Tracking analysis of augmented complex least mean square algorithm

The augmented complex least mean-square ACLMS algorithm is a suitable algorithm for the processing of both second-order circular proper and noncircular improper signals. In this paper, we provide tracking analysis of the ACLMS algorithm in the non-stationary environments. Using the established energy conservation argument, we derive a variance relation that contains moments that represent the effects of non-stationary environment. We evaluate these moments and derive closed-form expressions for the excess mean-square error EMSE and mean-square error MSE. The derived expressions, supported by simulations, reveal that unlike the stationary case, the steady-state EMSE, and MSE curves are not monotonically increasing functions of the step-size parameter. We also use this observation to optimize the step-size learning parameter. Simulation results illustrate the theoretical findings and match well with theory. Copyright © 2015 John Wiley & Sons, Ltd.

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