Adaptive filter theory (3rd ed.)
Adaptive filter theory (3rd ed.)
Vector Space Projections: A Numerical Approach to Signal and Image Processing, Neural Nets, and Optics
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
EURASIP Journal on Applied Signal Processing
Set-membership binormalized data-reusing LMS algorithms
IEEE Transactions on Signal Processing
Low-complexity constrained affine-projection algorithms
IEEE Transactions on Signal Processing
Frequency-Domain Set-Membership Filtering and Its Applications
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
A unified approach to the steady-state and tracking analyses ofadaptive filters
IEEE Transactions on Signal Processing
Partial-update NLMS algorithms with data-selective updating
IEEE Transactions on Signal Processing
An efficient robust adaptive filtering algorithm based on parallelsubgradient projection techniques
IEEE Transactions on Signal Processing
Transient analysis of data-normalized adaptive filters
IEEE Transactions on Signal Processing
Transient analysis of adaptive filters with error nonlinearities
IEEE Transactions on Signal Processing
Mean-square performance of a family of affine projection algorithms
IEEE Transactions on Signal Processing
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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 ε-normalized least mean square (ε-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 ε-NLMS. Extensive simulations show the close agreement between our theories and experiments.