NOMA in Cooperative Underlay Cognitive Radio Networks Under Imperfect SIC

In conventional cognitive radio (CR), the users in secondary network (SN) can only access the idle spectrum when users in primary network (PN) are absent. This novel strategy provides higher spectrum efﬁciency when detecting the presence of the PN. Hence, spectrum utilization of the traditional scheme can be further improved as exploiting application of non-orthogonal multiple access (NOMA). As combination of CR and NOMA, such CR-NOMA has been proposed to improve spectrum efﬁciency to adapt to requirements in 5G communications. In this study, the relaying scheme is employed in the SN of the proposed CR-NOMA and the relay is allowed to energy harvesting (EH) from the secondary transmitter to serve signal forwarding to distant secondary users. With this regard, the complex model of EH-assisted CR-NOMA is explored in outage behavior and throughput performance as awareness on imperfect successive interference cancellation (SIC) at the receiver. As most important results, the exact closed-form of the exact outage probability is derived for each NOMA destination by assuming that the channel coefﬁcients among considered links follow Rayleigh distribution. Furthermore, performance gap between two NOMA users can be controlled by various parameters such as transmit power, energy harvesting coefﬁcients and levels of imperfect SIC. Simulation results verify our analytical results.


I. INTRODUCTION
Considering as a candidate for the fifth generation (5G) wireless communication, a novel multiple access (MA) technique is recently required to investigate, namely non-orthogonal multiple access (NOMA). Comparing with the fourth generation (4G) systems, 5G systems will not be considered as its incremental version, future wireless systems have anticipated functionality, such as cloud-based applications and internetof-things (IoT). To adapt to these challenges, several requirements are considered, such as higher data rates, low latency, massive connectivity, higher spectral and power efficiency. For example, NOMA is proposed and widely conducted due to its characteristics such as superior spectral efficiency, balanced user fairness, intense connections and low access The associate editor coordinating the review of this manuscript and approving it for publication was Agustin Leobardo Herrera-May .
latency [1]- [5]. In addition, the non-orthogonal resource allocation is explored in NOMA to implement emerging networks such as satellite hybrid relaying network, unmanned aerial vehicle [6]. The challenging models are developed by the authors in [7]- [9], in which combination between relay schemes and NOMA is introduced as novel scheme, namely cooperative NOMA. The novel idea of NOMA is to divide the power domain for realizing multiple access (MA). In NOMA, different power levels are allocated for different users with respect to distinguished signals [10], [11]. Depending on channel conditions, base station differentiates power to users. In particular, users with poor channel conditions (weak users) are allocated higher power percentage than strong users which occupy better channel conditions. To deploy NOMA, the base station superimposes the multiple information messages to serve many destinations by exploiting superposition coding (SC) scheme. By deployment the second time slot employing beamforming in half-duplex (HD) manner. The other problem of maximising the data rate is performed for the strong user to satisfy the QoS of the weak user in SWIPT NOMA system at HD mode [31]. The formulated system performance problem need be solved with respect to satisfy both SE and EE requirements and the SWIPT is further jointly implemented. Of course, working in SWIPT NOMA system model in these systems isn't well addressed since interference constraint environment in CR has not been fully considered.
The extra benefits of CR-NOMA networks can be seen as deploying cooperative protocol in such NOMA [32]- [35]. In [32], primary and secondary users are able to receive unicast and multicast information by using NOMA respectively. In this scheme, to access to the primary spectrum the cooperation in the secondary network (SN) is required in such NOMA application. In addition, to enhance the secondary user fairness a two-stage cooperative strategy was investigated in a cooperative multicast CR-NOMA scheme as [33]. The exact expressions are derived to evaluate performance of two NOMA secondary destination users in term of outage probability [34]. They considered worse case as imperfect channel state information occurred and optimal power allocation coefficients can be found as examining different distances to adapt to the outage probability fairness for two users [34].
In other scenario, imperfect SIC is studied by introducing asymptotic expressions related to derived outage probabilities in two situations including when the interference constraint be infinity and when the transmit powers at some nodes be infinity [35]. In other context of NOMA, the strong primary user (PU) communicates confidential signal with multiple uniformly distributed PUs as external eavesdroppers are randomly located and they provided tractable formula to analyze the security and the reliability performance [36]. By exploiting the practical non-linear EH scheme from the RF signals, the secondary users are be able to harvest energy to securely transmit the secondary privacy information [37]. The authors in [38] presented distributed sequential coalition formation (DSCF) paradigm to solve the user grouping problem, where the primary user's spectrum band can be shared with multiple cognitive users within a group while achieving requirement of the primary user with respect to a minimum rate. In recent work [39], CR-NOMA network is deployed channels with capable of independent but necessarily identical distributed Nakagami-m fading channels and accurate closed-form analytical expressions are studied to highlight outage probability performance of two secondary NOMA users.

B. OUR CONTRIBUTIONS
In recent research, the authors in [24] derived exact closedform expressions for CR-NOMA system over Rayleigh fading channels and they targeted their analysis to evaluate outage performance of each secondary destination. However, it need be extended to general framework for such CR-NOMA considering Nakagami-m fading channels and limited VOLUME 8, 2020 power source occurs at the relay in practice. To fill the aforementioned gap, we emphasize on the outage and throughput performance of a CR-NOMA to implement in green communication by introducing wireless power transfer technique. Although CR-NOMA networks are studied as recent research [32], [33], however it is necessary to study a general frame work of CR-NOMA over Nakagami-m fading. Unlike recent work [39], they studied a cooperative underlay decode-andforward (DF) CR-NOMA networks with several assumptions at the secondary relay without EH, perfect SIC and imposed interference temperature constraint. In this study, main goal is that system performance need be evaluated as exploiting how EH-assisted relay remains performance of destination users. Such challenge for EH-assisted relay need be studied since relay does not have individual power due to difficulty in wiring of power grid to its location. The main contributions of this study is summarized as follows: 1) Different with [25], a CR-NOMA is studied to permit secondary network containing the secondary source intends to access the 5G spectrum to serve distant users over Nakagami-m fading and Rayleigh fading as well. In particular, secondary source employs NOMA to communicate with two destinations through wireless powered relay. Such CR-NOMA is expected to improve the spectrum utilization greatly compared with the traditional OMA scheme. 2) Impacts of EH parameters on system evaluation have not been well studied in [24], [34], [35]. We first propose two policies of wireless power transfer applied in secondary network to introduce EH-assisted CR-NOMA system. In such system, by reusing harvested energy it can be further improved energy efficiency with respect to serve distant users. Moreover, we also consider impact of the imperfect SIC to signal detecting on the receivers of CR-NOMA in practical applications. 3) We derive the closed-form expressions of the outage probability for two users. Under the high complexity in computation, it is necessary to explore asymptotic outage performance of each user to provide insight for such EH-assisted CR-NOMA. In addition, we examine two scenarios of optimal outage performance as considering how time/power splitting coefficients in EH protocol affect on system performance. Although it is difficult to obtain the closed-form expressions of optimal time/power splitting coefficients, however numerical method is enabled to tackle such optimization problem. 4) Simulation results show the performance comparison in various scenarios of the proposed scheme in terms of the outage probability and throughput, which show slightly different as comparison between time switching relaying (TS) and power splitting relaying (PS) EH model. The remainder of this paper is organized as follows. Section II defines the system and channel model with a definition of two EH protocols adopted in power constrained relay in such CR-NOMA. Section III consider CR-NOMA system over Rayleigh fading and derives expressions of outage probability for two users. To evaluate the insight performance, asymptotic outage behavior and throughput are further studied. The scenario of Nakagami-m fading adopted in CR-NOMA is presented in Section IV. Numerical results are presented in Section V. Finally, the paper is concluded in Section VI.
Notation: The cumulative distribution function (CDF) of a real-valued random variable X is denoted by F X (·), f X (·) stands for probability density functions (PDF), while Pr(·) symbolizes outage probability. Ei(·) is the exponential integral function.

II. SYSTEM MODEL
In Fig.1, a downlink cooperative underlay EH-assisted CR-NOMA is considered in this study. In this model, we only concern on performance of secondary network (SN) where consists of a secondary base station (node S), a relay (R) and two distant NOMA users (U 1 , U 2 ) . 1 Such SN is able to operate together with primary network (PN) containing primary transmitter (PT) and primary destination (PR). Due to long transmission distance and poor channel condition in the secondary network, no direct exists in transmission between secondary transmitter (S) and secondary destinations (U 1 , U 2 ). Two assumptions of wireless channels are studied, i.e. Rayleigh fading and Nakagami-m fading. We assume zero-mean additive white Gaussian noise samples of variance N 0 at all terminals. On the other hand, the energylimited relay nodes adopt linear EH circuits to harvest energy from the BS and receive the information in the same time and then utilizes the harvested energy to forward signal to far NOMA users by implementing decode-and-forward (DF) based relay. Moreover the interference from the PT to the users and relay of the SN is denoted by I P . It is assumed that I P ∼ CN (0, N 0 ε) as [34]. With regard to interference exists among two networks (SN, PN) these nodes are required the 1 We limit the number of users to guarantee performance of each user and to guarantee QoS since degraded performance occurs due to interference among three or four users reported in [9].  secondary transmit node k is given P k ≤ I th |h kP | 2 , k ∈ {S, R}. The channel gains are considered as Table 1.
To implement NOMA transmission, the source S sends the √ P S α i x i + n R to the relay R according to NOMA.
In this fixed power allocation scheme, i ∈ {1, 2} α i is the power allocation coefficients satisfying α 1 + α 2 = 1 and we call n R as the additive white Gaussian noise (AWGN) between BS and R.

A. TIME SWITCHING RELAYING PROTOCOL (TS)
Without loss of generality, three time slots are divided to serve the transmission in duration T for TS mode and T is assumed to be unity as shown in Fig. 2. In the second time slot with time (1 − δ) T /2, 0 < δ < 1 after EH period of δT , a source BS sends data to relay R, and the last time slot is used to signal transmission to distant users. In this mode, the relay employs TS to perform EH. As a result, the energy accumulated at the relay during allocated time is given as [23] With period of allocated phase, the maximum available transmit power of relay which benefits from the harvested energy and the transmit power at R is given as Here, R is required to transmit signal with powerP TS R which is constrained by both P TS R and I th at PR. Therefore, the transmit power in R can be constrained bȳ In such CR-NOMA, the received signals at R can be expressed as In the first phase, the signal to interference-plus-noise ratio (SINR) after treating x 1 as interference is given by It is worth noting that imperfect SIC occurs, the SINR of detect x 2 is given as where g SR ∼ CN (0, ζ λ SR ) with ζ (0 ζ < 1) denotes as the level of residual interference caused by imperfect SIC. 2

B. POWER SPLITTING RELAY PROTOCOL (PS)
Is this section, we consider the PS protocol and hence, the energy accumulated at the relay during fractional time T /2 is formulated aŝ Therefore, the maximum available transmit power of relay achieved from the harvested energy is given as Similarly, the transmit power at R in this PS mode is determined byP By exploiting PS, it can be shown the received signal at R as In the first phase, the SINR to detect x 2 after treating x 1 as interference can be given as 2 Here, the imperfect SIC model is adopted as in [24], where the imperfect SIC error follows Gaussian distribution. VOLUME 8, 2020 Similarly, in the situation of imperfect SIC, the SINR to detect x 2 is given as . (12)

C. SIGNAL PROCESSING IN THE SECOND PHASE
In the second phase using DF relaying mode, the received signal at U i , i = 1, 2 in terms of TS and PS protocols and they can be formulated by where u ∈ {TS, PS}, then user U 1 implements SIC by detecting x 2 while considering remaining signal x 1 as a noise.
In this case, the SINR is given by With imperfect SIC, the SINR after treating x 2 as noise where g 1 ∼ CN (0, ζ λ 1 ). Similarly, the SINR at U 2 is calculated by Remark 1: The system performance will depends on how each signal is detected at destinations. As observation in (14), (15), the first user employs the SIC to decode the desired message while the second user decodes its own signal by treating the interfering signal as a noise term in (16). In these expressions, power allocation factors α 1 and α 2 are main reason for performance gap among two users. We further verify such evaluation in simulation result section.

III. SCENARIO I: RAYLEIGH FADING
In this section, we examine the system performance in term of the outage probability in order to reveal the benefits of our proposed scheme.
Firstly, the PDF, CDF of wireless channel h j with mean λ j are defined respectively by and Then, we derive outage probability as main metric to evaluate system performance as following sections.

A. OUTAGE PERFORMANCE IN CASE OF TS
To successful detect signal x 1 at destination, it requires x 1 which can be detected at both relay, before SIC and after SIC operated at destinations. In particular, the outage probability of x 1 with imperfect SIC can be formulated as where γ TS thi = 2 2R thi /(1−δ) − 1 is the threshold SNR corresponding to target rates R thi for two users; R thi , i = 1, 2 as the target rate of user U i .
Fortunately, to solve (19), the lower bound outage probability computation is performed, i.e., OP TS 1 ≈ OP TS 1,lb . Therefore, we continue to compute other lower bound of outage probability for many cases onward. Thus, OP TS 1,lb is rewritten as Next, the first and second term of (20) are denoted by 1 . They can be derived as following the propositions.
Proposition 1: The first term 1 can be expressed as below where In addition, 2 is presented in Proposition 2 as below.

Proposition 2:
The second term 2 can be computed in closed-form as below in which, A 1 and A 2 are expressed respectively by where With the help of (21) and (22), we can obtain the closedform expression for outage probability of x 1 as By definition, we next examine the outage probability of x 2 and it can be expressed as We denote 3 = Pr γ TS 2 > γ TS th2 . Similarly, it can be solved 3 in Proposition 3.
Proposition 3: The closed-form expression for outage probability of 3 is expressed as Proof: With the help of (16), we can rewrite 3 as Then, we can simplify 3 as Similarly, after some manipulations we obtain the closedform expression for 3 .
It completes the proof. Finally, the outage probability of x 2 is given by Remark 2: Although the exact expressions for the outage probability can been obtained, it is of great difficulty to achieve further insights. In this regard, a simpler bound for the outage probability should be calculated. Furthermore, the power allocation factors, channel gains and threshold SNR are main parameters which influence on outage performance of the considered system. These findings provide important guidelines to implement such system in practice.

B. CONSIDERATION ON OUTAGE PERFORMANCE IN CASE OF PS
Similarly, the outage probability of x 1 in PS mode is given by Substituting (11) and (12) into (31) we have Similarly, 1 can be calculated as Then, with the help of (14) and (15) in case of PS scheme. It can be computed 2 as below where C PS = λ SP ηϑλ RP λ SR and ℘ PS i = λ SP ηϑλ i λ SR . Next, the outage probability of x 2 in case of PS is expressed by Similarly, 3 can be obtained as Finally, the outage probability of x 2 in PS can be expressed as VOLUME 8, 2020

C. ASYMPTOTIC OUTAGE BEHAVIOR ANALYSIS
The diversity order of x i is given as [26] where OP u i is denoted as the outage probability of x i with u stands for either TS or PS. The asymptotic analysis when ρ I → ∞ depends on the achievable outage probabilities.
It is noted that e −x ≈ 1 − x and Ei (−x) = ln (x) + C in [41, 3.351.4], where C is the Euler constant. Therefore, we can write ∞ (x) = (1 + x) (x (ln (x) + C) + (1 − x)). Next, the asymptotic outage probability of x 1 and x 2 in TS and PS can be expressed in (39) and (40) shown in the top of the next page. Moreover, substituting (39) and (40) into (38), the diversity orders of U i are equal to zeros.

IV. SCENARIO II: NAKAGAMI-m FADING
In this section, we examine the system performance in terms of outage probability in order to reveal the benefits of our proposed scheme. Firstly, the PDF and CDF of wireless channel h j with (j ∈ SR, SP, RP, 1, 2) are defined respectively by and where j = λ j m j , m j represents the fading severity factor. In this paper, we also assume m j as an integer number and m j 1. The equality in (42) is achieved by applying an equivalent relationship in [42, Eq.8.352.6].

A. OUTAGE PERFORMANCE IN CASE OF TS
To successful detect signal x 1 at destination, it is necessary to x 1 which can be detected at relay in two situation, i.e., before SIC and after SIC operated at the destinations. In particular, the outage probability of x 1 with imperfect SIC can be formulated as where γ TS thi 2 2R thi 1−δ − 1 is the decoding threshold of x i corresponding to target rates R thi for the user U i , i = 1, 2.
Proposition 4: In this case, we denote the first and the second probability term in (43) as¯ 1 and¯ 2 , respectively. Then, 1 can be obtained bȳ Proof: See Appendix C.
|h SP | 2 as the ratio of two Gamma random variables, the CDF of Z with γ > 0 can be expressed as By taking the first derivative of (45), the corresponding PDF can be obtained with γ > 0 as where ϒ = (m SR − 1)! (m SP − 1)!. Note that the CDF and PDF of the random variable Z −1 can be obtained through (45) and (46) by simple changing the subscript SR to SP and vice versa.
Lemma 2: For a set of parameters n ≥ 1, β > 0, µ > 0, the Proposition 5: Moreover, the closed-form expression of¯ 2 can be written as¯ It is noted that B 1 = B 1,1 − B 1,2 , where B 1,1 and B 1,2 are expressed respectively by In this case, B 2 = B 2,1 − B 2,2 − B 2,3 + B 2,4 and corresponding computations are follows Proof: See Appendix D. Finally, the closed-form outage probability of x 1 can be expressed as By definition, we next examine the outage probability of x 2 and it can be expressed as Proposition 6: Firstly, we define¯ 3 = Pr γ TS 2 > γ TS th2 . Then, it can be solved¯ 3 in the closed-form expression as where C 1 , C 1 and C 3 are written as below.
Proof: Based on (28), it is written as First, we continue to compute C 1 , C 2 and C 3 terms in (57). Accordingly, C 1 can be calculated as where . Then, C 2 is given as In final step, C 3 can be achieved as It completes the proof. Proposition 7: It can be computed outage performance of Proof: Using results from Proposition 3 and combining with (45), it leads to the final result.
It is the end of the proof.

B. CONSIDERATION ON OUTAGE PERFORMANCE IN CASE OF PS
Similarly, the outage probability of x 1 in PS mode with γ PS thi 2 2R thi − 1 is given by The first term in (63), 1 can be formulated as In next step, 1 can be computed bȳ Similarly, the second term of (63),¯ 2 can be obtained as 2 = 1 + 2 . It is noted that, I 3 = The outage probability of x 1 in PS mode can be achieved as follow We further define outage behavior of x 2 in PS mode as Similarly, we denote¯ 3 = Pr γ PS 2 > γ PS th2 . Then, the closed-form expression of¯ 3 can be given as (70), shown in the middle of the next page.
Now, the outage probability of x 2 can obtained as

V. THROUGHPUT PERFORMANCE
It can be further evaluated other metric, i.e. the overall throughput can be achieved based on obtained outage probabilities. In delay-limited mode, at fixed target rates R th1 , R th2 the throughput can be achieved. As a result, the overall throughput can be formulated as

VI. NUMERICAL RESULTS
In this section, to verify mathematical analysis, it is necessary to simulate and illustrate for proposed EH assisted CR-NOMA scheme. In this circumstance, the Nakagami-m fading channel model is performed to model the wireless channels. Moreover, we also simulate the linear harvesting model as intuitively indications shown in each figure. We set power allocation factors α 2 = 0.8, α 1 = 0.2, the target rates R th = R th1 = R th2 = 0.5 bit per channel use (BPCU) except for specific cases, ε = 0.5, the channel gains λ SP = λ RP = 0.1, λ SR = λ 2 = 1, λ 1 = 2 and m = m SR = m SP = m RP = m 1 = m 2 . Moreover, case of m = 1 is equivalent with the Rayleigh fading channel model. In these following figures, Monte-Carlo simulations are performed to validate the analytical results. The analytical and simulated outage probabilities for TS and PS schemes in the CR-NOMA system are shown in Fig. 4,  Fig. 5. To provide an objective evaluation, the outage probabilities for a special case of high ρ I are also provided. Such error floor lines confirmed the exactness of derived expressions. Outage performance in our paper is better in results reported in [40] at high ρ I region. The performance gaps among two users for TS and PS scheme depend on power allocation factors (α 1 , α 2 ) and ρ I . It is further confirmed that CR-NOMA is better than CR-OMA in term of outage probability. Such outage behavior will be improved at higher transmit power ρ I (it depends on I th ). This can be explained as follows: at higher SNR values, two destinations (users) receive a stronger signal to detect the desired signals, and  hence they provide less possibility of outage event. The considered outage performance in CR-NOMA system using PS scheme outperforms than that of TS scheme at whole range of ρ I . In general, it can be seen slight performance gap among two schemes (TS and PS). These illustrations show that error floor matches analytical curves at very high ρ I , it confirms exactness of our derived expressions. Performance of the first user is better than that of the first user when ρ I is less than 30 and this observation changes as ρ I overcome 30. The main reason is that that the first user applies the SIC procedure to decode the desired message in (14), (15) (which intuitively provides us with higher SNR value) while the second user decodes its own signal by treating the interfering signal as a noise term in (16). Furthermore, it is evident that the analytical curves match well with the simulated results. Fig. 5 also shows similar trends of outage probability, but it indicates how imperfect SIC affects outage performance. For example, ζ = 0.1 raises the worse performance compared with case of ζ = 0.01. While impact of amount of harvested energy on outage event can be clear seen in Fig. 6. As η = 0.7, VOLUME 8, 2020  better outage event for both users in two modes of EH can be achieved. Moreover, as the system SNR increases, the outage probability decreases and then reaches a fixed level, which leads the diversity order turns to zero. Such an observation is confirmed results derived in (38).
The slight performance change of two users versus EH efficiency factors η can be observed as in Fig. 8, it can be confirmed in wide range of 0 < η < 1 . Different ϑ = δ corresponding to two main parts, i.e. EH and information processing, leads to varying outage behavior. It can be seen that equal allocation for functions of EH and information processing exhibits better outage performance. The main reason is that the proposed CR-NOMA can balances roles to achieve wireless power and signal processing. It can be predicted that existence optimal ϑ = δ to happen lowest outage performance. Interestingly, the optimal performance can be obtained, as varying ϑ = δ from 0 to 1, it can be obtained minimum points of outage events for two users in two cases ρ I = 10(dB), ρ I = 20(dB).
In term of overall throughput, level of imperfect SIC contributes to increasing throughput as increasing ρ I .   Unfortunately, the ceilings of throughput can be observed at high value of ρ I . In similar way, Fig. 9 plots highest throughput corresponding to ζ = 0.01. It can be seen that 86190 VOLUME 8, 2020 at serious situation of imperfect SIC, such overall throughput is very low, i.e. it equals to 0.2 at ζ = 0.5. While R th1 = 0.2, R th1 = 0.5, R th1 = 1 are three cases of fixed target rates correspond to throughput as Fig. 10. The reason is that such throughput depends on both fixed target rates and achieved outage probability. In this case, outage performance is fixed by simulated parameters and throughput is mainly depend on the fixed target rates.
Unlike case of CR-NOMA over Rayleigh fading, the outage performance can be improved at m = 2 as Nakagami-m fading is considered as Fig. 11. Different with the Rayleigh distribution, one property of the Nakagami distribution is that the m parameter. We study how m can describe the fading severity of the propagation channel. In this study, we investigate the effect of channel fading on the performances of the CR-NOMA system by comparing the changes in the metrics two values of m parameters. It is confirmed correctness of our derived expressions.

VII. CONCLUSION
In this study, the system performance of the cooperative EHassisted CR-NOMA is examined in term of outage probability and throughput. In particular, the closed-form expressions for outage probability are derived to evaluate performance of users in secondary network over both Rayleigh fading and Nakagami-m fading with interference constraint from primary network. The derived closed-form expressions were validated by numerical results, and the outage events of two users were compared in term of EH protocol, i.e. TS and PS. They provided slight varying performance as comparison between TS and PS. The proposed CR-NOMA showed best outage performance as reasonable selection of time switching/power splitting factors in EH protocol. Moreover, the numerical results showed that the proper selection of power allocation factors and EH parameters can guarantee the performance fairness for both users.

APPENDIX A
Recall the part of expected outage probability, 1 can be expressed as Then, 1 can be determined by With the help of (17) and (18),F h j (x) = 1 − F h j (x) and after some mathematical transformation, we can simplify 1 as It completes the proof.

APPENDIX B
From the corresponding definition, we have term 2 as in (76), as shown at the bottom of the next page.
It is the end of the proof.

APPENDIX C
First, we denote the first and second term of (73) are P 1 and P 2 respectively. Then, based on (41), (42) and [42, 3.351.3], P 1 can be expressed as