Joint Optimization for Power-Splitting Relay-Assisted Over-the-Air Computation Networks

Relays can significantly improve the performance of over-the-air computation (AirComp) networks, especially when the sensors and the fusion center (FC) are far apart. However, the relay’s energy supply is a common constraint factor of relay-assisted AirComp networks. To address the power constrained issue, we introduce power-splitting (PS) relays into an AirComp network, where the relays can harvest energy from the transmitted signals of the sensors and the FC by the PS scheme and then forward the signals to the FC by using the harvested energy. Our objective is to minimize the computational mean square error (CMSE) at the FC by jointly optimizing the transmit coefficients at the sensors, the amplify and forward (AF) coefficients and PS ratios at the relays, and the de-noising factor at the FC, under the individual power constraints at the sensors and relays. The optimization problem is highly non-convex and difficult to solve. By exploiting the inexact block coordinate descent (IBCD) algorithm and the constrained concave-convex procedure (CCCP), we propose an IBCD-CCCP algorithm to solve the optimization problem effectively. Numerical results are presented to demonstrate the effectiveness of our scheme as compared to the baseline methods.