Information theoretic criteria for the determination of the number of signals in spatially correlated noise

The problem of determining the number of signals in high resolution array processing when the noise is spatially correlated (having an unknown covariance matrix) is examined. By considering a model in which two sensor arrays are well separated such that their noise outputs are uncorrelated, we develop a likelihood function whose maximum can be expressed in a very simple form involving the canonical correlation coefficients. This likelihood function, together with a choice of penalty functions, constitute a number of new information theoretic criteria suitable for the determination of the number of signals in an unknown correlated noise environment. Furthermore, it is demonstrated that the new criteria are applicable in the case when only one sensor array is available.