Cramer-Rao Bounds for Hybrid RSS-DOA Based Emitter Location and Transmit Power Estimation in Cognitive Radio Systems

In this paper, we consider cooperating secondary users (SUs) that are estimating the location and transmit power of an emitter that may be either a primary user (PU) or another SU in the cognitive radio (CR) context. Since SU devices need to be affordable and portable, their capabilities to estimate e.g. the direction of arrival (DOA) are very limited. In addition, the geographical distribution of SUs is random rather than optimized resulting in very stringent conditions for the localization. We therefore analyze possible benefits and performance of hybrid received signal strength (RSS)- DOA based emitter transmit power and position estimation by means of the Cramer-Rao bound (CRB). We show that the RSS-DOA hybrid approach can lead to significantly lower bounds compared to estimation based on only RSS or DOA. Assuming a special case of two SUs at equal distance from the emitter, we derive the CRBs in closed-form and demonstrate that for certain SU-emitter geometries, the RSS-only and DOA-only CRBs become infinite due to the inability to estimate one of the emitter's coordinates. Since those coordinates are orthogonal for RSS and DOA, the hybrid approach does not suffer from these geometries, resulting in a finite CRB. Results from Monte-Carlo simulations are provided which illustrate that significant theoretic gains are possible also for random SU and emitter placements. The results also show that biggest performance gains from joint processing of RSS and DOA are available when the number of cooperating SUs is fairly small, in the order of 2-5.