A Mathematical Framework for Radio Resource Assignment in UAV-Aided Vehicular Communications

Unmanned Aerial Vehicle (UAV), when equipped as communication relays, offer a flexible solution to extend Vehicle-to-Vehicle (V2V) communications beyond fixed infrastructure and Non-Line-of-Sight constraints. In this setting, the allocation of radio resources, across time, frequency and space through beamforming, is challenged by the mobility of Connected and Autonomous Vehicles (CAVs) and their temporal dependencies, as access opportunities depend on prior transmission outcomes such as queue backlog or failed attempts. This paper proposes a Radio Resource Assignment (RRA) framework for UAV-aided V2V networks with beamforming-capable UAV relays. The model discretizes time and space to account for mobility and to track the movement of groups of CAVs across beam segments. The model also incorporates Time Division Multiple Access (TDMA)-based scheduling, beam activation constraints, and realistic traffic generation patterns. Analytical expressions are derived for per-user success probability and system throughput under both, ideal and realistic conditions, and they are validated against simulations, confirming the accuracy of the proposed approximations. Numerical results highlight trade-offs involving UAV altitude and resource allocation interval, while a heuristic beam-activation optimization strategy is shown to further enhance performance, achieving up to 12% throughput gain over uniform activation.