Performance of direction-finding systems with sensor gain and phase uncertainties

In this paper we study the performance of direction-finding systems which attempt to estimate unknown array parameters (such as sensor gains and phases) in addition to the estimation of the directions of arrival (DOA), as a way of performing array self-calibration. We develop compact closed form expressions for the Cramér-Rao bound associated with the joint estimation of DOAs, gains, phases, and the signal covariance matrix. By evaluating the Cramér-Rao bound for selected cases we gain some insight into the performance of direction-finding systems in the presence of gain and phase uncertainties.