Generative Diffusion Model-Based Variational Inference for MIMO Channel Estimation

Efficient and accurate channel estimation with low pilot overhead is essential for massive multiple-input multiple-output (MIMO) wireless communication systems to achieve high spectral and energy efficiency. This work proposes a novel variational inference method for channel estimation by utilizing the generative diffusion model as a prior. Specifically, we first train a generative diffusion model to learn the score, i.e., the gradient of the log-prior distribution, of MIMO channels to serve as a prior in the channel estimation process. The training process is unsupervised and does not rely on specific pilot structures and signal-to-noise ratios (SNRs). Thus, the learned prior is generalizable and can be directly used for channel estimation under different pilot signals and SNRs without requiring re-training. Then, we propose a variational inference method to infer the posterior distribution of the MIMO channel under given pilots and received measurements by incorporating the learned prior. Finally, we estimate the MIMO channels by sampling from the derived posterior distribution. Our simulations under various wireless propagation environments and antenna architectures demonstrate that the proposed approach achieves over 5 dB reduction in normalized mean square error and faster channel recovery compared to state-of-the-art channel estimators. Additionally, the proposed approach exhibits robust estimation performance when the test channel distribution shifts from the training distribution, even outperforming the benchmarks without distribution shifts.