Volterra series

About: Volterra series is a research topic. Over the lifetime, 2731 publications have been published within this topic receiving 46199 citations.

Time-Domain Volterra-Based Digital Backpropagation for Coherent Optical Systems

Abstract: We propose a novel closed-form time-domain (TD) Volterra series nonlinear equalizer (VSNE) for the mitigation of Kerr-related distortions in polarization-multiplexed (PM) coherent optical transmission systems. The proposed TD-VSNE is obtained from the inverse Fourier analysis of a frequency-domain VSNE based on a frequency-flat approximation. Employing novel TD approximations, we demonstrate the equivalency between the VSNE algorithms formulated in time and frequency domains. In order to enhance the computational efficiency, we insert a power weighting time window in the TD-VSNE, yielding the weighted VSNE (W-VSNE) algorithm. We demonstrate that the convergence of the W-VSNE to its maximum performance is much faster than that of the TD-VSNE, thus requiring fewer parallel filters. Through numerical simulation of a 224-Gb/s PM-16QAM optical channel, we compare the performance/complexity tradeoff of the W-VSNE with the well-known split-step Fourier method (SSFM) and with the computationally optimized weighted SSFM (W-SSFM). Enabled by the use of fewer iterations and only two parallel W-VSNE filters, we demonstrate a reduction of up to $\sim$ 45% on computational effort and $\sim$ 70% on latency, in comparison with the W-SSFM.

Towards a Volterra series representation from a Neural Network model

Abstract: We have developed a Neural Network model able to reproduce some nonlinear characteristics of an electronic device. However, electronic devices nonlinear analysis requires an analytical model, that allows to draw conclusions about the device behavior. Such a model can be the Volterra series representation, which is a series that has some particular terms, named the “Volterra kernels”. We want to show in this work how a Volterra model can be built using the parameters of the proposed Neural Network model. We present a method for estimating the Volterra kernels using the Neural Network parameters and some simulation results.

Turbo Equalization of Non-Linear Satellite Channels Using Soft Interference Cancellation

Abstract: Satellite communication channels can be well described as non-linear functions with memory. The Volterra series representation provides accurate modeling of satellite channel dynamics, and thus, it constitutes a widely used approach to mathematically describe them. In this work, iterative correction of the non-linear distortion introduced by such channels is considered, by employing a soft interference canceller operating in a turbo equalization framework.

Parametric Characteristic Analysis for Generalized Frequency Response Functions of Nonlinear Systems

Abstract: In order to explicitly reveal the relationship between system frequency response functions and model parameters which define system nonlinearities, and consequently unveil a direct connection from model parameters to system frequency response characteristics, a parametric characteristic analysis approach is proposed for Volterra systems described by a nonlinear differential equation (NDE). The parametric characteristics of the generalized frequency response functions (GFRFs) for the NDE model are established, and some important properties are discussed, which can explicitly reveal what model parameters contribute and how these parameters affect the GFRFs. Based on the parametric characteristic analysis, it is demonstrated how the system frequency domain characteristics are related to the system time domain model parameters and how the output frequency response function can now be determined explicitly with a detailed polynomial structure. These new results provide a significant and novel insight into the analysis and design of nonlinear systems in the frequency domain. Several examples are included to illustrate the results.