Unfolded Deep Graph Learning for Networked Over-the-Air Computation

Over-the-air computation (AirComp) has emerged as a promising technology that enables simultaneous transmission and computation through wireless channels. In this paper, we investigate the networked AirComp in multiple clusters allowing diversified data computation, which is yet challenged by the transceiver coordination and interference management therein. Particularly, we aim to maximize the multi-cluster weighted-sum AirComp rate, where the transmission scalar as well as receive beamforming are jointly investigated while addressing the interference issue. From an optimization perspective, we decompose the formulated problem and adopt the alternating optimization technique with an iterative process to approximate the solution. Then, we reinterpret the iterations through the principle of algorithm unfolding, where the channel condition and mutual interference in the AirComp network constitute an underlying graph. Accordingly, the proposed unfolding architecture learns the weights parameterized by graph neural networks, which is trained through stochastic gradient descent approach. Simulation results show that our proposals outperform the conventional schemes, and the proposed unfolded graph learning substantially alleviates the interference and achieves superior computation performance, with strong and efficient adaptation to the dynamic and scalable networks.