Uplink Performance Analysis of PD-NOMA System

Abstract

Non-Orthogonal Multiple Access (NOMA) is one of the potential radio access methods suggested for 5G networks to improve the performance of 5G users. This research presents the work made on the 5G PD-NOMA system. The objective of the research is to analyze the bit error rate experienced by UEs under different channel models, different encoding techniques, and different modulation schemes. The MATLAB-based Uplink system model for PD-NOMA is developed to make in-depth studies on channel parameters, a path loss model, modulation techniques, and encoding techniques. This research utilizes BPSK modulation, lognormal, two-ray, and free-space channel models, convolutional encoding, and low-density parity check (LDPC) encoding techniques for investigation purposes. From the research obtained, it is found that LDPC code exhibits a lesser probability of error compared to convolutional coding on BPSK modulated data.

Full text

Uplink Performance Analysis of PD-NOMA System
Bollineni Krishna Sai
Department of Electronics Engineering
Madras Institute of Technology, Anna
University
Chennai, India
kskrishnaone@gmail.com
Ranjith V
Department of Electronics Engineering
Madras Institute of Technology, Anna
University
Chennai, India
ranjith3008v@gmail.com
Bhuvaneswari P.T.V
Department of Electronics Engineering
Madras Institute of Technology, Anna
University
Chennai, India
ptvbmit@annauniv.edu
Parameswaran Ramesh
Department of Electronics Engineering
Madras Institute of Technology, Anna
University
Chennai, India
parameswaran0789@gmail.com
Abstract— Non-Orthogonal Multiple Access (NOMA) is one
of the potential radio access methods suggested for 5G
networks to improve the performance of 5G users. This
research presents the work made on the 5G PD-NOMA system.
The objective of the research is to analyze the bit error rate
experienced by UEs under different channel models, different
encoding techniques, and different modulation schemes. The
MATLAB-based Uplink system model for PD-NOMA is
developed to make in-depth studies on channel parameters, a
path loss model, modulation techniques, and encoding
techniques. This research utilizes BPSK modulation,
lognormal, two-ray, and free-space channel models,
convolutional encoding, and low-density parity check (LDPC)
encoding techniques for investigation purposes. From the
research obtained, it is found that LDPC code exhibits a lesser
probability of error compared to convolutional coding on
BPSK modulated data.
Keywords—5G, Uplink PD-NOMA, Modulation, LDPC and
Path Loss Models
I. INTRODUCTION
Fifth Generation (5G) is an adaptable and expandable
networking technology that provides ubiquitous connectivity
to 5G users. It delivers a cloud-native core network with end-
to-end network-slicing functionality. It facilitates the
development of novel significance use case areas, namely
Enhanced Mobile Broadband (eMBB), ultra-reliable Reliable
Low Latency Communication (URLLC), and massive
machine-type communications (mMTC) [1].
Non-Orthogonal Multiple Access (NOMA) assumes high
spectral efficiency by combining superposition coding at the
transmitter with Successive Interference Cancellation (SIC)
at the receivers [2]. Unlike traditional Orthogonal Multiple
Access (OMA) [3] methods (e.g., Orthogonal Frequency
Division Multiple Access (OFDMA), etc.), NOMA serves
multiple UEs in the same degrees of freedom simultaneously
by separating them in the power domain.
Early studies mostly focused on downlink NOMA
systems [4], and only a few glanced at uplink NOMA. In this
research, the uplink PD-NOMA is examined by applying
diverse channel models and encoding strategies with BPSK
modulation. The focus of this investigation is to analyze the
performance of Low Density Parity Check (LDPC) code and
Convolution encode under various channel models, namely
Lognormal, Two-Ray, and Free Space BPSK modulated
data.
From the research, it is found that the BPSK modulated
data when encoded using LDPC resulted in a lesser BER
than when encoded with convolutional code.
The rest of the article is structured as follows: Section II
provides the existing state of the art on the investigation
made through the literature survey. The proposed
methodology involving encoding, modulation, and channel
models is represented in Section III. In Section IV, the
simulation results obtained through the investigation are
discussed. Finally, Section V highlights the implications of
the executed investigation, presenting the novelty attained.
II. LITERATURE SURVEY
In [5], authors have provided comprehensive survey
detailing the evolution of 5G with respect to various releases
of 3GPP. They have highlighted the changes in 5G
specifications, the kind of morality followed, and the features
supported to address various new services that can be
accomplished using 5G technology.
In [6], authors have provided a concise review of new
features of 5G. They have registered their observations on
highlighting the security issues prevailing in 5G and
provided research directions to address this issue. They have
detailed the service based architecture followed in the 5G
core network. The connection management procedures and
trust model needed to realize a secured architecture are also
presented.
In [7], authors have developed General Low Density
Parity Check (GLDPC) to reduce the latency of the 5G
communication system. In LDPC, a single parity check
constraint is adopted. This is replaced by a generalized
constraint. To accomplish this quasi-cycle, the GLDPC is
constructed. The developed work is validated over an
AWGN channel with QPSK modulation. From the result
obtained, it is evident that the developed GLDPC
outperformed the existing coding technique.
In [8], authors have provided a comparative analysis of
the BER performance of various higher-order digital
modulation schemes with respect to SNR over the AWGN
channel. To decrease BER for a specific SNR, matched
filters and convolutional encoding are used. From the results
obtained, it is observed that adaptive modulation combined
with filters and coding techniques obtained the highest
spectral efficiency.
In [9], authors have proposed an LDPC-coded APSK
scheme using FPGA-based hardware efficiency to suit
aeronautical telemetry applications. They have investigated

the design of APSK modulation for communication over
wireless channels. In this proposed scheme they have used
reconfigurable rate adaptive LDPC codes with code rate
ranging from 0.7 to 0.8 and 4 modulation formats 8-APSK,
16-APSK ,32-APSK and 64-APSK.
In [10], authors have proposed a novel power control
scheme and analyzed the performance in terms of outage
probability and resulted with achievable data rate in Uplink
NOMA system. From the results, it is demonstrated that the
outage performance of the first UE is proportional to the
target data rate and that the outage performance of the
second UE is largely impacted by the performance of the
first UE. Also, they have concluded that the NOMA scheme
achieves higher data rates compared to the OMA scheme.
The literature mentioned above details the Uplink system
used in PD-NOMA. This study has made an effort to
investigate the impact of NOMA using a power domain
method. Investigating the uplink performance of NOMA in
terms of channel model, encoding, and modulation is
addressed in this research.
III. PROPOSED METHODOLOGY
3.1 System Model for PD-NOMA
Fig. 1 System Model of Uplink PD-NOMA
Consider a PD-NOMA system having N numbers of User
Equipment (UE). Let each user who transmits the data be
represented by UTi, where i ranges from 1 to N. Data is
transferred from UE to the evolved node B (eNB). Data from
each UE is encoded, modulated, and transmitted through the
antenna to the eNB. The data is then broadcast to all UEs in
the downlink channel. The eNB allocates power to the UEs
in the downlink based on their distance with respect to the
eNB. The superposition of their data with allocated power is
done in the eNB. Successive Interference Cancellation (SIC)
is done in each of the UEs on the receiving side to reproduce
the transmitted data done in the eNB. In this research, all
considered UEs are assumed to be in the same cell.
3.2 System Scenario
In this scenario, the values of N and K are
considered to be 2. That is, the number of UEs that send the
data to the eNB is 2, and the number of UEs that receive it is
also 2. The data of both the UEs are independently encoded
and modulated before transmitting to the eNB.
Fig. 2 System Scenario
3.2 System Architecture
3.3.1Transmitter Section
Fig. 3 Transmitter Section
The developed PD-NOMA system consists of various
modules, namely an input traffic generator, an encoder, and a
modulator. Following section details the kind of schemes,
techniques used in each block.
Traffic Generator: In cellular communication, various
traffic generation models are used. In this research, a Poisson
distribution model is used to generate input data bits for each
UE.
Let the data generated by each UE be xi and the average
data rate of each user be λi
𝒇(𝒙) = (𝒆−𝝀i 𝝀𝒙i)/𝒙I (3.1)
where,
xi= Actual data that varies from i = 1 to 2
λi =Average data rate that varies from i = 1 to 2.
Convolutional encoder: In linear block codes, the
encoder transforms a k-bit of the message block into an n-bit
of the codeword. Code words are consequently made one at a
time [11]. Through the use of linear shift registers, a
convolutional code inserts an extra bit into the data stream,
as shown in Figure 4.
Fig. 4 Convolutional Encoder
Traffic
Generator
Encoder
Modulator
Channel
eNB

Low-density parity check (LDPC) encoder: The LDPC
generating matrix is referred to as a low-density matrix or
sparse matrix since it generates more zeros than ones. Two
base graphs are utilized as the generation matrix in 5G.
These two Base Graph types are specified in the specification
38.212 [7] (multiplexing and channel coding). According to
the expansion factor Zc, each entry in the base graph can be
further enlarged.
Modulator: In this research, the BPSK modulation
technique is being used to send the data. Every digital
modulation system represents digital data with a finite set of
distinct symbols. In PSK, there are a limited number of
phases, each with its own unique binary digit pattern.
Normally, each phase encodes the same number of bits [12].
A symbol that represents a specific phase is produced by
each bit pattern. In BPSK, a sinusoidal signal with
predetermined amplitude is transmitted. In BPSK, bit 0 is
modulated as a sinusoidal signal with phase 0 degrees, and
bit 1 is modulated as a sinusoidal signal of the same
amplitude with phases 180 degrees.
3.3.2Channel Models
A. Free Space Model
The inverse square rule of distance, which states that the
received power at a given distance from the transmitter
decays by a factor of the square of the distance [13], the
channel model developed by this rule, is the free space
model, which is expressed in equation 3.2.
(3.2)
Where,
Pr(d)=Received power at distance d in meters
Pt= Transmitted power in dB
Gt= Gain of Transmitting Antenna
Gr= Gain of Receiving Antenna
λ= Wavelength of Transmitted signal in meter
L= System loss
d= Distance between Transmitting and Receiving
antenna in meters
B. Two Ray Model
The propagation model that takes into account both direct
and ground-reflected propagation paths between transmitter
and receiver is the two-ray ground reflection model [14].
This was developed based on geometric topics. The channel
model expressed in equation (3.3) illustrates the construction
of the model.
(3.3)
Where,
hT = Height of Transmitting antenna in meter
hR = Height of Receiving antenna in meter
GT= Gain of transmitting antenna
GR= Gain of Receiving antenna
λ= Wavelength of Transmitted signal in meters
d= Distance between Transmitting and Receiving
antenna in meters
C. Log Normal Distribution
In probability theory, a continuous probability
distribution of a random variable with normally distributed
logarithm values is referred to as a lognormal distribution.
Only positive real values are included in a lognormal
distribution [15]. It is the simplest and most practical model
for engineering scientific measurements, as well as in the
medical and economic fields. The channel model expressed
in equation (3.4) adopts this distribution.
(3.4)
Where,
PL (d0) = Path loss at distance d0
n= Path loss exponent
IV. RESULTS AND DISCUSSION
4.1 Simulation Parameters
The parameters used to stimulate the above work in
MATLAB are presented in Table 4.1.
TABLE 1 Simulation Parameters
S.N
o
Parameter
Notat
ion
Two Ray
Model
Log
Normal
Model
Free
Space
Model
1.
Wavelength
0.3m
0.3m
0.3m
2.
Distance from
Transmitter
d
Variable
Variable
Variable
3.
Gain of
Transmitting
Antenna
GT
1
-
1
4.
Gain of
Receiving
Antenna
GR
1
-
1
5.
Height of
Transmitting
Antenna
hT
2m
-
-
6.
Height of
Receiving
Antenna
hR
30m
-
-
7.
Path Loss at
Reference
Distance
PL(d0)
-
52.44
-
8.
Path Loss
Exponent
n
-
3
-
9.
Power of
Transmitting
Antenna
Pt
1W
1W
1W
10.
Reference
Distance
d0
-
1m
-1
11.
System Loss
L
-
-
1
4.2 Performance Metrics
The performance of the developed PD-NOMA system is
analyzed in terms of BER for various channel models and
encoding techniques when BPSK modulation is used. The
channel models considered are free space, two-ray, and

lognormal distributions. The encoding technique analyzed
are LDPC and Convolutional coding.
4.3 Performance Analysis
4.3.1 BER Analysis of Encoding Schemes
In this section, the result of SNR vs. BER for BPSK
modulation is illustrated in Figure 5. It is found in general
that BER decreases as SNR increases. The convolutionally
coded data is found to have a lesser BER when compared to
the uncoded data for the given SNR.
Fig. 5 BER vs. SNR Analysis of Convolutional Encoder
Figure 6 represents the change in BER with respect to
SNR of LDPC-coded data. From the result, it is found that
the BER experienced by LDPC-coded data is less than that
of convolutional-encoded data.
Fig. 6 BER vs. SNR Analysis of LDPC Encoder
4.3.2 BER Analysis of Channel Models
Path loss models: The BER analysis for three different
channel models, namely a, b, and c, is simulated in
MATLAB version 2022b using the parameters mentioned in
Table 4.1.
From Figure 7, it is found that as the distance between
transmitter and receiver increases, BER also increases. The
power received by the receiver diminishes as the distance
increases, which causes the SNR to drop. The number of
errors in the received bits, or BER, increases as the signal-to-
noise ratio declines.
Fig. 7 Distance vs. BER Analysis of BPSK Transmission
From the above channel models, the free space channel
model shows a lower BER than other channel models at all
distances. The two-ray model shows a higher BER than the
free-space model because of the destructive interference of
two paths. The log-normal model shows a higher BER than
other channel models because of the high value of the path
loss exponent. For instant a distance of 500m, free space
model experience BER value of 10-30 and log normal gives
10-20 and two ray model shows BER approximately of 10-25.
V. CONCLUSION AND FUTURE WORK
In this research, an investigation of the PD-NOMA
uplink system is executed for different channel models,
BPSK modulation, and different encoding schemes. In the
5G system, due to its very high frequency (order of
gigahertz), the power decreases drastically with distance.
Hence, the BER also increases with respect to distance. So, a
greater number of antennas are required in 5G with a
comparatively small distance between transmitter and
receiver when compared to 4G. From the simulation results,
it is concluded that LDPC coding is more preferable than
convolutional coding as it offers a higher code rate and a
lower BER. Also, it is concluded that BPSK shows a lower
probability of error in the free space channel model
compared to both the two-ray model and the log-normal
model. This work can be extended to other channel models
and modulation schemes.
REFERENCES
[1] P. Ramesh and P. T. V. Bhuvaneswari, "Non Orthogonal Multiple
Access Requirements for 5G and Its Myths," 2022 IEEE Delhi
Section Conference (DELCON), New Delhi, India, 2022, pp. 1-6, doi:
10.1109/DELCON54057.2022.9752790.
[2] Chuan, L. I. N., Chang Qing, and L. I. Xianxu. "Uplink NOMA signal
transmission with convolutional neural networks approach." Journal
of Systems Engineering and Electronics 31.5, Year: 2020, pp. no:
890-898.
[3] Balevi, Eren. "Multiuser diversity gain in uplink NOMA." In 2018
IEEE 88th Vehicular Technology Conference (VTC-Fall), pp. no: 1-5.
IEEE, Year: 2018.
[4] Rabie, Khaled M., Bamidele Adebisi, Ebtihal HG Yousif, Haris
Gacanin, and Andrea M. Tonello. "A comparison between orthogonal
and non-orthogonal multiple access in cooperative relaying power
line communication systems." IEEE access, Vol.5, Year: 2017, pp.
no: 10118-10129.

[5] Ghosh, Amitabha, Andreas Maeder, Matthew Baker, and Devaki
Chandramouli. "5G evolution: A view on 5G cellular technology
beyond 3GPP release 15." IEEE access 7 (2019): pp.no:127639-
127651.
[6] Tang, Qiang, Orhan Ermis, Cu D. Nguyen, Alexandre De Oliveira,
and Alain Hirtzig. "A systematic analysis of 5g networks with a focus
on 5g core security." IEEE Access 10 (2022): 18298-18319.
[7] Liu, Yanfang, Pablo M. Olmos, and David GM Mitchell.
"Generalized LDPC codes for ultra-reliable low latency
communication in 5G and beyond." IEEE Access 6 (2018): 72002-
72014.
[8] Rajesh, M. N., B. K. Shrisha, Nishith Rao, and H. V. Kumaraswamy.
"An analysis of BER comparison of various digital modulation
schemes used for adaptive modulation." In 2016 IEEE International
Conference on Recent Trends in Electronics, Information &
Communication Technology (RTEICT), pp. 241-245. IEEE, 2016.
[9] Zou, Ding, and Ivan B. Djordjevic. "Real-time adaptive LDPC coded
APSK for aeronautical telemetry." In 2017 13th International
Conference on Advanced Technologies, Systems and Services in
Telecommunications (TELSIKS), pp. 321-325. IEEE, 2017.
[10] Zhang, Ningbo, Jing Wang, Guixia Kang, and Yang Liu. "Uplink
nonorthogonal multiple access in 5G systems." IEEE
Communications Letters 20, no. 3 (2016): 458-461.
[11] Mortazawi Molu, Mehdi, Kanapathippillai Cumanan, Manijeh
Bashar, and Alister Graham Burr. "On convolutional lattice codes and
lattice decoding using Trellis structure." IEEE Access (2017): 1-12.
[12] Zheng, Fu-Chun, and Stephen K. Barton. "Orthogonal on-off BPSK: a
convenient signaling scheme for near-far resistant detection in
DS/CDMA." IEEE transactions on vehicular technology 47, no. 3
(1998): 969-976.
[13] Dixit, Abhishek, and Virander Kumar Jain. "Analytical determination
of thresholds of LDPC codes in free space optical channel." IEEE
Open Journal of the Communications Society 2 (2020): 35-47.
[14] Olyaee, Maryam, Mohsen Eslami, Javad Haghighat, and Walaa
Hamouda. "Performance analysis of cellular downlink with
fluctuating two-ray channels under inter-cell interference." IEEE
Transactions on Vehicular Technology 69, no. 11 (2020): 13437-
13449.
[15] Panichkitkosolkul, Wararit, and Benjamas Tulyanitikul. "Performance
of statistical methods for testing the signal-to-noise ratio of a log-
normal distribution." In 2020 IEEE 7th International Conference on
Industrial Engineering and Applications (ICIEA), pp. 656-661. IEEE,
2020.
[16] Lahbib, Noura Derria, Maha Cherif, Moez Hizem, and Ridha
Bouallegue. "BER analysis and CS-based channel estimation and
HPA nonlinearities compensation technique for massive MIMO
system." IEEE Access 10 (2022): 27899-27911.
[17] P. R and B. P. T. V, "Performance Analysis of NOMA under Power
Control Mechanism," 2021 Innovations in Power and Advanced
Computing Technologies (i-PACT), Kuala Lumpur, Malaysia, 2021,
pp. 1-5, doi: 10.1109/i-PACT52855.2021.9696636.
[18] Wu, Zhanji, Kun Lu, Chengxin Jiang, and Xuanbo Shao.
"Comprehensive study and comparison on 5G NOMA
schemes." IEEE Access 6 (2018): 18511-18519.
[19] M. Kokilavani, R. Siddharth, S. Mohamed Riyaz, P. Ramesh, S.
Ezhilarasi and P. T. V. Bhuvaneswari, "Downlink Performance
Analysis of 5G PD-NOMA System," 2022 IEEE Global Conference
on Computing, Power and Communication Technologies
(GlobConPT), New Delhi, India, 2022, pp. 1-6, doi:
10.1109/GlobConPT57482.2022.9938331.