Journal ArticleDOI
A comparison of adaptive algorithms based on the methods of steepest descent and random search
Bernard Widrow,J.M. McCool +1 more
TLDR
This paper compares the performance characteristics of three algorithms useful in adjusting the parameters of adaptive systems: the differential (DSD) and least-mean-square (LMS) algorithms, both based on the method of steepest descent, and the linear random search (LRS) algorithm, based on a random search procedure derived from the Darwinian concept of "natural selection.Abstract:
This paper compares the performance characteristics of three algorithms useful in adjusting the parameters of adaptive systems: the differential (DSD) and least-mean-square (LMS) algorithms, both based on the method of steepest descent, and the linear random search (LRS) algorithm, based on a random search procedure derived from the Darwinian concept of "natural selection." The LRS algorithm is presented here for the first time. Analytical expressions are developed that define the relationship between rate of adaptation and "misadjustment," a dimensionless measure of the difference between actual and optimal performance due to noise in the adaptive process. For a fixed rate of adaptation it is shown that the LMS algorithm, which is the most efficient, has a misadjustment proportional to the number of adaptive parameters, while the DSD and LRS algorithms have misadjustments proportional to the square of the number of adaptive parameters. The expressions developed are verified by computer simulations that demonstrate the application of the three algorithms to system modeling problems, of the LMS algorithm to the cancelling of broadband interference in the sidelobes of a receiving antenna array, and of the DSD and LRS algorithms to the phase control of a transmitting antenna array. The second application introduces a new method of constrained adaptive beamforming whose performance is not significantly affected by element nonuniformity. The third application represents a class of problems to which the LMS algorithm in the basic form described in this paper is not applicable.read more
Citations
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Book
Phased Array Antenna Handbook
TL;DR: Details of Element Pattern and Mutual Impedance Effects for Phased Arrays and Special Array Feeds for Limited Field of View and Wideband Arrays are presented.
Journal ArticleDOI
Application of antenna arrays to mobile communications. II. Beam-forming and direction-of-arrival considerations
TL;DR: This paper provides a comprehensive and detailed treatment of different beam-forming schemes, adaptive algorithms to adjust the required weighting on antennas, direction-of-arrival estimation methods-including their performance comparison-and effects of errors on the performance of an array system, as well as schemes to alleviate them.
Journal ArticleDOI
Frequency-domain and multirate adaptive filtering
TL;DR: An overview is presented of several frequency-domain adaptive filters that efficiently process discrete-time signals using block and multirate filtering techniques, including convergence properties and computational complexities of the adaptive algorithms and the effects of circular convolution and aliasing on the converged filter coefficients.
Journal ArticleDOI
Fast, recursive-least-squares transversal filters for adaptive filtering
John M. Cioffi,Thomas Kailath +1 more
TL;DR: Fast transversal filter (FTF) implementations of recursive-least-squares (RLS) adaptive-filtering algorithms are presented in this paper and substantial improvements in transient behavior in comparison to stochastic-gradient or LMS adaptive algorithms are efficiently achieved by the presented algorithms.
Journal ArticleDOI
Robust minimum variance beamforming
R.G. Lorenz,Stephen Boyd +1 more
TL;DR: An extension of minimum variance beamforming that explicitly takes into account variation or uncertainty in the array response, via an ellipsoid that gives the possible values of the array for a particular look direction is introduced.
References
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Journal ArticleDOI
Adaptive noise cancelling: Principles and applications
Bernard Widrow,J.R. Glover,John M. McCool,J. Kaunitz,C.S. Williams,R.H. Hearn,James R. Zeidler,Jr. Eugene Dong,R.C. Goodlin +8 more
TL;DR: It is shown that in treating periodic interference the adaptive noise canceller acts as a notch filter with narrow bandwidth, infinite null, and the capability of tracking the exact frequency of the interference; in this case the canceller behaves as a linear, time-invariant system, with the adaptive filter converging on a dynamic rather than a static solution.
Journal ArticleDOI
An algorithm for linearly constrained adaptive array processing
TL;DR: A constrained least mean-squares algorithm has been derived which is capable of adjusting an array of sensors in real time to respond to a signal coming from a desired direction while discriminating against noises coming from other directions.
Book ChapterDOI
Stationary and nonstationary learning characteristics of the LMS adaptive filter
TL;DR: It is shown that for stationary inputs the LMS adaptive algorithm, based on the method of steepest descent, approaches the theoretical limit of efficiency in terms of misadjustment and speed of adaptation when the eigenvalues of the input correlation matrix are equal or close in value.