A simple technique to estimate the position of a given mobile source inside a building is based on the received signal strength. For this methodology to have a reasonable accuracy, radio visibility of the mobile by at least three access points is required. To reduce the number of the required access points and therefore simplify the underlying coverage design problem, we propose a novel scheme that takes into account the distribution of RF energy around the receiver. In other words, we assume that the receiver is equipped with a circular array antenna with beamforming capability. In this way, the spatial spectrum of the received power can be measured by electronically rotating the main lobe around the 360-degree field of view. This spatial spectrum can be used by a single receiver as a means for estimating the position of the mobile transmitter. In this paper, we investigate the feasibility of this methodology, and show the improvement achieved in the positioning accuracy.