Performance analysis of the DCT-LMS adaptive filtering algorithm

This paper presents the convergence analysis result of the discrete cosine transform-least-mean-square (DCT-LMS) adaptive "ltering algorithm which is based on a well-known interpretation of the variable stepsize algorithm. The time-varying stepsize of the DCT-LMS algorithm is implemented by the modi"ed power estimator to redistribute the spread power after the DCT. The performance analysis is considerably simpli"ed by the modi"cation of a power estimator. First of all, the proposed DCT-LMS algorithm has a fast convergence rate when compared to the LMS, the normalised LMS (NLMS), the variable stepsize LMS (VSLMS) algorithm for a highly correlated input signal, whilst constraining the level of the misadjustment required by a speci"cation. The main contribution of this paper is the statistical performance analysis in terms of the mean and mean-squared error of the weight error vector. In addition, the decorrelation property of the DCT-LMS is derived from the lower and upper bounds of the eigenvalue spread ratio, j .!9 /j .*/ . It is also shown that the shape of sidelobes a!ecting the decorrelation of the input signal is governed by the location of two zeros. Theoretical analysis results are validated by the Monte Carlo simulation. The proposed algorithm is also applied in the system identi"cation and the inverse modelling for a channel equalisation in order to verify its applicability. ( 2000 Elsevier Science B.V. All rights reserved.