  In order to improve the performance of Least Mean Square (LMS) based system
identification of sparse systems, a new adaptive algorithm is proposed which
utilizes the sparsity property of such systems. A general approximating
approach on $l_0$ norm -- a typical metric of system sparsity, is proposed and
integrated into the cost function of the LMS algorithm. This integration is
equivalent to add a zero attractor in the iterations, by which the convergence
rate of small coefficients, that dominate the sparse system, can be effectively
improved. Moreover, using partial updating method, the computational complexity
is reduced. The simulations demonstrate that the proposed algorithm can
effectively improve the performance of LMS-based identification algorithms on
sparse system.
