Two-Stage Heterogeneous Graph Neural Network for RIS-Aided Physical-Layer Security

Abstract

This paper investigates physical-layer security (PLS) enabled by graph neural networks (GNNs). We propose a two-stage heterogeneous GNN (HGNN) to maximize the secrecy energy efficiency (SEE) of a reconfigurable intelligent surface (RIS)-assisted multi-input-single-output (MISO) system that serves multiple legitimate users (LUs) and eavesdroppers (Eves). The first stage formulates the system as a bipartite graph involving three types of nodes-RIS reflecting elements, LUs, and Eves-with the goal of generating the RIS phase shift matrix. The second stage models the system as a fully connected graph with two types of nodes (LUs and Eves), aiming to produce beamforming and artificial noise (AN) vectors. Both stages adopt an HGNN integrated with a multi-head attention mechanism, and the second stage incorporates two output methods: beam-direct and model-based approaches. The two-stage HGNN is trained in an unsupervised manner and designed to scale with the number of RIS reflecting elements, LUs, and Eves. Numerical results demonstrate that the proposed two-stage HGNN outperforms state-of-the-art GNNs in RIS-aided PLS scenarios. Compared with convex optimization algorithms, it reduces the average running time by three orders of magnitude with a performance loss of less than $4\%$. Additionally, the scalability of the two-stage HGNN is validated through extensive simulations.

Figures (8)

• Figure 1: An RIS-aided MISO PLS system, where a BS serves multiple LUs in the presence of multiple Eves.
• Figure 2: Heterogeneous graph presentation and key node feature components: 1) Stage 1 constructs a bipartite graph consisting of three types of nodes corresponding to the BS-LU links, the BS-Eves links, and the BS-RIS links; 2) Stage 2 constructs a fully-connected graph consisting of two types of nodes corresponding to the BS-RIS-LU links and BS-RIS-Eve links.
• Figure 3: Neural architecture of the two-stage HGNN: 1) Stage 1 comprises a feature augmentation layer, $T_1$ GNN layers, and an output layer. It maps $\{{{\bf X}_{\rm B\text{-}R}, {\bf X}_{\rm B\text{-}U}, {\bf X}_{\rm B\text{-}E}}\}$ to $\{\bm \Phi, {{\widetilde{\bf {\bf X}}^{[T_1]}_{\rm B\text{-}U}}}, {{\widetilde{\bf {\bf X}}^{[T_1]}_{\rm B\text{-}E}}}\}$. 2) Stage 2 consists of a feature initialization layer, $T_2$ GNN layers, and an output layer. It takes $\{\widetilde{\bf h}_k({\bm\Phi}), \widetilde{\bf f}_m({\bm\Phi})\}$ and $\{{{\widetilde{\bf {\bf X}}^{[T_1]}_{\rm B\text{-}U}}}, {{\widetilde{\bf {\bf X}}^{[T_1]}_{\rm B\text{-}E}}}\}$ as inputs and outputs $\{{{\bf w}}_{k}, {{\bf z}}_{m}\}$.
• Figure 4: Illustration of key processes in Stage 1: 1) The feature augmentation layer maps $\{{\bf X}_{\rm B\text{-}R}, {\bf X}_{\rm B\text{-}U},{\bf X}_{\rm B\text{-}E}\}$ to $\{\widetilde{\bf X}^{[0]}_{\rm B\text{-}R},\widetilde{\bf X}^{[0]}_{\rm B\text{-}U},\widetilde{\bf X}^{[0]}_{\rm B\text{-}E}\}$ via GAT on four subgraphs. 2) The $\tau$-th GNN layer maps $\{\widetilde{\bf X}^{[\tau-1]}_{\rm B\text{-}R},\widetilde{\bf X}^{[\tau-1]}_{\rm B\text{-}U},\widetilde{\bf X}^{[\tau-1]}_{\rm B\text{-}E}\}$ combined with the residual terms $\{\widetilde{\bf X}^{[\tau-1]}_{\rm B\text{-}R},\widetilde{\bf X}^{[\tau-1]}_{\rm B\text{-}U},\widetilde{\bf X}^{[\tau-1]}_{\rm B\text{-}E},{\bf X}_{\rm B\text{-}R}, {\bf X}_{\rm B\text{-}U},{\bf X}_{\rm B\text{-}E}\}$ to $\{\widetilde{\bf X}^{[\tau]}_{\rm B\text{-}R},\widetilde{\bf X}^{[\tau]}_{\rm B\text{-}U},\widetilde{\bf X}^{[\tau]}_{\rm B\text{-}E}\}$ via GAT on four subgraphs. 3) The output layer maps $\{{{\widetilde{ {\bf X}}^{[T_1]}_{\rm B\text{-}R}}}[l,:]\}$ to $\{\phi_{l}\}$ using an MLP.
• Figure 5: Illustration of key processes in Stage 2: 1) The feature initialization layer employs two separate MLPs to map $\{{\widetilde{\bf h}_k},{\widetilde{\bf f}_m}\}$ to intermediate values, respectively. These values are then summed with $\{{{\widetilde{{\bf X}}^{[T_1]}_{\rm B\text{-}U}}}[k,:],{{\widetilde{{\bf X}}^{[T_1]}_{\rm B\text{-}E}}}[m,:]\}$ to obtain $\{\widetilde{\mathbf{X}}^{[0]}_{\rm B\text{-}R\text{-}U}[k,:],\widetilde{\mathbf{X}}^{[0]}_{\rm B\text{-}R\text{-}E}[m,:]\}$. 2) The $\tau$-th GNN layer maps $\{\widetilde{\mathbf{X}}^{[\tau-1]}_{\rm B\text{-}R\text{-}U},\widetilde{\mathbf{X}}^{[\tau-1]}_{\rm B\text{-}R\text{-}E}\}$ combined with the residual terms $\{\widetilde{\mathbf{X}}^{[\tau-1]}_{\rm B\text{-}R\text{-}U},\widetilde{\mathbf{X}}^{[\tau-1]}_{\rm B\text{-}R\text{-}E},{\bf X}_{\rm B\text{-}R\text{-}U},{\bf X}_{\rm B\text{-}R\text{-}E}\}$ to $\{\widetilde{\mathbf{X}}^{[\tau]}_{\rm B\text{-}R\text{-}U},\widetilde{\mathbf{X}}^{[\tau]}_{\rm B\text{-}R\text{-}E}\}$ via GAT on four subgraphs. 3) The output layer uses two separate MLPs to map $\{\widetilde{\mathbf{X}}^{[T_2]}_{\rm B\text{-}R\text{-}U}[k,:],\widetilde{\mathbf{X}}^{[T_2]}_{\rm B\text{-}R\text{-}E}[m,:]\}$ to $\{{{\bf w}}_{k},{{\bf z}}_{m}\}$, respectively.