Hardware- and Interference-Limited Cognitive IoT Relaying NOMA Networks With Imperfect SIC Over Generalized Non-Homogeneous Fading Channels

Internet-of-Things (IoT) technology has received much attention due to its great potential to interconnect billions of devices in a broad range of applications. IoT networks can provide high-quality services for a large number of users and smart objects. On the other hand, massive connectivity in IoT networks brings problems associated with spectral congestion. This issue can be solved by applying cognitive radio (CR) and non-orthogonal multiple access (NOMA) techniques. In this respect, this paper studies the performance of cooperative CR-NOMA enabled IoT networks over a generalized <inline-formula> <tex-math notation="LaTeX">$\alpha - \mu $ </tex-math></inline-formula> fading channel model. Closed-form analytical expressions of the end-to-end outage probability (OP) for the secondary NOMA users are derived using the Meijer’s G-function with a consideration of the impacts of the interference temperature constraint, primary interference, residual hardware impairments and imperfect successive interference cancellation. Moreover, to acquire some useful insights on the system performance, asymptotic closed-form OP expressions are provided. Additionally, the impact of <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> fading parameters on the outage performance is examined and, as a result, it is concluded that the system performance sufficiently improves as <inline-formula> <tex-math notation="LaTeX">$\alpha $ </tex-math></inline-formula> and/or <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula> increase. Furthermore, the outage performance of the proposed system model is shown to outperform that of an identical IoT network operating on orthogonal multiple access. Finally, the provided closed-form OP expressions are validated with Monte Carlo simulations.


I. INTRODUCTION
The Internet-of-Things (IoT) paradigm has recently received much attention, with research covering technology advances in several emerging wireless applications, such as deviceto-device (D2D) [1], body area networks [2] and vehicleto-vehicle [3] communications. By taking advantage of proximity, reuse, and hop gains of D2D communications [4], The associate editor coordinating the review of this manuscript and approving it for publication was Mauro Fadda .
IoT networks can deliver a superior performance in terms of energy consumption, spectral efficiency, and low latency [5]. On the other hand, due to the massive connectivity and high traffic volume, IoT networks demand more spectrum channels by over-loading the limited radio spectrum with a large number of devices [6]. Thus, increasing spectrum efficiency is a primary task for IoT networks.
As a remedy, non-orthogonal multiple access (NOMA) has recently gained attention as a key technology to mitigate spectrum scarcity faced by the wireless networks [7].
The primary idea of NOMA is to implement successive interference cancellation (SIC) and allow multiple users to share the same radio resources [8]. The NOMA techniques are mainly categorized into two general classes, i.e., code domain (CD) and power domain (PD) NOMA schemes. The CD-NOMA uses similar codes as in code division multiple access (CDMA) systems and achieves multiplexing gain. In this method, NOMA can utilize sparse or non-orthogonal cross-correlation sequences for each user [9]. On the other hand, in the PD-NOMA, which is considered to be the most prevalent scheme, a source transmits superpositioned messages of all interested users simultaneously; however, each message is assigned with different power level depending on the intended user's QoS level or channel condition [10]. The most well-known performance metrics for generic wireless networks are considered to be the outage probability (OP) and ergodic capacity, which can also be used to analyze performance in IoT networks. Moreover, there are key IoT challenges outlined in the literature, such as mobility, reliability, scalability, performance, security and so on [11]. Improving the OP is crucial in addressing the reliability aspect in IoT networks (as well as the concept of network lifetime [12]) while ensuring capacity is key to address the scalability and performance challenge.

A. RELATED WORKS
The performance of PD-NOMA networks has been analyzed in numerous research works. For instance, uplink NOMA systems were studied in terms of outage analysis in [13], where the authors considered dynamic ordering SIC receivers, while an advanced SIC receiver was proposed in [14]. Meanwhile, other works studied the performance analysis as well, but considering the downlink NOMA systems. For example, the OP and the achievable sum-rate for downlink NOMA systems were analyzed by considering randomly deployed users in [15]. Moreover, the OP of NOMA systems was investigated in [16], where the authors considered statistical channel state information (CSI) with the Nakagami-m channel models. In addition, power-bandwidth allocation and α-fair resource allocation are jointly studied under the assumption of imperfect SIC (ImpSIC) in [17] and [18], accordingly. Moreover, the authors in [19] and [20] studied the security aspects of hybrid automatic repeat request-assisted NOMA networks, where a security-required user is paired with a quality of service (QoS)-sensitive user to establish secure transmission.

1) RELAYING STRATEGIES IN NOMA SYSTEMS
Using relaying strategies in the NOMA networks can provide coverage extension and better reliability for IoT devices with short-range communication [21]- [23]. By leveraging the spectral diversity [24], a source node can improve its transmission range and performance by cooperatively communicating over a relay node. Depending on the relay behavior, there are two widely known relaying protocols, namely, decode-and-forward (DF) and amplify-and-forward (AF). In the DF, the received signal is decoded, re-encoded, and then forwarded to the next destination, while, the AF first amplifies the received signal and then forwards it to the destination [25]. Recent works on NOMA and cooperative communications can be categorized into two directions: (1) cooperative NOMA, where NOMA users with good channel conditions act as relays to assist those with poor channel conditions; and (2) relay-aided NOMA transmission, where one or more dedicated relays deliver signals to NOMA destination users.
Cooperative NOMA: The authors in [26] showed that the half-duplex (HD) cooperative NOMA outperforms both non-cooperative NOMA and cooperative orthogonal multiple access (OMA) techniques while the OP and ergodic capacity for the similar cooperative NOMA system were studied in [21], where the authors assumed DF relays working in full-duplex (FD) and considered arbitrary and optimal power allocation (PA) methods.
Relay-aided NOMA: The author in [27] derived analytical expressions for the OP and ergodic capacity for two-hop NOMA relaying systems over Rayleigh fading channels considering the HD relay mode, while the same performance metrics with the FD relaying were studied in [28]. Moreover, the outage performance was examined in [29], where a NOMA relaying system considering Nakagami-m fading channels was studied by assuming that the source transmits superimposed signal to multiple destinations with help of AF relay working in the FD regime. The authors considered a relay-aided NOMA network in [23], where the OP is analyzed for different relay selection schemes with multiple HD-DF relays. The advantages of using a relay in NOMA networks also imposed in [30] and [31]. For example, [30] studied a relay-based NOMA system with one transmitter communicating with two receivers via multiple relays employing AF and DF relaying modes, where NOMA nodes were ordered regarding their QoS requirements. Additionally, the cooperative NOMA system was studied in [31], where the authors proposed optimal relay selection schemes considering fixed and adaptive PAs at the relay nodes.

2) COGNITIVE RADIO INSPIRED NOMA SYSTEMS
Another technology that is offered as a solution for the spectrum deficiency problem is cognitive radio (CR) [32], [33]. The main concept of the CR is to provide unlicensed users, a.k.a secondary users (SUs), access to the licensed spectrum bands by avoiding harmful interference to licensed users, a.k.a., primary users (PUs), who are entitled to communicate at those bands. There are three main CR paradigms that allow broadcasting in the primary spectrum bands, i.e., interweave [34], underlay [35] and overlay [36]. In the underlay CR, which is the most popular CR approach, SUs can simultaneously broadcast with the PUs within the same frequency band on the condition that no harmful interference caused to the PUs. Thus, to avoid interference at the primary network, the SUs need to communicate with restricted transmit power, which restrains the SUs to short-range communication. The use of a relay node may allow underlay CR network to expand VOLUME 8, 2020 their communication links. On the other hand, the underlay CR does not need to sense the entire spectrum band to acquire access to communication, which is the principal advantage of this approach. Thus, the authors in [37] proposed two novel signal-to-noise (SNR) estimation methods for underlay CR-based industrial IoT, which aims are to handle non-data aided SNR estimations for multiple SUs. Moreover, a primary user detection model for CR-IoT using a hidden Markov model was proposed in [38] to improve the delay and throughput of the network.
Lately, the synergy of CR and NOMA technologies showed the capability of obtaining better spectrum efficiency and a significant decrease in the complexity of the power allocation (PA) design [39], [40]. For example, large-scale underlay CR networks with the NOMA scheme was studied in [39] to enhance the connectivity of SUs. The results exposed that thoughtful design of the PA factors and target data rates can show better performance for NOMA users than OMA ones. The authors in [40] studied the overlay paradigm, where the secondary NOMA transmit nodes delivered signal to SUs and helped primary transmitters by relaying their signals to primary destination users.
The benefit of cooperative communications has also been applied in CR-NOMA networks, especially for underlay CR approach, where SUs use short-range communication due to restricted transmit power [32], [41]. Moreover, a relaying node improves the coverage area and throughput of CR networks [42]. In relay-aided CR-NOMA networks, the cognitive network can obtain better throughput by implementing the main two strategies: 1) the cooperation among the PUs and SUs; 2) the cooperation uniquely among the SUs [43]. The authors in [44] compared the performance of licensed and unlicensed bands with that of the conventional relay network. The results showed that adopting cooperation in CR provides outstanding performance in wireless relay networks by reducing inter-cell interference. Also, a novel cooperative multicast CR-NOMA scheme was proposed in [41], where a two-stage cooperative strategy is applied to improve fairness among SUs. Besides, [32] considered a cooperative CR-NOMA network with unicast and multicast communication sessions of the PUs and SUs, respectively, where the cooperation was proposed to improve the outage performance of both PUs and SUs.

3) RESIDUAL TRANSCEIVER HARDWARE IMPAIRMENTS
All the aforementioned studies considered perfect radio frequency (RF) elements at the transceivers. This assumption is not practical as in real-time communication all transceivers experience different types of hardware impairments (HIs) [45], e.g., in-phase/quadrature imbalance, amplifier nonlinearities, quantization error, phase noise, etc. Despite there are exist several algorithms to mitigate the effect of such HIs, some residual transceiver hardware impairments (RTHIs) caused by various kinds of noise and inaccurate calibration can not be eliminated [46]. RTHIs have been examined considering various system models [47]- [51]. For instance, the authors in [47] showed that the transmit power can not eliminate the influence of RTHIs on the system performance. Meantime, the impact of HIs on NOMA networks was highlighted in [48]. Furthermore, in the context of CR, the authors in [49] investigated the OP of a dual-hop CR system with HIs over Rayleigh fading channels, where it was noted that the AF relaying scheme is less prone to the HIs than DF one. Moreover, a dual-hop relay-aided CR network over the Nakagami-m was examined in [50], where the impact of RTHIs and interference temperature constraint (ITC) on the OP of the system is studied. In real-time communications, it is hardly possible for NOMA users to perform error-free SIC detection. Therefore, the consideration of perfect SIC with all completely canceled interference is highly idealistic [51]. Thus, there is still a lack of research to analyze the impact of RTHIs and ImpSIC on CR-NOMA networks.

B. MOTIVATION AND MAIN CONTRIBUTIONS
Wireless medium is unpredictable, thus, the statistics of the wireless channel can be presented by various distributions. For instance, the long-term signal variation is mostly characterized by the Log-normal distribution and the short-term signal variation can be presented by various other distributions such as Rician, Rayleigh, etc. All the aforementioned studies of CR-NOMA mainly considered Rayleigh and Nakagami-m fading distributions whilst neglecting other distributions, i.e., Log-normal, Negative exponential, Weibull, etc. Therefore, this paper investigates the relay-aided CR-NOMA enabled IoT network using the generalized α − µ fading distribution and consisting of a primary transmitter and receiver as well as secondary source, relay and K destination users. It is worth pointing out that the joint investigation of CR and NOMA techniques can solve the spectrum shortage and interference issues in IoT networks. Moreover, generalized α − µ distribution fully covers all the above-mentioned statistical models, namely, Rician, Rayleigh, Nakagami-m, Log-normal, Negative exponential, Weibull, etc. In addition, to consider a more practical system model, the impact of RTHIs and ImpSIC on the performance of the proposed system model will be investigated as well. Different from [51], where the authors studied cooperative NOMA systems over α − µ distribution without considering interference-limited scenario, we investigate relay-aided underlay CR-NOMA systems considering primary and secondary interference terms.
The key contributions of this work are as follows: • We derive a novel unified closed-form analytical expression for the end-to-end OP of secondary NOMA users in the underlay CR-NOMA relaying network over the generalized α −µ statistical model, which provides accurate characterizations of the influence of RTHIs and ImpSIC on the OP of NOMA users. All analytical derivations are validated through Monte Carlo simulations, which verifies the correctness of analytical results. Moreover, the CR-NOMA network is shown to deliver superior per-formance in comparison with the conventional orthogonal (time-domain) CR relaying network.
• An asymptotic behavior of the system is studied, where the secondary transmit nodes do not cause any interference to the primary network or, in other words, primary users can tolerate any interference generated by the secondary network, i.e., ITC → ∞. This system model can also be considered as a conventional NOMA network. Furthermore, closed-form expressions for another asymptotic analysis of the OP at high signal-to-noiseratio (SNR) are obtained to gain more technical insights on the system performance.
• We use a non-homogeneous behavior of α − µ distribution in the proposed model by considering practical cases, where the CR-NOMA network experiences different channel fading from one time slot to another, i.e., Rayleigh / Nakagami-m, Rayleigh / Weibull, Nakagami-m / Weibull, Nakagami-m / Rayleigh, etc.
• The derived analytical expressions are used to evaluate the impact of several fading and system parameters on the network performance, where results demonstrate that the performance can be improved sufficiently as α and/or µ are/is increased.

C. NOTATIONS AND PAPER ORGANIZATION
Notation: Throughout this paper, f (·) and F (·) indicate the probability density function (PDF) and the cumulative distribution function (CDF) of a random variable (RV) , respectively. Pr[·] denotes probability and E [·] is the expectation operator. CN (ν, σ 2 ) denotes a complex circularly-symmetric Gaussian distribution with mean ν and variance σ 2 . Also, (a) = The remainder of the paper is organized as follows. Section II defines the system and channel model of the relay-aided CR-NOMA network while Section III derives new analytical and approximated expressions for the OP metric over non-homogeneous generalized α-µ fading channels. Section IV showcases numerical and simulation results according to the Matlab simulations to verify the accuracy of analytical derivations. Finally, concluding remarks and key findings of the paper are drawn in Section V.

II. SYSTEM AND CHANNEL MODEL A. SYSTEM TOPOLOGY
A downlink dual-hop CR-NOMA based IoT network is considered as shown in Fig. 1, where a secondary network consists of a source (S), which broadcasts individual messages to IoT devices denoted by D k , k ∈ A = {1, 2, . . . , K }, via a secondary relay (R) that operates in the HD-DF mode. On the other hand, the primary network consists of a primary transmitter (P T ) and a primary receiver (P R ). All nodes are assumed to be equipped with single antennas. Throughout the paper, we also assume that the CSI estimates stay static or quasi-static and are valid until the following CSI acquisition. All channel links, i.e., g j , j ∈ B = {SP, RP, SR, PR, P1, . . . , Pk, . . . , PK , A}, are subject to a quasi-static α − µ statistical fading model. The respective distances are represented by d j∈B , and τ denotes the path-loss exponent.
The PDF of the channel coefficient g j for a fading signal with envelope (r) following the α-µ distribution can be written as [53] where α j > 0 indicates an arbitrary parameter whiler stands for the α j −root mean value given byr = α j √ E [r α j ] and µ j ≥ 1 2 is the inverse of normalized variance of r α j given by . (2) Remark 1: Note that the α-µ distribution is the generic fading statistical model that describes small-scale fading channels such as Rayleigh (α = 2, µ = 1), Weibull (α is the fading parameter with µ = 1), Nakagami−m (µ is the fading parameter with α = 2), etc. [54].
Considering the IoT-based underlay CR paradigm, it is assumed that S and R are restricted with maximum allowed transmit power in order to avoid harmful interference at P R . Thus, to prevent such interference intervention, the transmit power of secondary transmit node i is restricted as [55] whereL i is the maximum transmit power at node i while L ITC,i is the ITC at P R caused by node i. Considering the proposed CR-NOMA relaying model, S transmits a superimposed message x = K k=1 √ ρ k x k to the VOLUME 8, 2020 secondary users via R within two time periods, where ρ k denotes the PA factor of message x k . Furthermore, different level of transmit power is assigned to each user to properly define each user during the SIC detection, i.e., ρ 1 > . . . > ρ k . . . > ρ K , with K k=1 ρ k = 1. By doing so, we assume that the communication link of D K is stronger compared to D K −1 , i.e., g 1 < . . . < g k . . . < g K .

B. TRANSMISSION PROTOCOL
During the 1 st time period, R receives the following signal from S is the aggregated distortion noise from transceiver; ϕ (·) = ϕ 2 t + ϕ 2 r represents the aggregate HI level from the transmitter and receiver. In practice, this level can be measured by the error vector magnitude (EVM) [45]; n (·) ∼ CN (0, σ 2 (·) ) is the additive white Gaussian noise (AWGN) term at each receive node; L P and x P are the transmit power and the message of P T , respectively.
The proposed system model constrained by the RTHIs and interference noises. Considering this, the instantaneous signal-to-noise-distortion-interference ratio (SNDIR) of decoding x k , with k ∈ {1, . . . , K − 1}, at R is written as where l ρ˜l, with 0 < l < 1, where l = 0 and l = 1 indicate perfect and no SIC, accordingly; k = K l=k+1 ρ l , c = 1 + ϕ 2 P and σ 2 (·) denotes the AWGN noise variance at each receive node. Now, considering that x k is decoded under the condition of ImpSIC, the SNDIR of D K to decode its own message x K can be written as where˜ K = K −1 l=1 l ρ˜l. In the 2 nd time period, R broadcasts the decoded superimposed signal K k=1 b kxk to all secondary NOMA users, where b k , with K k=1 b k = 1, is the PA factor allocated tox k . Thus, the NOMA user k receives the following signal , D k applies the SIC to decode the message of D j using the following SNDIR l=1 l b˜l and j = k l=j+1 b l . Further, when K − 1 secondary NOMA users' messages are decoded, D K detects its message by where˜ K = K −1 l=1 l b˜l. In real-time communication, the use of many NOMA users may not be feasible since the processing complexity of the SIC at receivers raises in a non-linear manner by the increased number of users [26]. Additionally, when the SIC error propagation exists, this complexity becomes more crucial [56]. Thus, for the sake of practicality, further we consider two PD secondary CR-NOMA users, i.e., D 1 and D 2 . Moreover, as it was shown in [57], in interference-limited networks such as large-scale networks, the system performance is mostly influenced by interference [58]. Hence, further, we assume that the AWGN is ignored. Hence, the signal-to-distortioninterference-ratios (SDIRs) of detecting messages of D 1 and D 2 at R in the 1 st time period can be respectively written as Then, in 2 nd time period, D 1 decodes its own message with the SDIR of Similarly, D 2 first detectsx 1 with the SDIR of Then, D 2 removes the message of D 1 from (7) and detects its own signal by the following SDIR Finally, the achievable data rate at D j can be given as where the factor 1 2 implies that two time periods are required.

III. OUTAGE PERFORMANCE
In this section, the exact OP for D 1 and D 2 is derived. The OP of D j is defined as the probability that the data rate achievable by D j is below a predefined target rate R th,j , i.e., The OP of D 1 can be expressed using (10), (12) and (15) as where θ i = 2 2R th,i − 1 is the SNR associated with the rate threshold of D i . The CDF of the RV γ R,1 , considering the ITC at P R , can be written as in (18), shown at the bottom of this page, where A. EXACT OUTAGE PROBABILITY Proposition 1: The CDF of γ R,1 in (18) can be written in a closed-form as in (19).
Similarly, using (12), the CDF of the RV γ 1 can be described as . Now, following the same step as in Appendix A, the CDF of γ 1 can be written in closed-form, as in (21), shown at the bottom of the next page, where Finally, by substituting (19) and (21) into (17) and after some algebraic manipulations, the exact OP of D 1 can be derived in its closed-form as in (23), shown on the next page.
The outage metric of D 2 can be calculated using Eqs. (11), (14) and (15) as Furthermore, by following the same procedure in obtaining the OP of D 1 , the closed-form OP for D 2 can be written as in (24), shown on the next page, where V = |g 2 | 2 ,
Using (15) and (23) or (24), the average throughput of D j is written as

B. ASYMPTOTIC ANALYSIS
In this section, we investigate the asymptotic behavior of the considered system model. First of all, we study a certain asymptotic case with a high SNR regime, i.e., {L S ; L R } → ∞, to understand the impact of the ITC on the outage performance of non-homogeneous fading parameters of the system. Therefore, considering the high SNR regime, the ITC becomes the dominant factor to determine the maximum VOLUME 8, 2020 allowed transmit power at S and R; hence, a fixed L ITC will limit the use of excessive power at secondary transmitters. Thus, considering the above assumption, the maximum allowed transmit power of S and R in (3) can be rewritten as Therefore, considering these new reformulated power constraints, we can write the high SNR asymptotic outage performance of D 1 and D 2 as in (27) and (28), respectively. We refer interested readers to Appendix B for the derivation steps.
72948 VOLUME 8, 2020 Moreover, it is reasonable to consider another asymptotic behavior of the system when the secondary transmit nodes do not cause any interference to the PN or, in other words, a PU can tolerate any interference generated by the SN, i.e., L ITC → ∞ or no ITC imposed. Thus, the power restrictions in (3) are simplified to L i ≤L i , i ∈ {S, R}, i.e., there are no power limits at the secondary transmitter i. Then, the derivations of corresponding outage metrics for D 1 and D 2 are shown in Appendix C.

IV. RESULTS DISCUSSION
This section presents numerical results to validate the analytical expressions derived above and provides thorough scrutiny of the impact of different system and fading parameters on the outage performance of the proposed system. The simulation parameters are as follows. The fixed PA factors are considered, if it is not stated otherwise, as ρ 1 = b 1 = 0.8 and ρ 2 = b 2 = 0.2. Moreover, for simplicity, we assume the same transmit power levels at the secondary transmit nodes, i.e., L = L S = L R , and the SNR threshold as θ 1 = θ 2 = θ = 3 dB. The rest system parameters are shown in Table 1. Fig. 2 compares the analytical SIR-based OP derived in Section III with the simulation results obtained using SINR in (5), and SNR (using the same equation, but considering interference-free regime). As we can see, in all cases, the outage performance of D 2 is superior compared to D 1 which can be explained by the impact of selected system parameters defined in Table 1. Regarding the SIR-versus SNR-based OP comparison, it shows that the OP of NOMA users degrades as the primary interference power level increases. For example, when the transmit SNR = 10 dB, D 1 obtains the OP of 0.01632 for the SNR-based system, while, for the SIR-based one, D 1 achieves 0.02064 and 0.1449 when L P = −10 dB and L P = 0, respectively. Then, when we compare SIRversus SINR-based system, it is noticed that there is a small OP degradation for the SIR-based system at low interference power level, i.e., L P = −10 dB. However, when L P = 0 dB, the SIR-and SINR-based outage performance show the same results for all transmit SNR regions, which justifies the assumption made in Section III. Finally, it is also important to highlight that the analytical results perfectly coincide with the Monte Carlo simulations in this and forthcoming figures, which validates the accuracy of analytical derivations. Fig. 3 demonstrates the OP comparison of the analytical CR-NOMA based IoT network with simulated CR-TDMA one. The proposed relay-aided CR-NOMA system requires two-time slots to convey messages to two NOMA-based IoT devices, whilst the TDMA-based model needs four-time slots to provide communication to the same users. Hence, for the purpose of a fair comparison of two systems, we consider the following system parameters for the TDMA system: 1) the data requirement is set as bi-fold of that for the NOMA model; 2) the transmit power at S and R is equal to 0.5 L. As Fig. 3 shows, both NOMA IoT devices of CR-NOMA outperform the TDMA ones in terms of the OP. Noticeably, the outage saturation for NOMA-based IoT devices begins at lower transmit SNR levels compared to those for the TDMA users. This happens due to (3), where transmit power of 0.5L rises the values of the ITC at P R , as a result, the level of transmit SNR where the OP curves start to saturate increases.    4 illustrates OP results for the Weibull (µ = 1) distribution and, its special case, Negative Exponential distribution by setting α = 1 and fixed µ = 1. Similar to other OP results, D 2 obtains better OP than D 1 . It is also noticed that the increase of the α value helps to obtain better OP. For example, when α = {3, 1.5, 1}, D 2 achieves the OP of 10 −1 at 15 dB, 22.5 dB and 32 dB, respectively. The worse OP result is shown by the Weibull curve with α = 0.5, where the OP starts to saturate after the OP of 0.5.
In Fig. 5, we evaluate the effect of the ITC on the OP versus the transmit SNR over Nakagami-m fading channels. We consider two scenarios: L ITC = 10 dB and L ITC = 20 dB. The plot shows that the higher value of the ITC, i.e., L ITC = 20 dB, allows achieving better OP performance for the CR-NOMA-based IoT devices, while the lower value of the ITC degrades the OP by starting its saturation at lower transmit SNR levels. Moreover, these saturation curves coincide with the high SNR approximations of the OP performance given by (27) and (28). Besides, we plot asymptotic case with no ITC, i.e., L ITC → ∞, and this mode shows the best outage performance with no OP curve saturation.
In Fig. 6, we illustrate the average throughput obtained from (25). Similarly to the outage performance, primary interference degrades the performance of an average throughput. The larger value of L P results in the lower achieved average throughput. Regarding the performance of two CR-NOMAbased IoT devices, it is noticed that D 2 shows a better average  throughput performance than D 1 . For example, in the case of L P = 0 dB and the transmit SNR of 30 dB, D 2 gains the highest average throughput of 4.8 bps/Hz and 5.7 bps/Hz when L ITC = 10 dB and L ITC → ∞, respectively. However, for D 1 , the saturation of the average throughput curves starts at moderate transmit SNR levels even for L ITC → ∞ mode. This can be explained by the next. Regarding (10) and (12), 72950 VOLUME 8, 2020  the SIR of D 1 has the message of D 2 as interference in its denominator. Thus, when the transmit power is increased, primary interference becomes to be neglectable and the SIR is independent on the transmit power and dependant on α 1 α 2 . This fact results in the average throughput curve saturation. Fig. 7 demonstrates simulated results on the PA factors based on the NOMA users' outage fairness (OF) over Rayleigh (α = 2; µ = 1) and Nakagami-m (α = 2; µ = 2) considering system parameters of the transmit SNR = 20 dB, L ITC = 10 dB and L P = 10 dB. It is observed that, for all d 1 values, the OP of D 1 is in an outage when θ > ρ 1 ρ 2 . However, when θ < ρ 1 ρ 2 , the OP of D 1 improves by increasing α 1 values, while that of D 2 decreases. All the OF-based PA factors derived from this figure are demonstrated in Table 2.
In Fig. 8, we present the results on the OP vs. the predefined SNR threshold using OF-based PA factors shown in Table 2 with the transmit SNR of 20 dB, L ITC = 10 dB and L P = 10 dB. The figure shows that the outage of D 1 , for all d 1 values, improves when the OF-based PA factors are considered. Especially, when the predefined SNR threshold is equal to 3 dB, the performance of both devices are the same as this SNR threshold value was considered for the PA optimization in Fig. 7. Therefore, it can be stated that OF-based PA factors can provide OF for both IoT devices. Fig. 9 investigates the impact of the fading parameters α and µ on the OP of D 1 . Here, we define the set of parameters that fully cover all possible system setup variations to evaluate the impact of α and µ. Hence, the channel links in each domain defined in Remark 2 and shown in Fig. 1 are defined as [(α, µ x , µ y , µ z ), (α 2 , µ q , µ u , µ w )]. The first two OP curves shown in the legend of the figure correspond to the  channel links following the Nakagami-m distribution (µ = 1 (i.e., Rayleigh) and µ = 2) with identical µ parameters per the system setup. It is perceived that the smaller value of µ degrades the OP of the system as µ depicts the number of multi-path components of the channel. Next, we consider the system setup with [(2, 2, 1, 1), (2, 1, 1, 1)] to support our aforementioned statement. As a result, we can see that the OP of D 1 improves respectively. Further, various system setups regarding the Weibull statistical model are considered. For example, curves with different α values (green lines) show that bigger α results in better outage performance. This can be explained by the fact that the fading parameter is related to the power exponent of the channel. To justify this statement, we set α = 3 (blue lines) and both system models outperform the first green line in means of the outage performance. Finally, the OP results related to the system is demonstrated considering the setup when the channel links in each domain follow two different fading models, i.e., Nakagami-m (with µ = 2) and Weibull (with α = 3). Another useful insight is that µ has higher impact on the outage than that of α. It can be found by comparing this line with the second OP curve (dashed red), that the latter obtains better outage with bigger µ and smaller α parameters. Fig. 10 plots the OP of D 2 considering three system conditions: ideal condition (ψ = 0; = 0), the ImpSIC (ψ = 0; = 0.1) and the ImpSIC and RTHIs (ψ = 0.1; = 0.1). We can observe that for the ideal condition the system obtains the best outage performance. However, the system with the ImpSIC shows slightly worse performance in terms of the OP. This is due to the fact that imperfect detection of the message x 1 at D 2 decreases the level of SDIR for detecting its own message x 2 , which, subsequently, results in lower obtained outage performance. Then, when the ImpSIC and RTHIs are considered, it is noticed that the OP further degrades since HIs add additional interference level on the system. Finally, it is worth to mention that the RTHIs and ImpSIC have more impact on the OP at high SNR levels compared to lower ones.

V. CONCLUSION
In this paper, we analyzed the performance of the downlink DF-based underlay CR-NOMA relaying network over different α-µ fading channels such as Weibull, Nakagami-m and Rayleigh. We assumed three realistic factors namely ITC, ImpSIC and RTHIs to consider a practical network. Accurate closed-form analytical expressions for the end-to-end OP of two end-users were derived taking into account the primary interference. Moreover, we examined the impact of the fading parameters α and µ on the outage performance and found that the system performance can be sufficiently enhanced as α and/or µ are increased. Additionally, we derived several useful insights on the system performance by obtaining approximated closed-form OP expressions. Finally, the provided analytical closed-form expressions were verified by Monte Carlo simulations. In the future, this system model can be extended by adding imperfect CSI for more practicality purpose. Moreover, some optimization problems, such as PA and the best relay selection among randomly located relays, will also be considered in the future work.

APPENDIXES APPENDIX A PROOF OF PROPOSITION 1
The term A in (18) can be rewritten as The PDFs X , Y and Z abide by the α − µ statistical model as shown in (1). Now, we modify these PDFs by applying the "change of variable" method [54]. Hence, the respective PDF can be rewritten as where ξ = {X , Y , Z } and λ ξ = µ ξ /r α ξ 2 . Then, using (A.2), the term A can be further calculated as where y = γ inc µ y ,λ y αy 2 (µ y ) . Now, by using the series representation of the lower incomplete Gamma function given by [59] we can re-express the term A as To the best of our knowledge, the OP expression given by (A.5) cannot be solved in closed form without imposing certain assumptions. Remark 2: It is important to note that the assumption of the same values of α does not limit our contribution, since this assumption of equal values is considered only for channel coefficients within one domain, while α parameter of the second domain may vary differently 1 i.e., α = α x = α y = α z and α 2 = α q = α v = α u = α w , where given indices correspond to the RVs. Simultaneously, parameters µ and λ can alter independently, which allow us to study not only the performance of the considered system with the same channel distributions, but also hybrid channels, i.e., Rayleigh / Weibull, Rayleigh / Nakagami-m, Weibull / Nakagami-m, Nakagami-m / Rayleigh, etc., for various values of m.
Keeping the assumption made in Remark 2 in mind, the term A 1 in (A.5) can be re-calculated as Now, inserting (A.6) into (A.5), we can write the term A in a closed-form as The second part of the CDF of γ R,1 , term B in (18), can be rewritten as follows  (18), the CDF of γ R,1 can be written in its closed-form as in (19), where θ 1 < ρ 1 ρ 2 +ϕ 2 SR , otherwise, F γ R,1 (θ 1 ) ∼ 1.

APPENDIX B DERIVATION OF HIGH SNR APPROXIMATED OUTAGE PROBABILITY
Considering the asymptotic ITC in (26), the CDF of γ R,1 for a high SNR can be written as (µ x + µ y ) λ µ x y µ x (µ x ) (µ y ) . (B.2) Then, after inserting (B.2) into (B.1) and some mathematical manipulations, the CDF of γ R,1 for a high SNR can be written in the closed-form as .
(B.3) VOLUME 8, 2020 Further, the CDFs of γ R,2 , γ 1 and γ 2 for the high SNR approximation can be calculated following the same steps as in (B.1)-(B.3). Finally, the high SNR approximated OP of D 1 and D 2 can be respectively found by using (17) and (22) and written as in (27) and (28), accordingly.

APPENDIX C DERIVATION OF OUTAGE PROBABILITY FOR NO ITC IMPOSED MODEL
Considering no transmit power restriction at secondary transmit nodes, i.e., L ITC → ∞, we can rewrite (19) as follows F ∞ γ R,1 (θ 1 ) = Pr dz. (C.1) Furthermore, applying the series representation of the lower incomplete Gamma function as in (A.4) and after some mathematical manipulations, (C.1) can be written in a closed-form as Finally, the OP of D 1 for the proposed asymptotic model can be derived after inserting (C.2) and (C.3) into (17). The OP for D 2 can be found similarly.