Security-reliability analysis in CR-NOMA IoT network under I/Q imbalance

Received 6 September 2023, accepted 4 October 2023, date of publication 26 October 2023, date of current version 1 November 2023. Digital Object Identifier 10.1109/ACCESS.2023.3327789 Security-Reliability Analysis in CR-NOMA IoT Network Under I/Q Imbalance HUNG NGUYEN 1, TAN N. NGUYEN 2, (Member, IEEE), BUI VU MINH 3, THU-HA THI PHAM4, ANH-TU LE 5, (Member, IEEE), AND MIROSLAV VOZNAK 5, (Senior Member, IEEE) 1HUTECH Institute of Engineering, HUTECH University, Ho Chi Minh City 70000, Vietnam 2Communication and Signal Processing Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 70000, Vietnam 3Faculty of Engineering and Technology, Nguyen Tat Thanh University, Ho Chi Minh City 754000, Vietnam 4Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City 70000, Vietnam 5Faculty of Electrical Engineering and Computer Science, VSB—Technical University of Ostrava, 70800 Ostrava, Czech Republic Corresponding author: Tan N. Nguyen ([email protected]) The research leading to the published results was supported by the European Union within the REFRESH project - Research Excellence For Region Sustainability and High-tech Industries ID No. CZ.10.03.01/00/22_003/0000048 of the European Just Transition Fund and by the Ministry of Education, Youth and Sports of the Czech Republic (MEYS CZ) through the project SGS ID No. SP 7/2023 conducted by VSB - Technical University of Ostrava. ABSTRACT This paper presents a controllable analysis framework for evaluating the reliability and security of underlay cognitive radio networks (CRs) relying on non-orthogonal multiple access (NOMA). In such systems, a secondary base station (BS) transmits confidential information to multiple secondary users uniformly distributed in the presence of a nearby located external eavesdropper. Moreover, transmit power constraints are introduced to limit the interference to the primary imposed by cognitive base stations. As an effective approach of multiple input single output (MISO) systems, the transmit antenna selection (TAS) is selected in the BS to improve the secrecy performance of the primary networks. Furthermore, we first consider the impact of quadrature-phase imbalance (IQI) to characterize the secure performance of the considered network in practice. Then, the degraded performance is evaluated in terms of outage probability (OP), intercept probability (IP), and effective secrecy throughput (EST) of two NOMA users. The optimal EST can be achieved through simulations while the results of OP and IP provide guidelines in the design of IQI-aware CR-NOMA systems. Finally, the trade-off between OP and IP with transmit signal-to-noise ratio (SNR) at the BS is investigated for reflecting the security characteristic. Finally, the trade-off between OP and IP with transmit signal-to-noise ratio (SNR) at the BS is studied for displaying the security characteristic. Numerical results show that increasing the number of transmit antennas at the BS and other main parameters improves performance. Moreover, when the system parameters are reasonably set, the secondary NOMA user in CR-NOMA can be reached secure requirements regardless of the controlled IQI. INDEX TERMS Non-orthogonal multiple access, cognitive radio, physical layer security, quadrature-phase imbalance. I. INTRODUCTION To tackle critical problems in fifth-generation (5G) wireless networks, security using encryption keys and complex encoding/decoding algorithms need to be addressed. Such cryptographic techniques are implemented on upper layers. However, significant challenges to tackle security in such The associate editor coordinating the review of this manuscript and approving it for publication was Chen Chen . networks arise when deploying traditional cryptographic paradigms in several future wireless networks. Different traditional methods, physical layer security (PLS) without complicated encoding/decoding algorithms or keys has been introduced as an alternative to solve security and provide secure data transmission [1],[2],[3],[4]. Recently, nonorthogonal multiple access (NOMA) is researched for future mobile communication networks to overcome the challenging requirements including high data speed, low VOLUME 11, 2023 2023 The Authors. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. For more information, see https://creativecommons.org/licenses/by-nc-nd/4.0/ 119045 H. Nguyen et al.: Security-Reliability Analysis in CR-NOMA IoT Network Under I/Q Imbalance latency, massive connectivity, and spectral efficiency [5],[6], [7],[8]. There are increasing research interests in the scenario of NOMA enabling PLS (e.g., [9],[10],[11],[12],[13],[14]). For example, research work in [9] and [10] investigated the PLS mechanism in NOMA networks with perfect knowledge of eavesdroppers’ channel state information (CSI). In [9], an anonymous user was treated as a potential eavesdropper, and an efficient secrecy rate maximization technique for downlink NOMA in a multiple-input multiple-output (MIMO) cellular network was presented. In another study, the PLS of a relay selection-based cooperative NOMA system was proposed with a fixed power allocation scheme for providing the secrecy performance of all the users subject to a predefined quality of service (QoS) requirement [10]. In addition, the results in [9] and [10] indicated that NOMA exhibits a significant secrecy performance improvement compared to traditional orthogonal multiple access (OMA). Moreover, a practical scenario without the instantaneous knowledge of the eavesdropper’s CSI at the transmitter was studied in [11],[12],[13], and [14]. In particular, to improve the secrecy performance the authors in [11] investigated some transmit antenna selection (TAS) schemes to benefit NOMA systems. The authors in [11] derived the exact closed-form formula of secrecy outage probability (SOP) and asymptotic SOP was further provided. Another work in [12] presented the scenario of randomly deployed users and eavesdroppers in large-scale networks with the exact and asymptotic expressions for the SOP. In other NOMA systems, a scheme was proposed to maximize the minimum confidential information rate under constraints of the SOP and transmit power [13]. Furthermore, to protect the confidential information of legitimate users, the authors in [14] studied an artificial noise (AN)-based beamforming scheme and examined a worse case of imperfect successive interference cancellation (SIC) which is applied to MISONOMA systems. Furthermore, [15],[16],[17], and [18] indicated that the systems based on NOMA outperform traditional OMA in terms of the secrecy performance. In addition, the authors in [16] and [17] deployed power allocation policies and beamforming to alleviate the impacts of internal eavesdroppers. In [16], the authors presented a NOMA-assisted multicastunicast system related to the threat from multicast receivers which intercept the unicasting information. The SOP was studied to show the performance of a cooperative NOMA vehicular communication (VC) system, in which the relay can be operated in either half-duplex (HD) or full-duplex (FD) modes [17]. The authors in [18] presented NOMA to enhance security by investigating the PLS of the information from the weak device against interception by the strong device. Recently, to provide coverage extension an outage minimization, underlay cognitive radio (CR)-based NOMA networks using a decode-and-forward (DF) relaying scheme were examined [19],[20],[21],[22]. In particular, cooperative CR-NOMA was investigated to allow secondary users to cooperate with primary users and then this mechanism compensates the primary spectrum consumption [19]. Moreover, cooperative CR-NOMA were studied in [20] and [21] in terms of the outage probability (OP) and throughput to exhibit the achievable performance gain of the considered system and then is compared with the performance of non-cooperative CR-NOMA networks. Different models of spectrum-sharing NOMA networks including underlay NOMA, overlay NOMA and cognitive NOMA was proposed in [23], in which a novel secondary NOMA-relay-assisted spectrum sharing scheme satisfies first the QoS of the primary user employing maximal ratio combining (MRC) and then the performance of the secondary user was maximized in terms of the sum-rate. The system model is introduced in [24], the primary network shares the spectrum with the secondary network to form such kind of cooperation and such cooperative NOMA-based spectrum sharing system allows the secondary transmitter to transmit the primary user’s information as well as its own information. In another work, a dual-hop underlay CRNOMA network is explored to show the end-to-end OP as the main performance metric for secondary NOMA users [25]. A multiuser multiple-input single-output (MISO) NOMA network using CR was studied subject to an individual QoS constraint and energy efficiency optimization for each primary user [26]. The outage performance of the CR-NOMA system is studied for two users which are benefited by the decode-and-forward scheme [27]. There is no interference from the primary transmitter to the secondary receivers as the assumption reported in [27], and the transmission from the relay does not make any interference to the primary receiver. The authors in [28] considered the situation that the interference occurs from the relay to the primary network while the interference occurs from the primary network to the secondary network. They examined the outage performance of a similar system in case of imperfect CSI. It can be guaranteed the QoS requirement of the quality of the service-sensitive user (QSU) in a cognitive power allocation scheme, while the hybrid automatic repeat request (HARQ) technique is applied to alleviate the SIC errors and enhance the secrecy performance of the security-required user (SRU) [29]. The authors in [30] investigated CR-inspired NOMA (CR-NOMA) networks using PLS with multiple primary and secondary users. To assist the cell-edge group considered as the primary user multicast group (PU-MG), the spectrum efficient CR-NOMA framework is proposed, in which the cell-center group designated as the secondary user multicast group (SU-MG) benefits from spectrum access opportunity [31]. They provided the system to allow the BS requires a pair of users from another multicast group located in its vicinity to perform relaying and jamming signal at the same time. Such a system is proven related to its improvement in terms of the reception reliability of the weaker users as well as ensuring minimum interception. In another work, the secondary users are employed the NOMA scheme to 119046 VOLUME 11, 2023 H. Nguyen et al.: Security-Reliability Analysis in CR-NOMA IoT Network Under I/Q Imbalance send the uplink privacy data, which is comminated by the eavesdropper [32]. A. RELATED WORK AND MOTIVATIONS The authors in [29],[30],[31], and [32] considered secure CR-NOMA networks with perfect hardware paradigms. Actually, according to the previous analysis, the inherent benefit can be achieved to enhance system performance by combining overlay CR with NOMA. In addition, CR-NOMA can improve secure performance and highly meet the real scenario of hardware impairment [33],[34],[35]. Although most of the wireless system is greatly degraded in terms of performance due to impacts of hardware impairments, IQI is known as the most significant source of analog impairments [33]. The performance and the effects of transmitter/receiver IQI in NOMA systems were considered in [33] and [34]. The performance of FD NOMA relaying systems is explored in the presence of in-phase and IQI [30]. Regarding the security of cooperative dual-hop NOMA for internet-of-thing (IoT) networks, the transceivers are considered in terms of a detrimental factor related to in-phase and IQI [34]. The PLS performance in underlay CR-NOMA networks under the impact of hardware impairment is still a topic of discussion, which motivates our study. However, there are some special issues to overcome for PLS in underlay CR-NOMA networks. Firstly, the application of NOMA in CR-NOMA networks establishes more interferences among users, increasing the complexity of transmission scheme design. Moreover, by implementing the TAS scheme in the CR-NOMA system, some improvement issues should be considered, which increases the difficulty of interference control. Furthermore, the existing works cannot be introduced PLS in CR-NOMA networks in the presence of hardware impairment (HI) and it is very challenging to achieve the closed-form formula for several secrecy metrics in such CRNOMA networks. We aim to fill these missing issues in this article. B. MAIN CONTRIBUTION AND ORGANIZATION Our main contributions and insights are summarized as: •We propose the secure CR-NOMA in secondary network transmission to provide high spectrum efficiency, which means the secondary transmitter first allocates power to satisfy the QoS of the first secondary user and then uses the rest of the power to serve the second user. We consider a scenario including two secondary users and an eavesdropper. A sector secrecy guard zone containing these users is invoked to evaluate PLS. Furthermore, TAS is deployed to improve PLS. •To provide the secure performance of the considered system, we derive the closed-form expressions of OP, intercept probability (IP), and effective secrecy throughput (EST), which shows that the secondary users can achieve better performance in the sector secrecy guard zone. Notably, the EST examines the optimal performance at the specific level of SNR at the BS. •We have investigated the performance of two secondary users, and it is shown that: i) the strong secondary user can get the same secure performance as comparing IQI and ideal cases, while the weak secondary user decreases its secure performance significantly;ii) when the key parameters of the system are reasonably constituted, the secondary user can be reached optimal EST ;iii) the resulting analysis shows that a high number of transmit antennas at the BS can be also implemented to enhance secrecy performance. In general, an easy choice of transmit power is provided to achieve higher secrecy performance for secondary users. The remainder of this paper is organized as follows. Section II introduces the system model of IQI-aware CR-NOMA. Section III, we derive the exact analytical expressions for the OP, IP, and EST. To verify our theoretical analyses, we provide numerical and simulation results in Section IV. Finally, we summarize the main achievements of this paper in Section V. II. SYSTEM MODEL This section provides details of the network setup and the main parameters of the system model can be seen in Table 1. Such considered CR-NOMA is illustrated in Fig. 1. FIGURE 1. System model of secure CR-NOMA. We recommend possible applications of such CR-NOMA in IoT systems as follows •The IoT applications of 6G cellular networks, where the BS or access point needs the assistance of the primary network (sharing spectrum) to directly talk to each IoT device. By employing NOMA, such a system can mitigate the situation of weak signals received at destinations due to obstacles or bad quality of transmission. We will evaluate the impact of the eavesdropper by considering it as an unwanted signal from adjacent IoT devices. •The actuators need reliable signals directly transmitted from a central controller industrial in the context of IoT or smart grid. In this scenario, it is critically important to ensure information secrecy, even if such an attacker intends to overhear transmission from a central controller. •As an emerging low power wide area networking (LPWAN) technique, NOMA benefits to Long Range VOLUME 11, 2023 119047 H. Nguyen et al.: Security-Reliability Analysis in CR-NOMA IoT Network Under I/Q Imbalance TABLE 1. Main parameter. Radio (LoRa) networking. In particular, it is vulnerable to eavesdropping attacks since LoRa technology utilizes a symmetric key cryptographic approach with the advanced encryption standard (AES), without any update. By exploiting PLS and CR-NOMA schemes, the access point is considered as a resilient approach which can be utilized to guarantee reliable communication for LoRa networking. In the context of CR-NOMA, we consider the secondary BS to be equipped with Nantennas, two legitimate users including user Di(i∈ {1,2}), and an eavesdropper (E). In this scenario, the primary network is assumed that a primary destination (PD) with an interference effect from the secondary network, shown in Figure 1. However, from the viewpoint of PLS, the unsecured transmission would occur in the presence of an eavesdropper in the considered zone (containing a group of NOMA users). It is assumed that all receivers meet additive white Gaussian noise (AWGN) with mean zero and variance N0. Furthermore, all the wireless channels are modeled to be independent quasi-static block Rayleigh fading channels. Furthermore, hz(z∈ {D1,D2,SP,E}) is the channel vector and modeled by CN (0, λz). First, the time-domain baseband representation of the IQI-impaired signal is formulated as [41] and [42] ˆx=ωt/rx+ ¯ωt/rx∗,(1) where xstands for the baseband transmitted signal under perfect transmitter/receiver (TX/RX) IQI matching. We denote x∗as the mirror signal after being affected by IQI. Regarding detailed IQI coefficients ωt/rand ¯ωt/rare expressed by [33] respectively ωt=(1+ϕtexp (jφt)) 2,(2a) ¯ωt=(1−ϕtexp (jφt)) 2,(2b) ωr=(1+ϕrexp (jφr)) 2,(2c) ¯ωt=(1−ϕrexp (jφr)) 2.(2d) It’s noticed that in the case of ideal IQI, these parameters should be ϕt=ϕr=1 and φr=φt=0o. To guarantee the normal operation of the primary network, the cognitive transmitter power at the BS should satisfy [28] PS=min IP ZSP ,Q,(3) To make the generality and easy to analyze the following performances, we denote Zz=max |hz|2,(z∈ {D1,D2,SP,E}). Noticing the principle of NOMA transmission, the BS transmits the superimposed signal xS= √21x1+√22x2to the secondary users Di. Then, by considering the existence of IQI on both the TX and the RF front-end, the received signal at Diand E are given respectively yi=ωihDiωSxS+ ¯ωS(xS)∗+ni + ¯ωihDiωSxS+ ¯ωS(xS)∗+ni∗,(4) yE=ωEhEωSxS+ ¯ωS(xS)∗+nE + ¯ωEhEωSxS+ ¯ωS(xS)∗+nE∗.(5) Next, the signal to interference plus noise ratio (SINR) at D1when decoding the own signal x1is given by 01,1=PSZD121ϑ1 PSZD122ϑ1+PSZD1ν1+υ1N0 ,(6) where ϑi=ωiωS+ ¯ωi¯ω∗ S2,νi=ωi¯ωS+ ¯ωiω∗ S2and υi= |ωi|2+|¯ωi|2,(i∈ {1,2}). In addition, it can be written ϑias ϑi≈|ωiωS|2+¯ωi¯ω∗ S2[3]. Similarly, the SINR at D2when decode interference signal x1is given by 02,1=PSZD221ϑ2 PSZD222ϑ2+PSZD2ν2+υ2N0 .(7) Applying SIC enabled at the dedicated receiver,1the SINR at D2when decoding the own signal x2is given by 02,2=PSZD222ϑ2 PSZD221¯ ϑ2+PSZD2ν2+υ2N0 ,(8) where ¯ ϑ2=ω2ωS−1+ ¯ω2¯ω∗ S2≈|ω2ωS−1|2+¯ω2¯ω∗ S2. Regarding signal processing at illegal users, the SINR at the eavesdropper when detecting signal x1and x2are expressed by [36] 0E,1=PSZE21ϑE PSZE22ϑE+PSνE|hE|2+υEN0 ,(9) 0E,2=PSZE22ϑE PSZE21¯ ϑE+PSZEνE+υEN0 ,(10) where ϑE=ωEωS+ ¯ωE¯ω∗ S2≈|ωEωS|2+¯ωE¯ω∗ S2, νE=ωE¯ωS+ ¯ωEω∗ S2, υE=|ωE|2+|¯ωE|2,¯ ϑE= ωEωS−1+ ¯ωE¯ω∗ S2≈|ωEωS−1|2+¯ωE¯ω∗ S2. 1In this consideration, we only study the two-users model for NOMA, the extended number of users can be analyzed in a similar way in term of mathematical perceptive [10],[11],[12],[13],[14],[15]. We also assume that fixed power allocation schemes corresponding to static signal decoding order are designed with SIC and non-SIC users at the receiver side. Such classification related to SIC ability is decided based on which is the strong user or not. 119048 VOLUME 11, 2023 H. Nguyen et al.: Security-Reliability Analysis in CR-NOMA IoT Network Under I/Q Imbalance III. SECURE PERFORMANCE ANALYSIS In this section, two secondary users, are considered for the downlink cognitive network in the context of the CR-NOMA. We first analyze the secondary secrecy performance, and then we compare the performance of two users and evaluate which factor make a significant influence on such secure performance. How IQI make influence the performance of legal users to remain their operation satisfying QoS requirement and more verification are expected based on such a main analysis. In particular, we provide details of the stepby-step derivations of secure metrics such as OP, IP, and EST. It is expected that we can claim the closed-form expressions for these metrics. A. CHANNEL MODEL In this case, adopting transmit antenna selection the probability density function (PDF) and cumulative density function (CDF) of channel Zzare given [46] respectively by fZz(x)= N X n=1N n(−1)n−1n λz e−nx λz,(11) FZz(x)=1− N X n=1N n(−1)n−1e−nx λz.(12) B. OUTAGE PROBABILITY Before determining OP, we denote Ri,i= {1,2}as target rates for users Dicorresponding QoS requirements. The outage probability of D1is determined by [44] OPD1=Pr 01,1< γ1−1.(13) where γ1=2R1−1. Proposition 1: The closed-form OP of D1can be given as (14), as shown at the bottom of the page, in which ψ1=γ1υ1 21ϑ1−γ1(22¯ ϑ1+ν1). Please refer to Appendix Afor detailed proof of derivation of (14). Next, we derive the OP of D2which is given by OPD2=Pr 02,2<2R2−1.(15) Replacing (3) and (8) into (15), we get OPD2=1−Pr 02,2>2R2−1 =1−Pr ρZD222ϑ2 ρZD221¯ ϑ2+ρZD2ν2+υ2 > γ2,ZSP <ρI ρ −Pr ρIZD222ϑ2 ρIZD221¯ ϑ2+ρIZD2ν2+ZSPυ2 > γ2,ZSP >ρI ρ, (16) where γ2=2R2−1. Following the approach of Appendix A, the closed-form OP of D2can be obtained, thus, we have (17), as shown at the bottom of the next page, in which ψ2=γ2υ2 22ϑ2−γ2(21¯ ϑ2+ν2). Remark 1: It can be concluded from proposition 1that the OPs of the two users are a decreasing function of the transmit SNR at the BS ρ. This implies that when the transmit power at the BS increases, the reliability performance of the two users is strengthened. In (16),(17), we found that the number of transmit antennas N, transmit SNR ρ, and channel gains are the main factors affecting secure performance metrics. Furthermore, decreasing the target rate Riof the two users can reduce the OP of these users. It means that reducing the requirement of target rates is another way to enhance reliability. As a result, we do not need to change the transmit power at the BS. C. INTERCEPT PROBABILITY In the context of the PLS technique, the eavesdropper can decode confidential information from the BS by applying a signal detection technique. As further metric, the IP of D1can be given as [44] IPD1=Pr 0E,1>2R1−1,(18) Proposition 2: The closed-form expression of IP for user D1is computed by IPD1= 1− N X nSP=1N nSP(−1)nSP−1e−nSPρI λSPρ  × N X nE=1N nE(−1)nE−1e−ψE,1nE ρλE + N X nE=1 N X nSP=1N nEN nSP(−1)nE+nSP−2 ×nSPρIλE ψE,1n1λSP +ρIλEnSP e−ψE,1nEλSP+ρIλEnSP ρλEλSP (19) where ψE,1=γ1υE 22ϑE−(γ221¯ ϑE+νE). Proof: See Appendix B. Looking at the performance of the second user, the IP of D2is given by IPD2=Pr 0E,2>2R2−1.(20) OPD1=1− N X n1=1N n1(−1)n1−1e−ψ1n1 ρλD1 1− N X nSP=1N nSP(−1)nSP−1e−nSPρI λSPρ  − N X n1=1 N X nSP=1N n1N nSP(−1)n1+nSP−2nSPρIλD1 ψ1n1λSP +ρIλD1nSP e−ψ1n1λSP+ρIλD1nSP ρλD1λSP (14) VOLUME 11, 2023 119049 H. Nguyen et al.: Security-Reliability Analysis in CR-NOMA IoT Network Under I/Q Imbalance Similarly, the closed-form expression of IP for user D2is formulated by IPD2= 1− N X nSP=1N nSP(−1)nSP−1e−nSPρI λSPρ  × N X nE=1N nE(−1)nE−1e−ψE,2nE ρλE + N X nE=1 N X nSP=1N nEN nSP(−1)nE+nSP−2 ×nSPρIλE ψE,2n1λSP +ρIλEnSP e−ψE,2nEλSP+ρIλEnSP ρλEλSP (21) where ψE,2=γ2υE 22ϑE−(γ221¯ ϑE+νE). Remark 2: It can be deduced from Proposition 2that the IP of the two users are different. Two values of power allocation 21,22result in a performance gap. Besides, channel gains also contribute to varying the reliability performance of these. In derived expressions, the number of transmit antennas at the BS, Nis a further factor reflecting an improvement of secure performance. Then, the level of IQI can be confirmed as a factor related to degraded performance when we consider two metrics, i.e. OP and IP. D. EFFECTIVE SECRECY THROUGHPUT In the previous section, OP and IP are the metrics to indicate reliability and security performance, respectively. These metrics are inadequate to evaluate the performance of both reliability and security. As a further evaluation, we compute EST to characterize the efficiency and security of the considered system. In particular, the EST of D1and D2are formulated respectively by τ1=R1Pr 01,1>2R1−1, 0E,1<2R1−1,(22) τ2=R2Pr 02,2>2R2−1, 0E,2<2R2−1.(23) Proposition 3: The closed-form expression of EST for user D1is given as (24), as shown at the bottom of the next page. Proof: See Appendix C. Similarly, the closed-form expression of EST for user D2is given as (25), as shown at the bottom of the next page. IV. NUMERICAL RESULTS We set main parameters before simulation as 21=0.75, 22=0.25, λD1=λD2=1, λE=0.1, R1=R2=1, (BPCU) in which BPCU is short for bit per channel use, ϕt=ϕr=1.05, φr=φt=20oand ϕt=ϕr=1, φr=φt=0ofor ideal IQI. FIGURE 2. The OP versus transmit ρ(dB) varying Nwith ρI=20 dB. FIGURE 3. The OP versus transmit ρI(dB) varying Nwith ρ=20 dB. Fig. 2illustrates the OP of two users versus the transmit SNR ρat the BS in such NOMA and we further compare system performance in two cases, i.e. IQI imbalance and ideal case. Such performance can be obtained from (14) and (17). It is important to report that the accuracy computation is achieved since the simulation of the derived expressions of OP is consistent with the results by performing the Monte-Carlo simulations. As expected, the OP increases as ρincreases and significant improvement is obtained with OPD2=1− N X n2=1N n2(−1)n2−1e−ψ2n2 ρλD2 1− N X nSP=1N nSP(−1)nSP−1e−nSPρI λSPρ  − N X n2=1 N X nSP=1N n2N nSP(−1)n2+nSP−2nSPρIλD1 ψ2n2λSP +ρIλD2nSP e−ψ2n2λSP+ρIλD2nSP ρλD2λSP (17) 119050 VOLUME 11, 2023 H. Nguyen et al.: Security-Reliability Analysis in CR-NOMA IoT Network Under I/Q Imbalance the number of antennas is N=2. As indicated from a mathematical perspective, OP in the ideal case for user D2clearly outperforms the IQI case. When N=1, the OP would be unchanged at a high SNR regime. That means OP performance is still limited at a high point of SNR because it depends on other parameters such as power allocation factors or channel gains. A similar trend of OP can be seen in Fig. 3 as we vary the interference power (related to ρI). FIGURE 4. The IP versus transmit ρI(dB) varying λEwith N=2 and ρ=20dB. In Fig. 4, we plot IP curves versus ρIunder many cases of λE. Significantly, we find that the Monte Carlo simulation curves match precisely with the analytical ones, which confirms the exactness of our analysis. We first observe that, for both users, the curves of IP increase due to the increase of ρI. It can be observed that a stronger channel of eavesdropper leads to worse performance, i.e. λEexhibits the worst IP for both users. In contrast with the reliability performance shown in Fig. 2and 3, the secrecy performance can be improved because of the increase in transmit power. In addition, there is a gap in the IP performance of the two users. This situation can be explained that different power factors 21,22allocated to different users. It demonstrates that careful selection of power allocation ratio can realize the tradeoff of the secrecy performance of two users. In a similar experiment, Fig. 5shows IP performance with some cases of target rates. It can be concluded that the better IP corresponds to the lower target rate required. In particular, the requirement for secrecy rate R1,R2of two users is certainly a factor to achieve varying IP performance. In another experiment, Fig. 6indicates that IP performance can be improved significantly if we increase transmit SNR ρ from -5dB to 15dB. However, IP keeps unchanged afterward. It can be explained that IP relies on many variables rather than only transmitting SNR. This is the limitation of IP performance at a high SNR regime. Fig. 7presents the effects of transmit SNR on the EST for user two users with different values of the number of transmit antennas N=1, N=2, and N=3. Interestingly, there τ1=R1 N X n1=1N n1(−1)n1−1e−ψ1n1 ρλD1 1− N X nE=1N nE(−1)nE−1e−ψE,1nE ρλE  1− N X nSP=1N nSP(−1)nSP−1e−nSPρI λSPρ . +R1 N X n1=1 N X nSP=1N n1N nSP(−1)n1+nSP−2nSPρIλD1 ψ1n1λSP +ρIλD1nSP e−ψ1n1λSP+ρIλD1nSP ρλD1λSP −R1 N X n1=1 N X nE=1 N X nSP=1N nSPN nEN n1(−1)nE+n1+nSP−3nSPλEλD1ρIe−n1ψ1λSPλE+λD1λSPnEψE,1+λD1λEρInSP λD1ρ n1ψ1λSPλE+λD1λSPnEψE,1+λD1λEρInSP . (24) τ2=R2 N X n2=1N n2(−1)n2−1e−ψ2n2 ρλD2 1− N X nE=1N nE(−1)nE−1e−ψE,2nE ρλE  1− N X nSP=1N nSP(−1)nSP−1e−nSPρI λSPρ . +R2 N X n2=1 N X nSP=1N n2N nSP(−1)n2+nSP−2nSPρIλD2 ψ2n2λSP +ρIλD2nSP e−ψ2n2λSP+ρIλD2nSP ρλD2λSP −R2 N X n2=1 N X nE=1 N X nSP=1N nSPN nEN n2(−1)nE+n2+nSP−3nSPλEλD2ρIe−n2ψ2λSPλE+λD2λSPnEψE,2+λD2λEρInSP λD2ρ n2ψ2λSPλE+λD2λSPnEψE,2+λD2λEρInSP . (25) VOLUME 11, 2023 119051 H. Nguyen et al.: Security-Reliability Analysis in CR-NOMA IoT Network Under I/Q Imbalance FIGURE 5. The IP versus transmit ρ(dB) varying R1,R2with N=2 and ρI=20 dB. FIGURE 6. The IP versus transmit ρ(dB) varying ρIwith N=2. FIGURE 7. The EST versus transmit ρ(dB) varying Nwith ρI=10(dB). is an optimal SNR that maximizes the EST of two users. It is important to have a set of transmit power at the BS and a higher number of transmit antennas can be selected to achieve optimal performance in terms of EST. We can see that the EST of the user D1outperforms that of the user D2and a big gap between the two users can be reported for three cases of N. FIGURE 8. The EST versus transmit ρ(dB) varying 21with ρ=10(dB) and N=2. Fig. 8presents the relationship between the EST and ρI with the different target date rates 2. It is worth noting that optimal EST still can be obtained by controlling the value of ρI. It means that there are optimal power allocation factors and ρIto guarantee secure performance for two users. Furthermore, it is more important to select a reasonable set of these parameters rather than increasing transmit SNR at the BS. V. CONCLUSION In this paper, we have studied secrecy performance for downlink in underlay CR-NOMA systems. It is more important to consider PLS and IQI problems in such systems to remain normal operation for the whole system. We deployed the TAS scheme for the base station to improve secure performance. Specifically, after the QoS of secondary users with high priority is satisfied, the suitable power allocation scheme and the number of transmit antennas at the base station can be adjusted to serve secondary users better. Considering the reasonable set of these parameters, we achieve optimal EST by numerical method, while still satisfying the OP, and IP performance for the proposed CR-NOMA systems. By limiting the impact of IQI, such a system still operates with acceptable secure performance. Moreover, our results have certain reference values for different demands of secondary users in such IQI-aware CR-NOMA systems. Especially, such a system model is beneficial to design the IoT in potential applications as recommended, in which some users have higher priority of services, and some users need higher security demand. In future works, more users and practical scenarios are goals for our study. APPENDIX A With the help (3) and (6), we can rewrite OPD1as (26), as shown at the bottom of the next page, in which γ1=2R1−1, ρ=Q N0and ρI=IP N0. 119052 VOLUME 11, 2023 H. Nguyen et al.: Security-Reliability Analysis in CR-NOMA IoT Network Under I/Q Imbalance Then, the first term of (26),A1can be calculated by A1=Pr ZD1> ψ1,ZSP <ρI ρ =¯ FZD1ψ1 2FZSP ρI ρ(27) where ¯ F(.)=1−F(.) and ψ1=γ1υ1 21ϑ1−γ1(22ϑ1+ν1). Based on (12),A1is obtained by A1= N X n1=1N n1(−1)n1−1e−ψ1n1 ρλD1 × 1− N X nSP=1N nSP(−1)nSP−1e−nSPρI λSPρ (28) Moreover, the second term of (26),A2is rewritten by A2=Pr ZD1>ψ1ZSP ρI ,ZSP >ρI ρ = ∞ Z ρI ρ fZSP (x)¯ FZD1ψ1x ρIdx (29) Putting (11) and (12) into (29),A2is re-expressed by A2= N X n1=1 N X nSP=1N n1N nSP ×(−1)n1+nSP−2nSP λSP ∞ Z ρI ρ e−ψ1n1x ρIλD1−nSPx λSP dx (30) The closed-form of A2can be formulated by A2= N X n1=1 N X nSP=1N n1N nSP(−1)n1+nSP−2 ×nSPρIλD1 ψ1n1λSP +ρIλD1nSP e−ψ1n1λSP+ρIλD1nSP ρλD1λSP (31) Substituting (28) and (31) into (26), it is obtained the closed-form OP of D1. It is the end of the proof. APPENDIX B Substituting (3) and (9) into (19), we have IPD1 =Pr PSZE21ϑE PSZE22ϑE+PSZEνE+υEN0 > γ1 =Pr ρZE21ϑE ρZE22ϑE+ρZEνE+υE > γ1,ZSP <ρI ρ | {z } B1 +Pr ρIZE21ϑE ρIZE22ϑE+ρIZEνE+ZSPυE >γ1,ZSP >ρI ρ | {z } B2 , (32) Similarly, it can be obtained the closed-form B1and B2respectively by B1=FZSP ρI ρ¯ FZEψE,1 ρ = 1− N X nSP=1N nSP(−1)nSP−1e−nSPρI λSPρ  × N X nE=1N nE(−1)nE−1e−ψE,1nE ρλE,(33) and B2= ∞ Z ρI ρ fZSP (x)¯ FZEψE,1x ρIdx = N X nE=1 N X nSP=1N nEN nSP(−1)nE+nSP−2 ×nSPρIλE ψE,1n1λSP +ρIλEnSP e−ψE,1nEλSP+ρIλEnSP ρλEλSP (34) where ψE,1=γ1υE 21ϑE−(γ122ϑE+νE). Putting (33) and (34) into (32), we complete the proof. APPENDIX C With the help (3),(6) and (9), we can rewrite τ1as (35), as shown at the top of the next page. OPD1=1−Pr PSZD121ϑ1 PSZD122ϑ1+PSν1ZD1+υ1N0 > γ1 =1−Pr ρZD121ϑ1 ρZD122ϑ1+ρZD1ν1+υ1 > γ1, ρ < ρI ZSP  | {z } A1 −Pr ρIZD121ϑ1 ρIZD122ϑ1+ρIZD1ν1+ZSPυ1 > γ1, ρ < ρI ZSP  | {z } A2 (26) VOLUME 11, 2023 119053