Accurate Analysis of Weighted Centroid Localization

Source localization of primary users (PUs) is a spectrum awareness feature that can be very useful in enhancing the functionality of cognitive radios (CRs). When the cooperating CRs have limited information about the PU, weighted centroid localization (WCL) based on received signal strength measurements represents an attractive low-complexity solution. This paper proposes a new analytical framework to accurately calculate the performance of WCL based on the statistical distribution of the ratio of two quadratic forms in normal variables. In particular, we derive an analytical expression for the root mean square error and an exact expression for the cumulative distribution function of the two-dimensional location estimate. The proposed framework accounts for the presence of independent and identically distributed shadowing as well as correlated shadowing with distance-dependent intensity. The methodology is general enough to include the analysis of the one-dimensional error, which leads also to the evaluation of the bias of the position estimate. Numerical results confirm that the analytical framework is able to predict the performance of WCL capturing all the essential aspects of propagation as well as CR network spatial topology.