MVDR adaptive sidelobes: extending Ruze´s formula and providing an exact calculation of the probability of sidelobe suppression

Author

Richmond, Christ D.

Author_Institution

Lincoln Lab., MIT, Lexington, MA, USA

fYear

2000

fDate

2000

Firstpage

73

Lastpage

76

Abstract

Exact finite sum expressions for the probability density function (PDF) and cumulative distribution function (CDF) for the magnitude response of the SCB MVDR beamformer are derived. Exact expressions for the mean and variance of this beam pattern are given which generalize and extend the classical results of Ruze (1952) as well as those of Gilbert and Morgan (1955) to this MVDR processor. These tools allow the exact prediction of the likelihood of interference in a given direction obtaining a specified level of sidelobe or mainlobe suppression by the adaptive beamformer. Sample support and degrees of freedom can be chosen to meet specifications with a certain level of probability. These useful calculations are facilitated by judicious exploitation of Sehlafli´s contour integral representation for the modified Bessel function

Keywords

Bessel functions; antenna radiation patterns; array signal processing; direction-of-arrival estimation; integral equations; interference suppression; probability; CDF; MVDR adaptive sidelobes; MVDR processor; PDF; Ruze´s formula; SCB MVDR beamformer; adaptive beamformer; beam pattern; calculation; contour integral representation; cumulative distribution function; degrees of freedom; exact finite sum expressions; magnitude response; mainlobe suppression; mean; modified Bessel function; probability density function; sample support; sidelobe suppression probability; variance; Adaptive arrays; Adaptive filters; Apertures; Distribution functions; Interference suppression; Laboratories; Least squares approximation; Probability density function; Signal to noise ratio; Stochastic processes;

fLanguage

English

Publisher

ieee

Conference_Titel

Sensor Array and Multichannel Signal Processing Workshop. 2000. Proceedings of the 2000 IEEE

Conference_Location

Cambridge, MA

Print_ISBN

0-7803-6339-6

Type

conf

DOI

10.1109/SAM.2000.877971

Filename

877971