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Generative Diffusion Models for High Dimensional Channel Estimation

Xingyu Zhou, Le Liang, Jing Zhang, Peiwen Jiang, Yong Li, Shi Jin

TL;DR

This work captures the structure of multiple-input multiple-output (MIMO) wireless channels via a deep generative prior encoded by DMs and develops a novel posterior inference method for channel reconstruction, which achieves high-fidelity channel recovery while reducing estimation latency by a factor of 10 compared to state-of-the-art schemes.

Abstract

Along with the prosperity of generative artificial intelligence (AI), its potential for solving conventional challenges in wireless communications has also surfaced. Inspired by this trend, we investigate the application of the advanced diffusion models (DMs), a representative class of generative AI models, to high dimensional wireless channel estimation. By capturing the structure of multiple-input multiple-output (MIMO) wireless channels via a deep generative prior encoded by DMs, we develop a novel posterior inference method for channel reconstruction. We further adapt the proposed method to recover channel information from low-resolution quantized measurements. Additionally, to enhance the over-the-air viability, we integrate the DM with the unsupervised Stein's unbiased risk estimator to enable learning from noisy observations and circumvent the requirements for ground truth channel data that is hardly available in practice. Results reveal that the proposed estimator achieves high-fidelity channel recovery while reducing estimation latency by a factor of 10 compared to state-of-the-art schemes, facilitating real-time implementation. Moreover, our method outperforms existing estimators while reducing the pilot overhead by half, showcasing its scalability to ultra-massive antenna arrays.

Generative Diffusion Models for High Dimensional Channel Estimation

TL;DR

This work captures the structure of multiple-input multiple-output (MIMO) wireless channels via a deep generative prior encoded by DMs and develops a novel posterior inference method for channel reconstruction, which achieves high-fidelity channel recovery while reducing estimation latency by a factor of 10 compared to state-of-the-art schemes.

Abstract

Along with the prosperity of generative artificial intelligence (AI), its potential for solving conventional challenges in wireless communications has also surfaced. Inspired by this trend, we investigate the application of the advanced diffusion models (DMs), a representative class of generative AI models, to high dimensional wireless channel estimation. By capturing the structure of multiple-input multiple-output (MIMO) wireless channels via a deep generative prior encoded by DMs, we develop a novel posterior inference method for channel reconstruction. We further adapt the proposed method to recover channel information from low-resolution quantized measurements. Additionally, to enhance the over-the-air viability, we integrate the DM with the unsupervised Stein's unbiased risk estimator to enable learning from noisy observations and circumvent the requirements for ground truth channel data that is hardly available in practice. Results reveal that the proposed estimator achieves high-fidelity channel recovery while reducing estimation latency by a factor of 10 compared to state-of-the-art schemes, facilitating real-time implementation. Moreover, our method outperforms existing estimators while reducing the pilot overhead by half, showcasing its scalability to ultra-massive antenna arrays.
Paper Structure (21 sections, 2 theorems, 49 equations, 14 figures, 1 table, 1 algorithm)

This paper contains 21 sections, 2 theorems, 49 equations, 14 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation and Preliminaries
  3. MIMO Channel Estimation
  4. Denoising Diffusion Generative Models
  5. Proposed Methods
  6. Diffusion Model-Based Channel Estimation
  7. Learning a DM for Wireless Channels
  8. Derivation of the Posterior Inference Algorithm
  9. DM-Based Quantized Channel Estimation
  10. Learning from Noisy Channel Realizations
  11. Numerical Results
  12. Experimental Details
  13. Full-Resolution Channel Estimation
  14. Low-Resolution Channel Estimation
  15. End-to-end Bit Error Rate (BER) Performance
  16. ...and 6 more sections

Key Result

Proposition 1

The update rule in (eq:condition_post) gives a posterior mean estimate of the latent variable $\mathbf{h}_{t-1}$ conditioned on $\mathbf{h}_t$ and $\mathbf{y}$, i.e., $\mathbb{E}[\mathbf{h}_{t-1}|\mathbf{h}_t,\mathbf{y}]=\int \mathbf{h}_{t-1} p_{t-1}(\mathbf{h}_{t-1}|\mathbf{h}_{t},\mathbf{y}){\rm d

Figures (14)

  • Figure 1: Block diagram of the proposed method, where (a) illustrates the forward diffusion involved in the training phase, and (b) depicts the reverse sampling step in the inference phase.
  • Figure 2: Block diagram of the SURE-DM's training flow.
  • Figure 3: NMSE with respect to the pilot density of the proposed DM-based channel estimator across various configurations (${\text{SNR} = \text{30}\;\text{dB}}$).
  • Figure 4: NMSE performance and estimation latency when $\alpha=1$.
  • Figure 5: NMSE performance when $\alpha=0.6$.
  • ...and 9 more figures

Theorems & Definitions (5)

  • Proposition 1
  • Remark 1
  • Remark 2
  • Proposition 2
  • Remark 3