Title :
Music and Model-Order Selection for Spherically Invariant Random Vectors
Author :
Bausson, Sébastien ; Forster, Philippe
Author_Institution :
PST Ville d´´Avray, Ville-d´´Avray
fDate :
Oct. 29 2006-Nov. 1 2006
Abstract :
Under Gaussian assumptions, the eigen decomposition of the sample covariance matrix (SCM) is the basis for MUSIC and Information Criterion methods. When signals are modeled by Spherically Invariant Random Vectors (SIRV), a natural extension of the SCM is the Normalized Sample Co- variance Matrix (NSCM). We show that the NSCM preserves the eigen subspaces of the covariance matrix of a signal plus white noise model. Moreover, the ratio of the arithmetic mean to the geometric mean of the NSCM lowest eigenvalues is asymptotically proportional to a chi2-distributed random variable. This allows one to estimate the number of signals and then to use MUSIC, as we show in simulations.
Keywords :
Gaussian processes; covariance matrices; eigenvalues and eigenfunctions; random processes; signal classification; signal sampling; vectors; white noise; Gaussian vector; MUSIC; NSCM; distributed random variable; eigen decomposition; information criterion method; model-order selection; multiple signal classification; normalized sample co-variance matrix; sample covariance matrix; signal plus white noise model; spherical invariant random vector; Arithmetic; Covariance matrix; Eigenvalues and eigenfunctions; Gain control; Multiple signal classification; Radar applications; Random variables; Sensor arrays; Sonar applications; White noise; MUSIC; NSCM; SIRV; model-order selection;
Conference_Titel :
Signals, Systems and Computers, 2006. ACSSC '06. Fortieth Asilomar Conference on
Conference_Location :
Pacific Grove, CA
Print_ISBN :
1-4244-0784-2
Electronic_ISBN :
1058-6393
DOI :
10.1109/ACSSC.2006.355171