  Deep neural networks (NNs) are considered a powerful tool for balancing the
performance and complexity of multiple-input multiple-output (MIMO) receivers
due to their accurate feature extraction, high parallelism, and excellent
inference ability. Graph NNs (GNNs) have recently demonstrated outstanding
capability in learning enhanced message passing rules and have shown success in
overcoming the drawback of inaccurate Gaussian approximation of expectation
propagation (EP)-based MIMO detectors. However, the application of the
GNN-enhanced EP detector to MIMO turbo receivers is underexplored and
non-trivial due to the requirement of extrinsic information for iterative
processing. This paper proposes a GNN-enhanced EP algorithm for MIMO turbo
receivers, which realizes the turbo principle of generating extrinsic
information from the MIMO detector through a specially designed training
procedure. Additionally, an edge pruning strategy is designed to eliminate
redundant connections in the original fully connected model of the GNN
utilizing the correlation information inherently from the EP algorithm. Edge
pruning reduces the computational cost dramatically and enables the network to
focus more attention on the weights that are vital for performance. Simulation
results and complexity analysis indicate that the proposed MIMO turbo receiver
outperforms the EP turbo approaches by over 1 dB at the bit error rate of
$10^{-5}$, exhibits performance equivalent to state-of-the-art receivers with
2.5 times shorter running time, and adapts to various scenarios.
