Detection tests for array processing in unknown correlated noise fields

This paper introduces two eigenvalue-based rules for estimating the number of signals impinging on an array of sensors along with a spatially correlated noise field. The first rule, called S, is derived under the assumption that the noise spatial covariance is block diagonal or banded. The assumption underlying the second detection rule, named T, is that the temporal correlation of the noise has a shorter length than that of the signals. In both cases, a matrix is built from the array output data covariances, the smallest eigenvalue of which is equal to zero under the hypothesis that the source number is overestimated. The sample distribution of the aforementioned smallest eigenvalue is derived and used to formulate the detection rules S and T. Both these rules are computationally quite simple. Additionally, they can be used with a noncalibrated array. The paper includes numerical examples that lend empirical support to the theoretical findings and illustrate the kind of performance that can be achieved by using the S and T detection rules.