![International Journal of Electrical and Computer Engineering (IJECE)
Vol. 12, No. 1, February 2022, pp. 445~452
ISSN: 2088-8708, DOI: 10.11591/ijece.v12i1.pp445-452 445
Journal homepage: http://ijece.iaescore.com
Beam division multiple access for millimeter wave massive
MIMO: Hybrid zero-forcing beamforming with user selection
Hong Son Vu1
, Kien Trung Truong2
, Minh Thuy Le1
1
School of Electrical Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam
2
Fulbright University Vietnam, Ho Chi Minh City, Vietnam
Article Info ABSTRACT
Article history:
Received Dec 29, 2020
Revised Jul 16, 2021
Accepted Aug 2, 2021
Massive multiple-input multiple-output (MIMO) systems are considered a
promising solution to minimize multiuser interference (MUI) based on
simple precoding techniques with a massive antenna array at a base station
(BS). This paper presents a novel approach of beam division multiple access
(BDMA) which BS transmit signals to multiusers at the same time via
different beams based on hybrid beamforming and user-beam schedule. With
the selection of users whose steering vectors are orthogonal to each other,
interference between users is significantly improved. While, the efficiency
spectrum of proposed scheme reaches to the performance of fully digital
solutions, the multiuser interference is considerably reduced.
Keywords:
Hybrid beamforming
Massive MIMO
mmWave This is an open access article under the CC BY-SA license.
Corresponding Author:
Minh Thuy Le
Department of Instrument and Industrial Informatics, School of Electrical Engineering, Hanoi University of
Science and Technology
No. 1 Dai Co Viet Street, Hai Ba Trung District, Hanoi, Vietnam
Email: thuy.leminh@hust.edu.vn
1. INTRODUCTION
Nowadays, the increasingly high number of mobile users has put pressure on current
communication systems adopting such techniques as time-division multiple access (TDMA) and frequency-
division multiple access (FDMA). The overload is especially intensified in the new 5th Generation system. In
order to tackle the problem of massive users and increase access capacity, beam division multiple access
(BDMA) has been proposed to the system [1], [2]. The BDMA scheme basically consists of three steps: i)
base station (BS) acquires channel coupling matrices (CCMs) from all user equipments (Ues) in its cell, ii)
user selection based on CCMs, then beams at BS are group into separated sub-sets, and iii) transmitting pilot
and data in the uplink and downlink. A selecting scheme within non-overlapping beams is proposed to
BDMA based on decomposition of the MU-MIMO channels into multiple single-user MIMO channels [1].
As a result, the overhead of channel estimation, as well as the processing complexity are improved
significantly at transceivers. Meanwhile, Jiang et al. [2] apply lyapunov-drift optimization framework for joint user
scheduling and beam selection method, thereby obtaining an optimal scheduling policy in a closed form.
The average channel capacity of wireless communication systems is heavily affected by fading
environments [3]-[6]. Especially, channel capacity degrades significantly it’sin the fading correlations
enivroments [7]. Massive multiple-input multiple-output (MIMO) techniques, for example, hybrid
beamforming architecture, were developed to attain the improving channel capacity of system in rich
scattering environments. Hybrid beamforming was deployed widely for millimeter wave (mmWave) massive
MIMO transmissions [8]-[11]. This architecture is considered the most effective solution to power
consumption and production costs problems of fully-digital architecture based on an additional layer of
analog phase shifters [12]. Moreover, the hybrid beamforming also achieves efficiency approximating to the](https://image.slidesharecdn.com/48157068850425804esr16jul29dec20f-211207060207/85/Beam-division-multiple-access-for-millimeter-wave-massive-MIMO-Hybrid-zero-forcing-beamforming-with-user-selection-1-320.jpg)
![ ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 12, No. 1, February 2022: 445-452
446
performance of digital solutions but at a much lower cost [13]. Transmit beamforming strategies for the
cellular downlink become the attractive topic [14]-[19]. There are several previous works proposed such
efficient beamforming strategies as zero-forcing beamforming (ZFBF) [14], [20]-[22], orthogonal
beamforming (OBF) [23], [24], and orthogonal random beamforming (ORBF) [4]. If the number of mobile
stations is higher than the number of antenna, user selection technique is essential to selects a group of users
for simultaneous transmission [25]. Works in [20], [21] proposed two selection algorithms for MIMO which
are semi-orthogonal user selection (SUS) and greedy user selection (GUS). In [21], by combining ZFBF with
SUS (ZFBF-SUS), the optimal sum rate could be achieved asymptotically with fully-digital, as the number of
users approaches infinity.
In this work, we study a low-complexity downlink-beamforming algorithm for step 2 in BDMA
scheme such that maximize sum capacity for the practical case when the number of downlink users exceeds
the number of antennas. Therefore, we propose a multiple access scheme that employs BMDA design with
hybrid beamforming structure and simple user-beam schedule, which not only reaches asymptotically
optimal in the sum-rate, but the average multiuser interference (MUI) energy can be minimized. In each time
slot, before the antenna weight vectors are updated base on ZFBF, the base station will select those mobile
stations such that the interference between them is minimal. To be specific, the system aims at
opportunistically schedule users whose steering vectors are as orthogonal as possible to each other.
Subsequently, this scheduling scheme will reduce the average multiuser interference MUI energy over all the
mobile stations (MSs).
The content of paper is organized as 5 sections. In section 2, we present the problem formulation,
and ZF with user selection algorithm is considered in section 3. Results and discussions are given in section 4
to demonstrate the effectiveness of our algorithm. Some conclusions are given in the last section. Notation:
uppercase boldface letters and lowercase boldface are described correspondingly for matrices and vectors.
The operators‖. ‖, (. )𝑇
, (. )𝐻
and |. | denote norm, transpose, Hermitian conjugate and modulus, respectively.
2. PROBLEM FORMULATION
Generally, the hybrid beamforming architecture could be divided into fully connected and partially
connected one [26]. While each radio-frequency (RF) chain of a fully connected architecture is mapped with
all antenna elements by phase shifter network, a partially connected hybrid transmitter connects each RF
chain to an antenna sub-array. In this paper, we conducted our proposed algorithm with fully connected
hybrid architecture as shown in Figure 1.
Figure 1. A fully connected hybrid beamformer
We consider a massive mmWave MIMO system with NT transmitted antennas and NRF RF chains at
BS serving NU mobile station (MS) with NR received antenna at each one. In this work, we concentrate on a
single block transmitted to NU users. The resulting signal x of dimension NT × 1 after hybrid beamforming
system is modeled as in (1):
x = F𝑅𝐹 × F𝐵𝐵 × s = F × s (1)
where FRF = [f1,RF, f2,RF, … , fNRF,RF] is analog beamforming matrix with fu,RF ∈ ℂNT×1
being the u-th analog
beamforming vector, the digital beamforming matrix FBB = [f1,BB, f2,BB, … , fNRF,BB] with fu,BB ∈ ℂNS×1
is the](https://image.slidesharecdn.com/48157068850425804esr16jul29dec20f-211207060207/85/Beam-division-multiple-access-for-millimeter-wave-massive-MIMO-Hybrid-zero-forcing-beamforming-with-user-selection-2-320.jpg)
![Int J Elec & Comp Eng ISSN: 2088-8708
Beam division multiple access for millimeter wave … (Hong Son Vu)
447
digital beamforming vector for the u-th user, and sU is the block data of u-th user. The received signal of the
u-th user can be expressed as (2):
𝑦𝑢 = H𝑢 ⋅ f𝑢,𝑅𝐹 ∙ f𝑢,𝐵𝐵 ⋅ 𝑠𝑢
⏟
𝑑𝑒𝑠𝑖𝑟𝑒𝑑
+ ∑ H𝑢 ∙ f𝑢,𝑅𝐹 ∙ f𝑖,𝐵𝐵 ⋅ 𝑠𝑖
𝑖≠𝑢
⏟
𝑖𝑛𝑡𝑒𝑟𝑓𝑒𝑟𝑒𝑐𝑒
+ 𝑛𝑢
⏟
𝑛𝑜𝑖𝑠𝑒 (2)
where y𝑢 ∈ ℂ𝑁𝑅×1
, H𝑢 ∈ ℂ𝑁𝑅×𝑁𝑇 is the MIMO channel matrix between the transmitter and the u-th receiver,
and nu ∈ ℂ𝑁𝑅×1
is the complex additive white gaussian noise with zero mean and variance of 𝜎2
for u-th
user. At u-th MS, the beamforming weight vector w combined the RF w𝑅𝐹 and baseband w𝐵𝐵 precoding
vectors. The decoded signal of the u-th receiver is given by (3):
𝑠̃𝑢 = w𝑢
𝐻
H𝑢f𝑢,𝑅𝐹f𝑢,𝐵𝐵𝑠𝑢 + w𝑢
𝐻
𝑛
̃𝑢 (3)
where 𝑛
̃𝑢 is the sum of complex additive white Gaussian noise (AWGN) and interference from other users.
The u-th user’s channel model of mmWave systems can be modeled as in (4) [27], [28]:
H𝑢 = √
𝑁𝑇𝑁𝑅
𝑁𝐿
∑ 𝛼𝑢,𝑙 ⋅ a𝑅(𝜙𝑢,𝑙
𝑟
, 𝜑𝑢,𝑙
𝑟
) ⋅
𝑁𝐿
𝑙=1
a𝑇
𝐻
(𝜙𝑢,𝑙
𝑡
, 𝜑𝑢,𝑙
𝑡
) (4)
where NL is the number of scatters of the u-th user’s channel, αu,l is the complex path gain, aR(u,l
r
, φu,l
r
) and
aT(u,l
t
, φu,l
t
) are received and transmitted steering vectors. In this work, a Nh × Nw uniform planar array
(UPA) is used, the steering vector can be rewritten [29]:
a(𝜙, 𝜑) =
1
√𝑁𝑇
[1, 𝑒𝑗𝑘𝑑(𝑠𝑖𝑛 𝜙 𝑠𝑖𝑛 𝜑+𝑐𝑜𝑠 𝜑)
, . . . , 𝑒𝑗𝑘𝑑((𝑁ℎ −1) 𝑠𝑖𝑛 𝜙 𝑠𝑖𝑛 𝜑+(𝑁𝑤−1) 𝑐𝑜𝑠 𝜑)
]
𝑇
(5)
where 𝑘 =
2𝜋
is the wavenumber and 𝑑 is the distance between two adjacent element antennas. Then, the
signal-to-interference plus noise ratio (SINR) of user uth
is (6),
𝑆𝐼𝑁𝑅𝑢 =
|H𝑢 ∙ f𝑢,𝑅𝐹 ∙ f𝑢,𝐵𝐵|
2
∑ |H𝑢 ∙ f𝑢,𝑅𝐹 ∙ f𝑖,𝐵𝐵|
2
𝑖≠𝑢 + 𝜎2
(6)
The beamforming cost function can now be formulated as (7):
max
F𝑅𝐹,F𝐵𝐵
∑ 𝑙𝑜𝑔2( 1 + 𝑆𝐼𝑁𝑅𝑢)
𝑁𝑈
𝑢=1
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜‖FRF. F𝐵𝐵‖2
= 1 (7)
3. PROPOSED ZF WITH GREEDY ALGORITHM
3.1. Proposed algorithm
We assumed that BS has the perfect channel state information (CSI). Therefore, angle of arrival
(AoA) and angle of departure (AoD) information {𝜙𝑢
𝑟
, 𝜑𝑢
𝑟
, 𝜙𝑢
𝑡
, 𝜑𝑢
𝑡 } is perfectly known. As a result, optimal
analog beamforming vector of u-th user could be computed (8):
f𝑢,𝑅𝐹
∗
= a𝑇(𝜙𝑢
𝑡
, 𝜑𝑢
𝑡 ), 𝑢 = 1 ÷ 𝑁𝑈 (8)
The optimization problem in (7) is rewritten (8):
max
F𝐵𝐵
∑ 𝑙𝑜𝑔2( 1 + 𝑆𝐼𝑁𝑅𝑢)
𝑁𝑈
𝑢=1
𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜‖F𝑅𝐹
∗
. F𝐵𝐵‖2
= 1 (9)
From (3), set g𝑢
𝐻
= w𝑢
𝐻
× H𝑢 × f𝑢,𝑅𝐹
∗
, then 𝐺 = [g1, g2, . . . , g𝑁𝑈
]
H
. According to a zero-forcing approach, in
case of 𝑁𝑇 > 𝑁𝑈, the optimal DBF matrix could be calculated as F 𝐵𝐵 = G†
= GH(GGH)−1
. Normalized](https://image.slidesharecdn.com/48157068850425804esr16jul29dec20f-211207060207/85/Beam-division-multiple-access-for-millimeter-wave-massive-MIMO-Hybrid-zero-forcing-beamforming-with-user-selection-3-320.jpg)
![ ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 12, No. 1, February 2022: 445-452
448
baseband precoder F 𝐵𝐵 is obtained F𝐵𝐵
∗
=
F 𝐵𝐵
‖F𝑅𝐹
∗ .FBB‖
. For 𝑁𝑇 < 𝑁𝑈, to select subset users, we proposed a low-
complexity algorithm, named ZF with user selection (ZFUS), as summarized in next.
Algorithm 1. ZF with user selection (ZFUS)
Initialization: 𝑁, NU, NT, NR, NRF, SNR, AoA and AoD {ϕu
r
, φu
r
, ϕu
t
, φu
t }
Beam search
− Find the user with the largest channel gain among 𝑁𝑈 users:
o 𝑠1 = 𝑎𝑟𝑔𝑚𝑎𝑥 H𝑢H𝑢
∗
− Set its steering vector as first element of signal subspace: A = [𝑎𝑇(𝜙1
𝑡
, 𝜑1
𝑡)]
− 𝑛 = 1;
Select users
− while(n < 𝑁 − 1)
𝑛 = 𝑛 + 1
𝑇ℎ𝑒 𝑝𝑟𝑜𝑗𝑒𝑐𝑡𝑖𝑜𝑛 𝑠𝑝𝑎𝑐𝑒: PA = AA†
𝑓𝑜𝑟 𝑖 = 1: NU
P(i) = ‖PA ∗ aT(ϕi
t
, φi
t
)‖2
𝑒𝑛𝑑
𝐹𝑖𝑛𝑑 𝑖 = 𝑎𝑟𝑔𝑚𝑖𝑛{P(i)}
𝑈𝑝𝑑𝑎𝑡𝑒 𝑠𝑖𝑔𝑛𝑎𝑙 𝑠𝑢𝑏𝑠𝑝𝑎𝑐𝑒: A = [𝑎𝑇(ϕ1
t
,φ1
t ), . . . , 𝑎𝑇(ϕi
t
, φi
t)]
end
• Obtain list of 𝑁 selected users
Analog beamforming: F𝑅𝐹 = [𝑎𝑇(ϕ1
t
, φ1
t ), . . . , 𝑎𝑇(ϕNRF
t
,φNRF
t
)]
Digital beamforming: F𝐵𝐵 = G†
= GH(GGH)−1
, where 𝐺 = [g1,g2, . . . , g𝑁]𝐻
End
There are two main steps in user selection: beam search and select user. In the first phase, based on
broadcast beam at BS side, we can find out UE with largest channel. Then, we set its steering vector
𝑎𝑇(𝜙1
𝑡
, 𝜑1
𝑡
) as first element of signal subspace A. For the next phase, by comparing orthogonality between
user’s steering vector and projection space, the algorithm will select (N − 1) users among the rest of
(NU − 1) users.
3.2. Computational complexity analysis
In this subsection, the computational complexity of the ZFUS algorithm is analyzed. The
implementation of ZFUS consist of two phases: User selection and beamforming vector calculation. Because
the latter requires only 𝑁 × 𝑁 matrix inversion to calculate beamforming weight, we focus on the complexity
of user selection phase. In the beam search step, we need one 2𝑁𝑇 matrix-matrix multiplication per user.
With 𝑁𝑈 users, we need 2𝑁𝑇𝑁𝑈 matrix-matrix multiplication. The complexity of the selecting user step can
be expressed as ∑ 𝑘
𝑁
𝑘=1 (8𝑁𝑇𝑘2
− 𝑁𝑇𝑘 + 2(𝑁𝑈 − 1)𝑁𝑇𝑘) = ∑ 𝑘
𝑁
𝑘=1 (8𝑁𝑇𝑘2
+ (2𝑁𝑈 − 3)𝑁𝑇𝑘). As a
result, the number of computations of running the ZFUS algorithm is 2𝑁𝑇𝑁𝑈 + ∑ (8𝑁𝑇𝑘2
+ (2𝑁𝑈 −
𝑁−1
𝑘=1
3)𝑁𝑇𝑘).
4. SIMULATION EVALUATION
The performance of proposed ZFUS algorithms will be illustrated numerically in terms of the
average MUI energy over all the MSs, system sum-rate capacity conditions used in our simulation are: i) the
inner distance of two adjacent antennas is 0.5𝜆, ii) the number of total users 𝑁𝑈 = 20 users with a 2x2 UPA
(𝑁𝑅 = 4) and the number of selected users 𝑁 = 4, and iii) the number of realizations is 500 for each
experiment. Figure 2 shows the system sum-rate capacity versus SNR in 256 × 16 system with uniform
planar array at both the transmitted and received side. It can be seen that the performance of ZFUS is
approached to fully digital precoding system with a small gap. When compared to analog beamforming
(ABF), Figure 2 shows that the ZFUS significantly improves the performance of system.
Next, we investigated the performance of three architectures following the number of base station
antennas. Figure 3 shows that spectral efficiency (SE) values of three systems rise rapidly as the number of
antennas increases from 16 to 250 elements. Though the SE of ZFUS is always higher than ABF about 4
bps/Hz, it could not reach asymptotically the fully digital system.
Finally, we study the Average of MUI energy over all the UTs versus number of BS antennas in
Figure 4. It’s clear that ZFUS can reduce MUI more effectively by selecting the user group with orthogonal
steering vector to each other. While the MUI value of the ABF is always greater than 0 dB, the ZFUS
maintains the MUI value below -15 dB. As the number of antennas increases, both the MUI value of ZFUS
and ABF tend to decrease.](https://image.slidesharecdn.com/48157068850425804esr16jul29dec20f-211207060207/85/Beam-division-multiple-access-for-millimeter-wave-massive-MIMO-Hybrid-zero-forcing-beamforming-with-user-selection-4-320.jpg)
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Compared to several relevant papers in Table 1, the performance of our proposed is better under the
same architecture and SNR. To reduce the computational complexity, Singh and Ramakrishna [30] use
subconnected structure and codebook method, this leads to decrease the spectral efficiency of system. In
contrast, though works in [31], [32] deployed the fully structure and zero-forcing method same as our work,
their spectral efficiency values are still lower than our work. It proves that the proposed user schedule help to
improve the performance of system.
Table 1. The comparison of our proposed and previous works
Paper Architectures Antenna Array Algorithms SE (b/s/Hz)
[30] Sub-connected
𝑁𝑇 = 2 × 8
𝑁𝑅 = 2 × 4
𝑁𝑈 = 1
ABF: codebook-based
DBF: a specified codebook of matrices
10@SNR 10 dB
[31] Fully connected
𝑁𝑇 = 64
𝑁𝑅 = 1
𝑁𝑈 = 2
ABF: Hermitian of downlink channel matrix
DBF: ZF
1.37@SNR 0 dB
[32] Fully connected
𝑁𝑇 = 64
𝑁𝑅 = 16
𝑁𝑈 = 4
ABF: beam steering codebook
DBF: ZF based on perfect CSI
6.8@SNR 0 dB
My Work Fully connected
𝑁𝑇 = 16 × 16
𝑁𝑅 = 4
𝑁𝑈 = 4
ABF: steering vector
DBF: ZF
10@SNR 0 dB
5. CONCLUSION
A new user selection algorithm is proposed for BDMA scheme of massive MIMO system in this
work. Based on deploying Zero-Forcing and new schedule in hybrid beamforming, the multiuser interference
(MUI) is significantly reduced when we increase the number of BS antenna. Simulated results confirmed that
proposed solution can attain spectrum efficiency (SE) as good as only digital beamforming.
ACKNOWLEDGEMENTS
Hong Son Vu was funded by Vingroup Joint Stock Company and supported by the Domestic
Master/Ph.D. Scholarship Programme of Vingroup Innovation Foundation (VINIF), Vingroup Big Data
Institute (VINBIGDATA), code VINIF.2020.ThS.66.
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BIOGRAPHIES OF AUTHORS
Hong Son Vu received his B.S (2019) and M. Sc (2021) degree in Electrical
Engineering from Hanoi University of Science and Technology. He is currently a research
assistant at Department of Instrumentation and Industrial Informatic (3I), School of
Electrical Engineering (SEE), Hanoi University of Science and Technology (HUST). His
current interests include signal processing and massive MIMO system. He can be contacted
at email: hongsonvu1996@gmail.com.](https://image.slidesharecdn.com/48157068850425804esr16jul29dec20f-211207060207/85/Beam-division-multiple-access-for-millimeter-wave-massive-MIMO-Hybrid-zero-forcing-beamforming-with-user-selection-7-320.jpg)
Beam division multiple access for millimeter wave massive MIMO: Hybrid zero-forcing beamforming with user selection
- 1. International Journal of Electrical and Computer Engineering (IJECE) Vol. 12, No. 1, February 2022, pp. 445~452 ISSN: 2088-8708, DOI: 10.11591/ijece.v12i1.pp445-452 445 Journal homepage: http://ijece.iaescore.com Beam division multiple access for millimeter wave massive MIMO: Hybrid zero-forcing beamforming with user selection Hong Son Vu1 , Kien Trung Truong2 , Minh Thuy Le1 1 School of Electrical Engineering, Hanoi University of Science and Technology, Hanoi, Vietnam 2 Fulbright University Vietnam, Ho Chi Minh City, Vietnam Article Info ABSTRACT Article history: Received Dec 29, 2020 Revised Jul 16, 2021 Accepted Aug 2, 2021 Massive multiple-input multiple-output (MIMO) systems are considered a promising solution to minimize multiuser interference (MUI) based on simple precoding techniques with a massive antenna array at a base station (BS). This paper presents a novel approach of beam division multiple access (BDMA) which BS transmit signals to multiusers at the same time via different beams based on hybrid beamforming and user-beam schedule. With the selection of users whose steering vectors are orthogonal to each other, interference between users is significantly improved. While, the efficiency spectrum of proposed scheme reaches to the performance of fully digital solutions, the multiuser interference is considerably reduced. Keywords: Hybrid beamforming Massive MIMO mmWave This is an open access article under the CC BY-SA license. Corresponding Author: Minh Thuy Le Department of Instrument and Industrial Informatics, School of Electrical Engineering, Hanoi University of Science and Technology No. 1 Dai Co Viet Street, Hai Ba Trung District, Hanoi, Vietnam Email: [email protected] 1. INTRODUCTION Nowadays, the increasingly high number of mobile users has put pressure on current communication systems adopting such techniques as time-division multiple access (TDMA) and frequency- division multiple access (FDMA). The overload is especially intensified in the new 5th Generation system. In order to tackle the problem of massive users and increase access capacity, beam division multiple access (BDMA) has been proposed to the system [1], [2]. The BDMA scheme basically consists of three steps: i) base station (BS) acquires channel coupling matrices (CCMs) from all user equipments (Ues) in its cell, ii) user selection based on CCMs, then beams at BS are group into separated sub-sets, and iii) transmitting pilot and data in the uplink and downlink. A selecting scheme within non-overlapping beams is proposed to BDMA based on decomposition of the MU-MIMO channels into multiple single-user MIMO channels [1]. As a result, the overhead of channel estimation, as well as the processing complexity are improved significantly at transceivers. Meanwhile, Jiang et al. [2] apply lyapunov-drift optimization framework for joint user scheduling and beam selection method, thereby obtaining an optimal scheduling policy in a closed form. The average channel capacity of wireless communication systems is heavily affected by fading environments [3]-[6]. Especially, channel capacity degrades significantly it’sin the fading correlations enivroments [7]. Massive multiple-input multiple-output (MIMO) techniques, for example, hybrid beamforming architecture, were developed to attain the improving channel capacity of system in rich scattering environments. Hybrid beamforming was deployed widely for millimeter wave (mmWave) massive MIMO transmissions [8]-[11]. This architecture is considered the most effective solution to power consumption and production costs problems of fully-digital architecture based on an additional layer of analog phase shifters [12]. Moreover, the hybrid beamforming also achieves efficiency approximating to the
- 2. ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 12, No. 1, February 2022: 445-452 446 performance of digital solutions but at a much lower cost [13]. Transmit beamforming strategies for the cellular downlink become the attractive topic [14]-[19]. There are several previous works proposed such efficient beamforming strategies as zero-forcing beamforming (ZFBF) [14], [20]-[22], orthogonal beamforming (OBF) [23], [24], and orthogonal random beamforming (ORBF) [4]. If the number of mobile stations is higher than the number of antenna, user selection technique is essential to selects a group of users for simultaneous transmission [25]. Works in [20], [21] proposed two selection algorithms for MIMO which are semi-orthogonal user selection (SUS) and greedy user selection (GUS). In [21], by combining ZFBF with SUS (ZFBF-SUS), the optimal sum rate could be achieved asymptotically with fully-digital, as the number of users approaches infinity. In this work, we study a low-complexity downlink-beamforming algorithm for step 2 in BDMA scheme such that maximize sum capacity for the practical case when the number of downlink users exceeds the number of antennas. Therefore, we propose a multiple access scheme that employs BMDA design with hybrid beamforming structure and simple user-beam schedule, which not only reaches asymptotically optimal in the sum-rate, but the average multiuser interference (MUI) energy can be minimized. In each time slot, before the antenna weight vectors are updated base on ZFBF, the base station will select those mobile stations such that the interference between them is minimal. To be specific, the system aims at opportunistically schedule users whose steering vectors are as orthogonal as possible to each other. Subsequently, this scheduling scheme will reduce the average multiuser interference MUI energy over all the mobile stations (MSs). The content of paper is organized as 5 sections. In section 2, we present the problem formulation, and ZF with user selection algorithm is considered in section 3. Results and discussions are given in section 4 to demonstrate the effectiveness of our algorithm. Some conclusions are given in the last section. Notation: uppercase boldface letters and lowercase boldface are described correspondingly for matrices and vectors. The operators‖. ‖, (. )𝑇 , (. )𝐻 and |. | denote norm, transpose, Hermitian conjugate and modulus, respectively. 2. PROBLEM FORMULATION Generally, the hybrid beamforming architecture could be divided into fully connected and partially connected one [26]. While each radio-frequency (RF) chain of a fully connected architecture is mapped with all antenna elements by phase shifter network, a partially connected hybrid transmitter connects each RF chain to an antenna sub-array. In this paper, we conducted our proposed algorithm with fully connected hybrid architecture as shown in Figure 1. Figure 1. A fully connected hybrid beamformer We consider a massive mmWave MIMO system with NT transmitted antennas and NRF RF chains at BS serving NU mobile station (MS) with NR received antenna at each one. In this work, we concentrate on a single block transmitted to NU users. The resulting signal x of dimension NT × 1 after hybrid beamforming system is modeled as in (1): x = F𝑅𝐹 × F𝐵𝐵 × s = F × s (1) where FRF = [f1,RF, f2,RF, … , fNRF,RF] is analog beamforming matrix with fu,RF ∈ ℂNT×1 being the u-th analog beamforming vector, the digital beamforming matrix FBB = [f1,BB, f2,BB, … , fNRF,BB] with fu,BB ∈ ℂNS×1 is the
- 3. Int J Elec & Comp Eng ISSN: 2088-8708 Beam division multiple access for millimeter wave … (Hong Son Vu) 447 digital beamforming vector for the u-th user, and sU is the block data of u-th user. The received signal of the u-th user can be expressed as (2): 𝑦𝑢 = H𝑢 ⋅ f𝑢,𝑅𝐹 ∙ f𝑢,𝐵𝐵 ⋅ 𝑠𝑢 ⏟ 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 + ∑ H𝑢 ∙ f𝑢,𝑅𝐹 ∙ f𝑖,𝐵𝐵 ⋅ 𝑠𝑖 𝑖≠𝑢 ⏟ 𝑖𝑛𝑡𝑒𝑟𝑓𝑒𝑟𝑒𝑐𝑒 + 𝑛𝑢 ⏟ 𝑛𝑜𝑖𝑠𝑒 (2) where y𝑢 ∈ ℂ𝑁𝑅×1 , H𝑢 ∈ ℂ𝑁𝑅×𝑁𝑇 is the MIMO channel matrix between the transmitter and the u-th receiver, and nu ∈ ℂ𝑁𝑅×1 is the complex additive white gaussian noise with zero mean and variance of 𝜎2 for u-th user. At u-th MS, the beamforming weight vector w combined the RF w𝑅𝐹 and baseband w𝐵𝐵 precoding vectors. The decoded signal of the u-th receiver is given by (3): 𝑠̃𝑢 = w𝑢 𝐻 H𝑢f𝑢,𝑅𝐹f𝑢,𝐵𝐵𝑠𝑢 + w𝑢 𝐻 𝑛 ̃𝑢 (3) where 𝑛 ̃𝑢 is the sum of complex additive white Gaussian noise (AWGN) and interference from other users. The u-th user’s channel model of mmWave systems can be modeled as in (4) [27], [28]: H𝑢 = √ 𝑁𝑇𝑁𝑅 𝑁𝐿 ∑ 𝛼𝑢,𝑙 ⋅ a𝑅(𝜙𝑢,𝑙 𝑟 , 𝜑𝑢,𝑙 𝑟 ) ⋅ 𝑁𝐿 𝑙=1 a𝑇 𝐻 (𝜙𝑢,𝑙 𝑡 , 𝜑𝑢,𝑙 𝑡 ) (4) where NL is the number of scatters of the u-th user’s channel, αu,l is the complex path gain, aR(u,l r , φu,l r ) and aT(u,l t , φu,l t ) are received and transmitted steering vectors. In this work, a Nh × Nw uniform planar array (UPA) is used, the steering vector can be rewritten [29]: a(𝜙, 𝜑) = 1 √𝑁𝑇 [1, 𝑒𝑗𝑘𝑑(𝑠𝑖𝑛 𝜙 𝑠𝑖𝑛 𝜑+𝑐𝑜𝑠 𝜑) , . . . , 𝑒𝑗𝑘𝑑((𝑁ℎ −1) 𝑠𝑖𝑛 𝜙 𝑠𝑖𝑛 𝜑+(𝑁𝑤−1) 𝑐𝑜𝑠 𝜑) ] 𝑇 (5) where 𝑘 = 2𝜋 is the wavenumber and 𝑑 is the distance between two adjacent element antennas. Then, the signal-to-interference plus noise ratio (SINR) of user uth is (6), 𝑆𝐼𝑁𝑅𝑢 = |H𝑢 ∙ f𝑢,𝑅𝐹 ∙ f𝑢,𝐵𝐵| 2 ∑ |H𝑢 ∙ f𝑢,𝑅𝐹 ∙ f𝑖,𝐵𝐵| 2 𝑖≠𝑢 + 𝜎2 (6) The beamforming cost function can now be formulated as (7): max F𝑅𝐹,F𝐵𝐵 ∑ 𝑙𝑜𝑔2( 1 + 𝑆𝐼𝑁𝑅𝑢) 𝑁𝑈 𝑢=1 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜‖FRF. F𝐵𝐵‖2 = 1 (7) 3. PROPOSED ZF WITH GREEDY ALGORITHM 3.1. Proposed algorithm We assumed that BS has the perfect channel state information (CSI). Therefore, angle of arrival (AoA) and angle of departure (AoD) information {𝜙𝑢 𝑟 , 𝜑𝑢 𝑟 , 𝜙𝑢 𝑡 , 𝜑𝑢 𝑡 } is perfectly known. As a result, optimal analog beamforming vector of u-th user could be computed (8): f𝑢,𝑅𝐹 ∗ = a𝑇(𝜙𝑢 𝑡 , 𝜑𝑢 𝑡 ), 𝑢 = 1 ÷ 𝑁𝑈 (8) The optimization problem in (7) is rewritten (8): max F𝐵𝐵 ∑ 𝑙𝑜𝑔2( 1 + 𝑆𝐼𝑁𝑅𝑢) 𝑁𝑈 𝑢=1 𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜‖F𝑅𝐹 ∗ . F𝐵𝐵‖2 = 1 (9) From (3), set g𝑢 𝐻 = w𝑢 𝐻 × H𝑢 × f𝑢,𝑅𝐹 ∗ , then 𝐺 = [g1, g2, . . . , g𝑁𝑈 ] H . According to a zero-forcing approach, in case of 𝑁𝑇 > 𝑁𝑈, the optimal DBF matrix could be calculated as F 𝐵𝐵 = G† = GH(GGH)−1 . Normalized
- 4. ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 12, No. 1, February 2022: 445-452 448 baseband precoder F 𝐵𝐵 is obtained F𝐵𝐵 ∗ = F 𝐵𝐵 ‖F𝑅𝐹 ∗ .FBB‖ . For 𝑁𝑇 < 𝑁𝑈, to select subset users, we proposed a low- complexity algorithm, named ZF with user selection (ZFUS), as summarized in next. Algorithm 1. ZF with user selection (ZFUS) Initialization: 𝑁, NU, NT, NR, NRF, SNR, AoA and AoD {ϕu r , φu r , ϕu t , φu t } Beam search − Find the user with the largest channel gain among 𝑁𝑈 users: o 𝑠1 = 𝑎𝑟𝑔𝑚𝑎𝑥 H𝑢H𝑢 ∗ − Set its steering vector as first element of signal subspace: A = [𝑎𝑇(𝜙1 𝑡 , 𝜑1 𝑡)] − 𝑛 = 1; Select users − while(n < 𝑁 − 1) 𝑛 = 𝑛 + 1 𝑇ℎ𝑒 𝑝𝑟𝑜𝑗𝑒𝑐𝑡𝑖𝑜𝑛 𝑠𝑝𝑎𝑐𝑒: PA = AA† 𝑓𝑜𝑟 𝑖 = 1: NU P(i) = ‖PA ∗ aT(ϕi t , φi t )‖2 𝑒𝑛𝑑 𝐹𝑖𝑛𝑑 𝑖 = 𝑎𝑟𝑔𝑚𝑖𝑛{P(i)} 𝑈𝑝𝑑𝑎𝑡𝑒 𝑠𝑖𝑔𝑛𝑎𝑙 𝑠𝑢𝑏𝑠𝑝𝑎𝑐𝑒: A = [𝑎𝑇(ϕ1 t ,φ1 t ), . . . , 𝑎𝑇(ϕi t , φi t)] end • Obtain list of 𝑁 selected users Analog beamforming: F𝑅𝐹 = [𝑎𝑇(ϕ1 t , φ1 t ), . . . , 𝑎𝑇(ϕNRF t ,φNRF t )] Digital beamforming: F𝐵𝐵 = G† = GH(GGH)−1 , where 𝐺 = [g1,g2, . . . , g𝑁]𝐻 End There are two main steps in user selection: beam search and select user. In the first phase, based on broadcast beam at BS side, we can find out UE with largest channel. Then, we set its steering vector 𝑎𝑇(𝜙1 𝑡 , 𝜑1 𝑡 ) as first element of signal subspace A. For the next phase, by comparing orthogonality between user’s steering vector and projection space, the algorithm will select (N − 1) users among the rest of (NU − 1) users. 3.2. Computational complexity analysis In this subsection, the computational complexity of the ZFUS algorithm is analyzed. The implementation of ZFUS consist of two phases: User selection and beamforming vector calculation. Because the latter requires only 𝑁 × 𝑁 matrix inversion to calculate beamforming weight, we focus on the complexity of user selection phase. In the beam search step, we need one 2𝑁𝑇 matrix-matrix multiplication per user. With 𝑁𝑈 users, we need 2𝑁𝑇𝑁𝑈 matrix-matrix multiplication. The complexity of the selecting user step can be expressed as ∑ 𝑘 𝑁 𝑘=1 (8𝑁𝑇𝑘2 − 𝑁𝑇𝑘 + 2(𝑁𝑈 − 1)𝑁𝑇𝑘) = ∑ 𝑘 𝑁 𝑘=1 (8𝑁𝑇𝑘2 + (2𝑁𝑈 − 3)𝑁𝑇𝑘). As a result, the number of computations of running the ZFUS algorithm is 2𝑁𝑇𝑁𝑈 + ∑ (8𝑁𝑇𝑘2 + (2𝑁𝑈 − 𝑁−1 𝑘=1 3)𝑁𝑇𝑘). 4. SIMULATION EVALUATION The performance of proposed ZFUS algorithms will be illustrated numerically in terms of the average MUI energy over all the MSs, system sum-rate capacity conditions used in our simulation are: i) the inner distance of two adjacent antennas is 0.5𝜆, ii) the number of total users 𝑁𝑈 = 20 users with a 2x2 UPA (𝑁𝑅 = 4) and the number of selected users 𝑁 = 4, and iii) the number of realizations is 500 for each experiment. Figure 2 shows the system sum-rate capacity versus SNR in 256 × 16 system with uniform planar array at both the transmitted and received side. It can be seen that the performance of ZFUS is approached to fully digital precoding system with a small gap. When compared to analog beamforming (ABF), Figure 2 shows that the ZFUS significantly improves the performance of system. Next, we investigated the performance of three architectures following the number of base station antennas. Figure 3 shows that spectral efficiency (SE) values of three systems rise rapidly as the number of antennas increases from 16 to 250 elements. Though the SE of ZFUS is always higher than ABF about 4 bps/Hz, it could not reach asymptotically the fully digital system. Finally, we study the Average of MUI energy over all the UTs versus number of BS antennas in Figure 4. It’s clear that ZFUS can reduce MUI more effectively by selecting the user group with orthogonal steering vector to each other. While the MUI value of the ABF is always greater than 0 dB, the ZFUS maintains the MUI value below -15 dB. As the number of antennas increases, both the MUI value of ZFUS and ABF tend to decrease.
- 5. Int J Elec & Comp Eng ISSN: 2088-8708 Beam division multiple access for millimeter wave … (Hong Son Vu) 449 Figure 2. Comparison of sum-rate capacity versus SNR with 𝑁_𝑇 = 16 × 16 Figure 3. Comparison of sum-rate capacity versus number of BS antennas Figure 4. Average of multiuser interference at BS
- 6. ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 12, No. 1, February 2022: 445-452 450 Compared to several relevant papers in Table 1, the performance of our proposed is better under the same architecture and SNR. To reduce the computational complexity, Singh and Ramakrishna [30] use subconnected structure and codebook method, this leads to decrease the spectral efficiency of system. In contrast, though works in [31], [32] deployed the fully structure and zero-forcing method same as our work, their spectral efficiency values are still lower than our work. It proves that the proposed user schedule help to improve the performance of system. Table 1. The comparison of our proposed and previous works Paper Architectures Antenna Array Algorithms SE (b/s/Hz) [30] Sub-connected 𝑁𝑇 = 2 × 8 𝑁𝑅 = 2 × 4 𝑁𝑈 = 1 ABF: codebook-based DBF: a specified codebook of matrices 10@SNR 10 dB [31] Fully connected 𝑁𝑇 = 64 𝑁𝑅 = 1 𝑁𝑈 = 2 ABF: Hermitian of downlink channel matrix DBF: ZF 1.37@SNR 0 dB [32] Fully connected 𝑁𝑇 = 64 𝑁𝑅 = 16 𝑁𝑈 = 4 ABF: beam steering codebook DBF: ZF based on perfect CSI 6.8@SNR 0 dB My Work Fully connected 𝑁𝑇 = 16 × 16 𝑁𝑅 = 4 𝑁𝑈 = 4 ABF: steering vector DBF: ZF 10@SNR 0 dB 5. CONCLUSION A new user selection algorithm is proposed for BDMA scheme of massive MIMO system in this work. Based on deploying Zero-Forcing and new schedule in hybrid beamforming, the multiuser interference (MUI) is significantly reduced when we increase the number of BS antenna. Simulated results confirmed that proposed solution can attain spectrum efficiency (SE) as good as only digital beamforming. ACKNOWLEDGEMENTS Hong Son Vu was funded by Vingroup Joint Stock Company and supported by the Domestic Master/Ph.D. Scholarship Programme of Vingroup Innovation Foundation (VINIF), Vingroup Big Data Institute (VINBIGDATA), code VINIF.2020.ThS.66. REFERENCES [1] C. Sun, X. Gao, S. Jin, M. Matthaiou, Z. Ding, and C. Xiao, “Beam division multiple access transmission for massive MIMO communications,” in IEEE Transactions on Communications, vol. 63, no. 6, pp. 2170-2184, Jun. 2015, doi: 10.1109/TCOMM.2015.2425882. [2] Z. Jiang, S. Chen, S. Zhou, and Z. Niu, “Joint user scheduling and beam selection optimization for beam-based massive MIMO downlinks,” in IEEE Transactions on Wireless Communications, vol. 17, no. 4, pp. 2190-2204, Apr. 2018, doi: 10.1109/TWC.2018.2789895. [3] J. Salz and J. H. Winters, “Effect of fading correlation on adaptive arrays in digital mobile radio,” in IEEE Transactions on Vehicular Technology, vol. 43, no. 4, pp. 1049-1057, Nov. 1994, doi: 10.1109/25.330168. [4] M. Sharif and B. Hassibi, “On the capacity of MIMO broadcast channels with partial side information,” in IEEE Transactions on Information Theory, vol. 51, no. 2, pp. 506-522, Feb. 2005, doi: 10.1109/TIT.2004.840897. [5] G. J. Foschini and M. J. Gans, “On limits of wireless communications in a fading environment when using multiple antennas,” in Wireless Personal Communications, vol. 6, no. 3, pp. 311-335, 1998, doi: 10.1023/A:1008889222784. [6] P. Varzakas, “Average channel capacity for Rayleigh fading spread spectrum MIMO systems,” in International Journal Communication Systems, vol. 19, no. 10, pp. 1081-1087, Feb. 2006, doi: 10.1002/dac.784. [7] Da-Shan Shiu, G. J. Foschini, M. J. Gans, and J. M. Kahn, “Fading correlation and its effect on the capacity of multielement antenna systems,” in IEEE Transactions on Communications, vol. 48, no. 3, pp. 502-513, Mar. 2000, doi: 10.1109/26.837052. [8] T. Lin, J. Cong, Y. Zhu, J. Zhang, and K. Ben Letaief, “Hybrid beamforming for millimeter wave systems using the MMSE criterion,” in IEEE Transactions on Communications, vol. 67, no. 5, pp. 3693-3708, May 2019, doi: 10.1109/TCOMM.2019.2893632. [9] A. A. Nasir, H. D. Tuan, T. Q. Duong, H. V. Poor, and L. Hanzo, “Hybrid beamforming for multi-user millimeter-wave networks,” in IEEE Transactions on Vehicular Technology, vol. 69, no. 3, pp. 2943-2956, Mar. 2020, doi: 10.1109/TVT.2020.2966122. [10] M. N. Kulkarni, A. Ghosh, and J. G. Andrews, “A comparison of MIMO techniques in downlink millimeter wave cellular networks with hybrid beamforming,” in IEEE Transactions on Communications, vol. 64, no. 5, pp. 1952-1967, May 2016, doi: 10.1109/TCOMM.2016.2542825. [11] K. Satyanarayana, M. El-Hajjar, P. Kuo, A. Mourad, and L. Hanzo, “Dual-function hybrid beamforming and transmit diversity aided millimeter wave architecture,” in IEEE Transactions on Vehicular Technology, vol. 67, no. 3, pp. 2798-2803, Mar. 2018, doi: 10.1109/TVT.2017.2737782.
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Ramakrishna, “On the feasibility of codebook-based beamforming in millimeter wave systems with multiple antenna arrays,” in IEEE Transactions on Wireless Communications, vol. 14, no. 5, pp. 2670-2683, May 2015, doi: 10.1109/TWC.2015.2390637. [31] J. Jing, C. Xiaoxue, and X. Yongbin, “Energy-efficiency based downlink multi-user hybrid beamforming for millimeter wave massive MIMO system,” in Journal China University Posts Telecommunication, vol. 23, no. 4, pp. 53–62, Aug. 2016, doi: 10.1016/S1005-8885(16)60045-6. [32] A. Alkhateeb, G. Leus, and R. W. Heath, “Limited feedback hybrid precoding for multi-user millimeter wave systems,” in IEEE Transactions on Wireless Communications, vol. 14, no. 11, pp. 6481-6494, Nov. 2015, doi: 10.1109/TWC.2015.2455980. BIOGRAPHIES OF AUTHORS Hong Son Vu received his B.S (2019) and M. Sc (2021) degree in Electrical Engineering from Hanoi University of Science and Technology. He is currently a research assistant at Department of Instrumentation and Industrial Informatic (3I), School of Electrical Engineering (SEE), Hanoi University of Science and Technology (HUST). His current interests include signal processing and massive MIMO system. He can be contacted at email: [email protected].
- 8. ISSN: 2088-8708 Int J Elec & Comp Eng, Vol. 12, No. 1, February 2022: 445-452 452 Kien Trung Truong earned his B.S. in Electronics and Telecommunications from Hanoi University of Science and Technology in Hanoi, Vietnam, in 2002, and his M.Sc. and Ph.D. in Electrical Engineering from the University of Texas at Austin in Austin, Texas, USA, in 2008 and 2012. He is currently a lecturer in engineering at Fulbright University Vietnam, Ho Chi Minh City, Vietnam. His current research interests include massive MIMO communications, millimeter-wave communications, and wireless energy harvesting. He was co-recipient of the 2013 EURASIP Journal on Wireless Communications and Networking Best Paper Award and the 2014 IEEE/KICS Journal of Communications and Networks Best Paper Award. He was a fellow of the Vietnam Education Foundation in 2006. He can be contacted at email: [email protected]. Minh Thuy Le graduated from Hanoi University of Science and Technology with a bachelor's degree in electrical engineering in 2006, a master's degree in electrical engineering in 2008, and Ph.D. (2013) degree in Optique and Radio Frequency from Grenoble Institute of Technology, France. She is a lecturer, as well as the group leader of the Radio Frequency group at the Department of Instrumentation and Industrial Informatics (3I), School of Electrical Engineering (SEE), Hanoi University of Science and Technology (HUST). Her current interests include built-in antennas, antenna arrays, beamforming, metamaterials, indoor localization and RF energy harvesting, wireless power transfer, autonomous wireless sensor. She can be contacted at email: [email protected].