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Exact Performance Analysis of the \epsilon -NLMS Algorithm for Colored Circular Gaussian Inputs

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2 Author(s)
Al-Naffouri, T.Y. ; Electr. Eng. Dept., King Fahd Univ. of Pet. & Miner., Dhahran, Saudi Arabia ; Moinuddin, M.

This paper presents exact mean-square analysis of the -NLMS algorithm for circular complex correlated Gaussian input. The analysis is based on the derivation of a closed form expression for the cumulative distribution function (CDF) of random variables of the form ∥ui∥D12/(ϵ + ∥ui∥D12) and using that to derive the first and second moments of such variables. These moments in turn completely characterize the mean square (MS) behavior of the ϵ-NLMS in explicit closed form expressions. Both transient and steady-state behavior are analyzed. Consequently, new explicit closed-form expressions for the mean-square-error (MSE) behavior are derived. Our simulations of the transient and steady-state behavior of the filter match the expressions obtained theoretically for various degrees of input correlation and for various values of ϵ.

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Signal Processing, IEEE Transactions on  (Volume:58 ,  Issue: 10 )