Multi-Slot Over-The-Air Computation in Fading Channels

IoT systems typically involve separate data collection and processing, and the former faces the scalability issue when the number of nodes increases. For some tasks, only the result of data fusion is needed. Then, the whole process can be realized in an efficient way, integrating the data collection and fusion in one step by over-the-air computation (AirComp). Its shortcoming, however, is signal distortion (computation error) when channel gains are different, which cannot be well solved by transmission power control alone in times of deep fading. To address this issue, in this paper, we propose a multi-slot over-the-air computation (MS-AirComp) method for the sum estimation in fading channels. Specifically, the transmissions are distributed over N slots and a threshold of channel gain is set for distributed transmission scheduling. Each node transmits its signal only once, in the slot when its channel gain first gets above the threshold, or in the last slot when its channel gain remains below the threshold. In this way, MS-AirComp exploits multiple slots to improve channel gains so as to facilitate power control. Analysis and simulations confirm that the proposed method effectively reduces the computation error meanwhile controlling transmission power, compared with state-of-the-art methods.