Analysis of Multiuser Detectors and Performance improvement in DS-
CDMA system using Multistage Multiuser Detection Techniques
J. RAVINDRABABU
1*
, DASI SWATHI
1
, J. V. RAVI TEJA
2
, J. V. RAVI CHANDRA
3
,
N. PRANAVI SRI1, SHAIK ARSHIYA1
1
E.C.E Department, P.V.P., Siddhartha Institute of Technology,
Vijayawada,
INDIA
2
FactSet Systems Pvt.Ltd,
Hyderabad, INDIA
3C.S.E Department, V.R. Siddhartha Engineering College,
Vijayawada,
INDIA
*Corresponding Author
Abstract: - The Direct Sequence Code Division Multiple Access (DS-CDMA) system faces several disruptions,
this is most crucial of which is the Multi Access Interference (MAI) caused by its users. The efficiency of the
system gradually declines as every quantity rises, and the MAI rises, especially in faded environments. This
work proposes a multiple-phase multiuser identification approach called Differencing Partial Parallel
Interference Cancellation (DPPIC), which improves the overall efficiency. The methods known as Differencing
Parallel Interference Cancellation (DPIC) and Partial Parallel Interference Cancellation (PPIC) are combined in
this methodology. Current solutions for Parallel Interference Cancellation (PIC) and PPIC have enhanced
overall effectiveness; however, this has come at the expense of increasing the complexity of computation. As
the variety of consecutive stages grows, the MAI falls. Using the DPIC approach may reduce the computational
burden without improving system functionality. The use of the Partial Differencing Parallel Interference
Cancellation (PDPIC) technique can enhance system performance while lowering the level of complexity.
According to the simulation findings, Bit Error Rate (BER) vs normalized signal strength (i.e., Eb / N0)
performs more effectively for the suggested DPPIC approach than for PIC, the PPIC, and PDPIC.
Key-Words: - Multiuser Detection, MAI, PIC, PPIC, DPIC, PDPIC, DPPIC.
Received: April 5, 2023. Revised: November 9, 2023. Accepted: December 7, 2023. Published: January 23, 2024.
1 Introduction
Multiple access techniques can be included in
modern mobile radio networks to maximize
efficiency while minimizing cost and better using
the available bandwidth and radio cell
infrastructure. Code Division Multiple Access
(CDMA) and Multi-Carrier Code Division Multiple
Access (MC-CDMA) are the two multiple access
methods. CDMA is now a fundamental component
of mobile phone networks. It uses communication
methods to transfer information among a single base
station and many endpoints. Although it presents a
difficulty to accommodate lots of users in a limited
region, the CDMA technology has significant
potential to function as an air gateway for future
high-rate mobile communication systems, [1], [2],
[3].
More recently, in collaborative multiuser
identification, multiuser disturbance is seen as data
instead of sound, [4]. Previous work on multiuser
identification has concentrated on creating less-
than-ideal recipients in the synchronized CDMA
paradigm, which have a lower computing
complexity while functioning greater than linearity
detectors, [5]. Owing to an MAI issue, multiuser
detection for the symbol-synchronous Gaussian
CDMA channel acted as the major factor in
numerous multiuser communications systems during
the last fifteen years. By taking employ of the
known pattern of multiple-user disruption, multiuser
identification may effectively demodulate
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DOI: 10.37394/232017.2024.15.1
J. Ravindrababu, Dasi Swathi, J. V. Ravi Teja,
J. V. Ravi Chandra, N. Pranavi Sri, Shaik Arshiya
E-ISSN: 2415-1513
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Volume 15, 2024
customers' non-orthogonal transmissions and solve a
variety of issues. When compared to traditional
matched filter (MF) reception, it may be employed
to lower MAI in direct sequence CDMA (DS-
CDMA) systems, which greatly enhances the
efficiency inside the structure, [6], [7], [8].
Every user of DS-CDMA technology has
simultaneous access to the whole spectrum allotted
to them. This is made feasible by the dispersion of a
series and the brief chip period used to disperse user
data across the whole spectrum that is available
speed. It also acts as a unique user ID, offering
various degrees of immunity from simultaneous
disruption, [9], [10].
2 Literature Review
Code division multiple access (CDMA) is a well-
designed contender to handle the downstream of cell
phone connections to achieve high data speeds.
Nonetheless, the CDMA system's efficiency is
significantly impacted when sending any kind of
signal across an intermittent range. To ensure that
overcome the disruption and characterize the
channel, multiuser detection (MUD) and channel
estimation are crucial. Reducing the user's signal
transmission error rate is the aim of the BBO
algorithms. The most effective answer to the
detection problem is selected by the criteria rates of
arrival and departure. As a result, both the user
sending signal disruption with the task that person
identification have been solved.
As MAI is a significant issue in DS-CDMA
systems due to its users, promising methods like
Multiuser Detection reported can be employed to
accomplish improved performance, [7]. The ideal
multiuser identifier for information discovery in
different access non-Gaussian stations has been
determined in, [10], [11]. When comparing optimal
multiuser identification in noisy conditions to
achieve the best multiuser identification possible
using a Gaussian distortion presumption, it was
demonstrated that significantly improved
performance may be achieved. A reduced
complexity Multiuser sensor built around the M-
estimator was developed and analyzed in, [12], as
the optimal technique is extremely CPU-intensive.
Specifically, the writers of, [12] exhibit that the
proposed multiuser detector offers a substantial
performance gain over the linear decorrelating
device when the ambient channel noise is non-
Gaussian. Additionally, an alternative M-estimator-
based multiuser detector that ensures a reduced
performance decrease in comparison to the ideal
multiuser identification was devised in, [11] if the
background noise is relatively reactive.
It is of relevance to build recipients to account
for this band's behavior, as DS-CDMA broadcasts
often occur across fade bands.
For submarine audio connections, [13], have
introduced a blind adaptive multi-user identification
technique based on Kalman filtering. In multi-user
communication underwater acoustic networks of
sensors, this method successfully improves system
ability, lowers the cost of transmission and control
of power expenses, increases the multi-user
interaction separation, and decreases or eliminates
ISI, MAI, and the near-far effect. All of these
benefits result in the efficient use of the accessible
restricted frequency band.
On reviewing the existing relevant literature, the
following observations are being made:
i. Different spreading sequences have
been investigated.
ii. Among all the multi-user detectors, the
overall BER performance was found
better in the maximum likelihood
detector/the optimum detector at the
cost of very high computational
complexity and thus not realistic for
implementation.
iii. Though the computational complexity
is found less in decorrelating detectors
and MMSE detectors, the calculation of
the inverse cross-correlation matrix is
difficult in these linear detectors.
iv. When the number of users rises, the
computing cost grows exponentially in
SIC, PIC, HIC and PPIC techniques.
Each type of interference cancellation
detector has its level of complexity,
processing time and BER performance.
In view of the above observations, there exists a
need to make studies to enhance visual DS-CDMA
system performance and reduce the difficulty of
computing. Further, interference cancellation
methods other than the existing ones are to be
explored for DS-CDMA systems.
The CDMA signal and channel model are
covered in the following chapter. Standard single-
user and multiuser detection methods are covered in
Section 3. The fourth section describes multiple
phases of detection techniques and noise.
Simulation results on the performance comparison
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of several multistage multiuser identification
approaches are presented in Section 5. An overview
of the results is provided within Chapter 6's results.
3 CDMA Signal and Channel Model
Any user will issued an authentication series of time
Tb, and Tb is the sign interval, in a K-user
synchronous DS-CDMA system using the low pass
comparable architecture, [12]. One way to describe
the kth user's signing series is
as
k n c b
L-1
n=0
S (t) = p(t-nT ) 0 t T (1)

where
n, 01nL
is a series of pseudo-random
noise (PN) with L wafers which can have numbers
in the range of {+1,−1}. The length of the pulse,
p(t), is Tc, where Tc is the chip interval and Tb =
LTc. It is reasonable to presume that all K signature
sequences contain units of energy without losing
variety.
, i.e.
2
0
( ) 1
Tb
k
S t dt
The cross-correlation for any two signature
sequences Sj and Sk is defined as
To keep things simple, we'll suppose that each
user transmits their data via basic antipodal
impulses. Since the transmission is synchronous, the
data or delay related to the transfer of a single bit
must be taken into account.
For K users, the combined broadcast message's
corresponding low pass can be written simply:
K
k=1
k k k( ) A b (t) (3)sxt
Where Ak, bk, and Sk(t) are the transmitted
amplitude, data bit, and signature sequences,
respectively, of the kth user.
The received signal via a fading channel can be
expressed as:
(4)r(t) = h(t)x(t)+n(t)
where
n(t)
is the noise with power spectral density
N0/2 and h(t) is complex fading coefficient given by
where
is Rayleigh distributed channel gain and
is the phase shift uniformly distributed
between 0 to 2π.
4 Conventional and Multiuser
Detection Schemes
4.1 Conventional Single-User Detection
Figure 1 shows the conventional single-user
detection system,
Fig. 1: Matched filter bank
K distinct single-input (continuous time) and
single-output (discrete time) filtering are used to
create the sensor without any joint processing.
Despite considering the presence of other (K-1)
active users in the system, every individual gets
demodulated independently, [8], [9], [10], [11]. The
kth matching filter's sample result is given by:
0
(6)( ) ( )
b
T
KK
y r t s t dt
The decision is made by:
b sgn( )
Kk
y
(7)
4.2 Multiuser Detection Scheme
All user information is simultaneously detected by
the multiuser sensor. Another name for it is
ligament identification. In the absence of MAI, It
()
h(t) = (t)e (5)
jt
(t)
()t
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addresses the process of demodulating digitally
encoded signals. One needs to be apt for suboptimal
multiuser detectors as it is too complex to use this
detector in practical applications like DS-CDMA
systems, [8], [9].
Figure 2 depicts the multiuser detecting
method's architecture. It utilizes an appropriate
filter-branch that transforms the discrete-time
sampled at the chip from the constant time signal
that arrived rate, allowing it to recognize all of the
sent signals from what was received without
obscuring any communicated data necessary
for decoding, [10], [11].
Fig. 2: Multi-user detector
4.2.1 MMSE Method
For identification, the decorrelating sensor just
needs to distribute events' correlations matrices R's
information, [8]. Multi-user identification relying on
the Minimum Mean Square Error (MMSE) criteria
has garnered an abundance of attention lately, [8].
Figure 3 depicts the MMSE sensor. The choice for
the kth user is determined by the linear mapping that
minimizes the mean-squared error between the
actual information and the result of the traditional
detection.
2 -1
sgn (( ) )kk
by

-2
RA
(8)
where
2
- Normalised cross-correlation
A - Amplitude of the signal
5 Interference Cancellation Schemes
Generally, speaking there are three types of
interfering cancellations strategies: hybrid
interference cancellation (HIC), parallel interference
cancellation (PIC), and successive interference
cancellation (SIC). It is discovered that the PIC
detector performs better than the SIC detector, [8].
Here isn't a justification for a single signal to be
given preference over the others under efficient
power regulation as all signal strengths are of the
same order. A parallel interference cancellation
(PIC) detector may be employed in these
circumstances. The PIC detector measures each bit
of the information and deducts based on the
intended user's signal the MAI imposed by all
interfering participants.
Fig. 3: MMSE Detector
5.1 Multistage Multiuser Parallel
Interference cancellation
To identify the data bits and eliminate disruption,
the PIC sensor goes through several iterations. The
information bits are initially calculated using the
MMSE. The subsequent phases execute signal
reconstructions for every user and remove the
estimated interference from every other user, [8].
The estimations of the information fragments plus
the previously determined user cross-correlations
are utilized throughout multiple-stage multiuser PIC
detectors to cancel out any interference in the results
of the MMSE detectors or results of previous
phases. Figure 4 depicts the multiple-stage PIC. The
choice for stage s+1 in the PIC detector's Sth stage
may be stated as, [8]:
( 1)
( 1)
sgn( )
ss
kk
bz
(9)
where
()
( 1)
1

s
s
k k j kj j
j
Z y A b
(10)
and
(1) k
k
zy
(11)
The peak amplitudes of each user's signals
received must be known by the PIC detector. The
receiving magnitudes must be calculated because
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the device that receives it lacks immediate
communication with this data. The multistage PIC
will function effectively if the magnitude of the
signal is correctly assessed in the preceding stage.
Nevertheless, the PIC is unable to ensure that
efficiency would increase in subsequent phases, [8].
Fig. 4: Multistage PIC detector
5.2 Multistage Multiuser Partial Parallel
Interference Cancellation
A biassed judgment statistics is produced by the
Multistage Multiuser PIC detector execution, which
is based on the subtraction of the interference
estimations. The bias has less impact on the latter
phases of noise elimination than it does on the initial
stage. Nonetheless, the impact of these inaccuracies
may be seen at subsequent stages if the bias
causes erroneous cancellation at the initial step,
[8], [9]. By dividing the magnitude predicted by
a partial-cancellation aspect (range: 0 to 1) that
changes depe nding on the stage of
postponements and system load K, one can easily
avoid the impact of the biassed decision
statistic and enhance the performance of
multistage parallel interference termination. A
multi-stage PPIC is displayed in Figure 5. In
this method, the partial factors 0.3, 0.4, and 0.5 are
used in first, second, and third stages.
Fig. 5: Partial PIC detector
Before subtracting the impact from the
magnitude estimations, the division must be
completed. This may be understood as adding a
partial cancellation factor to the solution (10) and
rearranging the results to, [8], [9], [10], [11].
()
( 1) ( )

s
ss
k k k j kj j
jk
Z y C A b
(12)
where
()s
k
C
is a partial cancellation factor
ranging from 0 to 1
5.3 Multi-stage Difference PIC (DPIC)
When detecting PICs multiple-stage if one
observes
( ) ( 1)
ss
kk
bb
, then it represents the
incremental technique's completion. The
differencing of the estimated bits can be computed in
two steps, rather than addressing each projected bit
array as in formula (10). As seen in Figure 6, the
input of each step becomes what is known as the
distinction approach, [1].
( ) ( ) ( 1)

s s s
k k k
x b b
, which
is called the differencing technique, [1], as shown in
Figure 6.
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()
( ) ( 1)

s
ss
k k j kj j
jk
Z Z A x
(13)
Fig. 6: Difference PIC detector using MMSE
5.4 Proposed Multi-stage Multiuser
Difference Partial PIC technique
(DPPIC)
The choice of statistics-based impact affects the PIC
approach. However, this issue can be lessened,
particularly by using the partial parallel interference
cancellation in the early phases of the anticipated
multiple access interference. The lowering of the
computational burden in a PIC approach is its most
significant and intriguing feature. A considerable
performance boost is provided by the partial PIC.
Either difference partial PIC (DPPIC) or partial
difference PIC (PDPIC) will be produced by
combining difference PIC (DPIC) and partial PIC
(PPIC). Figure 7 and Figure 8 display the DPPIC
and PDPIC diagrams. Except the fact that partial
components are multiplied before as well as
following differencing (in DPPIC and PDPIC),
these schematics are nearly identical.
()
( ) ( 1) s
s
ss
k k j kj j
kjk
Z Z A x
C




(14)
where
Fig. 7: Multi-stage PDPIC detector
()
( ) ( 1)
( ) ( 1)
s
ss
ss
ss
k k j kj k j kj k
kk
j k j k
Z Z A b A b
CC








(15)
Algorithm for PDPIC
For s = 2 to S
For k = 1 to K
End
End
End
(s) (s) (s-1)
jkk
x = b - b

(1)
1 MMSE
b sgn(y )
(2) (1)
1
( ( ))
K
k MF j ij ij j
j
z y A R diag R b
(2) (2)
11
sgn( )bZ
( ) ( ) ( 1)s s s
k k k
x b b

(s)
s
(s) (s-1)
k k j jk k
k
jk
Z =Z - A R x
C
(s+1) ( 1)
kk
b sgn( )
s
Z
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Fig. 8: Multi-stage DPPIC detector
Algorithm for DPPIC
For s = 2 to S
For k = 1 to K
End
()
( ) ( 1)
( ) ( 1)
s
ss
ss
ss
k k j kj k j kj k
kk
j k j k
Z Z A b A b
CC








End
End
6 Simulation Results
The DS-CDMA basic multistage multiuser discrete
time paradigm was applied. The customer's data is
disseminated via BPSK modulation and Kasami odd
spreading sequence techniques.
The system performance of multistage PIC,
PPIC, PDPIC, and DPPIC with the MMSE
multiuser detectors for different phases is displayed
in Figure 9, Figure 10, Figure 11 and Figure 12.
There are just three actions done into consideration
herein for clarity. Stage 3 system efficiency
surpasses both Stage 1 and Stage 2 system
efficiency.
0 5 10 15 20 25 30 35 40 45 50
10-6
10-5
10-4
10-3
10-2
10-1
BER
Eb/No
BER performance of multistage PI with MMSE for K=10
stage 1
stage 2
stage 3
Fig. 9: BER performance of multistage PIC with
MMSE, K=10 for three different stages
0 5 10 15 20 25 30 35 40 45 50
10-6
10-5
10-4
10-3
10-2
10-1
BER
Eb/No
BER performance of Multistage PPIC with MMSE for K=10
stage 1
stage 2
stage 3
Fig. 10: BER performance of multistage PPIC with
MMSE, K=10 for three different stages
Generally, speaking system efficiency improves
as the number of phases rises, but the computing
cost also does. As seen in Figure 13, Figure 14,
Figure 15 and Figure 16, the system's reliability
rapidly declines if the number of users grows along
with the BER.
(1)
1 MMSE
b sgn(y )
(1)
(2)
1
( ( ))
K
j
k MF j ij ij
j
z y A R diag R b
(2) (2)
11
sgn( )bZ
( ) ( ) ( 1)s s s
k k k
x b b

(s)
s
(s) (s-1)
k k j jk k
k
jk
Z =Z - A R x
C
(s+1) ( 1)
kk
b sgn( )
s
Z
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0 5 10 15 20 25 30 35 40 45 50
10-6
10-5
10-4
10-3
10-2
10-1
BER
Eb/No
BER performance of Multistage PDPIC with MMSE for K=10
stage 1
stage 2
stage 3
Fig. 11: BER performance of PDPIC with MMSE
K=10 for three different stages
0 5 10 15 20 25 30 35 40 45 50
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
BER
Eb/No
BER Performance of Multi stage DPPIC with MMSE For K=10
Stage 1
Stage 2
Stage 3
Fig. 12: BER performance of DPPIC with MMSE
K=10 for three different stages
0 5 10 15 20 25 30 35 40 45 50
10-6
10-5
10-4
10-3
10-2
10-1
BER
Eb/No
BER performance of multistage PIC with MMSE
K=10
K=15
K=20
K=25
K=30
Fig. 13: BER performance of 3rd stage PIC with
MMSE for K= different users
0 5 10 15 20 25 30 35 40 45 50
10-6
10-5
10-4
10-3
10-2
10-1
BER
Eb/No
BER performance of Multistage PPIC with MMSE
K=10
K=15
K=20
K=25
K=30
Fig. 14: BER performance of 3rd stage PPIC with
MMSE K= different users
0 5 10 15 20 25 30 35 40 45 50
10-6
10-5
10-4
10-3
10-2
10-1
BER
Eb/No
BER performance of Multistage PDPIC with MMSE
K=10
K=15
K=20
K=25
K=30
Fig. 15: BER performance of 3rd stage PDPIC with
MMSE K= different users
0 5 10 15 20 25 30 35 40 45 50
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
BER
Eb/No
BER Performance of Multi stage DPPIC with MMSE using third stage
K=10
K=15
K=20
K=25
K=30
Fig. 16: BER performance of 3rd stage DPPIC with
MMSE K= different users
A comparison of the simulated system
performance of PIC, PPIC, PDPIC, and DPPIC at
the third stage is shown in Figure 17. This chart
makes it clear that the suggested multiple phases
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DPPIC outperforms the others. The contrast of
PDPIC and DPPIC's computational difficulty is
displayed in Figure 18. The computational
complexity of DPPIC is somewhat higher in this
figure compared to that of PDPIC.
0 5 10 15 20 25 30 35 40 45 50
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
BER
Eb/No
BER Performance of different multi stage multi user detectors with MMSE using third stage for K 10
DPPIC
PDPIC
PPIC
PIC
Fig. 17: BER performance comparison of multi-
stage multi-user detectors at the third stage for K=10
0 5 10 15 20 25 30 35 40 45 50
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2x 106
K
S
Computational complexity
DPPIC
PDPIC
Fig. 18: Computational complexity between DPPIC
and PDPIC.
7 Conclusions
Employing multiple-stage multiuser approaches in
DS-CDMA systems can also minimize the
complexity of computation and Multiple Access
Interference. In the multistage PIC approach, bit
error rate (BER) drops and detection becomes more
dependable as the number of stages rises. The
ability to increase in subsequent phases cannot be
guaranteed by the PIC. In a DS-CDMA system, the
effectiveness of the Partial Parallel Interference
Cancellation (PPIC) technique is assessed.
Multistage PDPIC and DPPIC approaches can be
used to achieve both cost decrease and efficiency
enhancement simultaneously. Ultimately, it may be
concluded that DPPIC outperforms PIC, PPIC, and
PDPIC approaches, yet has a little higher
computational demand than PDPIC.
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[2] Rasadurai Kumaravel Performance
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[3] Srinivasa R. Vempati Multiuser Detection
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[4] Anwar Hassan Ibrahim “Significant of BER
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[5] Jiaqi Gu “Joint interference cancellation and
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WSEAS TRANSACTIONS on ELECTRONICS
DOI: 10.37394/232017.2024.15.1
J. Ravindrababu, Dasi Swathi, J. V. Ravi Teja,
J. V. Ravi Chandra, N. Pranavi Sri, Shaik Arshiya
E-ISSN: 2415-1513
9
Volume 15, 2024
codes in LinearMulti-User Detectors for DS-
CDMA system WSEAS Transactions on
Communications. Issue 11, vol. 11, November
2012.
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“Performance Analysis, improvement and
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detector with parallel interference
cancellation for DS CDMA System Using odd
kasami sequence WSEAS Transactions on
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Contribution of Individual Authors to the
Creation of a Scientific Article (Ghostwriting
Policy)
- J. Ravindra Babu, D. Swathi Identified the
problem statement and done the mathematical
Analysis.
- J. V. Ravi Teja, J. V. Ravi Chandra have
implemented the Algorithms in section 4.4.
- N. Pranavi Sri, Arshiya carried out the simulation
in section 5 using MATLAB.
Sources of Funding for Research Presented in a
Scientific Article or Scientific Article Itself
No funding was received for conducting this study.
Conflict of Interest
The authors have no conflicts of interest to declare.
Creative Commons Attribution License 4.0
(Attribution 4.0 International, CC BY 4.0)
This article is published under the terms of the
Creative Commons Attribution License 4.0
https://creativecommons.org/licenses/by/4.0/deed.en
_US
WSEAS TRANSACTIONS on ELECTRONICS
DOI: 10.37394/232017.2024.15.1
J. Ravindrababu, Dasi Swathi, J. V. Ravi Teja,
J. V. Ravi Chandra, N. Pranavi Sri, Shaik Arshiya
E-ISSN: 2415-1513
10
Volume 15, 2024