SHAFA: sparse hybrid adaptive filtering algorithm to estimate channels in various SNR environments

The l(p)-norm penalised (LP) normalised least mean square algorithm converges faster than the LP normalised least mean fourth algorithm does, but the latter can achieve better steady-state performance, particularly in regions with low signal-to-noise ratios (SNRs). To simultaneously take advantage of both merits, a sparse hybrid adaptive filtering algorithm is proposed in various SNR environments. Specifically, the authors construct a cost function that uses the statistical error term and sparse penalty term. The first term is designed by a hybrid error function of the second-and fourth-order statistical errors, respectively, and the second term is obtained using a sparse constraint function. The hybrid error term can be easily balanced by a proportional parameter alpha is an element of[0, 1]. Moreover, they devise a non-uniform step size in the proposed algorithm to further balance the convergence speed and estimation error. Simulation results are provided to validate the proposed algorithm in various SNR environments.