The nonlinear Schrödinger equation (NLSE) is often used as a master path-average model for fiber-optic links to analyze fundamental properties of such nonlinear communication channels. Transmission of a signal in nonlinear channels is conceptually different from linear communications. We use here the NLSE channel model to explain and illustrate some new unusual features introduced by nonlinearity. In general, NLSE describes the co-existence of dispersive (continuous) waves and localized (here in time) waves: soliton pulses. The nonlinear Fourier transform method allows one to compute for any given temporal signal the so-called nonlinear spectrum that defines both continuous spectrum (analog to conventional Fourier spectral presentation) and solitonic components. Nonlinear spectrum remains invariant during signal evolution in the NLSE channel. We examine conventional orthogonal frequency-division multiplexing (OFDM) and wavelength-division multiplexing (WDM) return-to-zero signals and demonstrate that both signals at certain power levels have soliton component. We would like to stress that this effect is completely different from the soliton communications studied in the past. Applying Zakharov–Shabat spectral problem to a single WDM or OFDM symbol with multiple sub-carriers, we quantify the effect of statistical occurrence of discrete eigenvalues in such an information-bearing optical signal. Moreover, we observe that at signal powers optimal for transmission, an OFDM symbol with high probability has a soliton component.

中文翻译：

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非线性信道中常规 OFDM 和 WDM 归零信号的非线性频谱

非线性薛定谔方程 (NLSE) 通常用作光纤链路的主路径平均模型，以分析此类非线性通信信道的基本特性。非线性信道中的信号传输在概念上不同于线性通信。我们在这里使用 NLSE 通道模型来解释和说明非线性引入的一些新的异常特征。一般来说，NLSE 描述了色散（连续）波和局部（时间上）波的共存：孤子脉冲。非线性傅里叶变换方法允许为任何给定的时间信号计算所谓的非线性谱，它定义了连续谱（类似于传统的傅里叶谱表示）和孤子分量。非线性频谱在 NLSE 信道中的信号演化过程中保持不变。我们检查了传统的正交频分复用 (OFDM) 和波分复用 (WDM) 归零信号，并证明在某些功率水平下的两种信号都具有孤子分量。我们要强调的是，这种效应与过去研究的孤子通信完全不同。将 Zakharov-Shabat 频谱问题应用于具有多个子载波的单个 WDM 或 OFDM 符号，我们量化了这种承载信息的光信号中离散特征值的统计出现的影响。此外，我们观察到在最适合传输的信号功率下，具有高概率的 OFDM 符号具有孤子分量。