DocumentCode :
1234332
Title :
Steady-State Mean-Square Performance Analysis of a Relaxed Set-Membership NLMS Algorithm by the Energy Conservation Argument
Author :
Takahashi, Noriyuki ; Yamada, Isao
Author_Institution :
Dept. of Commun. & Integrated Syst., Tokyo Inst. of Technol., Tokyo, Japan
Volume :
57
Issue :
9
fYear :
2009
Firstpage :
3361
Lastpage :
3372
Abstract :
This paper presents an analysis of the steady-state mean-square error (MSE) of the set-membership normalized least-mean square (SM-NLMS) algorithm with relaxation and regularization parameters. These parameters are introduced for the purpose of deriving in a unified way the steady-state MSE performances of the epsiv-normalized least mean square (epsiv-NLMS) algorithm and a special case of the adaptive parallel subgradient projection (PSP) algorithm. The approach of the paper is to employ the energy conservation relation as a starting point of our analysis. This relation enables us to avoid the transient analysis of the SM-NLMS algorithm, which is in general hard due to the nonlinearity of the SM-NLMS algorithm. As a result, a few nonlinear equations whose solutions are theoretical steady-state MSEs are derived, where two types of reasonable assumptions are introduced to overcome the nonlinearity of the SM-NLMS algorithm. Our results are generalizations of well-known results of the steady-state MSE of the epsiv-NLMS. Extensive simulations show the close agreement between our theories and experiments.
Keywords :
adaptive filters; adaptive signal processing; least mean squares methods; nonlinear equations; transient analysis; adaptive filters; adaptive parallel subgradient projection algorithm; adaptive signal processing; energy conservation argument; epsiv-normalized least mean square algorithm; nonlinear equations; relaxed set-membership NLMS algorithm; set-membership normalized least-mean square algorithm; steady-state mean-square error algorithm; steady-state mean-square performance analysis; transient analysis; Energy conservation relation; error-nonlinearity; hyperslab; projection; set-membership; steady-state MSE;
fLanguage :
English
Journal_Title :
Signal Processing, IEEE Transactions on
Publisher :
ieee
ISSN :
1053-587X
Type :
jour
DOI :
10.1109/TSP.2009.2020747
Filename :
4813247
Link To Document :
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