A Zero Attracting Natural Gradient Non-Parametric Maximum Likelihood for Sparse Channel Estimation

Abstract

The natural gradient (NG) based non-parametric maximum likelihood (NPML) adaptive algorithm gives better sparse channel estimation in terms of convergence rate as compared to stochastic gradient (SG) based NPML in the presence of additive non-Gaussian noise. The step-size of NG- NPML is proportional to the magnitude of respective active tap weights and hence achieves initial faster convergence. However, the mean square error (MSE) and bit error rate performance of both NG-NPML and SG-NPML is same. In this paper, we propose an algorithm to improve the MSE floor by introducing the l1 norm penalty in the cost function. This l1 norm penalty term introduces a zero-attractor (ZA) term in the NG- NPML weight update recursion which shrinks the coefficients of inactive taps and hence reduces the steady state MSE floor. We have also derived the stability condition for the proposed ZA-NG- NPML in terms of mean weight error. Improved performance of the proposed algorithm is validated by simulation for standardized channel model. © 2017 IEEE.