Title :
The performance of the GLRT for the spatial signals detection with a small number of observations
Author :
Bolkhovskaya, Olesya ; Maltsev, Alexander
Author_Institution :
Dept. of Stat. Radiophisics, Nizhny Novgorod State Univ., Russia
Abstract :
In this letter, the generalized likelihood ratio test (GLRT) is used for the detection of multidimensional Gaussian complex signals with unknown spatial covariance matrix on a background of additive Gaussian complex noise of a unknown power is solved. The exact analytical expressions for test-statistical moments were found for any numbers of observations. The expansion in a series of probability density functions of a resolving statistic for orthogonal Jacobi polynomials were obtained by method of moments. The accuracy of the GLRT-statistic cumulative distribution function approximation and the accuracy of threshold calculations for the given false alarm probability for various numbers of approximating series terms were checked by simulation. The results are correct for any number of samples.
Keywords :
AWGN; Jacobian matrices; antenna arrays; antenna theory; covariance matrices; maximum likelihood estimation; method of moments; multidimensional signal processing; signal detection; GLRT; additive Gaussian complex noise; antenna array; false alarm probability; generalized likelihood ratio test; method of moment; multidimensional Gaussian complex signal; orthogonal Jacobi polynomial; probability density function; spatial covariance matrix; test-statistical moments; Additive noise; Background noise; Covariance matrix; Function approximation; Gaussian noise; Multidimensional systems; Probability density function; Signal detection; Signal to noise ratio; Testing; -statistic; Antenna array; GLRT; detection task; generalized likelihood ratio test; probability density function;
Journal_Title :
Signal Processing Letters, IEEE
DOI :
10.1109/LSP.2004.835462
