Frame Slotted ALOHA Access Control and Node Cardinality Estimation for UAV Ad Hoc Networks

This paper investigates a wireless ad hoc network node registration and access system based on a hybrid Frame Slotted ALOHA and Time Division Multiple Access mechanism for Unmanned Aerial Vehicle (UAV) charging station cluster management scenarios. Based on combinatorial mathematics and the inclusion–exclusion principle, the exact conditional probability distribution of the number of successfully accessed nodes within a single frame is derived, and a closed-form analytical expression for the total system access delay as a function of node population is established, revealing the existence of an optimal operating point. Building upon this foundation, a Dynamic Access Probability (DAP) mechanism is introduced, which adaptively regulates the number of nodes participating in contention per frame, effectively suppressing collisions and significantly reducing the overall system access delay. To address the difficulty of obtaining the real-time node count in practical systems, a Probability Model-based Maximum Likelihood Estimation algorithm is further proposed, which takes the number of successfully accessed nodes observable in each frame as input to infer the current number of unaccessed nodes. Simulation results demonstrate that the PMLE algorithm achieves superior performance in both estimation accuracy and stability, effectively supporting the accurate operation of the DAP mechanism.