The use of the modified escalator algorithm to improve the performance of transform-domain LMS adaptive filters

This paper describes a new algorithm that improves the convergence performance of the transform-domain least mean-square (TRLMS) algorithm. The algorithm exploits the sparse structure of the correlation matrix of the transformed input process to derive a data dependent Gram-Schmidt orthogonalization type transform of the process. We show its faster convergence compared with the time-domain least mean-square (LMS) algorithm and the DCT or the DWT-based TRLMS algorithm. The Gram-Schmidt orthogonalization is realized using a modified adaptive escalator algorithm. The modification significantly reduces the computational complexity of the adaptive escalator algorithm and determines the computational complexity of the proposed algorithm.