Exact Outage Analysis of Cognitive Energy Harvesting Relaying Networks under Physical Layer Security

In this paper, we study the secure communication of cognitive energy harvesting relay networks when there exist multiple eavesdroppers who can overhear the message of the second hop, and multiple primary users are present. The data transmission from the secondary source to the secondary destination is assisted by the best decode-and-forward relay, which is selected by means of three relay selection schemes. We study the system security performance by deriving the exact analytical secrecy outage probability. These analytical expressions are then verified by comparison to the results of Monte Carlo simulations. Herein we evaluate and discuss the outage performance of the three schemes under variations in important system parameters: the number and locations of relay nodes, primary user nodes, and eavesdroppers; the transmit power threshold; the energy harvesting efficiency coefficient; the power splitting ratio; and the target secure rate.


Introduction
Recently, the simultaneous wireless information and power transfer (SWIPT) technique has attracted more and more attention in wireless networks as an efficient solution to prolong the lifetime of energy-constrained wireless devices.An ideal SWIPT was first proposed for the scenario in which the receiver can simultaneously harvest energy and detect information from the same received signal [1].Subsequently, practical energy harvesting receiver designs for SWIPT were proposed and studied, based on two architectures: powersplitting (PS) and time switching (TS) [2,9,10,12,22].In such designs, the signal received at the PS receiver is split into two parts, one for harvesting the energy and the other one for decoding the information; this splitting is carried out in accordance with a power splitting ratio.Within a time block, the TS receiver harvests energy from the received radio-frequency signal during an initial interval and then switches to decoding the information during the remaining interval.
As a means to combat multipath fading in wireless communication, cooperative communication is an effective solution that increases the diversity capacity [3,4].Decode-and-forward (DF) and amplify-andforward (AF) are the two main strategies applied at relay nodes in cooperative networks.In DF mode, the relay node detects information from the received signal and then re-encodes and forwards it in the next hop.In AF mode, the relay only amplifies the received signal and forwards it; this is simpler than DF, but has the drawback that the noise within the received signal is also amplified.Some performance metrics as outage probability, average sum-rate, and average symbol error rate for the semi-blind (partial channel state information) have been analyzed for the conditions of Rayleigh fading channels [5], the Nakagami-m fading environment [6], and the generalized-K fading channel [7].A hybrid AF-DF protocol has been considered for multihop relaying networks [8].Several works have addressed the application of energy harvesting techniques in energy-constrained relay nodes of cooperative systems.In [9], the authors design three wireless power transfer policies and analyzed their throughput in two-way relaying networks in which the TS architecture was employed at an energy-constrained AF relay node.In [10], the authors derive expressions of the throughput, outage probability, and ergodic capacity for a dual-hop relaying system, considering the use of both TS and PS architectures at an AF relay node.Other works have addressed the case of multiple sourceâĂŞdestination pairs communicating with each other via a DF energy harvesting relay [11,12].In [11], the authors focus on the distribution of harvested energy among the multiple users and their impact on the system performance in a TS architecture.In [12], the authors investigate the power allocation based on maximizing the total rate for a PS architecture.Optimal power and time fraction allocation, and optimal power allocation with a fixed time fraction have both been proposed to maximize the achievable average data rate in a DF energy harvesting relaying system [13].In [14], the authors study the performance analysis of an energy harvesting relaying network using the help of multiple relay nodes.Unlike the fixed locations considered in previous works, in [15] the authors considered multiple randomly located DF energy harvesting relay nodes, for which the density function for the wireless channels is characterized by stochastic geometry.
Cognitive radio is regarded as an efficient technique to enhance the spectrum efficiency in wireless communication systems [16].It allows secondary users (unlicensed users) to utilize the spectrum bands of primary users (licensed users) without interfering with primary usersâĂŹ communications.In the underlay mode of cognitive radio, secondary users transmit simultaneously with primary users over the same spectrum without degrading the quality of service of the primary transmission by keeping the interference to the primary users under a predefined threshold [17].The outage performance of a dual-hop underlay cognitive radio network over the independent non-identically distributed Nakagami-m fading channel is studied in [17].In [18], the authors extended [17] considering the best relay selection strategy in a cognitive relaying network with the presence of multiple AF relay nodes.An algorithm has been proposed to maximize the throughput in a cognitive AF [19] or DF [20] relaying network in which energy harvesting based on PS is applied at the relay.In another work, the PS and TS architectures were utilized at the best relay in an underlay cognitive DF relaying network [21].The impact of transceiver hardware impairments upon the outage performance and throughput of a DF two-way energy harvesting relaying network is considered in [22].
Due to the broadcast nature of the wireless medium, information can be overheard and extracted by unwanted eavesdroppers.Physical layer security (PLS) has received considerable attention from researchers as a means to solve this issue.Wyner first defined the achievable secrecy rate (ASR) as the maximum rate of reliable information sent from the source to its destination in the presence of eavesdroppers [23].Wyner showed that the communication between source and destination is secure when the ASR is larger than the required secrecy rate.Following this finding, PLS has been considered in Gaussian wiretap channels [24], and has been extended to broadcast channels [25] as well as to fading channels [26].Considering the PLS in CRN has attracted attention from various researchers [27][28][29][30].In [27] the authors studied the security of CRN with the presence of a multiple-antennas eavesdropper.Several relay selection strategies to choose two relays for secure communication in cognitive DF relay networks [28], i.e., the one relay help the source forward information to destination, the other relay confound the eavesdropper by transmitting the jamming signal.A secure switch-and-stay combining protocol is studied in CRN to overcome the limitation of the continuous requirement the channels state information at all relays [29].Secure communication of the AF and DF energy harvesting relaying networks under wiretapping by an eavesdropper has also been studied [30].The issue of eavesdropper's ability to collaborate, to exchange the information obtained from the source and relays, has been studied in [32].
To the best of our knowledge, there has been now study on the jointly energy harvesting technique in cognitive radio networks and under wiretapping of eavesdroppers.This motivates us to analyze the exact secrecy outage probability of the secure communication of the underlay cognitive relaying networks.In this model, we consider the communication between a secondary source and secondary destination based on the assist of multiple intermediate secondary relays under the presence of multiple primary users and eavesdroppers.For the performance evaluation and comparison, the exact expressions of the secrecy outage probability for three partial relay selection schemes are derived.Three relay selection schemes for choosing the one best relay, which harvests and decode the information from the received signal and forward to the destination, are presented as: 1) the maximum channel gain from the source to the relays, called the MaSR scheme, 2) the MiRP scheme stand for minimum channel gain from the relays to the primary users, 3) the minimum channel gain from the relays to the eavesdroppers, MiRE.The Monte Carlo simulations are used to verify our theoretical analysis.
The rest of the paper is organized as follows.Section 2 presents the system model and formulas expressing the three relay selection schemes.Section 3 presents the transmission operation of the system in which the energy harvesting-based power splitting architecture is applied at the selected relay.Section 4 presents secrecy outage probability analyses for the three schemes studied.Section 5 presents system performance with high Q/N 0 .Section 6 presents numerical results from the simulations and theoretical analyses.Finally, Section 7 presents our conclusions.
Notation: The notation CN (a, b) denotes a circularly symmetric complex Gaussian random variable (RV) with mean a and variance b.E {.} denotes mathematical expectation.The functions f X (.) and F X (.) present the probability density function (PDF) and cumulative distribution function (CDF) of RV X.The function

System model
As shown in Figure 1, we consider a system model of an underlay cooperative cognitive network under physical layer security.The secondary network consists a source node (S), a destination node (D), M energyconstrained relays (R m , m ∈ {1, 2, ..., M}) in cluster R, and L eavesdroppers (E l , l ∈ {1, 2, ..., L}) in cluster E; also, there are N primary receivers (P n , n ∈ {1, 2, ..., N }) in cluster P, located in the primary network.We note that the primary transmitters (not shown in Fig. 1) are located far enough from the secondary network that their interference to the secondary nodes can be ignored [21].Each node is equipped with a single antenna operating in half-duplex mode.
In Figure 1, we denote and R m − E l , respectively, where P n , R m , and E l denote the nth primary receiver in cluster P, the mth relay in cluster R, and the lth eavesdropper in cluster E. Thus, the corresponding channel gains , where β denotes the path loss exponent.We obtain the corresponding cumulative distribution functions (CDF) and probability density functions (PDF) of the RVs g χ as F g χ (x) = λ χ e −λ χ x and f g χ (x) = 1 − e −λ χ x , respectively.The distances between the two nodes in a cluster are insignificant compared to the distances between nodes not within the same cluster [30].Hence, we can denote

., L}; the parameters then can be denoted as
We assume that no direct links exist between S and D nor between S and cluster E due to deep shadowing [30], and that cluster E is located near D to allow eavesdropping on D [30].After the set up phase, the destination has perfect channel coefficients for all links [30]; then, D selects a best relay R b from the M available nodes to receive and harvest the energy from the RF signal, which is transmitted from S in the first hop and then decoded and forwarded to D under eavesdropping by L eavesdroppers in the second hop.
Three partial relay selection schemes are considered throughout this paper to increase the system performance as well as to reduce the power consumption of the source node.First, the relay R b is selected by maximizing the channel gain of the S − R m link (called the MaSR strategy) to increase the amount of harvested energy and the decoding performance at the relay.Second, to reduce the interference from the selected relay to all of the N primary receivers, the relay R b is chosen from the M available nodes that minimizes the channel gain of the R m − P n link (called the MiRP strategy).Third, R b is selected by minimizing the channel gain of the R m − E l link (called the MiRE strategy).These three relay selection schemes are formulated respectively as . . . . . .

Wiretapping channel
Cluster-P

Energy harvesting-based power splitting and transmission operation
In this section, we consider energy harvesting based on the power splitting protocol, with the power splitting ratio of ρ ∈ (0, 1) for energy harvesting and (1 − ρ) for decoding the source information at the best relay R b in the first time slot (i.e., the first time interval: T /2) [10, Fig. 3].The received signals for energy harvesting and for information decoding at R b are given respectively by is the adapted transmit power of the source S, with Q being the interference threshold for the primary receivers [27]; x (t) is the transmitted signal, with E |x (t)| 2 = 1; and n SR b (t) ∼ CN (0, N 0 ) denotes the additive white Gaussian noise (AWGN) at R b .
From (4), we obtain the following expression for the energy harvested at R b during time T /2: where 0 ≤ η ≤ 1 is the harvesting efficiency coefficient, which depends on the rectification process and the energy harvesting circuitry [19].The harvested noise energy is ignored because it is insignificant compared to the overall harvested energy [19].The RF signal expressed by ( 5) is downconverted to a baseband signal [10]; this baseband signal as sampled at R b can be expressed as where The achievable secrecy rates for the first hop ψ 1 can be obtained from (7), and for the second hop ψ 2 can be obtained from ( 8) and ( 9) as follows: where

Secrecy outage probabilities of relay selection schemes
In this section we analyze the secrecy outage probability (SOP) of the three relay selection schemes mentioned in Section 2: MaSR, MiRP, and MiRE.None of these SOP derivations include the assumption of high SNR used in previous work [14].The SOP is defined as the probability the achievable secrecy rate of the system, i.e., min (ψ 1 , ψ 2 ), is below a desired threshold secrecy rate ψ t (12) Substituting ( 10) and ( 11) into ( 12), we have where g is a new RV denoted as g The terms Pr 1 and Pr 2 can be expressed in the following multiple integral forms: where and . The PDF of g 3 is f g 3 (x 3 ) = λ RD e −λ RD x 3 for all three cases of relay selection schemes.And the PDFs of g, g 1 , and g 2 can be changed depending on the relay selection schemes as three subsection follows.

Secrecy outage probability of MaSR
The PDF of g 1 , g 2 can be obtained as the same way as in Eq. (A2) of Appendix A , and the PDF of g can be expressed as in Eq. (A5) of Appendix A, as follows.
The term Pr 1 can be expressed as follows, including substitution of the PDFs of g, g 1 , g 2 and g 3 into Eq.( 14) and subsequent manipulations.
Lemma 4.1.The following expression is valid for the integral I 1 .
where Φ (u, a, b, p) Similarly, we can obtain the following.
(21) Next, the term Pr 2 can be expressed as follows, including substitutions the PDFs of g, g 1 , g 2 and g 3 into Eq.( 15) and subsequent arrangements, similar to those used to obtain an expression for Pr 1.
The integral I 3 in Eq. ( 22) can be expressed as follows.
The secrecy outage probability of the system under the relay selection scheme MaSR can be obtained by combining Eqs. ( 13) and ( 19)âĂŞ(23) as follows.

Secrecy outage probability of MiRP
Under the MiRP relay selection scheme, the PDFs of the RVs g 1 and g are different from those given in Section 4.1.They are expressed as follows, including reference to proofs in Appendix C (Eq. C2) and Appendix A (Eq. A6), respectively And the PDF of g 2 and g 3 are expressed as same as Section 4.1.
By the same way shown in Section 4.1, substituting the PDFs of 4 RVs g, g 1 , g 2 , and g 3 into ( 14) and ( 15), the terms Pr 1 and Pr 2 can be derived after some manipulations as follows.
The secrecy outage probability of the system under relay selection scheme MiSP can be expressed as follows by substituting Eqs. ( 27) and ( 28) into Eq.(13).
Then, we can obtain the following expressions for Pr 1 and Pr 2 in this relay selection scheme as follows Pr 1 = Finally, the secrecy outage probability for the MiRE relay selection scheme can be expressed as follows.

System performance with high Q/N 0
To provide insight into how the system parameters impact the network performance, we derive the asymptotic secrecy outage probability in the high Q/N 0 of the considered system.At high Q/N 0 with respect to θ−1 ω 1 → 0.Then, the value of the integral I 1 in (B1) is increased and can be approximated as:

Numerical results
This section presents secrecy outage probability analyses of the three relay selection schemes considered for use in the underlay cognitive cooperative network under physical layer security, including both the analytical results and the results of Monte Carlo experiments each including 10 5 independent trials.The analyses considered a network in a two-dimensional plane, with the following coordinates for the source S, the destination D, the relay cluster, the primary user cluster, and the eavesdropper cluster: (0, 0), (1, 0), (x R , 0), (x P , y P ), and (x E , y E ), respectively.Hence, we have the distances d SD = 1, d SR = x R , d SP = (x P ) 2 + (y P ) 2 , d RD = (1 − x R ) 2 , and d RE = (x R − x E ) 2 + (y E ) 2 .In all simulations, we assumed the path loss β = 3, noise N 0 = 1, and the parameter µ = 1 [21].
Figure 2 shows secrecy outage probabilities of the three relay selection schemes studied versus the power splitting ratio ρ ∈ (0.01, 0.99), including both Monte Carlo simulation results and theoretical curves for each of three values for the number of relay nodes: M = 1, 3, and 5.The exact expressions for the secrecy outage probabilities of the MaSR, MiRP, and MiRE schemes are given as Eqs.( 24), (29), and (34), respectively.The simulated and theoretical results matched very closely, demonstrating the accuracy of our analysis.The three protocols all achieved the same performance in the case of M = 1 because no relay selection process is used when there is only one relay node in the system.

.
) where n c SR b (k) ∼ CN (0, µN 0 ), with µ > 0, denotes the AWGN at the converting unit.The relay R b decodes the information and then re-encodes it for forwarding to the destination D under eavesdropping by L eavesdroppers.The transmit power at R b is adapted, in order not to exceed the threshold Q, as P Rb = min The received sampled baseband signals at S and E l can be expressed respectively as

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Exact Outage Analysis of Cognitive Energy Harvesting Relaying Networks under Physical Layer Security EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 12 2018 -03 2019 | Volume 6 | Issue 18| e1

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Outage Analysis of Cognitive Energy Harvesting Relaying Networks under Physical Layer Security EAI Endorsed Transactions on Industrial Networks and Intelligent Systems 12 2018 -03 2019 | Volume 6 | Issue 18| e1