Volterra series

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

Modeling Methodology for Nonlinear Physiological Systems

Abstract: A general modeling approach for a broad class of nonlinear systems is presented that uses the concept of principal dynamic modes (PDMs) These PDMs constitute a filter bank whose outputs feed into a multi-input static nonlinearity of multinomial (polynomial) form to yield a general model for the broad class of Volterra systems Because the practically obtainable models (from stimulus-response data) are of arbitrary order of nonlinearity, this approach is applicable to many nonlinear physiological systems heretofore beyond our methodological means Two specific methods are proposed for the estimation of these PDMs and the associated nonlinearities from stimulus-response data Method I uses eigendecomposition of a properly constructed matrix using the first two kernel estimates (obtained by existing methods) Method II uses a particular class of feedforward artificial neural networks with polynomial activation functions The efficacy of these two methods is demonstrated with computer-simulated examples, and their relative performance is discussed The advent of this approach promises a practicable solution to the vexing problem of modeling highly nonlinear physiological systems, provided that experimental data be available for reliable estimation of the requisite PDMs

Mitigation of intra-channel nonlinearities using a frequency-domain Volterra series equalizer.

Abstract: We address the issue of intra-channel nonlinear compensation using a Volterra series nonlinear equalizer based on an analytical closed-form solution for the 3rd order Volterra kernel in frequency-domain The performance of the method is investigated through numerical simulations for a single-channel optical system using a 20 Gbaud NRZ-QPSK test signal propagated over 1600 km of both standard single-mode fiber and non-zero dispersion shifted fiber We carry on performance and computational effort comparisons with the well-known backward propagation split-step Fourier (BP-SSF) method The alias-free frequency-domain implementation of the Volterra series nonlinear equalizer makes it an attractive approach to work at low sampling rates, enabling to surpass the maximum performance of BP-SSF at 2× oversampling Linear and nonlinear equalization can be treated independently, providing more flexibility to the equalization subsystem The parallel structure of the algorithm is also a key advantage in terms of real-time implementation

Measuring Volterra kernels (II)

Abstract: Accurate measurement of Volterra kernels is an essential step in the modelling of weakly non-linear physical systems via the block box approach, and in model validation. This paper is a sequel to an earlier paper,1 where practical methods for measuring Volterra kernels were presented along with a quick method for measuring the second-order Volterra kernels. This paper extends that quick method for measuring higher-order frequency-domain Volterra kernels of weakly non-linear systems. We further developed the quick method to measure directly the points of the Volterra kernels which are located along one or more axes in the frequency domain, thus making our method complete and more accurate than that presented in Reference 1. We illustrate our method by actually measuring a weakly non-linear circuit whose Volterra kernels can be accurately calculated. the experimentally measured and the theoretically predicted results agree remarkably well.

Nonlinear Digital Pre-distortion of Transmitter Components

Abstract: We present a linear and nonlinear digital pre-distortion (DPD) tailored to the components of an optical transmitter. The DPD concept uses nonlinear models of the transmitter devices, which are obtained from direct component measurements. While the digital-to-analog converter and driver amplifier are modeled jointly by a Volterra series, the modulator is modeled independently as a Wiener system. This allows for a block-wise compensation of the modulator by a Hammerstein system and a pre-distortion of the electrical components by a second Volterra series. In simulations and extensive experiments, the performance of our approach for nonlinear DPD is compared to an equivalent linear solution as well as to a configuration without any DPD. The experiments were performed using M -ary quadrature-amplitude modulation ( M -QAM) formats ranging from 16- to 128-QAM at a symbol rate of 32 GBd. It is shown that the DPD improves the required optical signal-to-noise ratio at a bit error ratio of 2·10 −2 by at least 1.2 dB. Nonlinear DPD outperforms linear DPD by an additional 0.9 and 2.7 dB for higher-order modulation formats such as 64-QAM and 128-QAM, respectively.