Hybrid Digital and Analog Beamforming Design for Large-Scale Antenna Arrays

The potential of using of millimeter wave (mmWave) frequency for future wireless cellular communication systems has motivated the study of large-scale antenna arrays for achieving highly directional beamforming. However, the conventional fully digital beamforming methods which require one radio frequency (RF) chain per antenna element is not viable for large-scale antenna arrays due to the high cost and high power consumption of RF chain components in high frequencies. To address the challenge of this hardware limitation, this paper considers a hybrid beamforming architecture in which the overall beamformer consists of a low-dimensional digital beamformer followed by an RF beamformer implemented using analog phase shifters. Our aim is to show that such an architecture can approach the performance of a fully digital scheme with much fewer number of RF chains. Specifically, this paper establishes that if the number of RF chains is twice the total number of data streams, the hybrid beamforming structure can realize any fully digital beamformer exactly, regardless of the number of antenna elements. For cases with fewer number of RF chains, this paper further considers the hybrid beamforming design problem for both the transmission scenario of a point-to-point multiple-input multiple-output (MIMO) system and a downlink multi-user multiple-input single-output (MU-MISO) system. For each scenario, we propose a heuristic hybrid beamforming design that achieves a performance close to the performance of the fully digital beamforming baseline. Finally, the proposed algorithms are modified for the more practical setting in which only finite resolution phase shifters are available. Numerical simulations show that the proposed schemes are effective even when phase shifters with very low resolution are used.

I. Introduction

Millimeter wave (mmWave) technology is one of the promising candidates for future generation wireless cellular communication systems to address the current challenge of bandwidth shortage [1]–[3]. The mmWave signals experience severe path loss, penetration loss and rain fading as compared to signals in current cellular band (3G or LTE) [4]. However, the shorter wavelength at mmWave frequencies also enables more antennas to be packed in the same physical dimension, which allows for large-scale spatial multiplexing and highly directional beamforming. This leads to the advent of large-scale or massive multiple-input multiple-output (MIMO) concept for mmWave communications. Although the principles of the beamforming are the same regardless of carrier frequency, it is not practical to use conventional fully digital beamforming schemes [5]–[9] for large-scale antenna arrays. This is because the implementation of fully digital beamforming requires one dedicated radio frequency (RF) chain per antenna element, which is prohibitive from both cost and power consumption perspectives at mmWave frequencies [10].