Title :
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
fDate :
7/1/2006 12:00:00 AM
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;
Journal_Title :
Signal Processing, IEEE Transactions on
DOI :
10.1109/TSP.2006.874781
