A1 Pedro Lara

A1 Karen da S. Olinto

A1 Felipe R. Petraglia

A1 Diego B. Haddad

PB iet

T1 Exact analysis of the least-mean-square algorithm with coloured measurement noise

JN Electronics Letters

VO 54

IS 24

SP 1401

OP 1403

AB 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.

K1 adaptive filtering algorithms

K1 stochastic model

K1 above-mentioned independence assumption

K1 exact expectation analysis

K1 theoretical analyses

K1 least-mean-square algorithm

K1 current adaptive coefficients

K1 input vectors

K1 derivations tractable

K1 empirical results

K1 step-size parameter

K1 authors analysis

K1 least-mean-squares

K1 coloured additive noise

K1 exact analysis

K1 simplification

K1 coloured measurement noise

K1 statistical approximations

K1 statistical independence

K1 general analyses

DO https://doi.org/10.1049/el.2018.6675

UL https://digital-library.theiet.org/;jsessionid=oahobmgfiz0b.x-iet-live-01content/journals/10.1049/el.2018.6675

LA English

SN 0013-5194

YR 2018

OL EN