In this paper, the likelihood ratio detector for zero‐mean complex Gaussian vector signals in zero‐mean complex Gaussian vector noise is considered. The receiving apparatus is assumed to be spatially distributed, and only a single frequency of interest is treated. By simultaneous diagonalization of the signal and noise spatial covariance matrices, say S and N, a canonical form is found for the familiar detector appropriate to this problem. Using this canonical form, a number of special cases follow easily. First, for small signals such that all eigenvalues of SN−1 are less than 1, we obtain the approximate detector. We then obtain the usual matched filter and threshold for the plane‐wave signal case, and a generalization to the case of a signal which is a superposition of plane waves. Finally, for signals such that the smallest nonzero eigenvalue of SN−1 is greater than 1, we obtain the asymptotic detector. Few of the results presented are new, but it is hoped that their derivation in a unified way from the canonical detector will be illuminating. Our aim is to combine some standard communication‐theory techniques with some standard matrix‐theory results, in the setting of the acoustic array data‐processing problem.