Secure Beamforming Design in Relay-Assisted Internet of Things

TL;DR

This paper proposes a novel secure beamforming scheme for relay-assisted IoT systems under worst-case eavesdropper scenarios, optimizing secrecy rates with advanced convex optimization techniques.

Contribution

It introduces a cooperative NOMA secure transmission scheme with optimized beamforming and power control for IoT, considering both passive and active eavesdroppers.

Findings

Artificial noise-aided beamforming improves security against passive eavesdroppers.

Orthogonal-projection-based beamforming enhances security with active multi-antenna eavesdroppers.

Power control scheme effective for single antenna transmission scenarios.

Abstract

A secure downlink transmission system which is exposed to multiple eavesdroppers and is appropriate for Internet of Things (IoT) applications is considered. A worst case scenario is assumed, in the sense that, in order to enhance their interception ability all eavesdroppers are located close to each other, near the controller and collude to form joint receive beamforming. For such a system, a novel cooperative non-orthogonal multiple access (NOMA) secure transmission scheme for which an IoT device with a stronger channel condition acts as an energy harvesting relay in order to assist a second IoT device operating under weaker channel conditions, is proposed and its performance is analyzed and evaluated. A secrecy sum rate (SSR) maximization problem is formulated and solved under three constraints: i) Transmit power; ii) Successive interference cancellation; iii) Quality of Service. By considering both passive and active eavesdroppers scenarios, two optimization schemes are proposed to improve the overall system SSR. On the one hand, for the passive eavesdropper scenario, an artificial noise-aided secure beamforming scheme is proposed. Since this optimization problem is nonconvex, instead of using traditional but highly complex, bruteforce two-dimensional search, it is conveniently transformed into a convex one by using an epigraph reformulation. On the other hand, for the active multi-antennas eavesdroppers' scenario, the orthogonal-projection-based beamforming scheme is considered, and by employing the successive convex approximation method, a suboptimal solution is proposed. Furthermore, since for single antenna transmission the orthogonal-projection-based scheme may not be applicable a simple power control scheme is proposed.

Tables

Table 1. Table I: PARAMETERS AND THEIR MEANINGS

$N_s$	Number of Antennas of the Controller
$N_i$	Number of Antennas of the $D_i$
$N_e$	Number of Eavesdroppers
${𝐯}_i$	Transmit Beamforming Vector at Controller $S$
$s_i$	Transmitted Symbol for $D_i$
$\beta$	Power Splitting Ratio
$\tau$	Transmission Time Fraction
$𝐰$	Transmit Beamforming Vector at $D_1$
$𝐳$	Artificial Noise Vector
$P_s$	Total Transmit Power at Controller
$P_t$	Maximum Power Transmitted at $D_1$
$E$	Energy Harvested by $D_1$
$R_i$	Achievable Rate for Devices $D_i$, $i\in \{1,2\}$
$R_{sum}$	Secrecy Sum Rate for the IoT System
${\gamma }_i$	Received SINR at $D_i$
$\mu$	Mean of the Gaussian Noise Distribution
${\sigma }^2$	Noise Power

Equations

$${\mathbf{y}}_1^{[A]}=\sqrt{\left(1-\beta \right)}{\mathbf{H}}_{s1}\left({\mathbf{v}}_1{s}_1+{\mathbf{v}}_2{s}_2\right)+{\mathbf{n}}_1^{(1)},$$

$${\mathbf{y}}_2^{[A]}={\mathbf{H}}_{s2}\left({\mathbf{v}}_1{s}_1+{\mathbf{v}}_2{s}_2\right)+{\mathbf{n}}_2^{(1)},$$

$${\mathbf{y}}_e^{[A]}={\mathbf{G}}_{se}\left({\mathbf{v}}_1{s}_1+{\mathbf{v}}_2{s}_2\right)+{\mathbf{n}}_e^{(1)}.$$

$$\mathrm{SINR}{}_{1,s_2}^{[A]}=\frac{\left(1-\beta \right){\Vert {\mathbf{H}}_{s1}{\mathbf{v}}_2\Vert }^2}{\left(1-\beta \right){\Vert {\mathbf{H}}_{s1}{\mathbf{v}}_1\Vert }^2+{\sigma }^2},$$

$$\mathrm{SNR}{}_{1,s_1}^{[A]}=\frac{\left(1-\beta \right){\Vert {\mathbf{H}}_{s1}{\mathbf{v}}_1\Vert }^2}{{\sigma }^2}.$$

$${\mathrm{SINR}}_{2,s_2}^{[A]}=\frac{{\Vert {\mathbf{H}}_{s2}{\mathbf{v}}_2\Vert }^2}{{\Vert {\mathbf{H}}_{s2}{\mathbf{v}}_1\Vert }^2+{\sigma }^2}.$$

$$E=\beta \left({\Vert {\mathbf{H}}_{s1}{\mathbf{v}}_1\Vert }^2+{\Vert {\mathbf{H}}_{s1}{\mathbf{v}}_2\Vert }^2\right)\tau ,$$

$$P_t=\frac{E}{1-\tau }=\beta \left({\Vert {\mathbf{H}}_{s1}{\mathbf{v}}_1\Vert }^2+{\Vert {\mathbf{H}}_{s1}{\mathbf{v}}_2\Vert }^2\right).$$

$$\mathbf{x}=\mathbf{w}{s}_2+\mathbf{z},$$

$${\mathbf{y}}_2^{[B]}={\mathbf{H}}_{12}\mathbf{x}+{\mathbf{n}}_2^{(2)},$$

$${\mathbf{y}}_e^{[B]}={\mathbf{G}}_{1e}\mathbf{x}+{\mathbf{n}}_e^{(2)},$$

$${\mathrm{SINR}}_{2,s_2}^{[B]}=\frac{{\Vert {\mathbf{H}}_{12}\mathbf{w}\Vert }^2}{{\Vert {\mathbf{H}}_{12}\mathbf{z}\Vert }^2+{\sigma }^2}.$$

$${\mathrm{SINR}}_{2,s_2}={\mathrm{SINR}}_{2,s_2}^{[A]}+{\mathrm{SINR}}_{2,s_2}^{[B]}.$$

$${\mathbf{y}}_e={\mathbf{H}}_e\mathbf{s}+{\mathbf{n}}_e,$$

$$\displaystyle\mathbf{y}_{e}=\left[\begin{array}[]{c}\mathbf{y}_{e}^{[A]}\\ \mathbf{y}_{e}^{[B]}\end{array}\right],\mathbf{s}=\left[\begin{array}[]{c}s_{1}\\ s_{2}\end{array}\right],$$

$$\displaystyle\mathbf{H}_{e}=\left[\begin{array}[]{cc}\mathbf{G}_{se}\mathbf{v}_{1}&\mathbf{G}_{se}\mathbf{v}_{2}\\ \mathbf{0}_{N_{e}\times 1}&\mathbf{G}_{1e}\mathbf{w}\end{array}\right],$$

$$\displaystyle\mathbf{n}_{e}=\left[\begin{array}[]{c}\mathbf{n}_{e}^{(1)}\\ \mathbf{G}_{1e}\mathbf{z}+\mathbf{n}_{e}^{(2)}\end{array}\right].$$

$$R_e=I\left(s_i;{\mathbf{y}}_e\right)=\frac{1}{2}\log \left|{\mathbf{I}}_{N_e}+{\mathbf{H}}_e{\mathbf{H}}_e^H{\mathbf{Q}}_e^{-1}\right|=\frac{1}{2}\log$$

$$\left(1+\frac{\mathrm{Tr}\left({\mathbf{G}}_{\mathrm{se}}\left(\stackrel{[}{i}=1]2\sum {\mathbf{v}}_i{\mathbf{v}}_i^{\mathrm{H}}\right){\mathbf{G}}_{\mathrm{se}}^{\mathrm{H}}+{\mathbf{G}}_{1e}\mathbf{w}{\mathbf{w}}^{\mathrm{H}}{\mathbf{G}}_{1e}^{\mathrm{H}}\right)}{\mathrm{Tr}\left({\mathbf{Q}}_e\right)}\right),$$

$$R_1=I\left(s_1;{\mathbf{y}}_1\right)=\frac{1}{2}\log \left(1+\mathrm{SN}{\mathrm{R}}_{1,{\mathrm{s}}_1}\right),$$

$$R_2=I\left(s_2;{\mathbf{y}}_2\right)=\frac{1}{2}\log \left(1+\mathrm{SIN}{\mathrm{R}}_{2,{\mathrm{s}}_2}\right),$$

$$R_{sum}={\left[\stackrel{[}{i}=1]2\sum R_i-R_e\right]}^{+}.$$

$$\underset{{\mathbf{v}}_1,{\mathbf{v}}_2}{\max }$$

$$s.t.$$

$${\Vert {\mathbf{v}}_1\Vert }^2+{\Vert {\mathbf{v}}_2\Vert }^2\le P_s,{\Vert \mathbf{w}\Vert }^2+{\Vert \mathbf{z}\Vert }^2\le P_t,$$

$$\underset{{\mathbf{V}}_i⪰0,\mathbf{W}⪰0,\beta }{\max }$$

$$s.t.$$

$$\left(1+\frac{\mathrm{Tr}\left({\mathbf{W}}_2^2\right)}{\mathrm{Tr}\left({\mathbf{W}}_2^1\right)+{\sigma }^2}+\frac{\mathrm{Tr}\left({\mathbf{W}}_{12}\right)}{{\sigma }^2}\right)\ge r_2,$$

$$\frac{\left(1-\beta \right)\mathrm{Tr}\left({\mathbf{W}}_1^2\right)}{{\sigma }^2+\left(1-\beta \right)\mathrm{Tr}\left({\mathbf{W}}_1^1\right)}\ge \gamma ,$$

$$\frac{\mathrm{Tr}\left({\mathbf{W}}_2^2\right)}{\mathrm{Tr}\left({\mathbf{W}}_2^1\right)+{\sigma }^2}+\frac{\mathrm{Tr}\left({\mathbf{W}}_{12}\right)}{{\sigma }^2}\ge \gamma ,$$

$$\mathrm{Tr}\left(\mathbf{W}\right)+\mathrm{Tr}\left(\mathbf{\Sigma }\right)\le \beta \mathrm{Tr}\left(\stackrel{[}{i}=1]2\sum {\mathbf{W}}_1^i\right),$$

$$\mathrm{Tr}\left({\mathbf{V}}_1\right)+\mathrm{Tr}\left({\mathbf{V}}_2\right)\le P_s.$$

$${\theta }_1^2\ge \left(r_1-1\right){\sigma }^2,$$

$$\displaystyle\left[\begin{array}[]{cc}(1-\beta)&\theta_{1}\\ \theta_{1}&\mathrm{Tr}(\mathbf{W}_{1}^{1})\end{array}\right]\succeq\mathbf{0}.$$

$$2{\theta }_1^{(n)}{\theta }_1-({\theta }_1^{(n)}{)}^2\ge \left(r_1-1\right){\sigma }^2,$$

$$2{\psi }_1^{(n)}{\psi }_1-{\left({\psi }_1^{(n)}\right)}^2\ge D+{\sigma }^2\left(r_2-1\right),$$

$$\displaystyle\left[\begin{array}[]{cc}\frac{\mathrm{Tr}\left(\mathbf{W}_{12}\right)}{\sigma^{2}}&\psi_{1}\\ \psi_{1}&\mathrm{Tr}\left(\mathbf{W}_{2}^{1}\right)\end{array}\right]\succeq\mathbf{0},$$

$$\left(1-\beta \right)\mathrm{Tr}\left({\mathbf{W}}_1^2-\gamma {\mathbf{W}}_1^1\right)\ge \gamma {\sigma }^2.$$

$$2{\varphi }_1^{(n)}{\varphi }_1-({\varphi }_1^{(n)}{)}^2\ge \gamma {\sigma }^2,$$

Full text

I Introduction

The Internet of Things (IoT) is rapidly evolving as a complex platform connecting a very large number of communication devices, e.g. sensors, controllers and actuators [1]. However, achieving the required ubiquitous connectivity required for such IoT based communication systems becomes a vital and challenging task mainly because of the constraint of scarce bandwidth. In this context, nonorthogonal multiple access (NOMA) is advocated as a promising technique to support pervasive connectivity, so that the spectral efficiency of IoT systems can be significantly enhanced [2, 3, 4, 5, 6]. The key feature of NOMA is to implement the multiple access (MA) in the power domain while the time/frequency/code resources can simultaneously be shared by all users. Moreover, as compared to orthogonal MA (OMA), NOMA can achieve a better balance between sum rate and user fairness [7]. At the same time, as the wireless broadcast nature of radio propagation makes IoT communications susceptible to eavesdropping attacks, their security aspects need to be very carefully considered when designing such systems. In the past, conventional encryption techniques have been applied to prevent eavesdroppers from recovering the secret messages [8, 9]. However, such encryption-based techniques have inherent difficulties and vulnerabilities dealing with secret key management [1]. Fortunately, physical layer security (PLS) has shown a great deal of potential to more accurately distinguish the signals belonging to the legitimate receiver or the eavesdropper [10, 11, 12]. Unlike other encryption-based techniques, PLS techniques take advantage of the physical characteristics of wireless medium to ensure information-theoretic security independent of the eavesdropper’s computing capabilities [13, 14].

A. Motivation and Contributions

In the past, several PLS techniques based on the OMA secure transmission protocol, including multi-antennas techniques [15, 16], artificial noise (AN) [17, 18, 19, 20, 21, 22, 23] and cooperative jamming (CJ) [24, 25, 26] have been proposed. Aiming to further improve the secrecy of the fifth generation (5G) systems, Tian et al. [2] combined NOMA with multi-antennas techniques to optimize the secrecy sum rate (SSR) of 5G wireless system for applications where the channel state information (CSI) of eavesdroppers is available. In another approach, Hu et al. [1] have combined the AN assisted multi-antennas transmission technique with CJ in order to reduce the effects of the passive non-colluding eavesdroppers for the IoT downlink. However, since many IoT device transmitters have limited radio frequency (RF) power, allocating some power for AN or jamming signal may not be appropriate since this will restrict the coverage range of secure transmissions.

In order to fill this gap, in this paper a novel relay-assisted secure transmission scheme is proposed designed for energy-constrained IoT based communication systems, where one controller emits secret messages to two classes of devices operating in the presence of multiple colluding eavesdroppers. These IoT devices have diversified quality of service (QoS) requirements, and the channel conditions among them are quite different in the sense that the channel operating conditions for $D_{1}$ are much better then the channel conditions for $D_{2}$. In order to guarantee the confidentiality of data transmission and the QoS requirement of $D_{2}$, $D_{1}$ acts as an energy harvesting (EH) relay to help $D_{2}$. Assuming that the locations of all eavesdroppers are close to the controller, this worst-case positioning scheme will increase the probability of interception of the information signal. For this energy-constraint IoT system, a novel secure cooperative transmission scheme is proposed and its performance is analyzed and evaluated. Assuming that the CSI of the eavesdroppers is available, two operational scenarios are considered, namely the passive eavesdroppers and active eavesdroppers scenarios, for which two optimization. For maximizing the SSR of the IoT system under consideration under transmit power, QoS and successive interference cancellation (SIC) constraints. Within this framework, the primary contributions of this paper are summarized as follows:

• •

A cooperative simultaneous wireless information and power transfer (SWIPT) secure transmission protocol which takes into account the diversified QoS requirements of different IoT users, is proposed. Unlike secure transmission designs without SWIPT[1, 2], by employing the SWIPT-aided transmission protocol, device 1 forwards the information bearing signal and AN without introducing additional energy consumption.

• •

For the passive eavesdroppers scenario, an AN-aided secure beamforming scheme which jointly optimizes the transmit beamforming vectors, power splitting (PS) ratio and AN beamforming, is proposed. Since this optimization problem is non-convex, it is conveniently transformed into a convex form through the use of a epigraph reformulation (ER), instead of using the two-dimensional search [27] that requires high computational complexity.

• •

For the active eavesdroppers scenario, an orthogonal-projection-based secure beamforming design scheme which ensures the confidentiality of data transmission is proposed. As this challenging optimization problem is also non-convex, the NP-hard problem is reformulated into a trackable convex problem. Furthermore, for single antenna transmitters, the orthogonal-projection-based beamforming design problem simplifies to a power allocation problem which should not be solved via the orthogonal projection based method. Instead, a power control scheme is proposed through which via a transformation of the objective function and constraints the non-convex problem can be efficiently handled.

B. Related Previous Research

There has been recently a lot of interest from the information-theoretic point of view, to exploit PLS techniques in order to improve the security of wireless communication systems [21, 23, 24]. For example, considering multiple-input single-output channels (SISO), the cases of both direct transmission and CJ with a helper have been investigated under the assumption that CSI for the wiretap links is imperfect [22]. For multiple-input multiple-output (MIMO) channels, [25] proposed a CJ-aided SSR optimization scheme under the assumption that the power of the system is sufficient. Furthermore, [23, 26] have focused on studying the confidential information transmission of relay systems with the PLS techniques-aided. The secure transmission schemes introduced in these two papers are based on the assumption that available power of the considered relay systems is sufficient. More recently in [21], a robust secure beamforming design for MIMO two-way relaying system based on the AN and physical layer network coding has been introduced. Various performance evaluation results presented in [21] have shown that such beamforming design will further improve the security aspects of the two-way relaying system.

It is underlined that the above mentioned papers ([21, 23, 24, 22, 25, 26]) investigate various PLS issues encountered in different cooperative wireless communication systems without considering possible energy-limited constraints. Furthermore, these papers have not investigated the security transmission problem in connection with IoT type of wireless communication systems. On this topic, [1, 9, 14], different PLS-based secure transmission schemes have been presented for IoT systems. However these papers have not considered the energy-limited feature of IoT systems when designing the secure transmission beamforming.

To this end, it is necessary to solve the security problem of the energy-constrained IoT systems with EH-assisted. In this paper SWIPT is considered as an EH technique where the IoT transmitter forwards information signal and AN via the harvested energy only. Our work is different from above works in the following aspects: i) [1] investigates the secure transmission problem of IoT system, from an information-theoretic point of view, and only the CJ technique is used so that the coverage range of secure transmissions couldn’t be guaranteed; ii) [9] considers a variety of eavesdropping scenarios when designing the secure transmission protocols, but colluding eavesdroppers cases are not explored; iii) [14] considers a secure transmission for IoT under eavesdropper collusion. Although the scheme proposed in [14] is more general than that the schemes presented in [1] and [9], it has not considered secure beamforming design nor the energy-constrained problem. Note in our research here we not only provide secure beamforming designs, but also the energy-constrained problem is considered by combining the PLS technique with SWIPT.

C. Notation and Organization

The remainder of this paper is organized as follows: In Section II, we describe the system model and problem formulation. In Section III, AN-aided transmission beamforming design scheme is presented when eavesdroppers’ CSI is unavailable. In Section IV, by taking both the single-antenna and multiple-antenna scenarios into account, two SSR optimization schemes are proposed when the eavesdropper’s CSI is available. The performance evaluation results and discussion are provided in Section IV. The conclusions of the paper can be found in Section VI.

Boldface lowercase and uppercase letters denote vectors and matrices, respectively. The Hermitian transpose, Frobenius norm, and trace of the matrix $\mathbf{A}$ are denoted as $\mathbf{A}^{H}$, $\left\|\mathbf{A}\right\|$, and $\mathrm{Tr}(\mathbf{A})$, respectively, whereas rank$\left(\mathbf{A}\right)$ and $|\mathbf{A}|$ stand for the rank and the determinant of the matrix $\mathbf{A}$, respectively. By $\mathbf{A}\succeq\mathbf{0}$ or $\mathbf{A}\succ\mathbf{0}$ , it is meant that the matrix $\mathbf{A}$ is positive semidefinite or positive definite, respectively. $\mathbf{I}_{M}$ is the identity matrix of size $M\times M$. $\mathbb{C^{N\times M}}$ denotes an $N\times M$ complex matrix. $\mathrm{diag}\left(\mathbf{A}\right)$ is a diagonal matrix with the entries of matrix $\mathbf{A}$ as its diagonal entries. $\left[\cdot\right]^{+}\triangleq\mathrm{max}\left\{0,\,\cdot\right\}$. $|\cdot|$ and $\mathbb{E\left\{\cdot\right\}}$ denote the absolute value and the statistical expectation, respectively. $\succeq$ represents the property of semidefinite. $\mathcal{CN}\left(\mu,\sigma^{2}\right)$ denotes the circularly symmetric complex Gaussian distribution with mean $\mu$ and variance $\sigma^{2}$. $I\left(.;.\right)$ is the mutual information.

Additionally, a list of the most important system parameters and their meaning can be found in Table I.

II System model

As illustrated in Fig. 1, an IoT downlink secure communication system consisting of a controller, $S$, equipped with $N_{s}$-antenna and two user devices, $D_{i}(i\in\{1,2\})$111From now on, and unless otherwise specified, the index i will always takes values from the alphabet {1,2}. each equipped with $N_{i}$ antennas is considered. $S$ transmits confidential information to the $D_{i}$ in the presence of $N_{e}$ colluding eavesdroppers, Eves222It is noted that, although the proposed system model considers only two devices as a pair of users [28], this pairing can be generalized to multiple users following the methodology we have proposed in [29]. However, this extension is beyond the scope of our current research work and as such will not be considered here..

It is also assumed that $D_{1}$, which operates under better channel conditions, is used for receiving rather short control signal data. $D_{2}$, which operated under weak channel conditions, which is a device which deals with some background tasks, such as downloading multimedia files. As illustrated in Fig. 1, the Eves $G_{1e}$ are located close to each other and all of them are close to S. Clearly, such configuration will lead to higher probabilities of interception for the transmitted information signal.

To ensure the high targeted secrecy rate of $D_{2}$, $D_{1}$ acts as an EH relay to forward the information-bearing signal to $D_{2}$. More specifically, the received signal at $D_{1}$ is split into two parts: one for energy harvesting and the other for information decoding so that two stages will be involved in the cooperative NOMA secure transmission. At $D_{2}$ the two signals received are combined by a maximal ratio combining (MRC) diversity scheme. It is assumed that all the fading channels shown in Fig. 1 are independent quasi-static fading channels, which remain constant in one time slot but vary independently from one time slot to another. Next the detailed operation of the proposed communication system will be presented.

A. Direct Transmission Phase A

As illustrated in Fig. 1, during the $1^{st}$ stage of communication, S transmits over the channels $H_{s1}$ and $H_{s2}$ the information signals $s_{1}$ and $s_{2}$ which, after beamforming, are received by $D_{1}$ and $D_{2}$ as signals $y_{1}^{[A]}$ and $y_{2}^{[A]}$, respectively. These beamformed signals are also intercepted through the $G_{se}$ channel by the Eves, as $y_{e}^{[A]}$.

$D_{1}$ performs EH by employing a SWIPT receiver in order to perform the necessary PS. Noting that the received signals are also corrupted by independent additive white Gaussian noise (AWGN), they can be mathematically expressed as:

[TABLE]

In (1), $s_{i}$ is the transmitted information symbol for $D_{i}$, which has unity energy, i.e. $\mathbb{E}\left\{|s_{i}|^{2}\right\}=1;$ $\mathbf{v}_{i}\in\mathbb{C}^{N_{s}\times 1}$ is the transmit beamforming vector at $S$; $\mathbf{H}_{si}\in\mathbb{C}^{N_{i}\times N_{s}}$ and $\mathbf{G}_{se}\in\mathbb{C}^{N_{e}\times N_{s}}$ are the channel responses from $S$ to $D_{i}$ and Eves, respectively; $\beta\in\left[0,1\right]$ is the PS ratio; $\mathbf{n}_{i}^{(1)}\sim\mathcal{CN}\left(0,\sigma_{i}^{2}\mathbf{I}_{N_{i}}\right)$ and $\mathbf{n}_{e}^{(1)}\sim\mathcal{CN}\left(0,\sigma_{e}^{2}\mathbf{I}_{N_{e}}\right)$ are the additive white complex Gaussian noise vectors at $D_{i}$ and Eves, respectively. For simplicity and without any loss of generality, it is assumed that $\sigma_{1}^{2}=\sigma_{2}^{2}=\sigma_{e}^{2}=\sigma^{2}$. Since the channel conditions for both $D_{1}$ and Eves are better than that of $D_{2}$, clearly $\left\|\mathbf{H}_{s2}\right\|^{2}\leq\left\|\mathbf{H}_{s1}\right\|^{2},$ and $\left\|\mathbf{H}_{s2}\right\|^{2}\leq\left\|\mathbf{G}_{se}\right\|^{2}.$ The received signals $y_{1}^{[A]}$ and $y_{2}^{[B]}$ are decoded by employing the following SIC principles. For $D_{1}$, as it assumed that it operates under good channel conditions, it will first detect the message $s_{2}$, which is intended for $D_{2}$, and then eliminate it from the combined signal. On the contrary, $D_{2}$, as it operates under bad channel conditions, it will not try to eliminate $s_{1}$, which is intended for $D_{1}$, from the combined signal. Thus, from (1a), the received signal-to-interference-plus-noise-ratio (SINR) at $D_{1}$ for detecting $s_{2}$ can be mathematically expressed as

[TABLE]

which should be larger than or equal to a predefined threshold so that the QoS constraint at $D_{1}$ can be satisfied. Then,for the decoding of $s_{1}$ at $D$, the corresponding received signal-to-noise-ratio (SNR) is given by

[TABLE]

From (1b), the SINR at $D_{2}$ to detect $s_{2}$ becomes

[TABLE]

Furthermore, the energy harvested by $D_{1}$ can be formulated as [30]

[TABLE]

where $\tau=\frac{1}{2}$ is the transmission time fraction for the first phase, and the two phases have the same transmission duration. It is assumed that the energy harvested by $D_{1}$ is mainly used for transmitting information and AN. Therefore, the maximum power transmitted at $D_{1}$ is given by [31]

[TABLE]

B. Cooperative Transmission Phase B

During the 2nd phase of transmission, $s_{2}$ is beamformed by $\mathbf{w}\in\mathbb{C}^{N_{1}\times 1}$ and broadcast together with AN to $D_{2}$ with the harvested energy. Thus, the signal transmitted by $D_{1}$ can be expressed as

[TABLE]

where $\mathbf{z}$ is the AN beamforming vector generated by $D_{1}$, whose distribution follows $\mathcal{CN}(0,\mathbf{\boldsymbol{\Sigma}})$ with $\boldsymbol{\Sigma}\succeq\mathbf{0}.$ Then, the observations at $D_{2}$ and at the Eves can be expressed as

[TABLE]

respectively, where $\mathbf{H}_{12}\in\mathbb{C}^{N_{2}\times N_{1}}$ and $\mathbf{G}_{1e}\in\mathbb{C}^{N_{e}\times N_{1}}$ are the channel responses from $D_{1}$ to $D_{2}$ and to the Eves, respectively. $\mathbf{n}_{2}^{(2)}\sim\mathcal{CN}\left(0,\sigma^{2}\mathbf{I}_{N_{2}}\right)$ and $\mathbf{n}_{e}^{(2)}\sim\mathcal{CN}\left(0,\sigma^{2}\mathbf{I}_{N_{e}}\right)$ are the additive white complex Gaussian noise vectors at $D_{2}$ and Eves, respectively. Consequently, the SINR at $D_{2}$ to detect $s_{2}$ can be written as

[TABLE]

Thus, the combined SINR at $D_{2}$ becomes

[TABLE]

As previously noted, $s_{2}$ is jointly detected at $D_{2}$ from the signals received from $S$ and $D_{1}$ by employing MRC diversity reception.

From (1c) and (8b), the received signal of Eves for the two phases can be given by

[TABLE]

where

[TABLE]

From (11), the information sum rate leaked to the Eves can be written as [15]

[TABLE]

where $\mathbf{Q}_{e}=\mathbf{n}_{e}\mathbf{n}_{e}^{H}=\mathrm{diag}\left(\sigma^{2}\mathbf{I}_{N_{e}},\>\sigma^{2}\mathbf{I}_{N_{e}}+\mathbf{G}_{1e}\boldsymbol{\Sigma}\mathbf{G}_{1e}^{H}\right)$, $i\in\left\{1,2\right\},$ and the factor $\frac{1}{2}$ is introduced since the messages are transmitted in two consecutive phases [32]. Note that the minimum-mean-square-error criterion and SIC have been employed by Eves. The achievable rates of $D_{1}$ and $D_{2}$ are given by

[TABLE]

respectively. As pointed out it [32], it is very difficult to obtain the secrecy capacity region of the downlink wireless systems. Alternative, the rate difference between the legitimate sum rate and the information sum rate leaked to the Eves (i.e., $R_{e}$) can be computed as the secure performance measure. In this case, the SSR can be expressed as [2]

[TABLE]

To improve the security of the downlink for the cooperative communication system under consideration, an SSR maximization problem is formulated. The transmit power constraint at $S$, the SIC constraint at $D_{1}$ and the EH constraint should be satisfied in the SSR maximization problem. The EH constraint is that the achievable power for transmitting information bearing signal and AN is smaller than or equal to the energy harvested by $D_{1}$. According to the result given in [7], a higher sum rate can be obtained if $S$ allocates more power for the information-bearing signal $s_{1}$. However, such an approach is not applicable in the optimization problem consider here for which the user fairness and high targeted secrecy rate at $D_{2}$ should be ensured [7]. With the above in mind, the optimization problem considered in this paper can be formulated as

[TABLE]

where $P_{s}$ is the transmit power constraint at $S$, $\left\|\mathbf{w}\right\|^{2}$ and $\left\|\mathbf{z}\right\|^{2}$ are the allocated power for information transmission and AN, respectively. Note that (16b) indicates that the received SINR to decode $s_{2}$ should be no less than the SINR threshold $\gamma$, as (16b) relates to the SIC constraint at $D_{1}$ to ensure the necessary QoS decoding performance of $D_{2}$.

Next the NP-hard problem of (16) will be solved by optimizing $\mathbf{v}_{1},\mathbf{v}_{2}$, $\mathbf{w}$ as well as $\beta$ for the cases of passive and active Eves (see Sections III and IV, respectively).

III AN-aided secure beamforming design (ASBD) for the passive eavesdroppers case

In this section, it is assumed that the passive Eves’ CSI is not available at the transmitters $D_{1}$ and $S$. For example this occurs when the eavesdropping nodes in IoT systems are passive or malicious. Since in this case even the location of the Eves is hard to obtain [16], and thus obtaining CSI will be even more difficult, a AN-aided beamforming design scheme is proposed.

Zero-Forcing (ZF) Constraint on AN

Since $D_{1}$ has no CSI for the Eves, i.e., $D_{1}$ doesn’t know $\mathbf{G}_{1e}$, in order to eliminate the interference at $D_{2}$, a ZF condition on the AN beamforming is applied [21, 23]. In other words, the AN beamforming is designed so that it steers the signal into the null space of $\mathbf{H}_{12}$, so that $\mathbf{H}_{12}\mathbf{z}=\mathbf{0}$. In this way, $D_{1}$ cannot transmit AN to interfere the Eves selectively under the Zero Forcing constraint [33]. Hence, the AN $\mathbf{z}$ is in the form of $\mathbf{z}=\mathbf{H}_{\perp}\mathbf{n},$ where $\mathbf{H}_{\perp}=\mathbf{I}_{N_{2}}-\mathbf{H}_{12}\left(\mathbf{H}_{12}^{H}\mathbf{H}_{12}\right)^{-1}\mathbf{H}_{12}^{H}$ is the projection matrix onto the null space of $\mathbf{H}_{12}$. Note that the components of $\mathbf{n}$ are independent and identically distributed (iid) Gaussian variables, which follow $\mathcal{CN}\left(0,\sigma_{z}^{2}\right)$ so that the spatial covariance of AN can be expressed as $\boldsymbol{\Sigma}=\sigma_{z}^{2}\mathbf{H}_{\perp}\mathbf{H}_{\perp}^{H}\succeq\mathbf{0}$.

The SSR $R_{sum}$ is maximized only when $R_{e}$ is minimized. Thus, in order to minimize $R_{e}$, the power allocated for AN should be made as much as possible, under the EH and SIC constraints at $D_{1}$, the transmit power constraint at $S$ and QoS constraint at $D_{i}$. According to the semidefinite relaxation (SDR) technique, let $\mathbf{V}_{i}=\mathbf{v}_{i}\mathbf{v}_{i}^{H},\,i\in\left\{1,2\right\},\mathbf{W}=\mathbf{w}\mathbf{w}^{H}$ and drop rank-one constraints $\mathrm{rank}\left(\mathbf{V}_{i}\right)=1,\mathrm{\,rank}\left(\mathbf{W}\right)=1.$ Thus, the secure beamforming problem is reformulated as

[TABLE]

where $\mathbf{W}_{1}^{i}=\mathbf{H}_{s1}\mathbf{V}_{i}\mathbf{H}_{s1}^{H},$ $\mathbf{W}_{2}^{i}=\mathbf{H}_{s2}\mathbf{V}_{i}\mathbf{H}_{s2}^{H},\,i\in\left\{1,2\right\}$, $\mathbf{W}_{12}=\mathbf{H}_{12}\mathbf{W}\mathbf{H}_{12}^{H}$, $r_{i}$ is the predefined threshold of achievable ergodic rate of $D_{i}$, and $\frac{1}{2}\mathrm{log}(\cdot)$ is not included in (17b) and (17c) since the logarithmic function is a monotonically increasing function. It is noted that the optimization problem (17) is non-convex due to the non-convex constraints (17b)-(17f). Consequently, these non-convex constraints will be transformed into equivalent convex forms based on the idea of SCA, which can be used to iteratively approximate a non-convex optimization problems by an equivalent convex problem [34].

Transformation of (17b)

Based on the SCA method and the ER, (17b) can be replaced by the following two constraints

[TABLE]

Lemma 1**.**

For a standard convex function $g(x)$ and a concave function $f(x)$, if the constraint $g(x)\leq f(x)$ exists, then the constraint is convex [35].

Based upon the following Lemma, it is clear that (18a) is non-convex. Therefore, the first order Taylor expansion (FOTE) can be utilized to approximate (18a) with the following convex function

[TABLE]

where $\theta_{1}^{(n)}$ is the value of variable $\theta_{1}$ at the $n$-th iteration, i.e. the superscript $(n)$ denotes the point obtained during the $n$-th iteration. Note that the constraint (17b) is now replaced by two convex constraints, i.e., the linear matrix inequality constraint (18d) and the convex constraint (19).

Transformation of (17c)

Similarly, based on ER and FOTE, the non-convex constraint (17c) can be approximated by the following convex functions

[TABLE]

where $D=\mathrm{Tr}\left(\mathit{r}_{2}\mathbf{W}_{2}^{1}-\mathbf{W}_{2}^{1}-\mathbf{W}_{2}^{2}-\mathbf{W}_{12}\right)$.

Transformation of (17d)

The non-convex constraint (17d) is equivalently formulated as

[TABLE]

As (21) is still a non-convex constraint, ER and FOTE are employed to yield the following approximate convex constraint

[TABLE]

[TABLE]

Transformation of (17e)

Similarly, the non-convex constraint (17e) is converted to the following convex form

[TABLE]

[TABLE]

Transformation of (17f)

In the same manner, the non-convex constraint (17f) can be approximated by

[TABLE]

[TABLE]

Thus, the optimization problem (17) has been recast as

[TABLE]

[TABLE]

which is a semidefinite programming and its solution $(\mathbf{V}_{1}^{*},\mathbf{V}_{2}^{*},\mathbf{W}^{*},\boldsymbol{\Sigma}^{*})$ can be obtained by off-the-shelf optimization solvers, e.g., SeDuMi or Yalmip[36].

The convex problem (25) is solved in an iterative manner starting with the initial values of $\left(\theta_{1}^{\left(0\right)},\psi_{1}^{\left(0\right)},\phi_{1}^{\left(0\right)},\omega_{1}^{\left(0\right)},\varphi_{1}^{(0)}\right),$ as presented in Algorithm 1. During each iteration, $\left(\theta_{1}^{\left(n\right)},\psi_{1}^{\left(n\right)},\phi_{1}^{\left(n\right)},\omega_{1}^{\left(n\right)},\varphi_{1}^{(n)}\right)$ is updated based on the previously obtained solution until the SSR gap between two successive iterations is less than a predefined accuracy $\epsilon_{1}$. Moreover, based on Lemma 3.1 of [37], the solution $(\mathbf{V}_{1}^{*},\mathbf{V}_{2}^{*},\mathbf{W}^{*})$ yielded by SDR is rank-one. Then the beamforming vectors $\mathbf{v}_{1},\mathbf{v}_{2}$ and $\mathbf{w}$ are obtained by eigenvalue decomposition of $\mathbf{V}_{1},\mathbf{V}_{2}$ and $\mathbf{W}$, respectively.

Finally, the information rate leaked to Eves can be shown in (26) (in the top of the next page). Substituting (26) into (15) and replacing $(\mathbf{v}_{1},\mathbf{v}_{2},\mathbf{w})$ with $(\mathbf{v}_{1}^{*},\mathbf{v}_{2}^{*},\mathbf{w}^{*})$, the SSR of the IoT system under consideration can be computed.

IV Secure beamforming design for the active eavesdroppers case

When active Eves are present, their CSI can be estimated by $S$ and $D_{1}$ through leakage from the Eves’ receiver radio frequency (RF) frontend [16]. Thus, the AN-aided transmission beamforming design proposed in Section III may not be the best solution because of the presence of active Eves. In light of this, an orthogonal-projection-based transmission beamforming design is proposed for the SSR maximization problem defined in (16). For this scheme it is noted that the number of antennas at $D_{1}$ should be more than that of the Eves (i.e., $N_{1}>N_{e}$). For the case when $S$ and $D_{i}$ have single antennas, a simple power control scheme which optimizes the SSR is also proposed.

A. Multi-Antennas Configuration

The main idea behind the new approach can be explained as follows. Firstly, by using the available CSI of the Eves, a new design for the transmit beamforming $\mathbf{w}$ is proposed, which will deteriorate the quality of the signals received by the Eves due to the addition of AN. This design will be termed as Orthogonal-Projection-Based Secure Beamforming Design (OSBD) for Multi-Antennas Case. On that basis, by letting AN $\mathbf{z}=\mathbf{0}$, the transmitted signal from $D_{1}$ during the second phase becomes

[TABLE]

The observations at $D_{2}$ and Eves can be expressed as

[TABLE]

[TABLE]

respectively, where $\mathbf{w}$ lies in the null space of Eves’ channel $\mathbf{G}_{1e}$, i.e., $\mathbf{G}_{1e}\mathbf{w}=\mathbf{0}$. Therefore, $\mathbf{w}\mathbf{w}^{H}=\alpha\left(\frac{\mathbf{I}_{N_{1}}-\mathbf{Q}_{1e}}{\left\|\mathbf{I}_{N_{1}}-\mathbf{Q}_{1e}\right\|}\right)$ and $\mathbf{Q}_{1e}=\mathbf{G}_{1e}^{H}(\mathbf{G}_{1e}^{H}\mathbf{G}_{1e})^{-1}\mathbf{G}_{1e}$, where $\alpha\in\left[0,1\right]$ is a scale factor determining the power invested on transmit beamforming. The received SINRs at $D_{2}$ and Eves are given by

[TABLE]

[TABLE]

respectively, where $\mathbf{\Theta}=\mathrm{diag}\left(\sigma^{2}\mathbf{I}_{N_{e}},\>\sigma^{2}\mathbf{I}_{N_{e}}\right)$.

To solve the optimization problem (16), we first let $\mathbf{V}_{i}=\mathbf{v}_{i}\mathbf{v}_{i}^{H},i\in\{1,2\},\,\mathbf{W}=\mathbf{w}\mathbf{w}^{H},$ and drop rank-one constraints $\mathrm{rank}\left(\mathbf{V_{\mathit{i}}}\right)=1,\,\mathrm{rank}\left(\mathbf{W}\right)=1.$ Then, (16) can be reformulated as (30) (on the top of next page), where $\mathbf{W}_{e}^{i}=\mathbf{G}_{se}\mathbf{V}_{i}\mathbf{G}_{se}^{H}$, and the non-constraints (17d) and (17e) have been converted to convex forms as previously explained in Section III. It is noted that (30) is non-convex due to the non-convex objective function (30a) and the constraint (30b). However, by using FOTE and ER, (30b) can be approximated by the following convex constraint

[TABLE]

Since problem (30) is still non-convex its objective function will be transformed into the convex form based on the SCA method. For this, by introducing the slack variables $\tau$, $\mu_{i}\geq 0,i\in\{1,2\},$ the objective function can be alternatively reformulated as

[TABLE]

[TABLE]

where factor $\frac{1}{2}$ in (30) is omitted since it does not affect the monotonicity of (30). Then, the SCA can be implemented over (32). It can be seen that (32c) is equivalent to

[TABLE]

by the FOTE, (33) is transformed into

[TABLE]

where $x=e^{\mu_{1}^{(n)}}(\mu_{1}-\mu_{1}^{(n)}+1)$ is the FOTE of $e^{\mu_{1}}$ around the point $\mu_{1}^{(n)}.$ According to the ER method, (34) is transformed into the following convex form

[TABLE]

(32d) is non-convex and it is not suitable to handle the non-convex problem by adopting the ER method. Therefore, Proposition 1 is introduced to convert (32d) into a convex form.

Proposition 1**.**

For any non-negative variables $x,\,y,\,z$, a non-convex expression $xy\leq z$ can be approximated by the following convex constraint

[TABLE]

Proof:

According to the arithmetic-geometric mean (AGM) inequality, the approximation of the expression $xy\leq z$ can be expressed as

[TABLE]

where the former inequality holds with equality, if and only if, $\eta=\sqrt{y/x}$. Then the non-convex expression $xy\leq z$ can be replaced by $\frac{\left(\eta x\right){}^{2}+\left(y/\eta\right){}^{2}}{2}\leq z.$ It can be observed that $\left(\eta x\right){}^{2}+\left(y/\eta\right){}^{2}\leq 2z$ is a convex constraint based on Lemma 1, which completes the proof. ∎

Firstly, (32d) can be converted to

[TABLE]

where $\Xi=\mathrm{Tr}\left(\mathbf{W}_{2}^{2}+\mathbf{W}_{12}+\mathbf{W}_{2}^{1}\right)-e^{\mu_{2}}+\sigma^{2}$. Using the FOTE, (38) is then transformed into

[TABLE]

where $\Xi_{1}=\mathrm{Tr}\left(\mathbf{W}_{2}^{2}+\mathbf{W}_{12}+\mathbf{W}_{2}^{1}\right)-y+\sigma^{2}$ , $y=e^{\mu_{2}^{(n)}}(\mu_{2}-\mu_{2}^{(n)}+1)$. Finally, according to the Proposition 1, (39) can be approximated by the following constraint

[TABLE]

where $\eta^{(n)}$ can be updated by

[TABLE]

It is clear from Lemma 1 that now (40) is a convex constraint.

Employing FOTE and ER, we transform constraint (32e) as follows

[TABLE]

where $z=e^{\tau^{(n)}}(\tau-\tau^{(n)}+1)$. At this point, constraint (32e) is replaced by two convex constraints, i.e., the convex constraint (42a) and the linear matrix inequality constraint (42d).

So far, the optimization problem (30) has been reformulated as

[TABLE]

Consequently, for the active Eves case, the original optimization problem (16) has been transformed into the convex form. Then the solution $(\mathbf{V}_{1}^{*},\mathbf{V}_{2}^{*},\mathbf{W}^{*})$ of (16) is obtained by off-the-shelf optimization solver, e.g., SeDuMi and Yalmip. The algorithmic implementation of the proposed OSBD scheme is summarized in Algorithm 2. Note that problem (43) is handled iteratively with the initial value of $(\tau^{(0)},\mu_{1}^{(0)},\mu_{2}^{(0)},\varphi_{2}^{(0)},\phi_{2}^{(0)},\xi^{(0)}).$ For each iteration, $(\tau^{(n)},\mu_{1}^{(n)},\mu_{2}^{(n)},\varphi_{2}^{(n)},\phi_{2}^{(n)},\xi^{(n)})$ is updated with the solution obtained in the previous iteration until the rate gap between two successive iterations below the predefined accuracy. Moreover, the optimal solution $(\mathbf{V}_{1}^{*},\mathbf{V}_{2}^{*},\mathbf{W}^{*})$ yielded by SDR is rank-one, which is described in the following proposition.

Proposition 2**.**

If problem (43) is feasible, the beamforming vectors $\mathbf{v}_{1}$ , $\mathbf{v}_{2}$ and $\mathbf{w}$ can be exactly obtained by eigenvalue decomposition of $\mathbf{V}_{1}^{*},\mathbf{V}_{2}^{*}$ and $\mathbf{W}^{*}$, since $\mathbf{V}_{1}^{*},\mathbf{V}_{2}^{*}$ and $\mathbf{W}^{*}$ are rank-one.

Proof:

The transmit beamforming vectors are jointly optimized through the OSBD scheme. According to the rank reduction procedure of the semidefinite programming given in Lemma 3.1 of [37], $\mathbf{V}_{1}^{*}$ , $\mathbf{V}_{2}^{*}$ and $\mathbf{W}^{*}$ satisfy the following inequality

[TABLE]

Since from (17d) and (32c) it is observed that problem (43) is not feasible if $\mathbf{V}_{1}^{*}=\mathbf{0}$ or $\mathbf{V}_{2}^{*}=\mathbf{0}$, then, $\mathrm{rank}(\mathbf{V}_{1}^{*})=\mathrm{rank}(\mathbf{V}_{2}^{*})=1,$ and also $\mathrm{rank}(\mathbf{W}^{*})\leq 1$. Since $\alpha>0$, $\mathrm{rank}(\mathbf{W}^{*})\neq 0,$ then clearly there exits a $\mathbf{W}^{*}$ which satisfies $\mathrm{rank}(\mathbf{W}^{*})=1$ and concludes the proof. ∎

B. Single-Antenna Configuration

In applications where devices are equipped with a single antenna, the secure beamforming design problem analyzed in the previous subsection, simplifies to a power allocation problem. As there will be no diversity gain and in order to maximize the SSR and at the same time avoiding the AN interference to $D_{2}$, all the energy harvested by $D_{1}$ is used for information transmission. In other words, since the transmitted signal from $D_{1}$ during the second phase is represented as $x=\sqrt{P_{t}}s_{2}$, the EH constraint from (16) can be removed. Then, under the constraints of the transmit power at $S$ and the QoS requirement at $D_{i}$, the SSR is optimized. By conveniently introducing power allocation factors $\rho_{1}$ and $\rho_{2}$ as replacement of the beamforming vectors $\mathbf{v}_{1}$ and $\mathbf{v}_{2}$, respectively, the optimization problem is reformulated as

[TABLE]

[TABLE]

where $h_{1},h_{2}$ and $h_{12}$ are normalized main channel gains; $\mathbf{g}_{se}$ and $\mathbf{g}_{1e}$ are wiretap channels; $\gamma_{i},$ is target SINR of $D_{i}$; (45b) and (45d) are QoS constraints of $D_{i}$; And (45c) ensuring that $D_{1}$ can satisfactorily perform SIC. As this optimization problem (45) is a bilevel programming problem, with the outer level variable being $\beta$, it will be transformed into the convex one.

Following [6], it can be shown that at least one inequality constraint in (45) is satisfied with equality at the optimal solution when problem (45) is feasible. Otherwise, the optimization variables can be changed to increase the SSR until one of the constraints holds with equality.

For convenience of the analysis’ presentation, let us consider that the inequality constraint (45b) holds with equality at the optimal solution so that

[TABLE]

It is noted that the variables $\rho_{1}$ and $\rho_{2}$ are expressed as a function of $\beta$. Substituting (46) into (45c) and (45d), constraints (45c) and (45d) are rewritten as

[TABLE]

[TABLE]

respectively, where $\xi=P_{s}h_{1}h_{2}-\gamma_{2}h_{1}-\gamma_{1}\gamma_{2}h_{2},\zeta=\beta\left(\gamma_{2}h_{1}-P_{s}h_{1}h_{2}+P_{s}h_{1}h_{2}h_{12}\gamma_{1}+P_{s}h_{1}^{2}h_{12}\right).$ Since the optimization, problem (45) due to is still non-convex, a slack variable u is introduced to non-convex objective approximate the second term in (45a) by FOTE. In this way, the non-convex optimization problem (45) can be reformulated as

[TABLE]

[TABLE]

where $z=e^{\upsilon^{(n)}}\left(\upsilon-\upsilon^{(n)}+1\right).$ Since the optimization problem stated in (48) is now in convex form, its optimal solution can be readily obtained by the handy solver, e.g., SeDuMi or Yalmip. Note that if (45c) or (45d) hold with equality, a similar methodology can be followed to obtain an equivalent convex optimization problem. However, due to space limitations, the detailed procedure will not be presented here.

V Performance evaluation results and discussion

In this section, the SSR performance of the previously described cooperative relay-aided secure IoT communication systems will be presented. The various performance evaluation results have been obtained by extensive computer simulation experiments. It is assumed that the two legitimate users and $N_{e}$ eavesdroppers are deployed within a 8-meter$\times$8-meter network, while $S$ is located at the edge with coordinate $(0,4)$. $h_{Li}=10^{-3}d_{i}^{-\alpha_{i}},(i=1,2)$ and $h_{Le}=10^{-3}d_{e}^{-\alpha_{e}}$ represent the large-scale path losses, where $d_{i},(i=1,2)$ and $d_{e}$ are the distances from $S$ to $D_{i}$ and Eves, respectively, $\alpha_{1}=2,\alpha_{2}=4$ and $\alpha_{e}=2$ are the corresponding path loss exponents. The downlink channels $\mathbf{H}_{s1},\mathbf{H}_{12},\mathbf{G}_{se}$ and $\mathbf{G}_{1e}$ operate in the presence of Rician fading, as follows

[TABLE]

where $\mathbf{H}^{LoS}$ is the LOS deterministic component, $\mathbf{H}^{NLoS}$ is modeled as the small-scale Rayleigh fading following $\mathcal{CN}(0,1)$, and unless otherwise stated, with Rician factor $\Gamma=4$. The distribution of $\mathbf{H}_{s2}$ follows $\mathcal{CN}(0,1)$. Matlab is used as a simulation tool, and Yalmip is employed as an optimization solver. All the SSR curves are generated by averaging 500 independent channel realizations.

A. Performance Evaluation of Proposed AN-aided Scheme Without Eves’ CSI

Fig. 2 presents the SSR versus the number of iterations for different $N_{1}$ and $r_{1}$, where the SINR threshold $\gamma={2,3}$ in Fig. 2(a) and Fig. 2(b), respectively. We set the number of eavesdroppers, $N_{e}=3$, the transmit power constraint at $S$,$P_{s}=30\ \mathrm{dBm}$. These performance evaluation results clearly show that the proposed ASBD scheme converges to a stationary point in few iterations. Furthermore, the SSR performance improves as $\gamma$ (i.e., the QoS requirement of $D_{2}$) decreases. This happens because the harvested power at $D_{1}$ is larger if $\gamma$ become smaller, and then more power can be used to transmit AN.

Fig. 3 presents the SSR performance of the ASBD scheme versus the transmit power at $S$ for different values of $N_{1}$ by fixing $N_{s}=N_{2}=4$, $N_{e}=3$ and $\gamma=3$. For comparison purposes, the performance of the secure beamforming design scheme without AN-aided (denoted as “Without AN”) has been also obtained. These results clearly show that the SSR obtained by ASBD scheme is larger compared with the benchmarks. Furthermore, it is observed that, with the increase of $N_{1}$, the SSR achieved by different schemes is improved significantly.

Fig. 4 shows the SSR versus the predefined threshold of achievable ergodic rate of $D_{1}$ for different values of $N_{s}$, where $P_{s}=30\ \mathrm{dBm}$, $N_{1}=N_{2}=4$, $\gamma=3$. It can be seen that the SSR performance is enhanced as $r_{1}$ increases, which is consistent with previous findings presented in [7]. The reason is that the transmitter $S$ allocates more power to the strong user $D_{1}$ to satisfy the predefined threshold of achievable ergodic rate of $D_{1}$, which leads to the increasing of SSR. Meanwhile, compared with the OMA-based secure beamforming design with AN-aided (denoted as “OMA w/ AN”), the proposed design exhibits better SSR performance when $N_{s}$ increases.

B. SSR Comparison With Eves’ CSI

In Fig. 5, the convergence property of the proposed OSBD algorithm and the algorithm given in [2] for the active Eves case is presented, with $P_{s}=30\ \mathrm{dBm},$ $\gamma=3$, $N_{e}=3,N_{i}=4,N_{s}=\{2,4\}.$ It is noted that, although the algorithm of [2] also employs a NOMA transmission protocol and optimizes the SSR of downlink systems, it only considers the direct transmission link and does not use any physical layer security technology. From Fig. 5, consensus has been reached that the proposed algorithm converges to a stationary point in a fewer steps than that in [2], especially for higher values of $N_{s}$. To demonstrate the computational efficiency of the proposed approach, we give the time needed for the two algorithms to converge. Our proposed algorithm takes about 4.75 s for each independent channel realizations, while the time required for the algorithm given in [2] is about 7.11 s.

Fig. 6 illustrates the SSR performance of the proposed OSBD scheme for the active Eves case. Set $N_{e}=3,N_{i}=4,N_{s}=\{2,4\},\gamma=3$. We also consider the secure transmission design given in [2], the NOMA secure transmission protocol without relay-aided (denoted as “NOMA w/o EH”) as well as the conventional OMA-based secure beamforming design without relay-aided (denoted as “OMA w/o EH”) as baseline algorithms. As expected, the proposed OSBD scheme based on the cooperative secure transmission protocol can obtain higher secrecy rate than that in [2]. In addition, numerical results also indicate that the proposed scheme can achieve much better SSR performance than the other two benchmark schemes (i.e., NOMA w/o EH scheme and OMA w/o EH scheme). With the fixed $P_{s}$, we can observe that, as $N_{s}$ grows, the SSR performance becomes better in different schemes, since more array gains are provided.

Fig. 7 illustrates the SSR performance under different transmit powers of controller for the single-antenna configuration. Similar to Fig. 6, the three benchmarks are employed as baseline algorithms, where $N_{1}=N_{2}=N_{s}=1,N_{e}=3,\gamma_{1}=2,\gamma_{2}=3$. Obviously, the SSR performance of the proposed power control scheme outperforms that of the other three benchmarks, especially in large transmit power region. The reason is that the received signal at $D_{2}$ is consisted of two parts from the relay-assisted system so that the SSR of the IoT is further enhanced.

VI Conclusions

In this paper, we investigated the secure transmit beamforming design in the downlink IoT system. Taking diversified QoS requirements of IoT users into account, a novel relay-aided cooperative secure transmission strategy was proposed to further improve the SSR of the IoT system. Two Eves cases have been considered based on the availability of the CSIs of Eves. For the passive Eves case, ASBD scheme was proposed to jointly optimize the secure beamforming vectors, AN covariance matrix as well as PS ratio. For the active multi-antennas Eves case, OSBD scheme was proposed to maximize the SSR of the considered IoT system. When the transmitters (i.e., $S$ and $D_{1}$) are single-antenna configurations, the orthogonal-projection-based optimization problem is degraded into a power allocation problem and the optimal solution can be found by fully exploiting the specific property of the optimization problem. Various performance evaluation results have demonstrated the superiority of the proposed schemes compared to the existing benchmarks.

The proposed cooperative SWIPT secure transmission protocol can be applied to massively connected IoT systems in the future, such as Healthcare IoT, in which a large quantity of smart devices are involved in sensing health parameters and these devices are confined by the limited power. For Healthcare IoT applications, it is noted that security is a vital yet challenging requirement during data collection from patients to a centralized data collection center. Thus, as the proposed secure transmission scheme is capable of ensuring the security of Healthcare IoT, it could be very well used for such kind of applications.