Exact NFDM Transmission in the Presence of Fiber-Loss

Abstract

Nonlinear frequency division multiplexing (NFDM) techniques encode information in the so called nonlinear spectrum which is obtained from the nonlinear Fourier transform (NFT) of a signal. NFDM techniques so far have been applied to the nonlinear Schrödinger equation (NLSE) that models signal propagation in a lossless fiber. Conventionally, the true lossy NLSE is approximated by a lossless NLSE using the pathaverage approach which makes the propagation model suitable for NFDM. The error of the path-average approximation depends strongly on signal power, bandwidth and the span length. It can degrade the performance of NFDM systems and imposes challenges on designing high data rate NFDM systems. Previously, we proposed the idea of using dispersion decreasing fiber (DDF) for NFDM systems. These DDFs can be modeled by a NLSE with varying-parameters that can be solved with a specialized NFT without approximation errors. We have shown in simulations that complete nonlinearity mitigation can be achieved in lossy fibers by designing an NFDM system with DDF if a properly adapted NFT is used. We reported performance gains by avoiding the aforementioned path-average error in an NFDM system by modulating the discrete part of the nonlinear spectrum. In this paper, we extend the proposed idea to the modulation of continuous spectrum. We compare the performance of NFDM systems designed with dispersion decreasing fiber to that of systems designed with a standard fiber with path-average model. Next to the conventional path-average model, we furthermore compare the proposed system with an optimized path-average model in which amplifier locations can be adapted. We quantify the improvement in the performance of NFDM systems that use DDF through numerical simulations.Index Terms-Fiber-optic communication, nonlinear frequency division multiplexing, nonlinear Fourier transform, dispersion decreasing fiber.

Shortening Solitons for Fiber-Optic Transmission

“…Since ψ ∈ L 1 , this implies r −1 ψR ∈ L 1 and thus b ∈ L 1 . This in turn implies that F[b] is in L ∞ (and thus bounded), which together with (15) finally shows that F[b] ∈ L 1 . Assuming that ( 15) is indeed true, this finally implies b ∈ PW 1 π(1+β)/T .…”

“…With ideal distributed amplification, the normalized NSE (2) is equivalent to (1) (in the absence of noise). When the dispersion and nonlinearity coefficients are allowed to vary in space, then the normalization can also be exact for lumped amplification [15]. In this paper, we use the normalization from [16] for the constant coefficient case.…”

Experimental Demonstration of Nonlinear Frequency Division Multiplexing Transmission With Neural Network Receiver

“…The flatter power profile over distance comes at the price of additional noise sources and achieves only a limited reach extension [20], [21]. Instead of minimizing the fiber loss, an exact NFDM transmission can be achieved in the presence of fiber loss by making use of specially designed fibers with a dispersion coefficient decreasing over the fiber length [22]. This interesting approach, however, requires the fabrication of a novel fiber type and cannot be applied to legacy deployed systems.…”

Bounds on the Transmit Power of b-Modulated NFDM Systems in Anomalous Dispersion Fiber

“…The nonlinear Fourier transform (NFT) [ 1 ] is a mathematical tool to solve the normalized nonlinear Schrödinger equation (NSE) which is a model for an ideal lossless single-mode fiber obtained after suitable normalization and path averaging [ 2 ]. (The path average can be avoided by using tapered fibers [ 3 ].) Here, is the slowly varying pulse envelope, z is the location, and t is retarded time, all in normalized units.…”

“…NFDM has garnered much attention in recent years and many different NFDM system designs have been proposed [ 3 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 ]. A common problem with many NFDM designs is that the optimum transmit power decreases with signal duration, making it difficult to utilize signals significantly longer than the channel memory [ 10 , 11 , 18 , 19 , 20 ].…”