A statistical resolution theory of the beamformer-based spatial spectrum for determining the directions of signals in white noise

Due to its simplicity and ease of implementation, the beamformer-based spatial spectrum (BSS) is widely used in practice to determine the angles of arrival of signals in white noise in array processing. As the most important performance to this application, the resolution capability of the BSS is roughly assessed by a deterministic measure, borrowed from optics, which takes into account only the influence of the effective aperture of the linear array of sensors. For a linear array operating in a stochastic environment, resolving two incoming signals is essentially a random event, thereby demanding a probabilistic resolution measure. In the paper, the probabilistic performance of the BSS in resolving two incoming signals is studied. The author derives a simple expression, in a closed form, for its failure probability in distinguishing the two signals. The results reveal the way various parameters of signals, noise, and array of sensors affect the resolution performance. Computer simulations are also presented to confirm the validity of the theory