MCMC-Based Sparse Bayesian Learning for Channel Estimation Using Gaussian Mixture Models

This paper investigates the downlink channel estimation problem for frequency division duplex (FDD) multi-user massive multiple-input multiple-output (MIMO) systems. We model this problem within the sparse Bayesian learning (SBL) framework, where all unknowns are treated as random variables. Due to limited scattering at the base station, the channel exhibits sparsity in the angular domain. By introducing Gaussian mixture priors to characterize the user equipment internal sparsity and partially shared sparsity, we develop a Markov chain Monte Carlo (MCMC) method to implement Bayesian inference and accurately estimate all random variables in the model, including the channel matrix. Experimental results demonstrate that the MCMC-based SBL channel estimation algorithm outperforms existing approaches by over 5 dB in multi-user scenarios while reducing pilot overhead.