Normalized frequency-domain block sign algorithm using ℓ1-norm minimization

Abstract

In this letter, a normalized frequency-domain block sign-error algorithm (NFBSA) is proposed by minimizing the (Formula presented.) -norm of the posteriori error vector for filter weight. The NFBSA updates the filter weight vector by employing the sign value of the priori error vector, which can mitigate the impact of impulsive noise. Furthermore, a variable step-size algorithm (VSS) suitable for application in the NFBSA is proposed, which minimizes the (Formula presented.) -norm of the posteriori error vector with respect to the step-size. The system identification simulations are conducted using a first-order autoregressive signal as an input, assuming that impulsive noise occurs. The simulation results demonstrate that the NFBSA exhibits superior misalignment performance compared to the conventional time-domain sign algorithm, and the NFBSA with the proposed VSS outperformed other VSS-based sign algorithms.