Steady-State Mean-Square Performance Analysis of a Relaxed Set-Membership NLMS Algorithm by the Energy Conservation Argument

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 performa...

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Bibliographic Details
Published in:IEEE transactions on signal processing Vol. 57; no. 9; pp. 3361 - 3372
Main Authors: Takahashi, N., Yamada, I.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.09.2009
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Adaptive algorithm
Adaptive algorithms
Algorithm design and analysis
Algorithms
Applied sciences
Energy conservation
Energy conservation relation
Error analysis
error-nonlinearity
Exact sciences and technology
hyperslab
Information, signal and communications theory
Mean square error methods
Miscellaneous
Noise cancellation
Nonlinear equations
Nonlinearity
Performance analysis
Projection
Regularization
set-membership
Signal processing
Signal processing algorithms
Steady-state
steady-state MSE
Studies
Telecommunications and information theory
Transient analysis
Performance evaluation
set-membership
Energy conservation relation
steady-state MSE
Algorithm
Non linear phenomenon
Steady state
hyperslab
Mean square error
Non linear equation
error-nonlinearity
Relaxation
Simulation
Energy conservation
Signal processing
projection
Non linear effect
Transient analysis
Least mean squares methods
ISSN:1053-587X, 1941-0476
Online Access:Get full text
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Summary: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.
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ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2009.2020747