Graph Neural Network-based End-to-End Learning for Multi-User MIMO Systems

End-to-end (E2E) learning has recently been proposed to jointly design the modulator and symbol detector by using deep neural networks (DNNs). However, existing schemes lack sufficient capability to cancel multi-user interference (MUI) in uplink multi-user multiple-input multiple-output (MU-MIMO) systems. In this paper, we propose a graph neural network (GNN)-based E2E learning scheme that employs a GNN-based modulator to generate learned constellation points, and a GNN-based detector to cancel MUI. They are jointly optimized to minimize the symbol error rate (SER) performance loss. Simulation results demonstrate that the proposed E2E outperforms existing schemes with a predefined modulator. Specifically, it achieves an approximate 2 dB gain in a high MUI environment and surpasses even the maximum-likelihood (ML) detector in a low MUI condition.

💡 Research Summary

The paper addresses the critical challenge of multi‑user interference (MUI) in uplink multi‑user multiple‑input multiple‑output (MU‑MIMO) systems by proposing a novel end‑to‑end (E2E) learning framework that jointly designs the transmitter’s modulator and the receiver’s detector using graph neural networks (GNNs). Traditional deep‑learning‑based E2E schemes typically employ multilayer perceptrons (MLPs) for both sides but fail to capture the relational structure among users, leading to sub‑optimal performance especially when the number of users or antennas grows. By contrast, a GNN naturally encodes pairwise relationships as edges in a graph, making it well‑suited for modeling both the geometric relationships among constellation points at the transmitter and the interference patterns among users at the receiver.

The proposed architecture consists of two GNN modules: GNN_tx (the transmitter) and GNN_rx (the receiver). In GNN_tx, each node corresponds to a candidate constellation point, and edges encode the normalized Euclidean distance between points. Starting from an arbitrary set of complex points, the network performs L rounds of message passing (propagation, aggregation, readout) followed by a power‑normalization step that enforces the average‑power constraint. The resulting learned constellation set, denoted (\hat{\Omega}), replaces conventional fixed constellations (e.g., QAM) and is broadcast to all users by the base station after offline training.

At the receiver, GNN_rx integrates expectation propagation (EP) with a GNN. EP iteratively computes cavity means and variances for the soft symbol estimates, providing an initial probability distribution for each real‑valued component of the transmitted symbols. The GNN then refines these cavity probabilities by exploiting the graph where each node represents a real‑valued symbol component and edges capture the interference relationship between symbols of different users. Unlike prior work (e.g., GEPNet) that separately estimates real and imaginary parts, the proposed GNN directly outputs complex‑symbol probabilities, simplifying the pipeline. After each EP iteration, the refined probabilities are fed back into EP, and the process repeats for T iterations. The final refined probabilities are used to compute a cross‑entropy loss between the estimated and true user messages; gradients are back‑propagated jointly through both GNN_tx and GNN_rx, enabling simultaneous optimization of the constellation and the detector.

Simulation results are presented for a 4‑by‑4 MU‑MIMO system with 16‑QAM signaling under various signal‑to‑noise ratios (SNR) and MUI levels. In high‑MUI scenarios, the proposed E2E scheme achieves roughly a 2 dB gain at a symbol error rate (SER) of (10^{-4}) compared with the state‑of‑the‑art GEPNet that uses a predefined modulator. In low‑MUI conditions, the method even outperforms the optimal maximum‑likelihood (ML) detector, demonstrating that the learned constellation and GNN‑based interference cancellation can surpass classical optimal detection when interference is mild. Importantly, the online inference complexity of the combined GNN_tx/GNN_rx system is comparable to that of GEPNet, making the approach feasible for real‑time deployment in 5G/6G base stations.

Key contributions of the work are: (1) a unified GNN‑based E2E framework that co‑optimizes modulation and detection, (2) explicit modeling of MUI through graph edges, which yields robustness to increasing user/antenna counts, (3) a practical mechanism for distributing the learned constellation to users, and (4) empirical evidence that the approach can both exceed conventional deep‑learning baselines and, in certain regimes, surpass the theoretical ML benchmark. The authors suggest future extensions to larger‑scale networks, robustness to channel estimation errors, and hardware‑efficient implementations of the GNN modules.