A block LMS-type algorithm for sparse system identification with analysis

The LMS-type algorithms are effectively used in diverse adaptive filtering applications such as; blind system identification, channel equalization, etc. For some applications such as echo cancellation, which requires a large filter length, a very long time is required to estimate the coefficients via the conventional least-mean-square (LMS) algorithm. Actually, updating the filter coefficients block by block of the input data but not for each sample of input, users can get a very fast processing time depending on the block length. Additionally, the performance of the block-LMS (BLMS) algorithm can be improved by using a variable step-size in the update equation. Also, in system identification, if the unknown system is sparse, then the performance of the algorithm can be improved further by imposing a penalty term in the cost function of the BLMS algorithm which, in turn, helps in exploiting the sparsity of the unknown system. In this paper, we investigate the performance of recently proposed BLMS-type algorithm for sparse systems. The convergence analysis of the proposed algorithm is presented for the first time. Also, the effects of the zero-attracting coefficient, ρ, and the sparsity degree on MSD have been investigated. Finally, the performance of the algorithm is compared to those of the BLMS and the other previously proposed adaptive algorithms, in terms of convergence rate and mean-square-deviation (MSD). Simulations show that the proposed algorithm guarantees better performance than the other algorithms.