PERFORMANCE ANALYSIS OF NOMA IN
RAYLEIGH AND NAKAGAMI FADING CHANNEL
Prasheel N. Thakre
Assistant Professor, Department of Electronics and Communication Shri Ramdeobaba College of
Engineering and Management Nagpur, (India).
E-mail: thakrepn2@rknec.edu
Sanjay Pokle
Professor, Department of Electronics and Communication Shri Ramdeobaba College of Engineering
and Management Nagpur, (India).
E-mail: poklesb@rknec.edu
Radhika Deshpande
B.Tech Student, Department of Electronics and Communication Shri Ramdeobaba College of
Engineering and Management Nagpur, (India).
E-mail: deshpandera@rknec.edu
Samruddhi Paraskar
B.Tech Student, Department of Electronics and Communication Shri Ramdeobaba College of
Engineering and Management Nagpur, (India).
E-mail: paraskarsp@rknec.edu
Shashwat Sinha
B.Tech Student, Department of Electronics and Communication Shri Ramdeobaba College of
Engineering and Management Nagpur, (India).
E-mail: sinhasr@rknec.edu
Yash Lalwani
B.Tech Student, Department of Electronics and Communication Shri Ramdeobaba College of
Engineering and Management Nagpur, (India).
E-mail: lalwaniys@rknec.edu
Reception: 15/11/2022 Acceptance: 30/11/2022 Publication: 29/12/2022
Suggested citation:
Thakre, P. N., Pokle, S., Deshpande, R., Paraskar, S., Sinha, S., y Lalwani, Y. (2022). Performance analysis of
NOMA in Rayleigh and Nakagami Fading channel. 3C TIC. Cuadernos de desarrollo aplicados a las TIC, 11(2),
183-193. https://doi.org/10.17993/3ctic.2022.112.183-193
https://doi.org/10.17993/3ctic.2022.112.183-193
3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529
Ed. 41 Vol. 11 N.º 2 August - December 2022
183
ABSTRACT
Cellular connectivity is expanding rapidly in the modern world. The multiple access strategy is one of
the highly used methods for allocating the range of users in cellular network. Spectrum allocation is a
crucial element to take into account since cellular communication is becoming more and more
popular. NOMA is a channel access mechanism used in 5G mobile communication. It is also known as
non-orthogonal multiple access. NOMA is a potential strategy for enhancing spectral efficiency and
sum rate. Using the NOMA method, we evaluated the BER versus transmitted power of two users in
rayleigh and nakagami fading channels. In this NOMA setup, a single antenna is shared by two users.
Two users can accept the same frequency using 5G NOMA technology, but at different power levels.
The results of the MATLAB simulation show that the two user NOMA in the Nakagami channel
performs better than the Rayleigh channel in terms of Bit Error Rate vs. Transmitted Power.
KEYWORDS
NOMA, Rayleigh, Nakagami Fading, BER, Transmitted Power and Probability Density Function.
https://doi.org/10.17993/3ctic.2022.112.183-193
3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529
Ed. 41 Vol. 11 N.º 2 August - December 2022
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1. INTRODUCTION
One of the crucial requirements for 5th generation mobile systems is expanded data networks. The
development in this field aims to boost system throughput and capacity. This is a must-have
requirement given the rapid increase in mobile traffic that has just occurred. The network's increasing
traffic should be able to be handled by the multiple access strategy that is suggested Aditi Agrawal et
al. [2022] M. W. Baidas et al. [2018]. Early versions of multiple access strategies distributed users and
resources in an orthogonal way. But, in 5G, NOMA has been the centre of study. A mechanism called
as NOMA is used to make sure that there is equity in the deployment of forthcoming radio access
resources. The fifth generation must offer high connectivity, dependability, and low latency, therefore
this is necessary. In this type of design, NOMA surpasses OMA by roughly 30% B. Kim et al. [2019.
Superposition coding is used by the base station (BS) to broadcast in NOMA, while SIC is used to
decode the signals. Combining this SIC with an interference cancellation combining receiver will
boost capacity A. Benjebbour et al.[2013]. Non-orthogonal multiple access may be divided into 2
categories which are the domains of code and power C. Hsiung et al. [2019]. In NOMA domain, users
having poor channel conditions receive high power, while users having acceptable channel conditions
receive low power. While the less powerful user performs SIC, the more powerful user directly
decodes their own signal in the receiver. Because users may communicate in both good and bad
channel conditions, NOMA is more democratic than OMA P. N. Thakre et al. [2022]. In comparison to
other orthogonal users, the throughput of cell edge users improves owing to the intra beam SIC's
removal of interference D. K. Hendraningrat et al. [2020].
When fifth-generation systems connect large devices, improving spectrum allocation is essential.
NOMA helps to improve spectrum utilization. In this study, the simulation results of BER vs
transmitted power in two different fading channels are shown. This article has the advantage of
illustrating the BER of a system employing NOMA in two fading channels. To enhance the spectral
efficiency in 5-G communications, NOMA has been proposed. Spectrum distribution becomes
significant in a number of methods as user numbers increase A. Benjebbour et al. [2013]. In order to
improve a network's overall rate, outage probability, and ergodic capacity, multiple access approaches
are deployed. The importance of power allocation in network performance also increases along with
the number of users K. Wang et al. [2019] K. Higuchi et al. [2015] Y. Kishiyama et al. [2012]
Harada et al. [2014] Prasheel Thakre et al. [2022] Y. Saito et al. [2013]. Performance is assessed
using the users' BER calculations. Since the performance is usually acceptable, power domain NOMA
is properly assessed. Performance will be better with the distribution to NOMA users than with regular
OMA. Applications, like visible light communications, are also where NOMA is most commonly
employed. The most frequent issue with VLC is blockages; the dynamic user pairing strategy helps
with distribution of resource, which right away enhances the performance of the system Z. Xiao et al.
[2019] Y. Yin at al. [2019] . Combining user pairing with power allocation, the fractional transmit
power that results in low performance is used for resource allocation Y. Yin at al. [2019]. BER vs SNR
of two users was compared for various fading channels using NOMA approach and it was found that
Nakagami channel performs considerably better when compared to the Rayleigh and Rician channel in
BER vs SNR but transmit power isn’t considered for the different channels K. Higuchi et al. [2015].
Moreover, comparison of NOMA against OMA networks conveys that NOMA outperforms OMA and
provide better spectral efficiency and user fairness (C. Hsiung et al. [2019]. Closed-form expressions
of BER at near and far users of the considered downlink NOMA are calculated in the presence of SIC
over Nakagami fading channel A. Benjebbour et al. [2013]. The equations for average SNR,
achievable rate, and outage probability show that network users' ordered channel gains are equal to
their diversity orders M. W. Baidas et al. [2018]. NOMA has developed independently in every aspect
of wireless communication. Whenever there is a rise in users, the allocation of resources is also
considered to account for the effectiveness of the system.
https://doi.org/10.17993/3ctic.2022.112.183-193
3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529
Ed. 41 Vol. 11 N.º 2 August - December 2022
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2. NOMA SYSTEM MODEL
We consider Non-Orthogonal Multiple Access Scheme. Here, the BS superimposes the information
waveforms for its serviced users. Each user equipment employs Successive Interference Cancellation
to detect their own signals.
In a NOMA system with two users , suppose User 1 is a faraway user with a weak signal and User 2 is
a close user with a good signal.
The BS serves both users on the same frequency spectrum. h1 and h2 be the channels of far user and
near user respectively. The base station's signal can be described as follows:
where, P is the transmitted power, α is fractional coefficient of total power such that α1> α2,α1+α2=1
At the User 1, the received vector is expressed as:
(2)
or,
(3)
Now, direct decoding is performed to estimate x1
The SINR for decoding the 1st (far) user signal is given by:
(4)
The achievable rate(bps/Hz) of the User 1 is given as:
(5)
For User 2, the received vector is given as:
(6)
x=P(α1x1+α2x2)
y1=h1P(α1x1+α2x2)+w1
y1=h1Pα1x1+h2Pα2x2+w1
Desired
dominating
Interference
low power
Noise
γ
1=
α1P h1
2
α
2
P h
1
2
+
σ2
R
1=log21+
α1P h1
2
α2P h1
2+σ2
y2=h2Pα1x1+h2Pα2x2+w2
Interference
dominating
Desired
low power
Noise
https://doi.org/10.17993/3ctic.2022.112.183-193
3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529
Ed. 41 Vol. 11 N.º 2 August - December 2022
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Firstly, direct decoding for the x1 signal, then the concept of the SIC is applied as:
(7)
Now, direct decoding for the near user signal x2.
The SINR for decoding far users signal at near user is given by:
(8)
Hence the achievable rate(bps/Hz) will be:
(9)
After the far user's signal has been cancelled, the near user's SINR for decoding its own signal is:
(10)
The corresponding achievable rate(bps/Hz) is given as:
(11)
The three types of NOMA schemes that are now being employed in the broad spectrum are PD-
NOMA, waveform domain NOMA, and CD-NOMA, according to the survey and resources that are
currently accessible. The focus of most NOMA research is PD-NOMA, which necessitates a
substantial power differential between the signals allocated to various users. At the transmitters side
of a PD-NOMA system, superposition coding (SC) is used to create the signals of numerous users on
each subcarrier, which are dispersed over several users (In SC, although sharing the same time-
frequency-code resources, each user has their own power level. Each user's power level is determined
by the channel gain value; those with lower channel gain values receive greater power levels, and vice
versa. At the receiver side, the SIC approach is used to filter out extra user signals that interfere with
that band.
In terms of spectrum efficiency, NOMA's SIC method outperforms OMA. Between users 1 and 2, the
power is split. The power distribution to users has a considerable impact on the throughput of users in
the NOMA domain. The fairness of the users' Power allocation largely determines throughput.
3. FADING CHANNELS
During wireless propagation, fading refers to the degradation of the transmitted signal power caused
by a variety of factors. These variables include geographic location, time, radio frequency, and
atmospheric conditions like rainfall and lightning. There are different types of fading channels and
they are Rayleigh, Rician, Nakagami, Weibull fading channel, etc.
In this paper two fading channels Rayleigh and Nakagami are considered. Only NLOS components
between the transmitter and receiver are modelled in the Rayleigh. It is assumed that there is an
absence of Line-Of-Sight route between the transmitter and receiver. When multipath scattering occurs
with relatively high delay time spans and various groups of reflected waves, Nakagami fading takes
place. Table 1 shows a comparative study of Rayleigh and Nakagami fading channels taking few key
parameters into consideration.
γ
1,2=
α1P h2
2
α
2
P h
2
2+σ2
R
1,2 =log21+
α1P h2
2
α2P h2
2+σ2
γ
2=
α2P h2
2
σ2
R
2=log21+
α2P h2
2
σ2
https://doi.org/10.17993/3ctic.2022.112.183-193
3C TIC. Cuadernos de desarrollo aplicados a las TIC. ISSN: 2254-6529
Ed. 41 Vol. 11 N.º 2 August - December 2022
187