The design of point detector arrays, I

This paper considers the design of a detection system to optimally detect known signal fields--scalar functions of a vector argument--corrupted by an additive noise field. The detection system has as its inputs samples (in Space) of the signal-plus-noise field; each spatial sample is the output of a point detector. Optimal processing of the point-detector outputs, as well as the locations of the point detectors, is considered. For a fixed array and under assumptions that are often physically reasonable, the optimum detector is separable into a spatial combiner and a temporal processor. The probability of error of the optimum detector is a monotonic function of the array gain. Convenient expressions of the array gain are found for circular arrays; by using these expressions, optimal radii for circular arrays are found.