A Novel Hybrid Digital-Analog Beamforming Algorithm
with Uplink Training for TDD Systems
Yong Wang, Shu Fang, Binyan Lu, Chengyu Lu, Yiqian Xu
National Key Laboratory of Science and Technology on Communications,
University of Electronic Science and Technology of China,
Chengdu, China
Email: fangshu@uestc.edu.cn
Abstract—In contrast to conventional multiple-input-
multiple-output (MIMO) systems, precoding in millimeter
wave (mmWave) massive MIMO is envisioned to achieve
consider-able capacity improvement, but at the cost of highly
hardware complexity. As a cost-effective alternative, hybrid
digital-analog beamforming has drawn considerable attention.
In most conventional theoretical researches, ignoring practical
implementation, perfect channel state information (CSI) is
always assumed. However, whether FDD or TDD, in hybrid
beamforming architecture, it is extremely challenging for base
station (BS) to obtain perfect CSI. In this paper, based on the
channel reciprocity in TDD systems, we propose a novel hybrid
digital-analog beamforming algorithm with uplink training to
maximize the capacity performance. Owing to uplink training,
the requirement of CSI at eNodeB to conduct hybrid beamfor-
ming is graciously avoided. With practical RF hardware and
unit modulus constraints, the proposed scheme provides useful
low-complexity solutions in practical hybrid beam-forming
system designs. Simulation results validate the efficiency of the
proposed scheme compared with some existing hybrid
beamforming schemes.
Keywords-MIMO, mmWave, hybrid digital-analog beamfor-
ming, CSI, uplink training, RF hardware and unit modulus
constraints
I. INTRODUCTION
Millimeter wave (mmWave) communication is the new
spectral frontier for 5G wireless communication system [1],
[2], [3]. In mmWave bands, large chunks of underutilized
spectrum are available, enabling it to be potentially utilized
to provide significant system capacity improvements. And
thanks to the small wavelength, a large number of antenna
elements could be packed into small form factors, which is
appealing for massive MIMO. Large arrays can provide the
beamforming gain to overcome the main disadvantage of
mmWave communication, i.e., high pathloss, and achieve
good link quality. Furthermore, multiple data streams, via
precoding, could improve spectral efficiency and allow
systems to approach capacity limits [4], [5]. Thus, mmWave
massive MIMO system will potentially draw increasing
attention.
For traditional MIMO systems, there are many digital
beamforming (DB) design approaches in the past years,
mainly with few number of antennas, which could utilize all
the degrees of freedom of the channel to simultaneously
transmit multiple data streams. In DB, each antenna element
is required to be connected with a dedicated radio frequency
(RF) chain. Obviously, DB for large antenna arrays is
infeasible as it requires a huge number of RF chains, which
dramatically increases the system complexity, cost and
power consumption. Thus, the hybrid beamforming (HB)
structure consisting of a high-dimensional analog beam-
former in RF domain cascaded with a low-dimensional
digital beamformer in baseband via a small number of RF
chains will be suitable, as a tradeoff between performance
and cost [6]. And analog beamformer is often implemented
using a network of phase shifters [7], [8], which imposes unit
modulus constraints.
The followings are some works investigating the HB
design approaches. In [9], the analog and digital beam-
forming was considered to be designed jointly for both
spatial diversity and multiplexing systems. In [10], the HB
algorithm was developed to minimize the received signals'
mean-squared error with interference. Matching pursuit (MP)
algorithm [10] is utilized to design the HB architecture for
single-user massive MIMO systems in [6], [11]. Orthogonal
matching pursuit (OMP) algorithm [12] [13] operates the
orthogonalization processing on the selected dictionary
vector at each step, not as nonorthogonal in MP algorithm,
which naturally offers reasonably good performance.
Considering to the HB design for multiuser massive MIMO
systems, the author in [14] proposed a low-complexity HB
scheme, named phased zero-forcing (PZF), via ZF precoding
to maximize the sum rate of all users to approach the
performance of the traditional baseband ZF precoding. It is
considered as a virtually optimal linear precoding scheme in
massive MIMO systems. In [15], a convex optimization
based HB algorithm is proposed to minimize the transmit
power and maximize the signal to interference plus noise
ratio (SINR) in the worst case. Codebook based HB design is
another widely considered orientation, where the codebook
based HB schemes in [16], [17] are designed for wideband
mmWave wireless networks.
CSI obtained at eNodeB will directly determine the
accuracy of precoding and the efficiency of scheduling
algorithm. In most conventional theoretical researches on
HB design, ignoring whether it is practical to implement,
perfect or full CSI is always assumed. However in mmWave
massive MIMO systems, due to a large number of antenna
elements, obtaining full CSI at eNodeB is inevitably
challenging. In FDD systems, CSI required for DB can be
obtained via feedback. While the large number of antenna
elements leads to a large occupation of the downlink and
uplink resources being used for pilot transmissions and CSI