Widely Linear Complex-Valued Affine Projection Algorithm With a Sliding-Window Step-Size

In this work, to address the fixed step-size problem of the widely linear complex-valued affine projection algorithm (WL-CAPA), we propose a sliding-window step-size (SWSS) selection scheme, which results in the SWSS-WL-CAPA. To devise this scheme, we derive the mean-square deviation (MSD) recursion of WL-CAPA and obtain the optimal step-size at each iteration based on the comparison of MSD trends of the algorithm using two different step-sizes in the sliding-window. Interestingly, the SWSS scheme removes the length limitation of the step-size sequence with iterations, which allows the proposed algorithm to achieve better steady-state behavior. Furthermore, we develop a reset mechanism for enhancing the real-time tracking capability of the algorithm for unknown systems. The efficacy of the proposed algorithm is substantiated through the execution of simulations in scenarios of system identification and stereophonic acoustic echo cancellation.