Optimum detection of Gaussian signal fields in the multipath-anisotropic noise environment and numerical evaluation of detection probabilities

The optimum detector of Gaussian signal fields in the multipath-anisotropic noise environment is derived. The optimum detector consists of a series of matched quadratic filters and a decisionmaker. The filters are spatially and temporally matched to the eigenwaves of the signal-to-noise covariance, and the decisionmaker compares a quadratic form with a preassigned threshold. The optimum detector for single-path signals in isotropic white noise is the well-known delay-and-sum beamformer, which is widely used because of its simple structure. In the case of multipath signals in anisotropic noise, a substantial improvement in detection performance is possible over the beamformer. This is shown by numerically comparing the detection probability of the beamformer with that of the optimum detector for this case. In addition, we numerically evaluate the sensitivity of such an improvement to accurate knowledge of the signal and noise parameters that are required by the optimum detector. We also show the possibility of further improvement by the addition of a vertical segment to the commonly used horizontal linear array to provide sensitivity to the elevation angles of multipath signals.