Stochastic Model for the NLMS Algorithm with Correlated Gaussian Data

This paper proposes a new stochastic model for the normalized LMS (NLMS) algorithm under correlated input data. The proposed model is derived without invoking the simplifying assumption that x
^T
(n)x(n) has a chi-square distribution to determine E{1/[x
^T
(n)x(n)/N]}. Under correlated input data that assumption is not correct and thus the resulting model becomes inaccurate. Without considering such simplifying assumption, a high-order hyperelliptic integral has to be computed. The proposed model is based on tackling the solution of that integral. Numerical simulations verify the quality of the proposed model.