Stochastic Model for the LMS Algorithm with Symmetric/Antisymmetric Properties

This paper presents a stochastic model for the least-mean-square algorithm with symmetric/antisymmetric properties (LMS-SAS), operating in a system identification setup with Gaussian input data. Specifically, model expressions are derived to describe the mean weight behavior of the (global and virtual) adaptive filters, learning curves, and evolution of some correlation-like matrices, which allow predicting the algorithm behavior. Simulation results are shown and discussed, confirming the accuracy of the proposed model for both transient and steady-state phases