Learning to Beamform for Integrated Sensing and Communication: A Graph Neural Network With Implicit Projection Approach

Integrated sensing and communication (ISAC), as an important usage scenario of 6G, is capable of seamlessly integrating wireless sensing and communication for their mutual benefit. Taking full advantage of ISAC heavily relies on effectively solving resource allocation problems, which, however, are generally high-dimensional and non-convex, resulting in the optimization-based algorithms exhibiting high computation complexity and the traditional learning-based algorithms returning infeasible solutions. In this paper, we consider an ISAC scenario featured by multiple communication users and multiple sensing targets, aiming to develop an efficient and scalable algorithm that optimizes the radar transmit beampattern under the communication performance constraint. To this end, we propose a graph neural network (GNN) with implicit projection framework, where GNN captures the intricate interactions between communication users and sensing targets and meanwhile enables the joint optimization of communication and sensing beamforming matrices, and the projection module is applied to ensure the feasibility of the beamforming matrices design. Via capturing the permutation equivalence for communication matrices and the permutation invariance for the sensing matrix, the scalability of the proposed algorithm is guaranteed. Simulation results show that the proposed algorithm significantly reduces the computation complexity compared to the baselines, and achieves excellent algorithmic scalability and constraint satisfaction.