On the stochastic analysis of the NLMS algorithm for white and correlated Gaussian inputs in time-varying environments

• Stochastic analysis of the NLMS algorithm in time-varying environments.
• Accurate model expressions valid for white and correlated Gaussian inputs.
• Mean weight behavior described through a closed-form expression.
• Expression describing the MSE behavior in steady state.
• Simulation results ratifying the accuracy of the proposed stochastic model.

This paper presents a stochastic model of the normalized least-mean-square (NLMS) algorithm aiming to study its behavior in time-varying environments for both white and correlated Gaussian input data. Particularly, comparing with other stochastic models from the open literature, here, a more general representation of time-varying systems is considered, allowing to assess the obtained model in an extensive range of practical scenarios. Moreover, to derive the proposed model, some simplifying assumptions commonly considered in the literature are avoided, resulting in very accurate model expressions describing the algorithm behavior for both transient and steady-state phases. Thus, based on the proposed model expressions, the impact of the algorithm parameters on its performance is assessed and some tracking properties of the NLMS algorithm for white and correlated input data are analyzed. Through simulation results, the effectiveness of the proposed model is verified for different operating scenarios.