Coherence Effects on the Detection Performance of Quadratic Array Processors, With Applications to Large-Array Matched- Field Beamforming.

This memo documents part of the work performed on our 1987 IR&D effort. Matched-field beamforming is a generalization of plane-wave beamforming that takes into account both wavefront curvature and multipath. Long-range ocean acoustic detection with very large arrays necessitates matched-field beamforming, as conventional beamforming suffers limitations in this regime. However, the success of matched-field beamforming depends on the ability to precisely predict the Green's function, which describes propagation in the medium. In addition to deterministic effects, small-scale random inhomogeneities perturb the Green's function, causing decorrelation, or loss of coherence, across a large receiving array. Thus, a central issue in large-array matched-field beamforming is the signal coherence, or lack thereof, which inherently limits the detection performance. The effect of coherence on detection performance is examined here using an exponential-power-law model for the signal wavefront correlation. Detection performance is quantified by the small- signal deflection Signal-to-Noise Ratio (SNR) criterion, which is first reviewed in the general setting of quadratic detectors, and then applied to matched-field and optimal quadratic beamformers. Several suboptimal beamformers with reduced computational complexity are also developed and their SNR performance is compared to that of the matched-field and optimal beamformers. A central result of this study is that the detection performance of large arrays is significantly limited by the spatial coherence of the signal wavefront, and that the full potential of such arrays will not be realized unless the correlation characteristics are known and used to optimally process such signals. In particular, it is shown that one suboptimal processor, the subarray beamformer, is outstanding for this application in three respects: it can realize within 1 dB of optimal performance; is robust over a class of correlation functions; and, entails a computational burden no greater than full-array matched-field beamforming.