MMSE-Based Channel Estimation for Hybrid Beamforming Massive MIMO with Correlated Channels

In this paper, we study the channel estimation problem in microwave correlated massive multiple-input-multiple-output systems with reduced number of radio-frequency chains. We exploit the knowledge of the transmit and receive correlation between the antennas. Leveraging the fact that the channel entries are uncorrelated in its eigen-domain, we seek to estimate the channel in this domain. Due to reduced number of radio-frequency chains, channel estimation is performed in multiple time slots. Under a total energy budget, we aim to optimally design the hybrid precoder and combiner in each training time slot, in order to estimate the channel using the minimum mean squared error criterion. We show that the optimal precoder and combiner in each time slot are aligned to transmitter and receiver eigen-directions, respectively. The energy allocation of each eigen-direction determines the significance of each eigen-direction; more energy is allocated to the stronger eigen-directions. At low training energy budget, only significant part of the channel needs to be estimated. At high training energy budget, the energy is equally distributed among all eigen-directions. Simulation results show that the proposed channel estimation scheme can efficiently estimate correlated massive multiple-input-multiple-output channels within a few training time slots.