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

IoT systems typically involve separate data collection and processing, and face 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 when channel gains of nodes 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) framework for the sum estimation in fading channels. Compared with conventional data collection (one slot for each node) and AirComp (one slot for all nodes), MS-AirComp is an alternative policy that lies between them, exploiting multiple slots to improve channel gains so as to facilitate power control. Avoiding to obtain instantaneous channel gains of all nodes at the sink is a key point. Specifically, the transmissions are distributed over multiple 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. Theoretical analysis gives the closed-form of the computation error in fading channels, based on which the optimal parameters are found. Noticing that computation error tends to be reduced at the cost of more transmission power, a method is suggested to control the increase of transmission power. Simulations confirm that the proposed method can effectively reduce computation error, compared with state-of-the-art methods.