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Most array processing algorithms are based on the assumption that the signals are generated by point sources. This is a mathematical constraint that is not satisfied in many applications. In this paper, we consider situations where the sources are distributed in space with a parametric angular cross-correlation kernel. We propose an algorithm that estimates the parameters of this model using a generalization of the MUSIC algorithm. The method involves maximizing a cost function that depends on a matrix array manifold and the noise eigenvectors. We study two particular cases: coherent and incoherent spatial source distributions. The spatial correlation function for a uniformly distributed signal is derived. From this, we find the array gain and show that (in contrast to point sources) it does not increase linearly with the number of sources. We compare our method to the conventional (point source) MUSIC algorithm. The simulation studies show that the new method outperforms the MUSIC algorithm by reducing the estimation bias and the standard deviation for scenarios with distributed sources. It is also shown that the threshold signal-to-noise ratio required for resolving two closely spaced distributed sources is considerably smaller for the new method.>
Valaee et al. (1995) studied this question.