Graph Neural Network-Based Joint Access Probability and Power Control in Slotted ALOHA Networks with SINR Capture

In slotted ALOHA with spatial reuse, each device-to-device (D2D) link controls how often it transmits and at what power. Learning-based designs that combine these decisions model reception as packet collisions with a few discrete power levels or target uplink access with successive interference cancellation. This study consider N D2D pairs with SINR capture, Rayleigh fading and a per-link energy budget, and choose a continuous access probability and transmit power for every link to maximize proportional fairness. Its derive the per-link throughput in closed form and validate it by Monte Carlo simulation, prove that full power is the best common power when the budget is inactive and that the exact access step needs one round of local exchange, and build a reference solver that returns Karush–Kuhn–Tucker points. Per-link power control raises the geometric-mean throughput over the best common power by 3.6–29.4% on average, depending on density and budget. A single message-passing graph neural network, trained without labels on 10–50 links, recovers 92.2% of this gain at N = 20 and 93.0% at N = 50–200 (98.3–99.7% of the reference throughput), whereas fractional power control tuned per instance recovers at most 33%. With interference-based neighbour truncation, the network needs 5 message rounds instead of at least 78 and reaches the solver’s utility 4.4–19 times faster. All results hold within the stated model and test ranges.