2019 International Conference on Advanced Technologies for Communications (ATC)
An Investigation of Adaptive Digital Beamforming
Antenna for gNodeB 5G
1
Hong Son Vu1,2, Kien Trung Truong3, Le Thanh Bang2, Van Yem Vu1, Minh Thuy Le1
Department of Instrument and Industrial Informatics, Hanoi University of Science & Technology, Hanoi, Vietnam
2 Wireless Broadband center – Viettel High Technology Industries Corporation (VHT), Hanoi, Vietnam
3 Wireless Systems and Applications, Posts and Telecoms Institute of Technology, Hanoi, Vietnam
Email: thuy.leminh@hust.edu.vn,
Abstract — Beamforming and the direction of arrival (DOA)
estimation for the massive multi-input multi-output (MIMO) play
a significant role in the fifth-generation (5G) cellular networks.
Several existing DOA and beamforming algorithms are validated
for the MIMO antenna system in 5G gNodeB. The proposed nonblind adaptive beamforming algorithm using Recursive least
squares Dolph Chebyshev (RLS-DC) with Uniformly spaced
Linear Array (ULA) of 32 elements is presented in this paper.
The sidelobe level is suppressed from -14 dB to -30 dB while
steering area from -60o to +60o is obtained.
Keywords— Non-Blind Adaptive Beamforming (NBABF),
Direction of Arrival (DOA), Antenna array, Recursive LeastSquares - Dolph chebyshev (RLS-DC), MIMO, 5G
I.
INTRODUCTION
Industry 4.0 has been expanding to all fields and aspects
of life. In this revolution, it is apparent that the fifthgeneration (5G) cellular networks are a contributing factor to
the development. To be specific, 5G will solve the problems
that 3G and 4G are facing such as massive devices, low
latency, and higher data rate (up to 1Gbps). Several
companies in Vietnam in the past three years have been
developing 5G technology. To ensure the quality of
telecommunication network, the gNodeB base station plays
an important role; it is the main development target of
telecommunication companies in Vietnam. One of key
technologies in 5G gNodeB base station is the massive
MIMO with DOA and beamforming techniques.
In general, beamforming techniques is grouped by three
types including analog, digital and hybrid beamforming [1]
and[2]. In 5G base station, the digital and hybrid
beamforming techniques are commonly used to reduce
power consumption that is proportional to the number of
antenna element in the array. However, for the sub-6 GHz
gNodeB, digital beamforming is a good candidate as the
number of antenna element is less than a hundred. There are
two methods of digital beamforming [3]: switched and
adaptive beamforming. Adaptive beamforming algorithms
can be classified into two main types: non-blind adaptive
algorithms and blind adaptive algorithms [4]. Non-blind
adaptive algorithms require a reference signal, with the
objective of determining a weighted path of travel. By
contrast, blind adaptive algorithms do not require any
reference signal for training; this feature is clearly expressed
by the term ‘blind’. Nevertheless, blind adaptive algorithms
require more time to obtain the optimal value; therefore, it is
lower than the former in term of weight update rate. As the
massive MIMO with a large number of antenna elements, so
that the main challenge for fully digital beamforming in 5G
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gNodeB is the low computational of beamforming and
reduced number of Sounding Reference Signal (SRS).
Therefore, the non-blind adaptive beamforming is a good
candidate for gNodeB.
A beamformer consists of two main parts: DOA
estimation and beamforming. DOA is necessary to estimate
accurately the incoming signal equivalent to the direction of
radio waves from the UE. After the broadcast phase,
depending on the number of present UEs, a corresponding
number of desired main beams are generated corresponding
with the UE locations using adaptive beamforming
techniques such that each desired beam is steered towards
the associated UE. During the process of creating a beam,
we need to control sidelobe level. When the sidelobe level
(SLL) is too high, it will reduce the main beam's energy.
Some commonly non-blind algorithms are: least-meansquare (LMS) algorithm, the recursive-least-square (RLS)
algorithm, sample matrix inversion (SMI), and conjugate
gradient (CG) [4]. Among them, RLS algorithm has the best
beamforming in term of convergence speed [5].
Nevertheless, this algorithm only focused on creating the
desired main beam but not on managing the sidelobe level.
Therefore, we propose to improve RLS algorithm by
combining with Dolph-Chebyshev method to control SLL to
obtain the desired main beam as well as to suppress the
unwanted sidelobe.
The remainder of the paper is organized as follows:
Section I introduces 5G with MIMO and beamforming
techniques. Section II describes the proposed beamforming
algorithms; the simulation results is presented in section III.
Section IV concludes the paper.
II.
PROPOSED BEAMFORMING ALGORITHM FOR GNODEB
5G
The beamformer architecture of the proposed gNodeB is
described in Figure 1. The DOA estimation and
beamforming techniques are associated with each other as
mentioned in the introduction; the cooperation of DOA and
beamforming is presented in Figure 2.
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2019 International Conference on Advanced Technologies for Communications (ATC)
Figure 4. Geometry of ULAs of 2K elements
Figure 1. Block diagram of digital beamformer in 5G base
station
If a incident wave is coming to the array at the θ angle ,
the wave font arrives at k + 1 element sooner than at k
element; the differential distance along the two ray paths is
dsinθ. The array factor is defined as:
K
AF(θ ) =
∑ We
− jn 2 Π d sin θ
λ
n
n =− K
Figure 2. Block diagram of DOA and adaptive beamforming
cooperation
The flowchart of designing the proposed beamformer is
described as follows:
K
=
∑ae
 − n 2 Π d sin θ

j
+δ n 
λ


(1)
n
n =− K
where Wn = an e jδ n is the complex weight corresponding to
the excitation of the element nth.
Structure of a non-blind adaptive beamforming is
presented in Figure 5. For 5G base station, reference signal
can be Sounding Reference Signal which is sent from UE in
uplink. This signal creation is presented in [7] and gives the
θ angle. The weight vectors are then determined based on
SRS using suitable non-blind beamforming algorithms
Figure 5. A diagram of a non-blind adaptive beamforming
We will start first with the principle of RLS. The RLS
adaptive algorithm directly approximates the Wiener
solution using the least mean squares method to adjust the
weight vectors without placing additional burden
approximately an optimization process [8]. In the least mean
squares method, weight vectors are chosen to minimize the
objective function J w ,w* [9]. The objective function of the
RLS method can be rewritten as follows:
k
J w ,w* = ∑ µ k −1 e(i )
2
(2)
i =1
Figure 3. Flowchart of designing the proposed beamformer
In this study, the MIMO antenna array is a Uniformly
spaced Linear Array (ULA) consisting of 32 elements [6] as
shown in Figure 4.
978-1-7281-2392-9/19/$31.00 ©2019 IEEE
where e(i) is error signal, 0 < µ < 1 is forgetting factor, and μ
is selected close to 1. However, in a stationary environment,
μ is equal to 1 since all data in the past and present must
have equal weight [10]. Take the differential of objective
function
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J w ,w* according to w * and find its minimum.
2019 International Conference on Advanced Technologies for Communications (ATC)
k
 k k −1

H
k −1
*
∑ µ x(i) x (i)  w(k ) = ∑ µ x(i )d (i )
i
=
1
i
=
1


In order to improve and manage sidelobes level, this study
combined the RLS algorithm with the Dolph-Chebyshev
sidelobe level method. The Dolph-Chebyshev method
allows from the requirement of the sidelobe level to
calculate the source amplitude that excites the elements. The
idea of this method is to take the array coefficient into the
form of the Chebyshev polynomial. At that time, the array
factor has only one main maximum and the extra peaks will
be smaller than the maximum, exactly in accordance with
the requirement for the extra radiation level. Half-power
beam width of antenna array when equal excitation and
phase source excitation is calculated in [11].
(3)
Set
k
R (k ) = ∑ µ k −1 x(i ) x H (i )
(4)
i =1
And
k
P(k ) = ∑ µ k −1 x(i )d * (i )
(5)
i =1
The expression is obtained
w( k ) = R −1 ( k ) P ( k )
Π
 1.391λ  
HPBW (Uniform) ≈ 2  − cos −1 

 Π Kd  
2
(6)
Recursive implementation in (4) and (5) is obtained.
R (k ) = µ R( k − 1) + x (k ) x H (k )
*
P (k ) = µ P( k − 1) + x (k )d (k )
(8)
Weight of array when applying Dolph-Chebyshev [11]:
(7)
HPBW ( Dolph − Chebyshev ) = f ⋅ HPBW (Uniform)
It is possible to obtain the inverse matrix R −1 (k ) using
recursion according to R −1 ( k − 1) by using the lemma
inverse matrix [5], thus avoiding direct inversion R ( k ) at
each kth iteration.
2

f = 1 + 0.636  cosh (cosh −1 R0 ) 2 − Π 2 
R
 0

2
(9)
R
where R0 = 10 20 with R (dB) desired sidelobe level.
Then weights generated by the RLS algorithm are
multiplied by the weights generated by Dolph-Chebyshev.
The simulation results of RLS-DC algorithm are obtained as
in Section III.
III. SIMULATION RESULTS
A. Simulation Scenario
Given initial conditions in these simulations were chosen
regarding to the 3GPP requirements for the angular
resolution up to 5° for UE moving speed up to 0.5 m/s in 5G
wireless communications. With the estimated DOA by the
Root-MUSIC algorithm, this study simulates beamforming
algorithms with conditions: The array size is held to 32
elements, the number of samples is 1000 samples as the
values of SNR are varied from 10-50dB and is illustrated in
Figure 5. Holding SNR at 20dB and varying the number of
samples from 100 to 10000 samples, snapshots = 50. The
simulation frequency is 3.75GHz equivalent to the central
frequency of licensed 5G gnodeB station in Vietnam.
Simulation uses matlab program. And, this study ignores
mutual coupling effect between elements.
Figure 7. Assumption of the UE positioning for
beamforming simulations
Figure 6. Flow chart of RLS-DC algorithm
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2019 International Conference on Advanced Technologies for Communications (ATC)
B. Simulation Results
The simulation results are illustrated in Figure 7. It can
be seen that the RLS algorithm for the main beam direction
are right to the incoming signal direction of 00, eliminating
the direction of noise to -350. The first sidelobe beam is
reduced from - 14 dB with RLS to – 30 dB using RLS-DC.
In addition, when using RLS-DC algorithms, sidelobe level
were completely controlled under the expected value, - 30
dB in this case.
Figure 10. Four beams are generated by RLS-DC algorithm
(theta= -600, -300, 300 and 600)
IV. CONCLUSTION
In this paper, we proposed the non-blind adaptive
beamforming algorithms RLS-DC. The sidelobe level is
suppressed to 16 dB (from -14 dB to -30 dB) when applying
RLS-DC. The steering area from -600 to 600 is obtained with
low sidelobe level. The angular resolution is less than 5o for
UE moving speed up to 0.5 m/s to meet the 3GPP
requirement. RLS-DC is more suitable for embedded
computer implementation due to its fast convergence rate.
Figure 8. Array factor of ULA of 32 elements with RLS and
RLS-DC algorithm (SNR=20dB, 1000 samples, R=30dB)
In order to be able to compare the convergence rates of
the RLS-DC algorithm, this study simulated the objective
function after 50 iterations when the SNR are varied from
10 to 50 dB. The results are presented in Figure 8. It is
realized that the ratio of signal to noise increases; the ability
of convergence of algorithm is also smoother and at higher
level.
Figure 9. Objective function of RLS-DC after 50 iteration
In the case of four connected UEs at four direction, 4
beamformers corresponding to 4 desired beams are
generated towards the theta = -600, -300, 300 and 600 results
as in the following figure. We can easily realize that the
angle of the best sidelobe level is between -600 and 600.
978-1-7281-2392-9/19/$31.00 ©2019 IEEE
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