GNN-Based Structured Bayesian Inference for Multi-Grid Localized Statistical Channel Modeling

Localized statistical channel modeling (LSCM) is an efficient channel modeling framework recently proposed for wireless network optimization which learns the angular power spectrum (APS) of the downlink channel from the beam-wise reference signal receiving power (RSRP). However, the conventional LSCM is only based on RSRP measurements from one single geographical grid and ignores the inherent property of spatial consistency over wireless channels, resulting in suboptimal performance. To this end, we consider the LSCM in a manner of multiple geographical grids and further propose a novel graph-based approach for the multi-grid LSCM, called the accelerated Markovian variational Bayesian graph neural network (AMVB-GNN). The AMVB-GNN leverages a heterogeneous Markovian graph representation to capture the structured sparsity in the channel APSs and employs refined variational Bayesian inference (VBI) to learn the APSs of multiple grids. Notably, the design of AMVB-GNN eliminates the exact matrix inversion operations required in conventional VBI, thereby enhancing computational efficiency. Additionally, we demonstrate the partial permutation equivalence of AMVB-GNN, ensuring both interpretability and reliability. To address the issue of the demand for ground-truth APSs labels, we propose an unsupervised training loss function. Extensive simulation experiments validate the effectiveness and efficiency of the proposed AMVB-GNN model.