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Erasing Noise in Signal Detection with Diffusion Model: From Theory to Application

Xiucheng Wang, Peilin Zheng, Nan Cheng

TL;DR

This work addresses robust signal detection under AWGN with variable SNR by introducing a diffusion-model based intelligent signal transmission theory grounded in stochastic differential equations. It establishes a formal link between the diffusion denoising process and recovering the transmitted signal component $H s$ from the noisy observation $r$, showing that for any given SNR there exists a diffusion timestep $t$ and a scaling factor $\alpha$ to align distributions. It then proposes a DM-based detector using a diffusion transformer (DiT) with complexity $O(n^2)$ that estimates $h_t$ and $\epsilon_t$ to obtain $\hat{H s}$ and $\hat{s}$. Empirical results on BPSK and high-order QAM show significant SER reductions over ML with strong generalization across SNR and without fine-tuning, highlighting potential for 6G applications.

Abstract

In this paper, a signal detection method based on the denoise diffusion model (DM) is proposed, which outperforms the maximum likelihood (ML) estimation method that has long been regarded as the optimal signal detection technique. Theoretically, a novel mathematical theory for intelligent signal detection based on stochastic differential equations (SDEs) is established in this paper, demonstrating the effectiveness of DM in reducing the additive white Gaussian noise in received signals. Moreover, a mathematical relationship between the signal-to-noise ratio (SNR) and the timestep in DM is established, revealing that for any given SNR, a corresponding optimal timestep can be identified. Furthermore, to address potential issues with out-of-distribution inputs in the DM, we employ a mathematical scaling technique that allows the trained DM to handle signal detection across a wide range of SNRs without any fine-tuning. Building on the above theoretical foundation, we propose a DM-based signal detection method, with the diffusion transformer (DiT) serving as the backbone neural network, whose computational complexity of this method is $\mathcal{O}(n^2)$. Simulation results demonstrate that, for BPSK and QAM modulation schemes, the DM-based method achieves a significantly lower symbol error rate (SER) compared to ML estimation, while maintaining a much lower computational complexity.

Erasing Noise in Signal Detection with Diffusion Model: From Theory to Application

TL;DR

This work addresses robust signal detection under AWGN with variable SNR by introducing a diffusion-model based intelligent signal transmission theory grounded in stochastic differential equations. It establishes a formal link between the diffusion denoising process and recovering the transmitted signal component from the noisy observation , showing that for any given SNR there exists a diffusion timestep and a scaling factor to align distributions. It then proposes a DM-based detector using a diffusion transformer (DiT) with complexity that estimates and to obtain and . Empirical results on BPSK and high-order QAM show significant SER reductions over ML with strong generalization across SNR and without fine-tuning, highlighting potential for 6G applications.

Abstract

In this paper, a signal detection method based on the denoise diffusion model (DM) is proposed, which outperforms the maximum likelihood (ML) estimation method that has long been regarded as the optimal signal detection technique. Theoretically, a novel mathematical theory for intelligent signal detection based on stochastic differential equations (SDEs) is established in this paper, demonstrating the effectiveness of DM in reducing the additive white Gaussian noise in received signals. Moreover, a mathematical relationship between the signal-to-noise ratio (SNR) and the timestep in DM is established, revealing that for any given SNR, a corresponding optimal timestep can be identified. Furthermore, to address potential issues with out-of-distribution inputs in the DM, we employ a mathematical scaling technique that allows the trained DM to handle signal detection across a wide range of SNRs without any fine-tuning. Building on the above theoretical foundation, we propose a DM-based signal detection method, with the diffusion transformer (DiT) serving as the backbone neural network, whose computational complexity of this method is . Simulation results demonstrate that, for BPSK and QAM modulation schemes, the DM-based method achieves a significantly lower symbol error rate (SER) compared to ML estimation, while maintaining a much lower computational complexity.
Paper Structure (14 sections, 3 theorems, 33 equations, 10 figures, 2 tables)

This paper contains 14 sections, 3 theorems, 33 equations, 10 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. System Model and Problem Formulation
  4. DM-based Intelligent signal Transmission Theory
  5. SDE of Diffusion Procedure
  6. Relationship Between Diffusion Variable and Noisy Symbol
  7. DM-Based signal detection Method
  8. Simulation Results
  9. Implementation
  10. Comparisons with Other Methods
  11. Performance Analysis for High-Order QAM Modulation and Large-Scale MIMO
  12. Numerical Analysis on Theorem \ref{['theorem-1']} and Theorem \ref{['theorem-2']}
  13. Ablation Study
  14. Conclusion

Key Result

Theorem 1

Assuming the $\mathbb{E}_{\bm{x}_{0}\sim q(\bm{x}_{0})}\left[\|\bm{x}_{0}\|^{2}\right]=\gamma$, for any given $\mathbb{E}_{\bm{s}\sim\mathcal{S}}\left[\|\bm{Hs}\|^2\right]$ and noise density $\sigma^{2}$ of noisy channel, when following equation can be obtained.

Figures (10)

  • Figure 1: Block diagram of the signal detection method, (a) is the traditional signal detection system, and (b) is the proposed DM-based signal detection system.
  • Figure 2: The illustration of the inferencing and training procedure of the proposed DM on the left, and the details of the NN architecture on the right.
  • Figure 3: SER on different SNR and $N_r$ for different signal detection methods with BPSK modulation.
  • Figure 4: SER on different SNR and $N_r$ for different signal detection methods with 4-QAM modulation.
  • Figure 5: SER on 4$\times$4 MIMO with high-order QAM.
  • ...and 5 more figures

Theorems & Definitions (8)

  • Remark 1
  • Theorem 1
  • proof
  • Remark 2
  • Theorem 2
  • proof
  • Theorem 3
  • proof