Performance analysis of 2D optical code division multiple access through underwater wireless optical medium

International Journal of Electrical and Computer Engineering (IJECE)
Vol. 14, No. 2, April 2024, pp. 1665~1673
ISSN: 2088-8708, DOI: 10.11591/ijece.v14i2.pp1665-1673  1665
Journal homepage: http://ijece.iaescore.com
Performance analysis of 2D optical code division multiple access
through underwater wireless optical medium
Md. Rabiul Islam1
, Md. Jahedul Islam2
, Bithi Mitra3
, Md. Amzad Hossain1
, Jahedul Islam1
,
Shuvo Dev1
1
Department of Electrical and Electronic Engineering, Jashore University of Science and Technology, Jashore, Bangladesh
2
Department of Electronics and Telecommunication Engineering, Chittagong University of Engineering and Technology,
Chattogram, Bangladesh
3
Department of Electrical and Electronic Engineering, Northern University of Business and Technology Khulna, Khulna, Bangladesh
Article Info ABSTRACT
Article history:
Received Oct 11, 2023
Revised Nov 9, 2023
Accepted Dec 26, 2023
The performance of a two-dimensional optical code division multiple access
(2D-OCDMA) system using an underwater wireless optical (UWO) medium
is assessed in this work. The optical source is an LED with a working
wavelength of 532 nm, and the optical detector is a p–i–n photodiode. When
calculating the bit error rate (BER), the phase-induced intensity noise
(PIIN), thermal noises, and shot sounds are taken into account. The user
code address is set using 2D perfect difference (2D-PD) codes. Link
distance, inclination angle, beam divergence angle, transmitter power, and
the number of concurrent users are all taken into account when determining
the BER performance. For various water media, such as pure sea water
(PSW), clear ocean water (CLOW), and coastal ocean water (CSOW), the
performance of the suggested system is examined.
Keywords:
2D-optical code division
multiple access
Bit error rate performance
Perfect difference code
Underwater wireless optical
communication
Water types
This is an open access article under the CC BY-SA license.
Corresponding Author:
Md. Rabiul Islam
Department of Electrical and Electronic Engineering, Jashore University of Science and Technology
Jashore, Bangladesh
Email: mr.islam01@just.edu.bd
1. INTRODUCTION
In the latest times, underwater wireless optical communication (UWOC) is used in sea currents
monitoring, climate forecasting, underwater vehicle operation, climate condition recording, real-time
monitoring, forecasting, oceanography research, environmental research, the transmission of data between
ships, linking submarines to land [1], [2]. Due to optical absorption (OA) and optical scattering (OS), as well
as oceanic turbulence (OT), the shaping of UWOC is difficult, and it gets some obstacles that are very
challenging to overcome. Different seawater has different levels of impurities, different values of chlorophyll
concentration, and different refractive index, temperature, salinity. In contrast with terrestrial RF
communications, wireless communication in an underwater medium can be seriously affected by the
limitations of the channel environment, noise, and bandwidth. The underwater channel often exhibits
frequency dispersion, multipath propagation effects, severe attenuation, limited bandwidth and power
resources., which make the UWOC one of the most complex communication systems in nature [1]–[4].
For long distances (ranging in km) and short distances (few meters), the available data rate of
existing underwater acoustic communication is up to tens of kbps and up to hundreds of kbps, respectively
[5], [6]. Thus, the acoustic link can be categorized into very short, short, medium, long, and very long links
[7], depending upon the transmission distance. However, putting UWOC into practice is challenging, as it is
hampered by several obstacles that are tough to overcome. The fundamental disadvantage of UWOC is that

 ISSN: 2088-8708
Int J Elec & Comp Eng, Vol. 14, No. 2, April 2024: 1665-1673
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the link distance is a constraint. Only a distance of less than 100 meters can be reached for a communication
link [8]–[10]. An optical signal gets subjected to many hindrances, such as OA, OS, and OT while traveling
through a water medium, which causes the intensity loss of the receiver power, the spreading of the optical
beam, multipath interference [1], [11]. These unavoidable effects greatly degrade the quality of
communication [11], [12] in the UWOC system due to the impact of the refractive index variation of sea-
water, fewer impurities dissolved in seawater ( i.e., salt, colored biological materials, mineral components,
inorganic materials.), and changes in temperature and salinity of seawater [11], [12]. As a result, the
impediment of UWOC becomes a major concern while studying the improvement of the performance of the
system. Due to the lower absorption characteristics in the 400 to 600 nm, UWOC systems operate in this
region to transmit data. Optical code division multiple access (OCDMA) is one optical access method that
is attracting a lot of attention because of its many appealing qualities, including effective bandwidth
utilization, greater security, increased robustness, and improved spectral efficiency [2], [6], [13]–[19].
OCDMA's simultaneous multi-user access to the network on the same frequency leads to multi-user
interference (MUI), which is the main cause of the OCDMA system's performance decline. A common
method to lessen the impact of MUI is the 2D-OCDMA system with an interference cancellation receiver.
However, a code sequence with the property of a fixed in-phase cross-correlation value is used to reduce the
MUI [14]. As a result, since 2D-PD codes have a unity in-phase cross-correlation value, their application
will be advantageous [20]–[25]. Moreover, 2D-PDCs with spatial/spectral transceiver structures have been
shown to more effectively control phase-induce intensity noise (PIIN) and lessen the impact of MUI in
OCDMA [14].
2. SYSTEM MODEL
Figure 1 displays a schematic representation of the underwater wireless 2D-OCDMA. The signals
from all transmitters supporting U number of simultaneous users are combined together using a combiner and
then splitted to the corresponding receiver by the splitter. Here, 2D-perfect difference codes (2D-PDCs) are
used to address the user code sequence. The user binary data is modulated at the transmitter using a
broadband optical source and an on-off keying (OOK) modulator. The 2D-OCDMA encoder encodes the
modulated signal. The fiber Bragg gratings (FBGs) array structure can be used to build the encoder's
structure [14]. The signals are combined by the employment of a combiner and then transmitted through a
water medium. The received signal is first decoded at the receiver by a 2D-OCDMA decoder, which is
likewise built by FBGs [14]. A photodetector converts the decoded signal into photocurrent. In this system, a
balanced photodetector is employed to mitigate the MUI. Finally, the threshold detector is used to retrieve the
original data.
Figure 1. Schematic illustration of the underwater wireless 2D-OCDMA system

Int J Elec & Comp Eng ISSN: 2088-8708 
Performance analysis of 2D optical code division multiple access through … (Md. Rabiul Islam)
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3. SYSTEM ANALYSIS
The prior consideration of designing the UWOC system is to comprehend the link budget equation,
which can be given by (1) [1], [2].
𝑃𝑅𝐶 = 𝑃𝑇𝑅𝜂𝑇𝑅𝜂𝑅𝐶
𝐴𝑅 𝑐𝑜𝑠(𝜙)
2𝜋𝑑2[1−𝑐𝑜𝑠(𝜙0)]
𝑒𝑥𝑝 [−𝑐(𝜆)
𝑑
𝑐𝑜𝑠(𝜙)
] (1)
where 𝑃𝑅𝐶 and 𝑃𝑇𝑅 are the received and transmitted optical power, respectively, 𝜂𝑇𝑅 and 𝜂𝑅𝐶 are transmitter
and receiver efficiency, respectively, 𝜙 is the inclination angle, 𝜙0 is divergence angle, 𝐴𝑅 is area, 𝑑 is the
channel length. For an underwater optical channel, the total loss coefficient 𝑐(𝜆) is [2], [4].
𝑐(𝜆) = 𝑎(𝜆) + 𝑏(𝜆) (2)
where the absorption coefficient 𝑎(𝜆) is given by (3) [4], [5].
𝑎(𝜆) = 𝑎𝑥(𝜆) + 𝑎𝑠
0(𝜆) (
𝐶𝑐
𝐶𝑐
0)
0.602
+ 𝑎𝐹
0
𝐶𝐹 𝑒𝑥𝑝(−ℏ𝐹𝜆) + 𝑎𝐻
0
𝐶𝐻 𝑒𝑥𝑝(−ℏ𝐻𝜆) (3)
where 𝑎𝑥(𝜆) = 0.0445𝑚−1
at 532 nm, 𝑎𝑠
0(𝜆) = 0.0127𝑚−1
at 532 nm, which is known as the spectral
absorption coefficient of chlorophyll [6], [7]. For fulvic acid, the specific absorption coefficients are
𝑎𝐹
0
=35.959 𝑚2
/𝑚𝑔 and 𝑎𝐻
0
= 18.828 𝑚2
𝑚𝑔
⁄ , ℏ𝐻(= 0.01105 𝑛𝑚−1) and ℏ𝐹 = (0.0189 𝑛𝑚−1) are
constants. The fulvic acid concentration [4], [5].
𝐶𝐹 = 1.74098𝐶𝑐 𝑒𝑥𝑝 [1.2327 (
𝐶𝑐
𝐶𝑐
0)] (4)
Again, the humic acid concentration [4], [5].
CH = 0.19334Cc exp [1.2343 (
Cc
Cc
0)] (5)
Here, the value of 𝐶𝑐
0
is constant at 1 mg/m3
but the total concentration of chlorophyll, 𝐶𝑐 changes
with the types of water [1], [4], [5], [8]. In this evaluation, the water types considered are coastal ocean water
or CSOW (𝐶𝑐 = 0.83𝑚𝑔/𝑚3
), clear ocean water or CLOW (𝐶𝑐 = 0.31𝑚𝑔/𝑚3
) and pure sea water or PSW
(𝐶𝑐 = 0.005𝑚𝑔/𝑚3
) [8]. The scattering coefficients of sea water are the combination of various particles,
which can be small or large in size, with an approximate refractive index constant of 1.15 and 1.03,
respectively [9]. Therefore, the coefficient of scattering can be expressed as [4], [5].
𝑏(𝜆) = 𝑏𝑛(𝜆) + 𝑏𝑠𝑝
0 (𝜆)𝐶𝑠𝑝 + 𝑏𝑙𝑝
0
(𝜆)𝐶𝑙𝑝 (6)
where 𝑏𝑛(𝜆) g ff f f “ ” 𝑏𝑙𝑝
0
(𝜆) and 𝑏𝑠𝑝
0 (𝜆) are the
coefficients for large and small particles, respectively, causing an effective scattering phenomenon. These
coefficients can be defined as (7) to (9) [4], [5].
𝑏𝑛(𝜆) = 0.005826 (
0.4
𝜆
)
4.322
, m-1
(7)
𝑏𝑠𝑝(𝜆) = 1.151302 (
0.4
𝜆
)
1.7
, 𝑚2
𝑔
⁄ (8)
𝑏𝑙𝑝(𝜆) = 0.341100 (
0.4
𝜆
)
0.3
, (9)
For large and small particles, the total concentrations are 𝐶𝑙𝑝 and 𝐶𝑠𝑝 respectively, which can be denoted as
[4], [5], 𝐶𝑙𝑝 = 0.76284𝐶𝑐 𝑒𝑥𝑝 [0.03092 (
𝐶𝑐
𝐶𝑐
0)] ,
𝑔
𝑚3
⁄ , 𝐶𝑠𝑝 = 0.01739𝐶𝑐 𝑒𝑥𝑝 [0.11631 (
𝐶𝑐
𝐶𝑐
0)] ,
𝑔
𝑚3
⁄ .
For the estimation of system BER, noises such as PIIN, thermal noise, and shot noise are taken into
account; therefore, the SNR can be calculated as (10):
𝑆𝑁𝑅 =
𝐼𝑟
2
𝐼𝑡
2 (10)

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where 𝐼𝑡 is the total noise power and 𝐼𝑟 is receiver photocurrent. The current 𝐼𝑟 is given by (11) [6]:
𝐼𝑟 =
ℜ𝑃𝑅𝐶𝑤1
𝑀
(11)
where 𝑤1 is the code weight (CW) of spectral code sequence, M is the code length (CL) of spectral code
sequence, and ℜ is the of photodetector responsivity. If the variance due to thermal noise, shot noise and
PIIN are 𝐼𝑃𝐼𝐼𝑁
2
, 𝐼𝑆ℎ𝑜𝑡
2
and 𝐼𝑇ℎ𝑒𝑟𝑚𝑎𝑙
2
, respectively, then 𝐼𝑡 can be illustrated as (12):
𝐼𝑡
2
= 𝐼𝑃𝐼𝐼𝑁
2
+ 𝐼𝑆ℎ𝑜𝑡
2
+ 𝐼𝑇ℎ𝑒𝑟𝑚𝑎𝑙
2
(12)
The thermal noise is as (13) [6]:
𝐼𝑇ℎ𝑒𝑟𝑚𝑎𝑙
2
=
4𝐾𝑏𝑇𝑚𝐵𝑒
𝑅𝐿𝑜𝑎𝑑
(13)
where 𝑅𝐿𝑜𝑎𝑑 is the receiver load resistance, 𝐵𝑒 is the receiver electrical bandwidth, 𝑇𝑚 is the receiver noise
temperature and 𝐾𝑏 is Boltzmann constant. If 𝛥𝑓 is considered as the source bandwidth, the variance for PIIN
can be expressed according to 2D-PD code by (14).
𝐼𝑃𝐼𝐼𝑁
2
=
ℜ2
𝐵𝑒𝑃𝑅𝐶
2
2𝑀𝛥𝑓𝑤2
2𝑤1(𝑀𝑁−1)2 {(𝑤1𝑤2(𝑀𝑁 − 1) + 𝑤2(𝑈 − 1)(𝑀 − 1))
2
+
𝑤2
2(𝑈−1)2(𝑀−1)2
(𝑤1−1)2 } (14)
The shot noise is estimated by (15) [6].
𝐼𝑆ℎ𝑜𝑡
2
=
𝑒𝐵𝑒𝑃𝑟𝑒𝑐ℜ
𝑤2𝑀
{𝑤1𝑤2 +
2𝑤1(𝑈−1)(𝑁−1)
(𝑀𝑁−1)
+
2𝑤2(𝑈−1)(𝑀−1)
(𝑀𝑁−1)
+
4(𝑈−1)(𝑀−1)(𝑁−1)
(𝑀𝑁−1)
} (15)
At the receiver end, the SNR can be calculated as (16) [6].
𝑆𝑁𝑅 =
𝐼𝑟
2
𝐼𝑃𝐼𝐼𝑁
2 +𝐼𝑆ℎ𝑜𝑡
2 +𝐼𝑇ℎ𝑒𝑟𝑚𝑎𝑙
2 (16)
The performance of the system is defined by the BER calculation which can be written as (17) [6].
𝐵𝐸𝑅 =
1
2
𝑒𝑟𝑓𝑐 (√𝑆𝑁𝑅 8
⁄ ) (17)
4. RESULTS AND DISCUSSION
This section provides an examination of the proposed UWOCDMA system's BER performance for
various types of water. The following criteria were used to evaluate the system's performance: transmitter
inclination angle (𝜃𝑖) =15°, LED beam divergence angle (𝜃𝑏) = 40°, both the transmitter and receiver optical
efficiency = 0.9, data rate (Dr) = 0.5 GHz, receiver aperture area (Ar) = 0.01 m2
, temperature (𝑇) = 298 K,
Photo detector responsivity (ℜ) = 0.85, receiver load resistance (RL) = 100 Ω, (𝐵𝑒𝑙𝑒𝑐) =
250 MHz, transmitter power (Pt) = 30 dBm are considered.
The plot of BER versus distance of transmission for different water is shown in Figure 2,
considering the previously described parameter. It can be found from the figure that the BER increases
significantly with the increasing link length. The BER of 10-9
is gained in PSW, CLOW and CSOW at a link
distance of 14, 9.8, and 7 m, respectively. Therefore, it can be stated that in PSW, a larger area can be
covered when the system is considered to be subjected to PSW maintaining a BER of 10-9
. However, in
CSOW channel, the performance gets worse due to the scattering and the absorption of the optical signal
resulting from the increasing volume of impurities.
Figure 3 refers to the plot of BER versus number of simultaneous users when the transmission
distance is 6 m, and the transmitter power is 30 dBm. Since the number of simultaneous users becomes more,
the effect of MUI gets aggravated which results in the degradation of the system BER performance. It can be
determined that for a certain value of BER of 10-9
, around 250 and 244 users can be assigned simultaneously
in PSW and CLOW respectively. However, the system performance diminishes in CSOW since in this
medium the attenuation coefficient is dominated by scattering resulting from a great volume of impurities
and considerable concentration level of chlorophyll.

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Figure 4 illustrates the BER versus inclination angle curve when the link length is 7 m, beam
divergence angle is 50°, and transmitter power is 30 dBm. It can be noted that the BER value degrades with
the reduction of inclination angle. This is because the more the optical beam is aligned away from the axis of
transmitter-receiver joining the line, the value of BER goes upward. Thus, the system undertaking CSOW
channel cannot allow the beam to be inclined by a wide angle to get a targeted BER value. The results show
that the inclination angle is 70° in pure sea water which must be decreased to 52° and 10° in PSW and
CLOW respectively to get a fixed BER of 10-9
.
The plot of BER versus beam divergence angle is presented in Figure 5 assuming that the link length
is 10m and the inclination angle is 10°. From the figure, it can be noted that when the beam divergence angle
decreases, the BER becomes less. To achieve a target BER of 10-9
, the beam divergence angle must be at a
value of 18° and 40° in CSOW and CLOW which is lower than that in PSW. The reason behind this is that the
attenuation profile and the absorption increase majorly with the changes in the concentration of chlorophyll. In
addition to that the scattering occurs due to presence of organic and inorganic particles in the water. Moreover,
the volume of these particles is particularly excessive in CSOW and CLOW channel.
Figure 2. BER versus distance of transmission
curve
Figure 3. BER versus number of simultaneous users
curve
Figure 4. BER versus inclination angle curve Figure 5. BER versus beam divergence angle curve
In Figure 6, the plot for the required optical power versus underwater link distance for different types
of water is represented. Here, the effect of variation of underwater channel can be clearly explained. The
transmitted optical power requirement increases when the number of impurity particles increase in water. The
power requirement in PSW is lower CLOW than and CSOW. When the transmission link distance increases
then the optical power requirement increases. At a target BER value of 10-9
, the system needs 38.02 dBm in
CSOW channel, however, it declines to a value of 27.61 dBm in case of PSW for the same transmission length
of 10 m. Figure 7 represents the characteristics curve for the required optical power versus inclination angle

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for different types of water considering 𝜃0 is 50°, d is 7 m and U is 50. It can be observed that when
inclination angle increases then the required optical power is increased. This is because the inclination angle
increases when the transmitted optical beam aligns away from the axis which connects the transmitter and
receiver, thereby, degrading the system performance severely. As a result, the system requires more
transmitted optical power when the angle of inclination rises causing more differences between the optical
beam trajectory and the transmitter-receiver connecting axis. In order to get a fixed BER of 10-9
, the system
possesses 23.78 dBm for PSW whereas it increases to 26.75 and 31.81 dBm for CLOW and CSOW channel
respectively if the optical beam gets inclined by 40°.
Figure 8 shows the plot of required optical power versus number of simultaneous users for different
underwater channel considering d is 10 m, 𝜃0 is 50°, inclination angle is 15°. The performance of the proposed
system degrades with an extensive number of simultaneous users because of the impact of MUI. At a BER
value of 10-9
, the required optical power is 39.41, 32.60 and 28.90 dBm for CSOW, CLOW and PSW
respectively, when the number of simultaneous users 200. This is because in CSOW, the effect of an extensive
amount of impurities and high concentration of chlorophyll result in scattering and absorption of optical signal.
Thereby, the performance of the proposed system deteriorates immensely. Figure 9 presents the required
optical power versus beam divergence angle curve considering d is 10 m, 𝜃 is 10° and U is 50. From the result,
it can be noted that the system needs more optical power with the rising 𝜃0. Since the value of attenuation and
absorption coefficient reaches at a maximum value when the chlorophyll concentration is maximum, the signal
strength in CSOW falls down drastically. In addition to that both organic and inorganic compounds dissolved
in water causes scattering of the optical signal, therefore, the system possesses more optical power to uphold
the signal strength. At a fixed BER of 10-9
and beam divergence angle of 90°, the required power in CSOW is
33 dBm, which is reduced by 4 and 6 dB in CLOW and PSW. Hence, PSW water the performance is
comparatively better than other two channels due to the less amount of total loss coefficient.
Figure 6. Required optical power at BER of 10-9
versus underwater link distance curve
versus inclination angle curve
versus users curve
versus beam divergence angle curve

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5. CONCLUSION
In this paper, the BER performance of 2D-OCDMA system through UWO medium is analyzed,
where 2D-PDCs are implemented to set user addresses. The LED optical source with 532 nm operating
wavelength is employed, and two balance detectors are used for the purpose of eliminating the effect of MUI.
The thermal noise, shot noise and PIIN are considered in the calculation to investigate the system
performance with respect to transmission distance, inclination angle, beam divergence angle, and number of
simultaneous users. Moreover, the system performance is evaluated for different water mediums due to the
fact that it greatly depends on them. The underwater medium is dissolved with a high level of impurities, and
the chlorophyll concentration is affected severely due to the occurrence of scattering and absorption of the
optical signal. That is why the CSOW channel gives poor performance compared with other water channels.
It can be seen that when transmission link distance is increased, then the optical power requirement increases.
The system performance is more affected by MUI with increasing users. At a BER value of 10-9
, it can be
observed that approximately 250 and 244 users can simultaneously deliver signals in PSW and CLOW
respectively.
ACKNOWLEDGEMENT
This work is supported by the Directorate of Research and Extension (DRE), Chittagong University
of Engineering and Technology (CUET) under the project no. CUET/DRE/2023-2024/ETE/010.
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BIOGRAPHIES OF AUTHORS
Md. Rabiul Islam is acting as a lecturer in the Department of Electrical and
Electronic Engineering (EEE), Jashore University of Science and Technology (JUST), Jashore-
7408. Previously, he served as a faculty member in the Department of EEE, Bangladesh Army
University of Science and Technology (BAUST), Saidpur cantonment, Nilphamari from
January 1st
, 2019 to April 7th
, 2022. He received his M.Sc. and B.Sc. degree in Electrical and
Electronic Engineering at Khulna University of Engineering and Technology (KUET). He can
be contracted at email: mr.islam01@just.edu.bd.
Md. Jahedul Islam received the B.Sc. and M.Sc. degrees in electrical and
electronic engineering from the Khulna University of Engineering and Technology (KUET),
Khulna, Bangladesh, in 2009, and 2011, respectively, and the Ph.D. degree in electrical and
information engineering from The University of Sydney, Australia, in 2015. He is currently
professor with the Department of Electronics and Telecommunication Engineering, CUET. His
research interests include optical communications, nonlinear optics and photonics. He can be
contracted at email: jahed@cuet.ac.bd.
Bithi Mitra is acting as a lecturer in the Department of Electrical and Electronic
Engineering (EEE), Northern University of Business and Technology (JUST), Khulna. He
received his M.Sc. degree in electrical and electronic engineering at Khulna University of
Engineering and Technology (KUET). Before that he completed B.Sc. degree in Electrical and
Electronic Engineering (EEE) from Khulna University of Engineering and Technology
(KUET). She can be contracted at email: bithim49@gmail.com.
Md. Amzad Hossain j “ ”
Nuclear Radiation Laboratory, Department of Nuclear, Plasma, and Radiological Engineering,
University of Illinois at Urbana-Champaign (UIUC), USA since 01 May 2023. He is currently
working as an associate professor, Electrical and Electronic Engineering Department, Jashore
University of Science and Technology (JUST), Jashore 7408, Bangladesh. He can be
contracted at email: mahossain.eee@gmail.com.

1673
Jahedul Islam is a lecturer in the Department of Electrical and Electronic
Engineering at the Jashore University of Science and Technology (JUST). He received
his undergraduate degree from Khulna University of Engineering and Technology (KUET) in
the Department of Electrical and Electronic Engineering in 2020. He can be contracted at
email: j.islam@just.edu.bd.
Shuvo Dev is acting as a lecturer in the Department of Electrical and Electronic
Engineering (EEE), Jashore University of Science and Technology (JUST), Jashore-7408. He
is currently pursuing his M.Sc. degree from KUET (Khulna University of Engineering and
Technology) after completing his B.Sc. in EEE (Electrical and Electronic Engineering) from
the same institution. He can be contracted at email: s.dev@just.edu.bd.

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