Variable step-size affine projection algorithm for a non-stationary system

Affine projection algorithm (APA) has advantages when input signals are highly correlated with each other. To improve convergence rate and steady-state mean square deviation (MSD) of the APA, the step size variation concept based on theoretical MSD has been researched. However, structurally, the APA based on theoretical MSD cannot track the system change without the reset algorithm. The problem is, the reset algorithm would not operate when the system change occurs at early iteration. To overcome this drawback, we propose the variable step size APA attaching the noise-error relation. We apply it to a recent variable step-size APA, which is the optimal step-size APA (OS-APA), then the simulation results show that the proposed APA tracks the system change well without the reset algorithm, and has similar performance compared to the OS-APA for all iterations.