An improved stochastic model of the NLMS algorithm for correlated input data

This paper proposes an improved stochastic model for the normalized least-mean-square (NLMS) algorithm considering correlated input signals obtained from a spherically invariant random process (SIRP). A SIRP describes both Gaussian and a wide class of non-Gaussian processes, including the ones with Laplacian, K
₀
, and Gamma marginal density functions. Hence an approximate procedure for computing high-order hyperelliptic integrals arisen from the modeling process is developed. The resulting model outperforms other existing models discussed in the open literature. Through numerical simulations the accuracy of the proposed model is verified.