Joint Activity Detection and Channel Estimation for Asynchronous mMTC: A Model-Driven GNN Approach

This work investigates the joint activity detection and channel estimation (JADCE) problem in asynchronous uplink massive machine-type communications (mMTC), where a model-driven graph neural network (GNN) approach is developed under the variational inference framework. Specifically, we first formulate the JADCE problem as an equivalent channel estimation task and derive its optimal variational distribution. Then, all potential access time slots of each device are modeled as nodes to construct a homogeneous graph, and the learnable GNN layers are integrated with the variational inference process to efficiently infer the associated hyperparameters. To further reduce the computational complexity and enhance estimation performance, a residual-based aggregation strategy and a multi-task update architecture are incorporated into the GNN design. Finally, simulation results show that our approach achieves better performance in both channel estimation and activity detection compared with benchmarks, while maintaining acceptable computational complexity and strong scalability.