Detection nonidentifiability for independent Gaussian sources in nonuniform linear antenna arrays

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.