Weighted Centroid Localization in Cell-Free mMIMO: A Stochastic Geometry Perspective

This paper investigates the use of the weighted centroid localization (WCL) method for user localization in cell-free massive MIMO (CF-mMIMO) networks. This low-complexity algorithm operates solely on received power measurements from pilot transmissions, requiring no prior channel information or estimation. It enables coarse localization, which is valuable for various network management tasks while incurring minimal cost and overhead. Using a stochastic geometry-based analytical framework, we derive approximations for the localization mean-square error, providing insights into the performance and limitations of WCL. We also present an exact expression for the localization error cumulative distribution function, along with alternative approximations based on moment matching. The predictive capability of the proposed analytical framework is validated through extensive simulations that incorporate key practical impairments, such as multipath propagation, spatially correlated shadowing, and pilot contamination, that are analytically intractable. These results confirm the practical utility of our analysis in supporting the design of CF-mMIMO networks to meet specific localization performance targets.