Adaptive algorithm for sparse system identification: Zero-attracting LMS

This paper presents an adaptive algorithm using the unknown system sparsity to improve the system identification performance. A gradient descent recursion of the filter coefficient vector was deduced through introducing l1 norm, which has vital relationship with sparsity, to the cost function of LMS algorithm. Adding a zero-vector-approaching correction to the tap coefficient of the filter enables faster convergence of zero coefficients (which play a main role in sparse systems), thus notably increases the convergence speed and tracking speed in system identification. Simulation results show that the algorithm evidently improves the convergence performance of both general sparse systems and clustering sparse systems, and exhibits universal applicability and excellent robustness.