Bias-compensated LMS estimation for adaptive noisy FIR filtering

We investigate the parameter estimation of adaptive FIR filter with noisy input. When the filter input is corrupted by additive noise, the parameter estimation of traditional LMS algorithm is biased. For the noise is unknown, we propose an input noise variance estimation method under unconstrained condition based on the LMS algorithm and combine the bias-compensated LMS (BCLMS) algorithm by removing the noise-induced bias. Simulation results show that our proposed algorithm has better estimate accuracy than the bias-compensated LMS algorithm with the input noise variance estimation under constrained condition, and provides an unbiased estimate of the filter parameters under any different noise levels.