Novel normalized subband adaptive filtering algorithms with weights-dependent variable step-size

The normalized subband adaptive filtering (NSAF) algorithm is promising due to its effective decorrelation for colored inputs and low computational complexity. However, it has a performance trade-off between convergence rate and steady-state misadjustment when choosing the step-size. To address this issue, this paper introduces a novel variable step-size (VSS) scheme that minimizes the diagonal entries of the covariance matrix of NSAF concerning the individual step-size assigned to each filter weight, which gives rise to the filter weights-based VSS NSAF (WVSS-NSAF) algorithm. This algorithm achieves both fast convergence rate and low steady-state misadjustment simultaneously. To enhance the algorithm's usability, we propose a way of estimating the noise variance and a reset mechanism to ensure effective tracking capability. Furthermore, the VSS scheme is extended to handle impulsive noise environments by incorporating a generalized robust loss function, which originates the robust WVSS-NSAF (R-WVSS-NSAF) algorithm. Simulation results demonstrate that the proposed algorithms outperform the existing state-of-the-art methods.