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Convergence Analysis of Zero Attracting Natural Gradient Non-Parametric Maximum Likelihood Algorithm

Recently, a zero-attractor natural gradient non-parametric maximum likelihood (ZA-NG-NPML) algorithm has been proposed for sparse channel estimation in the presence of non-Gaussian noise. The ZA-NG-NPML outperforms existing sparse channel estimation algorithms in the presence of non-Gaussian noise in terms of mean square error (MSE) and convergence. In this brief, a rigorous second order convergence analysis of ZA-NG-NPML algorithm is presented and upper bound on the steady state mean square deviation of active and inactive taps is derived. Further, we also derive the upper bound on the steady state excess MSE for ZA-NG-NPML. Simulation results validate the derived upper bound.