Simplified high-order Volterra series transfer function for optical transmission links.

Mirko Gagni,Armando N Pinto,Fernando P Guiomar,Stefan Wabnitz

doi:10.1364/oe.25.002446

Abstract

We develop a simplified high-order multi-span Volterra series transfer function (SH-MS-VSTF), basing our derivation on the well-known third-order Volterra series transfer function (VSTF). We notice that when applying an approach based on a recursive method and considering the phased-array factor, the order of the expression for the transfer function grows as 3 raised to the number of considered spans. By imposing a frequency-flat approximation to the higher-order terms that are usually neglected in the commonly used VSTF approach, we are able to reduce the overall expression order to the typical third-order plus a complex correction factor. We carry on performance comparisons between the purposed SH-MS-VSTF, the well-known split-step Fourier method (SSFM), and the third-order VSTF. The SH-MS-VSTF exhibits a uniform improvement of about two orders of magnitude in the normalized mean squared deviation with respect to the other methods. This can be translated in a reduction of the overall number of steps required to fully analyze the transmission link up to 99.75% with respect to the SSFM, and 98.75% with respect to the third-order VSTF, respectively, for the same numerical accuracy.

Highlights

The digital back-propagation (DBP) method provides a very powerful technique to mitigate linear and nonlinear signal impairments in optical fiber transmission systems [1, 2]
We compared the normalized mean squared deviation (NSD) obtained with the standard split-step Fourier method (SSFM), with the typical third-order Volterra series transfer function (VSTF) method, and with the SH-MS-VSTF method
We consistently observed that the introduction of the complex factor in the nonlinear term of the third-order VSTF method allows for a drastic reduction of the amount of NSD

Summary

Introduction

The digital back-propagation (DBP) method provides a very powerful technique to mitigate linear and nonlinear signal impairments in optical fiber transmission systems [1, 2]. The huge computational effort that is required to numerically solve the nonlinear Schrödinger equation (NLSE) has so far limited the real-time application of the DBP approach [1, 3, 4]. This computational complexity problem is present for the direct propagation problem, which frequently limits both the analysis and the optimization of optical transmission links [5]. By making the key hypothesis of an approximately frequency-flat dependence for the higher-order terms, we are able to reduce the ninth-order VSTF expression to the commonly used third-order VSTF, plus a complex correction factor, and to generalize the expression to an higher number of spans.

Theoretical analysis

Simulation results and method validation

Findings

Discussion and conclusions