Bayesian mmWave Channel Estimation via Exploiting Joint Sparse and Low-Rank Structures

We consider the problem of channel estimation for millimeter wave (mmWave) systems, where both the base station and the mobile station employ a single radio frequency (RF) chain to reduce the hardware cost and power consumption. Recent real-world channel measurements reveal that the mmWave channels incur a certain amount of spread over the angular domains due to the scattering clusters. The angular spreads give rise to a joint sparse and low-rank channel matrix in the angular domain. To utilize this joint sparse and low-rank structure, we address the channel estimation problem within a Bayesian framework. Specifically, we adopt a matrix factorization formulation and translate the problem of channel estimation into one of searching for two-factor matrices. To encourage a joint sparse and low-rank solution, independent sparsity-promoting priors are placed on entries of the two-factor matrices, which aims to promote sparse factor matrices with only a few non-zero columns. Based on the proposed prior model, we develop a variational Bayesian inference method for the mmWave channel estimation. The simulation results show that our proposed method presents a considerable performance improvement over the state-of-the-art compressed sensing-based channel estimation methods.