. We optimize APSK constellations with 4, 8, and 16 points in terms of symbol error probability (SEP) under TS detection for several combinations of input power and fiber length. Our results show that APSK is a promising modulation format in order to cope with NLPN. As an example, for 16 points, performance gains of 3.2 dB can be achieved at a SEP of 10^-2 compared to 16-QAM by choosing an optimized APSK constellation. We also demonstrate that in the presence of severe nonlinear distortions, it may become beneficial to sacrifice a constellation point or an entire constellation ring to reduce the average SEP. Finally, we discuss the problem of selecting a good binary labeling for the found constellations. For the class of rectangular APSK a labeling design method is proposed, resulting in near-optimal bit error probability.Comment: Submitted to IEEE Transactions on Communication

Harnessing machine learning for fiber-induced nonlinearity mitigation in long-haul coherent optical OFDM

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).Coherent optical orthogonal frequency division multiplexing (CO-OFDM) has attracted a lot of interest in optical fiber communications due to its simplified digital signal processing (DSP) units, high spectral-efficiency, flexibility, and tolerance to linear impairments. However, CO-OFDM’s high peak-to-average power ratio imposes high vulnerability to fiber-induced non-linearities. DSP-based machine learning has been considered as a promising approach for fiber non-linearity compensation without sacrificing computational complexity. In this paper, we review the existing machine learning approaches for CO-OFDM in a common framework and review the progress in this area with a focus on practical aspects and comparison with benchmark DSP solutions.Peer reviewe

Nonlinearity and Noise Effects in Multi-level Signal Millimeter-Wave over Fiber Transmission using Single- and Dual-Wavelength Modulation

We transmit multilevel quadrature amplitude modulation (QAM) data-IEEE 802.16 schemes-at 20 MSps and an orthogonal frequency-division multiplexing (OFDM) 802.11 g signal (54 Mbps) with a 25 GHz millimeter-wave over fiber system, which employs a dual wavelength source, over 20 km of single mode fiber. Downlink data transmission is successfully demonstrated over both optical and wireless (up to 12 m) paths with good error vector magnitude. An analysis of two different schemes, in which data is applied to one (single) and both (dual) of the wavelengths of a dual wavelength source, is carried out. The system performance is analyzed through simulation and a good match with experimental results is obtained. The analysis investigates the impact of Mach-Zehnder modulator (MZM) and RF amplifier nonlinearity and various noise sources, such as laser relative intensity noise, amplified spontaneous emission, thermal, and shot noise. A comparison of single carrier QAM IEEE 802.16 and OFDM in terms of their sensitivity to the distortions from MZM and RF amplifier nonlinearity is also presented

Modelling and inverting complex-valued Wiener systems

We develop a complex-valued (CV) B-spline neural network approach for efficient identification and inversion of CV Wiener systems. The CV nonlinear static function in the Wiener system is represented using the tensor product of two univariate B-spline neural networks. With the aid of a least squares parameter initialisation, the Gauss-Newton algorithm effectively estimates the model parameters that include the CV linear dynamic model coefficients and B-spline neural network weights. The identification algorithm naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. An accurate inverse of the CV Wiener system is then obtained, in which the inverse of the CV nonlinear static function of the Wiener system is calculated efficiently using the Gaussian-Newton algorithm based on the estimated B-spline neural network model, with the aid of the De Boor recursions. The effectiveness of our approach for identification and inversion of CV Wiener systems is demonstrated using the application of digital predistorter design for high power amplifiers with memor

Machine learning for fiber nonlinearity mitigation in long-haul coherent optical transmission systems

Fiber nonlinearities from Kerr effect are considered as major constraints for enhancing the transmission capacity in current optical transmission systems. Digital nonlinearity compensation techniques such as digital backpropagation can perform well but require high computing resources. Machine learning can provide a low complexity capability especially for high-dimensional classification problems. Recently several supervised and unsupervised machine learning techniques have been investigated in the field of fiber nonlinearity mitigation. This paper offers a brief review of the principles, performance and complexity of these machine learning approaches in the application of nonlinearity mitigation

Efficient Parallel Carrier Recovery for Ultrahigh Speed Coherent QAM Receivers with Application to Optical Channels

This work presents a new efficient parallel carrier recovery architecture suitable for ultrahigh speed intradyne coherent optical receivers (e.g., ≥100 Gb/s) with quadrature amplitude modulation (QAM). The proposed scheme combines a novel low-latency parallel digital phase locked loop (DPLL) with a feedforward carrier phase recovery (CPR) algorithm. The new low-latency parallel DPLL is designed to compensate not only carrier frequency offset but also frequency fluctuations such as those induced by mechanical vibrations or power supply noise. Such carrier frequency fluctuations must be compensated since they lead to higher phase error variance in traditional feedforward CPR techniques, significantly degrading the receiver performance. In order to enable a parallel-processing implementation in multigigabit per second receivers, a new approximation to the DPLL computation is introduced. The proposed technique reduces the latency within the feedback loop of the DPLL introduced by parallel processing, while at the same time it provides a bandwidth and capture range close to those achieved by a serial DPLL. Simulation results demonstrate that the effects caused by frequency deviations can be eliminated with the proposed low latency parallel carrier recovery architecture.Fil: Gianni, Pablo. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Departamento de Electrónica. Laboratorio de Comunicaciones Digitales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Ferster, Laura. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Departamento de Electrónica. Laboratorio de Comunicaciones Digitales; ArgentinaFil: Corral Briones, Graciela. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Departamento de Electrónica. Laboratorio de Comunicaciones Digitales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Hueda, Mario Rafael. Universidad Nacional de Córdoba. Facultad de Ciencias Exactas Físicas y Naturales. Departamento de Electrónica. Laboratorio de Comunicaciones Digitales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Coherent Optical DFT-Spread OFDM

We consider application of the discrete Fourier transform-spread orthogonal frequency-division multiplexing (DFT-spread OFDM) technique to high-speed fiber optic communications. The DFT-spread OFDM is a form of single-carrier technique that possesses almost all advantages of the multicarrier OFDM technique (such as high spectral efficiency, flexible bandwidth allocation, low sampling rate and low-complexity equalization). In particular, we consider the optical DFT-spread OFDM system with polarization division multiplexing (PDM) that employs a tone-by-tone linear minimum mean square error (MMSE) equalizer. We show that such a system offers a much lower peak-to-average power ratio (PAPR) performance as well as better bit error rate (BER) performance compared with the optical OFDM system that employs amplitude clipping.Comment: This idea was originally submitted at Nov. 28th, 2009. After many times of rejection and resubmission, it was finally accepted by the journal of Advances in Optical Technologie

Capacity of a Nonlinear Optical Channel with Finite Memory

The channel capacity of a nonlinear, dispersive fiber-optic link is revisited. To this end, the popular Gaussian noise (GN) model is extended with a parameter to account for the finite memory of realistic fiber channels. This finite-memory model is harder to analyze mathematically but, in contrast to previous models, it is valid also for nonstationary or heavy-tailed input signals. For uncoded transmission and standard modulation formats, the new model gives the same results as the regular GN model when the memory of the channel is about 10 symbols or more. These results confirm previous results that the GN model is accurate for uncoded transmission. However, when coding is considered, the results obtained using the finite-memory model are very different from those obtained by previous models, even when the channel memory is large. In particular, the peaky behavior of the channel capacity, which has been reported for numerous nonlinear channel models, appears to be an artifact of applying models derived for independent input in a coded (i.e., dependent) scenario

Optical Signal Processing for High-Order Quadrature- Amplitude Modulation Formats

In this book chapter, optical signal processing technology, including optical wavelength conversion, wavelength exchange and wavelength multicasting, for phase-noise-sensitive high-order quadrature-amplitude modulation (QAM) signals will be discussed. Due to the susceptibility of high-order QAM signals against phase noise, it is imperative to avoid the phase noise in the optical signal processing subsystems. To design high-performance optical signal processing subsystems, both linear and nonlinear phase noise and distortions are the main concerns in the system design. We will first investigate the effective monitoring approach to optimize the performance of wavelength conversion for avoiding undesired nonlinear phase noise and distortions, and then propose coherent pumping scheme to eliminate the linear phase noise from local pumps in order to realize pump-phase-noise-free wavelength conversion, wavelength exchange and multicasting for high-order QAM signals. All of the discussions are based on experimental investigation