On the Terminal Location Uncertainty in Elliptical Footprints: Application in Air-to-Ground Links

Wireless transmitters (Txs) that radiate downward in a direction often generate circular footprints on the ground. The configurational flexibility of these footprints is inherently limited as coverage adjustments are restricted to variations in radius, the only parameter available for tuning. This simplification is inadequate for scenarios that require asymmetric coverage, extended service areas, or dynamic footprint adaptation due to antenna tilt or changes in altitude of unmanned aerial vehicles (UAVs). In specific scenarios, the use of elliptical cells can offer increased flexibility for providing user coverage due to unique network characteristics. For example, an elliptical footprint can be produced when a practical directional antenna with unequal azimuth and elevation half-power beamwidths is used in high-speed railway networks. Another common scenario involves the production of an elliptical footprint when an airborne Tx radiates at an angle by tilting its directional antenna by a few degrees. This paper aims to investigate for the first time the association between the random location of the user within an elliptical coverage area and the performance of a wireless communication link considering these scenarios. We assume a UAV as a Tx, although a tall cellular base station tower could also be employed without losing generality. To gain a deeper understanding of the impact of random location, we derive the relevant distance and signal-to-noise ratio metrics and examine the outage probability for a single-user link, as well as the throughput in a multiuser scenario. This analysis accounts for both random terminal locations and fading impairments in both cases. The findings provide valuable insights into the performance of comparable wireless systems.