Analysis and design of a signed regressor LMS algorithm for stationary and nonstationary adaptive filtering with correlated Gaussian data

A least mean square (LMS) algorithm with clipped data is studied for use when updating the weights of an adaptive filter with correlated Gaussian input. Both stationary and nonstationary environments are considered. Three main contributions are presented. The first, corresponding to the stationary c...

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Bibliographic Details
Published in:IEEE transactions on circuits and systems Vol. 37; no. 11; pp. 1367 - 1374
Main Author: Eweda, E.
Format: Journal Article
Language:English
Published: New York, NY IEEE 01.11.1990
Institute of Electrical and Electronics Engineers
Subjects:
Adaptive filters
Algorithm design and analysis
Applied sciences
Circuit properties
Circuits and systems
Convergence
Covariance matrix
Eigenvalues and eigenfunctions
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Estimation error
Exact sciences and technology
Filtering algorithms
Frequency filters
Least squares approximation
Steady-state
Computer simulation
Least squares method
Theoretical study
Adaptive filtering
Eigenvalue
Error detection
Performance
Algorithm
ISSN:0098-4094
Online Access:Get full text
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Summary:A least mean square (LMS) algorithm with clipped data is studied for use when updating the weights of an adaptive filter with correlated Gaussian input. Both stationary and nonstationary environments are considered. Three main contributions are presented. The first, corresponding to the stationary case, is a proof of the convergence of the algorithm in the case of a M-dependent sequence of correlated observation vectors. It is proven that the steady state mean square misalignment of the adaptive filter weights has an upper bound proportional to the algorithm step size mu . The second contribution, also belonging to the stationary case, is the derivation of the expressions of convergence time N/sub c/ and steady state mean square excess estimation error epsilon . It is shown that N/sub c/ is proportional to 1/( mu lambda ), with lambda being the minimum eigenvalue of the input covariance matrix. It is also shown that the product N/sub c/ epsilon is independent of mu . For a given epsilon , the convergence time increases with the eigenvalue spread of the input covariance matrix and the filter length, as well as its input noise power. The range of mu that achieves tolerable values of N/sub c/ and epsilon is determined. The third contribution is concerned with the nonstationary case. It is shown that the mean square excess estimation error is the sum of the two terms with opposite dependencies on mu . An optimum value of mu is derived.< >
ISSN:0098-4094
DOI:10.1109/31.62411