Secure Multiuser Scheduling for Hybrid Relay-Assisted Wireless Powered Cooperative Communication Networks With Full-Duplex Destination-Based Jamming

In this paper, we investigate secure communication in a hybrid relay (HR)-assisted wireless powered cooperative communication network (WPCCN), where an eavesdropper tries to intercept the data transmitted by a source user and the HR simultaneously. The HR has the ability to wireless powered the energy-constrained multiple users in the downlink and to relay the received confidential information in the uplink. In particular, the full-duplex destination-based jamming (FD-DBJ) strategy is exploited to improve the secrecy performance. Moreover, in order to conduct effective secure communications, we design two multiuser scheduling schemes, i.e., random user selection (RUS), and best user selection (BUS) based on the main channel quality. In order to evaluate the secrecy performance, we analytically derive the energy outage probability (EOP), the secrecy outage probability (SOP), and the hybrid outage probability (HOP), respectively. As such, we formulate the secrecy throughput (ST) maximization problem to optimize the predetermined transmission rate. Our analysis and numerical results reveal that: 1) The BUS scheme has better security performance. 2) Both of the energy conversion efficiency and the number of users have a positive effect on secrecy performance. 3) The FD-DBJ scheme is an effective method to achieve secure communications. 4) The time-switching factor and predetermined transmission rate have a crucial influence on the secrecy performance, which should be considered carefully in system design.

communication network composed of devices that harvest energy for information exchange needs can be called a wireless powered communication network (WPCN). Specifically, the battery of wireless terminals in WPCN can be remotely replenished by the ambient wireless transmitter or the power beacon (PB) with the help of EH technology, which is helpful to avoid the burden caused by frequent wired charging and battery replacement for communication devices [8]- [10]. As a result, WPC technology has attracted wide attention and has been generally explored in a variety of wireless communication system, such as cognitive radio networks [10], wireless sensor networks (WSNs) [11], IoT [12], [13] and so on.
The main obstacle to the wide application of WPC is the short transmission distance due to the dual path loss and fading, resulting in limited harvested energy at terminals. Intuitively, multi-antenna technology can be used to improve the efficiency of EH [14]. Unfortunately, this solution is not suitable to the devices of IoT, which is restricted to the cost and size owing to the user requirement for lightweight and miniaturization. Recently, the cooperative communication technology, which aims to achieve spatial diversity gain and to improve system performance without increasing complexity and quantity of the device, has been regarded as a promising approach to tackle above problem [15]- [17]. With the deepening of the research on the cooperative communication technology, its positive role in energy consumption and security has been paid more and more attention [18], [19]. In particular, a cooperative communication network with one or more wireless powered nodes is termed wireless powered cooperative communication network (WPCCN) [20], which can effectively expand the coverage and improve the throughout and energy efficiency of WPCN as well as alleviate the influence of node energy constraints on performance of wireless communication system [21]- [23]. Specifically, the WPCN with energy/ information relaying, which is regarded as a special case of cooperative networks, can also be considered as a WPCCN.
However, in addition to the above advantages, WPCCN faces more serious threats than traditional wireless networks in terms of security and privacy due to the complexity of network structure and the diversity of nodes, which makes it vulnerable to information interception and eavesdropping [24]. For example, the EH nodes can change their roles and become potential eavesdroppers who want to eavesdrop on information between the source and the controller, which raises a tough security challenge. In general, traditional cryptographic methods are used to ensure the confidentiality of data transmission. However, the higher computational complexity will lead to quite a few unfavorable factors, including network delay, excessive overhead and so on, which are sensitive to future networks. To mitigate this issue, physical layer security (PLS), which contributes to its low latency, low complexity and ability to be combined with other security approaches easily for enhancement of secrecy performance, has been supposed as a promising complement to the current methods of information security [25]- [27].

B. RELATED WORKS
Recently, there are numerous works on the PLS of WPCCN [12], [28]- [30]. Specifically, the authors in [28] proposed two schemes of joint relay and jammer selection to achieve the secure transmission in a WPCCN system with many wireless-powered intermediate nodes. A joint PB and relay selection secure strategy was designed for 5G wireless communications in [29], where a sensor user and multiple intermediate nodes acquire energy from a multi-antenna PB for information transmission. Furthermore, as the extend of [29], the authors in [12] proposed a secure transmission approach, in which the different relay selection schemes are compared and secure energy efficiency (SEE) maximization of the proposed strategies is solved. Differently, secrecy analysis of WPCCN with multiple multi-antenna relays under nonlinear EH and imperfect CSI was explored in [30]. Nevertheless, it should be noted that most of works paid attention to the enhancement of secrecy performance by means of multiple relays or multi-antenna technique, but neglected the important scenario with multiple users, which is considered as the main topology of future networks [31]- [34]. In fact, the multiuser scheduling is considered as an effective means of enhancing the PLS of wireless networks without consuming additional resources.
Meanwhile, the hybrid relay (HR) has been introduced in WPCCN to improve the transmission throughput, which plays a dual-role of PB and relay. Specifically, the HR charges the source user first and then forwards the information transmitted from the source user, i.e., adopting charge-thenforward (CTF) mode [35]- [41]. At present, the research on WPCCN is generally based on EH relay. The so-called EH relay means that the relay in the network has no stable energy supply, so it needs to use WPC technology to harvest energy from the RF signals broadcast by PB or other sources to forward the received information. Thus, the EH relay is an auxiliary information node, which is responsible for forwarding the confidential data. In contrast, another network model with HR is a special topological structure, in which the relay is powered by on-grid power. In the downlink, it can act as a PB to provide energy signals for the EH users, and in the uplink, it can be used as an information fusion node to receive the information of the source and assist in forwarding. The special structure makes HR show dual roles. In fact, compared with the base stations (BS), small HRs are cheaper and can be deployed on a large scale easily. Aided by the HRs, the number of wireless users accessing the network through BS can be greatly reduced. Meanwhile, the devices far from the BS can also achieve better uplink communication quality and downlink wireless powering service through the latest HR. In particular, the concept of HR is first described in [35], and both the working principle and the transmission performance of HR-assisted WPCCN are analyzed. Then, a full-duplex HR model is investigated in [36], where the channel capacity in harvest-use (HU) mode without the battery and in harvest-store-use (HSU) mode with infinite battery capacity is deduced, respectively. Furthermore, the authors in [37] and in [38] considered a HR model with multiple wireless powered users and multiple access points, in which they maximized the total transmission rate by adjusting the transmission power and time-switching factor of the HR. The authors in [39] explored the energy efficiency maximization for decode-and-forward (DF) and amplify-and-forward (AF) relay-assisted WPCCN through the joint optimization of the duration and the power allocation. The coverage probability of hierarchical wireless powered networks with the HR was discussed in [40]. In addition, the authors in [41] investigated the throughput of wireless-powered relaying systems with the buffer-aided HR.

C. OUR APPROACH AND CONTRIBUTION
Although the introduction of HR into the WPCCN can improve the transmission throughput, the potential malicious HR also poses a severe threat to the security of the WPCCN. It is noted that a malicious HR can intercept the signals transmitted from both of the source user and the legitimate HR, which deteriorates the secrecy performance. In addition, the information leakage from a data-fusion HR may cause greater losses. However, the secrecy of the HR-assisted WPCCN is overlooked in aforementioned works. Therefore, in this paper, we focus on the PLS of a HR-assisted WPCCN, where a HR charges multiple source users in the downlink and forwards the confidential information transmitted from a selected source user in the presence of a malicious HR as an eavesdropper. In order to achieve the secure transmission, we adopt the user selection scheme based on the channel quality from the source user to the HR and introduce the destination-based jamming (DBJ) generated from a full-duplex (FD) destination node, i.e., the FD-DBJ scheme. Specifically, the main contributions of this work are listed as follows: • We investigate the PLS in the HR-assisted WPCCN with FD-DBJ and introduce two secure multiuser scheduling schemes: 1) random user scheduling (RUS), i.e., the source user is selected randomly; 2) best user scheduling (BUS), i.e., an optimal source user is selected to transmit information based on the channel quality between the user and the HR. Furthermore, as for the considered system, we derive the exact closed-form expressions of energy outage probability (EOP), secrecy outage probability (SOP), and hybrid outage probability (HOP), respectively.
• Based on the performance analysis to the considered system, we further formulate the secrecy throughput (ST) optimization problem. Then, we propose a low-complexity ST maximization algorithm based on the Brent method to optimize the predetermined transmission rate, which achieves a balance between the communication throughput and secrecy.
• Simulation results show that the BUS scheme can make full use of the multiuser diversity gain and achieve better secrecy performance. Meanwhile, we can adjust some parameters, such as increasing the number of source users, improving the EH efficiency and enhancing the transmit power of the DBJ, to improve the secrecy performance of the considered multiuser WPCCN. In addition, we confirm that the FD-DBJ scheme is an effective method to achieve the secure communication.
In addition, both of the time switching factor and the predetermined transmission rate have a significant effect on the ST, which should be considered carefully aiming to secure and efficient communication.

D. ORGANIZATION
The rest of this paper is summarized as follows. We describe the system model and two secure multiuser scheduling strategies in Section 2. Section 3 analyzes the secrecy performance both the RUS and BUS schemes in terms of the exact expressions for EOP, SOP and HOP, and explores the ST optimization problem. Then, Section 4 discusses the simulation results. Finally, Section 5 states conclusions. Notation: Scalar variables are denoted by italic symbols. Vectors are denoted by boldface symbols. Given a complex number, |·| denotes its modulus. Given an event, Pr (·) denotes its probability of occurrence. E (·) denotes the expectation operation.

II. SYSTEM MODEL AND SIGNAL ANALYSIS A. SYSTEM MODEL
Consider a multiuser WPCCN with HR and FD-DBJ as illustrated in Fig. 1, which is composed of N source users (S n ), n = {1, . . . , N }, a HR (R), a destination (D), a passive eavesdropper (E), where the ''passive'' means that the channel state information (CSI) from S n , R and D to E are unavailable for the user scheduling. It is noted that the broadcast nature of radio propagation leads to any receivers within the coverage area of a radio transmitter being capable of overhearing the wireless transmission. This makes the wireless communication systems extremely vulnerable to the eavesdropping attack. In contrast of the active attack, the passive eavesdropping attack is hard to be discovered by the legitimate communication parties. In particular, in the HR-aided WPCCN, a malicious HR is easy to intercept considerable information transmitted from both of a source user and a legitimate HR, and in order to keep the network running for a long time, they must harvest energy by WPC technique from the HR to support data interaction [11], [12].  VOLUME 9, 2021 The HR and the destination are powered by on-grid power. Specifically, in the downlink, the HR powers multiple users based on the WPC technique, while it utilizes the decodeand-forward (DF) relay scheme to help the selected user to forward information in the uplink, which makes the HR as a data fusion center for multiple source nodes to improve the system performance. In fact, the HR charges other EH nodes as PB and the HR forwards information as the data fusion node can be considered as two independent processes, which can be realized by operating EH and the information transmission in different frequency bands [42]. In addition, the worse scenario is assumed, that is E can simultaneously intercept the information from S n and R. Then, due to the cost and size limitations, it is considered that S n , R and E are single antenna and HD devices. It is worth noting that above structure has important applications in many energy-limited systems, such as the data uploading network with devices for collecting information in dense environment and WSNs. In order to provide secure data transmission, the destination is equipped with two antennas and works in the FD mode, which can be transmitted the jamming signal to confuse the eavesdropper, and received the confidential information from the legitimate nodes simultaneously, i,e, the FD-DBJ scheme is exploited at the destination 1 [43], [44].

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Furthermore, the channel coefficients between nodes X and Y are denoted as h XY , in which X ∈ {S n , R, D}, Y ∈ {R, D, E}. In the considered system, all channels are assumed to be independent quasi-static Rayleigh fading as [11], [12], [45], which is a special case of Rician fading and can be treated as a fundamental work for more general Rician fading scenario. Therefore, the power gains of link |h XY | 2 are distributed exponentially with means 1/λ XY , i.e., 1/λ XY can fully characterize the signal attenuation caused by fading and path loss [46]. In addition, the direct S n → D link is not available due to the obstacles or severe attenuation [12], [29], so the source users must upload the confidential information by means of HR. Moreover, the N source users are considered to form a cluster. In fact, the assumption is generally adopted in the WPCCN with multiusers or multi-relays [11], [12], [45], which produces the identical mean power gains of the links S n → R, S n → E, R → S n . For simplicity, we define The entire transmission includes three phases. In the first phase, the HR transmits energy signal to power the multiple users before the information transmission. Then, the remaining time of the information transfer is further divided into two parts, one is that the selected user uploads the confidential data to HR, another is that the HR decodes and forwards it to the destination D, where the HR is served as the trusted relay and the new codewords are adopted to re-encode the information before forwarding for improving the secrecy performance [12], [28]. It is noted that the FD destination always sends the jamming in the whole information transmission process for degrading the channel quality of the eavesdropper. Thus, the division of time slot is shown as Fig. 2, in which T denotes a transfer time slot, αT is the time used for the HR to power all the alternative users, where α ∈ (0, 1) denotes time-switching factor, (1 − α) T /2 represents the time used to transmit the information and jamming in the first hop, and the remaining time is used for the information and jamming transfer of the second hop. For convenience, we set T = 1.

B. ENERGY HARVESTING AND SIGNAL ANALYSIS
According to the [29], [30], the harvested energy at each S n in the charging phase is given by where η denotes the energy conversion efficiency factor, which depends on the EH circuits and the rectification process; P R is the transmit power of the HR when it operates as PB; h RS n 2 is power gains of the links from the HR to S n .
It is worth noting that the nodes in WPCCN are passive users, compared with the energy harvested from HR, the received power from the external noise is very small, which makes the harvested energy from noise can be ignored [28], [30]. Furthermore, it is considered that all the harvested energy at each S n is used for transmitting data in the next block of information transfer, i.e., the harvest-use (HU) mode is adopted [11]. As such, the transmit power of S n is given by It is noted that, in practice, the energy harvester works in a non-linear mode with a saturation threshold [47], [48]. We note that the harvested energy within a time slot in the considered system is usually much smaller than the saturation threshold in the energy harvester, e.g., the capacitance. Thus, we assume that the non-linear effect of the energy harvester is negligible in our considered system, which is worth studying in future works.
Then, we assume that the optimal user is denoted by S n * . The received signals at HR and E in the first hop of information transmission are given by respectively, where x is the confidential information transmitted by S n * , z denotes the jamming signal transmitted by D.
And P S n * denotes the transmit power of the selected user, P D denotes the transmit power of the destination. h DE 1 denotes the power gain of the channel from the destination to E in the first hop. n R ∼ CN (0, N 0 ) and n E 1 ∼ CN (0, N 0 ) are AWGN at R and E, respectively. It should be noted that in line with [11], [24], [28], the jamming caused by the destination to the HR is neglected in (3). In fact, the HR and the destination are cooperative with each other, which makes the HR can eliminate the interference signal [49]. Thus, the signal-noiseratio (SNR) at R in the first hop is given by and the signal-to-interference-plus-noise ratio (SINR) at the eavesdropper E is given by where h S n * R 2 , h S n * E 2 and h DE 1 2 denote the power gains of the channel from S n * to R, S n * to E and D to E, respectively. For simplicity, we defineγ D = P D N 0 . Then, as [18], the secrecy capacity of the first hop is given by where (x) + = max (x, 0). Furthermore, in the next phase of information transmission, the received signals at D and E are given by respectively, where h DE 2 is the power gain of the channel from the destination to E in the second hop, n D ∼ CN (0, N 0 ) and n E 2 ∼ CN (0, N 0 ) are AWGN at D and E, respectively. It should be noted that the self-interference (SI) between the receive antenna and the transmit antenna at the destination is negligible in (8). 2 Similarly, the SNR at D and SINR at E are given by respectively, where |h RD | 2 , |h RE | 2 and h DE 2 2 denote the power gains of the links from the R to D, R to E and D 2 It is assumed that the separate-antenna deployment is adopted at the FD destination, i.e., each antenna is used for transmission or reception, respectively [43], [44]. With the help of the latest self-interference cancellation (SIC) technique, such as analog-circuit-domain, propagation-domain, and digital domain methods, SI can be effectively controlled in a negligible range [50], [51].
to E, respectively. And P R is the transmit power of HR when it forwards the confidential information. Similarly, for simplicity, we defineγ R = P R N 0 . It is worth noting that we consider the power of HR in time slot of charging and of forwarding information is set as the same. So we do not focus on the power optimization of HR in different time slots.
Thus, the secrecy capacity of the second hop is given by C. SECURE MULTIUSER SCHEDULING SCHEME In this part, we propose two different multiuser scheduling strategies: one is the random user scheduling (RUS), where the alternative user is selected randomly from the cluster of users for reducing computational complexity; another is the best user scheduling (BUS), where the best user can be determined based on the channel quality of S n → R for the improvement of the secrecy performance.

1) THE RUS SCHEME
In line with the RUS scheme, we select the node S n * among the candidates randomly. Thus, the probability density function (pdf) of h S n * R 2 is subjected to the exponential distribution with parameters 1/λ SR , which is given by It is noted that depending on the low computational complexity, the RUS scheme is especially suitable for the resource-limited and latency-sensitive scenarios. However, because the user who transmits information is scheduled randomly in RUS scheme, the diversity gain brought by multiple users cannot be acquired, which constricts the secrecy performance of the networks.

2) THE BUS SCHEME
For obtaining the diversity gain, the best user is scheduled based on the main channel quality between S n and HR. In particular, based on the CSI of the S n * → R links, the selected user S n * is given by Lemma 1: If X m , m ∈ {1, 2, · · · , M }, denotes the random variable subjecting to the independent and identical exponential distribution, the pdf and the cumulative distribution function (cdf) of X = max (X m ) is given by where x represents the independent random variable, 1/λ X denotes the average channel gain. As a result, based on Lemma 1, we have the pdf of h S n * R 2 in BUS as It is noted that we choose the best user based on the main link, which is independent of the wiretapping link, so the selected user is equivalent to a random one for Eve. Thus, it can be derived that |h RE | 2 and h DE 2 2 are subjected to the exponential distribution with parameters 1/λ RS , 1/λ SE , 1/λ RD , 1/λ RE and 1/λ DE , respectively. Remark 2: It is noted that for ensuring the effectiveness of the BUS strategy, in the uplink information transmission of the system, each alternative user first reports his CSI to the HR, then the HR collects all CSIs to analyze the channel quality of each user comprehensively and selects the best user to transmit confidential information. As per (14) and (17), it can be inferred that the multiuser diversity gain can be acquired for the BUS scheme, which is advantageous for the improvement of system performance. When the selected optimal source transmits confidential information, the networks will achieve a better diversity gain, leading to lower outage probability of the data, which is applicable for future energy-constrained networks.

III. SECRECY PERFORMANCE ANALYSIS A. HYBRID OUTAGE PROBABILITY
In fact, for the energy-limited future networks, aiming to keep the stable operation of the system, the internal EH nodes need a minimum energy (activation threshold) to activate the EH circuits and to maintain the continuous energy conversion. Otherwise, if the harvested energy of EH nodes is lower than the minimum threshold, the users will always stay in a silent state, resulting in the confidential information cannot be transmitted, i.e., the energy outage occurs [12]. Therefore, in the considered multiuser WPCCN, HOP is adopted as the proper metric commonly, which is closely related to the minimum energy threshold and secure transmission [12], [52]. The HOP, i.e., the outage probability that combining the EOP [53], [54] and SOP, can be given by where sch ∈ {RUS, BUS}, P HOP denotes the HOP of each scheme. P EOP denotes the EOP of the considered WPCCN, which is identical to each scheme due to the fact that it actually doesn't make any difference in the processes of energy consumption and EH for the wireless powered nodes. Above analysis will be proved in the following section based on the numerical results.
Specifically, when the energy harvested at each user is lower than the inherent activation threshold of the EH circuit, the network only performs energy transfer between the HR and the source users without confidential information transmission, leading to the energy outage [52]- [54]. Note that for ease of analysis, we assume that all the source devices have the same EH module and power conversion circuit, i.e., all the users have the identical activation threshold. As such, EOP is given by where A denotes the activation threshold, and T 1 = (1−α) A 2ηαP R . Obviously, it can be observed that when the EOP is small, the system will perform the information transmission. At this time, the SOP mainly depends on the relationship between the secrecy capacity of the system and the predetermined transmission rate, which means that the EOP has little impact on the HOP of the network, and the HOP will be restricted by the SOP. On the contrary, when the EOP is large, the harvested energy at the source user is not enough to support the data transmission, and the system will mainly perform the energy transmission, which leads to that the EOP of the system plays a major role in the overall system performance. Therefore, EOP can capture the energy efficiency of the considered WPCCN to a certain extent.
Remark 3: The data transmission will be interrupted if there is no active node in the networks. Thus, when the transmit power of HR is low, the harvested energy at wireless powered users is limited, resulting in the larger EOP, which is equivalent to increase the HOP of the HR-assisted WPCCN. It can be inferred that for maintaining the operation of the network in a long run, it is a very effective way to increase the transmit power of HR, which is helpful to arouse the enthusiasm of EH nodes for information transmission. In addition, it can be observed from (19) that the number of the source users has positive role on the EOP, the latter numerical results will confirm this conclusion.
On the other hand, P SOP in (18) denotes the SOP of each scheme, which is generally considered as a vital metric of PLS [28]- [30], [52]. In fact, when secrecy capacity of the system is lower than a predetermined transmission rate threshold R th , the networks incurs secrecy outage. Therefore, P (sch) SOP is given as where C (sch) s denotes the secrecy capacity of different schemes. For the DF relay protocol, the selected source node and HR can adopt the different codebooks for improving secrecy performance [55], [56]. In fact, when the selected source user and the HR use different codebooks to transmit the confidential information, the eavesdropper cannot VOLUME 9, 2021 combine the received signal during the two hops, i.e., the maximum ratio combination (MRC) is not available for the eavesdropper. Thus, securing each hop individually is sufficient to prevent the end-to-end transmission from being eavesdropped. To secure the wireless communications, the PLS (i.e., physical-layer security) techniques exploit the physical-layer characteristics of wireless channels [57], which can be supposed as an effective complement to the traditional cryptographic techniques based on the ''computationally secure'' [58]. Based on the Wyner's wiretap model [59], the PLS techniques can achieve the ''informationtheoretically secure'' if the wiretap channel from a source to an eavesdropper is a degraded version of the main channel from the source to its intended destination. As such, the secrecy of the wireless transmission aided by the PLS techniques is normally measured by the difference between the capacities of the main channel and that of the wiretap channel [60], [61], i.e., secrecy capacity. In the considered system, the secrecy capacity is given by in which C (sch) s1 and C (sch) s2 is the secrecy capacity of first hop and second hop, respectively. It is worth noting that for PLS, the secrecy capacity is the main index used for the performance evaluation of the system, where the ''secrecy'' is the ''secrecy'' in the field of PLS actually. Meanwhile, the ''secrecy'' in the paper can be understood as follows, i.e., the legitimate channel will be heard by the eavesdropped but stays confidential due to the jamming and the multiuser diversity gain.

1) SOP DERIVATION FOR THE RUS SCHEME
Based on the RUS scheme, the optimal source user is selected randomly in order to cut down the costs and complexity of considered networks, which means that each user can be scheduled for information transmission with the same probability. Thus, the exact SOP of the RUS scheme is given by whereλ SE = λ SE β andλ RE = λ RE β , K 1 (·) is the modified Bessel function of the second kind and {α, γ ; z} denotes the confluent hypergeometric function of the second kind [62], in which α = 1 and γ = 1, Proof : Appendix A shows the proof.

2) SOP DERIVATION FOR THE BUS SCHEME
On the other hand, for the achievement of the diversity gain, the optimal user is scheduled based on the main channel quality between S n and HR in the BUS scheme. As for the BUS scheme, the corresponding SOP is given by where 49780 VOLUME 9, 2021 Finally, as per (18), with the help of (19), (25) and (26), the HOP of the HR-assisted WPCCN with FD-DBJ for each scheme can be derived.
Remark 4: It can be observed that the HOP of each scheme is related to N , A ,γ R , andγ D . Therefore, we consider the overall performance as a function of the network parameters, including the number of users, the transmit power both of HR and FD-destination, the time-switching factor, the predetermined transmission rate and so on, which will afford some references for the engineering design.

B. SECRECY THROUGHPUT
Generally, when the secure transmission can be provided, the effectiveness of the data transmission is also an important evaluation metric to gain more insights. For the secrecy performance analysis, the ST, which can be defined as the average transmission rate of confidentiality achieving secure and reliable communication between the source users and the desired destination, is often used to measure the secure effectiveness of the considered networks [46]. Mathematically, the ST of above discussed schemes is given by where T (sch) s (R th ) denotes the ST of each secure scheme, 1 − P (sch) HOP (R th ) represents the probability of the confidential information can be transmitted reliably and safely.
Remark 5: It is noted that from (27), we find that the smaller R th has negative impact on the ST, i.e., if the R th is set too small, the ST will be small. On the other hand, the larger R th will lead to the P (sch) SOP close to 1, which brings out the larger P (sch) HOP as well as the smaller ST. Thus, there exists a optimal predetermined transmission rate denoted as R opt th to obtain the optimal ST denoted as T opt s . Specifically, the predetermined transmission rate optimization problem is given by It is worth noting that the expression in (28) has important guiding significance for engineering application, so it can play more practical role in the future energy-limited communication scenarios.

C. THE OPTIMIZATION OF PREDETERMINED TRANSMISSION RATE
In fact, the explicit expression for R opt th is hard to acquire. In order to solve the optimization problem (28) in low complexity, we adopt the Brent method, which is a globally optimization method for the optimization problem with a unimodal objective function [63]. Indeed, the Brent method is a root-finding algorithm method without the derivative, which combines the methods of the golden section and the inverse parabolic interpolation. Specifically, the Brent method gives the priority to the inverse parabolic interpolation, and resorts to the golden section search when the inverse parabolic interpolation is invalid [64]. It is noted that the objective function of the secrecy maximization problem is a unimodal function, which will be shown in the numerical results. Thus, the Brent method can globally solve the secrecy throughput maximization problem.
Then, we give a brief description of Brent method in the optimization R th when fixing α as shown in Algorithm 1. Firstly, we choose an initial triple υ 0 = (R th,1 , R th,3 , R th,2 ), where R th,1 < R th,3 < R th,2 within initial interval R th ∈ (0, 2.5). Then, we fit υ 0 by a parabola, where the maximum point R th,4 is given by If the fitting is invalid or R th,4 is located outside of the interval between R th,1 and R th,2 , R th,4 will be obtained by gold section search. Afterwards, compare the T  (R th,4 ) is larger, the triplet will be updated as υ 1 = (R th,3 , R th,4 , R th,2 ), otherwise, υ 1 = (R th,1 , R th,3 , R th,4 ). Finally, at each iteration, the interval of the triple becomes smaller, until the interval is smaller than the predefined tolerance. VOLUME 9, 2021

IV. NUMERICAL RESULTS AND DISCUSSION
In this section, we present numerical results to evaluate the secrecy performance of the HR-assisted WPCCN with FD-DBJ in this section. As [29], we adopt a simulation environment of linear topology, where the destination, the HR, and the multiple source users in a localized group are placed in horizontal way. Unless stated otherwise, we set the activation threshold as th = A /N 0 = 2 dB, the predetermined transmission rate as R th = 0.1 bit/s/Hz, the number of the users as N = 4, the time-switching factor as α = 0.5, and the energy conversion efficiency as η = 0.8, γ R = P R /N 0 = 30 dB, γ D = P D /N 0 = 20 dB, λ SR = λ RS = λ RD = 5, λ SE = λ RE = 10 and λ DE = 1. By comparison, we denote the optimal multiuser selection strategy (i.e., n * = arg max n (C s1 (n))) as the benchmark scheme.
In Fig.3, we plot P (sch) HOP versus γ R with different numbers of users N . At first, we observe that N plays a positive role on the performance of the system. Then, we observe that the BUS scheme can acquire much better secrecy performance than the RUS scheme. In contrast, we observe that the secrecy performance of the proposed BUS scheme is slightly worse than that of the benchmark scheme. However, it is noted that the benchmark scheme is hard to achieve in practice due to the fact that the source users and the HR are difficult to acquire the CSI relative to the eavesdropper. Thus, the proposed BUS scheme is still an efficient way to achieve the secure transmission. Meanwhile, we can further observe that for BUS scheme, the secrecy performance improves as N increases. In contrast, the value of N has no effect on the RUS scheme. It is because that the RUS scheme randomly selects the source from multiple users for information transmission, which means that the number of sources and the selection scheme are independent of each other. In Fig. 4, we plot P (sch) HOP versus γ R with different energy conversion efficiency factors η. It is illustrated in Fig. 4 that for a given N , η plays a positive role on the secrecy performance. This is due to the fact that the energy conversion efficiency of the considered WPCCN is dependent on the η. On the one hand, the increase of energy conversion efficiency enables more source users to exceed the energy threshold, which activates more users to participate in information transmission. On the other hand, larger η can ensure that the source nodes harvest more energy, which decreases the energy outage probability, i.e., P (sch) EOP , resulting in the decrease of P (sch) HOP . Moreover, we can also observe that the BUS scheme can achieve better secrecy performance than the RUS scheme, which demonstrates the validity of the BUS scheme again.
In Fig. 5, we plot the P (sch) HOP versus γ R with/without the DBJ (i.e., destination-based jamming). At first, we observe that the secrecy performance without the DBJ is considerable terrible, which is almost unacceptable for secure transmission in the considered system. In contrast, we find that P (sch) HOP in the case with the DBJ is relatively small, which illustrates the positive impact of the DBJ on the secrecy performance. Actually, the introduction of the DBJ can confuse malicious eavesdroppers effectively. In other words, stronger DBJ enables the channel quality of the eavesdropper to a lower level. It is worth mentioning that there exist feedback links between the HR and the destination, and hence the DBJ can be eliminated at the HR and the destination by the interference cancellation techniques. Thus, the introduction of the DBJ is conductive to improve the secrecy performance of the considered system.
In Fig.6, we plot T (sch) s versus α. We first observe that the function of T (sch) s with respect to α is an unimodal function. It can be explained by the fact that the source users cannot harvest sufficient energy to maintain their function when α is too small. In contrast, when α is exceedingly large, the transmission time is very short leading to large HOP, which causes the small value of the ST. Furthermore, we plot T (sch) s versus R th in Fig.7. Similarly, we also find that the function of T (sch) s with respect to R th is also an unimodal function, which proves that there exists a optimal predetermined transmission rate R opt th to maximum ST. It is consistent with the deduction in Remark 5.

V. CONCLUSION
In this paper, we explore the PLS of a HR-assisted multiuser WPCCN with FD-DBJ. In particular, two secure multiuser scheduling strategies are proposed for the improvement of the secrecy performance. The analytical closed-form expressions of EOP, SOP and HOP are derived for each scheme, and the maximization problem of ST is solved with help of the Brent method. For getting a deeper insight, the influence of key parameters on secrecy performance of the system is further discussed. Simulation results are provided to validate the correctness of our analysis.

APPENDIX A
Firstly, as per (22), P (RUS) SOP is given by P whereP (RUS) Then, with the help of (23), we havē where Furthermore, P 1 can be shown as: where Then, P 2 is given by where P 3 is given by It is noted that in line with (13), we have The reason is that for the RUS scheme, the optimal source user is selected randomly, which means that the RUS scheme have no diversity gain. VOLUME 9, 2021 Therefore, by inserting (34) into (33), P 2 is given by where K 1 (·) denotes the modified Bessel function of the second kind [62]. By inserting (36) into (32), P 1 is given by , and performing some mathematical manipulations,P (RUS) SOP1 in (31) is given bȳ On the other hand, as per (24), we havē where P a = Pr |h RD | 2 > β|h RE | 2 γ D y+1 + β−1 γ R . Then, P a is given by Similarly, by inserting (40) Finally, by substituting (38) and (41) where Furthermore, P 4 is given by where P 5 = Pr h S n * R 2 > βx γ D y+1 + ξ γ R h RS n *

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Then, P 5 is given by dz. (45) 49784 VOLUME 9, 2021 where P 6 can be calculated as As per (17), we have It is due to the fact that for the BUS scheme, the best user is scheduled on the main channel quality between S n and HR, which means that the BUS can obtain the diversity gain, resulting in the improving of the secrecy performance. By inserting (46) into (45), P 5 is given by By inserting (48) into (44), P 4 is given by On the other hand, as per (24),P (BUS) SOP2 is given bȳ where P b = Pr |h RD | 2 > β|h RE | 2 γ D y+1 + β−1 γ R . Then, P b is given by Similarly, by inserting (52) Finally, by substituting (50) and (53) into (42) and performing some mathematical manipulations, P (BUS) SOP in (26) can be derived.