Spectrum Graph Neural Network

A foundational GNN mechanism where nodes representing transmitters or frequency bins iteratively exchange hidden state vectors with their neighbors. Each message passing layer aggregates information from adjacent nodes using a permutation-invariant function (e.g., sum, mean, or max), then updates the node's representation via a learned neural network. After K layers, each node contains information from its K-hop neighborhood, enabling the model to reason about local interference patterns and global spectral occupancy. This approach is inherently distributed, making it suitable for decentralized spectrum coordination in cognitive radio networks.

The preprocessing step that defines the topology of the spectrum graph. Nodes represent transmitter-receiver pairs or individual frequency bins. Edges are weighted by the mutual interference between nodes, typically calculated using path loss models, geographic distance, or measured signal-to-interference-plus-noise ratio (SINR). Key construction strategies include:

• Threshold-based: Connect nodes if interference exceeds a predefined power level
• K-nearest neighbors: Connect each node to its K most interfering neighbors
• Delaunay triangulation: For spatial deployments, creating a planar graph Accurate graph construction is critical, as it determines the inductive bias of the GNN.

An enhancement over basic message passing where the GNN learns dynamic edge weights during training. Instead of using fixed, pre-computed interference values, a self-attention mechanism computes the importance of each neighboring node's message. This allows the model to:

• Focus on the most critical interferers in a dense environment
• Adapt to changing propagation conditions without re-engineering the graph
• Handle heterogeneous nodes with different transmit powers or priorities The attention coefficients are normalized across neighbors using a softmax function, producing a weighted sum that is robust to noisy or incomplete graph topologies.

A unified attention mechanism that simultaneously models dependencies across spatial dimensions (e.g., antenna elements or transmitter locations) and temporal dimensions (e.g., symbol periods or spectrum sensing intervals). Unlike separate spatial and temporal processing blocks, this approach computes attention scores across the full spatio-temporal tensor, capturing:

• Cross-term correlations: How interference at one location evolves over time
• Multi-user dynamics: Coordinated transmission patterns across the network This is particularly effective for massive MIMO beamforming and predictive spectrum access, where spatial and temporal features are deeply entangled.

A decision-making framework where a GNN serves as the policy network for a reinforcement learning agent. The agent observes the current spectrum graph state, and the GNN outputs Q-values for actions such as frequency selection or power adjustment. Key advantages:

• Generalization: The GNN's permutation invariance allows the policy to generalize to networks with varying numbers of nodes
• Scalability: A single trained policy can be deployed across different network topologies
• Multi-agent coordination: GNNs can facilitate implicit coordination between distributed agents sharing the same learned policy This approach is used for dynamic spectrum sharing in 5G and beyond.