Digital signal processing based on inverse scattering transform

Abstract

Through numerical modeling, we illustrate the possibility of a new approach to digital signal processing in coherent optical communications based on the application of the so-called inverse scattering transform. Considering without loss of generality a fiber link with normal dispersion and quadrature phase shift keying signal modulation, we demonstrate how an initial information pattern can be recovered (without direct backward propagation) through the calculation of nonlinear spectral data of the received optical signal. The technology of coherent optical communications has enabled a dramatic improvement of fiber-optic transmission systems. The introduction of advanced modulation formats [1] and digital signal processing (DSP) for coherent communications (see, e.g., [2][3][4] and references therein) led to practical implementation of systems with 100 Gb∕s channel rates. The key to this breakthrough is the possibility to mitigate the most important linear transmission impairments, such as fiber link dispersion and polarization-mode dispersion. In coherent fiber-optic communication systems, the received optical signal is digitized through high-speed analog-to-digital converters and then processed using DSP algorithms. The input signal is recovered with the accuracy allowed by the channel noise and the transmission effects that are not equalized by DSP. After the mitigation of linear effects, noise and nonlinear impairments become the key factors in limiting the performance of coherent fiber-optic communication systems. In this Letter, through numerical modeling we illustrate for the optical communication community the possibility of using the inverse scattering transform (IST) (see [5][6][7][8][9] and references therein)-a technique developed few decades ago in other areas of physics-for mitigation of nonlinear impairments in coherent optical communications. Without loss of generality, we illustrate the application of the IST to transmission of a quadrature phase shift keying (QPSK) signal in a normal dispersion fiber link. Note that, in general, the power of a signal transmitted through an optical fiber link is degraded by loss and has to be periodically recovered through optical amplification. In many important practical situations, averaging of such periodic loss and gain results in an effectively lossless propagation model-the nonlinear Schrödinger (NLS) equation [6,10]. Moreover, it has recently been experimentally demonstrated that fiber loss can be compensated continuously along a fiber span leading to effectively quasi-lossless transmission [11][12][13]. Therefore, the NLS equation is an important principal model that is used for demonstrating key techniques and approaches in optical fiber communications. In dimensionless units, the master equation reads [6,10]where s signβ 2 1 for normal and anomalous dispersion, respectively (β 2 is the group velocity dispersion coefficient); here we consider normal dispersion without loss of generality. The propagation distance z Z∕L D is normalized by the dispersion l...

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“…In recent years, there has been a growing interest in the alternative approach of designing fiber optical communication systems in which the nonlinearity is taken into account as an essential element rather than a destructive effect [12]. The core idea behind this approach is based on the fact that without perturbation the nonlinear Schrödinger equation (NLSE), which governs the propagation of optical signal in SSMF, belongs to the class of the so-called integrable nonlinear systems [13][14][15]. As a consequence, the field evolution over the NLSE channel can be presented within a special basis of nonlinear normal modes (nonlinear signal spectrum), including non-dispersive soliton (discrete) and quasi-linear dispersive radiation (continuous) modes.…”

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