Adaptive Uplink Scheduling and UAV Association in UAV-Assisted OFDMA Cellular Networks: A Game-Theoretical Approach

The rapid deployment of large-scale UAV-assisted cellular networks has emerged as an effective solution for delivering high-speed data services to ground users in areas where terrestrial base station (BS) infrastructure is inadequate. In this paper, we address a crucial problem in these networks by aiming to maximize the uplink total rate through joint optimization of Unmanned Aerial Vehicle (UAV) association and Orthogonal Frequency Division Multiple Access (OFDMA) subcarrier assignment. However, due to the mobility of pedestrians, fixed association and subcarrier assignments lack adaptation, and centralized optimization does not scale well, especially in large-scale UAV settings. To overcome these challenges, we formulate the joint optimization problem as an exact Constrained Potential Game, called the Subcarrier Assignment and UAV Association Game (SAUAG), based on game theory. In SAUAG, each user selfishness selects the most appropriate strategy with the objective of maximizing their own utility while still fulfilling the system’s Quality of Service (QoS) constraints. We analyze the conditions under which a Nash Equilibrium (NE) exists and provide rigorous proof of its existence.To mitigate the computational complexity typically associated with Best Response Dynamics (BRD), we introduce the Two-Step Better Response (TS-BR) algorithm, which significantly reduces the computational load while ensuring convergence to an NE. Furthermore, we proposed a distributed algorithm based on sequential play and demonstrated its effectiveness in achieving NE convergence. Through comprehensive simulations, the superiority of the proposed SAUAG and TS-BR algorithms was demonstrated, showing their potential in enhancing network performance and adaptability in UAV-assisted OFDMA networks with mobile ground users.