Optimal array processing with 3-D random arrays

In this paper, we derive the detection performance of an optimally beamformed 3-D random array system, assuming known Gaussian signal, noise, and interference statistics, and compare it with the performance of a conventional beamformed system. The receiver operating characteristics (ROC) are straightforward, nonlinear functions of the particular array realization and the second-order signal, noise, and interference statistics. Thus, a determination of the average ROCs (over the array ensemble) appears intractable. However, by making a reasonable approximation, we are able to derive an analytical expression for the average ROC for both conventional and optimal processing.