Efficient quadratic detection in perturbed arrays via Fourier transform techniques

Matched-field beamforming used in combination with a generalized likelihood ratio test is the most common detector structure in array processing situations. Unfortunately, various array perturbations caused by phase, calibration, propagation effects, or modeling errors can cause the sensor observations to become only partially correlated, limiting the performance of traditional matched-field beamformers that assume perfect coherence of the signal wavefronts. Quadratic array processing is optimal for many perturbed array problems; however, direct implementation poses a significant computational burden. We show that under certain conditions, the optimal quadratic detector for dealing with perturbed arrays can be approximately realized efficiently and robustly employing only discrete Fourier transforms to deal with spatial processing. In addition, we show that the proposed spatial processing allows for convenient integration of conventional frequency-domain methods for angle-of-arrival searches. Our proposed array detection structure provides the robustness and performance benefits of complicated quadratic processing at a computational cost comparable with that of traditional matched-field beamforming.