Sparse least mean mixed‐norm adaptive filtering algorithms for sparse channel estimation applications

Summary Sparse least‐mean mixed‐norm (LMMN) algorithms are developed to improve the estimation performance for sparse channel estimation applications. Both the benefits of the least mean fourth and least mean square algorithms are utilized to exploit a type of sparse LMMN algorithms. The proposed sparse‐aware LMMN algorithms are implemented by integrating an l 1 ‐norm or log‐sum function into the cost function of traditional LMMN algorithm so that they can exploit the sparse properties of the broadband multi‐path channel and achieve better channel estimation performance. The proposed sparse LMMN algorithms are equal to adding an amazing zero‐attractor in the update equation of the traditional LMMN algorithm, which aim to speed up the convergence. The channel estimation performance of the proposed sparse LMMN algorithms are evaluated over a sparse broadband multi‐path channel to verify their effectiveness. Simulation results depict that the sparse LMMN algorithms are superior to the previously reported sparse‐aware least mean square/fourth, least mean fourth and least mean square and their corresponding sparse‐aware algorithms in terms of both the convergence and steady‐state behavior when the broadband multi‐path channel is sparse. Copyright © 2016 John Wiley & Sons, Ltd.