Joint Optimization for Multi-Antenna AF-Relay Aided Over-the-Air Computation

Benefiting from exploiting the waveform superposition property in the multi-access channels, over-the-air computation (AirComp) has emerged as a promising technique to swiftly compute functions of data from a large number of sensors. To enlarge the wireless coverage area, a two-phase multi-antenna amplify-and-forward (AF)-relay aided AirComp system is considered, where all the sensors transmit sensing data during both two phases in a half-duplex AF relay system with direct links. We present efficient designs for optimizing the transmit scalar vectors at the sensors, the AF matrix at the relay, and the aggregation vector at the access point, which aims to minimize the mean-square-error (MSE) subject to the transmit power budgets at the relay and the sensors, respectively. To solve the resultant multiple variables coupled non-convex optimization problem efficiently, we develop an alternating optimization-based algorithm to obtain locally optimal solutions. Specifically, in each iteration, closed-form expressions are derived for each optimizing variable. Finally, the computation distortion improvement of our proposed design over baseline schemes is demonstrated via simulations.