Low-Complexity $$l_0$$ l 0 -Norm Penalized Shrinkage Linear and Widely Linear Affine Projection Algorithms

Abstract

In this paper, we propose an $$l_0$$l0-norm penalized shrinkage linear affine projection ($$l_0$$l0-SL-AP) algorithm and an $$l_0$$l0-norm penalized shrinkage widely linear affine projection ($$l_0$$l0-SWL-AP) algorithm. The proposed algorithms provide variable step-size by minimizing the noise-free a posteriori error at each iteration and introduce an $$l_0$$l0-norm constraint to the cost function. The $$l_0$$l0-SWL-AP algorithm also exploits noncircular properties of the input signal. In contrast with conventional AP algorithms, the proposed algorithms increase the estimation accuracy for time-varying sparse system identification. A quantitative analysis of the convergence behavior for the $$l_0$$l0-SWL-AP algorithm verifies the capabilities of the proposed algorithms. To reduce the complexity, we also introduce dichotomous coordinate descent (DCD) iterations to the proposed algorithms ($$l_0$$l0-SL-DCD-AP and $$l_0$$l0-SWL-DCD-AP) in this paper. Simulations indicate that the $$l_0$$l0-SL-AP and $$l_0$$l0-SWL-AP algorithms provide faster convergence speed and lower steady-state misalignment than the previous APA-type algorithms. The $$l_0$$l0-SL-DCD-AP and $$l_0$$l0-SWL-DCD-AP algorithms perform similarly to their counterparts but with reduced complexity.