I Introduction
THE next generation wireless communication systems call for advanced communication techniques that can achieve high spectral efficiency (SE) and provide massive connectivity in support of the escalating high data rate requirements imposed by the unprecedented proliferation of mobile devices [1]. Cognitive radio (CR) and nonorthogonal multiple access (NOMA) constitute promising techniques of achieving high SE [2][4]. Specifically, CR enables the secondary users (SUs) to exploit the frequency bands of the primary users (PUs) provided that the interference imposed on the PUs from the SUs is below a certain level. NOMA has a higher informationtheoretic rate region than orthogonal techniques albeit, which is achieved by increasing the receiver’s implementation complexity [4]. One of the main ideas for realizing NOMA is to exploit the power domain. Specifically, multiple users’ signals are superimposed by using different power levels and successive interference cancellation (SIC) is installed at the receiver for mitigating the mutual interference imposed by using nonorthogonal resources [5]. It is envisioned that applying NOMA in CR networks (CRNs) is capable of significantly improving the SE and the user connectivity [6], [7].
Meanwhile, the next generation wireless communication systems also need energyefficient techniques due to the everincreasing greenhouse gas emission concerns and explosive proliferation of powerlimited devices, e.g., sensors and mobile phones. Energyefficient techniques can be divided into two broad categories. One of the categories focuses on the techniques that can achieve high energy efficiency (EE) [8], [9], while the other one aims for recycling energy, where both wireless charging as well as simultaneous wireless information and power transfer (SWIPT) [10] fit. In this paper, we focus on SWIPT since it can simultaneously transmit information and achieve energy harvesting (EH). In SWIPT, the radio frequency (RF) signals carry not only information to the users, but also transfer energy for the energy harvesting receivers (EHRs). Compared to the conventional EH techniques, such as wind charging, SWIPT has an advantage in providing more stable and controllable amount of power for energylimited devices. Hence, it is of significant importance to study the application of SWIPT in NOMA CRNs that aim for supporting massive population of battery driven powerlimited devices.
However, due to the broadcast nature of NOMA as well as CR and the dual function of RF signals [11], [12], NOMA CRNs relying on SWIPT are vulnerable to eavesdropping. Malicious EHRs may intercept the confidential information transmitted to the PUs and the SUs [13]. Thus, it is vital to improve the security of NOMA CRNs using SWIPT. As an alternative to the traditional cryptographic techniques, physicallayer security exploits the physical characteristics (e.g., multipath fading, propagation delay, etc.) of wireless channels to achieve secure communications [16][17]. It was shown [16][17] that the secrecy rate of wireless communication systems directly depends on the accuracy of the channel state information (CSI). Moreover, the secrecy rate of SUs in CRNs is more severely limited [13], [18][22] since their transmission power should be controlled in order to protect the PUs’ quality of service. In order to improve the secrecy rate of SUs, multiple antennas, cooperative relaying, jamming and artificial noise (AN)aided techniques have been applied [18][22]. Moreover, the secrecy rate can be further improved by designing an optimal resource allocation scheme [18][22]. Furthermore, the secure energy efficiency can be enhanced by using ANaided techniques and designing the optimal resource allocation schemes [23], [24]. However, the performance gains achieved by using these techniques are significantly influenced by the accuracy of CSI. What’s worse, it is a challenge to obtain accurate CSI, especially for NOMA [25], [26]. Thus, it is important to design resource allocation schemes under the imperfect CSI.
Numerous investigations have been conducted for improving the security of the conventional OMA systems and efforts have been invested into conceiving secure NOMA systems [12], [27][30]. However, no contributions have been devoted to improving the security of NOMA CRNs using SWIPT. In this paper, in order to achieve secure communications, beamforming design problems are studied in multipleinput singleoutput (MISO) NOMA CRNs using SWIPT where a practical nonlinear EH model is applied as well as different CSI models are considered. An ANaided cooperative scheme is proposed for improving the security of the primary network. By using this scheme, the secondary network imposes artificial noise for jamming the malicious EHRs while aspiring to get a chance to access the frequency bands of the primary network. The related work and the motivation of our investigation are presented as follows.
Ia Related Work and Motivation
Beamforming design problems have been extensively studied both in conventional CRNs [31][36] and in conventional CRNs using SWIPT [13], [22], [38][41]. Recently, some efforts have also been dedicated to designing NOMA resource allocation schemes for improving their security [12], [27][30]. These contributions can be summarized as follows.
Due to the broadcast nature of the conventional CRNs, malicious SUs may intercept the confidential information transmitted to the legitimate SUs. In order to improve the security of CRNs, numerous secure physicallayer techniques have been proposed by using different CSI models [31][36]. In [31], a robust beamforming scheme has been proposed for MISO CRNs in the face of a bounded CSI error model. It was shown that as anticipated the secrecy rate of the SUs can be significantly improved by using multiple antennas techniques, by contrast it is reduced when the CSI inaccuracy goes up. By exploiting the relationship between multiantenna aided secure communications and cognitive radio communications, the authors of [32] designed an optimal beamforming scheme for MISOaided CRNs. In [33], the authors extended the contributions of [31] and [32]
into a fading channel and the secure throughput was maximized by optimizing both the beamforming vector and the transmission power. The authors of
[34] studied the robust beamforming design problem in MISO CRNs where realistic finitealphabet inputs are considered. A global optimization approach was proposed for designing an optimal beamforming scheme for maximizing the secrecy rate. Recently, the authors of [35] and [36] studied the beamforming design problems of secure MISO multiuser unicast CRNs and of mutlicast CRNs, respectively. Specifically, in [35], an ANaided beamforming scheme was proposed. It was shown that as expected the secrecy rate of SUs can be improved by imposing artificial noise on malicious SUs. Cooperation between the primary network and the secondary network was proposed in [36] where the secrecy rate of SUs was maximized under the maxmin fairness criterion.Since energy harvesting has not been considered in [31][36], the beamforming schemes proposed in these works are inappropriate in CRNs using SWIPT. Recently, the authors of [13], [22], [38][41] studied the resource allocation problems of various CRNs using SWIPT. In [13], a multiobjective optimization framework was applied in MISO CRNs with SWIPT. The beamforming scheme, the covariance matrix of AN and energy signals were jointly optimized. It was shown that there are several tradeoffs in CRNs using SWIPT, such as the tradeoff between the secrecy rate of SUs and the harvested power of EHRs. The authors of [13] only considered the bounded CSI error model. In [22], the authors studied the robust beamforming design problem both under the bounded CSI error model and the probabilistic CSI error model. It was shown that a performance gain can be obtained under the probabilistic CSI error model compared to the bounded CSI error model. Mohjazi et al. [37] extended the robust beamforming design problem into a multiuser MISO CRNs using SWIPT. The transmission power of the cognitive base station (CBS) was minimized by jointly optimizing the beamforming of CBS and the power splitting factor of the energyharvesting SUs. In order to further improve the secrecy rate and the harvested power of EHRs, an optimal precoding scheme was designed for multipleinput multipleoutput (MIMO) aided CRNs using SWIPT [38]. In [39], a cooperative mechanism and a robust beamforming scheme were proposed for improving the security of CRNs, where the energy signals were exploited to jam the malicious EHRs. The authors of [40] have studied robust resource allocation problems in MIMOaided CRNs using SWIPT under the probabilistic CSI error model. The contributions of [13], [22], [38][40] assumed an ideal linear EH model. However, practical power conversion circuits have a nonlinear endtoend wireless power transfer function. Hence, the robust resource allocation schemes proposed in these treatises would perform difficultly in the face of a realistic nonlinear power transfer characteristic. In [41], the robust beamforming design problem was studied in MISO CRNs using SWIPT, where a nonlinear EH model was used.
The abovementioned contributions were made for CRNs and CRNs with SWIPT where OMA is applied. However, these resource allocation schemes proposed in the abovementioned works are inappropriate or suboptimal in NOMA systems since NOMA schemes are very different from OMA. The authors of [12], [27][30] have studied the optimal resource allocation problems in NOMA systems in order to achieve secure communications. In [12], an optimal power allocation scheme was proposed for maximizing the secrecy sum rate of a singleinput singleoutput (SISO) NOMA system, where only an eavesdropper was assumed and a constant decoding order was applied. In [27], the authors considered a more general scenario, where a dynamic decoding order was considered. The sum secrecy rate was maximized by jointly optimizing the decoding order, the transmission rates and the power allocated to users. The secrecy rate maximization problems of MISO NOMA systems [28], [29] and MIMO NOMA systems [30] were investigated. It was shown that the secrecy rate achieved by using NOMA is higher than that achieved by using OMA, and that the secrecy rate of users can be improved by using multiple antennasaided techniques.
Although resource allocation problems have indeed been conceived for NOMA systems for achieving secure communications [12], [27][30], resource allocation schemes proposed in these contributions operated under the assumption that perfect CSI can be obtained. Moreover, these resource allocation schemes cannot work in NOMA CRNs using SWIPT since the interference between the primary network and the secondary network as well as the energy harvesting requirements of the EHRs are required to be considered. Furthermore, the robust resource allocation schemes proposed in conventional CRNs using SWIPT are inappropriate for NOMA CRNs using SWIPT due to the differences between NOMA and OMA. To the best of our knowledge, few investigations have been conduced for improving the security of NOMA CRNs using SWIPT. Thus, in order to achieve secure communications in NOMA CRNs using SWIPT, beamforming design problems are studied both under the perfect CSI model and the bounded CSI error model. These problems are challenging but meaningful. The reasons are from the following two perspectives. On the one hand, a practical nonlinear EH model is applied, but the EH form is more complex than the linear form. On the other hand, the mutual interference between the primary network and the secondary network as well as the interference among NOMA SUs have to be considered.
IB Contributions and Organization
In contrast to [12], [27][30], this paper studies the beamforming design problems of MISONOMA CRNs using SWIPT, where multiple malicious EHRs exist and a practical nonlinear EH model is applied. Both the perfect CSI and the bounded CSI error model are considered. In order to improve the security of the primary network, an ANaided cooperative scheme is proposed. The main contributions are summarized as follows:

The ANaided cooperative scheme is proposed for MISONOMA CRNs using SWIPT in order to improve the security of the primary network. By using this scheme, the CBS transmits a jamming signal to cooperate with the primary base station (PBS) for improving the security of the PUs. As a reward, the secondary network is granted to access the frequency bands of the primary network and provide SWIPT services both for the SUs and for the EHRs in the secondary network. Moreover, the covariance matrix of the jamming signals transmitted at CBS and the beamforming of the CBS and the PBS are jointly optimized.

Beamforming design problems are studied under both the perfect CSI model and the bounded CSI error model. In contrast to the works that only an eavesdropper was considered in the NOMA system [12], [27][30], we investigate a more general scenario, where multiple malicious EHRs exist. The total transmission power is minimized by jointly optimizing the transmission beamforming vectors of both the PBS and the CBS as well as the covariance matrix of the jamming signal transmitted at the CBS, subject to constraints on the secrecy rates of both the PUs and the SUs as well as on the energy harvesting requirements of the EHRs. A pair of algorithms are proposed for solving these challenging nonconvex problems. One of them relies on semidefinite relaxation (SDR) while the other is based on a carefully conceived cost function.

Our simulation results show that the proposed ANaided cooperative scheme can reduce the transmission power required in MISONOMA CRNs using SWIPT. Moreover, it is shown that the performance achieved by NOMA is proven to be better than that obtained by OMA, even when the CSI is imperfect. Furthermore, our simulation results also show that the algorithm based on the cost function outperforms the algorithm based on using SDR.
IC Organization and Notations
The remainder of this paper is organized as follows. The system model is presented in Section II. Our secure beamforming design problems are examined under the perfect CSI assumption in Section III. Section IV presents our secure beamforming design problems under the bounded CSI error model while our simulation results are presented in Section V. Finally, the paper is concluded in Section VI.
Notations:
Vectors and matrices are represented by boldface lower case letters and boldface capital letters, respectively. The identity matrix is denoted by
; and are the number of antennas of the PBS and the CBS, respectively; vec(A) denotes the vectorization of matrix A and it is obtained by stacking its column vectors. The Hermitian (conjugate) transpose, trace, and rank of a matrix A are denoted respectively by , Tr and Rank. represents the conjugate transpose of a vector . stands for an by dimensional complex matrix set. represents that is a Hermitian positive semidefinite (definite) matrix. and represent a by dimensional Hermitian matrix set and a Hermitian positive semidefinite matrix set, respectively. denotes the Euclidean norm of a vector. represents the absolute value of a complex scalar. means thatis a random vector, which follows a complex Gaussian distribution with mean
and covariance matrix . denotes the expectation operator. extracts the real part of vector .is the maximum eigenvalue of
. represents the set of all nonnegative real numbers. denotes the maximum between and .Ii System Model
In this section, we will describe the network model and security metrics in the downlink MISO NOMA CRNs using SWIPT under a practical nonlinear energy harvesting model. In [12], [27][30], only one eavesdropper has been considered in the designed NOMA systems and resource allocation schemes have been proposed. In this paper, the beamforming design problems are studied in a more general scenario, where multiple malicious EHRs exist. The detail description is presented in the following subsections.
Iia Network Model
Our downlink MISO NOMA CR network using SWIPT is shown in Fig. 1. In the primary network, unicastmulticast communications are exploited since they can provide high SE and massive connectivity. This scenario is widely encountered, for example in Internet of Things, wireless sensor networks and the cellular networks [35], [36]. Specifically, the PBS sends different confidential informationbearing signals to the PUs in the different clusters. And the primary users in each individual multicast cluster receive the same confidential informationbearing signal from the PBS. In the secondary network, the NOMA is applied since it can achieve high power transfer efficiency and SUs can perform SIC [6], [7]. In this case, the PBS broadcasts the information to the PUs in clusters and simultaneously transfers energy to EHRs. In the secondary network, the CBS provides SWIPT service to EHRs and to SUs by using NOMA. Due to the constrained size of devices, the PUs and SUs can only perform information decoding while the EHRs can only harvest energy from the RF signals [22], [35]. The primary network coexists with the secondary network by using the spectrum sharing mode. The PBS is equipped with antennas and the CBS is equipped with antennas. All the PUs, SUs and EHRs are equipped with a single antenna.
Due to the broadcast natures of NOMA and the dual function of RF signals in SWIPT, the EHR may eavesdrop and intercept the information transmitted by the PBS and the CBS. It is assumed that EHRs in each network can only intercept confidential information from the same network and the PUs in each cluster are respectively wiretapped by EHRs in the same cluster [36]. For example, PUs in the th cluster, where and , are wiretapped by the th EHR in the th cluster, where and and is the number of EHRs while is the number of PUs in the th cluster. In order to improve the security of both the primary network and the secondary network, an ANaided cooperative scheme is applied. Using this scheme, the CBS of Fig. 1 transmits a jamming signal to the primary network for improving the security of the PUs. As a reward, the primary network allows the secondary network to operate on its frequency bands. All the channels involved are assumed to be flat fading channels. In this paper, both the perfect CSI and imperfect CSI cases are studied. The performance achieved under the perfect CSI can be used as a bound in our analysis and provides meaningful insights into the design of MISO NOMA CRNs using SWIPT. The assumption has also been used in [11], [12], [18], [19].
IiB Security Metrics
Let denote the signal received at the th PU in the th cluster, represent the signal received at the th SU, denote the EH signal received at the th EHR in the th cluster and represent the EH signal received at the th EHR in the secondary network, respectively, where , ; , and , . These signals are respectively expressed as
(1a)  
(1b) 
(1c)  
(1d) 
where and are the channel vector between the PBS and the th PU as well as that between the CBS and the th PU in the th cluster, respectively; and denote the channel vector between the PBS and the th SU as well as that between the CBS and the th SU, respectively. Furthermore, and are the channel vector between the PBS and the th EHR and that between the CBS and the th EHR in the th cluster, respectively; and represent the channel vector between the PBS and the th EHR and that between the CBS and the th EHR in the secondary network, respectively. Still regarding to , and are the confidential informationbearing signal for the PUs in the th cluster and the corresponding beamforming vector, respectively. Furthermore, and represent the confidential informationbearing signal delivered for the th SU and the corresponding beamforming vector, respectively. Additionally, and denote the noise vector artificially generated by the PBS and the CBS. It is assumed that and . It is also assumed that and , where and are the AN covariance matrix. In , and respectively denote the complex Gaussian noise at the th PU in the th cluster and the th SU.
The secrecy rate of the th PU in the th cluster and the secrecy rate of the th SU, denoted by and , respectively, can be expressed as
(2a)  
(2b) 
where ; ; ; ; ; ; ; ; and . The expressions of , , , , and are given in . Without loss of generality, it is assumed that . Similar to [12], [27][28], it is assumed furthermore that the EHR in the secondary network has decoded SU ’s message before it decodes the SU ’s message,
. This overestimates the interception capability of EHRs and results in the worstcase secrecy rate of the SUs. This conservative assumption was also used in
[12], [27][28].(3a)  
(3b)  
(3c)  
(3d)  
(3e)  
(3f) 
IiC Nonlinear Energy Harvesting Model
In this paper, a practical nonlinear EH model is adopted. According to [41][43], the harvesting power of EHRs, denoted by , can be formulated as:
(4a)  
(4b)  
(4c) 
where is the set of EHRs in the primary network and the secondary network, namely, , and , , ; and represent parameters that reflect the circuit specifications, such as the resistance, the capacitance and diode turnon voltage [42]. Furthermore, is the maximum harvested power of EHRs when the EH circuit is saturated. In , is the RF power received at EHRs. Furthermore, when the EHRs are in the primary network and when the EHRs are in the secondary network. Note that the noise power is ignored, since it is small compared to the RF signal power [41][43].
Iii ANaided Beamforming Design Under Perfect CSI
In this section, an ANaided beamforming design problem is formulated in MISO NOMA CRNs using SWIPT under the perfect CSI. The CSI between the PBS and PUs as well as the CSI between the CBS and the SUs can be obtained through the feedback from the corresponding transmitters and the receivers [11], [12], [18], [19]. The CSI between the two networks can be obtained with the cooperation between the primary network and the secondary network [18], [33], [34]. The total transmission power is minimized subject to the constraints on both the secrecy rates of PUs and SUs as well as on the harvested power of EHRs in both the primary and the secondary networks. In order to solve the challenging nonconvex problem, again, a pair of suboptimal algorithms are proposed. One is based on SDR and the other is based on a cost function.
Iiia ANaided Beamforming Design Problem
In order to minimize the sum of the transmission power of the PBS and CBS, the beamforming weights and the AN covariance of the PBS and the CBS are jointly optimized under constraints of the secrecy rate of PUs as well as SUs and under the EH requirements of the EHRs. The power minimization problem is formulated as follows:
(5a)  
s.t.  
(5b)  
(5c)  
(5d)  
(5e)  
(5f)  
(5g) 
In , and are the minimum secrecy rate requirements of the th PU in the th cluster and of the th SU; and are the minimum EH requirements of EHRs in the primary and the secondary network. The constraints and are imposed to guarantee the secrecy rates of the PUs and SUs, respectively; the constraints and are the constraints that can satisfy the harvested power requirements of the EHRs in both the primary and secondary networks; and the constraint is the rankone constraint required for obtaining rankone beamforming. Note that the optimization objective of can be identified as the weight objective of a multipleobjective optimization problem that has two optimization objectives (e.g., the transmission power of the PBS and the CBS) with the same weight. Due to the constraints , and , is nonconvex and difficult to solve. In order to solve this problem, a pair of suboptimal schemes are proposed as follows.
IiiB Suboptimal Solution Based on SDR
To address the constraint , an auxiliary variable , , is introduced. Then, the constraint can be equivalently expressed as
(6a)  
(6b) 
where and . Using successive convex approximation (SCA), the constraints given by and can be approximated as and
(7a)  
(7b)  
(7c)  
(7d) 
(8a)  
(8b)  
(8c)  
(8d) 
where , , , , , and are auxiliary variables. Furthermore, , and are approximate values, and they are equal to , and , respectively, when the constraints are tight. Similarly, the constraint can be approximated as and . When , the secrecy rate constraint of the th SU can be formulated as
(9a)  
(9b)  
(9c)  
(9d)  
(9e)  
(9f)  
(9g)  
(9h) 
where , , , , , and are auxiliary variables. Furthermore, , and are approximate values, and they are equal to , and , respectively, when the constraints are tight. When , the secrecy rate constraint of the th SU can be formulated as
(10a)  
(10b)  
(10c)  
(10d)  
(10e)  
(10f)  
(10g)  
(10h)  
(10i) 
where , , , , , , and denote auxiliary variables. Furthermore, , and are approximate values and equal to , and , respectively, when the constraints are tight. Constraints and can be equivalently expressed as
(11) 
Based on and , using SDR, can be solved by iteratively solving , given as
(12a)  
(12b) 
where is the set including all optimization variables and auxiliary variables. is convex and can be efficiently solved by using the software CVX [22]. Algorithm 1 calculates the solution of . The details of Algorithm 1 are provided in Table 1, where denotes the minimum total transmission power at the th iteration.
Algorithm 1: The SCAbased algorithm for 
1: Setting: 
, , , , , , 
and the tolerance error ; 
2: Initialization: 
The iterative number , , , , , , 
, , and and ; 
3: Repeat: 
solve by using CVX for the given approximate values; 
obtain , , , , , , 
, and and ; 
if and 
Obtain optimal and ; 
else 
Obtain suboptimal and ; 
end 
update the iterative number ; 
calculate the total transmit power ; 
if 
break; 
end; 
4: Obtain resource allocation: 
, , and . 
Algorithm 1 does not guarantee that the optimal beamforming weights , can be obtained. If and
are of rankone, the optimal beamforming scheme can be obtained by the eigenvalue decomposition and the obtained eigenvectors are optimal beamforming. If
and are not of rankone, the suboptimal beamforming vectors can be obtained by using the Gaussian randomization procedure [22].IiiC Suboptimal Solution Based on Cost Function
Since and are semipositive definite, the ranks of and are equal to when their maximum eigenvalues are equal to its trace, namely, when we have and ; Otherwise, we have and . Thus, the rankone constraint can be equivalent to . From this insight, we can see that the smaller is, the more likely that the rankone constraints can be satisfied. By exploiting a cost function based approach, is reformulated into as
(13a)  
(13b) 
where is a cost factor. It may be readily shown that the minimum value can be obtained by using a large value. Since and are convex, is nonconvex. The following lemma is applied to solve the nonconvex problem .
Lemma 1 [45]: Let and denote the maximum eigenvalue of