Discrete-wavelet-transform recursive inverse algorithm using second-order estimation of the autocorrelation matrix

Abstract

The recursive least squares (RLS) algorithm was introduced as an alternative to least mean square (LMS) algorithm with enhanced performance. Computational complexity and instability in updating the autocolleltion matrix are some of the drawbacks of the RLS algorithm that were among the reasons for the introduction of the second-order recursive inverse (RI) adaptive algorithm. The 2nd order RI adaptive algorithm suffered from low convergence rate in certain scenarios that required a relatively small initial step-size. In this paper, we propose a new second-order RI algorithm that projects the input signal to a new domain namely discrete wavelet transform (DWT) as pre step before performing the agorthim. This transformation overcomes the low convergence rate of the second-order RI algorithm by reducing the self-correlation of the input signal in the mentioned scenatios. Expeirments are conducted using the noise cancellation setting. The performance of the proposed algorithm is compared to those of the RI, original second-order RI and RLS algorithms in different Gaussian and impulsive noise environments. Simulations demonstrate the superiority of the proposed algorithm in terms of convergence rate compared to those algorithms.