Bayes optimum array detection of targets of known location

Abstract

This paper presents a Bayes optimum approach to detecting a target of known location by processing the outputs of an array of sensors. Beamforming is not postulated a priori. The complex exponential Fourier series is used to represent the deterministic signals and random processes. Using Bayes decision theory, important existing results and new results are unified and presented in a single mathematical framework. Optimum receiver structures and performance are derived for detecting a known signal source in a Gaussian noise field. They are also derived for detecting a signal source which generates an uncertain waveform in either a spatially uncorrelated noise field or a noise field with spatial correlation due to a farfield noise source. Important new results concerning factorization of optimum array receivers are presented for detecting signal sources of known location which generate either known or uncertain waveforms. A technique for applying existing scalar results to array problems is presented for several cases. Detection performance results, in terms of the receiver operating characteristics (ROC), which are characterized in some cases by the detectability index, are presented for a number of situations.