A New Probability Density Function for Minimizing Geometric Dilution of Precision in Location-Aware Wireless Communications

Cellular site planners have long used propagation models for optimizing an architecture deployment strategy. The foundation of these models are a plethora of theoretical results that all contribute to a probabilistic understanding of this phenomenon. In lower-band frequencies, coverage and propagation phenomena were sufficient considerations for legacy infrastructure deployment; however, as cellular technology probes uncharted millimeter wave spectra and beyond, it is natural to inquire as to whether other metrics could contribute to an informed infrastructure deployment. As the benchmark goals for positioning accuracy grow more ambitious and location-aware communications becomes a reality, we argue that localization accuracy should also play a prominent role in cellular infrastructure deployment planning. To this end, we submit a new closed-form probability density function (PDF) to characterize the angular difference of a pair of base stations and a mobile terminal. The importance of the angular difference is demonstrated by showing that the Cramér-Rao lower bound for localization is solely a function of it and measurement accuracy. Further, we submit a computationally tenable algorithm for producing the required PDF. To demonstrate the power of the density, we show some base station deployments that are guaranteed to yield geometrically favorable environments for positioning. Finally, we demonstrate how this new distribution outperforms numerical analysis when planning wireless network architecture deployment for location-aware communications.