Limitations on the overlap-correlator method imposed by noise and signal characteristics

Limitations on the performance of the overlap-correlator method of forming a passive synthetic aperture are derived. The technique uses the overlap of the array in sequential positions to estimate a series of phase correction factors that compensate for the motion of the array over time. It is of primary interest to optimize this overlap with respect to the effects of random noise. By minimizing the variance of the estimates of the set of phase correction factors, it is found that the optimal overlap is one-half the length of the physical array. Using this optimal overlap, the bounds on the usable spatial response are then determined as a function of signal-to-noise ratio and the number of hydrophones in the physical array. The ability of the overlap-correlator algorithm to synthesize a coherent aperture is investigated for the case of multiple sources in the absence of noise