Graph Neural Networks versus Gated Recurrent Units Only for approximate bayesian MU-MIMO detectors

Multi-User Multiple-Input Multiple-Output (MU-MIMO) communications is one of the technological cornerstones of cellular systems, starting from 4G, up to 5G and beyond. Representation of this kind of transmission via a factor graph has been proven to be an effective way to define message-passing algorithms for detection. These algorithms may be classified into two main categories. The first class relies on vector message passing algorithms such as Vector Expectation Propagation (VEP), Vector Approximate Message Passing (VAMP) for example. This approach offers great performance at the cost of high computational complexity. The second class is composed of scalar message-passing algorithms on the graph that aim to reduce the complexity at the cost of performance degradation. Both of these approaches use some approximations during inference to estimate the posterior symbol distribution. Machine learning has received growing attention to cope with these approximations. In this work, we investigate the hybrid use of Graph Neural Networks (GNN), which can exploit the bipartite graph structure of the transmission, and Gated Reccurent Units (GRU), which can exploit the long-term dependency throughout the iterative process. We show that, contrarily to AMP, for VEP the GNN aggregation step has only a limited contribution to the overall performance and can be skipped to substantially reduce the algorithm complexity.