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Channel Knowledge Map Construction via Guided Flow Matching

Ziyu Huang, Yong Zeng, Shen Fu, Xiaoli Xu, Hongyang Du

TL;DR

This work addresses the ill-posed problem of constructing location-specific CKMs by proposing a deterministic, physics-informed approach based on guided flow matching with linear transport (LT-GFM). Instead of diffusion-based noise removal, CKMs are generated by solving a learned ODE along a straight LT path that transports a Gaussian prior to the target distribution, significantly reducing inference steps. The framework unifies CGM and SCM construction, incorporating environmental semantics (e.g., building masks and edges) and enforcing Hermitian symmetry for SCMs to preserve physical validity. Empirical results show LT-GFM achieves higher distributional fidelity (lower FID) and sharper textures, while accelerating inference by about 25× compared to DDPMs, with near-optimal eigen-structure preservation (MSI ~ 0.90). This combination of accuracy, physical consistency, and real-time performance positions LT-GFM as a practical CKM solution for next-generation, environment-aware wireless networks.

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 Fréchet Inception Distance (FID) and accelerates inference speed by a factor of 25 compared to DDPMs.

Channel Knowledge Map Construction via Guided Flow Matching

TL;DR

This work addresses the ill-posed problem of constructing location-specific CKMs by proposing a deterministic, physics-informed approach based on guided flow matching with linear transport (LT-GFM). Instead of diffusion-based noise removal, CKMs are generated by solving a learned ODE along a straight LT path that transports a Gaussian prior to the target distribution, significantly reducing inference steps. The framework unifies CGM and SCM construction, incorporating environmental semantics (e.g., building masks and edges) and enforcing Hermitian symmetry for SCMs to preserve physical validity. Empirical results show LT-GFM achieves higher distributional fidelity (lower FID) and sharper textures, while accelerating inference by about 25× compared to DDPMs, with near-optimal eigen-structure preservation (MSI ~ 0.90). This combination of accuracy, physical consistency, and real-time performance positions LT-GFM as a practical CKM solution for next-generation, environment-aware wireless networks.

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 Fréchet Inception Distance (FID) and accelerates inference speed by a factor of 25 compared to DDPMs.
Paper Structure (15 sections, 7 equations, 4 figures, 4 tables, 2 algorithms)

This paper contains 15 sections, 7 equations, 4 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. Guided Flow Matching Framework for CKM Construction
  4. Generative CKM Flow via Optimal Transport
  5. Training and Inferring
  6. Training Phase
  7. Inference Phase
  8. Simulation Results
  9. Simulation Setup
  10. Performance Metrics
  11. Fréchet inception distance (FID)
  12. Matrix similarity index (MSI)
  13. Numerical Results
  14. Ablation Study
  15. Conclusion

Figures (4)

  • Figure 1: CKM constructions using environment semantics.
  • Figure 2: Framework for different tasks in CKM constructions.
  • Figure 3: The block diagram of the training and inference phases of the proposed CKM construction framework.
  • Figure 4: The comparisons of constructed CGM on different methods