Cramer-Rao Bounds for Joint RSS/DoA-Based Primary-User Localization in Cognitive Radio Networks

TL;DR

This paper derives the Cramer-Rao Bound for joint RSS and DoA-based primary-user localization in cognitive radio networks, considering realistic error models and analyzing key parameters affecting localization accuracy.

Contribution

It introduces a joint CRB derivation that accounts for RSS-dependent DoA error variance, extending prior separate analyses and providing asymptotic bounds for random CR placement.

Findings

Joint RSS/DoA CRB is derived considering realistic error models.

Impact of network parameters on localization accuracy is thoroughly analyzed.

Asymptotic CRB matches numerical results for large, random CR placements.

Abstract

Knowledge about the location of licensed primary-users (PU) could enable several key features in cognitive radio (CR) networks including improved spatio-temporal sensing, intelligent location-aware routing, as well as aiding spectrum policy enforcement. In this paper we consider the achievable accuracy of PU localization algorithms that jointly utilize received-signal-strength (RSS) and direction-of-arrival (DoA) measurements by evaluating the Cramer-Rao Bound (CRB). Previous works evaluate the CRB for RSS-only and DoA-only localization algorithms separately and assume DoA estimation error variance is a fixed constant or rather independent of RSS. We derive the CRB for joint RSS/DoA-based PU localization algorithms based on the mathematical model of DoA estimation error variance as a function of RSS, for a given CR placement. The bound is compared with practical localization algorithms and the impact of several key parameters, such as number of nodes, number of antennas and samples, channel shadowing variance and correlation distance, on the achievable accuracy are thoroughly analyzed and discussed. We also derive the closed-form asymptotic CRB for uniform random CR placement, and perform theoretical and numerical studies on the required number of CRs such that the asymptotic CRB tightly approximates the numerical integration of the CRB for a given placement.