Abstract
For sparse system identification,recent suggested algorithms are 
-norm Least Mean Square ( -LMS), Zero-Attracting LMS (ZA-LMS), Reweighted Zero-Attracting LMS (RZA-LMS), and p-norm LMS (p-LMS) algorithms, that have modified the cost function of the conventional LMS algorithm by adding a constraint of coefficients sparsity. And so, the proposed algorithms are named -ZA-LMS, -RZA-LMS, p-ZA-LMS and p-RZA-LMS that are designed by merging twoconstraints from previous algorithms to improve theconvergence rate and steady state of MSD for sparse system. In this paper, a complete analysis was done for the theoretical operation of proposed algorithms by exited white Gaussian sequence for input signal. The discussion of mean square deviation (MSD) with regard to parameters of algorithms and system sparsity was observed. In addition, in this paper, the correlation between proposed algorithms and the last recent algorithms were presented and the necessary conditions of these proposed algorithms were planned to improve convergence rate. Finally, the results of simulations are compared with theoretical study (?), which is presented to match closely by a wide-range of parameters..
Keywords: Adaptive filter, -LMS, zero-attracting, p-LMS, mean square deviation, Sparse system identification.
