Robust Design for Multi-Carrier Multi-Relay Assisted Over-the-Air Computation Networks With Bounded Channel Uncertainties

Over-the-air computation (AirComp) has attracted vast attention due to its fast aggregation capacity for large scale distributed data. In order to further improve the computation performance of AirComp, we consider a multi-relay assisted AirComp network over a multi-carrier broadband channel, which can benefit from the multi-carrier diversity. Moreover, we take into account a more practical scenario with bounded channel uncertainties, and the worst-case computational mean square error (CMSE) is minimized by jointly designing the transmit and receiving scaling factors, as well as the amplification coefficient of each relay under the transmit power constraints. To handle the intractable non-convex robust optimization problem, we develop an efficient alternating optimization algorithm based on the cutting-set method (CSM). Numerical results are provided to validate the effectiveness of our proposed schemes.