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 non-orthogonal multiple access (NOMA) are promising due to their high SE and the capability of providing massive connectivity. CR enables the secondary network to access the spectrum band of the primary network as long as the interference caused to the primary network is tolerable [2]. Different from orthogonal multiple access (OMA), NOMA has the potential advantages in SE and user connectivity by using non-orthogonal resources at the cost of the receiver’s implementation complexity [3], [4]. It is envisioned that the application of NOMA into CR networks (CRNs) can significantly improve SE and user connectivity [5], [6].
Meanwhile, the next generation wireless communication systems also need energy-efficient techniques due to the ever increasing greenhouse gas emission concerns and explosive proliferation of power-limited devices, e.g., sensors and mobile phones. To that end, simultaneous wireless information and power transfer (SWIPT) has drawn great attentions [7]. It can simultaneously transmit information and achieve energy harvesting (EH). Particularly, radio frequency (RF) signals carry not only information, but also are identified as energy sources for EH. Compared with the conventional EH techniques, such as wind charging, SWIPT can provide a stable and controllable power for energy-limited devices. Thus, in NOMA CRNs with power-limited devices, it is of significant importance to study the application of SWIPT into NOMA CRNs.
However, due to the broadcasting nature of NOMA as well as CR and the dual function of RF signals [8]-[10], NOMA CRNs relying on SWIPT are vulnerable to eavesdropping. Malicious energy harvesting receivers (EHRs) may exist and intercept the confidential information transmitted to the primary users (PUs) and the secondary users (SUs) [8]. Thus, it is vital to improve the security of NOMA CRNs relying on SWIPT. As an alternative to the traditional cryptographic techniques, physical-layer security exploits the physical characteristics (e.g., multipath fading, propagation delay, etc.) of wireless channels to achieve secure communications. It was shown that the secrecy rate of wireless communication systems is limited by the channel state information (CSI) [11]. In order to improve the secrecy rate, multiple antennas, cooperative relay, jamming and artificial noise (AN)-aided techniques have been applied [12], [13].
Many investigations have been conducted to improve the security of the conventional OMA systems and initial efforts have been made to study secure transmission in NOMA systems [10], [14]-[16]. However, to authors’ best knowledge, few investigations have been conduced for improving the security of NOMA CRNs relying on SWIPT. The existing works for OMA systems relying on SWIPT can be categorized into two research lines based on the energy harvesting model, namely, the linear EH model [8], [17], [18] and the non-linear EH model [9], [19]-[21]. In [8], the authors studied robust beamforming design problems in MISO CRNs relying on SWIPT based on the linear EH model. Under this model, the harvested power linearly increases with the input power. The authors in [17] established a multiple-objective optimization framework in MISO CRNs relying on SWIPT. It was shown that there exist multiple tradeoffs, such as the tradeoff between the harvesting energy and the secrecy rate. In [18], the secure transmission problems were extended into multiple-input multiple-output (MIMO) CRNs. Obviously, the linear EH model is ideal due to the practical non-linear end-to-end power conversation circuit [9], [19]-[21]. Recently, the authors in [9], [19]-[21] proposed a non-linear EH model and studied resource allocation problems. In [9] and [19], beamforming design problems were studied in MISO systems relying on SWIPT based on the proposed non-linear EH model. It was shown that the harvesting energy achieved under the non-linear EH model may be higher than that obtained under the linear EH model. These problems were extended into MIMO systems relying on SWIPT in [20] and [21].
However, the beamforming schemes proposed in [8], [9], [17]-[21] are inappropriate to NOMA CRNs relying on SWIPT since NOMA is very different from OMA. Although the works in [10], [14]-[16] studied resource allocation problems in NOMA systems, these resource allocation schemes are unadaptable to NOMA CRNs relying on SWIPT. The reasons are from the following two perspectives. On the one hand, they were proposed for the conventional NOMA systems that do not need to consider the interference between the primary network and the secondary network. On the other hand, SWIPT was not applied and the EH requirement was not considered.
In this paper, in order to improve the security of the primary network, an AN-aided cooperative scheme is proposed. By using this scheme, the cognitive base station (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. The transmission beamforming and AN covariance matrix are jointly optimized to minimize the total transmission power of the network while the secrecy rate and the EH requirement are guaranteed. Simulation results show that our proposed cooperative scheme is efficient and NOMA outperforms OMA in terms of the power consumption.
The rest of this paper is organized as follows. Section II presents the system model. The AN-aided beamforming design problem is formulated in Section III. Section IV presents simulation results. The paper concludes with Section V.
Notations:
Boldface capital letters and boldface lower case letters represent matrices and vectors, respectively. The Hermitian (conjugate) transpose, trace, and rank of a matrix
A are represented respectively by , Tr and Rank.denotes the identity matrix. The conjugate transpose of a vector
is denoted by . denotes a -by- dimensional complex matrix set. represents that is a Hermitian positive semidefinite (definite) matrix. and denote a -by- dimensional Hermitian matrix set and a Hermitian positive semidefinite matrix set, respectively. denotes the Euclidean norm of a vector. The absolute value of a complex scalar is denoted by . means thatis a random vector and follows a complex Gaussian distribution with mean
and covariance matrix . denotes the expectation operator.Ii System Model
A downlink MISO NOMA CR network with SWIPT is considered in Fig. 1. In the primary network, multicast communications are exploited since they can provide high SE and massive connectivity but PUs’ receivers are simple, which cannot perform SIC. This scenario is widely encountered, for example in Internet of Things, wireless sensor networks, and cellular network [12]. In the secondary network, NOMA is applied since it can achieve high power transfer efficiency and SUs can perform successive interference cancellation (SIC) [5]. In this case, the PBS broadcasts information to PUs in clusters and simultaneously transfers energy to EHRs. In the secondary network, the CBS provides SWIPT service to EHRs and SUs by using NOMA. 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 broadcasting characteristic of NOMA and the dual function of RF signals, 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 PUs in each cluster are respectively wiretapped by EHRs in the same cluster. For example, PUs in the th cluster, where and , are wiretapped by the th EHR in the th cluster, where and . is the number of EHRs and is the number of PUs in the th cluster. In order to improve the security of the primary network, an An-aided 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. It is assumed that all CSI is assumed to be perfect [10], [14], [15]. The performance achieved under this assumption can be used as a bound analysis and provides meaningful insights into the design of MISO NOMA CRNs.
Let , , and denote the signal received at the th PU in the th cluster and the th SU, and the EH signal at the th EHR in the th cluster and the th EHR in the secondary network, respectively, where , ; , and , . These signals are respectively given as
(1a) | ||||
(1b) | ||||
(1c) | ||||
(1d) |
where and are the channel vector between the PBS and the th PU and 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 and that between the CBS and the th SU, respectively; 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 information-bearing signal for PUs in the th cluster and the corresponding beamforming vector, respectively; and represent the confidential information-bearing signal for the th SU and the corresponding beamforming vector, respectively; and denote the noise vector artificially generated by the PBS and the CBS for improving the security of these two networks. Without loss of generality, it is assumed that and . It is also assumed that and , where and are the AN covariance matrix to be designed. In , and respectively denote the complex Gaussian noise at the th PU in the th cluster and the th SU.
Let ; ; ; ; ; ; ; ; and . Based on , 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 are given as at the top of the next page. Without loss of generality, it is assumed that . Similar to [10], [14]-[16], it is assumed that the EHR in the secondary network has decoded SU’s ’s message before it decodes the SU’s ’s message, . This overestimates the interception capability of EHRs and results in the worst-case secrecy rate of SUs. This conservative assumption was used in [10], [14]-[16].
(3a) | ||||
(3b) | ||||
(3c) | ||||
(3d) | ||||
(3e) | ||||
(3f) |
In this paper, a practical non-linear EH model is adopted. According to [19]-[21], 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 turn-on voltage [19]; is the maximum harvested power of EHRs when the EH circuit is saturated. In , is the received RF power at EHRs; when EHRs are in the primary network and when EHRs are in the secondary network. Note that the noise power is ignored since it is small compared to the RF signal power [17]-[21].
Iii AN-aided Beamforming Design
Iii-a Problem Formulation
In order to minimize the total transmit power, the beamforming and the AN covariance of the PBS and the CBS are jointly optimized under constraints of the secrecy rate of PUs and SUs, the interference power caused to PUs and the EH requirement of EHRs. The power minimization problem is formulated as in the following.
(5a) | ||||
s.t. | ||||
(5b) | ||||
(5c) | ||||
(5d) | ||||
(5e) | ||||
(5f) | ||||
(5g) |
where and are the minimum secrecy rate requirements of the th PU in the th cluster and of the th SU; is the maximum tolerable interference power of the th PU in the th cluster; and are the minimum EH requirements of EHRs in the primary and the secondary network. Due to constraints , and , is non-convex and difficult to be solved. In order to solve this problem, a suboptimal scheme based on semidefinite relaxation (SDR) and successive convex approximation (SCA) is proposed.
Iii-B Suboptimal Solution
To address constraint , auxiliary variables , , are introduced. can be equivalently expressed as
(6a) | ||||
(6b) |
where and . Using SCA, constraints given by and can be approximated as and
(7a) | ||||
(7b) | ||||
(7c) | ||||
(7d) |
(8a) | ||||
(8b) | ||||
(8c) | ||||
(8d) |
where , , , , and are auxiliary variables. , and are approximate values, and they are equal to , and , respectively when the constraints are tight. Similarly, constraint can be approximated as and . When , the secrecy rate constraint of the th SU can be given as
(9a) | ||||
(9b) | ||||
(9c) | ||||
(9d) | ||||
(9e) | ||||
(9f) | ||||
(9g) | ||||
(9h) |
where , , , , and are auxiliary variables; , 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 given as
(10a) | ||||
(10b) | ||||
(10c) | ||||
(10d) | ||||
(10e) | ||||
(10f) | ||||
(10g) | ||||
(10h) | ||||
(10i) |
where , , , , , , and denote auxiliary variables; , 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 [8]. Algorithm 1 is given to solve . The details of Algorithm 1 are provided in Table 1. where denotes the minimum total transmission power at th iteration.
Algorithm 1: The SCA-based 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 , can be obtained. If and
are of rank-one, the optimal beamforming scheme can be obtained by the eigenvalue decomposition and the obtained eigenvectors are optimal beamforming. If
and are not of rank-one, the suboptimal beamforming vectors can be obtained by using the well-known Gaussian randomization procedure [8].Iv Simulation Results
The simulation settings are based on those used in [9] and [19]. All the involved channels are assumed to be Rayleigh flat fading. The number of channel realizations is
. The variances of noise at all users and EHRs are
dBm. The channel distributions are set as: , , , , , , and . The detailed simulation settings are given in Table III.Parameters | Notation | Typical Values |
---|---|---|
Numbers of antennas of the PBS | ||
Numbers of antennas of the CBS | ||
Numbers of the clusters | ||
Numbers of SUs | ||
The maximum harvested power | mW | |
Circuit parameter | ||
Circuit parameter | ||
The minimum secrecy rate of PUs | bits/s/Hz | |
The minimum secrecy rate of SUs | bits/s/Hz | |
The maximum interference power | mW | |
The minimum EH of EHRs in set | mW | |
The minimum EH of EHRs in set | mW | |
The tolerance error |
Fig. 2(a) shows the minimum transmission power versus the number of EHRs in the secondary network. It can be seen that the minimum transmission power consumed without the cooperative jamming scheme is larger than that consumed with our proposed cooperative jamming scheme. The reason is that our proposed cooperative jamming scheme is efficient for secure communication. As shown in Fig. 2(b), it only needs several iterations to converge to the minimum transmission power. This indicates the efficiency of our proposed algorithm. Fig. 2(c) is given to further verify that our proposed cooperative scheme is beneficial to improve the security of NOMA CRNs using SWIPT. It is also seen from Fig. 2(a) and Fig. 2(b) that NOMA outperforms OMA (time division multiple access is used) in terms of the power consumption.
V Conclusion
Secure communication was studied in a MISO NOMA CRN using SWIPT where a practical non-linear EH model was considered. An AN-aided cooperative jamming scheme was proposed to improve the security of both the primary and secondary network. The total transmission power was minimized by jointly optimizing the transmission beamforming and the AN covariance matrix. It was shown that our proposed cooperative jamming scheme is efficient to achieve secure communication. Simulation results also show that the performance achieved by using NOMA is better than that obtained by using OMA in terms of the power consumption.
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