  As one of the core technologies for 5G systems, massive multiple-input
multiple-output (MIMO) introduces dramatic capacity improvements along with
very high beamforming and spatial multiplexing gains. When developing efficient
physical layer algorithms for massive MIMO systems, message passing is one
promising candidate owing to the superior performance. However, as their
computational complexity increases dramatically with the problem size, the
state-of-the-art message passing algorithms cannot be directly applied to
future 6G systems, where an exceedingly large number of antennas are expected
to be deployed. To address this issue, we propose a model-driven deep learning
(DL) framework, namely the AMP-GNN for massive MIMO transceiver design, by
considering the low complexity of the AMP algorithm and adaptability of GNNs.
Specifically, the structure of the AMP-GNN network is customized by unfolding
the approximate message passing (AMP) algorithm and introducing a graph neural
network (GNN) module into it. The permutation equivariance property of AMP-GNN
is proved, which enables the AMP-GNN to learn more efficiently and to adapt to
different numbers of users. We also reveal the underlying reason why GNNs
improve the AMP algorithm from the perspective of expectation propagation,
which motivates us to amalgamate various GNNs with different message passing
algorithms. In the simulation, we take the massive MIMO detection to exemplify
that the proposed AMP-GNN significantly improves the performance of the AMP
detector, achieves comparable performance as the state-of-the-art DL-based MIMO
detectors, and presents strong robustness to various mismatches.
