Mean-square Analysis of the NLMS Algorithm

08/08/2021

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by   Tareq Y. Al-Naffouri, et al.

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This work presents a novel approach to the mean-square analysis of the normalized least mean squares (NLMS) algorithm for circular complex colored Gaussian inputs. The analysis is based on the derivation of a closed-form expression for the Cumulative Distribution Function (CDF) of random variables of the form (|| u||_ D_1^2)(|| u||_ D_2^2)^-1 where u is an isotropic vector and D_1 and D_2 are diagonal matrices and using that to derive some moments of these variables. These moments in turn completely characterize the mean-square behavior of the NLMS algorithm in explicit closed-form expressions. Specifically, the transient, steady-state, and tracking mean-square behavior of the NLMS algorithm is studied.