l0-norm penalized shrinkage LMS algorithm based DFE for underwater acoustic communication

In this paper, we propose an l₀-norm penalized shrinkage linear least mean squares (l₀-SH-LMS) algorithm for an adaptive decision feedback equalizer (DFE). The proposed algorithm utilizes the priori and the posteriori errors to calculate the varying step-size. Thus a larger coefficient produces a larger increment to accelerate the convergence, and a small coefficient gives a smaller increment to improve the estimation accuracy, so the algorithm can adapt to the time-varying channel efficiently. Meanwhile, a l₀-norm penalty term is introduced in the cost function to improve the applicability to a sparse system. Simulation results show that, compared with the conventional LMS-type algorithms, the proposed algorithm achieves better performance in both the convergence rate and steady-state misalignment for the sparse channels. When the proposed algorithm is applied to the DFE, the equalization performance is clearly improved.