Passive Detection with a Multi-Rank Beamformer of a Random Signal Common to Two Sensors

Motivated by passive source localization, we derive a generalized likelihood ratio for detecting a Gaussian signal common to two passive sensor arrays, measured in white Gaussian noises of unknown variances. The resulting detector is compared with a related detector that makes no such Gaussian signal assumption. These two detectors are called, respectively, second-order and first-order detectors. In the case where each passive sensor employs a known beamformer, performance is nearly identical. But for more general channel or beamformer models where the received signal is assumed only to lie in a low-dimensional subspace, the second-order detector can outperform the first-order detector.