# Secure Information Transmissions in Wireless-Powered Cognitive Radio Networks for Internet of Medical Things

Authors: Kun Tang; Wenjuan Tang; Entao Luo; Zhiyuan Tan; Weizhi Meng; Lianyong Qi
Journal: Security and Communication Networks
 (2020)

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## Abstract

In this paper, we consider the issue of the secure transmissions for the cognitive radio-based Internet of Medical Things (IoMT) with wireless energy harvesting. In these systems, a primary transmitter (PT) will transmit its sensitive medical information to a primary receiver (PR) by a multi-antenna-based secondary transmitter (ST), where we consider that a potential eavesdropper may listen to the PT’s sensitive information. Meanwhile, the ST also transmits its own information concurrently by utilizing spectrum sharing. We aim to propose a novel scheme for jointly designing the optimal parameters, i.e., energy harvesting (EH) time ratio and secure beamforming vectors, for maximizing the primary secrecy transmission rate while guaranteeing secondary transmission requirement. For solving the nonconvex optimization problem, we transfer the problem into convex optimization form by adopting the semidefinite relaxation (SDR) method and Charnes–Cooper transformation technique. Then, the optimal secure beamforming vectors and energy harvesting duration can be obtained easily by utilizing the CVX tools. According to the simulation results of secrecy transmission rate, i.e., secrecy capacity, we can observe that the proposed protocol for the considered system model can effectively promote the primary secrecy transmission rate when compared with traditional zero-forcing (ZF) scheme, while ensuring the transmission rate of the secondary system.


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## Body

## 1. Introduction

With the rapid development of wireless communication and networking technologies, an increasing number of devices need to be connected globally and communicate automatically. Therefore, the emerging of the Internet of Things (IoT) as a promising paradigm can achieve a fusing of the various technologies in 5G communication systems, which have been widely applied in smart cities, agriculture, and environment monitoring [1–6]. Moreover, the medical care and health care are becoming one of the most popular applications based on the IoT [7, 8], named the Internet of Medical Things (IoMT), which can collect the data from the medical devices and applications to improve the treatment effect, disease diagnosis, and patient experience, while reducing misdiagnosis rate and treatment cost. According to the investigation of relevant organizations, the market share of IoMT will reach to roughly 117 billion dollars by the end of 2020 [9]. However, with the increasing use of IoMT equipment, the huge demand for radio spectrum has become a serious problem. In addition, the allocated radio spectrums are often underutilized due to the inflexible spectrum policies [10]. In order to facilitate an effective utilization of spectrum resources, cognitive radio technology was introduced in which unlicensed nodes could communicate with each other in an opportunistic manner over a licensed frequency band without interrupting the primary transmissions [11–13].Yet, power supply is another key constraint on the development of IoMT. In general, an IoMT system usually contains a large number of small-size devices that are battery-powered and difficult to be replaced. In order to solve this problem, wireless-powered technology has been paid high attention. The devices with EH capabilities can convert energy from the surrounding environment into electricity for data transmission, such as solar, wind, or RF signals [14]. Especially with the synchronous development of antenna and circuit designs, wireless EH based on RF signals has attracted more attention due to its advantages of wireless, low cost, and small form implementation [15–17]. Furthermore, the amount of harvested energy is in milliwatts, which is enough to power small-size IoMT devices, such as medical data sensors for short-distance transmissions. Therefore, the combination of cognitive radio and EH in medical wireless sensor networks can greatly improve both the spectrum and energy efficiencies.Although adopting cognitive radio technology with EH can effectively improve the transfer efficiency for IoMT, the variety of medical devices in healthcare fields will introduce several security problems [18]. Since the energy-constraint sensors need to perform energy harvesting and then forward the sensitive patient data wirelessly, the other illegal sensors may be the potential eavesdropper to listen such confidential messages [19]. As an emerging field, a large number of healthcare manufacturers are rushing to utilize the IoT solutions in some applications without considering security. As a result, they will bring new security problems related to confidentiality, integrity, and availability. Furthermore, due to the limited capabilities, such as lack of effective computation and sufficient power supply, many sensors in IoMT cannot embed the encryption algorithm. Therefore, this lack of strong encryption across medical sensors makes themselves to be discovered and exploited by malicious users easily.


### 1.1. Related Work

To take the full advantage of the potential gains for wireless EH, the researchers developed simultaneous wireless information and power transmission (SWIPT) schemes in wireless networks that utilize RF signals to transmit energy and information to receivers. Chen et al. [20] applied the SWPIT in relay interference channels for multiple source-destination pair communication system, where each pair of link has a dedicated EH relay serving for relaying transmission. On this basis, the optimal power allocation ratio for each relay was deduced by adopting the distributed power allocation framework of game theory. A SWIPT scheme for amplify-and-forward (AF) bidirectional relaying network based on OFDM was proposed in [21], where a wireless-powered relay performed information processing and EH by utilizing two disjointed subcarrier groups, respectively. Based on the decode-and-forward (DF) mode, Shi et al. [22] designed an optimal resource allocation strategy to maximize the energy efficiency with the nonlinear SWIPT model under a two-way relay network. For cognitive radio networks with energy harvesting in IoT systems, Zhang et al. [23] analyzed the outage probability of a random underlay cognitive network with EH-based assistant relay. The two main challenges for cognitive radio sensor networks in IoT systems were considered in [24], where the authors developed an architecture and proposed an energy management strategy for achieving balance between the transmission performance of the networks and operational life. In [25], the insecure characteristic of electronic medical records based on eHealth systems was considered, and then a corresponding secure encrypted scheme to ensure the data security was proposed. In [26], Gurjar et al. investigated an overlaid spectrum sharing network with SWIPT for IoT systems, where a pair of SWIPT-based devices is used as the relay to assist the transmission of the primary signals. Considering information security in cognitive radio-based IoT systems, Salameh et al. [27] presented a novel algorithm for channel allocation with time-sensitive data under the scenario of jamming attacks. A secure relay selection scheme based on channel state information and battery state information was proposed for energy harvesting-based cognitive radio networks in IoT networks [28].


### 1.2. Motivation and Contributions

Unlike the abovementioned literates [27, 28], we consider an actual application scenarios for sanatorium or hospital under the cognitive radio-based IoTM networks to protect the patients’ sensitive medical information. Consider an indoor environment for sanatorium or hospital, where the PT intends to transmit its sensitive medical data to the PR, while the ST performs data monitoring and transfer to the SR. In this scenario, the node ST has lack of energy supply and need to scavenge energy from the primary transmitter, while ST can be regarded as the relay to opportunistically access the licensed primary channel. Meanwhile, we assume that an attacker is located near the PR to eavesdrop the PT’s medical data. Thus, to enable the secure transmission of the PT’s signal, we investigate a typical cognitive radio network with wireless-powered relay (CRN-WPR) and jointly design the optimal EH time ratio and secure beamforming vectors to maximize the secrecy transmission rate of the primary system, while effectively guaranteeing the secondary transmission rate. The main contributions are summarized as follows:(i)
We propose a corresponding protocol for EH and secrecy information transmission for a cognitive radio-based IoMT system, where the relay node ST is equipped with multiple antennas to perform EH at first and then transfer the sensitively primary signal with DF processing to the destination in security with its own signal.(ii)
In order to protect the sensitive medical data being sent from the PT, we formulate the optimization problem based on maximizing the secrecy transmission rate of the primary system while ensuring the transmission requirement of the secondary system. We adopt SDR and Charnes–Cooper transformation to transform the nonconvex optimization problem into a convex optimization problem to find a solution for the optimization problem. A corresponding algorithm is then developed. In addition, the zero-forcing (ZF) scheme is also applied to solve the optimization problem as a benchmark.(iii)
The numerical results of the influence for the secrecy transmission rate on the primary system under different system parameters are given, such as primary transmission power, number of antennas, and transmission distance. The results demonstrate excellent secure transmission performance with proposed scheme than ZF scheme.The rest of this paper is organized as follows. The Section2 introduces the system model and transmission protocol. Section 3 formulates the optimization problem and proposes the corresponding solution with secure beamforming. Furthermore, the ZF scheme is also adopted to solve the optimization as a benchmark. The Section 4 presents the simulation results and corresponding analyses. The Section 5 summarizes this paper.Notations: Throughout this paper, let ⋅H denote the conjugate transpose. I presents the identity matrix with appropriate dimension. x+ represents the maximum value between x and 0, while x∗ denotes the optimal value of x. ∏x⊥ denotes the orthogonal projection onto the orthogonal complement of the column space of x. ⋅ denotes the Euclidean norm of a vector or a matrix and ⋅ denotes the magnitude of a channel or the absolute value of a complex number. Table 1 lists the fundamental notations and parameters.Table 1
List of parameters and their physical meaning/expression.
Parameter
Meaning/expression
h
PST, hSS, hSME, hSPR
N
×
1 complex channel vectors of the PT-ST, ST-SR, ST-ME, and ST-PR, respectively
h
PP, hPME
Channel coefficients of the PT-PR and the PT-ME
α
Duration of energy harvesting
T
Total block time
x
e, xP
Transmit dedicated energy signal and confidential signal at PT
x
^
P, xS
Decoded primary signal and secondary signal at ST
P
P
PT’s transmission power
n
ST, nPR, nME, nSR
Received AWGN at ST, PR, ME, and SR
η
Energy conversion efficiency from signal power to circuit power
R
ST, RPR, RME, RSR
Achievable rate at ST, PR, ME, and SR, respectively
R
˜
PR, R˜ME
Overall transmission rates at PR and ME
R
SEC
Secrecy rate of the primary system
v
P, vS
Relaying beamforming vector and cognitive beamforming vector
E
ST
0
Initial power at the ST
r
S
Minimal transmission rate requirement for the secondary system
Γ
An auxiliary optimization variable to bound the achievable rate of the eavesdropper ME
β
Power allocation coefficient


## 1.1. Related Work

To take the full advantage of the potential gains for wireless EH, the researchers developed simultaneous wireless information and power transmission (SWIPT) schemes in wireless networks that utilize RF signals to transmit energy and information to receivers. Chen et al. [20] applied the SWPIT in relay interference channels for multiple source-destination pair communication system, where each pair of link has a dedicated EH relay serving for relaying transmission. On this basis, the optimal power allocation ratio for each relay was deduced by adopting the distributed power allocation framework of game theory. A SWIPT scheme for amplify-and-forward (AF) bidirectional relaying network based on OFDM was proposed in [21], where a wireless-powered relay performed information processing and EH by utilizing two disjointed subcarrier groups, respectively. Based on the decode-and-forward (DF) mode, Shi et al. [22] designed an optimal resource allocation strategy to maximize the energy efficiency with the nonlinear SWIPT model under a two-way relay network. For cognitive radio networks with energy harvesting in IoT systems, Zhang et al. [23] analyzed the outage probability of a random underlay cognitive network with EH-based assistant relay. The two main challenges for cognitive radio sensor networks in IoT systems were considered in [24], where the authors developed an architecture and proposed an energy management strategy for achieving balance between the transmission performance of the networks and operational life. In [25], the insecure characteristic of electronic medical records based on eHealth systems was considered, and then a corresponding secure encrypted scheme to ensure the data security was proposed. In [26], Gurjar et al. investigated an overlaid spectrum sharing network with SWIPT for IoT systems, where a pair of SWIPT-based devices is used as the relay to assist the transmission of the primary signals. Considering information security in cognitive radio-based IoT systems, Salameh et al. [27] presented a novel algorithm for channel allocation with time-sensitive data under the scenario of jamming attacks. A secure relay selection scheme based on channel state information and battery state information was proposed for energy harvesting-based cognitive radio networks in IoT networks [28].


## 1.2. Motivation and Contributions

Unlike the abovementioned literates [27, 28], we consider an actual application scenarios for sanatorium or hospital under the cognitive radio-based IoTM networks to protect the patients’ sensitive medical information. Consider an indoor environment for sanatorium or hospital, where the PT intends to transmit its sensitive medical data to the PR, while the ST performs data monitoring and transfer to the SR. In this scenario, the node ST has lack of energy supply and need to scavenge energy from the primary transmitter, while ST can be regarded as the relay to opportunistically access the licensed primary channel. Meanwhile, we assume that an attacker is located near the PR to eavesdrop the PT’s medical data. Thus, to enable the secure transmission of the PT’s signal, we investigate a typical cognitive radio network with wireless-powered relay (CRN-WPR) and jointly design the optimal EH time ratio and secure beamforming vectors to maximize the secrecy transmission rate of the primary system, while effectively guaranteeing the secondary transmission rate. The main contributions are summarized as follows:(i)
We propose a corresponding protocol for EH and secrecy information transmission for a cognitive radio-based IoMT system, where the relay node ST is equipped with multiple antennas to perform EH at first and then transfer the sensitively primary signal with DF processing to the destination in security with its own signal.(ii)
In order to protect the sensitive medical data being sent from the PT, we formulate the optimization problem based on maximizing the secrecy transmission rate of the primary system while ensuring the transmission requirement of the secondary system. We adopt SDR and Charnes–Cooper transformation to transform the nonconvex optimization problem into a convex optimization problem to find a solution for the optimization problem. A corresponding algorithm is then developed. In addition, the zero-forcing (ZF) scheme is also applied to solve the optimization problem as a benchmark.(iii)
The numerical results of the influence for the secrecy transmission rate on the primary system under different system parameters are given, such as primary transmission power, number of antennas, and transmission distance. The results demonstrate excellent secure transmission performance with proposed scheme than ZF scheme.The rest of this paper is organized as follows. The Section2 introduces the system model and transmission protocol. Section 3 formulates the optimization problem and proposes the corresponding solution with secure beamforming. Furthermore, the ZF scheme is also adopted to solve the optimization as a benchmark. The Section 4 presents the simulation results and corresponding analyses. The Section 5 summarizes this paper.Notations: Throughout this paper, let ⋅H denote the conjugate transpose. I presents the identity matrix with appropriate dimension. x+ represents the maximum value between x and 0, while x∗ denotes the optimal value of x. ∏x⊥ denotes the orthogonal projection onto the orthogonal complement of the column space of x. ⋅ denotes the Euclidean norm of a vector or a matrix and ⋅ denotes the magnitude of a channel or the absolute value of a complex number. Table 1 lists the fundamental notations and parameters.Table 1
List of parameters and their physical meaning/expression.
Parameter
Meaning/expression
h
PST, hSS, hSME, hSPR
N
×
1 complex channel vectors of the PT-ST, ST-SR, ST-ME, and ST-PR, respectively
h
PP, hPME
Channel coefficients of the PT-PR and the PT-ME
α
Duration of energy harvesting
T
Total block time
x
e, xP
Transmit dedicated energy signal and confidential signal at PT
x
^
P, xS
Decoded primary signal and secondary signal at ST
P
P
PT’s transmission power
n
ST, nPR, nME, nSR
Received AWGN at ST, PR, ME, and SR
η
Energy conversion efficiency from signal power to circuit power
R
ST, RPR, RME, RSR
Achievable rate at ST, PR, ME, and SR, respectively
R
˜
PR, R˜ME
Overall transmission rates at PR and ME
R
SEC
Secrecy rate of the primary system
v
P, vS
Relaying beamforming vector and cognitive beamforming vector
E
ST
0
Initial power at the ST
r
S
Minimal transmission rate requirement for the secondary system
Γ
An auxiliary optimization variable to bound the achievable rate of the eavesdropper ME
β
Power allocation coefficient


## 2. System Model and Transmission Protocol

### 2.1. System Model

We consider a cognitive radio network with wireless-powered relay (CRN-WPR) as shown in Figure1. The primary system is composed of a primary transmitter (PT) and a primary receiver (PR), while the secondary system consists of a secondary transmitter (ST) and a secondary receiver (SR). There also exists an eavesdropper (ME) whose purpose is to intercept the PT’s confidential data in the range of the primary system, where PT intends to send confidential data to PR. The primary system may be regard as the uplink of the transmission system with poor channel quality or lower rate. Therefore, the ST is willing to act as the relay for assisting the primary transmission while delivering its own data. We assume that the PT has a fixed power supply, while the ST may have limited battery storage, so it needs to obtain energy from the received RF signal. The ST is equipped with N antennas and other nodes operate in the half-duplex mode with a single antenna.Figure 1
The system model of a CRN-WPR. The green line denotes the first phase for energy harvesting and the blue lines and red lines represent the second and third information transmission phases from the PT and ST, respectively.All channels undergo the flat block Rayleigh fading channel, which is characterized by quasistatic state of the channel in one transmission-slot and independent change in different transmission-slots. LethPST, hSS, hSME, and hSPR be the N×1 complex channel vectors of the PT-ST, ST-SR, ST-ME, and ST-PR, respectively. The channel coefficients of the PT-PR and the PT-ME links are denoted by hPP and hPME. The global channel state information is available for the system, which is a common assumption in physical-layer security literatures [29, 30].


### 2.2. Energy Harvesting and Information Transmission

As depicted in Figure1, the EH and information transmission in one transmission-slot include three phases. In the first phase, the PT uses a portion of time αα∈0,1 of the total block time T to transmit the dedicated energy signal xe to ST for EH. Thus, the received signal at the ST can be expressed as(1)ySTI=PPhPSTxe+nST,where PP represents the transmission power of the node PT, xe denotes the unit-power energy signal, and nST∼CN0,δSTI is the received additive Gaussian white noise (AWGN) with variance of δST. For definiteness and without loss of generality, we assume T=1. Thus, the amount of harvested energy at the ST can be calculated as(2)EST=αηPPhPST2,where η∈0,1 is energy conversion efficiency. Note that the amount of scavenged energy from noise is neglected because the harvested energy from the thermal noise can be negligible compared to the energy signal.At the second phase of duration1−αT/2, the PT transmits confidential signal xP with power PP, the received signal at the ST is thus given as(3)ySTII=PPhPSTxP+nST.The achievable rateRST can be derived as(4)RST=1−αT2log21+PPhPST2δST.Due to the nature of the information broadcast, the PR and eavesdropper ME can also receive the signalxP and the received signals at the PR and ME are given as(5)yPRII=PPhPPxP+nPR,yMEII=PPhPMExP+nME,respectively, where nPR∼CN0,δPR and nME∼CN0,δME denote AWGN at PR and ME, respectively.During the third phase1−α/2, the node ST first decodes the received primary confidential signal x^P based on DF processing and then simultaneously forwards x^P and its own signal xS by utilizing the beamforming vectors vP∈ℂN×1 and vS∈ℂN×1, respectively. Therefore, the corresponding received signal at the PR and eavesdropper ME are expressed as(6)yPRIII=hSPRHvPx^P+hSPRHvSxS+nPR,yMEIII=hSMEHvPx^P+hSMEHvSxS+nPR,respectively. The PR attempts to retrieve x^P from yPRIII in the presence of the secondary signal xS. In the meanwhile, the eavesdropper also intends to intercept signal x^P. Thus, the achievable rates at the PR and ME in last two phases can be expressed as(7)RPR=1−αT2log21+PPhPP2δPR+hSPRHvP2hSPRHvS2+δPR,RME=1−αT2log21+PPhPME2δME+hSMEHvP2hSMEHvS2+δME.At the SR, the received signal is given by(8)ySR=hSSHvSxS+hSSHvPx^P+nSR.Similar to the PR, the SR treatsx^P as interference and then detects the desired secondary signal xS. The achievable rate at the SR is given by(9)RSR=1−αT2log21+hSSHvS2hSSHvP2+δSR.


## 2.1. System Model

We consider a cognitive radio network with wireless-powered relay (CRN-WPR) as shown in Figure1. The primary system is composed of a primary transmitter (PT) and a primary receiver (PR), while the secondary system consists of a secondary transmitter (ST) and a secondary receiver (SR). There also exists an eavesdropper (ME) whose purpose is to intercept the PT’s confidential data in the range of the primary system, where PT intends to send confidential data to PR. The primary system may be regard as the uplink of the transmission system with poor channel quality or lower rate. Therefore, the ST is willing to act as the relay for assisting the primary transmission while delivering its own data. We assume that the PT has a fixed power supply, while the ST may have limited battery storage, so it needs to obtain energy from the received RF signal. The ST is equipped with N antennas and other nodes operate in the half-duplex mode with a single antenna.Figure 1
The system model of a CRN-WPR. The green line denotes the first phase for energy harvesting and the blue lines and red lines represent the second and third information transmission phases from the PT and ST, respectively.All channels undergo the flat block Rayleigh fading channel, which is characterized by quasistatic state of the channel in one transmission-slot and independent change in different transmission-slots. LethPST, hSS, hSME, and hSPR be the N×1 complex channel vectors of the PT-ST, ST-SR, ST-ME, and ST-PR, respectively. The channel coefficients of the PT-PR and the PT-ME links are denoted by hPP and hPME. The global channel state information is available for the system, which is a common assumption in physical-layer security literatures [29, 30].


## 2.2. Energy Harvesting and Information Transmission

As depicted in Figure1, the EH and information transmission in one transmission-slot include three phases. In the first phase, the PT uses a portion of time αα∈0,1 of the total block time T to transmit the dedicated energy signal xe to ST for EH. Thus, the received signal at the ST can be expressed as(1)ySTI=PPhPSTxe+nST,where PP represents the transmission power of the node PT, xe denotes the unit-power energy signal, and nST∼CN0,δSTI is the received additive Gaussian white noise (AWGN) with variance of δST. For definiteness and without loss of generality, we assume T=1. Thus, the amount of harvested energy at the ST can be calculated as(2)EST=αηPPhPST2,where η∈0,1 is energy conversion efficiency. Note that the amount of scavenged energy from noise is neglected because the harvested energy from the thermal noise can be negligible compared to the energy signal.At the second phase of duration1−αT/2, the PT transmits confidential signal xP with power PP, the received signal at the ST is thus given as(3)ySTII=PPhPSTxP+nST.The achievable rateRST can be derived as(4)RST=1−αT2log21+PPhPST2δST.Due to the nature of the information broadcast, the PR and eavesdropper ME can also receive the signalxP and the received signals at the PR and ME are given as(5)yPRII=PPhPPxP+nPR,yMEII=PPhPMExP+nME,respectively, where nPR∼CN0,δPR and nME∼CN0,δME denote AWGN at PR and ME, respectively.During the third phase1−α/2, the node ST first decodes the received primary confidential signal x^P based on DF processing and then simultaneously forwards x^P and its own signal xS by utilizing the beamforming vectors vP∈ℂN×1 and vS∈ℂN×1, respectively. Therefore, the corresponding received signal at the PR and eavesdropper ME are expressed as(6)yPRIII=hSPRHvPx^P+hSPRHvSxS+nPR,yMEIII=hSMEHvPx^P+hSMEHvSxS+nPR,respectively. The PR attempts to retrieve x^P from yPRIII in the presence of the secondary signal xS. In the meanwhile, the eavesdropper also intends to intercept signal x^P. Thus, the achievable rates at the PR and ME in last two phases can be expressed as(7)RPR=1−αT2log21+PPhPP2δPR+hSPRHvP2hSPRHvS2+δPR,RME=1−αT2log21+PPhPME2δME+hSMEHvP2hSMEHvS2+δME.At the SR, the received signal is given by(8)ySR=hSSHvSxS+hSSHvPx^P+nSR.Similar to the PR, the SR treatsx^P as interference and then detects the desired secondary signal xS. The achievable rate at the SR is given by(9)RSR=1−αT2log21+hSSHvS2hSSHvP2+δSR.


## 3. Problem Formulation and Secure Beamforming

In this section, we first define the secrecy rate of the primary system, which is a critical performance index to illustrate the transmission security of the sensitive data [31, 32] and then formulate the optimization problem with maximizing the primary secrecy rate aiming to satisfy the minimum achievable rate for the secondary system and power constraint of the relay node ST. In order to effectively obtain the optimal parameters to keep data in safety, we also propose a mathematically efficient optimization scheme to solve the problem with a two-stage procedure.


### 3.1. Problem Formulation

Based on the DF cooperative communication scheme, the overall transmission rates at PR and ME equals the minimum rate of the two-hop transmissions, respectively [32], i.e.,(10)R˜PR=minRST,RPR,R˜ME=minRST,RME.Based on the definition of [33], the secrecy rate of the primary system for the considered secrecy CRN-WPR can be expressed as(11)RSEC=R˜PR−R˜ME+.Substituting the results of equation (8) into equation (9), the overall primary secrecy rate is then given as(12)RSEC=minRST,RPR−RME+.In the following, the EH ratio and secure beamforming vectors are jointly designed by maximizing the primary secrecy rate subject to the minimum achievable rate for the SR and power constraint of the ST. Mathematically, the considered optimization problem can be represent as P1:(13)maxα,vP,vSminRST,RPR−RME+s.t.C1:RSR≥rSC2:vP2+vS2≤2αηPPhPST2+EST01−αC3:0<α<1,where C1 means that the achievable rate of SR should be larger than or equal to minimum raterS and C2 denotes the transmission power constraint at the ST with EST0 representing the initial power at the ST.


### 3.2. Optimal Secure Beamforming Design

According to the analysis of formula (13), we can observe that (P1) is a nonconvex function, which is difficult to derive three optimal variables α,vP,vS concurrently. This section proposes a mathematically efficient optimization scheme with two-stage procedure for solving the (P1) as follows:(i)
In the stage I, we obtain the optimal secure beamformingvP∗,vS∗ for any given energy harvesting duration α(ii)
In the stage II, the global optimal solutionα∗,vP∗,vS∗ can be found based on one-dimension search over αIn the stage I, the maximization of the primary secrecy rate is equivalent to maximizing the achievable rate of the PR subject to an alternative upper bound on the achievable rate of ME. Thus, for a givenα=α0, RSTα0 is the constant value and the problem (P1) can be transformed into the following problem (P2):(14)maxvP,vS1−α0T2log21+PPhPP2δPR+hSPRHvP2hSPRHvS2+δPRs.t.C1:1−α0T2log21+hSSHvS2hSSHvP2+δSR≥rSC2:vP2+vS2≤2α0ηPPhPST2+EST01−α0C3:1−α0T2log21+PPhPME2δME+hSMEHvP2hSMEHvS2+δME≤Γ,where Γ represents an auxiliary optimization variable to bound the achievable rate of the eavesdropper ME, thus the maximum primary secure rate can be obtained by adjusting value of Γ. The optimal value of Γ∗ can be founded by one-dimension search since it is a nonnegative value. Note that the optimization problem (P2) is still nonconvex concerning with beamforming vectors vP and vS.Consideringlog2x is monotonically increasing function of x and defining HSPR=hSPRhSPRH, HSME=hSMEhSMEH, HSS=hSShSSH, VP=vPvPH, and VS=vSvSH, the problem (P2) can be denoted as a fractional programming problem, but the objective function is still nonconvex since two optimization variables VP and VS exist in the numerator and denominator of objective function, respectively. To solve the problem (P2) more effectively, the fractional programming problem can be equivalently reformulated to a convex SDR problem by utilizing Charnes–Cooper transformation [34]. Thus, we let(15)λ=1trHSPRVS+δSR,while defining V˜P=λVP and V˜S=λVS, the corresponding SDR of problem (P2) can be rewritten as (P3):(16)maxvP,vS,λtrHSPRV˜Ps.t.C1:trHSPRV˜S+λδSR=1,C2:trHSSV˜S−ΓStrHSSV˜P≥λΓSδSR,C3:trV˜P+trV˜S≤2λα0ηPPhPST2+EST01−α0C4:trHSMEV˜P−ΓetrHSMEV˜S≤λΓeδMEC5:V˜P≽0,V˜S≽0,λ>0,where ΓS=22rS/1−α0−1 and Γe=22Γ/1−α0−PPhPME2/δME−1.It must be noted that SDR cannot guarantee to derive the optimal solutionvP∗,vS∗ with rank-one. In the following, the first step is to prove that the rank of optimal V˜P∗ equals to one, and then we propose a method to structure the optimal V˜S∗ with rank-one when the rank of V˜S is greater than one.Letθ1, θ2, θ3, and θ4 represent the Lagrange multipliers, i.e., dual variables, related to constraints C1 to C4 in equation (16), respectively. Thus, the corresponding Lagrange function of problem (P3) can be expressed as(17)ℒV˜P,V˜S,θ1,θ2,θ3,θ4=trξV˜P+trψV˜P+ρ,where(18)ξ=HSPR−θ2ΓSHSS−θ3I−θ4HSME,ψ=−θ1HSPR+θ2HSS−θ3I+θ4ΓeHSME,and ρ denotes the residual information that is not related to the proof. According to the definition of Karush–Kuhn–Tucker conditions and Lagrange function of problem (P3), we have(19)ξ∗V˜P∗=0,ψ∗V˜S∗=0.Assuming the harvested energy and initial energy are all used for secure beamforming transmission in the third phase, the power constraint C3 in equation (16) is activated with equality, thus the dual variable θ3∗>0. Since the transmission channel vectors HSS≽0 and HSME≽0, we can derive that rank−θ2∗ΓSHSS−θ3∗I−θ4∗HSME=N. Furthermore, since rankHSPR≤1, it follows that rankξ∗≥N−1. Based on equation (19), we thus obtain rankV˜P∗=1.Defineκ∗=−θ1∗HSPR−θ2∗HSS−θ3∗I+θ4∗HSME, thus we have(20)ψ∗=κ∗+2θ2∗HSS.SinceHSPR≽0, HSS≽0, and HSME≽0, we can obtain that rank−θ1∗HSPR−θ2∗HSS−θ3∗I=N. Moreover, since rankHSME≤1, rankκ∗≥N−1 can be derived:(i)
Ifrankκ∗=N, we can obtain rankψ∗=N−1, thus it follows from equation (19) that rankV˜S∗=1 and V˜S∗ is equal to awwH, where w∈ℂN×1 denotes the spanning null space of ψ∗ and a>0. Thus, the corresponding optimal value of (P3) is V˜P∗/λ∗,V˜S∗/λ∗;(ii)
Ifrankκ∗=N−1, we can observe that rankV˜S∗>1 and thus it requires constructing a new solution with rank-one. First, we obtain the orthonormal basis u∈ℂN×1 of the null base of κ∗, which is defined as κ∗u=0 and ranku=1. Then, based on the expression of κ∗, we can further derive that HSSu=0. Thus, the optimal solution of V˜S∗ is given by(21)V˜S∗=buuH+awwH,where b≥0, w=1, and wHu=0. Finally, the optimal result of V^S∗ with rank-one can be rewritten as V^S∗=V˜S∗−buuH. Thus, the reconstructed optimal solution for (P3) is V˜P∗/λ∗,V^S∗/λ∗.For fixedα=α0, the optimal solutions Γ∗,V˜P∗,V˜S∗ can be obtained through one-dimension search Γ based on the following equation:(22)Γ∗,VP∗,VS∗=argmaxα=α0problemP3,thus, the optimal secure beamforming vectors vP∗,vS∗ can be obtained by adopting eigenvalue decomposition (EVD) of V˜P∗/λ∗ and V˜S∗/λ∗.In order to obtain the global optimal solution for problem (P1) in the second stage, one-dimension search related toα is then utilized. The optimal solution is chosen from the following equation:(23)α∗,Γ∗,vP∗,vS∗=argmaxα∈0,1problemP1.The whole algorithm process can be described in Algorithm1, which is shown as follows.Algorithm 1: Optimal secure beamforming design.
Initialize α=α0 and Γ=Γ0; define Γmax as a large positive real number; Δα and Δτ are all small positive real numbers as the iterative steps for one-dimension search
1
for a given α=α0 do S1-S4
2
S1: givenΓ=Γ0, then solve problem (P3) and derive the optimal solution V˜P∗,V˜S∗,λ∗ by utilizing CVX tools
3
S2: obtain optimalV˜P∗,V˜S∗ through the following procedures
4
if rankV˜P∗=1 and rankV˜S∗=1, then
5
The optimal solution for problem (P3) isV˜P∗/λ∗,V˜S∗/λ∗
6
else
7
Reconstruct an optimal solutionV˜P∗/λ∗,V^S∗/λ∗ for problem (P3) with rankV˜P∗=1 and rankV^S∗=1 based on equation (21)
8
end if
9
S3:let Γ=Γ+Δτ when Γ<Γmax and then go to S1-S2
10
S4:choose the optimal solution Γ∗,VP∗,VS∗ from equation (22) and derive optimal secure beamforming vectors VP∗,VS∗ by performing EVD
11
end for
12
Update α=α+Δα and S1-S4
Choose the optimal solution α∗,Γ∗,vP∗,vS∗ based on equation (23)


### 3.3. Secure Beamforming Based on Zero-Forcing Rule

This section investigates another secure beamforming solution based on zero-forcing (ZF) rule as a benchmark, in which the primary transmission will not be interfered by other transmissions. Therefore, based on the criterion of ZF rule [35], the beamforming vectors vS,ZF and vP,ZF for the primary and secondary systems should be in the null space of hSPR⊥ and hSS⊥, respectively, i.e., hSPRHvS,ZF=0 and hSSHvP,ZF=0. Since there exists an eavesdropper in the system to listen the primary’s confidential information, the beamforming vP,ZF should also be in the null space of hSME⊥, i.e., hSMEHvP,ZF=0. In order to be fair in secondary transmission power, we further define vP,ZF=βPSTv^P,ZF and vS,ZF=1−βPSTv^S,ZF with v^P,ZFHv^P,ZF=1 and v^S,ZFHv^S,ZF=1, where β represents the power allocation coefficient and PST=2αηPPhPST2+EST0/1−α denotes the secondary transmission power. Based on equations (13) and (14), the optimization problem based on the ZF rule can be formulated as (P4)(24)maxv^P,ZF,v^S,ZF1−αT2log21+PPhPP2+βPSThSPRHv^P,ZF2δPRs.t.C1:1−αT2log21+1−βPSThSSHv^S,ZF2δSR≥rSC2:1−αT2log21+PPhPME2δME≤ΓC3:hSPRHv^S,ZF=0,hSSHv^P,ZF=0,hSMEHv^P,ZF=0C4:0<α<1.Based on the objective function of the optimization problem (P4), we can observe that the optimalv^P,ZF should maximize the primary transmission rate under the constraint C3. Thus, the optimal vP,ZF can be obtained by utilizing the following optimization problem:(25)maxvP,ZFhSPRHv^P,ZF2s.t.hSSHv^P,ZF=0,hSMEHv^P,ZF=0.Since both the constraint functions in equation (25) include v^P,ZF, we thus can define a new matrix HS=hSSH;hSMEH and the constraint function can be rewritten as HSv^P,ZF=0. To satisfy the new constraint, v^P,ZF can be obtained by solving the orthogonal value of HS, which means that v^P,ZF should be the null space of HS. To obtain the maximization of hSPRHv^P,ZF2, the optimal v^P,ZF∗ should be chosen the one which is in the direction of the orthogonal projection of hSPRH on to the subspace HS⊥, where the optimal v^P,ZF∗ is given by(26)v^P,ZF∗=I−HSHSH/HS2hSPRI−HSHSH/HS2hSPR.Similarly, the optimalv^S,ZF∗ can be derived by analyzing the constraint function hSPRHv^S,ZF=0 in equation (24), where v^S,ZF∗ should be the null space of hSPR⊥, i.e., v^S,ZF∗ belongs to the subspace hSPR⊥. Here, we try to maximize the hSSHv^S,ZF2 so that more ST’s transmission power can be used to transfer primary data to effectively ensure the secure transmission of information in the primary system. Therefore, the optimal v^S,ZF∗ can be derived as(27)v^S,ZF∗=I−hSPRhSPRH/hSPR2hSSI−hSPRhSPRH/hSPR2hSS.According to (24), we can find that the objective function is an increasing function while C1 is a decreasing function with the increase of β and we can obtain the optimal β∗ through deriving the upper bound of β. Therefore, the optimal β∗ can be expressed as(28)β∗=1−δSR22rS/1−αT−1PSThSSHv^S,ZF∗2.Then, the optimal energy harvesting durationα∗ and Γ∗ can be derived by adopting one-dimensional search.


## 3.1. Problem Formulation

Based on the DF cooperative communication scheme, the overall transmission rates at PR and ME equals the minimum rate of the two-hop transmissions, respectively [32], i.e.,(10)R˜PR=minRST,RPR,R˜ME=minRST,RME.Based on the definition of [33], the secrecy rate of the primary system for the considered secrecy CRN-WPR can be expressed as(11)RSEC=R˜PR−R˜ME+.Substituting the results of equation (8) into equation (9), the overall primary secrecy rate is then given as(12)RSEC=minRST,RPR−RME+.In the following, the EH ratio and secure beamforming vectors are jointly designed by maximizing the primary secrecy rate subject to the minimum achievable rate for the SR and power constraint of the ST. Mathematically, the considered optimization problem can be represent as P1:(13)maxα,vP,vSminRST,RPR−RME+s.t.C1:RSR≥rSC2:vP2+vS2≤2αηPPhPST2+EST01−αC3:0<α<1,where C1 means that the achievable rate of SR should be larger than or equal to minimum raterS and C2 denotes the transmission power constraint at the ST with EST0 representing the initial power at the ST.


## 3.2. Optimal Secure Beamforming Design

According to the analysis of formula (13), we can observe that (P1) is a nonconvex function, which is difficult to derive three optimal variables α,vP,vS concurrently. This section proposes a mathematically efficient optimization scheme with two-stage procedure for solving the (P1) as follows:(i)
In the stage I, we obtain the optimal secure beamformingvP∗,vS∗ for any given energy harvesting duration α(ii)
In the stage II, the global optimal solutionα∗,vP∗,vS∗ can be found based on one-dimension search over αIn the stage I, the maximization of the primary secrecy rate is equivalent to maximizing the achievable rate of the PR subject to an alternative upper bound on the achievable rate of ME. Thus, for a givenα=α0, RSTα0 is the constant value and the problem (P1) can be transformed into the following problem (P2):(14)maxvP,vS1−α0T2log21+PPhPP2δPR+hSPRHvP2hSPRHvS2+δPRs.t.C1:1−α0T2log21+hSSHvS2hSSHvP2+δSR≥rSC2:vP2+vS2≤2α0ηPPhPST2+EST01−α0C3:1−α0T2log21+PPhPME2δME+hSMEHvP2hSMEHvS2+δME≤Γ,where Γ represents an auxiliary optimization variable to bound the achievable rate of the eavesdropper ME, thus the maximum primary secure rate can be obtained by adjusting value of Γ. The optimal value of Γ∗ can be founded by one-dimension search since it is a nonnegative value. Note that the optimization problem (P2) is still nonconvex concerning with beamforming vectors vP and vS.Consideringlog2x is monotonically increasing function of x and defining HSPR=hSPRhSPRH, HSME=hSMEhSMEH, HSS=hSShSSH, VP=vPvPH, and VS=vSvSH, the problem (P2) can be denoted as a fractional programming problem, but the objective function is still nonconvex since two optimization variables VP and VS exist in the numerator and denominator of objective function, respectively. To solve the problem (P2) more effectively, the fractional programming problem can be equivalently reformulated to a convex SDR problem by utilizing Charnes–Cooper transformation [34]. Thus, we let(15)λ=1trHSPRVS+δSR,while defining V˜P=λVP and V˜S=λVS, the corresponding SDR of problem (P2) can be rewritten as (P3):(16)maxvP,vS,λtrHSPRV˜Ps.t.C1:trHSPRV˜S+λδSR=1,C2:trHSSV˜S−ΓStrHSSV˜P≥λΓSδSR,C3:trV˜P+trV˜S≤2λα0ηPPhPST2+EST01−α0C4:trHSMEV˜P−ΓetrHSMEV˜S≤λΓeδMEC5:V˜P≽0,V˜S≽0,λ>0,where ΓS=22rS/1−α0−1 and Γe=22Γ/1−α0−PPhPME2/δME−1.It must be noted that SDR cannot guarantee to derive the optimal solutionvP∗,vS∗ with rank-one. In the following, the first step is to prove that the rank of optimal V˜P∗ equals to one, and then we propose a method to structure the optimal V˜S∗ with rank-one when the rank of V˜S is greater than one.Letθ1, θ2, θ3, and θ4 represent the Lagrange multipliers, i.e., dual variables, related to constraints C1 to C4 in equation (16), respectively. Thus, the corresponding Lagrange function of problem (P3) can be expressed as(17)ℒV˜P,V˜S,θ1,θ2,θ3,θ4=trξV˜P+trψV˜P+ρ,where(18)ξ=HSPR−θ2ΓSHSS−θ3I−θ4HSME,ψ=−θ1HSPR+θ2HSS−θ3I+θ4ΓeHSME,and ρ denotes the residual information that is not related to the proof. According to the definition of Karush–Kuhn–Tucker conditions and Lagrange function of problem (P3), we have(19)ξ∗V˜P∗=0,ψ∗V˜S∗=0.Assuming the harvested energy and initial energy are all used for secure beamforming transmission in the third phase, the power constraint C3 in equation (16) is activated with equality, thus the dual variable θ3∗>0. Since the transmission channel vectors HSS≽0 and HSME≽0, we can derive that rank−θ2∗ΓSHSS−θ3∗I−θ4∗HSME=N. Furthermore, since rankHSPR≤1, it follows that rankξ∗≥N−1. Based on equation (19), we thus obtain rankV˜P∗=1.Defineκ∗=−θ1∗HSPR−θ2∗HSS−θ3∗I+θ4∗HSME, thus we have(20)ψ∗=κ∗+2θ2∗HSS.SinceHSPR≽0, HSS≽0, and HSME≽0, we can obtain that rank−θ1∗HSPR−θ2∗HSS−θ3∗I=N. Moreover, since rankHSME≤1, rankκ∗≥N−1 can be derived:(i)
Ifrankκ∗=N, we can obtain rankψ∗=N−1, thus it follows from equation (19) that rankV˜S∗=1 and V˜S∗ is equal to awwH, where w∈ℂN×1 denotes the spanning null space of ψ∗ and a>0. Thus, the corresponding optimal value of (P3) is V˜P∗/λ∗,V˜S∗/λ∗;(ii)
Ifrankκ∗=N−1, we can observe that rankV˜S∗>1 and thus it requires constructing a new solution with rank-one. First, we obtain the orthonormal basis u∈ℂN×1 of the null base of κ∗, which is defined as κ∗u=0 and ranku=1. Then, based on the expression of κ∗, we can further derive that HSSu=0. Thus, the optimal solution of V˜S∗ is given by(21)V˜S∗=buuH+awwH,where b≥0, w=1, and wHu=0. Finally, the optimal result of V^S∗ with rank-one can be rewritten as V^S∗=V˜S∗−buuH. Thus, the reconstructed optimal solution for (P3) is V˜P∗/λ∗,V^S∗/λ∗.For fixedα=α0, the optimal solutions Γ∗,V˜P∗,V˜S∗ can be obtained through one-dimension search Γ based on the following equation:(22)Γ∗,VP∗,VS∗=argmaxα=α0problemP3,thus, the optimal secure beamforming vectors vP∗,vS∗ can be obtained by adopting eigenvalue decomposition (EVD) of V˜P∗/λ∗ and V˜S∗/λ∗.In order to obtain the global optimal solution for problem (P1) in the second stage, one-dimension search related toα is then utilized. The optimal solution is chosen from the following equation:(23)α∗,Γ∗,vP∗,vS∗=argmaxα∈0,1problemP1.The whole algorithm process can be described in Algorithm1, which is shown as follows.Algorithm 1: Optimal secure beamforming design.
Initialize α=α0 and Γ=Γ0; define Γmax as a large positive real number; Δα and Δτ are all small positive real numbers as the iterative steps for one-dimension search
1
for a given α=α0 do S1-S4
2
S1: givenΓ=Γ0, then solve problem (P3) and derive the optimal solution V˜P∗,V˜S∗,λ∗ by utilizing CVX tools
3
S2: obtain optimalV˜P∗,V˜S∗ through the following procedures
4
if rankV˜P∗=1 and rankV˜S∗=1, then
5
The optimal solution for problem (P3) isV˜P∗/λ∗,V˜S∗/λ∗
6
else
7
Reconstruct an optimal solutionV˜P∗/λ∗,V^S∗/λ∗ for problem (P3) with rankV˜P∗=1 and rankV^S∗=1 based on equation (21)
8
end if
9
S3:let Γ=Γ+Δτ when Γ<Γmax and then go to S1-S2
10
S4:choose the optimal solution Γ∗,VP∗,VS∗ from equation (22) and derive optimal secure beamforming vectors VP∗,VS∗ by performing EVD
11
end for
12
Update α=α+Δα and S1-S4
Choose the optimal solution α∗,Γ∗,vP∗,vS∗ based on equation (23)


## 3.3. Secure Beamforming Based on Zero-Forcing Rule

This section investigates another secure beamforming solution based on zero-forcing (ZF) rule as a benchmark, in which the primary transmission will not be interfered by other transmissions. Therefore, based on the criterion of ZF rule [35], the beamforming vectors vS,ZF and vP,ZF for the primary and secondary systems should be in the null space of hSPR⊥ and hSS⊥, respectively, i.e., hSPRHvS,ZF=0 and hSSHvP,ZF=0. Since there exists an eavesdropper in the system to listen the primary’s confidential information, the beamforming vP,ZF should also be in the null space of hSME⊥, i.e., hSMEHvP,ZF=0. In order to be fair in secondary transmission power, we further define vP,ZF=βPSTv^P,ZF and vS,ZF=1−βPSTv^S,ZF with v^P,ZFHv^P,ZF=1 and v^S,ZFHv^S,ZF=1, where β represents the power allocation coefficient and PST=2αηPPhPST2+EST0/1−α denotes the secondary transmission power. Based on equations (13) and (14), the optimization problem based on the ZF rule can be formulated as (P4)(24)maxv^P,ZF,v^S,ZF1−αT2log21+PPhPP2+βPSThSPRHv^P,ZF2δPRs.t.C1:1−αT2log21+1−βPSThSSHv^S,ZF2δSR≥rSC2:1−αT2log21+PPhPME2δME≤ΓC3:hSPRHv^S,ZF=0,hSSHv^P,ZF=0,hSMEHv^P,ZF=0C4:0<α<1.Based on the objective function of the optimization problem (P4), we can observe that the optimalv^P,ZF should maximize the primary transmission rate under the constraint C3. Thus, the optimal vP,ZF can be obtained by utilizing the following optimization problem:(25)maxvP,ZFhSPRHv^P,ZF2s.t.hSSHv^P,ZF=0,hSMEHv^P,ZF=0.Since both the constraint functions in equation (25) include v^P,ZF, we thus can define a new matrix HS=hSSH;hSMEH and the constraint function can be rewritten as HSv^P,ZF=0. To satisfy the new constraint, v^P,ZF can be obtained by solving the orthogonal value of HS, which means that v^P,ZF should be the null space of HS. To obtain the maximization of hSPRHv^P,ZF2, the optimal v^P,ZF∗ should be chosen the one which is in the direction of the orthogonal projection of hSPRH on to the subspace HS⊥, where the optimal v^P,ZF∗ is given by(26)v^P,ZF∗=I−HSHSH/HS2hSPRI−HSHSH/HS2hSPR.Similarly, the optimalv^S,ZF∗ can be derived by analyzing the constraint function hSPRHv^S,ZF=0 in equation (24), where v^S,ZF∗ should be the null space of hSPR⊥, i.e., v^S,ZF∗ belongs to the subspace hSPR⊥. Here, we try to maximize the hSSHv^S,ZF2 so that more ST’s transmission power can be used to transfer primary data to effectively ensure the secure transmission of information in the primary system. Therefore, the optimal v^S,ZF∗ can be derived as(27)v^S,ZF∗=I−hSPRhSPRH/hSPR2hSSI−hSPRhSPRH/hSPR2hSS.According to (24), we can find that the objective function is an increasing function while C1 is a decreasing function with the increase of β and we can obtain the optimal β∗ through deriving the upper bound of β. Therefore, the optimal β∗ can be expressed as(28)β∗=1−δSR22rS/1−αT−1PSThSSHv^S,ZF∗2.Then, the optimal energy harvesting durationα∗ and Γ∗ can be derived by adopting one-dimensional search.


## 4. Simulations and Analyses of Security Transmission Performance

In this section, we will verify the security transmission performance of the primary and transmission efficiencies of the secondary system by comparing the proposed scheme and ZF-based scheme. Unless stated otherwise, we assume that all noise power are normalized to unity, i.e.,δPR=δSR=δME=1. We also consider a scenario where the transmission distance between the PT and PR is 8 m, while the distance between the ST and SR is 3 m. Moreover, the ST is equipped with 4 antennas, and the energy harvesting efficiency is set as η=0.5. The transmission channel can be modeled as h=d−ϖ/2ejw with d and ϖ=3.5 denoting the distance and path loss exponent, respectively [36]. The minimum transmission rate of the secondary system and maximal auxiliary optimization variable is set to be rS=0.5bit/s/Hz and Γmax=1.0 bit/s/Hz, respectively.Figure2 illustrates the secrecy rate of the primary system with respect to the primary transmission power for different initial energies at the ST. In this figure, both the secrecy rates of the primary system with the proposed scheme and ZF scheme are improved with the increase of primary transmission power, respectively. Moreover, the proposed scheme outperforms the ZF scheme in terms of the primary’s secrecy rate. With the lower primary transmission power, the superiority of the proposed scheme is obvious and the primary secrecy rates with both schemes are close in high primary transmission power. With the increase of the initial energy at the ST, the secrecy rate gets better as shown in Figure 2 since the more transmission power will be utilized to assist the transmission of the primary signals.Figure 2
The secrecy rate of the primary system with respect to the primary transmission powerPP for different initial energies at the ST. The antenna number N = 4, dPST = 4 m, dSPR = dPP-dPST, dPME = dPP.Figure3 compares the secrecy rates of the primary system with the proposed scheme and ZF scheme against the antenna number at the ST. Obviously, with the increase of the antenna number, the secrecy rates gets better continually since more antennas will result in a higher spatial reuse efficiency. Similarly, the primary secrecy rate is always high for the proposed scheme.Figure 3
The secrecy rate of the primary system with respect to the number of antenna at the ST.PP = 10 dB, PST0 = 0 dB. dPST = 4 m, dSS = 2 m, dSPR = dPP-dPST, dSME = dSPR, dPME = dPP.Figure4 shows the primary secrecy rates with the proposed scheme and ZF scheme against the transmission distance between the PT and ST. From this figure, we can observe that the proposed scheme is superior to the ZF scheme in terms of the primary secrecy rate, regardless the position of the ST. With the increase of the dPST, the primary secrecy rates first become better and then become worse. When the transmission distance dPST is short, the secrecy rates get better with the increase of the dPST because more energy will be harvested for signal transmission and shorter distance for primary signal transferring. However, when the distance dPST is longer, the secrecy rates get worse since the amount of harvested energy will be decreased and more path-loss will result in a negative effect for the ST to process the PT’s signal. Furthermore, we can obtain that the optimal positions of the ST are roughly 3m and 4m for the proposed scheme and ZF scheme, respectively.Figure 4
The secrecy rate of the primary system with respect to the distance between the PT and ST.PP = 10 dB, PST0 = 0 dB, dSS = 2 m, dSPR = dPP-dPST, dSME = dSPR, dPME = dPP. The antenna number N = 4.Figure5 shows the secrecy rate of the primary system corresponding to the ST’s initial energy for different primary transmission power. In this figure, we can observe that the secrecy rates of the primary system with both the schemes are close with the increase of the ST’s initial energy, which further illustrates the proposed scheme is superior to the ZF scheme. Specifically, the proposed scheme outperforms the ZF scheme in a lower primary power range. However, in the higher initial primary power range, the gap of the secrecy rates of the primary system between the proposed scheme and the ZF scheme gets small. Therefore, the proposed scheme in this paper is more effective when the initial energy is small.Figure 5
The secrecy rate of the primary system with respect to the initialized transmission powerPST0 at the ST for different primary transmission power PP. dPST = 4 m, dSS = 2 m, dSPR = dPP-dPST, dSME = dSPR, dPME = dPP. The antenna number N = 4.Figure6 shows the achievable rate of the secondary system with respect to the primary transmission power. From the figure, the throughput of the secondary system with both the scheme is enhanced with the increase of the primary transmission power, which because of more energy will be harvested for the signal transmission. In the meanwhile, the propose scheme outperforms the ZF scheme, which verifies the effectiveness of the proposed scheme.Figure 6
The transmission rate of the secondary system with respect to the primary transmission powerPP. PST0 = 10 dB. dPST = 4 m, dSS = 2 m, dSPR = dPP-dPST, dSME = dSPR, dPME = dPP. The antenna number N = 4.


## 5. Conclusions

This paper studied the secure transmission problem for the cognitive radio-based IoMT with energy harvesting when the sensitive medical data sent from the PT can be listened by a malicious eavesdropper. For the sake of protecting the security of the sensitive data, we formulate the corresponding optimization problem and propose a novel algorithm for jointly designing the optimal EH duration and secure beamforming vectors to maximizing the primary secrecy transmission rate while ensuring the transmission requirement of the secondary system. In fact, the number of eavesdroppers may usually be more than one, and the proposed scheme still can be utilized to obtain optimized beamforming vectors. The numerical results presents excellent secure transmission performance with the proposed scheme than zero-forcing scheme, which can be implemented into the IoMT devices to effectively protect the security of the sensitive data.



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*Source: 7542726-2020-02-24.xml*