  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.
