Maximizing Minimum Phase Difference Based Hybrid Beamforming for Multiuser
mmWave Massive MIMO systems
Yadi Ding/Anzhong Hu
School of communication engineering
Hangzhou Dianzi University
Hangzhou, China
e-mail: 962134287@qq.com/huaz@hdu.edu.cn
Abstract—In this paper, we propose a hybrid beamforming
algorithm based on maximizing the minimum phase difference
for millimeter-wave (mmWave) massive multiple-input
multiple-output (MIMO) multiuser systems. The proposed
algorithm uses the channel gain threshold and the correlation
characteristic of the array response vectors to select vector sets
that provide higher signal power from analog beamforming
vector codebook. Then, inter-user interference is measured by
the phase difference between the analog beamforming vector
and the main propagation path array response vector.
Additionally, the criterion of maximizing the minimum phase
difference is proposed to suppress the strongest inter-user
interference. Analysis and simulation results show that the
proposed algorithm can provide higher system sum rate with
lower computational complexity than traditional approaches.
Keywords-multiple-input multiple-output (MIMO);
millimeter-wave (mmWave); multiuser; interference; complexity;
I. INTRODUCTION
With the rapid development of wireless communication,
low-band spectrum cannot meet the growing needs of
communication [1]. Researchers have shifted their attention
to underutilized millimeter-wave (mmWave) bands [2].
MmWave communication bandwidth is generally up to 8
GHz, which can provide high capacity [3]. However, the
signal transmission in mmWave band endures a high path
loss. For example, signals at 60 GHz suffer from 28 dB
higher path loss than that at 2.4 GHz band [4]. Fortunately,
the short wavelength facilitates the deployment of large
arrays to compensate for path loss. Thus, the combination of
mmWave and massive multiple-input multiple-output
(MIMO) has great research prospects.
Conventional MIMO systems typically use full digital
processing for optimal performance. However, full digital
processing requires an independent radio frequency (RF)
chain for each antenna. The large number of antennas in
MmWave massive MIMO systems require a large number of
RF chains, which will result in high power consumption and
high complexity [5]. For single-user mmWave MIMO
systems, researchers have proposed some hybrid
beamforming (HBF) techniques that include analog
beamforming (ABF) and digital beamforming (DBF). In [6],
authors generalize orthogonal matching pursuit (OMP)
algorithm, which iteratively finds the codebook vector with
the strongest correlation with the rest of the channel. In [7], a
greedy algorithm is proposed, in which only one element in
the ABF matrix is optimized in each iteration. In [8], authors
propose a beamforming algorithm without any codebook, in
which the signal space generated by the singular value
decomposition of the channel matrix constitutes the ABF
matrix.
For multiuser mmWave MIMO systems, there are also
several HBF schemes. In [9], a beam steering algorithm is
proposed, in which the transmitter selects the codebook
vectors with the strongest correlation with the channel
vectors as the ABF vectors. However, this method only
maximizes the signal power and cannot effectively suppress
inter-user interference. In order to reduce inter-user
interference, [10] proposes a Gram-Schmidt based method.
The method orthogonalizes the channel vectors of multiple
users, then forms ABF vectors with orthogonalized vectors
such that the ABF vectors are orthogonal to the partial
channel vectors. But phase shifts of arbitrary accuracy is
necessary, which is hard in practice.
In this paper, a HBF algorithm based on maximizing the
minimum phase difference is proposed for uplink multiuser
mmWave massive MIMO systems with limited array
response vectors as the ABF vector codebook. For each user,
the method first selects a path with path loss lower than the
average path loss value. Then, a candidate ABF vector set is
formed by selecting vectors from the codebook which result
into smallest phase difference value. Finally, the minimum
value of the phase differences between the phases
corresponding to the vectors in the candidate ABF vector set
and the direction-of-arrival (DOA) of other user channels are
calculated, and the vector that maximizes the minimum value
is selected as the ABF vector for each user. The main
contributions of this paper are as follows. 1) The candidate
ABF vector set ensures a high received signal power. In
addition, maximizing the minimum phase difference avoids
the strongest inter-user interference. As a result, the proposed
approach can form a more reasonable compromise between
improving power and suppressing interference than the
approaches in [9] and [10]. 2) Since only the phase
differences need to be calculated, the computational
complexity of the proposed approach is lower than that of the
methods in [9] and [10].
Notations: Matrices and vectors are in boldface, with
uppercase letters for matrices and lower case letters for
vectors.
denotes the element in the
th row and the