Joint Optimization for Over-the-Air Computation in AF Relay-Assisted Cognitive Radio Networks

This paper investigates the over-the-air computation (AirComp) in a cognitive radio (CR) data network, which contains a primary network, a secondary network, and an amplifyand-forward (AF) relay. There are sensors in each network that transmit data to their corresponding access point (AP). The aim of the AF relay is to improve the computation performance of the two networks. We study the sum mean-square-error (MSE) minimization problem, named as SMSE-min problem, subject to the transmit power constraints at the AF relay and the sensors in the two networks. It is not trivial to obtain the optimal solution of the formulated non-convex problem due to the coupled optimization variables. We propose an alternating optimization algorithm for alternatively optimizing four sub-problems about the aggregation beamforming at two APs, transmit scaling factors at the sensors, and the AF matrix at the relay, and obtain the locally optimal solution, where the closed-form solution can be obtained in each sub-problem. Numerical results show the superior sum MSE performance of our proposed scheme