Analysis and design of adaptive volterra filters for system identification in time varying environment

Abstract

To satisfy the ever-increasing demand for the nonlinear system identification in various fields of engineering, as well as to tackle the system nonlinearities in the presence of non-Gaussian noise, interest has peaked in the adaptive nonlinear signal processing techniques. The nonlinear systems are conventionally modeled using the polynomial paradigms, whose output signals can be related to the input signals through the truncated Volterra series expansion. The nonlinear Volterra filter exhibits property that it depends linearly on the coefficients of the filter itself; therefore the principles of optimum linear filter theory can be naturally extended to the optimum nonlinear Volterra filter theory. These nonlinear filters are attractive because these may be able to approximate a large class of nonlinear systems with great parsimony in the use of coefficients. The nonlinear adaptive filtering techniques for the system identification (based on the Volterra model) are widely used for the identification of nonlinearities in the domain of communication and signal processing applications. We first present the variable forgetting factor (VFF) least squares (LS) algorithm for the polynomial channel paradigm, which provides improved tracking performance under the nonstationary environment. The main focus is on updating VFF, when each time-varying fading channel is considered to be a first-order Markov process. It may be inferred from the simulation results that in addition to efficient tracking under the frequency-selective fading wireless channels, the incorporation of proposed numeric variable forgetting factor (NVFF) in LS algorithm reduces the computational complexity. Subsequently, the improved tracking capability of a numeric variable forgetting factor recursive least squares (NVFF-RLS) algorithm is presented for the first-order and second-order time-varying Volterra systems under the nonstationary environment.