Performance analysis of signed correlation algorithm with recursive estimation of signed data covariance for fast convergent and robust adaptive filters

This paper derives a new adaptation algorithm named signed correlation algorithm with recursive estimation of signed data covariance (SCA-RESDC) that combines signed correlation algorithm (SCA) for complex-domain adaptive filters with recursive estimation of signed data covariance matrix of a strongly correlated filter reference input process. The SCA-RESDC achieves significant improvement in filter convergence speed of the SCA, while it preserves robustness of the latter algorithm against two types of impulse noise intruding adaptive filtering systems: one in observation noise and another at filter input. Analysis of the SCA-RESDC under Long Filter Assumption is fully developed for theoretically calculating filter convergence. Through experiment with simulations and theoretical calculations of filter convergence for the SCA-RESDC, we demonstrate its effectiveness in making adaptive filters fast convergent and robust in the presence of both types of impulse noise. Good agreement between simulated and theoretical convergence shows the validity of the analysis.