Channel Knowledge Map Construction via Guided Flow Matching

2026-01-06

arXiv.org

AI Summary

This work addresses the ill-posed inverse problem in constructing high-fidelity Channel Knowledge Maps (CKMs) under sparse channel observations, where accuracy and real-time performance are notoriously difficult to balance. The authors propose a Linear Transport-guided Flow Matching (LT-GFM) framework that models CKM generation as an ordinary differential equation (ODE) following a linear optimal transport trajectory, thereby discarding the iterative denoising mechanism of conventional diffusion models and drastically reducing inference steps. By integrating environmental semantic embeddings with Hermitian symmetry constraints, the method enables physically informed joint modeling of channel gain maps and spatial correlation graphs. Experiments demonstrate that LT-GFM achieves 25× faster inference than DDPM while attaining higher distributional fidelity at a lower Fréchet Inception Distance (FID).

Technology Category

• Planning, Routing, and Scheduling: Planning with Language Models
• Machine Learning: Large Multimodal Models (LMMs)
• Computer Vision: Diffusion Models for Vision

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems

Abstract

The efficient construction of accurate channel knowledge maps (CKMs) is crucial for unleashing the full potential of environment-aware wireless networks, yet it remains a difficult ill-posed problem due to the sparsity of available location-specific channel knowledge data. Although diffusion-based methods such as denoising diffusion probabilistic models (DDPMs) have been exploited for CKM construction, they rely on iterative stochastic sampling, rendering them too slow for real-time wireless applications. To bridge the gap between high fidelity and efficient CKM construction, this letter introduces a novel framework based on linear transport guided flow matching (LT-GFM). Deviating from the noise-removal paradigm of diffusion models, our approach models the CKM generation process as a deterministic ordinary differential equation (ODE) that follows linear optimal transport paths, thereby drastically reducing the number of required inference steps. We propose a unified architecture that is applicable to not only the conventional channel gain map (CGM) construction, but also the more challenging spatial correlation map (SCM) construction. To achieve physics-informed CKM constructions, we integrate environmental semantics (e.g., building masks) for edge recovery and enforce Hermitian symmetry for property of the SCM. Simulation results verify that LT-GFM achieves superior distributional fidelity with significantly lower Fr\'echet Inception Distance (FID) and accelerates inference speed by a factor of 25 compared to DDPMs.

Problem

• Channel Knowledge Map
• ill-posed problem
• data sparsity
• real-time wireless applications
• spatial correlation map

Innovation

• guided flow matching
• channel knowledge map
• linear optimal transport
• deterministic ODE
• physics-informed generation