Secure beamforming design of SWIPT relay network with multiple users and eavesdroppers

This paper studies the secure beamforming design for simultaneous wireless information and power transfer (SWIPT) in a amplify-and-forward (AF) relay networks with multiple users and eavesdroppers. Each user node adopts the power splitting (PS) scheme to decode information and harvest energy simultaneously. Our objective is to minimize the total relay transmit power under the constraints of secure transmission rate and energy harvesting requirements by jointly optimizing the beamforming matrix, artificial noise covariance matrix and PS ratios. For this non-convex problem, we propose a two-stage optimization approach to convert the original problem into two sub-problems. The first subproblem uses semidefinite relaxation (SDR) technique to transform the original problem into a convex problem, and then finds the optimal solution of the second subproblem through k-dimensional exhaustive search algorithm. Furthermore, we also propose a low complexity suboptimal solution scheme based on particle swarm optimization (PSO) algorithm. Simulation results show that the proposed scheme saves transmitting power and achieves better performance than other schemes.


Introduction
The life span of traditional wireless devices is limited by the power supply capacity, simultaneous wireless information and power transfer (SWIPT) technology can solve the energy scarcity problem in energy-constrained wireless networks by harvesting the energy of radio frequency (RF) signals into wireless devices, which is widely regarded as a promising technology [1]- [4]. Compared with 4G networks, 5G energy consumption will increase exponentially, and energy efficiency has become one of its key indicators, therefore, SWIPT technology is of great significance for 5G [5]. In recent years, this technology has attracted widespread attention and intense research [6]. In general, SWIPT has two primary energy harvesting schemes, namely, time switching (TS) and power splitting (PS) [7]- [9]. For the TS, the user node switches between information decoding (ID) and energy harvesting (EH), while with PS, the user node splits the received signal into two parts for ID and EH. It has been shown in [8] that the TS scheme switches between the two modes instantaneously, which can be regarded as a special case of the PS scheme. So, the performance of the PS scheme is usually better than the TS scheme. In this paper, we focus on the PS scheme.
The wireless information in SWIPT systems is more vulnerable to eavesdropping than other wireless networks due to the inherent characteristics of SWIPT and the open nature of wireless channel. Therefore, how to achieve secure communication in the SWIPT wireless network is a crucial issue. Although the cryptographic technology guarantees the communication security of the application layer to a certain extent, it might not be suitable in the SWIPT system because the SWIPT system requires sophisticated encryption, decryption algorithms and critical distribution protocols [10]. Fortunately, this problem can be solved at the physical layer by using the physical characteristics of wireless channels, such as channel fading [11] and interference [12], especially the design of beamforming and artificial noise (AN) [13] has become two key technologies to ensure the secure transmission of wireless communication.
In recent years, security of SWIPT network physical layer has attracted wide attention of researchers. In [14]- [15], the authors proposed a secure transmission scheme based on zero forcing (ZF) technology. A problem of maximizing the secrecy rate in a multi-input single-output (MISO) SWIPT system is described in [14], and the author in [15] considered the secure transmission scheme of two-user SWIPT cooperative zero forcing interference. However, the research models are all in simple scenes, and in the face of complex comprehensive network, zero-forcing interference cannot play its role significantly. Besides, in [16], a amplify-and-forward (AF) beamforming was designed to maximize the secrecy rate in full duplex wireless-powered relay network. But the model only considers simple scenarios, without the general scenario with multiple eavesdroppers. Therefore, we consider a more general model with multiple eavesdropping nodes and multiple user nodes in this paper.
In addition, in [17], the author studies the physical security in more complex MISO-SWIPT relay model by considering the dual-function nodes capable of information decoding and energy collection. The signal sent by the base station is forwarded to the user node through multiple single-antenna relay nodes. Although multiple user nodes and multiple eavesdropping nodes are considered, the author's relay system is composed of multiple single-antenna relays. However, as one of the key technologies of LTE, multi-antenna technology can greatly improve system capacity and link reliability, and it has been widely used [18].
Based on the above research, in this paper, we consider the secure beamforming design of SWIPT multi-antenna AF relay system with multiple eavesdropping nodes and multiple user nodes. Each user node adopts the PS scheme to decode information and harvest energy simultaneously. At the same time, AN is also added in the relay to confuse these eavesdropping nodes. We study the joint design of beamforming matrix, AN covariance and PS ratios to minimize the relay transmission power under the constraints of secure transmission rate and energy harvesting requirements. The main contributions of this paper are summarized as follows: 1) We study the physical layer security of SWIPT relay networks with multiple eavesdropping nodes and multi-users, and propose a joint AF beamforming and AN scheme to interfere with the eavesdropping nodes to ensure secure transmission; 2) Unlike traditional networks, user nodes use PS schemes for information decoding and energy collection, and by jointly optimizing beamforming, AN, and PS ratios, the total transmission power of the relay network is saved; 3) We propose a robust secure beamforming design, use a two-stage optimization method and semidefinite relaxation technique to solve the original non-convex problem. Moreover, we also propose a low complexity suboptimal solution scheme based on particle swarm optimization (PSO) algorithm to provide secure transmission and promote effective energy harvesting.

System Model and Problem Formulations
As illustrated in figure 1, we consider a SWIPT relay system with a source S, an AF relay R, K user nodes U s and L eavesdropping nodes E s , where the AF relay is equipped with M receive antennas and M transmit antennas. Let denote the channel vector from the S to the R, from the R to the kth U and the lth E, respectively. Each user node adopts the PS scheme to ID and EH. The signal attenuation from the relay to the user, and the eavesdropping node is the same, and the lineof-sight (LOS) is dominant for this short-distance attenuation case [10], hence we assume that the channel is an independent Rician fading channel, and channel coefficients will not change until next  [17], we assume that the eavesdropping nodes are closer to the user nodes, and there is no direct link from the source node to the user nodes and the eavesdropping nodes, which requires long-distance forwarding through the relay. Hence, information leakage occurs in the relay forwarding stage. Since the AF relay work in half-duplex mode, one transmission cycle consists of two phases.
S R y   f n (1) where s   is the confidential message sent by the source node, represents the additive white Gaussian noise introduced by the relay.
In the second phase, the relay employs the beamforming matrix to forward the information. In the meantime, the relay emits artificial noise [19] to confuse the E s as well as improve energy harvesting at the Us. Therefore, the transmission signal of the relay can be expressed as (2) Since the relay processing information delay is minimal, it can be ignored. The power transmitted by the relay node can be expressed as In the remainder of this paper, we use index denote the additive white Gaussian noise introduced by the kth user and the lth eavesdropping node, respectively.
We assume that each user node is equipped with a power splitter to decode information and harvest energy. Specifically, at the kth user node, (0,1) portion signal is used for information decoding, and (1 ) k   portion of the signal is used for energy harvesting [8]- [9]. Thus, after PS, the equivalent received signals of the kth user for information decoding and energy harvesting are expressed as ( ( s ) ) , denote the noise added by the kth user node during signal processing. Therefore, the signal-interference to noise (SINR) of the kth user node is expressed as On the other hand, the energy harvested by kth user node is expressed as 2 2 (1 )( , denotes the energy harvesting efficiency. In addition, the SINR of the lth eavesdropping node is expressed as 2 2 ( ) we consider communication security from the perspective of individual confidentiality. According to [20]- [21], an individual achievable security rate of the kth user can be expressed as Our objective is to minimize the total power consumption at the AF relay while maintaining the achievable secrecy rate and energy harvesting constraints at each user node. Specifically, the power minimization problem can be formulated as Where k r and k e are the secure transmission rate and energy harvesting of the kth user, respectively. Since the optimization variables , , k  V W are coupled in the optimization problem formula, and the constraints involve quadratic terms, the problem (12) is non-convex, making it difficult to solve.

Secure Beamforming Design
In this section, we propose a two-stage optimization method to transform the original problem into two sub-problems to solve the global optimization of problem (12). The first non-convex sub-problem is solved by semidefinite relaxation (SDR) technique, and then the optimal solution of the second subproblem is sought by K-dimensional exhaustive search. Furthermore, facing the extremely high complexity of K-dimensional exhaustive search algorithm, we propose a PSO-based low-complexity algorithm to solve the original problem.

Two-stage optimization method
In this subsection, we develop a two-stage optimization method to deal with the problem (12 (12) is equivalent to the following problem (14) Let   k   denote the optimal solution of problem (14), problem (12) and problem (13) (14). Therefore, we will solve problem (13) for a fixed set of k  at first in the follwing.

SDR-based optimal solution for problems (13)
For a given k  , problem (13) is also a non-convex problem. In this paper, SDR technology will be used to deal with this non-convex problem.
According to the idea of SDR technology in [19], we define . As a standard routine of SDR, we drop the rank-one constraint and recast problem (15) Problem (16) is a convex semidefinite programming problem that can be solved using standard optimization software packages, such as CVX [22].
Notably, though, the problem (14) can be solved directly by k-dimensional exhaustive searche for all possible combinations of , k k   , but the complexity of k-dimensional exhaustive search is too high to be implemented in practice. Therefore, in the next section, we propose a low complexity heuristic algorithm based on PSO to solve this problem (14).

SDR-based optimal solution for problem (14)
The PSO algorithm has been widely used in the field of wireless communication due to its advantages of simple implementation, high solution quality, and fast convergence speed [23]. In this paper, PSO algorithm first randomly generates a group of particles   . In addition, remember the best position of each previous particle (previous optimal), expressed as ( ) [ ] n i Px . After finding these two optimal values, the algorithm updates the velocity and position of the ith particle in each iteration according to following equation Where ω is the inertia weight, c 1 and c 2 are two constant accelerations, 1  and 2  are random numbers uniformly distributed in [0, 1]. This process is repeated until the termination condition is satisfied or the maximum number of iterations is reached. The details are summarized in Algorithm The computational complexity of Algorithm 1 is mainly based on the swarm size S, the maximum number of iterations N, and the complexity in evaluating the fitness value in problem (16), which has the computational complexity of

Simulation Results
In this section, numerical simulation is presented to evaluate the performance of we proposed scheme in SWIPT multi-antenna relay system. The simulation experiment parameters are set as follows:  . It can be observed that the algorithm only needs about four iterations to achieve convergence, which shows that the algorithm has fast convergence and therefore has low computational complexity. Figure 3 depicts the relay transmit power of four different schemes versus the minimum secrecy rate requirement of each user node with It is clear to see that the relay transmit power increases as the secrecy rate requirement increases. Our proposed method is superior to other schemes while the No-AN scheme is the worst design. This phenomenon indicates that AN is conducive to a SWIPT system. Besides, it can be seen from the figure that when the security rate is small, the relay transmit power increases slowly, whereas when the security rate is large, the relay total transmission power rises quickly.  . It is observed from the figure that the relay transmit power increases with the increase of 0 e , and the scheme proposed in this paper achieves better performance than other schemes. Figure 5 shows the relay transmit power versus the number of eavesdropping node L. It is clear to see that the relay transmission power consumption of all schemes increases with the increase of the number of eavesdropping nodes L, and our proposed design has a better performance gain than other schemes. Moreover, it can be seen from the figure that when K≥5, the zero-forcing scheme is significantly increased, which further indicates that the number of eavesdropping nodes L has a significant influence on the performance of the zero-forcing system.

CONCLUSION
In this paper, the security of multiple user nodes and multiple eavesdropping nodes in a multi-antenna AF relay network based on SWIPT is studied. This paper proposed an artificial noise-assisted secure beamforming design. Under the constraints of secrecy rate and energy harvesting, the goal of minimizing the total transmission power of the relay system is achieved by jointly optimizing the beamforming matrix, AN covariance and PS ratios. The two-stage optimization method and semidefinite relaxation technique are used to solve the optimal solution of the original problem. In this paper, it shows that a kdimensional exhaustive search is difficult to achieve. Hence, a low complexity suboptimal solution based on the PSO algorithm is proposed. Simulation results show that the proposed scheme saves transmission power and has better performance than other scheme while ensuring a secure transmission rate.