Wavefield modeling and array processing. III. Resolution capacity

For pt.II see ibid., vol.42, no.10, p.2560, 1994. We use here the wavefield modeling formalism in order to derive some fundamental limitations on the performance of passive arrays. We first derive upper bounds on both the ideal and effective resolution capacities, and show that the effective resolution capacity is bounded by the effective rank of the relevant sampling matrix, i.e., is determined by the array structure. We then study how the resolution capacity is affected when the sources are constrained to lie within an angular sector. We also look at the case where the source spectra are known a priori to be flat, and show that, contrary to the common opinion, if the array satisfies the spectral sampling condition, the effective wideband resolution capacity is bounded by the same bound as the narrowband one. We conclude by examining the interesting phenomenon of resonance in arrays. We show that these resonances, far from being mathematical artifacts, can manifest quite dramatically in the performance of arrays