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Information about primary transmitter location is crucial in enabling several key capabilities in cognitive radio networks, including improved spatio-temporal sensing, intelligent location-aware routing, as well as aiding spectrum policy enforcement. Compared to other proposed non-interactive localization algorithms, the weighted centroid localization (WCL) scheme uses only the received signal strength information, which makes it simple to implement and robust to variations in the propagation environment. In this paper we present the first theoretical framework for WCL performance analysis in terms of its localization error distribution parameterized by node density, node placement, shadowing variance, correlation distance and inaccuracy of sensor node positioning. Using this analysis, we quantify the robustness of WCL to various physical conditions and provide design guidelines, such as node placement and spacing, for the practical deployment of WCL. We also propose a power-efficient method for implementing WCL through a distributed cluster-based algorithm, that achieves comparable accuracy with its centralized counterpart.