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.
