Edge Feature Encoding

Encoded features must reflect the governing physics of radio propagation. A path loss value of -120 dB should map to a numerically distinct vector space compared to -60 dB, preserving the logarithmic nature of signal decay.

• Encode distance-dependent features like path loss and delay spread
• Preserve reciprocity when applicable (edge features should be symmetric for TDD systems)
• Avoid encoding physically impossible combinations that could mislead the message-passing function

Raw edge features like channel gain (spanning orders of magnitude from 10⁻¹² to 10⁻⁶) destabilize neural network training. Apply logarithmic transformation and z-score normalization to constrain values to a stable range.

• Convert linear power values to dB or dBm scale
• Normalize to zero mean and unit variance across the training set
• Use min-max scaling to bound features within [0, 1] or [-1, 1] for activation function compatibility

A single edge should encode heterogeneous properties into a unified vector. Concatenate static features (distance, antenna gain) with dynamic features (instantaneous fading, interference power) to capture both long-term topology and short-term channel conditions.

• Static features: path loss exponent, antenna bore sight angle, terrain type
• Dynamic features: small-scale fading coefficient, current SINR, buffer status
• Categorical features: line-of-sight indicator, link type (handover vs. interference)

Wireless links are inherently asymmetric due to differing transmit powers, noise figures, and interference environments. Edge features must encode directionality explicitly, either through directed edge vectors or by concatenating forward and reverse channel measurements.

• Represent a directed edge from BS to UE with features: [Tx power, Rx sensitivity, interference at UE]
• For undirected GNN architectures, create two directed edges with distinct feature vectors
• Include relative orientation features like angle-of-arrival and angle-of-departure

Augment raw measurements with graph-theoretic features that capture the edge's structural role. The importance of a link in message passing depends not just on its own properties but on its position within the broader interference topology.

• Edge betweenness centrality: how many shortest paths cross this edge
• Local clustering coefficient: how interconnected the edge's endpoints are
• Jaccard similarity of neighbor sets between the two connected nodes
• Graph distance to the nearest cell edge or coverage hole

For dynamic GNNs processing time-series topology snapshots, edge features must maintain temporal consistency. Encode not just the current state but also delta features that capture how the edge has changed since the previous timestep.

• Include first-order differences: Δpath loss, Δinterference power
• Encode exponential moving averages to smooth noisy measurements
• Add a stale flag indicating if the measurement exceeds its coherence time
• Align feature indices across timesteps for consistent model interpretation

The numerical representation of signal attenuation between a transmitter and receiver as an edge feature. This is the most critical physical-layer parameter in cellular GNNs.

• Typically encoded in decibels (dB) using log-distance models
• Captures large-scale fading effects due to distance and obstacles
• Often combined with shadow fading as a stochastic component
• Directly informs the message-passing weight between base station and user equipment nodes

A multi-dimensional edge feature encoding both magnitude and phase of the wireless channel response. Unlike scalar path loss, this captures the complex-valued nature of the propagation environment.

• Includes small-scale fading coefficients (Rayleigh, Rician)
• Encoded as real and imaginary parts or magnitude/phase pairs
• Essential for beamforming and MIMO precoding optimization
• Enables GNNs to reason about coherent combining and interference nulling

Geometric edge attributes derived from the Euclidean distance between node pairs, serving as a fundamental inductive bias for spatial relationships in cellular topologies.

• Raw distance in meters as a continuous feature
• Inverse distance weighting to emphasize proximity
• Binned distance categories for discretized learning
• Often combined with antenna height differences for 3D topologies

A normalized edge weight quantifying how strongly a transmission from one cell impacts the Signal-to-Interference-plus-Noise Ratio (SINR) at a receiver in another cell.

• Derived from path loss ratios between serving and interfering links
• Values range from 0 (no interference) to 1 (dominant interferer)
• Forms the basis of the interference graph adjacency matrix
• Critical input for GNN-based resource block allocation and power control

An edge feature encoding the likelihood or frequency of user equipment transitioning between two cells, transforming mobility patterns into graph structure.

• Derived from historical handover event counters
• Encoded as a probability or log-count normalized by time
• Includes directional information (A→B vs B→A)
• Enables GNNs to predict future handover sequences and optimize mobility robustness

The practice of concatenating heterogeneous connection properties into a single edge feature vector, allowing the GNN to jointly reason about diverse physical and logical relationships.

• Combines path loss, distance, interference, and load differentials
• Requires feature normalization to prevent scale dominance
• May include one-hot encoded categorical attributes (e.g., LOS/NLOS)
• Enables rich, context-aware message functions in MPNN frameworks