TELKOMNIKA Telecommunication Computing Electronics and Control
Vol. 23, No. 2, April 2025, pp. 306~315
ISSN: 1693-6930, DOI: 10.12928/TELKOMNIKA.v23i2.26562  306
Journal homepage: http://telkomnika.uad.ac.id
Graphene-based THz antenna with a wide bandwidth for future
6G short-range communication
Md. Kawsar Ahmed1
, Md. Sharif Ahammed1
, Md. Ashraful Haque1
, Narinderjit Singh Sawaran
Singh2
, Jamal Hossain Nirob1
, Redwan A. Ananta1
, Kamal Hossain Nahin1
, Liton Chandra Paul3
1
Department of Electrical and Electronic Engineering, Daffodil International University, Dhaka, Bangladesh
2
Faculty of Data Science and Information Technology, INTI International University, Nilai, Malaysia
3
Department of Electrical, Electronic and Communication Engineering, Pabna University of Science and Technology, Pabna,
Bangladesh
Article Info ABSTRACT
Article history:
Received Aug 7, 2024
Revised Dec 28, 2024
Accepted Jan 23, 2025
In this study, we present the design and investigation of a terahertz (THz)
frequency antenna optimized for the 2-10 THz range, featuring both single-
element and multiple-input multiple-output (MIMO) configurations, with a
focus on industrial and innovative applications to enhance future 6G
communication systems. The antenna, constructed on a polyimide substrate
with dimensions of 90×30 µm, achieves a bandwidth from 4.0328 to 10
THz. The MIMO configuration, which includes two ports, demonstrates
excellent isolation with a value of -27 dB. The proposed antenna system
achieves a gain of 12.38 dB and an efficiency of 89%, making it highly
appropriate for THz communication applications. Furthermore, the envelope
correlation coefficient (ECC) of 0.002 and diversity gain (DG) of 9.99
affirm the antenna’s effectiveness in MIMO systems. A resistance
inductance capacitance (RLC) circuit model was employed to accurately
represent the S11 curve, ensuring precise characterization of the antenna’s
performance. These results underscore the probability of the proposed
antenna for high-speed, short-range communication systems.
Keywords:
Graphene
High bandwidth
Industrial and innovation
Microstrip patch antenna
Multiple-input multiple-output
antenna
Resistance inductance
capacitance This is an open access article under the CC BY-SA license.
Corresponding Author:
Narinderjit Singh Sawaran Singh
Faculty of Data Science and Information Technology, INTI International University
Persiaran Perdana BBN, Putra Nilai, Nilai 71800, Negeri Sembilan, Malaysia
Email: narinderjits.sawaran@newinti.edu.my
1. INTRODUCTION
The rapid growth of wireless communication technologies has spurred the exploration of novel
frequency bands to meet the growing demand for high data rates and huge bandwidths [1]. Among these, the
terahertz (THz) frequency range, ranging from 0.1 to 10 THz, has garnered significant interest due to its
potential to support ultra-fast data transmission and high-capacity communication systems [2]. Unlike
conventional microwave and millimeter-wave frequencies, the THz band offers an extensive bandwidth that
can facilitate data rates exceeding hundreds of gigabits per second (Gbps) [3]. This makes it particularly
suitable for emerging applications such as ultra-high-definition video streaming, high-speed wireless
networks, and next-generation mobile communications [4].
However, designing antennas that operate efficiently at THz frequencies poses several challenges,
including high propagation losses, fabrication precision, and material selection [5]. The choice of substrate
material is vital, as it affects the antenna’s impedance matching, bandwidth, and radiation efficiency [6]. In
this study, we employ a polyimide substrate due to its favorable dielectric properties, low-loss tangent, and
mechanical flexibility, making it an ideal candidate for THz applications [7].
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Multiple-input multiple-output (MIMO) technology has become a cornerstone in modern wireless
communications, offering significant enhancements in channel capacity, spectral efficiency, and signal
reliability [8]. By deploying multiple antennas at together the transmitter and receiver, MIMO systems
activity spatial diversity and multiplexing gains. This technology is especially promising in the THz domain,
where it can mitigate the effects of high path loss and limited power output of THz sources [9]. Our research
attention is on the design and investigation of a THz antenna system that incorporates MIMO technology,
aiming to achieve high gain, broad bandwidth, and low mutual coupling between elements.
A key aspect of antenna design is the accurate modeling of its impedance characteristics, typically
represented by the S11 parameter. In this work, we employ a resistance inductance capacitance (RLC) circuit
model to simulate the S11 curve of the proposed MIMO antenna, providing a detailed understanding of its
resonant behavior and input impedance. The RLC model helps to capture the complex interaction between
the antenna elements and the substrate, offering insights into optimizing the design for improved
performance.
This paper presents a comprehensive investigation of a THz antenna system, covering both single-
element and MIMO configurations. The proposed antenna demonstrates a bandwidth range of
4.0328-10 THz, which is better compared to [10]-[14], which is shown in Table 1, a gain of 12.38 dB better
then [10], [11], [13], and an efficiency of 89% [10], [11], [13]. The MIMO configuration, with two ports,
achieves excellent isolation of -27 dB, an envelope correlation coefficient (ECC) of 0.002, and a diversity
gain (DG) of 9.99, indicating robust MIMO performance. These characteristics highlight the antenna’s
potential for high-speed, short-range communication systems.
Table 1. Performance evalution of the proposed MIMO antenna in comparison to related work
2. DESIGN METHOD
2.1. Single element design
In our single-element antenna design process, we start with a circular patch shape, changing its
shape in several steps to improve performance. We use graphene for the patch material, a circular patch
shape with radius ‘r’, placed on a substrate, and copper as the ground material. Both patch and ground have a
thickness of 0.75 micrometers and substrate dimensions are 30 micrometers in length and 25 micrometers in
width [15]. A circular slot is in the center of the substrate and two square slots are on either side of the feed
line, flanked by two insets. Further modifications include a rectangular ground plane (30 by 25 micrometers)
with a central circular structure of radius ‘r’ [16]. There is also an inset ground along the feed line. These
modifications and our target improve impedance matching, bandwidth, gain, and radiation pattern. We then
simulate the antenna using CST software to evaluate the return loss, radiation pattern, and gain, gaining
insight into its behavior across different conditions and frequencies. We can see the design in Figure 1.
2.2. Analysis of the result of the single element by using graphene and copper
First, we attempted to design a single-element antenna, using copper for both the patch and ground.
In the second stage design patch and ground graphene. In the third stage we use copper we use patch
materials graphene and ground materials, copper. At this stage, we tried to find the best results in graphene
and copper combinations [17]. We can see the design changes in Figure 2. In the first step for Figure 2(a) and
for the second step Figure 2(b) we get the result return loss -38 dB and -44 dB. In the third stage, we get the
result frequencies 5.66 and 7.94 return loss -66.48 and -75.25 dB for proposed Figure 2(c), this is our propped
single-element antenna result and shown graphically in Figure 2(d). Substrate width (sw)=25 micrometer,
substrate thickness (st)=3 micrometer radios (r)=10 micrometer slot1 (s11)=2 micrometer, ground width
Ref Resonance
(THz)
BW
(THz)
Isolation
(dB)
Gain
(dB)
Efficienc
y (%)
ECC
(dB)
DG
(dB)
Substrate
material
Board
size
(μm2
)
MIMO
configuration
[10] 1.89 1.59 -25 4.60 74.5 15.6×
10-10
≈10 SiO2 38×25 -
[11] - 0.114 -17 4.4 94 0.006 9.97 Rogers
RO4835-T
2000×1
000
2×2
[12] 10.51 1 - - - - - Silicon
dioxide
- -
[13] 2.3, 3.2, 4.5 0.038,
0.043,
0.06
-17, -30, -
23
5 60 0.2 9.99 Polyimide 50×40
[14] 2.8 1.5 - - - - - RT/duriod6
010
- -
Proposed 8.096 (4.032
8-10)
-27.62 12.38 -89.0 9.99 Polyimide 90×30 2×2
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(bw)=25 micrometer, ground length (bl)=30 micrometer, patch thickness (t)=0.75 micrometer, feedline width
(fw)=3 micrometer feedline length (fl)=6 micrometer, edge-to-edge gap1 (d)=3.5 micrometer, edge-to-edge
gap2 (d2)=4 micrometer, inset length (x)=0.5 micrometer, and inset width (y)=4 micrometer.
Figure 1. Front and ground views of single-element configuration
(a) (b) (c)
(d)
Figure 2. Evolutionary progression and result of single element; (a) first step, (b) second step, (c) proposed
singlement element antenna, and (d) graphics
2.3. Single element vs multiple-input multiple-output
In our current endeavors focused on global 5G applications, our developmental trajectory is centered
on advancing antenna technology for forthcoming 6G applications [18]. In this section, we will try to find the
difference between single-element antenna and MIMO. Initially, a shift from single-element antennas to
MIMO configurations, marked a transformative progression. This advancement is primarily motivated by the
pursuit of enhanced performance, efficiency, and adaptability within wireless communication systems.
Additionally, cognitive technologies such as AI are leveraged to enable high-speed, low-latency
communications operating at existing radio frequencies and achieving speeds significantly surpassing those
of fifth-generation networks [19]. The transition from single-element antennas to MIMO configurations
allows us to harness spatial diversity, multiplexing gain, and improved spectral efficiency. These attributes
are crucial for meeting the escalating demands for higher data rates, reduced latency, and expanded network
capacity in 6G networks. From our single-element antenna to MIMO, our range of mobility and work is
wide.
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2.4. Multiple-input multiple-output antenna
In this section, we will explain the conversion technique in a MIMO formation. At this stage, it is
decided to convert to a MIMO configuration for increasing antenna performance and spatial diversity,
increasing capacity, facilitating multipath exploitation, and more extensive, more unknown information or
search results. The section details the details of the microstrip MIMO patch antenna. In our MIMO antenna
design methodology, we explain how to build a 2-port MIMO configuration using a single-element antenna
as a basic element, with the goal of spatial diversity, interference mitigation, power enhancement, multipath
absorption, and signal reception through height to do [20]. Improve protection This important advance is
motivated by the need to ensure the optimal orientation of the antenna elements, thus achieving the necessary
level of isolation important for superior performance. To realize the optimal MIMO antenna configuration,
we initially used two single-element antennas. The basic patch and ground structure of a single-element
antenna is laid out like a single-element antenna. Next, we use decoupling in MIMO to improve the results.
At this stage, the decoupling length and width were changed to 30 micrometers and 40 micrometers, and the
decoupling area ground was all copper [21]. Conversion to a MIMO formation achieves the best results. We
can see the proposed MIMO antenna in Figure 3.
Figure 3. Comparative analysis MIMO antenna and performance antenna configurations
3. RESULT ANALYSIS OF PROPOSED MIMO ANTENNA
3.1. Reflection and transmission coefficient
The reflection coefficient, also acknowledged as the S₁₁ parameter, serves as a pivotal metric in
evaluating antenna performance, offering valuable insights into the efficacy of power transfer between the
transmission line and the antenna. It governs the magnitude of radio frequency (RF) power redirected from a
microstrip patch antenna back toward the feed line. Defined as a ratio expressed in decibels (dB), it
juxtaposes reflected power against incident power from the feed line. A diminished reflection coefficient,
denoted by a negative dB value, signifies minimal power reflection and optimal impedance matching, which
is pivotal for efficient power transfer and antenna performance [22]. Conventionally, an exemplary value for
a well-matched antenna is deemed to be -10 dB or lower. The meticulously engineered microstrip patch
antenna showcases auspicious attributes, characterized by dual resonant frequencies situated at 8.096 THz, as
depicted in Figure 4. At both resonance frequencies, commendable return loss values are attained, peaking at
-35.23 dB at 8.096 THz. Such performance translates into efficient signal transmission and negligible
reflections at the resonant frequencies, significantly enhancing the antenna’s overall efficacy. Furthermore,
the antenna boasts a commendable bandwidth spanning 5.968 THz (ranging from 4.0315 THz to 10 THz),
denoting the spectrum of frequencies over which it maintains satisfactory performance [23].
3.2. Gain and efficiency
Gain is a crucial factor in the performance of MIMO systems, impacting coverage, signal strength,
and data rate. It measures the system’s ability to effectively focus and direct transmitted and received signals,
reducing unwanted noise from other directions. Higher gain results in stronger signals reaching a wider area,
thus extending the system’s coverage range. The simulated gain for the proposed MIMO antenna is
illustrated in Figure 5. The antenna demonstrates a peak gain of 12.38 dB, with gains of 11.92 dB at resonant
frequencies of 8.096 THz respectively. This suggests a potentially more focused radiation pattern, making the
antenna suitable for applications requiring extended coverage. Efficiency is also crucial in MIMO systems,
directly impacting power consumption, data rate, and overall performance [24]. It measures how effectively
the system converts input power into useful transmitted or received signal power. In the case of microstrip
patch antennas, efficiency is particularly significant as it directly influences overall antenna performance.
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A higher efficiency indicates a greater proportion of input power being converted into useful radiated power,
enhancing signal strength and communication quality [25]. The simulated efficiency gains for the proposed
MIMO antenna, depicted in Figure 5, show a high efficiency of 89%, consistently exceeding 86% across its
range. This indicates superior performance in changing input power into useful radiated power, contributing
to enhanced signal strength and communication quality.
Figure 4. Reflection coefficient of the proposed
MIMO antenna
Figure 5. Efficiency and gain of the proposed MIMO
antenna
3.3. The envelope correlation coefficient
The ECC holds significant importance in MIMO systems, as it directly impacts the system’s
capability to leverage spatial diversity and achieve optimal channel capacity [26]. It quantifies the association
between the envelopes of signals received by different antennas within the MIMO system. Essentially, it
measures the similarity or correlation in the amplitudes of received signals across multiple antennas. In the
context of MIMO systems, a low ECC, preferably close to zero, is desirable for optimal performance. We can
see the ECC in Figure 6. This is because a low ECC indicates a high level of diversity among the multiple
antennas, which is advantageous for maximizing system performance.
3.4. Diversity gain
DG is essentially what we use to measure the development in system performance due to the
practice of multiple antennas and to experience independent fading. Additionally, MIMO systems contribute
significantly to improved system reliability, coverage, and capacity. One of the primary goals of MIMO
systems is to achieve DG. The value of DG can be calculated below.
The simulated DG for the suggested MIMO antenna is shown in Figure 7. It can be seen that the
antenna achieves the lowest DG of 9.99. This value of DG suggests a considerable improvement in signal
reliability and robustness due to the use of multiple antennas in a MIMO system [5].
Figure 6. ECC of the proposed MIMO antenna Figure 7. DG of the proposed MIMO antenna
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4. RADIATION PATTERN
The radiation pattern of an antenna is a graphical representation of the radiation dispersion from the
antenna with respect to spatial direction. It is important to consider the orientation and properties of the E
field and the H field when designing and placing antennas [27]. A magnitude of 22.4 dB V/m is associated
with the E field lobe at theta =90°, a half-power beam width of 52°, and an H field magnitude of 900. As for
the main lobe magnitude, it is -38.5 dBA/m, and the HPBW is 54.30 degrees. The half-power beam width is
124.6°, the E field of the primary lobe at =90° in the H-field is 8 dBV/m, and the magnitude for the H field of
the lobe at =90° is -29.2 dB A/m. Figure 8 shows that the E-field, with theta =0 degrees, has an HPBW of
89.9 degrees and a primary lobe magnitude of 17.1 dB V/m [28].
Figure 8. Simulated radiation pattern of recommended MIMO antenna
5. RESISTANCE INDUCTANCE CAPACITANCE EQUIVALENT CIRCUIT
In this section, we design an advanced antenna system to meet future wireless communication
requirements. Our initial step involved developing an RLC circuit model to analyze the electromagnetic
behavior of the system [29]. Figure 9 illustrates the equivalent circuit of the proposed MIMO antenna. The
project aimed to precisely characterize the performance characteristics of the antenna structure and
understand the complex relationships between its electrical components. To ensure accuracy, we
meticulously extracted the R-L-C parameters directly from our antenna simulations using sophisticated tools
such as CST Studio. In our antenna design, the patch element plays a crucial role in achieving two separate
resonance frequencies. We utilized two parallel circuit configurations with resistance (R1), capacitance (C1),
and inductance (L1) to construct these resonance frequencies carefully. Additionally, another two parallel
circuits consisting of (L2+C3), (R2+C4), and R3 are responsible for the slot placed beside the feedline of the
antenna. By combining these circuit elements, we created a model that accurately replicates the behavior of
our single-element antenna [30]. When transitioning to a MIMO configuration, we accounted for mutual
impedance between antenna elements using a parallel circuit of L3, R4, R5, and C5. To verify the accuracy
of the Agilent advanced design system (ADS) simulation, we conducted a comparative test between the
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results of the CST simulation and a parallel circuit simulation, focusing on the S11 parameter. Figure 9
provides a detailed assessment of the accuracy and reliability of our R-L-C circuit model by comparation the
simulation results of both the circuit and CST simulations. This model can estimate the performance of the
future MIMO antenna. The simulation results obtained using CST, along with the equivalent RLC circuit
results from ADS, are displayed in Figure 10.
Figure 9. Final equivalent circuit is the result of the proposed MIMO antenna
Figure 10. Simulated equivalent circuit reflection coefficient in ADS and CST
6. CONCLUSION
The proposed THz antenna, designed for the 3-10 THz frequency range, exhibits outstanding
performance in both single-element and MIMO configurations. It provides a wide bandwidth from 4.0328 to
10 THz, a high gain of 12.38 dB, and an efficiency of 89%, meeting the stringent demands of contemporary
THz communication systems. The MIMO configuration achieves superior isolation at -27 dB and
demonstrates low ECC and high DG, indicative of excellent MIMO capabilities. The incorporation of an
RLC circuit model enables the precise representation of the S11 curve, ensuring an accurate characterization
of the antenna’s input impedance and resonant behavior. The use of a polyimide substrate further enhances
the antenna’s performance and applicability. The findings of this study highlight the proposed antenna’s
potential for high-speed, short-range communication, making it a promising candidate for integration into
advanced THz systems.
ACKNOWLEDGEMENT
We would like to extend my heartfelt gratefulness to the Faculty of Graduate Studies and the
Department of Electrical and Electronic Engineering at Daffodil International University, Bangladesh, for
their invaluable support and support throughout this journey.
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Graphene-Based Metamaterial Absorbers,” in IEEE Magnetics Letters, vol. 9, pp. 1-5, 2018, doi: 10.1109/LMAG.2018.2878946.
BIOGRAPHIES OF AUTHORS
Md. Kawsar Ahmed is currently pursuing his studies in the field of Electrical
and Electronic Engineering at Daffodil International University. He successfully finished his
Higher Secondary education at Agricultural University College, Mymensingh. He is presently
employed as an Assistant Administrative Officer at the Office of Students’ Affairs at Daffodil
International University (DIU) in Bangladesh. The areas of his research focus encompassed
microstrip patch antennas, terahertz antennas, and applications related to 4G and 5G
technologies. He can be contacted at email: kawsar33-1241@diu.edu.bd.
Md. Sharif Ahammed is a student of Daffodil International University and
pursuing a B.Sc. in the Electrical and Electronics Department. He passed from Government
Bangabandhu College with a higher secondary. Microstrip patch antenna, terahertz antenna,
and 5G application are some of his research interests. He can be contacted at email: sharif33-
1152@diu.edu.bd.
Md. Ashraful Haque is doing Ph.D. at the Department of Electrical and
Electronic Engineering, Universiti Teknologi PETRONAS, Malaysia, He got his B.Sc. in
Electronics and Electronic Engineering (EEE) from Bangladesh’s Rajshahi University of
Engineering and Technology (RUET) and his M.Sc. in the same field from Bangladesh’s
Islamic University of Technology (IUT). He is currently on leave from Daffodil International
University (DIU) in Bangladesh. His research interest includes microstrip patch antenna, sub 6
5G application, and supervised regression model machine learning on antenna design. He can
be contacted at email: limon.ashraf@gmail.com.
Narinderjit Singh Sawaran Singh is an Associate Professor in INTI
International University, Malaysia. He graduated from the Universiti Teknologi PETRONAS
(UTP) in 2016 with Ph.D. in Electrical and Electronic Engineering specialized in Probabilistic
methods for fault tolerant computing. Currently, he is appointed as the research cluster head
for computational mathematics, technology and optimization which focuses on the areas like
pattern recognition and symbolic computations, game theory, mathematical artificial
intelligence, parallel computing, expert systems and artificial intelligence, quality software,
information technology, exploratory data analysis, optimization algorithms, stochastic
methods, data modelling, and computational intelligence-swarm intelligence. He can be
contacted at email: narinderjits.sawaran@newinti.edu.my.
TELKOMNIKA Telecommun Comput El Control 
Graphene-based THz antenna with a wide bandwidth for future 6G short-range … (Md. Kawsar Ahmed)
315
Jamal Hossain Nirob is a student in the Department of Electrical and Electronic
Engineering (EEE) at Daffodil International University. His educational journey began at
Maniknagar High School, where he successfully completed his Secondary School Certificate
(SSC). Following that, he pursued higher studies at Ishwardi Government College, obtaining
his Higher Secondary Certificate (HSC). With a strong enthusiasm for expanding
communication technology, he has focused his research on wireless communication,
specifically on microstrip patch antennas, terahertz antennas, and applications of 5G and 6G.
He can be contacted at email: jamal33-1243@diu.edu.bd.
Redwan A. Ananta has accomplished his undergraduate studies in the field of
Electrical and Electronics at Daffodil International University. He completed his higher
secondary education at Adamjee Cantonment College. His research focus encompasses
wireless communication, specifically microstrip patch antenna, terahertz antenna, and 5G, and
6G applications. He can be contacted at email: redwan33-1145@diu.edu.bd.
Kamal Hossain Nahin currently pursuing a degree in Electrical and Electronic
Engineering at Daffodil International University. His educational journey began at Ishwardi
Govt College for his Higher Secondary Certificate (HSC). As a budding researcher in the
communication field, he is passionate about wireless communication, focusing on microstrip
patch antennas, terahertz antennas, and their potential applications in future 5G and 6G
technologies. He can be contacted at email: kamal33-1242@diu.edu.bd.
Liton Chandra Paul holds the position of Assistant Professor in the Electrical,
Electronic, and Department of Communication Engineering at Pabna University of Science
and Technology (PUST). He completed his Master’s degree in Electrical and Electronic
Engineering and Bachelor’s degree in Electronics and Telecommunication Engineering at
Rajshahi University of Engineering & Technology (RUET) in 2012 and 2015, respectively.
During his academic journey, he actively participated in various non-profit social welfare
organizations, making significant contributions to their endeavors. In addition to becoming the
department’s first-class first boy of the third batch (academic session 2007–2008), he received
the University Gold Medal for his exceptional academic achievement in earning a B.Sc. in
Electronics & Telecommunication Engineering. At the IEEE ICCIT 2021, one of his research
projects won the Prof. Syed Mahbubur Rahman Best Paper Award. He was awarded the
Research Excellence Award in 2022 and the Outstanding Researcher Award in 2023 from
PUST. He received several research grants from various institutions. He has authored
numerous publications for int’l conferences and peer-reviewed journals. He held the positions
of Vice Chair (Technical) of the IEEE Young Professionals BDS (2022–2023) and Counselor
for the IEEE PUST Student Branch (2020–2021). Currently, he is acting as an advisor for the
IEEE PUST Student Branch. In addition, he effectively carried out a number of other duties
assigned by PUST, including assistant director of the Student Advisor Office, additional
director of the Institutional Quality Assurance Cell (IQAC), and assistant provost of
Bangabandhu Sheikh Mujibur Rahman Hall. He also serves as a reviewer for many int’l
reputed conferences and journals of different reputed publishers, including IEEE, Springer
Nature, Elsevier, Wiley, Cambridge University Press, IET, Hindawi, MDPI, Taylor, and
Francis. He has affiliations with different national and int’l professional bodies like the
Institute of Engineers Bangladesh (IEB) and the Institute of Electrical and Electronics
Engineers (IEEE), including IEEE-APS, IEEE-MTTS, IEEE-ComSoc, IEEE-SPS, and IEEE-
WIE. His research interests are RFIC, MIMO, machine learning, bio-electromagnetics,
microwave technology, antennas, phased arrays, mmWave, metamaterials, absorber,
metasurfaces, and wireless sensors. He can be contacted at email: litonpaulete@gmail.com.

Graphene-based THz antenna with a wide bandwidth for future 6G short-range communication

  • 1.
    TELKOMNIKA Telecommunication ComputingElectronics and Control Vol. 23, No. 2, April 2025, pp. 306~315 ISSN: 1693-6930, DOI: 10.12928/TELKOMNIKA.v23i2.26562  306 Journal homepage: http://telkomnika.uad.ac.id Graphene-based THz antenna with a wide bandwidth for future 6G short-range communication Md. Kawsar Ahmed1 , Md. Sharif Ahammed1 , Md. Ashraful Haque1 , Narinderjit Singh Sawaran Singh2 , Jamal Hossain Nirob1 , Redwan A. Ananta1 , Kamal Hossain Nahin1 , Liton Chandra Paul3 1 Department of Electrical and Electronic Engineering, Daffodil International University, Dhaka, Bangladesh 2 Faculty of Data Science and Information Technology, INTI International University, Nilai, Malaysia 3 Department of Electrical, Electronic and Communication Engineering, Pabna University of Science and Technology, Pabna, Bangladesh Article Info ABSTRACT Article history: Received Aug 7, 2024 Revised Dec 28, 2024 Accepted Jan 23, 2025 In this study, we present the design and investigation of a terahertz (THz) frequency antenna optimized for the 2-10 THz range, featuring both single- element and multiple-input multiple-output (MIMO) configurations, with a focus on industrial and innovative applications to enhance future 6G communication systems. The antenna, constructed on a polyimide substrate with dimensions of 90×30 µm, achieves a bandwidth from 4.0328 to 10 THz. The MIMO configuration, which includes two ports, demonstrates excellent isolation with a value of -27 dB. The proposed antenna system achieves a gain of 12.38 dB and an efficiency of 89%, making it highly appropriate for THz communication applications. Furthermore, the envelope correlation coefficient (ECC) of 0.002 and diversity gain (DG) of 9.99 affirm the antenna’s effectiveness in MIMO systems. A resistance inductance capacitance (RLC) circuit model was employed to accurately represent the S11 curve, ensuring precise characterization of the antenna’s performance. These results underscore the probability of the proposed antenna for high-speed, short-range communication systems. Keywords: Graphene High bandwidth Industrial and innovation Microstrip patch antenna Multiple-input multiple-output antenna Resistance inductance capacitance This is an open access article under the CC BY-SA license. Corresponding Author: Narinderjit Singh Sawaran Singh Faculty of Data Science and Information Technology, INTI International University Persiaran Perdana BBN, Putra Nilai, Nilai 71800, Negeri Sembilan, Malaysia Email: narinderjits.sawaran@newinti.edu.my 1. INTRODUCTION The rapid growth of wireless communication technologies has spurred the exploration of novel frequency bands to meet the growing demand for high data rates and huge bandwidths [1]. Among these, the terahertz (THz) frequency range, ranging from 0.1 to 10 THz, has garnered significant interest due to its potential to support ultra-fast data transmission and high-capacity communication systems [2]. Unlike conventional microwave and millimeter-wave frequencies, the THz band offers an extensive bandwidth that can facilitate data rates exceeding hundreds of gigabits per second (Gbps) [3]. This makes it particularly suitable for emerging applications such as ultra-high-definition video streaming, high-speed wireless networks, and next-generation mobile communications [4]. However, designing antennas that operate efficiently at THz frequencies poses several challenges, including high propagation losses, fabrication precision, and material selection [5]. The choice of substrate material is vital, as it affects the antenna’s impedance matching, bandwidth, and radiation efficiency [6]. In this study, we employ a polyimide substrate due to its favorable dielectric properties, low-loss tangent, and mechanical flexibility, making it an ideal candidate for THz applications [7].
  • 2.
    TELKOMNIKA Telecommun ComputEl Control  Graphene-based THz antenna with a wide bandwidth for future 6G short-range … (Md. Kawsar Ahmed) 307 Multiple-input multiple-output (MIMO) technology has become a cornerstone in modern wireless communications, offering significant enhancements in channel capacity, spectral efficiency, and signal reliability [8]. By deploying multiple antennas at together the transmitter and receiver, MIMO systems activity spatial diversity and multiplexing gains. This technology is especially promising in the THz domain, where it can mitigate the effects of high path loss and limited power output of THz sources [9]. Our research attention is on the design and investigation of a THz antenna system that incorporates MIMO technology, aiming to achieve high gain, broad bandwidth, and low mutual coupling between elements. A key aspect of antenna design is the accurate modeling of its impedance characteristics, typically represented by the S11 parameter. In this work, we employ a resistance inductance capacitance (RLC) circuit model to simulate the S11 curve of the proposed MIMO antenna, providing a detailed understanding of its resonant behavior and input impedance. The RLC model helps to capture the complex interaction between the antenna elements and the substrate, offering insights into optimizing the design for improved performance. This paper presents a comprehensive investigation of a THz antenna system, covering both single- element and MIMO configurations. The proposed antenna demonstrates a bandwidth range of 4.0328-10 THz, which is better compared to [10]-[14], which is shown in Table 1, a gain of 12.38 dB better then [10], [11], [13], and an efficiency of 89% [10], [11], [13]. The MIMO configuration, with two ports, achieves excellent isolation of -27 dB, an envelope correlation coefficient (ECC) of 0.002, and a diversity gain (DG) of 9.99, indicating robust MIMO performance. These characteristics highlight the antenna’s potential for high-speed, short-range communication systems. Table 1. Performance evalution of the proposed MIMO antenna in comparison to related work 2. DESIGN METHOD 2.1. Single element design In our single-element antenna design process, we start with a circular patch shape, changing its shape in several steps to improve performance. We use graphene for the patch material, a circular patch shape with radius ‘r’, placed on a substrate, and copper as the ground material. Both patch and ground have a thickness of 0.75 micrometers and substrate dimensions are 30 micrometers in length and 25 micrometers in width [15]. A circular slot is in the center of the substrate and two square slots are on either side of the feed line, flanked by two insets. Further modifications include a rectangular ground plane (30 by 25 micrometers) with a central circular structure of radius ‘r’ [16]. There is also an inset ground along the feed line. These modifications and our target improve impedance matching, bandwidth, gain, and radiation pattern. We then simulate the antenna using CST software to evaluate the return loss, radiation pattern, and gain, gaining insight into its behavior across different conditions and frequencies. We can see the design in Figure 1. 2.2. Analysis of the result of the single element by using graphene and copper First, we attempted to design a single-element antenna, using copper for both the patch and ground. In the second stage design patch and ground graphene. In the third stage we use copper we use patch materials graphene and ground materials, copper. At this stage, we tried to find the best results in graphene and copper combinations [17]. We can see the design changes in Figure 2. In the first step for Figure 2(a) and for the second step Figure 2(b) we get the result return loss -38 dB and -44 dB. In the third stage, we get the result frequencies 5.66 and 7.94 return loss -66.48 and -75.25 dB for proposed Figure 2(c), this is our propped single-element antenna result and shown graphically in Figure 2(d). Substrate width (sw)=25 micrometer, substrate thickness (st)=3 micrometer radios (r)=10 micrometer slot1 (s11)=2 micrometer, ground width Ref Resonance (THz) BW (THz) Isolation (dB) Gain (dB) Efficienc y (%) ECC (dB) DG (dB) Substrate material Board size (μm2 ) MIMO configuration [10] 1.89 1.59 -25 4.60 74.5 15.6× 10-10 ≈10 SiO2 38×25 - [11] - 0.114 -17 4.4 94 0.006 9.97 Rogers RO4835-T 2000×1 000 2×2 [12] 10.51 1 - - - - - Silicon dioxide - - [13] 2.3, 3.2, 4.5 0.038, 0.043, 0.06 -17, -30, - 23 5 60 0.2 9.99 Polyimide 50×40 [14] 2.8 1.5 - - - - - RT/duriod6 010 - - Proposed 8.096 (4.032 8-10) -27.62 12.38 -89.0 9.99 Polyimide 90×30 2×2
  • 3.
     ISSN: 1693-6930 TELKOMNIKATelecommun Comput El Control, Vol. 23, No. 2, April 2025: 306-315 308 (bw)=25 micrometer, ground length (bl)=30 micrometer, patch thickness (t)=0.75 micrometer, feedline width (fw)=3 micrometer feedline length (fl)=6 micrometer, edge-to-edge gap1 (d)=3.5 micrometer, edge-to-edge gap2 (d2)=4 micrometer, inset length (x)=0.5 micrometer, and inset width (y)=4 micrometer. Figure 1. Front and ground views of single-element configuration (a) (b) (c) (d) Figure 2. Evolutionary progression and result of single element; (a) first step, (b) second step, (c) proposed singlement element antenna, and (d) graphics 2.3. Single element vs multiple-input multiple-output In our current endeavors focused on global 5G applications, our developmental trajectory is centered on advancing antenna technology for forthcoming 6G applications [18]. In this section, we will try to find the difference between single-element antenna and MIMO. Initially, a shift from single-element antennas to MIMO configurations, marked a transformative progression. This advancement is primarily motivated by the pursuit of enhanced performance, efficiency, and adaptability within wireless communication systems. Additionally, cognitive technologies such as AI are leveraged to enable high-speed, low-latency communications operating at existing radio frequencies and achieving speeds significantly surpassing those of fifth-generation networks [19]. The transition from single-element antennas to MIMO configurations allows us to harness spatial diversity, multiplexing gain, and improved spectral efficiency. These attributes are crucial for meeting the escalating demands for higher data rates, reduced latency, and expanded network capacity in 6G networks. From our single-element antenna to MIMO, our range of mobility and work is wide.
  • 4.
    TELKOMNIKA Telecommun ComputEl Control  Graphene-based THz antenna with a wide bandwidth for future 6G short-range … (Md. Kawsar Ahmed) 309 2.4. Multiple-input multiple-output antenna In this section, we will explain the conversion technique in a MIMO formation. At this stage, it is decided to convert to a MIMO configuration for increasing antenna performance and spatial diversity, increasing capacity, facilitating multipath exploitation, and more extensive, more unknown information or search results. The section details the details of the microstrip MIMO patch antenna. In our MIMO antenna design methodology, we explain how to build a 2-port MIMO configuration using a single-element antenna as a basic element, with the goal of spatial diversity, interference mitigation, power enhancement, multipath absorption, and signal reception through height to do [20]. Improve protection This important advance is motivated by the need to ensure the optimal orientation of the antenna elements, thus achieving the necessary level of isolation important for superior performance. To realize the optimal MIMO antenna configuration, we initially used two single-element antennas. The basic patch and ground structure of a single-element antenna is laid out like a single-element antenna. Next, we use decoupling in MIMO to improve the results. At this stage, the decoupling length and width were changed to 30 micrometers and 40 micrometers, and the decoupling area ground was all copper [21]. Conversion to a MIMO formation achieves the best results. We can see the proposed MIMO antenna in Figure 3. Figure 3. Comparative analysis MIMO antenna and performance antenna configurations 3. RESULT ANALYSIS OF PROPOSED MIMO ANTENNA 3.1. Reflection and transmission coefficient The reflection coefficient, also acknowledged as the S₁₁ parameter, serves as a pivotal metric in evaluating antenna performance, offering valuable insights into the efficacy of power transfer between the transmission line and the antenna. It governs the magnitude of radio frequency (RF) power redirected from a microstrip patch antenna back toward the feed line. Defined as a ratio expressed in decibels (dB), it juxtaposes reflected power against incident power from the feed line. A diminished reflection coefficient, denoted by a negative dB value, signifies minimal power reflection and optimal impedance matching, which is pivotal for efficient power transfer and antenna performance [22]. Conventionally, an exemplary value for a well-matched antenna is deemed to be -10 dB or lower. The meticulously engineered microstrip patch antenna showcases auspicious attributes, characterized by dual resonant frequencies situated at 8.096 THz, as depicted in Figure 4. At both resonance frequencies, commendable return loss values are attained, peaking at -35.23 dB at 8.096 THz. Such performance translates into efficient signal transmission and negligible reflections at the resonant frequencies, significantly enhancing the antenna’s overall efficacy. Furthermore, the antenna boasts a commendable bandwidth spanning 5.968 THz (ranging from 4.0315 THz to 10 THz), denoting the spectrum of frequencies over which it maintains satisfactory performance [23]. 3.2. Gain and efficiency Gain is a crucial factor in the performance of MIMO systems, impacting coverage, signal strength, and data rate. It measures the system’s ability to effectively focus and direct transmitted and received signals, reducing unwanted noise from other directions. Higher gain results in stronger signals reaching a wider area, thus extending the system’s coverage range. The simulated gain for the proposed MIMO antenna is illustrated in Figure 5. The antenna demonstrates a peak gain of 12.38 dB, with gains of 11.92 dB at resonant frequencies of 8.096 THz respectively. This suggests a potentially more focused radiation pattern, making the antenna suitable for applications requiring extended coverage. Efficiency is also crucial in MIMO systems, directly impacting power consumption, data rate, and overall performance [24]. It measures how effectively the system converts input power into useful transmitted or received signal power. In the case of microstrip patch antennas, efficiency is particularly significant as it directly influences overall antenna performance.
  • 5.
     ISSN: 1693-6930 TELKOMNIKATelecommun Comput El Control, Vol. 23, No. 2, April 2025: 306-315 310 A higher efficiency indicates a greater proportion of input power being converted into useful radiated power, enhancing signal strength and communication quality [25]. The simulated efficiency gains for the proposed MIMO antenna, depicted in Figure 5, show a high efficiency of 89%, consistently exceeding 86% across its range. This indicates superior performance in changing input power into useful radiated power, contributing to enhanced signal strength and communication quality. Figure 4. Reflection coefficient of the proposed MIMO antenna Figure 5. Efficiency and gain of the proposed MIMO antenna 3.3. The envelope correlation coefficient The ECC holds significant importance in MIMO systems, as it directly impacts the system’s capability to leverage spatial diversity and achieve optimal channel capacity [26]. It quantifies the association between the envelopes of signals received by different antennas within the MIMO system. Essentially, it measures the similarity or correlation in the amplitudes of received signals across multiple antennas. In the context of MIMO systems, a low ECC, preferably close to zero, is desirable for optimal performance. We can see the ECC in Figure 6. This is because a low ECC indicates a high level of diversity among the multiple antennas, which is advantageous for maximizing system performance. 3.4. Diversity gain DG is essentially what we use to measure the development in system performance due to the practice of multiple antennas and to experience independent fading. Additionally, MIMO systems contribute significantly to improved system reliability, coverage, and capacity. One of the primary goals of MIMO systems is to achieve DG. The value of DG can be calculated below. The simulated DG for the suggested MIMO antenna is shown in Figure 7. It can be seen that the antenna achieves the lowest DG of 9.99. This value of DG suggests a considerable improvement in signal reliability and robustness due to the use of multiple antennas in a MIMO system [5]. Figure 6. ECC of the proposed MIMO antenna Figure 7. DG of the proposed MIMO antenna
  • 6.
    TELKOMNIKA Telecommun ComputEl Control  Graphene-based THz antenna with a wide bandwidth for future 6G short-range … (Md. Kawsar Ahmed) 311 4. RADIATION PATTERN The radiation pattern of an antenna is a graphical representation of the radiation dispersion from the antenna with respect to spatial direction. It is important to consider the orientation and properties of the E field and the H field when designing and placing antennas [27]. A magnitude of 22.4 dB V/m is associated with the E field lobe at theta =90°, a half-power beam width of 52°, and an H field magnitude of 900. As for the main lobe magnitude, it is -38.5 dBA/m, and the HPBW is 54.30 degrees. The half-power beam width is 124.6°, the E field of the primary lobe at =90° in the H-field is 8 dBV/m, and the magnitude for the H field of the lobe at =90° is -29.2 dB A/m. Figure 8 shows that the E-field, with theta =0 degrees, has an HPBW of 89.9 degrees and a primary lobe magnitude of 17.1 dB V/m [28]. Figure 8. Simulated radiation pattern of recommended MIMO antenna 5. RESISTANCE INDUCTANCE CAPACITANCE EQUIVALENT CIRCUIT In this section, we design an advanced antenna system to meet future wireless communication requirements. Our initial step involved developing an RLC circuit model to analyze the electromagnetic behavior of the system [29]. Figure 9 illustrates the equivalent circuit of the proposed MIMO antenna. The project aimed to precisely characterize the performance characteristics of the antenna structure and understand the complex relationships between its electrical components. To ensure accuracy, we meticulously extracted the R-L-C parameters directly from our antenna simulations using sophisticated tools such as CST Studio. In our antenna design, the patch element plays a crucial role in achieving two separate resonance frequencies. We utilized two parallel circuit configurations with resistance (R1), capacitance (C1), and inductance (L1) to construct these resonance frequencies carefully. Additionally, another two parallel circuits consisting of (L2+C3), (R2+C4), and R3 are responsible for the slot placed beside the feedline of the antenna. By combining these circuit elements, we created a model that accurately replicates the behavior of our single-element antenna [30]. When transitioning to a MIMO configuration, we accounted for mutual impedance between antenna elements using a parallel circuit of L3, R4, R5, and C5. To verify the accuracy of the Agilent advanced design system (ADS) simulation, we conducted a comparative test between the
  • 7.
     ISSN: 1693-6930 TELKOMNIKATelecommun Comput El Control, Vol. 23, No. 2, April 2025: 306-315 312 results of the CST simulation and a parallel circuit simulation, focusing on the S11 parameter. Figure 9 provides a detailed assessment of the accuracy and reliability of our R-L-C circuit model by comparation the simulation results of both the circuit and CST simulations. This model can estimate the performance of the future MIMO antenna. The simulation results obtained using CST, along with the equivalent RLC circuit results from ADS, are displayed in Figure 10. Figure 9. Final equivalent circuit is the result of the proposed MIMO antenna Figure 10. Simulated equivalent circuit reflection coefficient in ADS and CST 6. CONCLUSION The proposed THz antenna, designed for the 3-10 THz frequency range, exhibits outstanding performance in both single-element and MIMO configurations. It provides a wide bandwidth from 4.0328 to 10 THz, a high gain of 12.38 dB, and an efficiency of 89%, meeting the stringent demands of contemporary THz communication systems. The MIMO configuration achieves superior isolation at -27 dB and demonstrates low ECC and high DG, indicative of excellent MIMO capabilities. The incorporation of an RLC circuit model enables the precise representation of the S11 curve, ensuring an accurate characterization of the antenna’s input impedance and resonant behavior. The use of a polyimide substrate further enhances the antenna’s performance and applicability. The findings of this study highlight the proposed antenna’s potential for high-speed, short-range communication, making it a promising candidate for integration into advanced THz systems. ACKNOWLEDGEMENT We would like to extend my heartfelt gratefulness to the Faculty of Graduate Studies and the Department of Electrical and Electronic Engineering at Daffodil International University, Bangladesh, for their invaluable support and support throughout this journey.
  • 8.
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     ISSN: 1693-6930 TELKOMNIKATelecommun Comput El Control, Vol. 23, No. 2, April 2025: 306-315 314 [29] M. M. Khader, J. F. Gómez‐Aguilar, and M. Adel, “Numerical study for the fractional RL, RC, and RLC electrical circuits using Legendre pseudo‐spectral method,” International Journal of Circuit Theory and Applications, vol. 49, no. 10, pp. 3266–3285, Oct. 2021, doi: 10.1002/cta.3103. [30] R. Mishra, R. Panwar and D. Singh, “Equivalent Circuit Model for the Design of Frequency-Selective, Terahertz-Band, Graphene-Based Metamaterial Absorbers,” in IEEE Magnetics Letters, vol. 9, pp. 1-5, 2018, doi: 10.1109/LMAG.2018.2878946. BIOGRAPHIES OF AUTHORS Md. Kawsar Ahmed is currently pursuing his studies in the field of Electrical and Electronic Engineering at Daffodil International University. He successfully finished his Higher Secondary education at Agricultural University College, Mymensingh. He is presently employed as an Assistant Administrative Officer at the Office of Students’ Affairs at Daffodil International University (DIU) in Bangladesh. The areas of his research focus encompassed microstrip patch antennas, terahertz antennas, and applications related to 4G and 5G technologies. He can be contacted at email: kawsar33-1241@diu.edu.bd. Md. Sharif Ahammed is a student of Daffodil International University and pursuing a B.Sc. in the Electrical and Electronics Department. He passed from Government Bangabandhu College with a higher secondary. Microstrip patch antenna, terahertz antenna, and 5G application are some of his research interests. He can be contacted at email: sharif33- 1152@diu.edu.bd. Md. Ashraful Haque is doing Ph.D. at the Department of Electrical and Electronic Engineering, Universiti Teknologi PETRONAS, Malaysia, He got his B.Sc. in Electronics and Electronic Engineering (EEE) from Bangladesh’s Rajshahi University of Engineering and Technology (RUET) and his M.Sc. in the same field from Bangladesh’s Islamic University of Technology (IUT). He is currently on leave from Daffodil International University (DIU) in Bangladesh. His research interest includes microstrip patch antenna, sub 6 5G application, and supervised regression model machine learning on antenna design. He can be contacted at email: limon.ashraf@gmail.com. Narinderjit Singh Sawaran Singh is an Associate Professor in INTI International University, Malaysia. He graduated from the Universiti Teknologi PETRONAS (UTP) in 2016 with Ph.D. in Electrical and Electronic Engineering specialized in Probabilistic methods for fault tolerant computing. Currently, he is appointed as the research cluster head for computational mathematics, technology and optimization which focuses on the areas like pattern recognition and symbolic computations, game theory, mathematical artificial intelligence, parallel computing, expert systems and artificial intelligence, quality software, information technology, exploratory data analysis, optimization algorithms, stochastic methods, data modelling, and computational intelligence-swarm intelligence. He can be contacted at email: narinderjits.sawaran@newinti.edu.my.
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    TELKOMNIKA Telecommun ComputEl Control  Graphene-based THz antenna with a wide bandwidth for future 6G short-range … (Md. Kawsar Ahmed) 315 Jamal Hossain Nirob is a student in the Department of Electrical and Electronic Engineering (EEE) at Daffodil International University. His educational journey began at Maniknagar High School, where he successfully completed his Secondary School Certificate (SSC). Following that, he pursued higher studies at Ishwardi Government College, obtaining his Higher Secondary Certificate (HSC). With a strong enthusiasm for expanding communication technology, he has focused his research on wireless communication, specifically on microstrip patch antennas, terahertz antennas, and applications of 5G and 6G. He can be contacted at email: jamal33-1243@diu.edu.bd. Redwan A. Ananta has accomplished his undergraduate studies in the field of Electrical and Electronics at Daffodil International University. He completed his higher secondary education at Adamjee Cantonment College. His research focus encompasses wireless communication, specifically microstrip patch antenna, terahertz antenna, and 5G, and 6G applications. He can be contacted at email: redwan33-1145@diu.edu.bd. Kamal Hossain Nahin currently pursuing a degree in Electrical and Electronic Engineering at Daffodil International University. His educational journey began at Ishwardi Govt College for his Higher Secondary Certificate (HSC). As a budding researcher in the communication field, he is passionate about wireless communication, focusing on microstrip patch antennas, terahertz antennas, and their potential applications in future 5G and 6G technologies. He can be contacted at email: kamal33-1242@diu.edu.bd. Liton Chandra Paul holds the position of Assistant Professor in the Electrical, Electronic, and Department of Communication Engineering at Pabna University of Science and Technology (PUST). He completed his Master’s degree in Electrical and Electronic Engineering and Bachelor’s degree in Electronics and Telecommunication Engineering at Rajshahi University of Engineering & Technology (RUET) in 2012 and 2015, respectively. During his academic journey, he actively participated in various non-profit social welfare organizations, making significant contributions to their endeavors. In addition to becoming the department’s first-class first boy of the third batch (academic session 2007–2008), he received the University Gold Medal for his exceptional academic achievement in earning a B.Sc. in Electronics & Telecommunication Engineering. At the IEEE ICCIT 2021, one of his research projects won the Prof. Syed Mahbubur Rahman Best Paper Award. He was awarded the Research Excellence Award in 2022 and the Outstanding Researcher Award in 2023 from PUST. He received several research grants from various institutions. He has authored numerous publications for int’l conferences and peer-reviewed journals. He held the positions of Vice Chair (Technical) of the IEEE Young Professionals BDS (2022–2023) and Counselor for the IEEE PUST Student Branch (2020–2021). Currently, he is acting as an advisor for the IEEE PUST Student Branch. In addition, he effectively carried out a number of other duties assigned by PUST, including assistant director of the Student Advisor Office, additional director of the Institutional Quality Assurance Cell (IQAC), and assistant provost of Bangabandhu Sheikh Mujibur Rahman Hall. He also serves as a reviewer for many int’l reputed conferences and journals of different reputed publishers, including IEEE, Springer Nature, Elsevier, Wiley, Cambridge University Press, IET, Hindawi, MDPI, Taylor, and Francis. He has affiliations with different national and int’l professional bodies like the Institute of Engineers Bangladesh (IEB) and the Institute of Electrical and Electronics Engineers (IEEE), including IEEE-APS, IEEE-MTTS, IEEE-ComSoc, IEEE-SPS, and IEEE- WIE. His research interests are RFIC, MIMO, machine learning, bio-electromagnetics, microwave technology, antennas, phased arrays, mmWave, metamaterials, absorber, metasurfaces, and wireless sensors. He can be contacted at email: litonpaulete@gmail.com.