Exact Expectation Analysis of the Deficient-Length LMS Algorithm
For researchers in adaptive filtering, this work removes two common simplifying assumptions to improve modeling accuracy of deficient-length LMS, though it is an incremental theoretical advance.
This paper presents the first exact expectation analysis of the deficient-length LMS algorithm without relying on the independence assumption or sufficient-order configuration, providing state equations for mean and mean-square performance that are valid for non-white and non-Gaussian inputs and yield a stability bound for the step size.
Stochastic models that predict adaptive filtering algorithms performance usually employ several assumptions in order to simplify the analysis. Although these simplifications facilitate the recursive update of the statistical quantities of interest, they by themselves may hamper the modeling accuracy. This paper simultaneously avoids for the first time the employment of two ubiquitous assumptions often adopted in the analysis of the least mean squares algorithm. The first of them is the so-called independence assumption, which presumes statistical independence between adaptive coefficients and input data. The second one assumes a sufficient-order configuration, in which the lengths of the unknown plant and the adaptive filter are equal. State equations that characterize both the mean and mean square performance of the deficient-length configuration without using the independence assumption are provided. The devised analysis, encompassing both transient and steady-state regimes, is not restricted neither to white nor to Gaussian input signals and is able to provide a proper step size upper bound that guarantees stability.