%0 Electronic Article
%A Pedro Lara
%A Karen da S. Olinto
%A Felipe R. Petraglia
%A Diego B. Haddad
%K adaptive filtering algorithms
%K stochastic model
%K above-mentioned independence assumption
%K exact expectation analysis
%K theoretical analyses
%K least-mean-square algorithm
%K current adaptive coefficients
%K input vectors
%K derivations tractable
%K empirical results
%K step-size parameter
%K authors analysis
%K least-mean-squares
%K coloured additive noise
%K exact analysis
%K simplification
%K coloured measurement noise
%K statistical approximations
%K statistical independence
%K general analyses
%X In general, theoretical analyses of adaptive filtering algorithms employ statistical approximations in order to render the derivations tractable. Among such hypotheses, the statistical independence between the current adaptive coefficients and past input vectors is a very popular one. Unfortunately, this simplification gives rise to discrepancies with respect to empirical results, especially for large values of the step-size parameter. In this Letter, this issue is overcome by the usage of an exact expectation analysis (i.e. a stochastic model that does not employ the above-mentioned independence assumption) of the least-mean-squares adaptive algorithm. The authors analysis is also generalised in order to address the common case of coloured additive noise, an issue that is so far missing from the literature. The accuracy of the advanced model is verified through simulations.
%@ 0013-5194
%T Exact analysis of the least-mean-square algorithm with coloured measurement noise
%B Electronics Letters
%D November 2018
%V 54
%N 24
%P 1401-1403
%I Institution of Engineering and Technology
%U https://digital-library.theiet.org/;jsessionid=2h1blrh3l9e71.x-iet-live-01content/journals/10.1049/el.2018.6675
%G EN