A Retransmission Framework for Over-the-Air Computation Under Time-Varying Channel Fading

In computing-oriented communication scenarios, over-the-air computation (AirComp) directly computes results by leveraging the waveform superposition of wireless multiple access channels (MACs), eliminating the need to recover individual edge device (ED) signals. This approach enhances efficiency but faces challenges in maintaining low function distortion under deep fading. In this article, we propose a new retransmission-based AirComp framework that incorporates a channel prediction model to mitigate function distortion. Our framework introduces a performance analysis and optimization strategy involving cross-timeslot receiver combining. The optimal transmission coefficients and denoising factors are derived to minimize computing mean squared error (MSE) and reduce sum-power consumption. We design and analyze AirComp retransmission schemes that account for channel state information (CSI) estimation errors in the initial timeslot. Simulations validate the effectiveness of our framework, which markedly decreases the MSE and power consumption, e.g., by about 61% and 55%, compared to existing benchmarks, demonstrating its superior noise resilience and significantly alleviated the impact of imperfect CSI. These results highlight the potential of our framework to enable efficient and reliable AirComp in time-varying fading channels, particularly for resource-constrained Internet of Things (IoT) environments.