Scheduled-Step-Size Affine Projection Algorithm

An approach for scheduling the step sizes of an adaptive filter using the affine projection algorithm (APA) is proposed so that its mean-square deviation (MSD) learning curve can be guided along a pre-designed trajectory. This approach eliminates the parameter-tuning process and does not require estimating un-measurable stochastic quantities. Furthermore, a step-size lower bound is derived in random-walk-modeled environments that leads the adaptive filter to achieve the smallest steady-state MSD, while in stationary environments, the closer to zero the step size is, the smaller the steady-state MSD. For efficient memory usage in practice, the schedule is modified from full-table step sizes to a few down-sampled step sizes without performance degradation. In a simulation, the scheduled-step-size APA exhibits fast convergence and produces small steady-state error not only for a white signal but also for various colored input signals for a properly chosen projection order. The proposed algorithm also demonstrates greater robustness over different signal-to-noise ratios than the existing variable-step-size APAs.