Performance and Cramer–Rao Bounds for DoA/RSS Estimation and Transmitter Localization Using Sectorized Antennas

Using collaborative sensors or other observing devices equipped with sectorized antennas provides a practical and low-cost solution to direction-of-arrival (DoA) and received signal strength (RSS) estimation, as well as noncooperative transmitter (TX) localization. In this paper, we study the performance and theoretical bounds of DoA/RSS estimation and localization using sectorized antennas. We first show that the sector-power measurements at an individual sensor form a sufficient statistic for DoA/RSS estimation and TX localization. Motivated by that, we then derive the Cramer-Rao bound (CRB) on DoA/RSS estimation based on sector-powers and study its asymptotic behavior. Moreover, we derive an analytical expression for the mean square error (MSE) of a practical sectorized-antenna-based DoA estimator, compare its performance to the derived CRB, and study its asymptotic properties. Next, we derive the CRB for localization based on sector-powers. The resulting CRB is a lower bound for a localization system where the DoA/RSS estimates, obtained from sector-powers at individual sensors, are fused together into a location estimate. Moreover, the CRB also covers the more general case of a localization system where the sector-powers from individual nodes are directly fused together, without an intermediate DoA/RSS estimation step. We compare the obtained CRB to a localization approach employing an intermediate DoA/RSS estimation step and observe that skipping this intermediate processing step may result in a substantially improved localization performance. Finally, we study the influence of various important system parameters, such as the number of sensors, sectors, and measurement samples, on the achievable estimation and localization performance. Overall, this paper demonstrates and quantifies the achievable DoA/RSS estimation and localization performance of sectorized antennas and provides comprehensive design guidelines for sector-power based low-complexity localization systems.