Proportionate adaptive filtering algorithms based on mixed square/fourth error criterion with unbiasedness criterion for sparse system identification

Two novel adaptive filtering algorithms based on the mixed square/fourth error criterion are proposed for solving sparse system identification problems. Motivated by the fact that the proportionate update scheme can enhance the tracking ability of the system, we develop a proportionate least mean square/fourth (PLMS/F) algorithm in this paper. Combining the proportionate update scheme and the LMS/F algorithm, the proposed PLMS/F algorithm shows superiority for non-Gaussian noise environments. Moreover, to further improve the performance of the PLMS/F algorithm in the noisy input cases, a bias-compensated PLMS/F algorithm is developed by incorporating an unbiased criterion to compensate the bias caused by input noises. Simulation results in the context of the sparse system identification framework demonstrate that the proposed PLMS/F and bias-compensated PLMS/F algorithms can achieve excellent identification performance in terms of steady-state misalignment and convergence speed under noisy input and non-Gaussian output noise environments.