Relay Selection for Over-the-Air Computation Achieving Both Long Lifetime and High Reliability

In a general wireless sensor network, a sink node collects data from each node successively and then post-processes the data to obtain useful information. However, conventional methods have a scalability problem: the data collection/processing time increases with the number of nodes, and frequent transmission collisions degrade spectrum efficiency. If only statistical values of the data are needed, using over-the-air computation (AirComp) can efficiently perform data collection and computation. However, AirComp also has its problems: when the channel gain of a node is too low, (i) the transmission power of that node will be high, decreasing the lifetime of that node and the entire network, and (ii) sometimes, the computation error still occurs even though the maximal transmission power is used. To jointly solve these two problems, in this paper we investigate the relay communication for AirComp and study a relay selection protocol. The basic method selects an ordinary node with a good channel condition as a relay node, considering both computation error and power consumption. This method is further enhanced to explicitly consider network lifetime in relay selection. Extensive simulation evaluations confirm that the proposed method helps to prolong the lifetime of the entire network and reduce computation errors as well.