On the resolution capacity of wideband sensor arrays

Summary form only given. The superresolution estimation of bearings of wideband sources using fewer sensors than sources has been addressed. The fundamental limits on the maximum number, D_max, of wideband sources uniquely resolvable by a passive sensor array, called the resolution capacity of the array, has been studied. The source signals are assumed to be uncorrelated zero-mean, second-order stationary, and ergodic wideband random processes occupying a common bandwidth. The array is assumed to be uniform and linear, and L >> 1 Nyquist-rate samples of its output are assumed to be collected into a snapshot supervector. N >> 1 such snapshots are assumed to be available. It has been shown that if each of the source power spectral densities is specified by M unknown parameters, then a (not necessarily sharp) bound is given by D_max ≤ L(2K - 1)/(M + 1), where K is the number of sensors. Furthermore, if each of the source power spectral densities can be represented by a weighted sum of M linearly independent basis functions, a sharp upper bound on D can be obtained in terms of the rank of a certain matrix that depends on the specific basis functions chosen. For the specific case of M basis functions derived from linear combinations of polynomials or order less than M + 1, the bound D_max = KL/(2M), which is tight, has been obtained. These results suggest that in the case of uncorrelated wideband signals, the resolution capacity of a given array is essentially limited only by the observation interval, rather than by the number of sensors.