Variable step-size NLMP algorithm with a gradient-based weighted average in impulsive environments

For the problem of adaptive filtering in non-Gaussian alpha stable distribution noise environment, a variable step-size normalized least mean p norm (VSS-NLMP) algorithm with gradient-based weighted average is proposed. The Euclidean norm of the smoothed gradient vector, which can track the variation of the mean square deviation (MSD) at iteration, and fractional low order moments of the system error are used to update the step-size parameter in recursion. The weighted average of the gradient vector reduces the noise effectively. The update and convergence of the proposed algorithm are formulated in this paper. The simulation results indicate that the proposed algorithm has better performance compared to the existing VSS-NLMP algorithms.