Estimating the number of signals in presence of colored noise

Abstract

In this paper, statistical ranking and selection theory is used to estimate the number of signals present in colored noise. The data structure follows the well-known Multiple Signal Classification (MUSIC) model. We deal with the eigenanalyses of a matrix, using the MUSIC model and colored noise. The data matrix can be written as the product of a covariance matrix and the inverse of second covariance matrix. We propose a multistep selection procedure to construct a confidence interval on the number of signals present in a data set. Properties of this procedure are stated and proved. Those properties are used to compute the required parameters (procedure constants). Numerical examples are given to illustrate our theory.