Sparsity-Aware Logarithmic Hyperbolic Cosine Normalized Subband Adaptive Filter Algorithm With Step-Size Optimization

To enhance the filtering accuracy of the traditional sign subband adaptive filter (SSAF) algorithm and its individual-weighting-factors variant, this brief proposes the logarithmic hyperbolic cosine normalized subband adaptive filter algorithm (LHCNSAF) and its sparsity-aware version through minimizing the LHC cost function. As the combination of mean-square-error and mean-absolute-error criterion, the presented LHCNSAF demonstrates higher filtering accuracy under white Gaussian background noise and impulse noise environments than SSAF-type algorithms, with almost no increase in computational complexity. To tackle the trade-off between filtering accuracy and convergence behavior caused by the fixed step-size, an effective variable step-size scheme is also devised based on the transient model of proposed algorithms through minimizing the mean-square deviation (MSD) at each iteration with some reasonable assumptions. Additionally, the stability and complexity analysis are also provided. Finally, the computer simulations certify the proposed algorithms possess good performance in terms of convergence speed, steady-state error, and tracking capability via contrasting with the considering algorithms under system identification application.