Channel estimation is a fundamental task in communication systems and is critical for effective demodulation. While most works deal with a simple scenario where the measurements are corrupted by the additive white Gaussian noise (AWGN), this work addresses the more challenging scenario where both AWGN and structured interference coexist. Such conditions arise, for example, when a sonar/radar transmitter and a communication receiver operate simultaneously within the same bandwidth. To ensure accurate channel estimation in these scenarios, the sparsity of the channel in the delay domain and the complicate structure of the interference are jointly exploited. Firstly, the score of the structured interference is learned via a neural network based on the diffusion model (DM), while the channel prior is modeled as a Gaussian distribution, with its variance controlling channel sparsity, similar to the setup of the sparse Bayesian learning (SBL). Then, two efficient posterior sampling methods are proposed to jointly estimate the sparse channel and the interference. Nuisance parameters, such as the variance of the prior are estimated via the expectation maximization (EM) algorithm. The proposed method is termed as DM based SBL (DM-SBL). Numerical simulations demonstrate that DM-SBL significantly outperforms conventional approaches that deal with the AWGN scenario, particularly under low signal-to-interference ratio (SIR) conditions. Beyond channel estimation, DM-SBL also shows promise for addressing other linear inverse problems involving structured interference.

翻译：信道估计是通信系统中的一项基础任务，对有效解调至关重要。大多数工作处理的是测量值仅受加性高斯白噪声（AWGN）污染的简单场景，而本研究则解决了AWGN与结构化干扰共存的更具挑战性的场景。例如，当声纳/雷达发射机与通信接收机在同一带宽内同时工作时，就会出现此类情况。为确保在这些场景下实现精确的信道估计，本研究联合利用了信道在时延域的稀疏性以及干扰的复杂结构。首先，基于扩散模型（DM）的神经网络学习结构化干扰的分数，而信道先验被建模为高斯分布，其方差控制信道稀疏性，类似于稀疏贝叶斯学习（SBL）的设置。随后，提出了两种有效的后验采样方法来联合估计稀疏信道和干扰。先验方差等冗余参数通过期望最大化（EM）算法进行估计。所提出的方法被称为基于DM的SBL（DM-SBL）。数值仿真表明，DM-SBL显著优于处理AWGN场景的传统方法，尤其是在低信干比（SIR）条件下。除信道估计外，DM-SBL在解决其他涉及结构化干扰的线性逆问题方面也显示出潜力。