Wireless Personal Communications

https://doi.org/10.1007/s11277-021-08455-7

Hybrid Beamforming for Massive MIMO Using Rectangular

Antenna Array Model in 5G Wireless Networks

Thupalli Sai Priya1 · Kondala Manish1 · P Prakasam1

Accepted: 28 March 2021

© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2021

Abstract
Fifth and future generation (5G and B5G) wireless networks aim to serve users with higher
data rates and lower latency. Data traffic due to the rapid growth in communication has
motivated the study of Multiple Input Multiple Output (MIMO) systems. They utilize mul-
tiple antennas in both transmitter and receiver sides. It is necessary to improve the existing
technology to achieve fast and reliable communication. In this research work, a rectangular
array antenna based hybrid beamforming in a massive MIMO model has been proposed to
improve the spectral efficiency of the system. Thus channel capacity with small RF chains
is used. To achieve the high signal strength in the main lobe, Chebyshev tapering has been
used to suppress the side lobes signals. In this manner, the proposed Hybrid Beamforming
for Massive Output MIMO has been realized with a small complexity and higher spectral
efficiency. In this research work, the spectral efficiency of both proposed Hybrid and fully-
digital beamforming with a different number of RF chains for a various number of antennas
at the transmitter, the receiver side has been analyzed. From the simulation results, it has
been observed that the proposed rectangular array antenna based Hybrid beamforming in a
massive MIMO system reduces the computational complexity up to 99% as compared with
conventional fully digital beamforming to achieve the same spectral efficiencies, which is a
productive model for 5G wireless networks.

Keywords 5G Wireless networks · Massive MIMO · Hybrid beamforming · Rectangular

antenna array · Spectral efficiency

* P Prakasam
prakasam.p@vit.ac.in
Thupalli Sai Priya
thupallisai.priya2017@vitstudent.ac.in
Kondala Manish
kondala.manish2017@vitstudent.ac.in
1
School of Electronics Engineering, Vellore Institute of Technology, Vellore 632014, India

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1 Introduction

Innovation is continuously changing the manner of communication with the world. As

pushed ahead, new technologies such as connected vehicles, autonomous drones, three-
dimensional (3D) media, artificial intelligence (AI), Blockchain, Internet of Everything
(IoE) are escalating the network traffic as appeared by predicted statistics in [1], 2]. Taking
a look at the next decade, the innovations have become unpredictable in the new wireless
technologies, as the number of voice and data communications is exponentially growing in
accordance with Cooper’s law. This was explained by researcher Martin Cooper [3]. User
needs have ever increased and the current mobile communications have minimal systems
and have compelled the researchers to come up with more advanced and efficient technolo-
gies. The 3G network (Wideband-CDMA), which is termed as Mobile Broadband, with
Code-Division Multiple Access (CDMA) Supported video conferencing, GPS, mobile TV,
etc. The 4G network (Long-Term Evolution) with Ultra-Broadband internet service and
CDMA. They concentrated on desegregating the terminals, networks, and applications,
supported high-speed applications, wearable devices, mobile TV, interactive multimedia,
etc.
The 5G network with a speed 10 × than 4G uses a scalable orthogonal frequency-divi-
sion multiplexing (OFDM) framework and New Radio (NR) technology in millimeter-wave
(mmWave) spectra to elevate over its predecessor [4], 5]. Along with that wireless world
wide web internet service supports autonomous robotics in medical applications, autono-
mous unmanned vehicles and video streaming with high quality. The fifth-generation (5G)
network was first globally launched by Verizon in April 2019. The 4G and 5G technolo-
gies have concentrated on increasing the speed and reducing the latency in personalized
communication. A detailed comparison of 2G, 3G, 4G & 5G is given in Table 1. Mov-
ing further beyond 5G that is into B5G communication, it is supposed to be structured in
such a way that it will move towards using the full potential of high-speed communication.
Reducing latency is not only the constraints in mobile-to-mobile communication but also
machine-to-machine communication [6], 7]. The 5G networks are employed now. There
are possible improvements in present technologies to support the new challenges in future
innovations. This is Beyond fifth-generation (B5G) [1]. Present 5G technologies face Cov-
erage issues, Emerging applications challenges, D2D (Device to Device) communication
and vulnerabilities, mobile edge computing issues, network orchestration, slicing, etc.
These issues are to be rectified by the development of Internet of Everything (IoE) ser-
vices, future generation (B5G) wireless system with Network intelligence, fast spectrum
reallocation, enhanced mobile broadband (eMBB), Ultra-reliable low latency commu-
nications (URLLC), peer-to-peer communication, security and privacy, enhanced senses
where human senses improve the quality of interaction, battery duration, energy, etc. [8]

Table 1  Comparison of various mobile network technology generations

Generation Maximum speed Delay (ms) Download ­time* Bandwidth

2G 0.3 Mbps 300–1000 35–40 min 25 MHz

3G 42 Mbps 50–100 45 s–1 min 25 MHz
4G 1 Gbps 20–30 5–8 s 100 MHz
5G 10 Gbps 1–10 <1 s 30 GHz–300 GHz

(*Average application file size being 38 Mb for IOS, 15 Mb for Android)

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Hybrid Beamforming for Massive MIMO Using Rectangular Antenna…

by enabling higher frequency bands, communications with large intelligent surfaces, trans-
ceivers with integrated receiver bands, edge artificial intelligence(AI), integrated terres-
trial, airborne and satellite networks [9]. In order to meet the requirements of the 5G net-
works mentioned above and to achieve the smooth functioning of future network traffic,
massive MIMO mmWave technologies employed in Heterogeneous networks (HetNets) [7]
are emerging. These core technologies provide a better quality of service (QoS) when com-
pared with the existing communication technologies.

1.1 Motivation

Due to the technology development and increase in demand, fifth-generation networks

(5G) are facing problems to provide the service for more number of users. Therefore, the
5G network service has to provide the service to mobile users with high data rates and low
latency. This is the bottleneck of the existing wireless networks. This motivated the authors
to do the present research work in a different direction. The area throughput of any wireless
network is given by
( )
Area throughput = B(Hz) × D cells∕km2 × SE(bits∕s∕Hz∕cell) (1)

where B, D and SE are bandwidth, mean cell density and spectral efficiency per cell respec-
tively. Therefore from Eq. (1), it has been found that the average throughput is depending
on the three metrics. Hence, the area throughput can be increased by optimizing the above
mentioned three metrics to meet the requirement of future generation networks. Therefore,
area throughput can be increased by either allocating more bandwidth or densifying the
cellular network, or improving the spectral efficiency per cell. But due to the limitation in
the frequency band, allocating more bandwidth is the bottleneck for the wireless industry.
Also densifying the cell with more BSs will create a shadowing effect in the coverage.
Therefore an optimal throughput demands an increase in the area by optimizing the spec-
tral efficiency per cell.
Also, Shannon’s channel capacity is defined by
( )
S
C = B × log2 1 + bits/s (2)
N
where S and N are the signal and noise power respectively. Equation (2) also can be rewrit-
ten as
C = B × SE (3)
From Eqs. (2) and (3), it is observed that to increase and optimize the channel capacity
as well as the spectral efficiency, the power of the transmitting signal (S) may be increased.
But increasing the signal power beyond a certain limit will also increase the complexity
in wireless networks. Hence, this motivated the present work to propose the rectangular
antenna array-based Hybrid Beamforming for massive MIMO systems for increasing the
channel capacity and spectral efficiency per cell without increasing the transmitted signal
power.
The rest of the paper is structured as follows: The detailed literature has been reviewed
in Sect. 2. Section 3 explains the system model and rectangular antenna array model for the
proposed system. The experimental results and analysis have been investigated in Sect. 4.
Section 5 concludes and directs for future research.

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 T. S. Priya et al.

2 Literature Review

Massive MIMO is a large scale antenna system with radio antenna technology. This
enhanced the number of antennas at transmitter and receivers by a few orders of magnitude
more than conventional MIMO enabling multiple signal paths, thus increasing the array
gain than before [10]. Going large from multi-user MIMO (MU-MIMO) originated mas-
sive MIMO, which offered vast degrees of freedom (DoF). It could be utilized by using
beamforming techniques if channel state information (CSI) was available. The CSI was the
signal propagation (transmitter to receiver) information [1]. The additional antennas could
be used for minimal areas to bring a vast improvement in massive MIMO throughput and
radiated energy efficiency. Beamforming was a technique used in massive MIMO which
navigated the signals produced from an array of antennas in a particular required direction.
The various channel parameters were extracted using the perturbation-aided opportunis-
tic method. This had been utilized to generate the pre-coders for temporarily correlated
mmWave MIMO systems [11]. A coherent combination of all received signals took place
at the receivers by a diverging scale factor to enlarge the Signal-to-Noise Ratio, which was
received. In mmWave massive MIMO, the issue of power consumption and cost due to
mixed analog/digital signal components at each antenna could be overruled by designing
different topologies of hybrid beamforming [12]. The hybrid beamforming topology had
a reduced number of RF systems when compared with analog/digital beamforming tech-
niques. This gave rise to multi-stream digital processing (Baseband). Also, following this,
analog processing (Baseband or RF) took place. [13].
The error performance and average sum rate of the mmWave MU-MIMO might also
be increased using a partially connected structure (PCS) hybrid beamforming mechanism
[14]. The reported PCS mechanism was formed by combining the beam patterns using the
information of azimuth and elevation angles. The mmWave communication was a favora-
ble technology that could overcome the bandwidth shortage issue for the next generation
wireless communication [15, 16]. The mmWave technology utilized a very high frequency
between 30 and 300 GHz, the wavelength between 1 and 10 mm, and the maximum band-
width of 252 GHz. Although mmWave frequencies experienced path loss and absorption
issues when compared with normal frequency ranges, a large number of antennas was
stacked within minimal areas. This increased the deployment of large scale antennas array
systems at the transceivers, which could possibly deal with propagation issues of the chan-
nel [17]. Ultra-Dense Networks (UDN) was a crammed development of small cell base
stations (SBS) within the limit of macrocell base stations (MBS). It was obvious that UDN
was an adequate way to accelerate network capacity, throughput, SE, EE and coherent cov-
erage for networks.
The combination of mmWave Technology, UDN and massive MIMO cooperatively pro-
duced HetNets architecture. The critical aspects of combined mmWave massive MIMO
technology were by merging the feature of mmWave BW and antenna array gains of mas-
sive MIMO technology. This had become the central element of next-generation cellular
networks such as 5G communication [18]. Antenna Pre-coding and array combining tech-
niques could be used to utilize the array gain of the massive number of antennas of MIMO
[19]. The deployment of devoted RF chain hardware was required for each antenna, which
could increase the cost as well as power consumption peculiarly for mmWave technologies.
Therefore, it was necessary to innovate in the antenna system design that would use the
potential gain from a stack of low-cost antennas using a less amount of costly RF systems.
[20]

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Hybrid Beamforming for Massive MIMO Using Rectangular Antenna…

Hu et al. [17] had explained the significant effect on Spectrum efficiency, channel
capacity and energy efficiency in Massive MIMO systems. It was described that there was
a higher requirement of Massive MIMO in the future due to its increased performance
in many aspects. The different combinations, such as fully connected phase shifters and
switching networks in massive MIMO had been elaborated [20]. Also, the optimal design
of the pre-coder and the combiner was explained with the constraint of minimum mean
square error (MSE). The authors had come up with different combinations of phase shifters
and switches while increasing the number of both. The mathematical expression regarding
the Greedy Ration Trace Maximization (GRTM) was also explained where each iteration
was added with one RF chain that had an optimal combinational vector, which was added
to the previously K selected vectors.
Ahmed et al. [21] had focused on the work on the hybrid beamforming application.
Hybrid beam forming had been categorized into hybrid beamforming architecture, manag-
ing the available resources, various numbers of antennas on transmitter and receiver sides,
the hybrid beamforming in HetNets and microcells. Future research problems, challenges
and open issues had been listed. The impact of the downlink MU-MIMO system channel
with hybrid beamforming had been explained [22]. They had demonstrated that by uti-
lizing more RF chains and Analog-to-digital converters (ADCs), the performance of the
MU-MIMO could be increased. Huang et al. [23] proposed the framework for optimizing
the transmitting and receiving beamformers jointly by using the extreme learning machine
mechanism for Millimeter-Wave Multi-User MIMO Systems.
The hybrid beamforming technique for different frequencies and only for a selective
channel had been proposed [24], 25]. They had addressed the issue related to maximiz-
ing the spectral efficiency in SU-MIMO by utilizing a little feedback consideration. Ini-
tially, they had developed a hybrid analog–digital codebook design for mmWave systems
and further, the pre-coding algorithm had been proposed based on Gram Schmidt orthogo-
nalization. A generalized hybrid beamforming scheme for mmWave MIMO systems using
singular value decomposition (SVD) to reduce the complexity and number of RF chains
[26]. Also, the energy consumed by the mmWave massive MIMO could also be reduced
by a fully complex Zero Forcing mechanism by reducing the number of RF chains [27].
Soleimani et al. [28] investigated the design of a simplified user clustering algorithm which
was based on the DFT. In this proposed method mobile users available in the same and
overlapping angular bins were grouped together as a single cluster to find the optimal solu-
tion for mmWave MIMO systems.
Molisch et al. [29] explained the usage of many hybrid-multiple antenna transceivers
that combined large dimensional analog pre and post-processing. The study involved vari-
ous structures of different combinations of transmitters and receivers. Second-order chan-
nel states were mainly used, which provide better SNR and interference ratio. The main
difference between structures of different complexities had been explained and the design
aspects for the operation of mmWave frequencies were listed as future problems. The dif-
ference between bit error rate (BER) performance of the hybrid pre-coding and the BER
performance of the receiving beamforming of mmWave-massive MIMO systems had been
explained [30]. A detailed analysis had been done on hybrid precoding technique as well
as receiver combining technique for various configurations, and it had been concluded that
processing played a vital role than diversity when flawless CSI was present at transmitter
and receiver sides. When the number of antennas and users were equal, an unacceptable
error performance had been found at high SNR rates also [31].
Noordin et al. [32] had proposed various uniform circular arrays (UCA) configurations
implementation for hybrid beamforming. A detailed explanation of these arrays and a

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 T. S. Priya et al.

comparison had also been given. It shows the configuration which would be able to enable
the phased antenna array to scan azimuthally with very few changes in its sidelobe levels
and the widths of the beam. The Particle Swarm Optimization (PSO) method had been
used to calculate the complex weights for the antennas to adapt to the changing environ-
ments which had been used to increase the information rate in hybrid pre-coding methods
[33]. Busari et al. [34] had presented a framework for the design of Hybrid Beamforming
(HBF) architecture which utilized the subarray spacing as a key parameter. The perfor-
mance of the HDF architecture had been analyzed using the single-path terahertz (THz)
channel model.

2.1 Research Contribution

Based on the above literature survey, it has been observed that still a lot of opportunities
are there to improve the spectral efficiency of the massive MIMO which can be used in 5G
wireless networks by increasing the channel capacity and area throughput. Hence in this
research work, the following contribution has been done:

1. A rectangular antenna array-based hybrid beamforming model for a massive MIMO

system has been introduced as a system model.
2. The rectangular array antenna geometry has been analyzed and also the practical antenna
has been introduced.
3. The spectral efficiency analysis has been carried out for different array sizes to conclude
the impact of RF chains in hybrid beamforming as compared with conventional fully
digital beamforming.
4. Bit Error Rate (BER) has been computed for various SNR to prove the superiority of
the proposed rectangular array antenna based MIMO system.

3 System and Channel Model

The system model considered in this proposed work is illustrated in Fig. 1. The mas-
sive MIMO system has been considered. It is a multi-user system with multiple streams
whose downlink is equipped with 3-D N ­ tRF RF chains and uplink
­ t antenna arrays with N
RF
is equipped with 3-dimensional ­Nr antenna arrays and ­Nr RF chains. Let N ­ r denote the
number of streams received at each receiver. The proposed hybrid MIMO system model
has been configured such that NtRF < Nt and NrRF < Nr.
A transmitter is likely to be sectored to lesser the interference and increase the beam-
forming gain. The foremost thought of beamforming or large antenna arrays [35] is the
excellent flexibility where the beam can be steered when there is a multiple user environ-
ment. Most beam steering flexibility comes with the fully digital MIMO beamforming
technique, but the cost is high for this technique. The best outcome can be brought by com-
bining the beamforming techniques of digital, analog system, and the RF domain, which
has lower flexibility when compared to a fully digital MIMO system at a low cost.
In conventional (fully digital) MIMO systems, both the number of RF chains and the
number of antennas are equal on the transmitter side for pre-coding and number of anten-
nas on the receiver side for combining. The performance analysis of a conventional fully
digital MIMO system is compared with the Hybrid MIMO system using hybrid pre-coding

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Hybrid Beamforming for Massive MIMO Using Rectangular Antenna…

Fig. 1  System model for massive MIMO system with hybrid beamforming

and combining. It depicts that there is a negligible loss in Hybrid MIMO when compared
with fully digital conditions. Conventional fully digital beamforming technique demands a
dedicated RF chain corresponding to a particular antenna. Hence it will be extremely costly
and complex. Whereas, with a fewer number of RF chains, as shown in Fig. 1, the Hybrid
beamforming techniques promise to reduce the complexity of the hardware and also cost.
Their performance is analyzed and discussed in Sect. 4.
To reduce the complexity in hardware, a hybrid MIMO system with digital and analog
pre- coding architecture has been considered (Fig. 1). The transmitted signal at the base
station side is given by.

∑
K
x = T RF T BBk Sk (4)
k=1

where T BBk ∈ ℂNt ×Nt is denoted as the analog beamforming matrix and T RF ∈ ℂNt ×Ns is
RF RF

denoted as the digital beamforming matrix. After the BS analog pre-coder where the sig-
nals go through analog phase shifters, the signals are processed digitally and then again
up-converted to the carried frequency through RF chains and Sk ∈ ℂNs ×T denotes the data
stream of the kth user.
The signal received for the kth user is given by
√
yk = 𝜌Hk x + nk (5)

where Hk is the Nt × Nr channel matrix between the BS and kth user which can be rep-
resented as:

⎡ H11 H12 ⋯ H1Nt ⎤

⎢ H H22 ⋯ H2Nt ⎥
Hk = ⎢ 21 ⎥ (6)
⎢ ⋮ ⋮ ⋱ ⋮ ⎥
⎣ HNr 1 HNr 2 ⋯ HNr Nt ⎦

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 T. S. Priya et al.

For user k, where 𝜌 is the average received power and nk is the Additive White Gauss-
ian Noise (AWGN) with zero mean and σ 2 covariance.
The finally processed discrete signal at the receiver side is given by

S̃ k = R*BB R*RF yk (7)

k k

where RRFk ∈ ℂNr ×Nr is denoted as the analog combiner matrix and RBBk ∈ ℂNs ×Nr is
RF RF

denoted as digital combiner matrix. The received signal is processed first analog domain
and then it has been processed in the digital domain and then down-converts the signal
through RF chains. Equation (7) may be rewritten as
√
S̃ k = 𝜌R*BB R*RF Hk T RF T BBk Sk + R*BB R*RF nk (8)
k k k k

The spectral efficiency achieved by this proposed hybrid beamforming massive

MIMO is given by
[ ( )]
𝜌 −1 * * * * *
SE = log2 det INs + Sn RBB RRF Hk T RF T BBk T BB T RF Hk RRFk RBBk (9)
Ns k k k k

where Sn = 𝜎 2 R*BB R*RF RRFk RBBk is the noise covariance matrix of analog–digital
k k
combiner.

3.1 Rectangular Antenna Array Model

The rectangular antenna array model is shown in Fig. 2. Let the source be in the far-field
of the receive antenna array.
Assume that every element of the rectangular antenna array is having either isotropic
or omnidirectional radiation pattern. The received signals due to the far-field source of
the four array elements can be obtained using the expressions given below.

Fig. 2  Rectangular antenna array

geometry

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Hybrid Beamforming for Massive MIMO Using Rectangular Antenna…

R1 = 1 (10)

R2 = e−j2𝜋dy sin𝜃∕𝜆 (11)

R3 = e−j2𝜋dx cos 𝜃∕𝜆 (12)

R4 = e−j2𝜋 (dy sin 𝜃+dx cos 𝜃)∕𝜆 (13)

It is observed that as per the vector geometry, the resultant signal is depending upon the
relative phase of the above four vector components. Therefore the resultant field received at
the rectangular antenna array due to the far-filed source is given by
R = R1 + R2 + R3 + R4 (14)
However in the proposed Hybrid Beamforming for Massive MIMO using Rectangular
Antenna Array Model, Nt x Nr rectangular array antenna is considered. The resultant signal
can be written as

∑ ∑
Nt −1 Nr −1
RT = e−j2𝜋 (mdy sin𝜃+ndx cos𝜃)∕𝜆 (15)
n=0 m=0

The range of n and m is 0 to Nt − 1 and 0 to Nr − 1 respectively.

3.2 Bit Error Rate, Spectral Efficiency and Channel Capacity

The proposed system model has been analyzed by computing spectral efficiency, channel
capacity and BER over SNR for a different combination of transmitter and receiver anten-
nas is very important for MIMO systems.
SNR is a ratio of the strength of the received signal to the strength of noise in the oper-
ating frequency range. Noise commonly includes unwanted signals, environmental noises,
which end up as interference. SNR is generally used as an indicator to assess the quality of
the communication channel. The relationship between BER and SNR is inversely related,
i.e., high SNR causes low BER and SNR is measured in decibels(dB) The SNR and BER
formulae are given by:
Signal Power
SNR = 10 × log10 dB (16)
Noise Power

Bits in Error
BER = (17)
Total bits received
The channel matrix hji of the massive MIMO channel matrix can be represented as
(6), where it is a complex Gaussian random variable that models fading gain between the
ith transmitter and jth receiver antenna. And in terms of spectral efficiency, the spectral
efficiency and the channel capacity of the various system can be calculated using Eqs.
(19)–(24). The spectral efficiency and the channel capacity of the conventional system is
given by

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 T. S. Priya et al.

( )
S
SESISO = log2 1 + bits/s/Hz/cell (18)
N
( )
S
CSISO = B ∗ log2 1 + bit/s (19)
N
The spectral efficiency and the channel capacity of the SIMO as well as MISO system
is given by
( )
S
SESIMO = SEMISO = log2 1 + n bits/s/Hz/cell (20)
N
( )
S
CSIMO = CMISO = B ∗ log2 1 + n bit/s (21)
N
where n = ­Nr is the number of antennas on the receiver side for SIMO and n = ­Nt is the
number of antennas on the transmitter side for MISO.
The Spectral efficiency and the channel capacity for the MIMO is given by
( )
S
SEMIMO = log2 1 + Nt ∗ Nr ∗ bits/s/Hz/cell (22)
N
( )
S
CMIMO = B ∗ log2 1 + Nt ∗ Nr ∗ bit/s (23)
N
It has been proven theoretically and practically that massive MIMO shows the highest
spectral efficiency and channel capacity. Thus the average area throughput increases with
the increased number of transmitting and receiving antennas.

4 Experimental Results and Discussions

This section deals with the practical antenna configuration and the results obtained for
the proposed rectangular antenna array based Hybrid Beamforming for massive MIMO
systems.

4.1 Rectangular Antenna Array Structure

Figure 3 represents a developed Rectangular antenna array with a 4X4 antenna array struc-
ture using polyhedron material.
There are a total of 12 planar arrays that transmit an equal amount of power individu-
ally and each of these is connected to a single receiving antenna placed in a device. The
proposed array antenna is capable of forming the radiation beams in all directions in a
3D manner. This is done to maximize the efficiency and serve User Equipment (UE) with
higher data rates and low latency. The average size of the receiving antenna device is con-
sidered to be from 0.9 to 1.5 m.
The developed Rectangular Antenna Array-based Hybrid Beamforming model for
massive MIMO has been simulated and verified using MATLAB R2019b. The parame-
ters assumed for the simulation are tabulated in Table 2. First, the radiation pattern and
azimuth pattern without and with Chebyshev Tapering for various rectangular array size

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Hybrid Beamforming for Massive MIMO Using Rectangular Antenna…

Fig. 3  Rectangular antenna array structure

Table 2  Parameters assumed for Parameters Range

simulation
Radius of the cell 400 m
Number of Transmitting Antenna Array Upto 256 × 256
Number of Receiving Antenna Upto 65
Arrangement of Antenna Rectangular
Polarization
Array
Separation distance between Antenna (mm) λ/2
SNR 20 dB

for the developed model has been simulated using the parameter shown in Table 2. After
that, the spectral efficiency improvement using the developed Rectangular Antenna Array
based Hybrid Beamforming in massive MIMO for 5G has been simulated for various data
streams and compared with conventional fully digital beamforming technique. At last, the
BER performance versus SNR has been analyzed.

4.2 3D Radiation and Azimuth Patterns

In this subsection, the simulation and an analysis of radiation and azimuth patterns for vari-
ous rectangular antennas array has been carried out. Different types of patterns with differ-
ent array sizes are considered and analysis of their spectral efficiency, BER vs SNR perfor-
mance has been done.
The simulated beam pattern and azimuth pattern without and with Chebyshev taper-
ing for different rectangular array sizes of 4 × 4, 8 × 8, 12 × 12 and 16 × 16 have been
illustrated in Figs. 4, 5, 6 and 7 respectively. From the simulation, it has been observed
that there is a clear distinction in radiation as well as azimuth patterns without and with

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 T. S. Priya et al.

Fig. 4  Beam patterns—4 × 4 rectangular array a 3D Pattern without Tapering b 3D Pattern with Chebyshev
Tapering c Azimuth Pattern without Tapering d Azimuth Pattern with Chebyshev Tapering

Chebyshev tapering. For the basic design parameters, the number of antennas taken for
Fig. 4 are ­Nrow = 4, ­Ncol = 4 (4 × 4) and an element spacing of ƛ = [0.5 0.5]. The lattice
structure used is rectangular in nature and an amplitude taper is applied in the antenna
structure. The element used is an isotropic antenna with a propagation speed of 3 × ­108
(m/s) and a signal frequency of 300 MHz without any steering. The usage of a 2D-Azimuth
pattern is done with a polar coordinate system into consideration.
The main problem that arose is that the formation of Side lobes that were present in the
radiation pattern. These are unwanted ones and they lead to reception or transmission of
energy in directions that are not required. Amplitude Taper/Amplitude Weighting can be
used to reduce the side lobes’ directivity in different array sizing. Amplitude taper is used
from the centre of the array to the end of the array to control the minor lobe levels. These
arrays are non-uniformly excited. The improved main beams can be achieved in the desired
direction by controlling the side lobes on the linear array using amplitude tapering. This is
nothing but a steerable antenna array and this can achieve the desired results.
In Fig. 4, where a 4 × 4 antenna array is considered, there are many side lobes and one
main lobe. But since the antenna array number is very small i.e. only 16 antennas compared
to other antenna array configurations considered which has a higher number of antennas.

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Hybrid Beamforming for Massive MIMO Using Rectangular Antenna…

Fig. 5  Beam patterns—8 × 8 rectangular array a 3D Pattern without Tapering b 3D Pattern with Chebyshev
Tapering c Azimuth Pattern without Tapering d Azimuth Pattern with Chebyshev Tapering

It is observed that too many side lobes are present in it that can act as the main lobe also.
It means that the signal power of the antenna is very small but it covers more area which
is not a required feature. By increasing the antenna size of 64, where it is an 8 × 8 antenna
array, form Fig. 5, it is observed that the number of side lobes have increased but are not as
functional as the main lobe and the directional power of the 8X8 antenna array increased
with the increase in the number of antennas and the signal power is increased in a specific
direction.
The process of beamforming and beam steering is gradually increased with the increase
in the number of antennas. The radiation pattern and azimuth pattern of the 12 × 12 antenna
array configuration have been computed and illustrated in Fig. 6. It is observed that as
compared with the 4 × 4 and 8 × 8 array antenna, even though the number of side lobes is
higher, the directivity of the side lobes is decreased. After incorporating Chebyshev Taper-
ing, the directivity of the side lobes is reduced further for providing better directivity for
the main lobe. The antenna array configuration of 16 × 16 has been simulated and shown
in Fig. 7. The main difference between normal 3D patterns and 3D patterns with Cheby-
shev tapering is that the number of side lobes formed in the 3D patterns with Chebyshev
tapering will be very small. In the 3D patterning with Chebyshev tapering, it is observed
that the patterns formed have a small number of side lobes even in 4 × 4 antenna array size

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 T. S. Priya et al.

Fig. 6  Beam patterns—12 × 12 rectangular array a 3D Pattern without Tapering b 3D Pattern with Cheby-
shev Tapering c Azimuth Pattern without Tapering d Azimuth Pattern with Chebyshev Tapering

compared to that of a 3D pattern formed without tapering. The reduction of sidelobe signal
gain is due to the change in excitation amplitude done by Chebyshev amplitude tapering.
In the previous generation of wireless communication systems, the signal that is dis-
sipated is bidirectional and the amount of power that will be received by each user is low.
On observing the azimuth pattern in Fig. 7, it is observed that the number of side lobes
is formed with less intensity/directivity and the directivity of the main lobe is very high.
From the above illustrations, it has been observed that if the antenna is configured with
rectangular array geometry with Chebyshev amplitude tapering then the signal strength
achieved is higher with lower side lobes such that the signal can be focused in a required
single direction.

4.3 Spectral Efficiency for Different Rectangular Array Antennas

In this subsection, the performance of the proposed Rectangular Antenna Array-based

Hybrid Beamforming model for massive MIMO has been analyzed by computing the spec-
tral efficiency. The spectral efficiency has been computed for the proposed hybrid beam-
forming and fully conventional digital beamforming. It has been generated with a different
number of antenna and RF chains. The spectral efficiency has been simulated for a differ-
ent number of data streams with various SNR ranging from −40s to 20 dB. The simulated

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Hybrid Beamforming for Massive MIMO Using Rectangular Antenna…

Fig. 7  Beam patterns—16 × 16 rectangular array a 3D Pattern without Tapering b 3D Pattern with Cheby-
shev Tapering c Azimuth Pattern without Tapering d Azimuth Pattern with Chebyshev Tapering

spectral efficiency for the various number of the rectangular antenna array is shown in
Figs. 8, 9, 10, 11 and 12.
Initially, 36 × 4 massive MIMO system is considered with rectangular planar arrays at
transmitter and receiver, and the number of RF chains at each end is ­Nrf = 4. The spectral
efficiency of the proposed rectangular array antenna based Hybrid beamforming of 36 ×
4 massive MIMO systems for various numbers of data streams N ­ s has been simulated and
shown in Fig. 8. It has been observed that instead of fully digital beamforming, the number
of base stations required is 4 or 36 whereas the same spectral efficiency has been achieved
by the proposed Hybrid beamforming with 16 RF chains with different data streams. Fig-
ure 9 shows the spectral efficiency achieved in a 64 × 16 massive MIMO Hybrid beam-
forming model with N ­ rf = 4 at both ends for various transmitting data streams ­Ns = 1, 2 and
3. It has been observed that, that instead of 1024 RF chains in conventional fully digital
beamforming, the proposed rectangular array antenna based Hybrid Beamforming with
256 RF chains can achieve almost the same spectral efficiency.
The spectral efficiency achieved for 64 × 16 massive MIMO Hybrid beamforming sys-
tem with ­Nrf = 8 for different data streams has been illustrated in Fig. 10. It has been found
that, that instead of 1024 RF chains in conventional fully digital beamforming, Hybrid
Beamforming with 512 RF chains can achieve the same spectral efficiency. From Figs. 9

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 T. S. Priya et al.

Fig. 8  Spectral efficiency of fully

conventional digital and pro-
posed rectangular array antenna
based Hybrid beamforming mas-
sive MIMO systems with ­Nt = 36,
­Nr = 4 and ­Nrf = 4

Fig. 9  Spectral efficiency of fully

conventional digital and pro-
posed rectangular array antenna
based Hybrid beamforming mas-
sive MIMO systems with ­Nt = 64,
­Nr = 16 and ­Nrf = 4

and 10 it has been observed that with an increase in the number of RF chains with the same
number of antennas, the spectral efficiency can be increased to meet out the spectral effi-
ciency of the conventional fully digital beamforming. More data streams can be transmit-
ted simultaneously at large SNRs by activating additional RF chains due to the improved
spectral efficiency. Thus, an increase in RF chains improves spectral efficiency. The differ-
ence in spectral efficiency between the system using 4RF & 8RF chains is very minimal
and thus hybrid MIMO systems with fewer RF chains can be preferred for the efficient
transmission of signals with lower complexity.
To explore the performance of larger antenna arrays, Fig. 11 plots the spectral efficiency
achieved for 256 × 64 rectangular array antenna based hybrid beamforming MIMO system
with ­Nrf = 8 at both ends where spectral efficiency is almost the same with a very minimal
deviation in a fully digital system and hybrid system. The spectral efficiency achieved for
the 256 × 64 massive MIMO Hybrid beamforming system with ­Nrf = 8 and ­Nrf = 16 for dif-
ferent data streams has been illustrated in Figs. 11 and 12 respectively. It can be observed

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Hybrid Beamforming for Massive MIMO Using Rectangular Antenna…

Fig. 10  Spectral efficiency of

fully conventional digital and
proposed rectangular array
antenna based Hybrid beamform-
ing massive MIMO systems with
­Nt = 64, ­Nr = 16 and ­Nrf = 8

Fig. 11  Spectral efficiency of

fully conventional digital and
proposed rectangular array
antenna based Hybrid beamform-
ing massive MIMO systems with
­Nt = 256, ­Nr = 64 and ­Nrf = 8

that the spectral efficiency of the hybrid beamforming in a massive MIMO system perfectly
matches with the spectral efficiency of a fully digital MIMO system when the RF chains
are increased from ­Nrf = 8 to ­Nrf = 16 in the hybrid MIMO system. From the above analy-
sis, it has been proved that a larger rectangular antenna array with hybrid beamforming
techniques matches the spectral efficiency nearly equal to the fully digital beamforming
techniques with less number of antennas as well as RF chains. This will lead to low com-
putational complexity and enhance the performance of the system thus showing an advan-
tage over conventional fully digital MIMO systems.
The computed spectral efficiencies for both fully digital conventional beamform-
ing and the proposed rectangular antenna array based hybrid beamforming in massive
MIMO system with a different number of RF chains at SNR = 20 dB are compared and
tabulated in Table 3. It is observed that for 64 × 16 massive MIMO system, almost the
same spectral efficiency of that fully digital beamforming has been achieved if the num-
ber of RF chain has been varied from 64 to 16. This will decrease the % of reduction of

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 T. S. Priya et al.

Fig. 12  Spectral efficiency of

fully conventional digital and
proposed rectangular array
antenna based Hybrid beamform-
ing massive MIMO systems with
­Nt = 256, ­Nr = 64 and ­Nrf = 16

Table 3  Spectral efficiencies of fully conventional digital and proposed Hybrid beamforming massive
MIMO systems at SNR = 20 for different rectangular antenna array structures and RF chains
Number of data streams ­Ns Spectral efficiency (bits/s/Hz) % of reduction
in number RF
Fully digital Hybrid chains

36 × 4 Antennas 88.89%
36 × 4 RF chains 4 × 4 RF chains
1 14.04 13.95
2 24.8 24.4
3 33.5 32.24
64 × 16 Antennas 98.45%
64 × 16 RF chains 4 × 4 RF chains
1 16.1 15.69
2 29.51 27.99
3 41.6 38.15
64 × 16 Antennas 93.75%
64 × 16 RF chains 8 × 8 RF chains
1 16.1 16.01
2 29.51 29.14
3 41.6 40.77
256 × 64 Antennas 99.60%
256 × 64 RF chains 8 × 8 RF chains
1 19 18.64
2 35.6 34.42
3 51.19 48.77
256 × 64 Antennas 98.44%
256 × 64 RF chains 16 × 16 RF chains
1 19 18.87
2 35.6 35.17
3 51.19 50.33

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Hybrid Beamforming for Massive MIMO Using Rectangular Antenna…

RF chains from 93.75 to 98.45%. Similarly, for the 256 × 64 massive MIMO system, the
same spectral efficiency of that fully digital beamforming has been achieved if the num-
ber of RF chains has been varied from 256 to 64. This will decrease the % of reduction
of RF chains from 98.44 to 99.60%. From Table 3, it has been observed that rectangular
array antenna-based Hybrid beamforming in a massive MIMO system reduces the com-
putational complexity up to 99.60% as compared with conventional fully digital beam-
forming to achieve the almost same spectral efficiencies.

4.4 BER Analysis vs SNR

The BER performance metrics with different SNR for different rectangular antenna
array size of SISO, SIMO, MISO and MIMO has been simulated and compared. An
upgraded SNR suggests a shrunk BER which is nothing but a reduced error rate leading
to better performance. The BER has been computed for different SNR ranging from − 30
to 10 dB. The simulated BER with various SNR for 4 × 4 antenna array configuration
is shown in Fig. 13. It shows that there is a total gain of around 12 dB in MIMO over
the SISO. Also, there is around 6 dB gain in MIMO over the MISO/ SISO for the same
BER. Also, it has been observed that a massive MIMO array attains the same BER as
compared with SISO, SIMO, MISO at lower SNR. This will make the massive MIMO
more suitable for the noisy environments also.
For the 8 × 8 rectangular array configuration, the BER has been computed for vari-
ous SNR and illustrated in Fig. 14. From Fig. 14, it is found that there is a total gain
of 24 dB in MIMO over the SISO and 12 dB gain over the MISO/SISO with the same
BER. It has been depicted by comparing Figs. 13 and 14 that by increasing the number
of array antenna elements from 4 × 4 to 8 × 8 for a MIMO system, it is possible to
increase the antenna gain of 7 dB. Thus, by increasing the number of antennas on the
transmitter and receiver side, array gain can be increased and thus the performance can
be escalated. From the above simulation, it is observed that the MIMO is more suitable
for a noisy environments and also if the number of array elements of the antenna is
increased.

Fig. 13  BER vs SNR—4 × 4

array configuration in SISO,
SIMO/MISO, MIMO systems

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 T. S. Priya et al.

Fig. 14  BER vs SNR—8 × 8

array configuration in SISO,
SIMO/MISO, MIMO system

5 Conclusion

In this research work, a rectangular array antenna based Hybrid beamforming model in
massive MIMO for 5G mobile network has been proposed. In order to increase the main
lobe signal strength and also to suppress the side lobes, Chebyshev tapering has been
used. The proposed rectangular antenna array model has been simulated for various
array elements such as 4 × 4, 8 × 8, 12 × 12 and 16 × 16. The radiation pattern and Azi-
muth patterns have been generated with and without Chebyshev tapering. Also the BER
of the proposed MU-MIMO for various antenna arrays has been simulated and com-
pared with existing methods. From the spectral efficiency metric evaluation, it has been
observed that the proposed rectangular array antenna based Hybrid beamforming in a
massive MIMO system reduces the computational complexity up to 99% as compared
with conventional fully digital beamforming to achieve the same spectral efficiencies.
Therefore, the proposed method may solve the challenges faced by 5G wireless technol-
ogy. While reducing the cost, the number of RF chains, hybrid beamforming carried out
an outstanding performance. Thus, rectangular antenna array-based hybrid beamform-
ing in massive MIMO indicate excellent performance and lesser cost when compared to
conventional fully digital beamforming. Further, the spectral efficiency can be increased
by utilizing the 3-D rectangular array antenna model in the future. Also, the proposed
rectangular array antenna based Hybrid beamforming in a massive MIMO system can
be designed and deployed in future work.

Funding NA

Declarations

Conflict of interests The authors declare that there is no conflict of interest regarding the publication of this
paper and that the work presented in this article is not supported by any funding agency.

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Hybrid Beamforming for Massive MIMO Using Rectangular Antenna…

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and
institutional affiliations.

Thupalli Sai Priya is doing B.Tech Electronics and Communication

Engineering at Vellore Institute of Technology, Vellore, India. Her
area of research includes transmission techniques in 5G and B5G,
Blockchain and network engineering.

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Hybrid Beamforming for Massive MIMO Using Rectangular Antenna…

Kondala Manish is doing B.Tech Electronics and Communication

Engineering at Vellore Institute of Technology, Vellore, India. His area
of research includes transmission techniques in 5G and B5G, data
communication and data sciences.

P Prakasam is a Senior Member in IEEE and also he is member of

IEEE Communication Society, Solid State Circuits Society and Prod-
uct Safety Engineering Society. He is a Professor in School of Elec-
tronics Engineering, Vellore Institute of Technology, Vellore, India.
He obtained his Ph.D from Anna University Chennai in 2010. He is an
Associate Editor of IEEE Access, Array (Elsevier), Peer-to-Peer Net-
working and Applications (Springer) and also an editor-in-chief of
Journal of Signal Processing and Wireless Networks. He is also a Lead
Guest Editor for Special Issue on P2P Computing for Beyond 5G Net-
work (B5G) and Internet-of-Everything (IoE), Peer-to-Peer Networks
and Applications, Springer. He has authored over 130 research publi-
cations various journals and conferences out of which 37 publications
have been indexed by SCI/SCIE/EI. He has more than 5 monographs/
books, 3 book chapters, 11 Indian patents, and 2 Best Paper Awards.
He is a reviewer of more than 20 journals in various publishers which
includes IEEE, Elsevier and Springer journals. He has served more
than 20 conferences as technical advisory/reviewer committee. His
special areas of interest are Signal Processing, Wireless Networks, Machine/Deep Learning, 5G Networks
and applications of signal processing in Mobile Communication Systems.

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