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

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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.

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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.

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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

1=

α1P h1

P h

σ2

1=log21+

α1P h1

α2P h1

2+σ2

y2=h2Pα1x1+h2Pα2x2+w2

Interference

dominating

Desired

low power

Noise

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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 user’s 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 transmitter’s 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.

y′

2

=h2Pα1x1+h2Pα2x2+w2−h2Pα1^

x1

1,2=

α1P h2

P h

2+σ2

1,2 =log21+

α1P h2

α2P h2

2+σ2

2=

α2P h2

σ2

2=log21+

α2P h2

σ2

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Table I. Comparison between rayleigh and nakagami fading channel.

4. PERFORMANCE OF NOMA IN RAYLEIGH AND

NAKAGAMI FADING CHANNEL

From Fig. 1, we can infer that for a two user NOMA to maintain user fairness, the system has

given the distant user more power and the close user less. Secondly, we conclude that as power

increases, the BER for both users decreases. Also, at a particular value of transmit power, BER

value for user who is located distantly from the base station is more compared to user nearer.

Fig. 1. BER vs Transmitted power graph for rayleigh channel.

Fig. 2 shows the Probability Density Function for Nakagami channel for different m values.

From the literature survey, we infer that mu should be greater than 1 so that it corresponds to

lesser fading than Rayleigh fading and omega is mostly taken 1.

mu=2 , w=1 and mu=5 and w=1 might be considered as the best values.

Parameters Rayleigh fading channel Nakagami fading channel

SNR For 1000 samples, SNR=0.9 For 1000 samples, SNR=0.35

Power

Consumption

More power consumption Less power consumption

BER vs SNR

BER vs SNR values for Rayleigh

are lower as compared to

Nakagami

BER vs SNR values for

Nakagami are higher as

compared to Rayleigh

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Fig. 2. PDF curve for nakagami-m channel for different values of mu and omega.

In Fig. 3, BER vs Transmit power has been plotted for Nakagami fading channel using different values

of mu and omega as shown.

Fig. 3. BER vs Transmitted power graphs for nakagami channel (mu=5, omega=1) and (mu=2, omega=1).

5. CONCLUSION

NOMA is favored for 5G communications because it offers a strong connection, stability, and

minimal latency. Large-scale networking is facilitated by this NOMA's improved spectrum

efficiency. In this study, the performance analysis of two different fading channels—Rayleigh

and Nakagami—for wireless NOMA communication is assessed. According to our research,

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when power increases in a Rayleigh fading channel, the bit error rate drops, greater power is

distributed to far users while low power is distributed to nearby users, ensuring user fairness.

Similar findings are obtained with Nakagami fading, although the BER performance is

superior to that of Rayleigh fading. The Nakagami channel performs better than the Rayleigh

channel in terms of Bit Error Rate. A rise in BER might be reduced by the employment of

several coding techniques or differentiation strategies.

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AUTORS BIOGRAPHY

P. N. Thakre has received Bachelor’s degree in Electronics Engineering from

RTM Nagpur University in 2010. He has done M.Tech. in Electronics

Engineering from Shri Guru Gobind Singhji Institute of Engineering and

Technology, Nanded University in 2013. Presently he is pursuing Ph. D. from

Shri Ramdeobaba College of Engineering and Management, RTM Nagpur

University, under the fellowship of Visvesvaraya PhD Scheme for Electronics &

IT. His research area includes Non-Orthogonal Multiple Access (NOMA) for

5G Wireless Communication Systems and Wireless channel Estimation

Algorithms. Presently he is working as Assistant Professor in Electronics & Communication

Engineering Department, Shri Ramdeobaba College of Engineering and Management, Nagpur.

D r. S. B. Pokle has received Bachelor’s degree in Electronics and

Telecommunication Engineering from Govt. College of Engineering Pune,

Pune University in 1993. He has done M.Tech. in Electronics Engineering

and Ph. D. in Electronics from Visvesvaraya National Institute of Technology

Nagpur. His research area includes designing aspects of MIMO-OFDM

Wireless Communication Systems and Wireless channel Estimation

Algorithms. He has published 74 research papers in the reputed national and

international Journals and presented papers in the reputed national and international

conferences. This includes 06 SCI indexed and 04 Scopus indexed publications. He has guided

several projects in the area of signal processing, Digital image processing, Artificial

intelligence etc. at post-graduation level and graduate level. He has delivered many Expert

lectures in reputed Engineering institutions and also worked as judge in many national level

technical competitions. He is approved supervisor for Ph. D. under R.T.M. Nagpur University,

Nagpur. 07 candidates has been awarded Ph.D., and 01is pursuing Ph.D. under his guidance.

He is member of technical societies like ISTE and IEEE. He has total 26 years of experience

which includes 3 years industry and 23 years of teaching experience. He worked as Head of

department for 10 years. Presently he is working as Professor in Electronics & Communication

Engineering Department, Shri Ramdeobaba College of Engineering and Management, Nagpur.

Also, he is appointed as Chairman, Board of Studies Electronics Engineering by RTM Nagpur

University, Nagpur.

Ms. Radhika Deshpande is pursuing 4th year B.E. in the department of

Electronics and Communication Engineering, at Shri Ramdeobaba College of

Engineering and Management, Nagpur.

E-mail: deshpandera@rknec.edu

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Ms. Samruddhi Paraskar is pursuing 4th year B.E. in the department of

Electronics and Communication Engineering, at Shri Ramdeobaba College of

Engineering and Management, Nagpur.

E-mail: paraskarsp@rknec.edu

Mr. Shashwat Sinha is pursuing 4th year B.E. in the department of Electronics

and Communication Engineering, at Shri Ramdeobaba College of Engineering

and Management, Nagpur.

E-mail: sinhasr@rknec.edu

Mr. Yash Lalwani is pursuing 4th year B.E. in the department of Electronics

and Communication Engineering, at Shri Ramdeobaba College of Engineering

and Management, Nagpur.

E-mail: lalwaniys@rknec.edu

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