Abstract
In practical array detection problems, the noise field statistics may vary spatially and temporally. In this paper, the problem of detecting a farfield signal source which generates a known signal field at an array aperture is considered. Space-time samples of the noise field are assumed to be zero-mean Gaussian random variables whose second moments are random variables. Bayes optimum receivers and their performance are derived for several different joint statistical characterizations of the second moments. The results are believed to be the first detection performance results, in terms of the ROC, for optimum array processors in uncertain noise power environments. It is shown that, for certain characterizations, the optimum processor in uncertain noise power either requires spatial processing which is not accomplished by a beamformer or requires spatial processing in addition to that provided by a beamformer. For noise power correlation which decreases rapidly as a function of spatial and temporal coordinates, the optimum nonlinearity is determined to be a limiter.
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