The use of wireless sensor networks is rapidly increasing. Also the demand of ubiquitous location sensors is swiftly expanding. Hence, energy and location-awareness come into focus of research today. A prospective approach for low-power locating sensor networks is received signal strength indicator (RSSI)-based direction finding. The presented approach is based on RSSI difference measurements retrieved by a array of directed antennas. In this paper, fundamental limits of RSSI-based direction finding are evaluated, beyond the Cramer-Rao Lower Bound (CRLB). That is not applicable for the design of a localization system topology due to the nature of the gain difference function that leads to an unbounded variance of the unbiased estimator. Thus, a maximum likelihood (ML) approach to the RSSI-based direction finding is presented. The ML estimator yields a limited variance for all signal directions. However, that benefit comes at the expense of being biased. Beyond treating direction estimates, mean square position errors are compared for both, the unbiased and the ML estimator.