A Proportionate Diffusion LMS Algorithm for Sparse Distributed Estimation

Abstract

We propose a new diffusion least mean squares algorithm that utilizes adaptive gains in the adaptation stage for the sparse distributed estimation problem. We derive the optimal gains that attain a minimum mean-square deviation and propose an adaptive gain control method. We provide the mean stability analysis to establish sufficient condition for the algorithm to converge in the mean sense. The algorithm achieves higher convergence speed than the sparsity-constrained algorithms, regardless of the sparsity of the vector of interest.