NDLI: A comparison of adaptive algorithms based on the methods of steepest descent and random search

Content Provider	IEEE Xplore Digital Library
Author	Widrow, B. McCool, J.
Copyright Year	1963
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.
Sponsorship	IEEE Antennas and Propagation Society
Starting Page	615
Ending Page	637
Page Count	23
File Size	1932783
File Format	PDF
ISSN	0018926X
Volume Number	24
Issue Number	5
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1976-09-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Adaptive algorithm Least squares approximation Broadband antennas Phased arrays Application software Receiving antennas Transmitting antennas Antenna arrays Adaptive systems Performance analysis
Content Type	Text
Resource Type	Article
Subject	Condensed Matter Physics Electrical and Electronic Engineering

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