On the Role of Sparsity and Intra-vector Correlation in mmWave Channel Estimation

In this paper, we study the role of sparsity and intra-vector correlation in the problem of multiuser multiple-input multiple-output millimeter wave channel estimation. In order to estimate the channel, we formulate a zero mean correlated Gaussian prior with covariance matrix designed for incorporating known correlation models and inducing spatial sparsity. Using the prior model, we develop a Bayesian algorithm based on evidence maximization to recover the correlated sparse vector. The solution to the hyperparameter update in the resulting algorithm is obtained as a fixed-point iteration. We empirically evaluate the proposed algorithm in terms of the normalized mean squared error in channel estimation under orthogonal pilots, and compare it against genie-aided estimators and standard sparse recovery algorithms. The results demonstrate that utilizing correlation can provide significant performance gains, even with imperfect channel covariance information.