Robust Bias Compensation Method for Sparse Normalised Quasi-Newton Least-Mean with Variable-Mixing-Norm Adaptive Filtering

Input noise causes inescapable bias to the weight vectors of the adaptive filters during the adaptation processes. Moreover, the impulse noise at the output of the unknown systems can prevent bias compensation from converging. This paper presents a robust bias compensation method for a sparse normalized quasi-Newton least-mean (BC-SNQNLM) adaptive filtering algorithm to address this issue. We have mathematically derived the biased-compensation terms in an impulse noisy environment. Inspired by the convex combination of adaptive filters' step sizes, we propose a novel variable-mixing-norm method to accelerate the convergence for our BC-SNQNLM algorithm, which is referred to as BC-SNQNLM-VMN. Simulation results confirm that the proposed method significantly outperforms other comparative works regarding normalized mean-squared deviation (NMSD) in the steady state.