Joint Access Point Activation and Power Allocation for Cell-Free Massive MIMO Aided ISAC Systems

Cell-free massive multiple-input multiple-output (MIMO)-aided integrated sensing and communication (ISAC) systems are investigated where distributed access points jointly serve users and sensing targets. We demonstrate that only a subset of access points (APs) has to be activated for both tasks, while deactivating redundant APs is essential for power savings. This motivates joint active AP selection and power control for optimizing energy efficiency. The resultant problem is a mixed-integer nonlinear program (MINLP). To address this, we propose a model-based Branch-and-Bound approach as a strong baseline to guide a semi-supervised heterogeneous graph neural network (HetGNN) for selecting the best active APs and the power allocation. Comprehensive numerical results demonstrate that the proposed HetGNN reduces power consumption by 20-25\% and runs nearly 10,000 times faster than model-based benchmarks.