Wireless positioning in Non-Line-of-Sight (NLoS) scenarios presents significant challenges due to multipath effects that lead to biased measurements and reduced positioning accuracy. This paper revisits electromagnetic field theory related to diffraction and in the context of wireless positioning and proposes a novel positioning technique that greatly improves accuracy in NLoS environments dominated by diffraction. The method is applied to a critical public safety use case: precisely locating at-risk individuals within buildings, with a particular focus on improving 3D positioning and z-axis accuracy. By leveraging the Geometrical Theory of Diffraction (GTD), the approach introduces an innovative NLoS path length model and a new NLOS positioning technique. Using Fisher information analysis, we establish the conditions required for 3D positioning and derive lower bounds on positioning performance for both 3D and z-axis estimates for the proposed NLOS positioning technique. Additionally, we propose an algorithmic implementation of the proposed NLoS positioning method using non-linear least squares estimation, which we term D-NLS. The positioning performance of our proposed NLOs positioning technique is validated using an extensive ray-tracing simulation. The numerical results highlight the superiority of our approach in outdoor-to-indoor environments, which directly estimates NLoS path lengths and delivers significant performance enhancements over existing methods for both 3D and z-axis positioning scenarios.

The advent of 5G positioning techniques by 3GPP has unlocked possibilities for applications in public safety, vehicular systems, and location-based services. However, these applications demand accurate and reliable positioning performance, which has led to the proposal of newer positioning techniques. To further advance the research on these techniques, in this paper, we develop a 3GPP-compliant 5G positioning testbed, incorporating gNodeBs (gNBs) and User Equipment (UE). The testbed uses New Radio (NR) Positioning Reference Signals (PRS) transmitted by the gNB to generate Time of Arrival (TOA) estimates at the UE. We mathematically model the inter-gNB and UE-gNB time offsets affecting the TOA estimates and examine their impact on positioning performance. Additionally, we propose a calibration method for estimating these time offsets. Furthermore, we investigate the environmental impact on the TOA estimates. Our findings are based on our mathematical model and supported by experimental results.

For emergency response scenarios like firefighting in urban environments, there is a need to both localize emergency responders inside the building and also support a high bandwidth communication link between the responders and a command-and-control center. The emergency networks for such scenarios can be established with the quick deployment of Unmanned Aerial Vehicles (UAVs). Further, the 3D mobility of UAVs can be leveraged to improve the quality of the wireless link by maneuvering them into advantageous locations. This has motivated recent propagation measurement campaigns to study low-altitude air-to-ground channels in both 5G-sub6 GHz and 5G-mmWave bands. In this paper, we develop a model for the link in a UAV-assisted emergency location and/or communication system. Specifically, given the importance of Line-of-Sight (LoS) links in localization as well as mmWave communication, we derive a closed-form expression for the LoS probability. This probability is parameterized by the UAV base station location, the size of the building, and the size of the window that offers the best propagation path. An expression for coverage probability is also derived. The LoS probability and coverage probabilities derived in this paper can be used to analyze the outdoor UAV-to-indoor propagation environment to determine optimal UAV positioning and the number of UAVs needed to achieve the desired performance of the emergency network.