Adaptively Biasing the Weights of Adaptive Filters

It is a well-known result of estimation theory that biased estimators can outperform unbiased ones in terms of expected quadratic error. In steady state, many adaptive filtering algorithms offer an unbiased estimation of both the reference signal and the unknown true parameter vector. In this correspondence, we propose a simple yet effective scheme for adaptively biasing the weights of adaptive filters using an output multiplicative factor. We give theoretical results that show that the proposed configuration is able to provide a convenient bias versus variance tradeoff, leading to reductions in the filter mean-square error, especially in situations with a low signal-to-noise ratio (SNR). After reinterpreting the biased estimator as the combination of the original filter and a filter with constant output equal to 0, we propose practical schemes to adaptively adjust the multiplicative factor. Experiments are carried out for the normalized least-mean-squares (NLMS) adaptive filter, improving its mean-square performance in stationary situations and during the convergence phase.