Detection nonidentifiability for independent Gaussian sources in nonuniform linear antenna arrays

Abstract

Nonidentifiability with respect to detection is derived, and is found to be the condition that the covariance matrix of a mixture of a particular number of independent Gaussian sources plus noise is identical to that of another mixture of a different number of such sources. This condition is formulated in terms of the rank-deficiency of some matrix that is related to the antenna geometry's co-array. We propose and discuss a method to determine the detection identifiability or otherwise of any given nonuniform linear antenna array.