Abstract
The coefficient reuse strategy is able to improve the steady-state performance of adaptive filter algorithms, especially in very challenging low signal-to-noise scenarios. This paper advances deterministic and stochastic models that predict various learning characteristics of the LMS algorithm with coefficient reuse. First-order and second-order analyzes are derived for the sufficient order case and then extended for the tracking and deficient length scenarios. An exact expectation analysis, which does not employ the ubiquitous independence assumption, is presented for a particular configuration of the algorithm, and its results suggest that, except in the first phase of the learning process, the decay in mean-square deviation of the coefficient vector is governed by an almost-sure theoretical analysis. The simulation results confirm the equations obtained in the theoretical analysis.
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