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

TL;DR

This paper introduces a diffusion model-based signal detection method that outperforms traditional maximum likelihood estimation in noise reduction, with theoretical backing and practical effectiveness demonstrated through simulations.

Contribution

The paper develops a novel mathematical theory for signal detection using stochastic differential equations and introduces a diffusion model approach with a scalable technique for various SNRs.

Findings

Lower symbol error rate (SER) for BPSK and QAM compared to ML estimation.

Reduced computational complexity of the proposed method.

Theoretical demonstration of noise reduction effectiveness.

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.