A shrinkage variable step size for normalized subband adaptive filters

The conventional normalized subband adaptive filter (NSAF) using a constant step-size generally faces an inherent trade-off between the steady-state misalignment and the convergence rate. We propose herein a variable step-size NSAF algorithm by minimizing the mean-square deviation (MSD) between the optimal weight vector and the weight vector estimate with the utilization of the shrinkage denoising technique. With the estimation error involved in the step-size adaptation for each subband individually, the proposed algorithm is capable of tracking non-stationary environments. Without the explicit whitening assumption of the input signal in each subband, the proposed algorithm exhibits low steady-state MSD even when the input signal of each subband is colored. Simulation results validate the low misalignment and good tracking ability of the proposed algorithm in system identification application.