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Physical layer security transmission scheme based on artificial noise in cooperative SWIPT NOMA system

Abstract

Aiming at high energy consumption and information security problem in the simultaneous wireless information and power transfer (SWIPT) multi-user wiretap network, we propose a user-aided cooperative non-orthogonal multiple access (NOMA) physical layer security transmission scheme to minimize base station (BS) transmitted power in this paper. In this scheme, the user near from BS is adopted as a friendly relay to improve performance of user far from BS. An energy harvesting (EH) technology-based SWIPT is employed at the near user to collect energy which can be used at cooperative stage. Since eavesdropper in the downlink of NOMA system may use successive interference cancellation (SIC) technology to obtain the secrecy information of receiver, to tackle this problem, artificial noise (AN) is used at the BS to enhance security performance of secrecy information. Moreover, semidefinite relaxation (SDR) method and successive convex approximation (SCA) technique are combined to solve the above non-convex problem. Simulation results show that in comparison with other methods, our method can effectively reduce the transmitted power of the BS on the constraints of a certain level of the secrecy rates of two users.

Introduction

High-speed transmission rates of smart terminals in fifth-generation (5G) wireless communication systems require vast spectrum resources [1, 2]. Traditional orthogonal multiple access (OMA) approaches are difficult to meet the needs of high-speed, real-time and wide-bandwidth in 5G. Researchers proposed NOMA technique, one of the key technologies of 5G, to provide higher spectral efficiency (SE) of multiple users. Keypoint of NOMA is multiple non-orthogonal access of power domain. Thus, multiple users can be served by the same resource block (time domain, frequency domain and code domain). However, due to mutual interference of non-orthogonal signal, the receiver has to use the SIC technique to extract desired information from received signal [3,4,5].

For the purpose of improving the performance of NOMA, the mode of effectively combining NOMA and cooperative technique has been attracted great attentions. The existing cooperative NOMA mainly can be divided into two types including the user-assisted and the relay-assisted. For example, J. Men and J. Ge explored the outage probability of the cooperative NOMA relay network by deriving a closed-form expression [6]. A two-stage relay selection scheme was presented to research the outage performance of the cooperative NOMA system in [7,8,9]. Z. Ding proposed a half-duplex user-aided cooperative NOMA scheme to achieve the maximum diversity gain, and the simulation results indicate that the proposed cooperative NOMA scheme could improve the outage probability [10]. S. L. Talbot and B. Farhang-Boroujeny presented a cooperative beamforming NOMA scheme which performed intrabeam superposition coding of a multi-user signal at the transmitter and the spatial filtering of interbeam interference followed by the intrabeam SIC at the destination [11].

In addition, energy efficiency (EE) is another concern of 5G. Since radio frequency (RF) signals can carry information and transmit energy simultaneously, they can be used not only for information vehicle but also for energy collection of the system. At present, a technology which can effectively extend the service life of energy-limited device called SWIPT has been proposed [12]. Different from traditional EH technologies, such as solar and wind, SWIPT provides stable and controllable energy for wireless applications while transmitting the necessary information contained in RF signal. For this reason, there are many relevant studies on SWIPT that have been appeared in the recent several years. Early studies on SWIPT have assumed that the entire signal can transmit both information and energy, exposing a fundamental trade-off between power and information transfer [13]. But this simultaneous transfer is unrealistic, since the EH operation employed in the RF domain destroys the information content. In order to practically achieve SWIPT, the received signal has to be allocated into two distinct parts, one for information decoding and another for EH [14]. Specifically, Zhang proposed two practical receiver architectures to handle the technical limitations of existing circuit designs, namely time-switching (TS) receiver and PS receiver. If TS is performed, the receiver switches in time between EH and information decoding. In this case, signal allocating is employed in the time domain. So, the entire signal received in one time slot is used either for EH or information decoding. The TS scheme allows for a simple hardware implementation at the receiver but requires accurate time synchronization. The PS scheme has higher receiver complexity compared to TS and requires the optimization of the PS factor [15]. However, Krikidis and Timotheou indicated that the PS technology achieves lower outage probability and higher gain than those of TS for applications with delay constraints. It is intuitive since the signal received in one time slot is used for both power transfer and information decoding when the PS protocol is performed. [14]. In order to further meet practical scenario, in contrast to the most of existing works which apply an ideally linear EH model, Zhou and Chu adopted the practical nonlinear EH model to capture the nonlinear characteristics of EH circuits and designed the resource allocation schemes for SWIPT networks[16].

Motivated by the requirements of 5G and the advantages of NOMA and SWIPT, using SWIPT to enhance SE and EE in NOMA system which contains energy-limited devices is a hotspot today [17].Liu and Ding introduce SWIPT into NOMA system to extend self-sustaining time of system. This strategy employs the near users as EH relays to improve communication quality of far users. Outage rates with respect to three kinds of relay selection schemes are evaluated in single-input single-output (SISO) scenario. The analytical results demonstrate that SWIPT technology can effectively enhance EE of conventional NOMA systems without jeopardizing its diversity gain [18]. Xu and Ding proposed a SWIPT NOMA cooperative transmission strategy to design a joint beamformer and power-distribution in multi-input single-output (MISO) scene with the perfect channel state information (CSI) model [19]. Furthermore, a joint design of the PS ratio and beamformer was studied in the imperfect CSI model [20]. However, the security of cooperative transmission is not involved in their work. Thus, the private information is easily intercepted and eavesdropped from open wireless channel [21, 22]. To overcome this issue, the cooperative jamming (CJ) technique can be introduced for transmitting AN to degrade the quality of the wiretap link. The existing CJ technique mainly can be classified into three different types including the source-aided CJ, relay-aided CJ and the destination-aided CJ. The source-aided CJ refers to combining information bearing signal with AN injected by the source [23]. In order to improve security of network, Moradikia et al. employed the AN which is injected by the idle transmitter in the scene of untrusted relays and passive eavesdroppers existing [24]. The relay-aided CJ describes the relay nodes of the system chosen to work as a jammer [25]. Liu Y combined cooperative relay with CJ technique to interfere eavesdropper. The research shows that their method can effectively improve the secrecy rate [26]. Zhou and Chu used AN technique to improve the information security of users in the SWIPT NOMA system which has an untrusted energy harvesting receiver [27]. The destination-aided CJ considers the AN transmitted by the destination [28]. A novel cooperative secure unmanned aerial vehicle-assisted propagation protocol has been presented by M. Tatar Mamaghani. For the purpose of enhancing physical-layer security and propagation reliability, they employed destination-assisted CJ as well as SWIPT at the unmanned aerial vehicle mounted relay [29]. Furthermore, Hu Z explored physical layer security of SWIPT relay network with imperfect the CSI model. An algorithm is presented to optimize secret rate of SWIPT network in the constraints of relay forward power and eavesdroppers SINR [30]. Cao and Wang studied the security transmission of uplink NOMA with the aid of the EH receivers. One of the EH receivers is selected as a friendly jammer that adopts the energy harvested from the RF signals to transmit the AN for interfering the eavesdropper [31]. However, the collaboration secrecy scheme of SWIPT and NOMA is not involved in their work. Thus, it motivates us to use AN-aided cooperative strategy to enhance physical-layer security of MISO SWIPT NOMA system. The main contributions of this paper are summarized as follows.

  • We propose a source-aided CJ SWIPT NOMA strategy, where the near user serves as an EH relay to help the far user to improve the secrecy rate. By applying the PS protocol, the near user can simultaneously receive information and harvest energy used for the forwarding stage. In addition, multiple antennas and AN-aided techniques are exploited to protect the private information.

  • The above scheme can be described as the problem of minimizing transmitted power from BS subject to secrecy rate of each user. To tackle this problem, we need to jointly optimize beamforming vector, AN covariance matrix and PS ratio. Unfortunately, it is NP-hard. So, variable slack technique is combined with SCA method to get suboptimal solution of the original problem. The simulation results verify the proposed scheme which not only guarantees information security but also reduces BS’s energy consumption.

The paper is organized as follows. In Sect. 2, we first introduce the system model and the problem formulation of the cooperative SWIPT NOMA in MISO system. Next, an SCA-based iterative algorithm is proposed to solve the joint AN-aided beamforming design and power splitting control problem. Then, we present numerical results on the performance of different schemes in Sect. 3. Finally, we conclude the paper in Sect. 4.

Notations: Boldface capital letters and boldface lowercase letters denote matrices and vectors, respectively. \(\mathbb {C}\) represents the complex domain. \(\mathbb {E}|\cdot |\) denotes the expectation operator. The superscript \((\cdot )^{T}\) and \((\cdot )^{H}\) denote the transpose and (Hermitian) conjugate transpose, respectively. \({{\mathrm{Tr}}(\cdot )}\) represents the trace of a matrix. \(||\cdot ||\) denotes the magnitude of a complex number. \(\mathcal {CN}(\mathbf {0},\mathbf {X})\) denotes the circularly symmetric complex Gaussian distribution with mean vector \(\mathbf {0}\) and covariance matrix \(\mathbf {X}\).

Methods/experimental

System model and problem formulation

Consider a downlink in an MISO system is depicted in Fig. 1. BS is equipped with \({N}_t\) antennas. Two users and a passive eavesdropper are equipped with a single antenna, respectively. For simplicity, supposing eavesdropper and user 2 do not have a direct link, and the eavesdropper is distributed outside the security area center on user 2 near from BS (eavesdropper in the security will be detected by user 2). Similar to reference [32], we assume that some handshaking mechanisms are introduced in the medium access control (MAC) protocol of user 1 and user 2 to inhibit the interception occurring in the security area center on user 2. Specifically, user 1 and user 2 can employ a particular MAC protocol to exchange data while the eavesdropper without MAC protocol may only intercept the data from the BS without MAC protocol. Assume that the channel quality of the user 2 and the eavesdropper is better than that of user 1, respectively. For example, consider an indoor sensor communication scenario where user 2 and eavesdropper are closer to the BS than user 1.

Cooperative SWIPT NOMA transmission scheme is divided into two phases. In the first phase, the eavesdropper intercepts the transmitted signal from BS, and user 1 receives the transmitted signal from BS while user 2 performs SWIPT technique based on PS protocol. The PS protocol achieves SWIPT by allocating the received radio frequency signal at the user 2 into two streams of different power levels using a PS factor: one signal stream is converted to baseband for information decoding, and the other is sent to the rectenna circuit for EH. Assume that the harvested energy at the user 2 is only used for information forwarding at the second stage, while the energy for maintaining circuit, signal processing, etc., is neglected. When the harvested energy is more than the energy needed to information forwarding at user 2, there is an energy buffer at the secondary transmitter to store the excess energy. In the second phase, user 2 uses harvested energy in phase 1 to forward the message received in phase 1 to user 1, while user 1 employs maximal-ratio combination (MRC) criterion to accumulate and decode the messages received in two phases. Since the eavesdropper is distributed outside the security area center on user 2 near from BS, eavesdropper cannot receive the transmitted signal from user 2. Details of the process are presented next.

In the first transmission phase, in order to improve the security of the BS’s transmitted signal and reduce the risk of information leakage, an AN vector \(\mathbf {v}\in \mathbb {C}^{{N}_{t}}\) is added to the transmitted signal. Therefore, the transmitted signal from the BS is described as \(\mathbf {s}=\mathbf {w}_{1}{s}_{1}+\mathbf {w}_{2}{s}_{2}+\mathbf {v}\), where \({s}_{1},{s}_{2}\in \mathbb {C}\) are information bearing messages for user 1 and user 2, respectively. And \(\mathbf {w}_{1},\mathbf {w}_{2}\in \mathbb {C}^{{N}_{t}}\) are the corresponding transmitted beamformers. We assume that the power of the transmitted symbol is normalized, i.e., \(\mathbb {E}|{s}_{1}|^{2}=\mathbb {E}|{s}_{2}|^{2}=1\), and the AN vector \(\mathbf {v}\sim \mathcal {CN}(\mathbf {0},\mathbf {S})\), where \(\mathbf {S}\) is the covariance matrix of AN to be designed. Then, the signal received at user 1 is given by

$$\begin{aligned} y_{1}^{(1)} = \widetilde{\mathbf {h}}_{1}^{H} \left( \mathbf {w}_{1}{s}_{1}+\mathbf {w}_{2}{s}_{2}+\mathbf {v}\right) + {n}_{1}^{(1)}, \end{aligned}$$
(1)

where \(\widetilde{\mathbf {h}}_{1}^{H}\in \mathbb {C}^{{N}_{t}}\) is the channel impulse response vector between the BS and user 1, and \({n}_{1}^{(1)}\sim \mathcal {CN}(0,\sigma _{1}^{2})\) represents the additive Gaussian white noise (AWGN) at user 1. Then, the signal-to-interference-plus-noise-ratio (SINR) received by user 1 for \({s}_{1}\) can be expressed as

$$\begin{aligned} \mathrm{SIN}\mathrm{R}_{1}^{(1)} = \frac{|{{\widetilde{\mathbf {h}}_1^H}{\mathbf {w}_1}}|^2}{{|{\widetilde{\mathbf {h}}_1^H{\mathbf {w}_2}}|^2} + {|{\widetilde{\mathbf {h}}_1^H{\mathbf {v}}}|^2} + \sigma _1^2}, \end{aligned}$$
(2)

by defining \(\mathbf {h}_1=\widetilde{\mathbf {h}}_1/\sigma _1\), (2) is transformed as

$$\begin{aligned} \mathrm{SIN}\mathrm{R}_{1}^{(1)} = \frac{{\mathbf {h}_1^H}{\mathbf {w}_1}{\mathbf {w}_1^H}{\mathbf {h}_1}}{{\mathbf {h}_1^H}\left( {\mathbf {w}_2}{\mathbf {w}_2^H} + {\mathbf {S}} \right) {\mathbf {h}_1} + 1}. \end{aligned}$$
(3)
Fig. 1
figure1

The system model

Fig. 2
figure2

The power splitting architecture at user 2

As shown in Fig. 2, the power splitting architecture with respect to user 2, is introduced to perform SWIPT. Hence, the received signal for information decoding at user 2 can be described as

$$\begin{aligned} y_{2}^{(1)} = \sqrt{1-\rho } \widetilde{\mathbf {h}}_{2}^{H} \left( \mathbf {w}_{1}{s}_{1}+\mathbf {w}_{2}{s}_{2}+\mathbf {v}\right) + {n}_{2}^{(1)}, \end{aligned}$$
(4)

where \(\rho \in [0,1]\) is the PS ratio of energy harvesting to be optimized later, \(\widetilde{\mathbf {h}}_{2}^{H}\in \mathbb {C}^{{N}_{t}}\) is the channel impulse response vector between the BS and user 2, \({n}_{2}^{(1)}\sim \mathcal {CN}(0,\sigma _{2}^{2})\) represents the AWGN.

According to the NOMA principle, SIC is performed at user 2. Specifically, user 2 first decodes user 1’s message (i.e., \({s}_{1}\)) and then subtracts this message from the received signal to decode its own message [33]. Therefore, the SINR received at user 2 to decode \({s}_{1}\) can be expressed as

$$\begin{aligned} \mathrm{SIN}\mathrm{R}_{2,{s}_1}^{(1)} = \frac{(1-\rho ){\mathbf {h}_2^H}{\mathbf {w}_1}{\mathbf {w}_1^H}{\mathbf {h}_2}}{(1-\rho ){\mathbf {h}_2^H}\left( {\mathbf {w}_2}{\mathbf {w}_2^H} + {\mathbf {S}} \right) {\mathbf {h}_2} + 1}, \end{aligned}$$
(5)

where \(\mathbf {h}_2=\widetilde{\mathbf {h}}_2/\sigma _2\).

Then, user 2 subtracts \({s}_{1}\) from \(y_{2}^{(1)}\) to further decode its own message \({s}_{2}\). The corresponding SINR can be described as

$$\begin{aligned} \mathrm{SIN}\mathrm{R}_{2,{s}_2}^{(1)} = \frac{(1-\rho ){\mathbf {h}_2^H}{\mathbf {w}_2}{\mathbf {w}_2^H}{\mathbf {h}_2}}{(1-\rho ){\mathbf {h}_2^H}{\mathbf {S}} {\mathbf {h}_2} + 1}. \end{aligned}$$
(6)

On the other hand, the energy harvested by user 2 is modeled as [34]

$$\begin{aligned} {E}=\rho \left( {|{{\widetilde{\mathbf {h}}_2^H}{\mathbf {w}_1}}|^2}+{|{{\widetilde{\mathbf {h}}_2^H}{\mathbf {w}_2}}|^2}+{|{{\widetilde{\mathbf {h}}_2^H}{\mathbf {v}}}|^2}\right) \eta , \end{aligned}$$
(7)

where \(\eta\) is the ratio of the first phase in a transmission time slot, and we assume that the two phases have the same transmission duration, then \(\eta =0.5\).

Thus, in the second phase, the transmitted power of user 2 related to forwarding messages is

$$\begin{aligned} {P}_t=\frac{{E}}{1-\eta }=\rho \left( {|{{\widetilde{\mathbf {h}}_2^H}{\mathbf {w}_1}}|^2}+{|{{\widetilde{\mathbf {h}}_2^H}{\mathbf {w}_2}}|^2}+{|{{\widetilde{\mathbf {h}}_2^H}{\mathbf {v}}}|^2}\right) . \end{aligned}$$
(8)

In addition, the signal received at the eavesdropper can be expressed as

$$\begin{aligned} y_{e}^{(1)} = \widetilde{\mathbf {f}}^{H} \left( \mathbf {w}_{1}{s}_{1}+\mathbf {w}_{2}{s}_{2}+\mathbf {v}\right) + {n}_{e}^{(1)}, \end{aligned}$$
(9)

where \(\widetilde{\mathbf {f}}^{H}\in \mathbb {C}^{{N}_{t}}\) is the channel impulse response vector between the BS and eavesdropper, and \({n}_{e}^{(1)}\sim \mathcal {CN}(0,\sigma _{e}^{2})\) represents the AWGN at eavesdropper. Then, the SINR received by eavesdropper for the message \({s}_1\) can be expressed as

$$\begin{aligned} \mathrm{SIN}\mathrm{R}_{e,{s}_1}^{(1)} = \frac{{\mathbf {f}^H}{\mathbf {w}_1}{\mathbf {w}_1^H}{\mathbf {f}}}{{\mathbf {f}^H}\left( {\mathbf {w}_2}{\mathbf {w}_2^H} + {\mathbf {S}} \right) {\mathbf {f}} + 1}. \end{aligned}$$
(10)

where \(\mathbf {f}=\widetilde{\mathbf {f}}/\sigma _{e}\).

The eavesdropper then performs the SIC, subtracts \({s}_1\) from its signal to further decode the other message \({s}_2\). The corresponding SINR can be described as

$$\begin{aligned} \mathrm{SIN}\mathrm{R}_{e,{s}_2}^{(1)} = \frac{{\mathbf {f}^H}{\mathbf {w}_2}{\mathbf {w}_2^H}{\mathbf {f}}}{{\mathbf {f}^H}{\mathbf {S}} {\mathbf {f}} + 1}. \end{aligned}$$
(11)

In the second phase, user 2 forwards the message to user 1 with the harvested energy. At this point, the signal received at user 1 is

$$\begin{aligned} y_{1}^{(2)} = \sqrt{{P}_t}{g}_{1}{s}_{1} + {n}_{1}^{(2)}, \end{aligned}$$
(12)

where \({g}_{1}\in \mathbb {C}\) is the channel coefficient from user 2 to user 1, and \({n}_{1}^{(2)}\sim \mathcal {CN}(0,\sigma _{1}^{2})\) is the AWGN at user 1. Note that we consider the case of \(\sigma _{1}^{2}=\sigma _{2}^{2}\) for the simplicity of exposition. Thus, the SINR received by user 1 for \(s _{1}\) can be given by

$$\begin{aligned} \mathrm{SIN}\mathrm{R}_{1,{s}_1}^{(2)} = \rho {g}\left( {\mathbf {h}_2^H}({\mathbf {w}_1}{\mathbf {w}_1^H}+{\mathbf {w}_2}{\mathbf {w}_2^H} + {\mathbf {S}} ){\mathbf {h}_2}\right) , \end{aligned}$$
(13)

where \({g}=|{g}_1|^2\).

In communication systems, MRC usually be performed following synchronization, channel estimation and channel equalization (in the sampling domain). Since synchronization, channel estimation and channel equalization are not main concerns in this paper, similar as reference[19] and[35], we assume each channel has been completely synchronized before performing the MRC. So, user 1 can combine the signals received from the BS and the user 2 to jointly decode the message. The equivalent SINR at user 1 can be written as

$$\begin{aligned} \mathrm{SIN}\mathrm{R}_{1,{s}_1}&{}={}&\mathrm{SIN}\mathrm{R}_{1}^{(1)}+ \mathrm{SN}\mathrm{R}_{1,{s}_1}^{(2)}\nonumber \\= & {} \frac{{\mathbf {h}_1^H}{\mathbf {w}_1}{\mathbf {w}_1^H}{\mathbf {h}_1}}{{\mathbf {h}_1^H}\left( {\mathbf {w}_2}{\mathbf {w}_2^H} + {\mathbf {S}} \right) {\mathbf {h}_1} + 1}+\rho {g}\left( {\mathbf {h}_2^H}\left( {\mathbf {w}_1}{\mathbf {w}_1^H}+{\mathbf {w}_2}{\mathbf {w}_2^H} + {\mathbf {S}} \right) {\mathbf {h}_2}\right) . \end{aligned}$$
(14)

Therefore, according to the SINR of the legitimate user and the eavesdropper, the secrecy rate \({R}_1\) and secrecy rate \({R}_2\) of the user 1 and the user 2 are defined as follows

$$\begin{aligned} {R}_1= & {} {\min }\left\{ 0.5\mathrm{log}_2\left( 1+\mathrm{SIN}\mathrm{R}_{1,{s}_1}\right) ,0.5\mathrm{log}_2\left( 1+\mathrm{SIN}\mathrm{R}_{2,{s}_1}^{(1)}\right) \right\} \nonumber \\&-0.5\mathrm{log}_2\left( 1+\mathrm{SIN}\mathrm{R}_{e,{s}_1}^{(1)}\right) \end{aligned}$$
(15a)
$$\begin{aligned} {R}_2= & {} 0.5\mathrm{log}_2\left( 1+\mathrm{SIN}\mathrm{R}_{2,{s}_2}^{(1)}\right) -0.5\mathrm{log}_2\left( 1+\mathrm{SIN}\mathrm{R}_{e,{s}_2}^{(1)}\right) . \end{aligned}$$
(15b)

we want to minimize the transmitted power of the BS while guaranteeing the level of secrecy rates related to users. The optimization problem can be expressed as follow

$$\begin{aligned}&\mathbf {P}_1:{}\min \limits _{\rho ,\mathbf {w}_1,\mathbf {w}_2,\mathbf {S}}{} {{\mathrm{Tr}}}\left( {\mathbf {w}_1}{\mathbf {w}_1^H}+{\mathbf {w}_2}{\mathbf {w}_2^H} + {\mathbf {S}} \right) \end{aligned}$$
(16a)
$$\begin{aligned}&\quad {\mathrm {s.t.}}\,C0:{R}_1\ge \gamma _1,\end{aligned}$$
(16b)
$$\begin{aligned}&\quad C1:{R}_2\ge \gamma _2,\end{aligned}$$
(16c)
$$\begin{aligned}&\quad C2:0\le \rho <1,\end{aligned}$$
(16d)
$$\begin{aligned}&\quad C3:\mathbf {S}\succeq 0, \end{aligned}$$
(16e)

where \(\gamma _1\) and \(\gamma _2\) represent the minimum required secret rate thresholds with respect to user 1 and user 2, respectively. The constraint C0 is to ensure \({s}_1\) can be successfully decoded at user 2 meanwhile guarantee the SINR requirement of user 1 satisfied, and the constraint C1 ensures the secure transmission of message \({s}_2\) at user 2. Observing equ (15.a) and equ (15.b), we can find that \(\rho\), \(\mathbf {w}_1\) and \(\mathbf {w}_2\) are coupled together in the \({R}_1\) and \({R}_2\). Thus, P1 is a nonconvex problem and is difficult to solve. In the following, we will firstly employ SDR technique to reformulate P1 and then approximately solve the reformulated problem with an SCA-based iterative algorithm.

$$\begin{aligned} \begin{aligned} {R}_{1,s_1}&=\frac{{\left[ {{{{\mathrm{Tr}}}}\left( {\left( {{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {F}}}} \right) + 1} \right] }}{{\left\{ {\frac{{\left[ {{{{\mathrm{Tr}}}}\left( {\left( {{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_1}} \right) + 1} \right] }}{{\left[ {{{{\mathrm{Tr}}}}\left( {\left( {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_2}} \right) + 1} \right] }} + \rho g{{{{\mathrm{Tr}}}}}\left( {\left( {{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_2}} \right) } \right\} \left[ {{{{\mathrm{Tr}}}}}\left( {\left( {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {F}}}} \right) +1\right] }}\\ {R}_{2,s_1}&=\frac{{\left[ {(1 - \rho ){{{\mathrm{Tr}}}}\left( {({{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {H}}_2}} \right) + 1} \right] \left[ {{{{\mathrm{Tr}}}}\left( {({{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {F}}}} \right) + 1} \right] }}{{\left[ {(1 - \rho ){{{\mathrm{Tr}}}}\left( {({{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {H}}_2}} \right) + 1} \right] \left[ {{{{\mathrm{Tr}}}}\left( {({{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {F}}}} \right) + 1} \right] }}\\ {R}_{2,s_2}&=\frac{{\left[ {(1 - \rho ){{{\mathrm{Tr}}}}\left( {{\mathbf {S}}{{\mathbf {H}}_2}} \right) + 1} \right] \left[ {{{{\mathrm{Tr}}}}\left( {\left( {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {F}}}} \right) + 1} \right] }}{{\left[ {(1 - \rho ){{{\mathrm{Tr}}}}\left( {\left( {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_2}} \right) + 1} \right] \left[ {{{{\mathrm{Tr}}}}\left( {{\mathbf {S}}{{\mathbf {F}}}} \right) + 1} \right] }} \end{aligned} \end{aligned}$$
(17)

AN-aided beamforming design and power splitting control

Let \({\mathbf {W}_1}={\mathbf {w}_1}{\mathbf {w}_1^H}\), \({\mathbf {W}_2}={\mathbf {w}_2}{\mathbf {w}_2^H}\) and drop rank-one constraints \(\mathrm rank({\mathbf {W}_1})=1\), \(\mathrm rank({\mathbf {W}_2})=1\). P1 can be relaxed to P2, given as

$$\begin{aligned}&\mathbf {P}_2: \min \limits _{\rho ,\mathbf {W}_1,\mathbf {W}_2,\mathbf {S}}{} {{\mathrm{Tr}}\left( {\mathbf {W}_1}+{\mathbf {W}_2}+ {\mathbf {S}} \right) }\end{aligned}$$
(18a)
$$\begin{aligned}&\quad {\mathrm {s.t.}}\quad C4:{R}_{1,s_1}\leqslant {2^{ - {\gamma _1}}},\end{aligned}$$
(18b)
$$\begin{aligned}&\quad C5:{R}_{2,s_1}\leqslant {2^{ - {\gamma _1}}},\end{aligned}$$
(18c)
$$\begin{aligned}&\quad C6:{R}_{2,s_2}\leqslant {2^{ - {\gamma _2}}},\end{aligned}$$
(18d)
$$\begin{aligned}&\quad C7:0\le \rho <1,\end{aligned}$$
(18e)
$$\begin{aligned}&\quad C8:\mathbf {S}\succeq 0,\mathbf {W}_1\succeq 0,\mathbf {W}_2\succeq 0, \end{aligned}$$
(18f)

where \({{\mathbf {H}}_1} \triangleq {{\mathbf {h}}_1}{\mathbf {h}}_1^H\), \({{\mathbf {H}}_2} \triangleq {{\mathbf {h}}_2}{\mathbf {h}}_2^H\) and \({{\mathbf {F}}} \triangleq {{\mathbf {f}}}{\mathbf {f}}^H\). Moreover, \({R}_{1,s_1}\) and \({R}_{2,s_1}\) represent the secrecy rates of message \(s_1\) at user 1 and user 2, respectively. \({R}_{2,s_2}\) represents that of message \(s_2\) at user 2(c.f. (17)). Due to the constraints C4, C5 and C6 are still non-convex, they are converted to the following equivalent by introducing exponential auxiliary variables [36]. The constraint C4 is equivalently expressed as

$$\exp \left( {{x_1} - {y_1} - {y_2}} \right) \leqslant {2^{ - {\gamma _1}}},$$
(19a)
$${\mathrm{Tr}}\left( {\left( {{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {F}}}} \right) + 1 \leqslant \exp \left( { x_1}\right) ,$$
(19b)
$$\frac{{\left[ {{\mathrm{Tr}}\left( {\left( {{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_1}} \right) + 1} \right] }}{{\left[ {{\mathrm{Tr}}\left( {({{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {H}}_1}} \right) + 1} \right] }} +\rho g{\mathrm{Tr}}\left( {\left( {{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_2}} \right) \geqslant \exp \left( {{y}_1}\right),$$
(19c)
$${\mathrm{Tr}}\left( {\left( {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {F}}}} \right) + 1 \geqslant \exp \left( { y_2}\right) ,$$
(19d)

where \(x_1\), \(y_1\), \(y_2\) are exponential auxiliary variables. Here, only (19b) and (19c) remain as non-convex constraints. By using the first-order Taylor expansion approximation, the non-convex constraint (19b) can be approximated as

$$\begin{aligned} {{\mathrm{Tr}}}\left( {({{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {F}}}} \right) + 1 \leqslant \exp \left( {\widetilde{ x_1}}\right) \left( { x_1} - {\widetilde{ x_1}} + 1\right) , \end{aligned}$$
(20)

where \(\widetilde{x}_1\) is an approximate value, and it is equal to \({x}_1\), when the corresponding constraints are tight.

Furthermore, by introducing an auxiliary variable \({x_2} \geqslant 0\), constraint (19c) can be equivalently expressed as

$$\begin{aligned}&{{\mathrm{Tr}}}\left( {\left( {{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_1}} \right) \geqslant {x_2}{\mathrm{Tr}}\left( {\left( {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_1}} \right) + x_2 - 1, \end{aligned}$$
(21a)
$$\rho g{{{\mathrm{Tr}}}}\left( {\left( {{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_2}} \right) \geqslant \exp \left( { y_1}\right) - { x_2}.$$
(21b)

For constraint (21a), an approximate convex constraint is produced by using the arithmetic-geometric mean (AGM) inequality \(xy \leqslant z\). That is, for any nonnegative variable x, y and z, if and only if \(a = \sqrt{y/x}\), the following formula holds

$$\begin{aligned} 2xy \leqslant {(ax)^2} + {(y/a)^2} \leqslant 2z. \end{aligned}$$
(22)

Therefore, constraint (21a) is approximated by a convex constraint as follows

$$\begin{aligned}&{\left( {{{\widetilde{a}}_1}{x_2}} \right) ^2} + {\left( {{\mathrm{Tr}}\left( {({{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {H}}_1}} \right) /{{\widetilde{a}}_1}} \right) ^2}\leqslant 2{\mathrm{Tr}}\left( {\left( {{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_1}} \right) + 2 - 2{ x_2}, \end{aligned}$$
(23)

where \(\widetilde{a}_1\) is an approximate value, which is updated after each iteration by the following formula

$$\begin{aligned} {\widetilde{a}_1} = \sqrt{{\mathrm{Tr}}\left( {\left( {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_1}} \right) /{ x_2}}. \end{aligned}$$
(24)

Using epigraph reformulation [37], the constraint (21b) can be transformed into a non-convex quadratic constraint and a convex LMI constraint as below

$${u^2} \geqslant \exp ({y_1}) - {x_2},$$
(25a)
$$\begin{aligned}&\left[ {\begin{array}{*{20}{c}} {g\rho }&{}u \\ u&{}{{\mathrm{Tr}}\left( {\left( {{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_2}} \right) } \end{array}} \right] \succeq 0. \end{aligned}$$
(25b)

And then, the non-convex quadratic inequality constraint (25a) is still approximated by Taylor expansion as

$$\begin{aligned} 2\widetilde{u}u - {\widetilde{u}^2} \geqslant \exp ({y_1}) - {x_2}, \end{aligned}$$
(26)

where \(\widetilde{u}\) is an approximate value.

Similar to C4, constraint C5 is approximated as

$$\exp \left( {{x_3} + {x_4} - {y_3} - {y_4}} \right) \leqslant {2^{ - {\gamma _1}}},$$
(27a)
$${\left( {{{\widetilde{a}}_2}(1 - \rho )} \right) ^2} + {\left( {{\mathrm{Tr}}\left( {\left( {{\mathbf {W}}_2} + {\mathbf {S}}\right) {{\mathbf {H}}_2}} \right) /{{\widetilde{a}}_2}} \right) ^2}\leqslant 2\exp \left( {\widetilde{ x_3}}\right) \left( { x_3} - {\widetilde{ x_3}} + 1\right) - 2,$$
(27b)
$${\mathrm{Tr}}\left( {({{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {F}}}} \right) + 1\leqslant \exp \left( {\widetilde{ x_4}}\right) \left( { x_4} - {\widetilde{ x_4}} + 1\right) ,$$
(27c)
$$2\widetilde{t}t - {\widetilde{t}^2} + 1 \geqslant \exp \left( {y_3}\right) ,$$
(27d)
$$\begin{aligned}&\left[ {\begin{array}{*{20}{c}} {1 - \rho }&{}t \\ t&{}{{\mathrm{Tr}}\left( {({{\mathbf {W}}_1} + {{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {H}}_2}} \right) } \end{array}} \right] \succeq 0, \end{aligned}$$
(27e)
$${\mathrm{Tr}}\left( {({{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {F}}}} \right) + 1 \geqslant \exp ({ y_4}).$$
(27f)

where \({\widetilde{x}_3}\), \({\widetilde{x}_4}\), \({\widetilde{t}}\) and \({\widetilde{a}_2}\) are approximate values. In addition, \({\widetilde{a}_2}\) is updated after each iteration by the following formula

$$\begin{aligned} {\widetilde{a}_2} = \sqrt{{\mathrm{Tr}}\left( {({{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {H}}_2}} \right) /(1 - \rho )} \end{aligned}$$
(28)

Similar to C5, constraint C6 is approximated as

$$\exp \left( {{x_5} + {x_6} - {y_5} - {y_6}} \right) \leqslant {2^{ - {\gamma _2}}},$$
(29a)
$${\left( {{{\widetilde{a}}_3}(1 - \rho )} \right) ^2} + {\left( {{\mathrm{Tr}}\left( {{\mathbf {S}}{{\mathbf {H}}_2}} \right) /{{\widetilde{a}}_3}} \right) ^2}\leqslant 2\exp ({\widetilde{x}_5})({x_5} - {\widetilde{x}_5} + 1) - 2,$$
(29b)
$${\mathrm{Tr}}\left( {({{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {F}}}} \right) + 1 \leqslant \exp ({\widetilde{ x}_6})({{ x}_6} - {\widetilde{ x}_6} + 1),$$
(29c)
$$2\widetilde{q}q - {\widetilde{q}^2} + 1 \geqslant \exp ({y_5}),$$
(29d)
$$\begin{aligned}&\left[ {\begin{array}{*{20}{c}} {1 - \rho }&{}q \\ q&{}{{\mathrm{Tr}}\left( {({{\mathbf {W}}_2} + {\mathbf {S}}){{\mathbf {H}}_2}} \right) } \end{array}} \right] \succeq 0, \end{aligned}$$
(29e)
$${\mathrm{Tr}}\left( {{\mathbf {S}}{{\mathbf {F}}}} \right) + 1 \geqslant \exp ({y_6}).$$
(29f)

where \({\widetilde{x}_5}\), \({\widetilde{x}_6}\), \({\widetilde{q}}\) and \({\widetilde{a}_3}\) are approximate values. Moreover, \({\widetilde{a}_3}\) is updated after each iteration by the following formula

$$\begin{aligned} {\widetilde{a}_3} = \sqrt{{\mathrm{Tr}}\left( {{\mathbf {S}}{{\mathbf {H}}_2}} \right) /(1 - \rho )}. \end{aligned}$$
(30)

Therefore, P2 can be approximated as P3 as follows

$$\begin{aligned}&\mathbf {P}_3:{}\min \limits _{\rho ,\mathbf {W}_1,\mathbf {W}_2,\mathbf {S},{{x_{i,}}{y_i},u,t,q}}{} {{\mathrm{Tr}}\left( {\mathbf {W}_1}+{\mathbf {W}_2} + {\mathbf {S}} \right) } \nonumber \\&\quad {\mathrm {s.t.}} \mathrm {(18e),(18f)(19a),(19d), (20), (23), (25b),(26),(27), (29)} \end{aligned}$$
(31)

where \(i \in \left\{ {1,2,3,4,5,6} \right\}\). We can see that P3 is a standard convex optimization problem. According to the solution of P3, an iterative algorithm using SCA can be developed to solve P1, the specific solution process is shown in Table 1. In addition, if the solution \((\mathbf {W}_1^*,\mathbf {W}_2^*)\) yielded by SDR is rank-one, then the optimal beamforming vectors \(\mathbf {w}_1^*\) and \(\mathbf {w}_2^*\) are obtained by eigenvalue-decomposition of \(\mathbf {W}_1^*\) and \(\mathbf {W}_2^*\), respectively. Otherwise, the suboptimal solution can be yielded by using Gaussian randomization procedure [38].

Table 1 The SCA-based algorithm

Results and discussion

In this section, some simulation results are shown to demonstrate the performance of the proposed AN-aided cooperate SWIPT NOMA transmission scheme. Consider that two legitimate users and a passive eavesdropper (located outside of the “security zone”) are randomly deployed in an \(5m \times 6m\) area, and the BS is fixed at the edge with a coordinate \(\left( {0m,2.5m} \right)\). This scenario is suitable for an indoor sensor communication scenario. \(\tilde{h_1}\) is the standard Rayleigh fading coefficient. The distance-dependent path loss is modeled by \({P_L} = {10^{ - 3}}{d^{ - \alpha }}\), in which d and \(\alpha\) denote the Euclidean distance and path loss exponent, respectively. Using the Rician fading channel model, the downlink channels are modeled as

$$\begin{aligned} {\widetilde{\mathbf {h}}_2}= & {} \sqrt{\frac{K}{{1 + K}}} {\mathbf {h}}_2^{{\text {LOS}}} + \sqrt{\frac{1}{{1 + K}}} {\mathbf {h}}_2^{{\text {NLOS}}}\\ {\widetilde{\mathbf {f}}}= & {} \sqrt{\frac{K}{{1 + K}}} {\mathbf {f}}^{{\text {LOS}}} + \sqrt{\frac{1}{{1 + K}}} {\mathbf {f}}^{{\text {NLOS}}}\\ { g_1}= & {} \sqrt{\frac{K}{{1 + K}}} g_1^{{\text {LOS}}} + \sqrt{\frac{1}{{1 + K}}} g_1^{{\text {NLOS}}} \end{aligned}$$

where K denotes the Rician factor, \({\mathbf {h}}_2^{{\text {LOS}}}\), \({\mathbf {f}}^{{\text {LOS}}}\) and \(g_1^{{\text {LOS}}}\) are the line-of-sight (LOS) deterministic components, \({\mathbf {h}}_2^{{\text {NLOS}}}\), \({\mathbf {f}}^{{\text {NLOS}}}\) and \(g_1^{{\text {NLOS}}}\) are the Rayleigh fading components. The detailed simulation parameters are given in Table 2.

Table 2 Simulation parameters

We introduce some other transmission strategies, namely the AN-aided NOMA strategy, Non-AN SWIPT NOMA strategy and AN-aided time division multiple access (TDMA) strategy.

  • In the AN-aided NOMA strategy, the system still performs the NOMA strategy. However, SWIPT is not executed at user 2, i.e., the cooperative transmission stage is removed in the system. So, in this strategy, power splitting is not to be considered.

  • In the Non-AN SWIPT NOMA strategy, we do not add an AN to transmitted signal from the BS in the system. Therefore, AN covariance matrix optimizing is not to be considered in this strategy.

  • In the AN-aided TDMA strategy, the system performs the time division multiple access (TDMA) mode, i.e., the BS transmits information to user 1 or user 2 at different dynamic time intervals.

Figure 3 describes minimum transmission power of the BS with respect to the number iterations of the proposed algorithm. The minimum required secrecy rate of user 1 is set to be 0.5 Bits/s/Hz. The minimum required secrecy rate of user 2 is set to be 0.3 Bits/s/Hz, 0.5 Bits/s/Hz or 0.7 Bits/s/Hz, respectively. It can be found that only few iterations are required to achieve the minimum transmission power of the BS in all case, which indicates that the proposed algorithm is effective.

Fig. 3
figure3

The minimum transmission power of the BS versus the number of iterations

Figure 4 shows minimum transmission power of the BS with respect to secrecy rate of user 1 and secrecy rate of user 2, respectively. It can be found that in all cases, NOMA transmission strategies are superior to the TDMA transmission strategy, indicating the advantage of NOMA in improving the system SE. Moreover, our strategy obtains smaller transmission power of the BS than that of other NOMA strategies.

Fig. 4
figure4

The minimum transmission power of the BS versus the secrecy rates under different algorithms

Since user 1 far from BS while user 2 near from BS, their secrecy rates have different impacts on transmission power. Firstly, we analyze the influence of user 1’s secrecy rate on transmission power when the secrecy rate of user 2 was fixed. Again, we analyze the influence of user 2’s secrecy rate on transmission power when the secrecy rate of user 1 was fixed.

Figure 5 describes the minimum transmission power of the BS versus the secrecy rate of user 1, where the secrecy rate of user 2 is fixed by 0.5 Bits/s/Hz. Compared with that of other transmission strategies, the transmission power of the proposed AN-aided SWIPT NOMA strategy is the lowest, which demonstrates that the collaboration between SWIPT and NOMA is effective. It is also found that the power of the proposed scheme is slightly lower than that of the Non-AN NOMA SWIPT transmission strategy.

Fig. 5
figure5

The minimum transmission power of the BS versus the secrecy rate of user1

Figure 6 shows the minimum transmission power of the BS versus the secrecy rate of user 2, where the secrecy rate of user 1 is fixed by 0.5 Bits/s/Hz. We observe that the curves of the three NOMA transmission strategies are more smooth than that of TDMA transmission strategy. This indicates that the NOMA transmission strategies are robust with respect to the near user rate, i.e., under the same transmitted power constraint and far user secrecy rate, the NOMA can significantly increase the secrecy rate of the near user compared to that of TDMA. On the other hand, we find that gap of transmission power between AN-aided SWIPT NOMA strategy and AN-aided NOMA strategy decreases gradually with increasing secrecy rate requirement. Moreover, gap of transmission power between AN-aided and Non-AN strategies decreases gradually with increasing the secrecy rate. It clearly demonstrates that gain of user in BS caused by SWIPT-cooperative and AN-aided techniques decrease gradually with the increasing of secrecy rate.

Fig. 6
figure6

The minimum transmission power of the BS versus the secrecy rate of user 2

Figure 7 describes the minimum transmission power of the BS with respect to the number of BS’s antennas, where the secrecy rate of user 1 and the secrecy rate user 2 are fixed by 0.5 Bits/s/Hz. We can find that the transmission power of all methods reduces with the number of BS’s antenna. It is intuitive since the diversity gain of system can be enhanced by increasing the number of BS’s antennas. Compared with that of TDMA transmission scheme, the transmission power of other three NOMA schemes are lower. This shows that the NOMA transmission schemes are robust. Similar to Fig. 5, it is also found that the power of the proposed scheme is slightly lower than that of the Non-AN NOMA SWIPT transmission strategy.

Fig. 7
figure7

The minimum transmission power of the BS versus the number of BS’s antennas

Table 3 Relationship among PS ratio, secrecy rate of user 1, secrecy rate of user 2

Table 3 shows the relationship among the PS ratio, the secrecy rate of user 1 and the secrecy rate of user 2. It can be seen that the PS ratio decreases sharply with the user 2’s secrecy rate increasing, but increases slowly with the user 1’s secrecy rate increasing. This is because the power related to the information decoding of the user 2 is completely determined only by \(1-\rho\). Higher secrecy rate requirement of user 2, more power needs to be allocated. Different from that of user 2, the secrecy rate of user 1 is determined by two parts (the transmission signal of the BS and user 2), and thus is less sensitive to the PS ratio than that of user 2.

Conclusions

To promote the physical-layer security of the downlink in the MISO system, we propose an AN-aided cooperate SWIPT NOMA strategy. In the scene of one SIC-capable eavesdropper, we explore a cooperative transmission scheme based on multi-antenna, AN-aided, and PS techniques to minimize transmitted power of the BS while satisfying secrecy rate of all legitimate users. This NP-hard problem needs to jointly optimize the beamforming vector of multi-antenna, the covariance matrix of AN-aided and the PS ratio. Thus, we design a suboptimal algorithm by using SDR and SCA techniques to tackle the above NP-hard problem. Simulation studies verify the effectiveness of the proposed transmission scheme.

Availability of data and materials

Data sharing not applicable to this paper since no datasets were analyzed during current study.

Abbreviations

NOMA:

Non-orthogonal multiple access

SWIPT:

Simultaneous wireless information and power transfer

CSI:

Channel state information

SIC:

Successive interference cancellation

BS:

Base station

SDR:

Semidefinite relaxation

SCA:

Successive convex approximation

PS:

Power splitting

AN:

Artificial noise

5G:

Fifth-generation

OMA:

Orthogonal multiple access

SE:

Spectral efficiency

EE:

Energy efficiency

RF:

Radio frequency

EH:

Energy harvesting

TS:

Time-switching

CJ:

Cooperative jamming

SISO:

Single-input single-output

MISO:

Multiple-input single-output

MRC:

Maximal-ratio combination

AWGN:

Additive Gaussian white noise

SINR:

Signal-to-interference-noise-ratio

LOS:

Line-of-sight

TDMA:

Time division multiple access

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Acknowledgements

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Funding

This work was supported by the National Science Foundation Council of China (61771006, 61976080), Key research projects of university in Henan Province of China (19A413006, 20B510001), First-class Discipline Training Foundation of Henan University (2018YLTD04), the Programs for Science and Technology Development of Henan Province (192102210254), the Talent Program of Henan University (SYL19060110).

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Y.J was responsible for investigating the AN-aided beamforming design and power splitting control method that are suitable to be implemented. Z.H conceived and designed the study. D.X drafted the manuscript and revised it critically. All authors read and approved the final manuscript.

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Correspondence to Zhentao Hu.

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Jin, Y., Hu, Z., Xie, D. et al. Physical layer security transmission scheme based on artificial noise in cooperative SWIPT NOMA system. J Wireless Com Network 2021, 144 (2021). https://doi.org/10.1186/s13638-021-02020-3

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Keywords

  • SWIPT
  • NOMA
  • Power splitting (PS)
  • Secrecy communication
  • AN