We propose GRAM-DIFF, a Gram-matrix-guided diffusion framework for semi-blind multiple input multiple output (MIMO) channel estimation. Recent diffusion-based estimators leverage learned generative priors to improve pilot-based channel estimation; but they do not exploit second-order structural information estimated from data symbols. In practical systems, the channel Gram matrix can be estimated from received symbols and it provides realization-level information about channel subspace structure. The proposed method integrates a pre-trained angular-domain diffusion prior with two complementary guidance mechanisms: a novel Gram-matrix guidance term that enforces second-order consistency during the reverse diffusion process, and likelihood guidance from pilot observations. Signal-to-noise ratio (SNR)-matched initialization and adaptive guidance scaling ensure stability and low inference latency. Simulations on 3GPP and QuaDRiGa channel models demonstrate consistent normalized mean-squared error (NMSE) improvements over deterministic diffusion baselines, achieving 4 to 6 dB SNR gains at an NMSE of 0.1 over the baseline in Fest et al. (2024). The framework exhibits graceful degradation under coherence-time constraints, smoothly reverting to likelihood-guided diffusion when data-based Gram estimates become unreliable.

翻译：我们提出了GRAM-DIFF，一种用于半盲多输入多输出（MIMO）信道估计的格拉姆矩阵引导扩散框架。现有的基于扩散的估计器利用学习到的生成先验来改进基于导频的信道估计，但它们并未利用从数据符号中估计出的二阶结构信息。在实际系统中，可以从接收符号中估计出信道格拉姆矩阵，它提供了关于信道子空间结构的实现级信息。所提出的方法将预训练的角域扩散先验与两种互补的引导机制相结合：一种新颖的格拉姆矩阵引导项，在反向扩散过程中强制执行二阶一致性；以及来自导频观测的似然引导。信噪比（SNR）匹配的初始化和自适应引导缩放确保了稳定性和低推理延迟。在3GPP和QuaDRiGa信道模型上的仿真表明，与确定性扩散基线相比，该方法在归一化均方误差（NMSE）上取得了持续的改进，在NMSE为0.1时，相较于Fest等人（2024）的基线，实现了4至6 dB的SNR增益。该框架在相干时间约束下表现出优雅的性能退化，当基于数据的格拉姆矩阵估计变得不可靠时，能够平滑地回退到似然引导的扩散。