A block LMS-type algorithm with a function controlled variable step-size for sparse system identification

Block least-mean-square algorithm has a very fast processing time compared to the conventional LMS algorithm. This is due to the updating mechanism of the filter coefficients. Filter coefficients are updated for each sample input for the LMS algorithm. This process is faster with BLMS algorithm as the filter coefficients are updated for blocks of the input sequence instead. The BLMS algorithm can also be improved in the same manner as LMS by using different approaches such as variable step-size and/or sparsity. This paper proposes a new BLMS-type algorithm with a function controlled variable step-size LMS for sparse system identification. The performance of the proposed algorithm is compared to that of the BLMS algorithm in terms of convergence rate and mean-square-deviation. The effects of the filter length, sparsity degree and signal-to-noise ratio (SNR) on MSD were also investigated. Simulations prove that the proposed algorithm always outperforms the BLMS algorithm.