Proportionate NLMS with Unbiasedness Criterion for Sparse System Identification in the Presence of Input and Output Noises

This brief proposes a bias-compensated proportionate normalized least mean square (BCPNLMS) method for identifying sparse system when subjected to the noisy input. The proposed BCPNLMS algorithm, which combines the proportionate scheme and the unbiasedness criterion, is able to identify the system parameters with better steady-state accuracy and faster convergence speed than conventional NLMS, bias-compensated NLMS, and PNLMS algorithms. Robustness and high identification accuracy with noisy input can be achieved by introducing the bias-compensation term derived from the unbiasedness criterion. Simulation results on sparse system identification confirm the excellent performance of the proposed BCPNLMS in the presence of both input and output noises.