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A novel secure relay selection strategy for energyharvestingenabled Internet of things
EURASIP Journal on Wireless Communications and Networking volume 2018, Article number: 264 (2018)
Abstract
In this article, we focus on the problem of relay selection for the cooperative cognitive radiobased Internet of things. In such systems, a pair of primary user devices (PUs) can only communicate with each other through a relay. The relay is selected from a set of multislot energyharvesting (EH)enabled secondary user devices (SUs). The charging and discharging process of an SD’s battery is formulated as a finite state Markov chain, and we can derive the corresponding analytical expression of steadystate distribution. Consider the nonauthority of SUs, we analyze the outage performance when SUs are trusted and untrusted. When SUs are trusted, we provide the theoretical analysis expression and the lower bound expression for the outage probability. On the contrary, we propose a destinationassisted jamming strategy to secure primary communication if SUs are untrusted. In addition, we propose a Vickrey auctionbased EHenabled relay selection strategy which can be applied to the secondary system. For this auction strategy, SUs without direct links can transmit signals by selecting an EHenabled SU as a relay. The winning SU in the process of auction can earn reward. Finally, the simulation results verify that the EHbased transmission can obtain excellent system performance without consuming excess energy, and we also study the effect of different parameters on system outage performance.
Introduction
Internet of things (IoT) is emerging as a new paradigm to achieve network convergence in 5G mobile communications. It definitely requires mass data exchanging and sharing among numerous mobile nodes, e.g., machinetomachine (M2M) and devicetodevice (D2D), and forms a data volume that is far greater than the traditional mobile communication and wireless access [1]. Therefore, the shortage of spectrum resources becomes a bottleneck for the IoT development. A reliable and efficient technology, called as the cooperative cognitive radio (CCR), greatly improves the spectral efficiency of IoT applications. In CCRbased IoT, a secondary user (SU) is asked to assist primary users (PUs) to achieve primary signal transmission. In return, the SU can get a certain spectrum as a reward to transmit its own data [2, 3]. In this case, the opportunistic access for SUs can promote spectrum utilization significantly [4, 5].
Yet, an IoT system contains a large number of lowcost devices that may only be powered by batteries [6, 7]. These energylimited devices, usually in the edge of a network [8], may cause cooperative communication to not work properly. Accordingly, some works introduce energyharvesting (EH) technology to solve such restriction and achieve better energy efficiency [9, 10]. This technology can realize the reuse of energy resources. An SU with EH technology can harvest energy from the ambient environment [11, 12], e.g., solar energy, thermal energy, and sound energy. Additionally, it can also harvest energy from the surrounding electromagnetic field generated by other communication nodes, which is defined as the wireless powered communication (WPC) technology [13]. The WPCenabled SU is powered by radio frequency (RF) signals in the electromagnetic field and can convert the RF signals into a direct current that can be used in subsequent communications. As a result, the EH technology may increase the battery life of SUs by replenishing energy from various energy sources [14] and SUs can assist PUs without consuming additional energy to achieve secure and reliable cooperative data transmission.
The WPC technology is widely used in wireless communication systems. One of the most popular research topics is the application of simultaneous wireless information and power transfer (SWIPT) technology to relay networks. Specifically, for a twohop cooperative network, a relay employs a part of the received source signals for energy harvesting in the first phase of communication and the remaining is forwarded in the second phase. However, the harvested energy of the relay may be very limited due to the constraints of time slot and low EH conversion efficiency. Thus, this model can only be applied to near field communications. In order to use more energy for cooperative communications, multislot EH technology can be utilized. In the multislot mode, the energy harvested in each time slot can be accumulated in a battery and used for data transmission when the battery’s energy exceeds a certain threshold. Thus, primary data transmission can be assisted by using multiple multislot EHenabled SUs.
In this paper, we study the optimal singlerelay selection problem for the energylimited CCRbased IoT and then analyze the outage performance of PUs. To the best of our acknowledge, this is the first time to discuss a relay selection strategy based on multislot EH for CCRbased IoT. Compared with traditional relay selection strategies, our proposed strategy is based on both SUs’ channel state information (CSI) and battery state information (BSI). In addition, the selected SU as a relay adopts the amplifyandforward (AF) mode rather than the decodeandforward (DF) model in [15–18]. Different from the assumption of the infinite battery capacity in [19], we set the SUs’ battery capacity is limited to satisfy the actual requirements. In our analysis, we formulate the accumulation process of SUs’ battery energy as a finite state Markov chain to obtain the steadystate probability of BSI. However, we cannot fully guarantee the credibility and integrity of primary data forwarding due to the existing nonauthorized SUs. An untrusted SU may spoof PUs by pretending to be a relay in exchange for its own data opportunistic transmit [20]. In this case, the outage probability of primary transmission may increase significantly. More seriously, the untrusted SU may cause various malicious behaviors, e.g., poisoning signals injection [21, 22], phishing attacks [23, 24], or private information leakage [25, 26]. Therefore, we analyze the outage probability of our relay selection strategy for the scenarios of trusted and untrusted SUs. When SUs are untrusted, we design a destinationassisted jamming strategy to ensure secure primary communication, and provide a Vickrey auctionbased secondary system relay selection strategy to encourage SUs cooperation [27].
The main contributions of the paper are summarized as follows.

We propose a relay selection strategy based on CSI and BSI. This strategy can select an SU from several multislot EHenabled SUs as a relay to assist primary data transmission. Modeling the energy accumulation process of SU’s battery as a finite state Markov chain, we can finally achieve PUs’ reliable transmission without consuming SUs’ additional energy.

We analyze the outage probability of primary data transmission in the case of trusted and untrusted SUs. When SUs are trusted, we derive the theoretical analysis expression and the lower bound expression of outage probability. For the untrusted SUs, we propose a destinationassisted jamming strategy to ensure secure communication.

For the EHenabled secondary system in CCRbased IoT, we propose a Vickrey auctionbased relay selection strategy. SUs without direct links can employ other EHenabled SUs as relays to conduct secondary data transmission. These EHenabled SUs bid as relays to gain rewards.

The experiments of this paper is carried out on MATLAB platform. The relevant parameters are set according to the real wireless environment. The observation demonstrate excellent outage probability in both trusted and untrusted scenarios when using our strategy. This paper further exploits similar network parameters to analyze the secondary data forwarding rate based on the Vickrey auction and verifies the personal rationality of secondary users.
The rest of the paper is organized as follows. In Section 2, we review the related work, and then, the network model and necessary preliminaries are presented in Section 3. The relay selection strategy and the Markov model of SU’s battery are illustrated in Section 4. Next, Section 5 analyzes the outage probability of the system. In Section 6, we propose a Vickreyauctionbased relay selection strategy for secondary systems. Finally, we analyze and discuss the performance of our work in Sections 7 and 8, and conclude our work in Section 9.
Notations: In this paper, we denote uppercase and lowercase bold letters as matrices and vectors, respectively. \(\sqrt {\cdot }\) and · stand for the square root and the absolute value of a vector. E[ ·] represents the statistical expectation of random variables.
Related work
WPC technology generally appears in three basic network models, namely wireless power transfer networks (WPTNs), wireless powered communication networks (WPCNs), and SWIPTenabled networks. In WPTNs, there exists a dedicated RF transmitter to power the EHenabled devices. These devices can receive sufficient and uninterruptible power. Obviously, this mode should be applied to the network with high system performance requirements [28]. And in WPCNs, a dedicated RF transmitter powers an EHenabled device and the device uses the harvested energy to communicate with the RF transmitter. In addition, another SWIPTbased mode is the upsurge of current research. Since the RF signal carries information and energy at the same time, this mode can harvest energy from part of the received signals and use this energy to forward the remaining part of the received signals.
For the SWIPT technology, there exist two practical relay policies to achieve energy harvesting and information processing, i.e., power splitting relaying (PSR) and time switching relaying (TSR). Gao in [29] suggested selecting a SWIPTenabled SU as a relay to maximize system throughput with the energy constraint and the requirement of the signal to interference plus noise ratio (SINR). In [30], Salem and Hamdi analyzed the secrecy capacity of an AF multiantenna network with a SWIPTenabled relay. The authors in [31] provided the maximal secrecy rate with the assistance of several SWIPTenabled relays which are capable of simultaneous interference. Furthermore, Raghuwanshi et al. [32] discussed the secrecy performance of a dualhop cognitive radio network (CRN) with a SWIPTenabled relay.
Yet, the assumptions of existing EHbased works are too idealized. They always assume that only one time slot is used to harvest energy and the EH efficiency is high. In practice, the energy harvested in one time slot is very limited, and the EH efficiency is very low^{Footnote 1}. Therefore, it is difficult to ensure the reliability of the system with EHenabled relays or jammers for the singleslot harvesting mode. Instead of using the energy harvested in one transmission slot to immediately send data, we store the harvested energy with the help of a battery and adaptively used for transmissions. This mode is called as the multislot EH technology that have investigated in many articles [15–18, 33]. In [15], Zhou et al. proposed a multislot EHbased PSR strategy with distributed beamforming for wireless powered multirelay cooperative networks. Intuitively, relay (jammer) selection based on the energy status in multislot EHbased networks is a question worth exploring. In [16], the authors separately studied the problem of singlerelay and multirelay selection in a distributed wireless powered cooperative communication (WPCC) network. They formulated the energy accumulation process of relays as a twostate Markov chain and analyzed the outage performance of the system. Unlike [16], the authors in [17] studied the outage performance of a multirelay selection strategy based on an energy threshold in a WPCC network. They modeled the relay energy accumulation process as a finite state Markov chain. Actually, the singlerelay optimal selection is more reasonable and environmentfriendly than the multirelay selection in the energylimited WPCC networks. Therefore, the authors in [18] studied the singlerelay selection problem in a basic twohop communication model. In addition, most articles analyzed the DF relay selection problem in WPCC networks. Nevertheless, the AF mode requires lower processing power and complexity at the relay node then the DF mode, but little works discussed the AF single relay selection problem [33], which inspired the work of this article.
Network model
In this paper, we consider a CCRbased IoT that consists of a pair of PUs and K SUs as depicted in Figs. 1 and 3. All nodes are equipped with a single antenna and operate in halfduplex mode. We assume that the direct link between two PUs does not exist due to deep fading or obstacles. One PU as a source, abbreviated as PU−S, can only communicate with its destination, i.e., PU−D, via a relay (SU−R) selected from the K SUs. Here, SUs are considered as lowpower devices and they can be powered by RF signals sent by PU−S. Each SU equipped with a RFEH circuitry can convert the received RF power into direct current that can be recharged in a finitesize battery. For simplicity, all batteries have unified capacity of E_{max} energy units. We consider two scenarios, namely trusted SUs and untrusted SUs, and introduce them separately in the following subsections.
Moreover, other network parameters are defined as follows. The wireless channel between nodes i and j experience a quasistatic Rayleigh block fading with the channel fading coefficient h_{i,j}. In other words, these channels remain constant within a time slot and obey independent complex Gaussian distribution, e.g., \({h_{i,j}} \in CN\left (0,d_{i,j}^{ \alpha }\right)\). Thus, the channel gain g_{i,j}=h_{i,j}^{2} is exponentially distributed with mean \({{\bar {g}}_{i,j}}=2d_{i,j}^{( \alpha)}\), where d_{i,j} is the Euclidean distance between nodes i and j, and α represents the path loss factor. Assuming SUs are located closely, we have \({{\bar {g}}_{S,{R_{i}}}} = {{\bar {g}}_{S,R}},{{\bar {g}}_{D,{R_{i}}}} = {{\bar {g}}_{{R_{i}}}}, D={{\bar {g}}_{D,R}}\).
Network model with trusted SUs
The network model with trusted SUs is depicted as Fig. 1. When all SUs are trustworthy, the time slot T of entire transmission duration is divided into two phases, as shown in Fig. 2. Without lose of generality, we consider a normalized transmission time slot (i.e., T=1). In the first phase, PU−S transmits its private signals s_{1} to SUs. The selected SU−R, e.g., SU−R_{l}, receives the signals, and the other SUs harvest energy from the received signals. In the second phase, SU−R_{l} employs the AF mode to forward the signals to PU−D, and the other SUs keep in idle mode^{Footnote 2}.
According to the description of our transmission model, we provide mathematical expressions of signal transmission in two phases.
In the first phase, the received signals at SU−R_{k} can be expressed as follows,
where \(n_{R_{k}}\) is the additive white Gaussian noise (AWGN) at SU R_{k}. If an SU not be selected as a relay, it is in the EH mode, and the amount of harvested energy at the SU−R_{k} can be expressed as:
where \({P_{S}}\triangleq \mathrm {E}\left [s_{1}^{2}\right ]\) is the transmit power of PUS, and 0≤η≤1 denotes energy harvesting efficiency which depends on the EH circuitry and the rectification process. If an SU is selected as the best relay (i.e. SU−R_{l}), it is in the signal processing mode.
In the second phase, the selected relay is in the information forward (IF) mode. SU−R_{l} amplifies and forwards signals \(\phantom {\dot {i}\!}{s_{2}}=\rho y_{R_{l}}\) to PU−D. Here, ρ is an amplification factor that can be defined as below:
Therefore, the received signals at PU−D is as follows:
where \({P_{R}}\triangleq \mathrm {E}\left [s_{2}^{2}\right ]\) represents transmit power of SU−R_{l} and \(n_{D}^{\left (2 \right)} \sim CN\left ({0,\sigma ^{2}} \right)\) is AWGN at PU−D. According to the received signals of the second phase in (4), the corresponding SINR at PU−D can be calculated by:
where \(\delta _{i,j}=\frac {P_{i}g_{i,j}}{\sigma ^{2}}\) is the signal to noise ratio (SNR). Thus, the channel rate is given by:
Network model with untrusted SUs
The network model with untrusted SUs has been slightly modified on the previous model, which is described in Fig. 3. Since SUs are nonauthorized users, in many cases, we cannot ensure that they are completely reliable. As we know, the confidentiality of signals transmitted by PU−S may be very high, and the SUs has no authority to know specific messages. Like many untrusted relay network definitions, in general, SUs are assumed trusted at the service level [34–37] but untrusted at the data level. Thus, the SU selected as relay may be able to eavesdrop the PU’s signals and other unselected SUs harvest energy^{Footnote 3}. Therefore, different from [16, 18], the selected SU exploits the AF mode in our network model. In addition, there is another reason that we have to exploit the AF mode is that the DF mode may greatly increase the risk of eavesdropping due to the decoding signals.
In order to avoid malicious behaviors (e.g., eavesdropping), we employ cooperative jamming schemes to deal with the untrusted relay. Signals to achieve cooperative jamming can be classified into the sourceassisted method, friendly jammerassisted one, and the destinationassisted one. The first one is designed based on the principle that the legitimate signals and jamming signals are sent at the source simultaneously [38, 39]. The precondition for this method to be feasible is that the destination is aware of jamming signals. This requires additional channel resources to negotiate before communication. Then, the second one is to transmit jamming signals that only degrade the reception quality of eavesdroppers when the source or the relay transmits the legitimate signals [40, 41]. The disadvantage of this method is that the cooperative jammingbased secure transmission must have a trusted jammer. It may be difficult to achieve in reality due to selfishness of network nodes. In our work, we exploit the third one, i.e., the destinationassisted jamming methods, to design an antieavesdropping mechanism [42]. Here, we assume that PU−D sends artificial noise (AN) to prevent eavesdropping when PU−S sends legitimate signals.
The time slot allocation in the untrusted scenario is shown in Fig. 4. In the first phase, PU−S transmits its private signals s_{1} to SUs, and PU−D broadcasts AN v to prevent eavesdropping and provides additional energy sources simultaneously.
Specifically, the received signals in the first phase at SU−R_{k} can be expressed as:
Thus, the amount of harvested energy at SU−R_{k} can be derived as follows:
where \({P_{S}}\triangleq \mathrm {E}\left [s_{1}^{2}\right ]\) and \({P_{D}}\triangleq \mathrm {E}\left [v^{2}\right ]\) are the transmit power of PU−S and PU−D. According to (7), the SINR at SU−R_{l} in the first phase is defined as:
Similar to the trusted case, SU−R_{l} will forward signals \({s_{2}}=\rho y_{R_{l}}^{(1)}\) to PU−D and the other SUs keep in the idle mode in the second phase. Thus, ρ can be defined as:
Therefore, the received signals at PU−D is as follows,
where \({P_{R}}\triangleq \mathrm {E}\left [s_{2}^{2}\right ]\) represents transmit power of SU−R_{l} and \(n_{D}^{\left (2 \right)} \sim CN\left ({0,\sigma ^{2}} \right)\) is AWGN at PU−D. Since v in \(y_{R}^{(1)}\) is the AN transmitted by PU−D itself in the first phase, we assume that PU−D can easily remove the interference by selfinterference cancelation (SIC) technology. As a result, (11) can be rewritten as follows:
Then, the corresponding SINR at PU−D can be calculated by:
According to [43], the secrecy rate is defined as the difference between the main channel rate and the eavesdropping channel rate. Thus, we can obtain the secrecy rate as follows:
where [x]^{+}= max{0,x}.
Relay selection and energy storage model
In this section, we propose a relay selection strategy when an SU is trusted or untrusted. Then, the charging and discharging process of an SU’s battery is modeled as a finite state Markov chain and the analytical expression for steadystate distribution is derived.
Relay selection strategy
Unlike traditional relay selection (RS) strategies in [44, 45], our proposed RS strategy based on the CSI of wireless channels and SUs’ BSI. At the beginning of a transmission time slot, each SU checks if the remaining energy of its battery reaches a energy threshold. Here, the energy threshold is defined as E_{th}=P_{R}/2^{Footnote 4}. Then, SUs that satisfy the threshold condition constitute a subset Ω with cardinality Ω. The subset Ω is defined as follows:
where e_{k} donates the remaining energy of SU_{k}’s battery at the beginning of the transmission time slot.
Each SU in the subset Ω may send a pilot signal to PU−S, which contains their CSI^{Footnote 5}. According to the CSI, PU−S can select the best SU as a relay to obtain the maximum channel rate R_{D} or the secrecy rate R_{S}. Therefore, PU−S will notify all SUs the number of the selected SU when it broadcasts signals. And the selected SU will be in the IF mode, while the other SUs will be in the EH mode. In the trusted scenario, the selected SU can be expressed as:
And in the untrusted scenario, the selected SU can be expressed as:
With the proposed RS strategy, we can guarantee secure and reliable communication of PUs without using the additional energy of SUs. As we know, many works put forward various multirelay selection methods. They will achieve more secure transmission performance at the cost of higher energy consumption. Obviously, they cannot achieve in the limited energy CCRbased IoT due to the scarce energy. In addition, the multirelay forwarding strategy need to apply the beamforming technology [17, 46]. This means that more resources need to be consumed to complete time synchronization and beamforming vector design, which will greatly increase the computational complexity. Therefore, in this paper, our RS strategy is designed to select one optimal relay.
Markov model of the SU’s battery
In our battery model, the process of charging and discharging of the battery of an SU is an important part to achieve cooperative communication. In general, the charging or discharging behavior of an SU is a discretetime stochastic process. Therefore, the battery life of SU_{k} at the beginning of each transmission time slot can be modeled as a finitestate discretetime Markov chain (MC). Different from two states of the battery life (empty or full) mentioned in [16], we assume a finite state space S={s_{0},...,s_{L}}, where L denotes the number of discrete energy levels. We defined that s_{0}=0 and s_{1}=E_{max}/L, which are referred as energy levels. The remaining energy of SU_{k}’s battery is e_{k}=i·s_{1} if SU_{k} is in state s_{i}. Moreover, the energy threshold is defined as E_{th}=s_{th}=th·s_{1}, where th∈{1,...,L}.
The transition probability matrix of SU_{k}’s MC is defined as \({\mathbf {P}^{k}} = {\left [p_{i,j}^{k}\right ]_{(L + 1) \times (L + 1)}}\). Next, we provide the analysis of the transition probability form s_{i} to s_{j} of an arbitrary SU. For the sake of simplicity, we employ p_{i,j} instead of \(p_{i,j}^{k}\) in the following analysis.
The battery’s state remains unchanged (s _{0}≤s _{i}=s _{j}<s _{L})
There are two reasons a battery’s energy may remain unchanged.

An SU belongs to subset Ω (s_{i}≥s_{th}) but is not selected as a relay. Then, the SU is in EH mode and the energy harvested at this time slot is less than an energy level s_{1}.

An SU does not belong to subset Ω (s_{i}<s_{th}) and the energy harvested of the SU at this time slot is less than an energy level s_{1}.
Thus, the transition probability is given by:
where E denotes the harvested energy of SU_{k} which is given by (2) and (8).
On one hand, we assume that each SU in Ω has an equal chance to be selected as the best relay with probability \(\frac {1}{{\Omega }}\) if s_{i}≥s_{th}. Here, we replace \(\frac {1}{{\Omega }}\) by the lowerbound \(\frac {1}{K}\) for simplicity. Therefore, the probability of a not selected SU in set Ω is \(\frac {{K  1}}{K}\). The transition probability p_{i,i} can be further derived as follows:
where F_{E}(·) is the cumulative distribution function (CDF) of variable E. The specific expression of F_{E}(·) is given by Lemma 1.
Lemma 1
For the trusted scenario, the CDF of E can be expressed as:
And that of E for the untrusted scenario is:
Proof
Please see Appendix Appendix A. □
On the other hand, when s_{i}<s_{th}, we can also derive the transition probability p_{i,i} as follows:
The empty battery is partially charged (s _{0}=s _{i}<s _{j}<s _{L})
When an SU’s battery is in state s_{0}, the SU must not belong to subset Ω, i.e., s_{i}<s_{th}. In this case, an empty battery is partially charged to level s_{j} only if the SU is in EH mode and the energy harvested at this time slot is between s_{j} and s_{j+1}. The transition probability can be calculated as follows:
The nonfull battery is partially charged (s _{0}<s _{i}<s _{j}<s _{L})
Similar to the unchanged state described in 4.2.1, there are two cases for this result.

An SU belongs to subset Ω (s_{i}≥s_{th}) but is not selected as a relay. Then, the SU is in EH mode and the energy harvested at this time slot is between s_{j}−s_{i} and s_{j+1}−s_{i}.

An SU does not belong to subset Ω (s_{i}<s_{th}), and the energy harvested of the SU at this time slot is between s_{j}−s_{i} and s_{j+1}−s_{i}.
Thus, the transition probability is:
If s_{i}≥s_{th}, the SU must belong to subset Ω. Similar to (19), the transition probability p_{i,i} can be further expressed as:
And if s_{i}<s_{th}, the transition probability p_{i,j} can be further expressed as:
The nonfull battery is fully charged (s _{0}<s _{i}<s _{j}=s _{L})
A nonfull battery is fully charged, there are two cases for this result.

An SU belongs to subset Ω (s_{i}≥s_{th}) but is not selected as a relay. Then, the SU is in EH mode and the energy harvested at this time slot is larger than s_{L}−s_{i}.

An SU does not belong to subset Ω (s_{i}<s_{th}), and the energy harvested of the SU at this time slot is larger than s_{L}−s_{i}.
Thus, the transition probability is given by:
When s_{i}≥s_{th}, the SU must belong to subset Ω. The transition probability p_{i,i} can be further expressed as:
When s_{i}<s_{th}, the transition probability p_{i,j} can be further expressed as:
The empty battery is fully charged (s _{0}=s _{i}<s _{j}=s _{L})
This case happens only when an SU is in EH mode and the energy harvested at this time slot is larger than level s_{L}. Thus, the transition probability is given by:
The battery remains fully charged (s _{0}<s _{i}=s _{j}=s _{L})
This case happens only when an SU belongs to subset Ω (s_{i}≥s_{th}) but is not selected as the best relay. Thus, the transition probability can be given as:
The battery is discharged (s _{0}<s _{j}<s _{i}≤s _{L})
The battery discharge occurs only when an SU belongs to subset Ω (s_{i}≥s_{th}) and is selected as the best relay. Additionally, it is true only when s_{j}=s_{i}−s_{th} and the probability of everything else case is 0. Then, we can derive the transition probability for this case as follows:
Through the above analysis of all possible cases, we can easily obtain the transition probability matrix \({\mathbf {P}} \triangleq {[p_{i,j}]_{(L + 1) \times (L + 1)}}\) of any SU. In addition, through the above analysis, we can find that the transition probability matrix of each SU is consistent. The reason is that all the channels related to SUs are distributed identically, e.g., \({\bar {g}_{S,{R_{i}}}} = {\bar {g}_{S,R}}\) and \({\bar {g}_{{R_{i}},D}} = {\bar {g}_{D,{R_{i}}}} ={\bar {g}_{R,D}}\). Since the above MC model is finitestate, irreducible, and positive recurrent, P is irreducible and row stochastic. We define that π=(π_{0},π_{1},...,π_{L}) is the steadystate distribution vector of SU_{k}. With reference to [17], π can be found by solving a set of balance equations π=Pπ and the normalization equation \(\sum \limits _{0}^{L} {\pi _{i}} = 1\). Futhermore, we can obtain the unique steadystate distribution vector π by solving the following equation,
where I is a (L+1)×(L+1) unit matrix, B is a (L+1)×(L+1) matrix with all elements are one, and b is a (L+1)×1 vector with all elements are one.
Outage performance analysis
In order to evaluate the secrecy performance of our proposed model, we use the outage probability to evaluate system performance.
Outage analysis for the trusted scenario
When SUs are trusted, there may be only two cases in which an outage event occurs, i.e.,

At the beginning of the transmission, there are no SU that satisfies the energy threshold. The subset Ω is empty, namely, Ω=0.

The subset Ω is not empty, but the channel rate R_{D} achieved by using the selected relay is less than a certain rate R_{th}.
Hence, the outage probability can be expressed as follows:
where \({R_{D,i}^{*}} = {\underset {S{U_{i}} \in \Omega }{\max }} {R_{D,i}}\) is the channel rate achieved by using the optimal relay in the set Ω. Here, R_{D,i} is given by (6). The first item to the right of the above equation can be calculated as:
and the second item to the right can be given by:
where K is the total number of SU_{s}. Pr[ R_{D}<R_{th}] is the traditional outage probability, i.e., the channel rate R_{D} is less than the predetermined channel rate R_{th}. Obviously, Pr[ R_{D}<R_{th}] can be converted to \(\Pr [\gamma _{D} < \theta ]={F_{{\gamma _{D}}}}(\theta)\). Here, γ_{D} is given by (5), \(\phantom {\dot {i}\!}\theta ={2^{2{R_{th}}}}  1\), and \({F_{{\gamma _{D}}}}(t)\) is the CDF of γ_{D}.
We aim to find the optimal SU that can achieve the maximum γ_{D,i} in set Γ={γ_{D,i},i=1,2,3⋯k},k=Ω. Because the variables in Γ are independently and identically distributed, the equations of \({f_{{\gamma _{D,i}}}}(\theta)={f_{\gamma _{D} }}(\theta)\) and \({f_{{\gamma _{D,i}}}}(\theta)={f_{\gamma _{D} }}(\theta)\) hold, where \({f_{{\gamma _{D,i}}}}(\theta)\) is the probability density function (PDF) of γ_{D,i}. According to Section 2.2.2 in [47], we exploit the knowledge of order statics to provide the PDF of the j^{th} smallest order statics of Γ as follows,
The maximum value means the k^{th} smallest value. If we define j=k, we can get the PDF of the maximum statics, i.e.,
And the CDF of the maximum order statics of Γ can be easily derived by integrating the PDF in (42), which is given by:
And finally, we have:
Next, we will provide an integral form, a closedform, and a lower bound of Pr[ R_{D}<R_{th}].
For the sake of simplicity, we define \(X=\delta _{{R_{l}},D}=\frac {P_{R_{l}}g_{{R_{l}},D}}{\sigma ^{2}}\) and \(Y=\delta _{S,{R_{l}}}=\frac {P_{S}g_{S,R_{l}}}{\sigma ^{2}}\). Since \(g_{{R_{l}},D}\) and \(g_{S,{R_{l}}}\) are random variables that obey exponential distribution, X and Y are exponentially distributed with mean \(\bar {x} = \frac {{{P_{{R_{l}}}}{{\bar {g}}_{{R_{l}},D}}}}{{{\sigma ^{2}}}}\) and \(\bar {y} = \frac {{{P_{S}}{{\bar {g}}_{S,{R_{l}}}}}}{{{\sigma ^{2}}}}\). Thus, we can easily derive that \(\gamma _{D} = \frac {{XY}}{{X + Y + 1}}\). And the integral form of Pr[R_{D}<R_{th}] can be expressed as follows:
where F_{X}(·) is the CDF of X and f_{Y}(·) is the PDF of Y.
However, (41) is extremely complicated for actual calculations. It is difficult to obtain the final result using existing mathematical calculation software. To cope with this challenge, we can derive the PDF and the CDF of γ_{D} according to [48], i.e.,
and
where K_{0}(·) and K_{1}(·) are the zeroorder and the firstorder modified Bessel function of the second kind. The specific solution of (42) and (43) is to first obtain the PDF and CDF of γ_{D} under Nakagamim fading. And let the fading factor of x and y equal to 1 (m_{x}=m_{y}=1); then, Nakagamim fading becomes Rayleigh fading. Accordingly, we can get the above formulas by substituting m_{x}=m_{y}=1 into the PDF and CDF of γ_{D} under Nakagamim fading. The closedform of Pr[R_{D}<R_{th}] is as follows:
Furthermore, we provide the closedform expression of the lower bound of Pr[R_{D}<R_{th}] in Lemma 2.
Lemma 2
We assume that \(P_{out}^{LB}\) is the lower bound of Pr[R_{D}<R_{th}], i.e.,
Proof
Please see Appendix Appendix B. □
Outage analysis for the untrusted scenario
When SUs are untrusted, the reason for the interruption time is the same as the above. Hence, the outage probability can be expressed as follows:
where \({R_{S,i}^{*}}= {\underset {S{U_{i}} \in \Omega }{\max }}{R_{S,i}}\) is the channel rate achieved by using the optimal relay in the set Ω. Here, R_{D,i} is given by (14). The first term to the right of (46) is the same as that of (35), and the second term to the right of (46) can be given by:
where Pr[ R_{S}<R_{th}] denotes that the secrecy rate R_{S} is less than the predetermined secrecy rate R_{th}. Obviously, it is very difficult to get a integral form or a closedform expression of Pr[ R_{S}<R_{th}] because there exist three random variables in R_{S}. We will give the results in subsequent simulations results section.
Vickrey auctionbased secondary system relay selection strategy
After assisting a PU, the selected SU will obtain a certain amount of time to occupy the PU’s spectrum to achieve its own data transmission. In our work, we not only consider the above transmission strategy of PUs in energylimited CCRbased IoT, but also investigate the secure and reliable transmission strategy of SUs. In the former case, PUs employ an SU as a relay to assist their communication, and the spectrum resource is used as a reward for the SU. However, in the latter case, the SUs are all rational users, and they do not voluntarily consume limited energy to assist other SUs in their transmission. In general, cooperation among them should be based on the improvement of their own earnings. Thus, we will propose a secondary system relay selection strategy based on Vickrey auction in this section.
In general, the Vickrey auction combines advantages of the English auction and the sealed price auction [27]. Theoretically, it is an effective auction mechanism because the optimal strategy for each candidate is based on the valuation of the subject matter. This is obviously a trading method that conforms to the principle of incentive compatibility. Moreover, since an auction is ultimately obtained by the bidder with the highest willingness to pay, it is also a configuration mechanism that enables the buyer and the seller to achieve Pareto optimality.
In our system, the secondary system is decentralized. We exploit Bitcoin mechanism to achieve an auction incentive. The original intention of this approach is that Bitcoin is a decentralized peertopeer(P2P) digital currency [49]. With the idea of blockchain in Bitcoin [50, 51], we can implement decentralized creditbased P2P transactions in distributed systems without mutual trust, by means of data encryption, time stamping, distributed consensus, and economic incentive. Thus, the blockchain technology ensures the normal and reliable circulation of Bitcoin.
Introducing the Bitcoin mechanism, in our work, the secondary system model is composed of a pair of SUs (SUS and SUD) that need to communicate with each other and K energylimited relays (SURs). Similar to the description in primary system, SUS wants to communicate with SUD. Yet, there does not exist a direct link between SUS and SUD due to deep fading or obstacles. Thus, it is necessary to employ another SU to be a relay to assist the secondary pair users communication. In our system, relays are all EHenabled SUs and their battery energy should be harvested from the surrounding RF signals. The calculation process of the system channel rate is similar to Section 3.1, where the results are given directly below,
where \(\delta _{i,j}^{SU}=\frac {P_{i}^{SU}g_{i,j}^{SU}}{\sigma ^{2}}\) is the corresponding SNR.
In the Vickrey auction, the bidder that submits the lowest bid wins the auction, but the auctioneer pays the secondlowest amount bid to the winner. Here, we define that the auctioneer is SUS and the bidders are K candidate relays. And the characteristic of bidders are the CSI between SUS and SUD, e.g., \(g_{S,R}^{SU}\) and \(g_{R,D}^{SU}\). Then, we provide the valuation of bidder R_{i} as follows:
where \(R_{D,i}^{SU}\) denotes the channel rate of SUD when using R_{i} as a relay and \(R_{D,th}^{SU}\) is the expected channel rate of SUD. E_{i} represents the energy that the relay R_{i} needs to consume when satisfying the channel rate requirement of SUS. Each relay calculates the corresponding bid \({b_{i}^{'}}\) according to its own E_{i} based on a certain unit price rule, and:
where e_{i} indicates the remaining battery energy of the R_{i} at this time and b_{0} is the upper payment of SUS. Therefore, B={b_{1},b_{2}⋯b_{K}} is the biding set of relays.
In auctions, we need to ensure both the user’s integrity and the user’s personal rationality. Integrity means that regardless of other bidders’ bid, the user’s optimal strategy is given the honest bid, and false prices cannot improve their own utility. Intuitively, integrity is used to ensure that the auction process is fair and effective. Personal rationality means that the auctioneer’s and bidder’s utilities are positive. It is used to ensure the enthusiasm of the auction parties in participating in the auction. We will explain the details of this two requirements separately below.
Integrity: Vickrey auction guarantees the integrity of the auction users. In other words, for the relay selection strategy proposed by this section based on the Vickrey auction, the only dominant strategy is that all relays honestly bid. Next, we will give the corresponding proof. According to the principle of Vickrey auction, we assume that R_{i}’s bid b_{i} is the lowest price, and R_{j}’s bid b_{j} is the second lowest price (where the relay whose bid is 0 does not participate in the bid because its energy is not enough). Thus, R_{i} is the winning relay and its utility function can be expressed as:
Accordingly, there exist different behaviors of relays in various situations.

When \(b_{i}\neq {b_{i}^{'}}\) and R_{i} loses the auction, the utility of R_{i} is 0.

When \(b_{i}>b_{i}^{'}\) and R_{i} wins the auction, the utility of R_{i} is b_{j}−b_{i} which is lower than \(b_{j}b_{i}^{'}\), and R_{i} lost \(b_{i}b_{i}^{'}\) compared to honest bid.

When \(b_{i}< b_{i}^{'}\) and R_{i} wins the auction, the utility of R_{i} still \(b_{j}b_{i}^{'}\), because R_{i} really consumes the energy of the corresponding value \(b_{i}^{'}\). Thus, the utility of R_{i} has not been improved. And even if R_{j} adopts the strategy of \(b_{j}< b_{j}^{'}\), the utility of R_{i} will decrease.
Personal rationality: From (51), we can see that relays always have nonnegative utilities. Then, we can get the utility function of SUS as:
Obviously, we can also find that SUS always have a nonnegative utility. Therefore, our auction strategy can guarantee the personal rationality of the auction parties. Next, we will specify the steps of the proposed relay selection strategy as follows.

SUS determines the expected channel rate \({R_{D,th}^{SU}}\), broadcasts it to all relays, and then waits for response.

All candidate relays calculate their own E_{i} based on (48) and compare it to their own battery’s remaining energy e_{i}. If E_{i}>e_{i}, the candidate may set its own bid b_{i}=0. Otherwise, it calculates the corresponding bid \({b_{i}^{'}}\) according to a certain unit price rule. For \(b_{i}^{'}\), the candidate will set b_{i}=0 if \({b_{i}^{'}}>{b_{0}}\) and set \(b_{i}={b_{i}^{'}}\) otherwise. Then, all relays sent their bids to SUS.

After receiving K bids, SUS will perform the decisionmaking process. If all bids are 0, the transmission is terminated; if only one nonzero bid b_{i}, R_{i} is the winner and SUS will pay R_{i}b_{0}; if there are more than one nonzero bid, the candidate relay with the lowest bid is the winner and SUS pays the second lowest price;

SUS broadcasts its messages which contains the number of the selected relay, and all relays will receive the messages. In this case, the winner assists SUS to forward messages and others will harvest energy or complete its own services.
Numerical results
Analysis of PUs’ outage performance
In this subsection, we will present numerical results via Monte Carlo simulation to evaluate the outage performance of PUs in CCRbased IoT. This network consists of a pair of PUs and some energyharvestingenabled SUs. For simplicity, unless otherwise noted, the simulation parameters are set in Table 1.
Figure 5a and b depict the outage performance of system with trusted SUs under different numbers of SUs and discrete energy levels. In the legend of these two figures, “Sim” indicates the results obtained by Monte Carlo simulation, “Ana” denotes the theoretical values obtained by (43), and “LB” represents the lower bound value given by Lemma 2. In these two figures, the results of exact analysis and the lower bound closely match the simulated results. Figure 5a demonstrates that the outage probability decreases gradually as the number of SUs increases. In addition, we can also find that the higher battery capacity E_{max}, the lower outage probability can be achieved. When E_{max}=20 mW, the ideal outage performance (less than 10^{−4}) can be achieved if the number of SUs K is greater than 6. Yet, when E_{max}=10 mW, the same performance can be achieved only when K>9. In Fig. 7,we set th=L/2+1 and E_{th}=E_{max}/2. The result shows that the outage probability gradually decreases and tends to be stable as the energy discrete levels L increases. And the outage probability will increase as the predetermined rate R_{th} increases. When the given rate reaches 7 bit/s/Hz, the system outage is too high to work.
Figures 6, 7, and 8 compare the outage probability in the case of trusted and untrusted scenarios. In these figures, “T” indicates the trusted SUs, while “U” denotes the untrusted ones. Figure 6 shows the impact of the number of SUs K and the battery capacity E_{max} on the outage performance in the two scenarios. Obviously, the outage probability decreases gradually with the number of SUs increases. And we can increase the battery capacity E_{max} to improve the system performance.
The impact of EH efficiency η on outage probability is studied in Fig. 7 with different predetermined rate R_{th}. With the increase of η, the outage probability gradually decreases. Moreover, it can be seen that the outage probability increases accordingly by increasing the predetermined rate R_{th}. In the case of trusted SUs, the curves for R_{th}=1 bit/s/Hz and R_{th}=3 bit/s/Hz are almost coincident. This can be interpreted as the effect of the predetermined rate R_{th} on the outage performance is very small at low predetermined rate case.
Figure 8 plots the effect of threshold energy levels th on outage performance in both cases. In this figure, we set different noise power σ^{2}=− 30,− 40,− 50 dBm. From the figure, we can see that the system is almost outage in untrusted SUs case when σ^{2}=−30 dBm. In addition to the curve of σ^{2}=−30 dBm, we can find the optimal value th on the other curves to achieve the lowest outage probability. And the optimal th also gradually decreases as the noise power decreases. The reason is that the same secure performance can be achieved by using lower transmit power when noise power is lower. Thus, we can conclude that the outage performance achieved by trusted SUs is superior to that of untrusted SUs when consuming the same energy. This is because part of the system power has to be used to broadcast AN due to eavesdropping. Yet, according to our cooperative jamming strategy, we can still achieve excellent performance by adjusting the corresponding parameters when SUs are untrusted
Next, in Figs. 9 and 10, we study the effect of EH efficiency η on outage performance under different power allocations for the trusted and untrusted SUs. From Fig. 9, it can be observed that the outage performance achieved by different power allocation strategies is slightly different. When η is relatively small, we should exploit higher P_{S} to achieve lower outage probability. On the contrary, properly increasing P_{D} can achieve better outage performance when η is larger. However, we should allocate more energy to broadcast messages instead of AN because η is still relatively small in practice. And when SUs are fully trusted, all system power is used to transmit messages. Thus, the larger the P_{S}, the lower outage probability can be achieved, which can be showed in Fig. 10.
Finally, we provide the the impact of SNR on outage performance with different distance between PUS and SUs in Fig. 11. Here, we assume that SNR=P/σ^{2} with P=20 dBm and σ^{2}=10∼−70 dBm^{Footnote 6}. From this figure, we know that the system is completely outage if SNR is less than 30 dBm, and the outage probability gradually decreases and tends to be stable along with increasing SNR. In addition, we can also find that the closer the distance between SUs and PUS is, the lower outage probability can be reached. Also, the larger SNR can obtain the more stable outage probability. This is because when an SU is closer to PUS, it can harvest energy faster, which leads to the lower probability of energy shortage.
Analysis of Vickrey auctionbased relay selection strategy
In this subsection, we analyze the performance of the secondary system with our proposed relay selection strategy based on Vickrey auction. This network consists of a pair of SUs and K energylimited SURs. The transmit power of SUS and noise variance of the system are set to be 20 dBm and − 50 dBm, respectively. In addition, the distance between two SUs is 10 m and the SURs are located in the middle of two SUs. The path loss factor α is 3. For simplicity, we assume that the market price of 1 mW is 1 Bitcent in the following simulation figures^{Footnote 7}.
In Fig. 12a, the result shows the effect of the expected channel rate \(R_{D,th}^{SU}\) of SUS on the utility of the winning relay for different network scales. We can easily know that the utility of the winning relay is always positive no matter how the number of relays and the expected channel rate \(R_{D,th}^{SU}\) change. This result also further verifies the personal rationality of bidders. Additionally, we can also find that when the number of relays increases, the utility of winning relay decreases. This result is quite reasonable because the auction competition becomes more intense when the number of relays increases, and the difference between the lowest bid and the second lowest bid is smaller. Furthermore, the utility of the winning relay also gradually increases along with increasing \(R_{D,th}^{SU}\). This can be explained by the fact that when SUS needs higher requirements, the difference between relays appear to be more pronounced, which may lead to different energy consumption.
The effect of the expected channel rate \(R_{D,th}^{SU}\) on the auctioneer SUS’s payment is shown in Fig. 12b. In order to evaluate our proposed strategy, we define an average payment that is computed by traversing all relays. According to the figure, we know that the SUS’s payment may be growth when the expected channel rate \(R_{D,th}^{SU}\) grows. Also, we can draw the conclusion that SUS’s payment is much smaller than the average one of traversal all the relays.
Discussion
According to the analysis of numerical results in Section 7, it is obviously to observe that the proposed strategy enables the CCRbased IoT the ability to cope with the secure forwarding problem and limited energy problem simultaneously. We can obtain excellent outage performance of primary communication without consuming additional energy of selected secondary users. Therefore, this strategy is valuable for data transmission among lowend devices in IoT networks.
The experiments in this paper is carried out on MATLAB platform, and we exploit relevant parameters similar to a real wireless environment. Regardless of whether the trusted or untrusted SU acts as a relay node, the outage probability is only slightly different. The reason is that we employ different power allocation strategies for various scenarios. This observation may provide a unique vision to study data secure sharing among lowend devices with different attribute. In addition, it is worth noting that there is still an issue about secondary data exchanging due to the lack of legal spectrum licences for lowend devices. Then, we analyze the effect of the expected secondary data rate on the utility of the winning relay based on the Vickrey auction. The results demonstrate the positive utility of the winner and also prove the personal rationality of a bidder during the auction.
Yet, the efficiency of energy conversion is still a bottleneck in EHenabled CCRbased IoT. In future work, we would like to focus on improving the conversion efficiency and design scalable cooperative secure relays to enhance unit energy utilization.
Conclusions and future works
A relay selection strategy based on CSI and BSI in EHenabled CCRbased IoT is proposed in this paper. Some lowend devices treated as SUs with EH capabilities can be selected as helpers of a pair of primary users. The outage probability is used to analyze transmission performance of PUs in both trusted and untrusted SU scenarios. When an SU is selected as a relay, it will be in IF state and the unselected SUs harvest energy from signals transmitted by PUS. For untrusted SUs, we adopt a destinationassisted jamming strategy to prevent eavesdropping. And we formulate the energy accumulation process of SUs’ batteries as a finite state Markov chain and derive the corresponding steadystate probability. For energylimited secondary systems, we propose a relay selection strategy based on Vickrey auction. According to numerical results, we know that many parameters have effects on the outage performance of CCRbased IoT. Specifically, the outage probability is inversely proportional to the maximum battery capacity, the number of relays, the channel rate threshold, and the EH efficiency. And there exist the optimal energy threshold that can minimize the outage probability. Moreover, the accuracy of the theoretical analysis and the lower bound analysis are also confirmed via simulation results.
In this article, we assume that all CSI is perfectly known by using a channel estimation scheme. Yet, it is difficult to acquire the accurate CSI in wireless data transmission because of defects of channel estimation algorithms or dynamic channel state. Thus, we further study a secure relay selection method for an EHenabled CCRbased IoT with imperfect CSI. In addition, we will discuss the outage performance of the noncentralized distribution of SUs in the same scenario as well as the secure data sharing among SUs in this scenario.
Appendix A
For both trusted and untrusted SUs, the energy harvested via the EH mode in a time slot is given by (2) and (8), respectively. For convenience, we use E_{1} and E_{2} to represent the harvested energy in these two scenarios. In addition, we define \(g_{S} = \frac {\eta }{2}{P_{S}}{g_{S,{R_{k}}}}\), where \(g_{S,{R_{k}}}\) is a random variable that obeys exponential distribution. Thus, g_{S} is an exponentially distribution with mean \({\bar {g}_{S}}=\frac {1}{2}{P_{S}}\eta {{\bar {g}}_{S,{R_{k}}}}\). And the PDF and CDF of g_{S} can be calculated as follows.
and
Then, the CDF of E_{1} is the CDF of g_{s}, which can be expressed as:
Next, in order to obtain the CDF of E_{2}, we first obtain its probability density function (PDF). Similarly, we define \(g_{D} = \frac {\eta }{2}{P_{D}}{g_{D,{R_{k}}}}\) based on (8). Here, \(g_{D,{R_{k}}}\) is also a random variable that obeys exponential distribution, which will lead to g_{D} as an exponentially distribution with mean \({\bar {g}_{D}}=\frac {1}{2}{P_{D}}\eta {{\bar {g}}_{D,{R_{k}}}}\). Thus, E_{2} is the sum of two exponential random variables. We first compute the joint probability distribution of g_{S} and g_{D}, which can be given by:
where \({f_{G_{S}}}(g_{S})\) and \({f_{G_{D}}}(g_{D})\) are PDFs of g_{S} and g_{D}. The equality (a) holds due to the independence of g_{S} and g_{D}. Because E=g_{S}+g_{D}, we can easily obtain that g_{S}=E−g_{D}. Considering the nonnegativity of the exponential distribution, we know that the value range of g_{S} is [0,E_{2}]. Therefore, the PDF of E_{2} can be calculated as follows.
Then, we can get the CDF of E_{2} by integrating (57), which can be derived as follows.
And the proof of Lemma 1 is completed.
Appendix B
Here, we utilize the inequality \(\frac {q_{1} q_{2}}{q_{1} + q_{2} + 1} < \frac {q_{1} q_{2}}{q_{1} + q_{2}} \). Thus, it is easy to see that γ_{D} in (5) is upper bounded by:
Accordingly, \( P_{out}^{LB}\) can be rewritten as:
In order to get the lower bound \(P_{out}^{LB}\), we need to get the CDF of γ. At first, we define that X_{1}=1/X and Y_{1}=1/Y. Then, we can get the CDF of X_{1} as:
where F_{X}(·) is the CDF of X. Thus, the PDF of X_{1} can be calculated by deriving x_{1} for (61), which is as below.
And the PDF of Y_{1} is:
Similar to the calculation in [52], the moment generating function (MGF) of X_{1} and Y_{1} is as follows.
and
Next, we further define that:
Since X_{1} and Y_{1} are mutually independent random variables, the MGF of Z=X_{1}+Y_{1} is the product of the MGFs of x and y, which is given by:
Then, we can easily obtain the CDF of γ as:
where F_{Z}(·) is the CDF of Z. Using the differential nature of the Laplace transform, F_{Z}(·) can be computed by performing an inverse Laplace transform on M_{Z}(s)/s. Thus, we can get the CDF of γ as follows.
And the proof of Lemma 2 is completed.
Notes
 1.
The EH efficiency is often assumed to reach 90% or even 100% in many articles.
 2.
Unselected SUs may continue to harvest energy in the second phase. And the transmission power of the selected SU−R is negligible compared with PU’s transmission power in the first phase.
 3.
The main task of an SU is to harvest energy to assist PU’s communication. We assume that the unselected SUs will only be in the EH mode and will not eavesdrop on the PUs’ messages.
 4.
The reason we define the energy threshold is that the time for the relay to send signals is half a time slot, i.e., 1/2 in this paper.
 5.
Here, we assume that the energy used to send the pilot signal can be negligible.
 6.
In fact, the AWGN is not severe in practical applications. In order to illustrate the effectiveness of the proposed strategy, the noise power is set to be σ^{2}=10∼−70 dBm here.
 7.
For practical applications, energy can be expressed into different value according to different unit price rule.
Abbreviations
 AF:

Amplifyandforward
 AWGN:

Additive white Gaussian noise
 AN:

Artificial noise
 BSI:

Battery state information
 CCR:

Cooperative cognitive radio
 CDF:

Cumulative distribution function
 CRN:

Cognitive radio network
 CSI:

Channel state information
 D2D:

Devicetodevice
 DF:

Decodeandforward
 EH:

Energy harvesting
 IoT:

Internet of things
 M2M:

Machinetomachine
 MGF:

moment generating function
 PDF:

Probability density function
 PSR:

Power splitting relaying
 PU:

Primary user
 RS:

Relay selection
 SINR:

Signaltointerferenceplusnoise ratio
 SNR:

Signaltonoise ratio
 SU:

Secondary user
 SWIPT:

Simultaneous wireless information and power transfer
 TSR:

Time switching relaying
 WPC:

Wireless powered communication
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This work was financially supported by NSFC 61471028, 61871023, and 61572070 and the Fundamental Research Funds for the Central Universities 2017JBM004 and 2016JBZ003.
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Huo, Y., Xu, M., Fan, X. et al. A novel secure relay selection strategy for energyharvestingenabled Internet of things. J Wireless Com Network 2018, 264 (2018). https://doi.org/10.1186/s1363801812814
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Keywords
 Energy harvesting
 Physical layer security
 Outage probability
 Markov chain
 Cooperative cognitive radio networks