Bias-compensated generalized mixed norm algorithm via CIM constraints for sparse system identification with noisy input

A sparse bias-compensated least generalized mixed norm algorithm is developed for sparse system identification (SSI) with noisy input. The l_p-norm and l_q-norm are mixed to define a novel cost function (called generalized mixed norm, GMN) for adaptive filtering algorithm (AFA) in system identification. Furthermore, a bias-compensated least GMN algorithm is proposed for the case that the input is corrupted by additive noise. Finally, we develop a novel sparsity aware AFA by combining BCLGMN and the correntropy induced metric for SSI. We further provide computer simulation results that the proposed algorithm outperforms other well-known algorithms only employing single criterion for SSI under non-Gaussion noise environments, especially for the noise combined by long and short tail noise distributions or the impulsive noise.