Tracking analysis of augmented complex least mean square algorithm

Summary 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.