Distributed Combinatorial Optimization of Downlink User Assignment in mmWave Cell-free Massive MIMO Using Graph Neural Networks

Millimeter wave (mmWave) cell-free massive MIMO (CF mMIMO) is a promising solution for future wireless communications. However, its optimization is non-trivial due to the challenging channel characteristics. We show that mmWave CF mMIMO optimization is largely an assignment problem between access points (APs) and users due to the high path loss of mmWave channels, the limited output power of the amplifier, and the almost orthogonal channels between users given a large number of AP antennas. The combinatorial nature of the assignment problem, the requirement for scalability, and the distributed implementation of CF mMIMO make this problem difficult. In this work, we propose an unsupervised machine learning (ML) enabled solution. In particular, a graph neural network (GNN) customized for scalability and distributed implementation is introduced. Moreover, the customized GNN architecture is hierarchically permutation-equivariant (HPE), i.e., if the APs or users of an AP are permuted, the output assignment is automatically permuted in the same way. To address this combinatorial problem, we relax it to a continuous problem, and introduce an information entropy-inspired penalty term. The training objective is then formulated using the augmented Lagrangian method (ALM). The test results show that the realized sum-rate outperforms that of the generalized serial dictatorship (GSD) algorithm and is very close to an upper bound in a small network scenario, while the upper bound is impossible to obtain in a large network scenario.