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Flow matching-based generative models for MIMO channel estimation

Wenkai Liu, Nan Ma, Jianqiao Chen, Xiaoxuan Qi, Yuhang Ma

TL;DR

The paper tackles the slow sampling bottleneck of diffusion-model based MIMO channel estimation by introducing a flow matching (FM) framework. It develops a conditional FM approach that learns a velocity field guiding a deterministic probability flow from a noisy input to the true channel, enabling efficient Euler-solver sampling with a straight-line trajectory. A time-conditioned UNet architectures processes complex CSI as real-valued channels, trained to predict the velocity field, and evaluated on CDL-C mmWave channels where it achieves high NMSE with only 1–20 iterations, significantly reducing computation compared to diffusion-based sampling. The results demonstrate strong accuracy and dramatic speedups, suggesting FM-based channel estimation is a viable, scalable method for real-time CSI in high-dimensional MIMO settings.

Abstract

Diffusion model (DM)-based channel estimation, which generates channel samples via a posteriori sampling stepwise with denoising process, has shown potential in high-precision channel state information (CSI) acquisition. However, slow sampling speed is an essential challenge for recent developed DM-based schemes. To alleviate this problem, we propose a novel flow matching (FM)-based generative model for multiple-input multiple-output (MIMO) channel estimation. We first formulate the channel estimation problem within FM framework, where the conditional probability path is constructed from the noisy channel distribution to the true channel distribution. In this case, the path evolves along the straight-line trajectory at a constant speed. Then, guided by this, we derive the velocity field that depends solely on the noise statistics to guide generative models training. Furthermore, during the sampling phase, we utilize the trained velocity field as prior information for channel estimation, which allows for quick and reliable noise channel enhancement via ordinary differential equation (ODE) Euler solver. Finally, numerical results demonstrate that the proposed FM-based channel estimation scheme can significantly reduce the sampling overhead compared to other popular DM-based schemes, such as the score matching (SM)-based scheme. Meanwhile, it achieves superior channel estimation accuracy under different channel conditions.

Flow matching-based generative models for MIMO channel estimation

TL;DR

The paper tackles the slow sampling bottleneck of diffusion-model based MIMO channel estimation by introducing a flow matching (FM) framework. It develops a conditional FM approach that learns a velocity field guiding a deterministic probability flow from a noisy input to the true channel, enabling efficient Euler-solver sampling with a straight-line trajectory. A time-conditioned UNet architectures processes complex CSI as real-valued channels, trained to predict the velocity field, and evaluated on CDL-C mmWave channels where it achieves high NMSE with only 1–20 iterations, significantly reducing computation compared to diffusion-based sampling. The results demonstrate strong accuracy and dramatic speedups, suggesting FM-based channel estimation is a viable, scalable method for real-time CSI in high-dimensional MIMO settings.

Abstract

Diffusion model (DM)-based channel estimation, which generates channel samples via a posteriori sampling stepwise with denoising process, has shown potential in high-precision channel state information (CSI) acquisition. However, slow sampling speed is an essential challenge for recent developed DM-based schemes. To alleviate this problem, we propose a novel flow matching (FM)-based generative model for multiple-input multiple-output (MIMO) channel estimation. We first formulate the channel estimation problem within FM framework, where the conditional probability path is constructed from the noisy channel distribution to the true channel distribution. In this case, the path evolves along the straight-line trajectory at a constant speed. Then, guided by this, we derive the velocity field that depends solely on the noise statistics to guide generative models training. Furthermore, during the sampling phase, we utilize the trained velocity field as prior information for channel estimation, which allows for quick and reliable noise channel enhancement via ordinary differential equation (ODE) Euler solver. Finally, numerical results demonstrate that the proposed FM-based channel estimation scheme can significantly reduce the sampling overhead compared to other popular DM-based schemes, such as the score matching (SM)-based scheme. Meanwhile, it achieves superior channel estimation accuracy under different channel conditions.

Paper Structure

This paper contains 12 sections, 18 equations, 4 figures, 1 table, 2 algorithms.

Table of Contents

  1. Introduction
  2. PRELIMINARIES AND PROBLEM FORMULATION
  3. MIMO Channel Estimation
  4. Flow Model and ODE Solver
  5. Proposed FLOW MATCHING-BASED CHANNEL ESTIMATION
  6. Conditional Flow Matching for Channel Estimation
  7. Training and Sampling for MIMO Channel Estimation
  8. Numerical Results
  9. Simulation Setup
  10. Performance Evaluation of the Proposed FM-based Channel Estimation
  11. CONCLUSION
  12. Acknowledgment

Figures (4)

  • Figure 1: Convolution-based UNet architecture.
  • Figure 2: Comparison of NMSE performance for various SNRs with length of pilot $T=75$, M=16, N=64, and the noise parameter $\tilde{\sigma}=0.1$.
  • Figure 3: Comparison of NMSE of FM-based method at various the noise parameter $\tilde{\sigma}$ with pilot length $T = 75$, and M=16, N=64.
  • Figure 4: Comparison of NMSE performance for various SNRs with length of pilot $T=145$, M=32, N=128, and the noise parameter $\tilde{\sigma}=0.1$.