Hybrid Analog-Digital Channel Estimation and Beamforming: Training-Throughput Tradeoff

This paper develops hybrid analog-digital channel estimation and beamforming techniques for multiuser massive multiple-input multiple-output (MIMO) systems with limited number of radio frequency (RF) chains. For these systems, first, we design novel minimum-mean-squared error (MMSE) hybrid analog-digital channel estimator by considering both cases with perfect and imperfect channel covariance matrix knowledge. Then, we utilize the estimated channels to enable beamforming for data transmission. When the channel covariance matrices of all user equipments (UEs) are known perfectly, we show that there is a tradeoff between the training duration and throughput. Specifically, we exploit the fact that the optimal training duration that maximizes the throughput depends on the covariance matrices of all UEs, number of RF chains, and channel coherence time (T_c). We also show that the training time optimization problem can be formulated as a concave maximization problem where its global optimal solution can be obtained efficiently using existing tools. The analytical expressions are validated by performing extensive Monte Carlo simulations.