Theoretical Performance Analysis of Sparse System Identification Using Incremental and Diffusion Strategies Over Adaptive Networks

This paper is dedicated to the complete theoretical analysis of the distributed sparsity aware algorithms in the sparse system estimation and identification tasks. To do so, we took the famous zero attracting least mean square and regularized zero attracting least mean square (RZA-LMS) algorithms and extended them with the diffusion and incremental distributed strategies, in this manner we get 4 sparsity aware distributed algorithms and 2 distributed algorithms by considering the LMS-diffusion and LMS incremental algorithms. Then we applied theoretical analysis to these networks and derived network and node mean square deviation values for all of them. Up until now, no attempt has been made about the theoretical analysis of incremental strategies in the estimation of sparse values and we derive them in this paper by induction through the theoretical analysis of the diffusion strategies. Several simulations are designed to compare the theoretical and simulation findings and also to compare the performances of the incremental and diffusion sparsity aware algorithms. The results show the correctness of our analysis by the existing match between the theoretical and simulation outcomes. Also, the results present the superiority of the incremental strategies (especially with the RZA-LMS-incremental algorithm) than the diffusion strategies in all sparse system identification tasks in the same conditions.