In this paper, we propose an \(l_0\)-norm penalized shrinkage linear affine projection (\(l_0\)-SL-AP) algorithm and an \(l_0\)-norm penalized shrinkage widely linear affine projection (\(l_0\)-SWL-AP) algorithm. The proposed algorithms provide variable step-size by minimizing the noise-free a posteriori error at each iteration and introduce an \(l_0\)-norm constraint to the cost function. The \(l_0\)-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 \(l_0\)-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 (\(l_0\)-SL-DCD-AP and \(l_0\)-SWL-DCD-AP) in this paper. Simulations indicate that the \(l_0\)-SL-AP and \(l_0\)-SWL-AP algorithms provide faster convergence speed and lower steady-state misalignment than the previous APA-type algorithms. The \(l_0\)-SL-DCD-AP and \(l_0\)-SWL-DCD-AP algorithms perform similarly to their counterparts but with reduced complexity.
['Youwen Zhang', 'Shuang Xiao', 'Dajun Sun', 'Lu Liu']
Low-Complexity l_0-Norm Penalized Shrinkage Linear and Widely Linear Affine Projection Algorithms