Learning-Based Slotted Over-the-Air Computation in Multi-Cluster Networks with Channel Awareness

Over-the-air computation (AirComp) enables simultaneous data collection and aggregation from massive devices. However, in the conventional one-slot AirComp approach, signal amplitude mismatches caused by time-varying channel fading inevitably lead to computation errors. In this paper, we propose a multi-slot framework for AirComp tasks with clustered sensors, which leverages time diversity to deal with the instantaneous intra-cluster channel gain disparity caused by time-varying fading, enhancing the performance of a multi-cluster AirComp system. In particular, each aggregation task is assigned across multiple time slots, with only one task served per time slot, and a channel gain threshold is set to guide transmission scheduling. Consequently, we intend to minimize the system computation error by jointly optimizing the transmission and scheduling strategies. The problem is an NP-hard mixed-integer nonlinear program optimization model with intricate coupling among optimization variables, which is solved with a soft actor-critic-based approach. Simulation results validate the convergence and performance of the proposed algorithm, demonstrating the effectiveness of our design.