Fast recursive least squares adaptive second-order volterra filter and its performance analysis

Abstract-This paper presents a fast, recursive least squares (RLS) adaptive nonlinear filter. The nonlinearity is modeled using a second-order Volterra series expansion. The structure presented in the paper makes use of the ideas of fast RLS multichannel filters and has a computational complexity of 0 (N') multiplications per time instant where N - 1 represents the memory span in number of samples of the nonlinear system model. This compares with 0 (N 6) multiplications required for direct implementation. A theoretical performance analysis of the steady-state behavior of the adaptive filter operating in both stationary and nonstationary environments is presented in the paper. The analysis shows that, when the input is zero mean, Gaussian distributed, and the adaptive filter is operating in a stationary environment, the steady-state excess mean-squared error due to the coefficient noise vector is independent of the statistics of the input signal. The results of several simulation experiments are included in the paper. These results show that the adaptive Volterra filter performs well in a variety of situations. Furthermore, the steady-state behavior predicted by the analysis is in very good agreement with the experimental results.