The signal detectability gain performance index, for array receiving systems, is employed to derive the spatial detectability characteristics of some simple one‐, two‐, and three‐dimensional configurations. Analytical results are obtained in terms of array geometry, dimensionality, and space‐time correlation structure of the interference field. The analytical treatment is predicated upon decision theoretic foundations for waveform signal and noise structures. Homogeneous and isotropic Gaussian interference fields are assumed. Particular array‐geometry examples treated are linear, triangular, rectangular, and isosceles pyramidal, employing three and four elements. Analyses of the spatial detectability gain characteristics are achieved for the above configurations. Illustrations of the detectability gain are given in a plane passed through the array coordinate system, for 360° about the main lobe, with various permutations in array parameters. Various advantages of the two‐ and three‐dimensional configurations, over the one‐dimensional configuration and the associated conditions, are discussed.