Hybrid Analog and Digital Beamforming Design for Channel Estimation in Correlated Massive MIMO Systems

Abstract

In this paper, we study the channel estimation problem in correlated massive multiple-input-multiple-output (MIMO) systems with a reduced number of radio-frequency (RF) chains. Importantly, other than the knowledge of channel correlation matrices, we make no assumption as to the structure of the channel. To address the limitation in the number of RF chains, we employ hybrid beamforming, comprising a low dimensional digital beamformer followed by an analog beamformer implemented using phase shifters. Since there is no dedicated RF chain per transmitter/receiver antenna, the conventional channel estimation techniques for fully-digital systems are impractical. By exploiting the fact that the channel entries are uncorrelated in its eigen-domain, we seek to estimate the channel entries in this domain. Due to the limited number of RF chains, channel estimation is typically performed in multiple time slots. Under a total energy budget, we aim to design the hybrid transmit beamformer (precoder) and the receive beamformer (combiner) in each training time slot, in order to estimate the channel using the minimum mean squared error criterion. To this end, we choose the precoder and combiner in each time slot such that they are aligned to transmitter and receiver eigendirections, respectively. Further, we derive a water-filling-type expression for the optimal energy allocation at each time slot. This expression illustrates that, with a low training energy budget, only significant components of the channel need to be estimated. In contrast, with a large training energy budget, the energy is almost equally distributed among all eigen-directions. Simulation results show that the proposed channel estimation scheme can efficiently estimate correlated massive MIMO channels within a few training time slots. TABLE I SUMMARY OF RELATED WORKS Frequency Channel Model Assumption Estimation Technique Reference CS-based [15], [21]-[24], [27], [29], [30] mmWave Parameteric Sparsity Beam training followed by CS-based resolution refining [28] ESPRIT [25] MUSIC [31] PASTd [32], [33] Microwave and mmWave Kronecker Known Channel Correlations MMSE [34], [35] training approach, while a subsequent CS algorithm refines the resolution. As an alternative to adaptive CS algorithms, traditional random CS approaches exploiting pseudo-random weights are used in a phased array MIMO system with a hybrid structure [24], [29]. The authors of [23] apply random CS with simpler analog beamformers, where the network of switches is replaced with the phase-shifter network 1 . In [30], the CSbased channel estimation algorithm extended to a mmWave communication system equipped with one-bit analog-to-digital converters (ADCs) and HB. The authors of [25], [31]-[33] propose non-CS-based techniques to estimate the channel in massive MIMO systems with the hybrid precoder/combiner structure. Assuming the parametric channel model, the authors in [31] exploit twodimensional beamspace multiple signal classification (MU-SIC) to estimate the path directions followed by a leasts...