Secrecy Outage Probability and Fairness of Packet Transmission Time in a NOMA System

In this paper, we analyze the secrecy outage probability (SOP) and the fairness of average packet transmission time for a non-orthogonal multiple access (NOMA) system which consists of a base station (BS) and two legal NOMA users in the presence of an eavesdropper (Eve). In order to extract the superimposed signal, the Eve is considered in two modes, i.e., successive interference cancellation (SIC) mode and parallel interference cancellation (PIC) mode. Accordingly, we analyze the secrecy performance of the considered system by deriving a new exact expression for SOP. Furthermore, the optimal power allocation between two legal users is determined such that the average transmission time from BS to two legitimate users are approximately equal to achieve the fairness of average packet transmission time. Monte Carlo simulations are provided to verify our analytical results.


I. INTRODUCTION
Radio frequency is one of the most important resources in wireless communication. However, it has been exhausted due to outburst demands of wireless services. This problem becomes more serious as the era of Internet of things (IoT) is coming, in which massive wireless devices want to have connections to exchange information. To overcome the problem of massive connections and shortage of spectrum, NOMA has been proposed as a promising technique in the fifth generation (5G) networks due to its superior spectral efficiency [1], [2].
Furthermore, multiple users in NOMA can share the same radio resources such as the code-domain or power-domain [3]. In code-domain NOMA, different users are assigned different codes and multiplexed over the same time-frequency resources, such as multiuser shared access (MUSA) [4], sparse code multiple access (SCMA) [5], The associate editor coordinating the review of this manuscript and approving it for publication was Xiaofei Wang . and low-density spreading (LDS) [6]. In contrast, users in power-domain NOMA are assigned different power levels on the basis of channel state information for communication, and users use SIC or PIC technique to process the received signal. This approach has been received much attention from both academia and industry recently.
Due to the broadcast nature of wireless communication, the transmitted signal may be overheard by Eves over illegal channels, this results in a lot of challenges in solving security problems for wireless networks. To measure the security risk, the concept of physical layer security (PLS) was introduced by Wyner from an information-theoretical perspective [7], i.e., the secrecy capacity is defined as the subtraction between the capacity of main channel and the one of Eve. Accordingly, many works addressing on the secrecy performance analysis for different systems has been studied [8]- [11]. However, there are a few results related to the NOMA technique [12]- [22].
More specifically, in [12], authors investigated the maximization of the secrecy sum rate (SSR) of single input VOLUME 8, 2020 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ single output (SISO) NOMA system, where each user has a predefined quality of service requirement. They derived the closed-form expression of an optimal power allocation policy to maximize the SSR. On the basic of [23], the optimal power allocation to maximization of the secrecy rate for the strong user subject to a maximum allowable SOP while satisfying non-secure transmission rate requirement to the weak user was considered. The physical layer security (PLS) of using NOMA in large-scale network where both NOMA users and Eve have been spatially randomly deployed. Also, a protected zone around the source node has been introduced to enhance the security of a random network [13]. Y. Liu et al. derived a new analytical SOP expression for characterizing the system secrecy performance in both single antenna and multi-antenna scenarios [14]. In the single antenna scenario, they outlined a protected zone around the BS to create a forbidden area where Eves are impossible to access. Taking the advantages of multi-antennas technique, artificial noise is generated at the BS for further improving the security. The authors of [24] proposed a novel beamforming design to enhance PLS of NOMA with the aid of of artificial noise. The work in [15] derived exact expressions for SOP of full-duplex relay (FRD) and half-duplex relay (HRD) NOMA systems. The results showed that the SOP of FRD outperforms the one of HRD. Subject to the Rayleigh fading, Chinh et al. have calculated closed-form expressions for the outage probability and secrecy capacity in the NOMA system [16]. Considering the imperfect self-interference cancellation, in [17], the secrecy outage probabilities of NOMA has been analyzed. The literature [19] investigated SOP of two-user SISO and multiple-input single-out (MISO) NOMA systems with different transmit antenna selection strategies and proposed an effective power allocation policy to obtain the diversity order.
Given the secrecy outage and quality of service constraints, authors proposed a NOMA scheme that is able to minimize the transmit power and then reduces the risk of eavesdropping [18]. Regarding the security issues for cooperative NOMA communication, in [25], authors proved that combination of full-duplex and artificial noise technique at relays can improve the physical layer security significantly. The authors of [26] proposed new cooperative jamming NOMA scheme to improve secrecy performance. In particular, the source actively sends jamming signals while the relay is forwarding. They concluded that the NOMA outperforms than orthogonal multiple access (OMA) in terms of secrecy rate. In [20], the secrecy performance of cooperative NOMA system for both amplify-and-forward and decodeand-forward protocols have been analyzed.
Apart from the above performance aspects, fairness of NOMA system also has received much attention. The authors of [21] proposed power allocation techniques to maximize fairness in term of data-rate under instantaneous channel state information at transmitter and average channel state information among users of a NOMA downlink. X. Chen et al. studied the proportional fairness-based scheduling scheme to enhance uplink NOMA performance [22]. However, the impact of security and fairness in NOMA system has not been investigated yet. Motivated by all of the above, in this paper, we introduce the concept of fairness of average packet transmission time, and then examine the secrecy outage probability of each user in the presence of an Eve who can operate in one of the interference cancelation modes to extract desired signal, named SIC or PIC technique. Accordingly, our major contributions are summarized as follows: • An analytical expression of the SOP for each user and whole system are derived for both SIC and PIC mode.
• The expression of packet timeout probability for each user in NOMA system is obtained.
• Fairness of average packet transmission time is introduced and the algorithm to determine power coefficient to obtain the approximation fairness is implemented. To the best of our knowledge, there is no previous work addressing on this problem.
The rest of this paper is organized as follows. In Section II, the system and channel model are introduced. In Section III, the SOP of each user and SOP system for both PIC and SIC mode are derived. Section IV analyses packet timeout probability. Section V calculates average packet transmission time from BS to two users. In Section VI, the fairness of system in term of average transmission time is considered. In Section VIII, numerical result examples are provided to verify the analytical expressions. Finally, Section IX summarizes the paper.

II. SYSTEM MODEL AND PERFORMANCE METRICS
In this section, we describe the system model and channel assumptions. Thereafter, the performance metrics are also presented to evaluate the performance of a single user as well as the whole system.

A. SYSTEM MODEL AND CHANNEL ASSUMPTIONS
Let us consider a NOMA system as shown in Fig. 1, in which the BS wants to simultaneously communicate with two users U 1 and U 2 in the presence of an Eve at the same time. The BS is able to allocate its transmit power corresponding to the quality of channel for each user. It means that higher power 79638 VOLUME 8, 2020 level is allocated to the user staying far away from the BS, i.e., U 2 , while a lower power level will be assigned to the user near by the BS, i.e., U 1 .
Given this context, symbols g 1 , g 2 and g e denote the channel coefficients of the BS→U 1 , BS→U 2 , and BS→Eve links, respectively. We also assume that users are operating in the indoor environment and there is no-line-of sight among users. Accordingly, all channels are modeled as Rayleigh fading, and the channel gain |g i | 2 (i ∈ {1, 2, e}) are random variables (RVs) distributed following exponential distribution with channel mean gain i . Thus, the probability density function (PDF) and cumulative distribution function (CDF) of X i = |g i | 2 are formulated, respectively, as follows: It is noted that the considered Eve is able to apply SIC or PIC technique to decode the superimposed signal from the BS. SIC technique was proposed from 1990 [27], wherein, the receiver will detect and then cancel other signals until it receives its own desired signal. Each user decodes its own signal by treating the signal of other users with lower power coefficients as noise [28]. In order to further improve performance of SIC, adaptive SIC and recently advanced SIC were proposed [29], [30]. In contrast to SIC, the PIC technique allows the Eve to cancel the interference in parallel [31]. In other words, the Eve with PIC technique has multiuser detection ability and is smarter than that with SIC technique [28]. For communication, the BS transmits a superimposed signal x which is a mixture signal of x 1 and x 2 to U 1 and U 2 as where P is transmit power of BS, α j (j ∈ {1, 2}) is power allocation coefficient corresponding of the user U j which satisfies the condition α 1 + α 2 = 1. Here, U 2 (far user) is allocated a high power level, i.e., α 2 = 1 − α 1 > 0.5, while U 1 (near user) is assigned a lower power level, i.e., α 1 < 0.5. Accordingly, the received signal at the U 1 , U 2 , and the Eve is formulated as where n i is additive white Gaussian noise (AWGN) with zero-mean and variance N 0 . Since the BS allocates a higher power level to the signal of U 2 , according to the principle of NOMA, the received signal at U 2 can be decoded by considering the signal of U 1 as an interference, while U 1 can decode its signal directly [24]. As a result, the signal-to-noise ratio (SNR) and signal-to-interference-plus-noise ratio (SINR) at U 1 and U 2 can be expressed, respectively, as Further, the Eve is in the zone of the BS so it also eavesdrops signals from the BS, and then it can apply advanced signal processing techniques like SIC or PIC to decode the eavesdropped signals. In the SIC mode, the Eve can decode the signal of U 1 directly, while it can decode the signal of U 2 by treating the signal of user U 1 as interference. As a consequence, the SNR and SINR have the similar forms given in (5) and (6), i.e, where γ SIC E,1 is the SNR at Eve when it tries to decode the signal of U 1 , and γ SIC E,2 is the SINR at the Eve when it manages to decode the signal of U 2 .
In the PIC mode, the Eve is assumed to be smarter than U 1 and U 2 , i.e., it is able to decode the signal of multi-user at the same time and the interference caused by other signals can be cancelled effectively. Therefore, the instantaneous SNR of the Eve when it detects the information of U 1 is the same SNR of Eve in the SIC mode, i.e, while the SNR decoded at the Eve regarding to U 2 can be expressed as It is clear to see that the SNR in the PIC mode is always greater than or equal the one of SIC mode. In the following, we analyze the impact of SIC and PIC mode of the Eve on the security issues for the considered system.

B. PERFORMANCE METRICS 1) SECRECY OUTAGE PROBABILITY (SOP)
It is worth to remind that the secrecy capacity is defined as the subtraction between the capacity of the main channel C M and the one of illegitimate channel C E [7], i.e., Accordingly, the SOP is defined as the probability that instantaneous secrecy capacity is dropped below a secrecy target rate R s , i.e., This can be expressed by words that the decreasing of O sec leads to increasing of the security level. VOLUME 8, 2020

2) PACKET TIMEOUT PROBABILITY (PTP)
When the BS sends packets with size of L to users U 1 and U 2 , it is expected to know how many percent that the packet is dropped given a specific channel condition. Here, the packet is dropped if its instantaneous transmission time T is greater than a predefined threshold, t out , i.e.,

3) FAIRNESS OF USERS
In this paper, we consider the case that both users request to have the same quality of service, thus resource should be allocated so that there is the at least different average packet transmission time among users, i.e., where E[T i ] is expected packet transmission time from the BS to the user U i .

III. SECRECY PERFORMANCE ANALYSIS
In this section, we derive the analytical expression for the SOP in both SIC and PIC mode of the Eve.

A. THE SOP WITH SIC MODE OF AN EVE
In the SIC mode, we assume that the Eve, U 1 , and U 2 have the same capability in interference cancellation.

1) THE SOP WITH SIC MODE OF AN Eve FOR A SINGLE USER
As we know that the Eve want to eavesdrop the information of both users U 1 and U 2 . According to the definition in (11), we can express the instantaneous secrecy capacities of U 1 (C SIC U 1 ) and U 2 (C SIC U 2 ), respectively, as follows: , B is the system bandwidth, and symbols γ U 1 , γ U 2 , γ SIC E,1 and γ SIC E,2 are formulated in (5), (6), (7) and (8), respectively.
On this basis, the SOP of U 1 , which is defined as the instantaneous secrecy capacity dropped below a predefined secrecy target rate is calculated as Next, we use [32, 3.5] to obtain the SOP of U 1 as where δ 1 = 2 R 1 /B − 1 and R 1 is the secrecy target rate of U 1 . In order to simplify the integral (17), we need to find the CDF and PDF of γ U 1 and γ SIC E,1 , respectively. Applying exponential distribution [33], the CDF of γ U 1 can obtain as follows: where where λ e 1 = N 0 α 1 P e . Thus, the PDF of γ SIC E,1 is obtained easily by differentiating (20) Substituting (19) with t = δ 1 + (δ 1 + 1)x and (21) into (17), the SOP of U 1 is obtained as Similarly, the SOP of U 2 can be rewritten on the basis of (16) as where δ 2 = 2 R 2 /B − 1 and R 2 is the secrecy target rate of U 2 . In order to solve (23), we need to find the CDF and PDF of γ SIC E,2 and γ U 2 , respectively.
Using exponential distribution, the CDF of γ SIC E,2 is obtained as where λ e = N 0 P e . In addition, the PDF of γ U 2 is derived as follows: where Substituting (24) and (26) into (23) yields the SOP of user U 2 as where I 1 and I 2 are defined as follows: and here, A 1 , B 1 and C 1 are defined as

2) THE SOP WITH SIC MODE OF AN Eve FOR A NOMA SYSTEM
The BS broadcasts the signals to U 1 and U 2 . Therefore, outage happens when either C SIC U 1 or C SIC U 2 falls below their own target rates. Given this definition, the SOP of system can be expressed as where After some mathematical manipulations, we arrive at SOP SIC as follows: where K , A 2 , A 3 , B 2 , G, H are defined as In this mode, the SOP of U 1 , i.e., O PIC U 1 , is the same as that in SIC mode and is expressed in (22). On the other hand, the secrecy capacity of channel from the BS to U 2 is given by (43) Accordingly, the SOP at U 2 for SIC mode of the Eve can be expressed as Similar to approach of (22), we need to find the CDF and PDF of γ PIC E,2 and γ U 2 to solve (44) as follows: where λ e 2 = N 0 α 2 P e and PDF of f γ 2 (x) is expressed in (26). Substituting (26) and (45) into (44) we can obtain the expression of the SOP for user U 2 as follows: where I 1 is defined as in (28) and I 3 is expressed as follows: here, A 4 , B 3 , and C 2 are defined, respectively, as where and F 3 (x) are defined as follows: After some mathematical manipulations, the SOP PIC can be obtained as follows: where ψ, A 5 , A 6 , J are defined as

IV. PACKET TIMEOUT PROBABILITY
In Section IV, V, and VI, we derive the packet timeout probability, and the average packet transmissions time for each user without considering the PIC and SIC mode of the Eve. This is because the Eve operates in passive mode and do not affect to the packet transmission rate. Note that the BS needs to transmit each packet to U 1 and user U 2 with bandwidth-normalized entropyB (nats/Hz) and within a defined time-out t out . Symbol T j (j ∈ {1, 2}) denotes the time that takes to transmit a packet from the BS to U j (including packets dropped). Following the third Shannon theorem [34], we can express the time T j that takes a transmit packet as where γ j are defined in (5) and (6). Given the channel conditions, the outage probability P out is defined as the probability that the packet transmission time T j exceeds the interval t out , i.e., Accordingly, the packet timeout probability P (1) out can be expressed as In order to solve (61), we need to find the CDF and PDF of T 1 . First, we use exponential distribution to calculate the CDF of T 1 as The PDF of T 1 then can be derived by differentiating (62) w.r.t t as follows: By substituting (62) into (61), the outage probability of U 1 is expressed as follows: On the other hand, let T (1) suc denotes the transmission time of a packet that is not dropped, i.e., [35] By applying Bayes'rule [35], the probability of an event T (1) suc takes places that can be expressed as Accordingly, we can express the CDF of T (1) suc as follows [35]: Differentiating both side of (67) w.r.t x, the PDF of packet timeout can be expressed as [35] f T (1) Substituting (63) into (68), the PDF f T (1) suc (t) can be rewritten as Similar to P (1) out , packet timeout probability P (2) out from the BS to user U 2 can be expressed as 79642 VOLUME 8, 2020 In order to solve (70), we need to find the CDF and PDF of T 2 . The CDF of T 2 can be formulated as Similar to the approach of the CDF of T 1 , we have . The PDF of T 2 can be derived by differentiating (72) w.r.t t as follows: Substituting (72) into (70), we can obtain the closed-form expression for the outage probability of U 2 as On the other hand, let T (2) suc denotes the transmission time that the packet is not dropped, i.e., Similar to (67) and (68), the CDF and PDF of T (2) suc can be expressed as Substituting (73) into (77), the PDF of packet transmission time without being timeout can be rewritten as where

V. AVERAGE PACKET TRANSMISSION TIME
Average transmission time is defined as the time that takes to transmit a packet from the BS to the users (including packets dropped).

A. AVERAGE PACKET TRANSMISSION TIME FROM THE BS TO U 1
Let us start with the average transmission time of packet without timeout as Substituting (63) into (79), we obtain the first moment of packet transmission time from the BS to user U 1 without timeout as follows: Finally, by applying the law of total expectation [35], the first moment of packet transmission time T 1 (including dropped packets) can be given by where P (1) out and E[T (1) suc ] are given by (64) and (80), respectively.

B. AVERAGE TRANSMISSION TIME FROM THE BS TO U 2
Similar to E[T (1) suc ], we obtain the first moment of packet transmission time from the BS to user U 2 without timeout as follows: (2) suc ] = where =B/ log e 1 α 1 and I 5 is defined as We finally obtain the first moment of packet transmission time T 2 (including dropped packets) by applying the law of total expectation as follows [35]: out )E[T (2) suc ] + t out P (2) out , where P (2) out and E[T (2) suc ] are given by (74) and (82), respectively.

VI. THE FAIRNESS OF PACKET TRANSMISSION TIME
In this section, we investigate the problem of optimal power allocation for each user to achieve the average packet transmission time E[T 1 ] from the BS to U 1 is the same one from the BS to U 2 . Thus, the problem can be formulated as follows: where α * 1 is the power allocation coefficient satisfied criteria that minimum the difference between average packet transmission time from BS to user U 1 and user U 2 . Accordingly, we propose Algorithm 1 to determine the power allocation coefficient α * 1 with desirable accuracy.

Algorithm 1 Solution to Determine the Power Allocation
where ν is desirable accuracy and ζ is increasing step.

VII. DISCUSSION AND EXTENSION
Our analysis can be extended to the more general case in which the Eve is more powerful hardware such as having multiple antenna. We assume that Eve is equipped with N antennas and each antenna branch experiences i.i.d channel fading.

A. EVE WITH MULTIPLE ANTENNAS IN SIC MODE
According to (15) and (16), the secrecy capacity for signals s 1 and s 2 at the j th branch antenna of Eve can be expressed as follows: where j ∈ {1, 2, .., N }. Therefore, the security outage happens either minimum C SIC U 1 (j) or minimum C SIC U 2 (j) falls below their own target rates. Given this definition, the SOP of the system can be written as After some mathematical manipulations, we arrived at SOP SIC N as follows: where |g e,i * | 2 = max j∈{1,2,...,N } {|g e(j) | 2 }, f |g e,i * | 2 is PDF of |g e,i * | 2 , F 1 (x) and F 2 (x) are defined in (34), (34), respectively. In order to solve the (91), we need to find CDF and PDF of |g e,i * | 2 . Let us start with the CDF of |g e,i * | 2 as follows: Pr |g e(j) .
Here, we assume that all branches of antenna have the same channel mean gain, i.e., e(1) = e(2) = · · · = e(N ) = e [36]. Thus (92) can be rewritten as Substituting (94) into (88), the SOP of NOMA system can be rewritten as follows: where χ and ν are defined as

B. EVE WITH MULTIPLE ANTENNAS IN PIC MODE
Similar to SIC mode, the secrecy capacity for signals s 1 and s 2 at the i th branch antenna of Eve in PIC mode can be expressed as follows: Therefore, the SOP of system can be expressed as After some mathematical manipulations, we obtained SOP PIC N as follows: where F 3 (x) is defined as in (52) and

VIII. NUMERICAL RESULTS
In this section, we provide numerical results for evaluating the secrecy performance and fairness of the considered system. We use Monte Carlo simulations by averaging results for independent loop. The system parameters is as follows: •  Fig. 2 illustrates the impact of the transmit SNR of the BS on the SOP for the both of SIC and PIC modes. We can see that the SOP is significantly lower for SIC mode compared to that for the PIC mode in the entire range of the considered transmit SNR of the BS. This is a fact that the Eve with the PIC mode can use the multi-user detection ability to distinguish the superimposed mixture. Furthermore, the SOP increases with the higher transmit SNR of the BS for the both of the SIC and PIC modes; this is because that the actual secrecy capacity decreases when the Eve receives a stronger signal from the BS.  U 1 in the both SIC and PIC modes are the same and constant as SNR increases. This is because the transmit SNR exists in numerator and denominator of the secrecy capacity formula of U 1 (15) (can be written as B log 2 1+α 1 γ BS |g 1 | 2 1+α 1 γ BS |g e | 2 where γ BS = P/N 0 ). Thus, as the transmit SNR increases, both numerator and denominator concurrently increase. It means that the secrecy capacity of U 1 does not change, i.e., U 1 has approximately constant SOP. Furthermore, the SOP of U 2 for both SIC and PIC mode increase when the transmit SNR increases. This is due to the same reason as discussed in Fig. 2, i.e., actual secrecy capacity decreases when the Eve receives a stronger signal from the BS. In addition, the SOP of U 2 in PIC mode is higher than that in SIC mode. This is due to the Eve with the PIC mode can use the multi-user detection ability to distinguish the superimposed mixture.  We can observe that changing the value of power coefficient has a little impact on the SOP of U 1 , U 2 , and NOMA system. This phenomenon can be explained as that U 1 , U 2 , and Eve use SIC technique in this case. When α 1 increases, the SINR of signal x 1 at U 1 and Eve concurrently increases while the SINR of signal x 2 at U 2 and Eve concurrently deteriorates. Accordingly, the secrecy capacity of signal x 1 and x 2 does not change as α 1 increases. This conclusion is also verified again by Fig. 5. Fig. 5 plot the SOP with the SIC mode of the Eve for U 1 , U 2 and NOMA system versus channel mean gain of Eve. It is obvious that the SOP with increasing of e , the SOP of both U 1 , U 2 and NOMA system becomes worse. This is due to that e increases, i.e., Eve is more near to BS so Eve is able to decode signal better, therefore the SOP of both U 1 , U 2 and NOMA system deteriorates. Another observation is that the curves with different power allocation coefficient have the same plots. The SOP of both U 1 , U 2 and NOMA system is  not affected with the adjustment of α 1 . This confirms the conclusion in Fig. 4. Fig. 6 investigates the impact of the power allocation coefficient α 1 on the SOP with the PIC mode of the Eve. Note that this power allocation coefficient must be between 0 and 0.5. We can observe that the SOP of user U 2 and NOMA system increases quickly as increasing coefficient α 1 . It is because when the power allocation coefficient α 1 increases, the SINR of U 2 decreases more quickly than the SNR at the Eve (base on (8) and (10)). This leads to a decrease of the secrecy capacity of U 2 . It means that the SOP of U 2 and NOMA system increase. Fig. 7 shows the impact of the number of antennas of the Eve on the SOP. It is clear that the SOP of system in both SIC and PIC mode increases as the number of antennas of Eve increases. This is due to that the higher number of the antennas lead to the higher diversity gain at the Eve.    8 illustrates the relationship between the average transmission time of NOMA system and the transmit SNR. We see that the average transmission time from the BS to U 1 is lower than the one from the BS to U 2 . This is due to the fact that mean channel gain of U 1 better than that one of U 2 . Fig. 9 illustrates the effects of the power allocation coefficient α 1 on the average transmission time from the BS to U 1 and U 2 . It is observed that there is an α 1 that makes the average transmission time from the BS to U 1 and U 2 is the same, i.e., α * 1 . With initialized value is 10 −3 , desirable accuracy σ = 10 −5 , increasing step ζ = 10 −3 , α * 1 is approximately 0.035. Fig. 10 plots the impact of the transmit SNR on the packet timeout probability of both U 1 and U 2 . We can see that the packet timeout probability of both users decreases when the transmit SNR of the BS increases. This is due to the fact that the transmit SNR increases to induce a higher transmission rate and thus the transmission time of packet decreases. On the other hand, the packet timeout probability reduces  very fast in the high regime of the transmit SNR of about SNR ≥ 14 dB. This is because the packet transmission time decreases as increasing the transmit SNR.

IX. CONCLUSION
In this paper, we investigated the secrecy performance and the fairness of packet transmission time for a power domain NOMA system in the presence of an Eve. In particular, an Eve is considered in two working modes: PIC and SIC. Accordingly, the secrecy performance in terms of the SOP of each user and NOMA system for the both of PIC and SIC modes of the Eve has been conducted over Rayleigh fading channel. In addition, the expression of the average packet transmission time from the BS to U 1 and U 2 as well as the packet timeout probability is derived to evaluate the fairness of system. Accordingly, the optimal power allocation coefficient of U 1 algorithm for guaranteeing the fairness of packet transmission time is proposed. We verified the correctness of our analysis by using Monte Carlo simulations. The numerical results indicate that the SOP of each user as well as a NOMA system for SIC mode of the Eve significantly outperforms that for PIC mode of the Eve and the system achieves the fairness of packet transmission time with proposed power allocation coefficient.
TAM NINH THI-THANH received the bachelor's degree in applied mathematics and informatics, in 2006, and the master's degree from Hanoi University of Science, Vietnam National University (VNU), Vietnam, in 2009. She is currently a Lecturer with the Faculty of Information Technology, National Academy of Education Management (NAEM), Vietnam. Her research interests include wireless communication, physical-layer security, reliable communication, and communications theory.