Two discrete-time interference channel models are developed for information transmission over a single span of optical fiber using wavelength-division multiplexing (WDM) and lumped amplification. The models are derived from the nonlinear Schroedinger (NLS) equation by including the nonlinear phenomena of self-phase modulation (SPM) and cross-phase modulation (XPM) but ignoring four-wave mixing (FWM), polarization effects and group velocity dispersion (GVD) within WDM bands. The first model also ignores GVD across WDM bands, referred to as group velocity mistmatch (GVM). For the case of two users, a new technique called "interference focusing" is proposed where each carrier achieves the capacity pre-log 1, thereby doubling the pre-log of 1/2 achieved by using conventional methods. For three users, interference focusing is also useful under certain conditions. The second model captures GVM and the effect of filtering at the receivers in addition to SPM and XPM. In a 3-user system, it is shown that all users can achieve the maximum pre-log factor 1 simultaneously by using interference focusing, a time-limited pulse and a bank of filters at the receivers.
Wireless power transfer and backscatter communications have emerged as promising solutions for energizing and communicating with power limited devices. Despite some progress in wirelessly powered backscatter communications, the focus has been concentrated on backscatter and energy harvester. Recently, significant progress has been made on the design of transmit multisine waveform, adaptive to the Channel State Information at the transmitter (CSIT), in point-to-point backscatter system. In this paper, we leverage the work and study the design of transmit multisine waveform in a multiuser backsc…
We consider the information channel described by Schrödinger equation with additive Gaussian noise. We introduce the model of the input signal and the model of the output signal receiver. For this channel, using perturbation theory for the small nonlinearity parameter, we calculate the first three terms of the expansion of the conditional probability density function in the nonlinearity parameter. At large signal-to-noise power ratio we calculate the conditional entropy, the output signal entropy, and the mutual information in the leading and next-to-leading order in the nonlinearity parameter…
In this Letter we analyze the benefit of digital compensation of fiber nonlinearity, where the digital signal processing is divided between the transmitter and receiver. The application of the Gaussian noise model indicates that, where there are two or more spans, it is always beneficial to split the nonlinearity compensation. The theory is verified via numerical simulations, investigating transmission of single channel 50 GBd polarization division multiplexed 256-ary quadrature amplitude modulation over 100 km standard single mode fiber spans, using lumped amplification. For this case, the ad…
An upper bound to the information capacity of a wavelength-division multi- plexed optical fiber communication system is derived in a model incorporating the nonlinear propagation effects of cross-phase modulation (XPM). This work is based on the paper by Mitra et al., finding lower bounds to the channel capacity, in which physical models for propagation are used to calculate statistical properties of the conditional probability distribution relating input and output in a single WDM channel. In this paper we present a tractable channel model incorporating the effects of cross phase modulation. …
A new probabilistic shaping distribution that outperforms Maxwell-Boltzmann is studied for the nonlinear fiber channel. Additional gains of 0.1 bit/symbol MI or 0.2 dB SNR for both DP-256QAM and DP-1024QAM are reported after 200 km nonlinear fiber transmission.
Mitsubishi Electric Research Laboratories（三菱电机研究实验室）
Recently, data-driven approaches motivated by modern deep learning have been applied to optical communications in place of traditional model-based counterparts. The application of deep neural networks (DNN) allows flexible statistical analysis of complicated fiber-optic systems without relying on any specific physical models. Due to the inherent nonlinearity in DNN, various equalizers based on DNN have shown significant potentials to mitigate fiber nonlinearity. In this paper, we propose a turbo equalization (TEQ) based on DNN as a new alternative framework to deal with nonlinear fiber impairm…
Eindhoven University of Technology（埃因霍温理工大学）；Memorial University（纪念大学）
Machine learning techniques have recently received significant attention as promising approaches to deal with the optical channel impairments, and in particular, the nonlinear effects. In this work, a machine learning-based classification technique, known as the Parzen window (PW) classifier, is applied to mitigate the nonlinear effects in the optical channel. The PW classifier is used as a detector with improved nonlinear decision boundaries more adapted to the nonlinear fiber channel. Performance improvement is observed when applying the PW in the context of dispersion managed and dispersion…
Nonlinearity Compensation for Coherent Optical Satellite Communications
Cnr-Istituto di Elettronica e di Ingegneria dell’Informazione e delle Telecomunicazioni (CNR-IEIIT)（意大利国家研究委员会电子与信息与电信工程学院研究所）；Telecommunications, Computer Engineering, and Photonics (TeCIP) Institute, Scuola Superiore Sant’Anna（圣安娜高等学院电信、计算机工程与光子学研究所）；National Laboratory of Photonic Networks, CNIT（意大利国家信息技术研究中心光网络国家实验室）；Universitas Mercatorum（梅卡托姆大学）
Constellation shaping is a practical and effective technique to improve the performance and the rate adaptivity of optical communication systems. In principle, it could also be used to mitigate the impact of nonlinear effects, possibly increasing the information rate beyond the current limit dictated by fiber nonlinearity. However, this appealing idea is frustrated by the difficulty of designing an effective shaping strategy that takes into account the nonlinearity and long memory of the fiber channel, as well as the possible interplay with other nonlinearity mitigation strategies. As a result…
The first-order (FO) perturbation theory has been widely investigated to design the digital nonlinearity compensation (NLC) technique to deal with the intra-channel fiber nonlinearity effect in coherent optical communication systems. The main advantages of the perturbation theory-based approach are the possibility of the implementation on a single stage for the entire fiber link and one sample per symbol operation. In this paper, we propose to extend the FO perturbation theory-based NLC (FO-PB-NLC) technique to the second-order (SO), referred to as the SO-PB-NLC, to enhance the NLC performance…
A fiber optic channel is modeled in a variety of ways; from the simple additive white complex Gaussian noise model, to models that incorporate memory in the channel. Because of Kerr nonlinearity, a simple model is not a good approximation to an optical fiber. Hence we study a fiber optic channel with finite memory and provide an achievable bound on channel capacity that improves upon a previously known bound.
In optical communication systems, short blocklength probabilistic enumerative sphere shaping (ESS) provides both linear shaping gain and nonlinear tolerance. In this work, we investigate the performance and complexity of ESS in comparison with fiber nonlinearity compensation via digital back propagation (DBP) with different steps per span. We evaluate the impact of the shaping blocklength in terms of nonlinear tolerance and also consider the case of ESS with a Volterra-based nonlinear equalizer (VNLE), which provides lower complexity than DBP. In single-channel transmission, ESS with VNLE achi…
Chalmers University（查尔莫斯大学）；Duke University（杜克大学）；Eindhoven University of Technology（埃因霍温理工大学）
For the efficient compensation of fiber nonlinearity, one of the guiding principles appears to be: fewer steps are better and more efficient. We challenge this assumption and show that carefully designed multi-step approaches can lead to better performance-complexity trade-offs than their few-step counterparts.
A lower bound on the capacity of the split-step Fourier channel is derived. The channel under study is a concatenation of smaller segments, within which three operations are performed on the signal, namely, nonlinearity, linearity, and noise addition. Simulation results indicate that for a fixed number of segments, our lower bound saturates in the high-power regime and that the larger the number of segments is, the higher is the saturation point. We also obtain an alternative lower bound, which is less tight but has a simple closed-form expression. This bound allows us to conclude that the sat…
We propose two novel techniques to implement sequence selection (SS) for fiber nonlinearity mitigation, demonstrating a nonlinear shaping gain of 0.24 bits/s/Hz, just 0.1 bits/s/Hz below the SS capacity lower bound.
