Volterra series

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

A digital method of modeling quadratically nonlinear systems with a general random input

Abstract: Without assuming particular statistics of the input, a practical digital method of estimating linear and quadratic transfer functions of a nonlinear time-invariant system that can be described by Volterra series of up to second order is presented. The method is tested and validated by analyzing input-output data of a known quadratically nonlinear system. It is used when there is little knowledge about the input statistics or the input is non-Gaussian. It is also noted that the ordinary coherence functions cannot be used in explaining the input-output power transfer relationship of a quadratic system excited by a non-Gaussian input signal. With respect to the practical application of the method, the relationship between the mean square errors involved in the transfer function estimates and the number of averages taken from the spectral estimation is qualitatively discussed. >

Band-Limited Volterra Series-Based Digital Predistortion for Wideband RF Power Amplifiers

Abstract: The continuously increasing demand for wide bandwidth creates great difficulties in employing digital predistortion (DPD) for radio frequency (RF) power amplifiers (PAs) in future ultra-wideband systems because the existing DPD system requires multiple times the input signal bandwidth in the transmitter and receiver chain, which is sometimes almost impossible to implement in practice. In this paper, we present a novel band-limited digital predistortion technique in which a band-limiting function is inserted into the general Volterra operators in the DPD model to control the signal bandwidth under modeling, which logically transforms the general Volterra series-based model into a band-limited version. This new approach eliminates the system bandwidth constraints of the conventional DPD techniques, and it allows users to arbitrarily choose the bandwidth to be linearized in the PA output according to the system requirement without sacrificing performance, which makes the DPD system design much more flexible and feasible. In order to validate this idea, a high-power LDMOS Doherty PA excited by various wideband signals, including 100-MHz long-term evolution advanced signals, was tested. Experimental results showed that excellent linearization performance can be obtained by employing the proposed approach. Furthermore, this technique can be applied to other linear-in-parameter models. In future ultra-wideband systems, this new technique can significantly improve system performance and reduce DPD implementation cost.

Analytical Foundations of Volterra Series

Abstract: In this paper we carefully study the analysis involved with Volterra series. We address system-theoretic issues ranging from bounds on the gain and incremental gain of Volterra series operators to the existence of Volterra series operator inverses, and mathematical topics such as the relation between Volterra series operators and Taylor series. The proofs are complete, and use only the basic facts of analysis. We prove a general Steady-state theorem for Volterra series operators, and then establish a general formula for the spectrum of the output of a Volterra series operator in terms of the spectrum of a periodic input. This paper is meant to complement recent work on Volterra series expansions for dynamical systems.

On the Theory of Bilinear Time Series Models

Abstract: SUMMARY The theory of bilinear time series models is considered in this paper The sufficient conditions for asymptotic stationarity of the bilinear time series models are derived, and the expressions for the variance and covariance are obtained The conditions for the invertibility of the model are also included The estimation of the parameters of the scalar bilinear time series model is considered The bilinear models are fitted to sunspot numbers and also to a P-wave of a nuclear explosion The forecasting of sunspot numbers is also considered

Volterra series transfer function of single-mode fibers

Abstract: A nonrecursive Volterra series transfer function (VSTF) approach for solving the nonlinear Schrodinger (NLS) wave equation for a single-mode optical fiber is presented. The derivation of the VSTF is based on expressing the NLS equation In the frequency domain and retaining the most significant terms (Volterra kernels) in the resulting transfer function. Due to its nonrecursive property and closed-form analytic solution, this method can excel as a tool for designing optimal optical communication systems and lumped optical equalizers to compensate for effects such as linear dispersion, fiber nonlinearities and amplified spontaneous emission (ASE) noise from optical amplifiers. We demonstrate that a third-order approximation to the VSTF model compares favorably with the split-step Fourier (recursive) method in accuracy for power levels used in current optical communication systems. For higher power levels, there is a potential for improving the accuracy by including higher-order Volterra kernels at the cost of increased computations. Single-pulse propagation and the interaction between two pulses propagating at two different frequencies are also analyzed with the Volterra method to verify the ability to accurately model nonlinear effects. The analysis can be easily extended to include inter-channel interference in multi-user systems like wavelength-division multiple-access (WDM), time-division multiplexed (TDM), or code-division multiplexed (CDM) systems.