Modeling and Capacity Analysis of UAV-Assisted Three-Tier Heterogeneous Wireless Networks

Sudden disasters frequently disrupt terrestrial cellular infrastructure, severely degrading network capacity in affected regions and necessitating the rapid restoration of uplink connectivity for rescue and monitoring operations. To address this challenge, we propose a systematic capacity analysis framework for a three-tier emergency wireless network comprising a device access layer, an unmanned aerial vehicle (UAV) relay layer, and a backhaul layer. First, within the access layer, heterogeneous ground devices are modeled using a Poisson point process (PPP). We analyze the uplink transmissions under non-orthogonal multiple access (NOMA), deriving the coverage probability and ergodic capacity while accounting for imperfect successive interference cancellation (SIC). Next, in the relay layer, multiple concurrent flows are scheduled via time-frequency resource allocation across end-to-end UAV links, incorporating practical communication constraints and multihop packet-loss effects. To balance throughput and fairness, we introduce a joint resource allocation scheme that maximizes a novel satisfaction function. In the backhaul layer, the capacity between UAVs and base stations (BSs) is characterized under space-division multiple access (SDMA) with directional beamforming, explicitly modeling the impact of antenna-orientation jitter at both the UAV and BS sides. Finally, the overall end-to-end system capacity is formulated as the bottleneck capacity among the three tiers. Analytical and simulation results validate the accuracy of the proposed theoretical model. Furthermore, comparative evaluations demonstrate that the proposed resource allocation scheme for the UAV relay layer significantly improves allocation fairness among concurrent flows relative to conventional baselines.