Graph Neural Network DPD

Unlike traditional per-element DPD, GNN DPD represents the entire antenna array as a graph structure. Each node corresponds to an individual power amplifier (PA) branch, while edges encode the spatial relationships and mutual coupling between elements. This allows the model to explicitly learn how distortion in one PA affects its neighbors, capturing the cross-coupling physics that conventional models ignore. The graph topology can be static (based on physical array geometry) or dynamically learned during training.

GNN DPD employs message passing—the core mechanism of graph neural networks—to propagate information between connected nodes. During each iteration:

• Each PA node aggregates hidden state vectors from its neighbors
• The aggregated information is transformed via a neural network function to update the node's representation
• Multiple message-passing layers enable the model to capture both direct coupling (adjacent elements) and indirect coupling (second-order effects across the array) This iterative exchange allows the GNN to build a distributed understanding of the array's nonlinear behavior.

A critical advantage of GNN DPD is its inherent scalability. Because the graph neural network uses weight sharing across nodes—the same neural network parameters are applied to every PA—the model complexity does not explode with array size. A GNN trained on a 16-element sub-array can generalize to a 64-element or 128-element array without retraining the core architecture. This contrasts sharply with Volterra MIMO DPD, where the number of coefficients grows combinatorially with the number of antennas.

GNN DPD naturally integrates with beamforming-aware linearization. As beamforming weights change, the effective active impedance seen by each PA shifts, altering its nonlinear characteristics. The GNN can accept beamforming coefficients as edge features or node conditioning inputs, allowing a single model to adapt its predistortion across all steering angles. This eliminates the need for separate DPD lookup tables per beam direction, a major limitation of conventional approaches in hybrid beamforming architectures.

By embedding the physical structure of the array into the model architecture, GNN DPD introduces a powerful inductive bias. The model inherently understands that:

• Distortion effects are local (strongest between adjacent elements)
• The array exhibits permutation symmetry (the same physics applies to each PA)
• Spatial relationships are translation-invariant (coupling depends on relative position, not absolute index) This domain knowledge dramatically reduces the amount of training data required compared to black-box deep neural networks, enabling few-shot adaptation to new array configurations.

GNN DPD is well-suited for over-the-air (OTA) linearization architectures. When feedback is captured from a far-field observation receiver, the received signal contains the combined distortion from all PAs and their mutual coupling. The GNN can be trained end-to-end using this composite feedback signal, learning to decompose the far-field distortion back into per-element predistortion coefficients. This enables single-receiver DPD for the entire array, significantly reducing feedback hardware complexity.

A signal processing method to mitigate unintended electromagnetic interaction between adjacent antenna elements. While traditional approaches use matrix inversion or adaptive filtering, GNN-based DPD learns the coupling topology directly from data.

• Models both linear coupling (signal leakage) and nonlinear coupling (distortion products mixing between branches)
• GNN message-passing layers naturally implement distributed cancellation across the array
• Critical for maintaining beam pattern integrity in mmWave phased arrays

The variation in impedance seen by an individual power amplifier due to beam steering in a phased array. As beamforming weights change, the load-pull effect causes each PA's nonlinear behavior to shift dynamically.

• Creates a time-varying distortion profile that static DPD cannot track
• GNNs capture how impedance changes propagate through the coupling network
• Enables beamforming-aware linearization without per-beam calibration tables

A linearization method that explicitly models the S-parameter coupling network between antenna elements to decouple and linearize the array's radiated field. GNN-based approaches extend this by learning the coupling matrix from operational data.

• Traditional coupling matrix DPD requires network analyzer measurements of all S-parameters
• GNNs can infer the effective coupling topology during online training
• Combines physical structure (known array geometry) with learned parameters (unknown coupling coefficients)

A dimensionality reduction technique for massive MIMO linearization that identifies and compensates for the dominant spatial modes of nonlinear distortion. GNNs extend this by learning nonlinear manifold representations of the distortion space.

• Reduces computational complexity from O(N²) to O(K) where K << N elements
• GNN autoencoders can discover low-dimensional latent representations of array distortion
• Enables scalable linearization for arrays with 64 to 256+ elements

A complexity-reduction technique that identifies and selects only the most significant basis functions from a large candidate set. GNNs inherently perform sparse modeling by learning which inter-element connections matter most.

• Traditional Volterra MIMO models suffer from exponential basis function growth
• GNN attention mechanisms naturally prune weak coupling edges during training
• Results in compact models suitable for real-time FPGA implementation