Transient Analysis of the Bias-Compensated LMS Algorithm

Abstract

In most supervised adaptive filtering settings, only the additive noise of the reference signal is taken into account. However, in many practical situations the excitation data is also immersed in noise, which leads to a bias in the estimation procedure. In order to mitigate such issue, adaptive algorithms with bias compensation schemes have been proposed. This paper advances for the first time a stochastic model that predicts the average and mean-square learning behavior of the bias-compensated least mean squares algorithm in the transient region. Asymptotic predictions can also be obtained as a result of the devised analysis. Tracking capabilities and the impact of employing sub-optimal length adaptive filter are also considered, without restricting the input signal to be neither white nor Gaussian. Results indicate that the proposed analysis reveals accurate agreement with simulation results.