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

This paper designs 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 square error (MMSE) hybrid analog-digital channel estimator by considering both perfect and imperfect channel covariance matrix knowledge cases. 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 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 {for some system parameter settings} where its global optimal solution is obtained efficiently using existing tools. In particular, when the base station equipped with $64$ antennas and $1$ RF chain is serving one single antenna UE, $T_c=128$ symbol periods ($T_s$) and signal to noise ratio of $10$dB, we have found that the optimal training durations are $4T_s$ and $20T_s$ for highly correlated and uncorrelated Rayleigh fading channel coefficients, respectively. The analytical expressions are validated by performing numerical and extensive Monte Carlo simulations.