Achieving Cooperative Diversity in Over-the-Air Computation via Relay Selection

Abstract

In this paper, we consider a relay selection scheme and analyze the corresponding cooperative diversity for over-the-air computation (AirComp) systems, where multiple source nodes transmit their signals over a wireless multi-access channel to achieve fast data aggregation. We first formulate the power control problems to minimize the computation mean square error (MSE) at the fusion center, and introduce the concept of MSE outage probability and diversity order in the context of AirComp. When there are no relays but multiple receive antennas at the fusion center, we propose an antenna selection scheme that selects the best antenna for reception. We then characterize its outage performance and prove that the AirComp diversity order is equal to the number of receive antennas. Motivated by the analogy between multiple-relay systems and multiple-antenna systems, we develop a relay selection scheme in relay-aided AirComp where only the best relay is chosen to amplify and forward its received signal to the fusion center. We show that the relay selection scheme can achieve the full diversity order, which is equal to the number of relays, and an outage performance comparable to AirComp with the same number of receive antennas.