Exact analysis of the least‐mean‐square algorithm with coloured measurement noise. Issue 24 (1st November 2018)

• Record Type: Journal Article
• Authors: Lara, Pedro; Olinto, Karen da S.; Petraglia, Felipe R.; Haddad, Diego B.
• Is Part Of: Electronics letters. Volume 54:Issue 24(2018)
• Page Start: 1401
• Page End: 1403
• Publication Date: 2018-11-01
• Subjects: least mean squares methods -- adaptive filters -- filtering theory -- stochastic processes; statistical independence -- current adaptive coefficients -- input vectors -- simplification -- empirical results -- step‐size parameter -- exact expectation analysis -- stochastic model -- above‐mentioned independence assumption -- least‐mean‐squares -- authors analysis -- coloured additive noise -- exact analysis -- least‐mean‐square algorithm -- coloured measurement noise -- general analyses -- theoretical analyses -- adaptive filtering algorithms -- statistical approximations -- derivations tractable; Electronics -- Periodicals; 621.381
• DOI: 10.1049/el.2018.6675
• Languages: English
• ISSNs: 0013-5194

Abstract

Abstract : 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.