mmWave Channel Estimation via Compressive Covariance Estimation: Role of Sparsity and Intra-Vector Correlation

In this work, we address the problem of multiple-input multiple-output mmWave channel estimation in a hybrid analog-digital architecture, by exploiting both the underlying spatial sparsity as well as the spatial correlation in the channel. We accomplish this via compressive covariance estimation, where we estimate the channel covariance matrix from noisy low dimensional projections of the channel obtained in the pilot transmission phase. We use the estimated covariance matrix as a plug-in to the linear minimum mean square estimator to obtain the channel estimate. We present a new Gaussian prior model, inspired by sparse Bayesian learning (SBL), which incorporates parameters to capture the channel correlation in addition to sparsity. Based on this prior, we develop the Corr-SBL algorithm, which uses an expectation maximization procedure to learn the parameters of the prior and update the posterior channel estimates. A closed form solution is obtained for the maximization step based on fixed-point iterations. To facilitate practical implementation, an online version of the algorithm is developed which significantly reduces the latency at a marginal loss in performance. The efficacy of the prior model is studied by analyzing the normalized mean squared error in the channel estimate. Our results show that, when compared to a genie-aided estimator and other existing sparse recovery algorithms, exploiting both sparsity and correlation results in significant performance gains, even under imperfect covariance estimates obtained using a limited number of samples.