Análise Estatística do Algoritmo LMS no Domínio Transformado

Abstract

This work presents a statistical analysis of the transform-domain least-mean-square (TDLMS) algorithm for both stationary and nonstationary environment, resulting in a more accurate model than those discussed in the current open literature. The motivation to analyze such an algorithm comes from the fact that this presents, for correlated signals, a higher convergence speed as compared with other adaptive algorithms that possess a similar computational complexity. Such a fact makes it a highly competitive alternative to applications considering colored input signals. The TDLMS algorithm has an orthogonal transformation stage, providing a separation of the input signal into different frequency bands. The intra-band samples are correlated, being the larger the number of bands, the higher is the correlation. Up to our knowledge, there is no other statistical model of this adaptive algorithm, providing a general and accurate solution, taking into account such correlations. In this way, this work proposes an accurate model allowing for these existing intra-band correlations. Project parameters are obtained from the statistical model, such as upper bound for the step size, optimum step-size value, and algorithm misadjustment. Through numerical simulations, a good agreement between the Monte Carlo method and the predictions from the proposed statistical model is verified for both white and colored Gaussian input signals.