Detection of an unknown rank-one component in white noise

Author

Besson, Olivier ; Kraut, Shawn ; Scharf, Louis L.

Author_Institution

Dept. of Avionics & Syst., ENSICA, Toulouse

Volume

54

Issue

7

fYear

2006

fDate

7/1/2006 12:00:00 AM

Firstpage

2835

Lastpage

2839

Abstract

We consider the detection of an unknown and arbitrary rank-one signal in a spatial sector scanned by a small number m of beams. We address the problem of finding the maximal invariant for the problem at hand and show that it consists of the ratio of the eigenvalues of a Wishart matrix to its trace. Next, we derive the generalized-likelihood ratio test (GLRT) along with expressions for its probability density function (pdf) under both hypotheses. Special attention is paid to the case m=2, where the GLRT is shown to be a uniformly most powerful invariant (UMPI). Numerical simulations attest to the validity of the theoretical analysis and illustrate the detection performance of the GLRT

Keywords

eigenvalues and eigenfunctions; matrix algebra; probability; signal detection; white noise; Wishart matrix; eigenvalues; generalized-likelihood ratio test; numerical simulations; probability density function; spatial sector scan; uniformly most powerful invariant; unknown rank-one signal component detection; white noise; Aerospace electronics; Detectors; Eigenvalues and eigenfunctions; Numerical simulation; Performance analysis; Probability density function; Sensor arrays; Statistics; Testing; White noise; Array processing; Wishart matrices; detection; eigenvalues; maximal invariant statistic;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2006.874781

Filename

1643925