Impact of untrusted relay on physical layer security in non orthogonal multiple access networks

Impact of Untrusted Relay on Physical Layer Security in Non Orthogonal Multiple Access Networks Vol (0123456789) Wireless Personal Communications https //doi org/10 1007/s11277 019 06219 y 1 3 Impact[.]

Impact of Untrusted Relay on Physical Layer Security

in Non‑Orthogonal Multiple Access Networks

Dinh‑Thuan Do 1,2  · Minh‑Sang Van Nguyen 3

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Abstract

In this study, the wireless sensor network is investigated in scenario of untrusted relay required to user at far distance In particular, an untrusted relay assists long distance trans-mission in  situation of non-existence of the direct link between source and destination This paper employs non-orthogonal multiple access (NOMA) scheme to serve large num-ber of users at different allocated power levels to adapt secure criteria Specifically , to evaluate the security performance we first examine the secure outage probability (SOP) and then strictly positive secrecy capacity (SPSC) is studied To further characterize the trade-off between system security and other controlling coefficients, we then investigate the impacts of power allocation factors and power levels of the eavesdropper In order to find tractable expressions to provide additional insights in term of the performance evaluation, the asymptotic expressions regarding both SOP and SPSC are performed in high signal-to-noise ratio (SNR) region In addition, secure performance of considered NOMA network

is compared in two modes related to untrusted relay, including Amplify-and-Forward and Decode-and-Forward mode Finally, simulation results are presented to corroborate the proposed methodology

Keywords Strictly positive secrecy capacity · Non-orthogonal multiple access · Jamming signal · Secure outage probability · Physical layer security

* Dinh-Thuan Do

dodinhthuan@tdtu.edu.vn

Minh-Sang Van Nguyen

sangnguyen.fet@gmail.com

1 Wireless Communications Research Group, Ton Duc Thang University, Ho Chi Minh City,

Vietnam

2 Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam

3 Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City, Vietnam

1 Introduction

To familiarize substantially growth regarding the throughput in the fifth generation (5G) networks, it required the unprecedented evolution of new Internet-enabled smart devices, and related applications and services Considering several techniques to improve the spec-tral efficiency, key architectures such as novel multiple access (MA) techniques, cognitive radio, heterogeneous networks, millimeter wave communications, input multiple-output (MIMO) for large-scale networks can be implemented to upgrade current networks Regarding MA schemes including orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA), these considered main categories are deployed to primarily pro-vide multiple access methodology In MA, it is introduced that signals distinguishing a explicit resource block can be employed by multiple users [1 2] More specifically, code-domain NOMA and power-code-domain NOMA are classified for NOMA upon exploring the multiplexing gain from the different domains [3]

Lately, cooperative jamming and artificial noise (AN) assisted model to improve physi-cal layer security (PLS), even if the the legitimate receivers have worse channel conditions than the eavesdroppers [4 5] Goel and Negi in [6] proposed a technique by generating

AN at the transmitter to decrease the eavesdroppers reception In principle, improving the security by producing AN at the transmitter is different scheme compared with a detrimen-tal effect of noise and interference, because it destroys the channel conditions of eaves-droppers without disturbing those of the legitimate receivers The perfect and imperfect channel state information (CSI) at both the transmitter and receiver are examined in an

AN based multi-antenna assisted secure transmission scheme affected by colluding eaves-droppers [7] As a further development, the authors in [8] using both beamforming and sectoring techniques to achieve the secrecy enhancement in wireless Ad Hoc networks Specially, the authors in [8 12] presented an effective technique to confuse the eavesdrop-per by deploying AN at the legitimate transmitter As an effective method to enhance the system security, the authors in [9] have also been performed cooperative full-duplex relay

In [7], a relay networks can be able to largely improve the physical layer security through using AN-aided strategy In other trends, many secure transmission strategies are intro-duced, for example cooperative beamforming (CB) [8] and cooperative jamming (CJ) [9]

by conveying the benefits of AN assistance in cooperation with relaying transmission It can be realized the randomness and time-varying nature of the wireless channels to sup-port for network security without deploying any encryption algorithm, PLS is proposed in both information security and wireless communications [13] Zhang et al proved that the secrecy sum rate performance of NOMA better than the one of the conventional OMA in scenario of the security performance of single-input-single-output (SISO) NOMA system [14] Qin et al [15] derived new secrecy outage probability (SOP) in forms of exact and asymptotic expressions to explore physical channel-assisted security of NOMA networks

in large-scale networks wherein spatially randomly location deployment for both NOMA users and eavesdroppers Furthermore, the authors in [16] presented the exact and asymp-totic expressions for SOP in term of the secrecy performance in case of NOMA employ-ing multiple antenna and artificial noise as well To improve the secrecy performance

of a MIMO system, optimal antenna selection (OAS) and suboptimal antenna selection (SAS) schemes are proposed which based on whether the base station has the global chan-nel state information (CSI) of both the main and wiretap chanchan-nels [17], and those perfor-mance were compared with the outdated space time transmission (STT) scheme The the exact and asymptotic SOP in closed-form expressions is derived for an underlay MIMO

system system [18] Recently, stochastic geometry model is deployed in networks wherein the physical layer security was considered for applications in 5G NOMA [19] Later, sin-gle antenna and multiple-antenna stochastic geometry networks were untaken in [20] in which two different schemes were suggested to evaluate the secrecy performance In [21], their results showed that optimal designs of decoding order, transmission rates, and power allocated to each user are examined to satisfy secrecy considerations in a new design of NOMA

To the best of the authors’ knowledge, the analysis of the physical layer security in coop-erative NOMA systems is still considered in few related works In particular, the design of system to examine secrecy performance for cooperative NOMA is still not perfect in in many scenarios related to signal or channel at physical layer As a result, these observation motivate us to perform analytical expressions as detailed study in this work The secure performance of NOMA using untrusted relay circumstance in cooperative manner is exam-ined as main aim of this work We focus on a related scenarios reflected in [22–25] to answer this important question However, these papers did not consider system model with assistance of untrusted relay Furthermore, in order to examine practical situation regarding the network security, wherein AN-aided relay and related illegal channel between source and untrusted relay is in degrading performance due to imperfect AN cancellation The pri-mary contributions of the paper are shortened as follows We comprehensively investigate the design of NOMA against the untrusted relay (eavesdropper) under the secrecy outage constraint

The main contributions of this paper can be shown as:

– The new architecture related to untrusted relay-aware NOMA communication is inves-tigated and the main impacts of related channel gains and secure target rates on system performance are studied Such system model is built as combination of the unstrusted reaying model and NOMA protocol in unique system model to evaluate secure in physi-cal layer

– We derive some analytical expressions of SOP and SPSC in term of signal-to-noise ratio (SNR) In this paper, the wiretap network model is constructed according to the technical characteristics of both NOMA and untrusted relaying network In addition, new asymptotic expressions of these important secure metrics including SOP and SPSC are derived in special case of high SNR at source node

– The power allocation factor for two separated signals in NOMA is derived to evaluation optimal secure performance of such NOMA system The interesting finding exhibits power fractions which can be chosen reasonably to achieve balancing optimal perfor-mance for both SOP and SPSC

– Moreover, the accuracy of the derived results are validated via Monte-Carlo simula-tions The results show that the SOP, SPSC corresponding distinctive characterizations

of secure performance for the such proposed NOMA system with selected key param-eters are investigated to provide insights in practical design

The remainder of this paper is organized as follows: Sect. 2 presents the system model and signal analysis with secure capacity deployed in NOMA system is investigated In Sect. 3, we derive the analytical expressions of SOP and SPSC in AF mode of concerned NOMA while DF mode is considered as a benchmark as present in Sect. 4 Section 5

examines the simulation results Finally, Sect. 6 completes with conclusion remarks for the paper and reviews the important results

2 System Model

We consider an untrusted relaying NOMA network shown in Fig. 1, where a source (S) com-municates with two destination nodes (D1, D2) through an untrusted relay (R) In this paper,

it can be assumed that source node S generates the artificial noise (AN) signal, the

destina-tion node can cancel it prior to informadestina-tion decoding which is different with the untrusted relay It is further assumed that the untrusted relay node is considered in situation of non-colluding, it is refer as they independently intercept the information More importantly, we assume that design of AN precoding matrix related to the jammer is performed in such a way that the jamming signal is injected to only degrade the untrusted relay’s channel It is

assumed that a straight link between S and destination nodes are unavailable due to deep fading Consider a NOMA system including two users (D1, strong user, and D2, weak user)

can be deployed in several networks such as mobile network, sensor wireless

communica-tion or IoT systems In such system model, S is situated in the center point within cover-age range regarding serving cell, and users D1 and D2 are very near with border of such

cell where contains received signal at weak level of power We extra undertake that single antenna equipped in all nodes in the network It is familiarity with works in the literature all the channels exhibit independent Rayleigh fading In additional assumption, it is recalled that block Rayleigh fading is applied, i.e., each channel is still constant in one block and changes via different the coherence blocks Initially, the superimposed mixture is transmit-ted in the first time slot, (𝛼1s1+ 𝛼2s2)

from S to the relay, where s i (i = 1, 2) is the unit power

signal received by user D i and 𝛼 i denoted as the power allocation factor To achieve

destina-tion node’s QoS requests, it is required that 𝛼1≥ 𝛼2 and these allocated coefficients must be

constrained by equation 𝛼2

1+ 𝛼2

2= 1 In addition, noise term namely additive white

Gauss-ian noise (AWGN) happens at each receiver with zero mean and varGauss-iance N0 We call P s , P r

are transmit power at source and relay respectively We denote the fading coefficients

cor-responding link between source and relay is g s,r while link between relay and destination

users D i are g r,i We denote 𝛺1, 𝛺2 as the Rayleigh channel parameters corresponding to g s,r ,

g r,i , respectively Similar to many works in literature, it is noted that two links from relay to two destination in NOMA scheme is similar and average channel gain is the same In our proposed scheme, full channel state information (CSI) of the communication links should be available at the node where need it to obtain related calculations

Considering secure performance in this work, to make it possible for reliable and secure communication between S and destination nodes, we utilized the widely-adopted Wyners

Fig 1 System model of secure NOMA under impact of untrusted relay

wiretap code [26] This coding scheme consists of the codeword transmission rate, R0 and

confidential information rate, R i The rate increment of R e = R0− R i is the expense of confusing listener The untrusted relay will try attempt to overhear on the ongoing

trans-missions from S to two destination nodes The untrusted relay nodes are assumed to be

non-colluding which means that they intercept the information independently It worth not-ing that the jammnot-ing signal intends to eavesdropper will affect the received signal at the untrusted relay, i.e using artificial noise signal It is practical that relay can be classify between pure signal from source transfers to destination and artificial noise term ([24, 25])

It is worth noting that relay in such NOMA is assumed to detach received mixture signal as destination using SIC Detailed explanations of untrusted relay to detect its own signals is beyond the scope of our paper

The transmission in such system model is divided into two phases In the first phase, the received signal at the untrusted relay can be expressed as

For AF scheme in untrusted relaying NOMA network, two users employ two concur-rence time slots to obtain received signal via help of relay which is called as untrusted

device Then, the expected signal can be computed at D i as

where 𝜔 r,i stands for noise term concerning as additive Gaussian noise and it’s

characteri-zation of zero mean and variance N0 It is noted that the amplifying factor is G in AF mode

given by

Without loss of generality, we assume that P r = P s , then the the amplifying factor is re-expressed as

where 𝜌 = P s ∕N0= P r ∕N0 denotes the average SNR achieved at legal links

Then, the instantaneous signal-to-interference-plus-noise ratio (SINR) at D1 can be computed by

Following principle of NOMA, to detect signal need be achieved at receiver it requires

implementation of successive interference cancellation (SIC) to signal s i is obtained for

user D i As a result, the received SNR at D2 can be expressed by

(1)

y r = g s,r�

𝛼1s1+ 𝛼2s2�√

P s + 𝜔 r

(2)

y AF r,i = Gy r g r,i + 𝜔 r,i

(3)

P s ||g s,r||2

+ N0

(4)

||g s,r||2

+1

𝜌

(5)

𝛾 r,1 AF= ||g r,1||2

||g s,r||2

𝛼2 1

||g r,1||2

||g s,r||2

𝛼22+1

𝜌 ||g r,1||2

+1

𝜌 ||g s,r||2

+ 1

𝜌2

(6)

𝛾 r,2 AF = 𝜌||g s,r||2

||g r,2||2

𝛼2 2

||g r,2||2

+ ||g s,r||2

+1

𝜌

Hence, considering link between the relay and user, the AF-based transmission capacity from can be written as

In this work, it is assumed that jamming signal is imperfect canceled at the untrusted relay

to distinguish the superimposed mixture It worth noting that the received average SNR corresponding with the illegal link in situation in which untrusted relay is activated

where 𝜅 is affected factor due to imperfect jamming signal cancellation.

It worth noting that channel gain in S–R link in case that existence of jamming signal

is different with case that main channel of S–R link reserved for pure signal

communica-tion Therefore, we call 𝜌 E is SNR corresponding with jamming-aware channel and average

channel gain denoted by 𝜆0

Similarly, the channel capacity from the relay for received signal related jamming signal can be computed as

Therefore, the secrecy rate of the AF-based NOMA systems for user is formulated by

where [x]+= max {x, 0}.

As benchmark of AF-NOMA, we consider scenario of DF untrusted relay, in which the

relay initially decodes its received superimposed message from S in the first phase and then

re-encodes and onwards it to the destination in the second phase Then, the received signals

at D i can be shown as

The equivalent SNR in DF-NOMA case is expressed by

The channel capacity of a DF relaying system is related to min{C S −R , C R −Di}

, where C S −R

and C R −Di denote the capacity from S to relay and relay to D i , respectively Hence, the capacity of the main channels for D1 is

And, the capacity of the main channels for D2 is

(7)

C AF r,i =1

2log2

(

1+ 𝛾 AF r,i

)

(8)

𝛾 E,i AF = 𝛼2i 𝜌𝜅||g s,r||2

= 𝛼2i 𝜌 E ||g s,r||2

,

(9)

C E,i AF=1

2log2

(

1+ 𝛾 AF E,i

)

(10)

C AF

C AF r,i − C AF E,i

]+

,

(11)

y DF r,i = g r,i�

𝛼1s1+ 𝛼2s2�√

P s + 𝜔 r,i

(12)

𝛾 r,i DF= min

{

𝜌||g s,r||2

𝛼12 𝜌||g s,r||2

𝛼2

, 𝜌||g r,i||2

𝛼12 𝜌||g r,i||2

𝛼2

}

(13)

C DF S −D1=1

2log2

(

1+ min

{

𝜌||g s,r||2

𝛼2 1

𝜌||g s,r||2

𝛼2

, 𝜌||g r,1||2

𝛼2 1

𝜌||g r,1||2

𝛼2

})

Similarly, the capacity of the eavesdropping channel is

By conveying definition of the secrecy capacity, it can be expressed for considered

DF-based NOMA systems at D i as

3 Secure Performance Analysis in Case of AF‑Based NOMA System

3.1 SOP Performance Analysis

In this subsection, we evaluate the secrecy performance in terms of SOP metrics Moti-vated by novel results from [27], we further analyse secure performance in untrusted sce-nario To achieve tractable form of derived formula, we also provide the asymptotic SOP

analysis The SOP is initiated by the fact that R successfully intercepts the source private

signals, which reflects the secure communication In NOMA systems, with regard to the help of untrusted relay for forwarding two signals transmitted from the source to D1 and

D2, respectively Therefore, outage event occurs when C AF

1 , C AF

2 drop under their own

target rates R i respectively To evaluate the secrecy performance comprehensively of the untrusted relay NOMA network, the secure performance can be further illustrated by SOP

In particular, we can expressed SOP in such NOMA network for evaluate secrecy per-formance as

where C i

th= 22R i

Proposition 1 The approximation of secure performance in DF-NOMA can be found by

where 𝜉1= 1−𝛼

2C1

th

𝛼2𝛼2C1

th , A = C2

th 𝜌 E

𝜌 , B = C2

th−1

𝜌𝛼2

3.2 SPSC Analysis

In other metric, existence of secrecy capacity should be determined In particular, we consider SPSC as fundamental benchmark which is evaluated to further confirmation on

(14)

C DF S −D2=1

2log2

(

1+ min

{

𝜌||g s,r||2

𝛼22, 𝜌||g r,2||2

𝛼22

})

(15)

C DF

R −Ei= 1

2log2

(

1+ 𝛼2

i 𝜌 E ||g s,r||2)

(16)

C DF i =[

C DF,i S −Di − C DF

R −Ei

]+

(17)

SOP AF= Pr(

C AF1 < R1or C AF2 < R2)

=1 − Pr

(

1+ 𝛾 AF r,1

1+ 𝛾 AF E,1

> C1th,1

+ 𝛾 AF r,2

1+ 𝛾 AF E,2

> C2th

)

=1 − Pr 1,

(18)

SOP AF= 1 +

(

e−

(

𝜉1

𝜌E 𝛺1

)

− 1

)

𝛺2

𝛺1A + 𝛺2e

−

(

1

(1−A)𝛺1+

1

𝛺2

)

B

secrecy performance In term of the SPSC, secrecy capacity performance corresponding with an AF relaying NOMA system is computed as

Due to influence of jamming signal, it can be noted that 𝜌 > 𝜌 E , hence we can obtain new expression as

Then, we further obtain the following formula as

Remark 1 According to [(19) and (21)], we state that for the scenario of untrusted relay happens in main transmission, changing the channel gain factors of all transmission hops can effectively enhance the secrecy performance including SOP and SPSC metrics of such NOMA communications Moreover, the secrecy performance of the NOMA scheme will

be influenced by the varying of the predefined threshold secure rates Thus, a good tradeoff between key parameters and secrecy performance is introduced by the numerical simula-tion in following secsimula-tion In addisimula-tion, the jamming scheme make worse performance of untrusted relay and then evaluation of impact of jamming on secure performance is also careful considered in these circumstances

4 Secure Performance Analysis in Case of DF‑Based NOMA System

4.1 SOP Analysis in DF‑NOMA

Regarding on DF-based NOMA systems, the SOP can be computed by

(19)

SPSC AF= Pr(

C AF

1 > 0, C AF

2 >0,)

= Pr(

𝛾 AF r,1 > 𝛾 AF E,1 , 𝛾 AF r,2 > 𝛾 AF E,2

)

(20)

SPSC AF= Pr

(

||g s,r||2

< 1

𝜌 E 𝛼22, min

{

𝜌||g s,r||2

, 𝜌||g r,2||2}

> 𝜌 E ||g s,r||2

)

= Pr

(

||g s,r||2

< 1

𝜌 E 𝛼2

2, ||g r,2||2

> 𝜌 E ||g s,r||2

𝜌

)

(21)

SPSC AF= ∫

1

𝜌E 𝛼2

0

exp

(

−𝜌 E x

𝜌𝛺2

) 1

𝜆0exp

(

−x

𝜆0

)

dx

=1

𝜆0∫

1

𝜌E 𝛼2

0

exp

(

−

(

𝜌 E

𝜌𝛺2 + 1

𝜆0

)

x

)

dx

𝜆0𝜌 E + 𝛺2𝜌

[

1− exp

(

−

(

𝜌 E

𝜌𝛺2 + 1

𝜆0

) 1

𝜌 E 𝛼2 2

)]

(22)

SOP DF = Pr(

C DF1 < R1or C2DF < R2)

=1 − Pr(

C DF1 > R1or C DF2 > R2)

=1 − Pr 2

Similar to the analysis done in previous subsection related AF mode, we can obtain an upper bound of instantaneous SINR as 𝜌|g s,r|2

𝛼2

𝜌|g s,r|2

𝛼2 +1≈ 𝜌|g r,1|2

𝛼2

𝜌|g r,1|2

𝛼2 +1 ≈𝛼

2

𝛼2 Then, it is noted that

Pr2 can be expressed as

Proposition 2 Secure outage event in DF-NOMA can be computed in closed-form expres-sion as below

4.2 SPSC Analysis in DF‑NOMA

In similar manner, we also have 𝜌|g s,r|2

𝛼2

𝜌|g s,r|2

𝛼2 +1 ≈ 𝜌|g r,1|2

𝛼2

𝜌|g r,1|2

𝛼2 +1≈ 𝛼

2

𝛼2 Then, the SPSC for a DF case can be expressed as

We consider the situation in untrusted relay where the condition 𝜌 > 𝜌 E is satisfied There-fore, SPSC in such DF case can be obtained easily after several computation steps

(23)

Pr 2 < Pr

⎛

⎜

⎜

⎜

⎝

1+𝛼

2

𝛼2

1+ 𝛼2

1𝜌 E ��g s,r��2 > C1

th,

1+ min

�

𝜌��g s,r��2

𝛼2

2, 𝜌��g r,2��2

𝛼2 2

�

1+ 𝛼2

2𝜌 E ��g s,r��2 > C2

th

⎞

⎟

⎟

⎟

⎠

= Pr 2 < Pr

�

��g s,r��2

< 𝜉1

𝜌 E, 1+ min

�

𝜌��g s,r��2

𝛼22, 𝜌��g r,2��2

𝛼22

�

> C2th

�

1+ 𝛼2

2𝜌 E ��g s,r��2��

(24)

SOP DF= 1 − 𝛺2e

−B

𝛺2

𝜆0A + 𝛺2

{ exp

(

−

(

A

𝛺2 + 1

𝜆0

)

B (1 − A)

)

− exp

(

−

(

A

𝛺2 + 1

𝜆0

)

𝜉1

𝜌 E

)}

(25)

SPSC DF= Pr�

C DF

1 > 0, C DF

2 >0,�

≈ Pr

⎛

⎜

⎜

⎜

⎝

1+𝛼

2

𝛼2

1+ 𝛼2

1𝜌 E ��g s,r��2 >1,

1+ min�

𝜌��g s,r��2

𝛼22, 𝜌��g r,2��2

𝛼22

�

1+ 𝛼2

2𝜌 E ��g s,r��2 >1

⎞

⎟

⎟

⎟

⎠

(26)

SPSC DF = Pr

(

||g s,r||2

< 1

𝛼2

2𝜌 E , ||g r,2||2

> 𝜌 E ||g s,r||2

𝜌

) ,

= ∫

1

𝛼2

2𝜌E

0

exp

(

−𝜌 E x

𝜌𝛺2

) 1

𝜆0exp

(

− x

𝜆0

)

dx

=1

𝜆0∫

1

𝛼2

2𝜌E

0

exp

(

−

(

𝜌 E

𝜌𝛺2 + 1

𝜆0

)

x

)

dx

As a result, it can be expressed SPSC in DF-NOMA as below

5 Simulation Results

Unless otherwise stated, regarding on untrusted relay-aware NOMA, source transmission

power, P s= 1 (J/s) and path loss exponent m = 3 (which corresponds to an urban cellular

network environment ) In practice, different rates are assigned for different users, but in

this study we set the secure target rate, R i= 3 (bits/s/Hz) in the both transmission links for simple analysis The distances in each hop of relaying NOMA system are normalized to unit value For simplicity, similar noise variances at the relay and the destination nodes are

assumed, i.e., different kinds of noise variance is set as N0= 0.01 Power allocation

fac-tors for NOMA 𝛼2

1= 0.2, 𝛼2

2= 0.8 except to specific simulation results The mean values,

𝛺1, 𝛺2 of the exponential random variables in two hop of relaying NOMA, respectively, are set to 1

Figure 2 shows the SOP versus transmit SNR at source achieved by the proposed AF-NOMA scheme, where a close agreement between the simulated and analytical results can

be observed, and they match verwy well in high SNRregime For a comparison, the SOP achieved by the proposed scheme we change power allocation factors From this figure, we have the following informative observations such as high SNR such NOMA system is more secure In particular, simulation and analytical lines are matched very well only at high SNR This is consistent with Proposition 1, in the sense that the proposed NOMA scheme not only intentionally decreases the capability for eavesdropper, but also effectively cre-ates channel difference for same link S–R, thus guaranteeing a forceful secure AF-NOMA transmission Furthermore, the power allocation factor has different impacts on the secure

(27)

𝜆0𝜌 E + 𝜌𝛺2

[

1− exp

(

−

(

𝜌 E

𝜌𝛺2 + 1

𝜆0

) 1

𝛼2

2𝜌 E

)]

SNR (dB)

10-2

10-1

10 0

SOP AF: α1 = 0.55 Sim.

SOP AF: α1 = 0.65 Sim.

SOP AF: α1 = 0.75 Sim.

SOP AF: α1 = 0.85 Sim.

Fig 2 SOP of untrusted relay AF-NOMA versus transmit SNR at source as varying 𝛼1