A zero-attracting variable step-size LMS algorithm for sparse system identification

In this paper, new adaptive algorithms are proposed to improve the performance of the variable step-size LMS (VSSLMS) algorithm when the system is sparse. The first proposed algorithm is the zero-attracting (ZA) VSSLMS. This algorithm outperforms the standard VSSLMS if the system is highly sparse. However, the performance of the ZA-VSSLMS algorithm deteriorates when the sparsity of the system decreases. To further improve the performance of the ZA-VSSLMS filter, the weighted zero-attracting (WZA)-VSSLMS algorithm is introduced. The algorithm performs the same or better than the ZA-VSSLMS if the system is highly sparse. On the other hand, when the sparsity of the system decreases, it performs better than the ZA-VSSLMS and better or the same as the standard VSSLMS algorithm. Also, both proposed algorithms have the same order of computational complexity as that of the VSSLMS algorithm (O(N)). For a system identification setting, the results indicate the high performance of the proposed algorithms in convergence speed and/or steady-state error under sparsity condition compared with the standard VSSLMS algorithm.