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On Physical-Layer Security in Underlay Cognitive Radio Networks with Full-Duplex Wireless-Powered Secondary System Jiliang Zhang, Gaofeng Pan, and Hui-Ming Wang

Abstract—In this paper, we consider an underlay cognitive radio system, in which a source in a secondary system transmits information to a full-duplex (FD) wirelesspowered destination node in the presence of an eavesdropper. In particular, the destination node is equipped with a single receiving antenna and a single transmitting antenna to enable FD operation. The receiving antenna can simultaneously receive information and energy from the source through power-splitter architecture. The received energy is then used in the transmitting antenna to send jamming signals to degrade the eavesdropper’s decoding capacity. Upper and lower bounds of probability of strictly positive secrecy capacity (SPSC) have been derived. Numerical results show that under the condition that the interference from the source and destination at primary user’s receiver is smaller than the interference temperature limit, upper and lower bounds merge together to become the exact SPSC. Index Terms—Cognitive radio networks, full-duplex, simultaneous wireless information and power transfer, probability of strictly positive secrecy capacity.

I. I NTRODUCTION Benefitting from the joint advantages of cognitive radio (CR) technique and information-theoretic security by characterizing the properties of physical channels in wireless communication, physical-layer (PHY) security in CR networks (CRNs) has attracted considerable attention in literatures [1]-[6]. A thorough understanding of PHY security in CRNs was presented in [1] and [2]. The authors in [3] derived the analytical expression for secrecy outage probability (SOP) over Nakagami-m fading channels. Later, Ref. [4] extended the work of [3] into single-input multiple-output systems with generalized selection combining. Based on a realistic spectrum sensing method, Zou et. al. proposed both single and multiple relay selection schemes, and analyzed intercept probability as well as outage probability (OP) of those two proposed relay selection schemes in [5]. Considering a multiple-input single-output CRN under slow fading channels in the presence of multiple eavesdroppers, the

secrecy throughput maximization problems were investigated in [6]. To ensure secure communication, an effective way is to send jamming signals to interfere the eavesdroppers with the help of extra cooperative relays, and this is also referred to cooperative jamming (CJ) [7]-[10]. Considering the scenario that relays either help to transmit useful information or to broadcast jamming signals to interfere eavesdroppers, the authors in [7] derived a closed-form expression for SOP, and proposed two relay and jammer selection schemes for SOP minimization. In [8], opportunistic CJ and relay chatting schemes were proposed by using OP as the metric for performance evaluation. Optimal jamming noise structure in terms of secrecy rate was proposed in [9]. In a two-way relay system with a single antenna, Wang et. al. proposed a novel hybrid cooperative beamforming and jamming scheme to ensure the PHY security when an eavesdropper was present to overhearing the information in [10]. When no cooperative relays are available, artificial noise (AN), which is used to only interfere the eavesdroppers [11], can be generated by the systems equipped with multiple antennas to degrade the decoding capability of eavesdroppers [11]-[15]. In [12], a lower bound on the ergodic secrecy capacity for an AN scheme was presented for a multiple-input multiple-output (MIMO) system when quantized and perfect channel state information are respectively available at the transmitter and the receiver. Considering a multi-tier heterogeneous cellular system in which the positions of the base stations, the authorized users, and the eavesdroppers are modeled as a Poisson point process, Wang et. al. [13] studied the PHY security in terms of a proposed mobile association policy, connection and secrecy probabilities of the ANaided secrecy transmission, the network-wide secrecy throughput, and secrecy throughput minimization for each user. The authors in [14] first proposed a framework for an AN assisted secure MIMO system in the presence of an eavesdropper with multiple antennas, and then derived a closed-form analytical expression for ergodic secrecy rate. In [15], the authors first introduced the

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definition of the secrecy outage region, and then derived the analytical expression for SOP in an AN-aided secure transmission system with a massive-antenna transmitter over Rician fading channels. Note that all the aforementioned works are limited to half-duplex modes. In nowadays, recent advanced technology can allow communication systems to work in full-duplex (FD) modes, which can simultaneously receive and transmit data on the same frequency spectrum [16]. Considering a FD base station simultaneously transmitting and receiving data to a receiver and with the constraint of transmitting power minimization, the authors in [17] proposed a transmitter beamforming to mitigate self-interference and to imrpove the PHY security. Lee [18] investigated the secrecy rate of FD relays subject to a total transmit power constraint in a multihop wireless relaying system. Ref. [19] investigated the secrecy performance in terms of SOP in a FD relaying system, and proposed a FD jamming scheme to improve the secrecy performance. However, operating in FD modes consumes extra energy for transmitting. It is a serious concern for those terminals powered by batteries due to the limited operational lifetime. To tackle this problem, energy harvesting (EH) from radio frequency (RF) has gained a lot of interest, and emerged as a promising solution to energy-constrained communication systems [20]. Simultaneous wireless information and power transfer (SWIPT) technique is proposed based on that RF signals can carry both information and energy [21]. Considering three different transmission modes, namely instantaneous transmission, delay-constrained transmission, and delay tolerant transmission, the authors in [22] investigated the OP and ergodic capacity of FD relaying in SWIPT systems. In [23], a new protocol for a FD wirelesspowered relay with self-energy recycling and uninterrupted information transmission was proposed in SWIPT systems. Ref. [24] introduced a novel energy-recycling FD radio architecture to gain advantages in the spectral efficiency as well as energy consumption. Considering optimal, zero-forcing and maximum ratio combining precoding schemes at the relay, the analytical expression for OP was obtained in a FD wireless-powered relaying system in [25]. It is promising and interesting to consider PHY security under CRNs with the application of FD in a wirelesspowered system. To the best of our knowledge, no such work has been reported in literature. Motivated by this, a four-nodes SWIPT system consisting of one secondary source, one secondary destination, one eavesdropper, and one primary user receiver is considered. Main contributions of this paper are as follows:

1) We propose a FD wireless-powered secondary system. In particular, the secondary destination is equipped with two isolated antennas to ensure FD operation. Power splitting (PS) receiver is easy to be implemented as it just splits the received signal into two streams, which are used for information decoding and energy harvesting, according to the PS factor. Thus, PS receiver is implemented in the receiving antenna to obtain both information and energy. The harvested energy is stored in battery and used by the transmitting antenna in the next symbol duration to generate jamming signals to confuse the eavesdropper. 2) Upper and lower bounds of probability of strictly positive secrecy capacity (SPSC) are derived, and also verified with Monte Carlo simulation results. This paper is organized as follows. In Section II, we present the system model and the proposed full-duplex wireless-powered secondary system. In Section III, the upper and lower bounds of probability of strictly positive secrecy capacity are presented. In Section IV, Monte Carlo simulation results are taken to evaluate the derived SPSC. Finally, the paper is concluded in Section V.

II. S YSTEM M ODEL In structure of the paper, we consider a FD wirelesspowered system in underlay CRNs as illustrated in Fig. 1. Four nodes are considered: a source (S), a destination (D) and an eavesdropper (E) in the secondary system, and a PU Rx in the primary system. It is assumed that S, E and PU Rx are equipped with a single antenna, while D is equipped with two isolated antennas (one for receiving and the other for transmitting) to enable FD operation. We also assume that D has no external power supply, and only relies on EH from S for transmitting. PS protocol is adopted in the receiver at D to coordinate information receiving and EH. At beginnings, S first sends a symbol to “wake up” D in the first symbol duration, and D receives and stores the energy in the battery. From second symbol onwards, S transmits confidential information to D, while D simultaneously receives the signal and generates jamming signals to confuse E using the energy stored in the battery. It is assumed that the battery equipped in D is able to be charged and discharged simultaneously [23], [26]. We further assume that all links experience independent and identical Rayleigh fading. It is also assumed that the channel state information is available. In practical communications, those channel state information can be estimated through training and analog feedback [14].



D and E treat the received signals from D as interference. Thus, the signal-to-interference-plus-noise ratio (SINR) of the received signal at D and E can be represented as

PU_Rx

ℎ𝑆𝑃

S

γD =

ℎ𝑆𝐷

ℎ𝐷𝑃

D

ℎ𝐷𝐷

(1 − ρ)Ps |hSD |2 2 + σ2 PD |hDD |2 + (1 − ρ)σD C

(3)

(1 − ρ)Ps |hSD |2 = 2 + σ2 ρηPs |hSD,p |2 |hDD |2 + (1 − ρ)σD C

ℎ𝑆𝐸

and

ℎ𝐷𝐸

Ps |hSE |2 γE = 2 PD |hDE |2 + σE

E Fig. 1: System Model.

The information signal received at D is p p yD = 1 − ρ Ps hSD Xs + nD p + PD hDD XD + nc

(4)

Ps |hSE |2 = 2 ρηPs |hSD,p |2 |hDE |2 + σE

respectively. For mathematical tractability, it is assumed that interference is dominated and this is also of practical (1−ρ)|hSD |2 , interest [22], [28]. Thus, we have γD ≈ ρη|h |2 |h |2 SD,p

2

(1)

where Ps denotes the transmitted power at S, hSD is the channel coefficient for S-D link, Xs is the transmitted symbol at S, and nD is the additive white Gaussian 2. noise (AWGN) with zero mean and a variance of σD ρ (0 < ρ < 1) is the PS factor, and nc is the signal processing noise at D, which is also modeled 2 as AWGN √ with zero mean and a variance of σc . The term, PD hDD XD , in (1) represents the instantaneous residual loopback interference due to FD operation after imperfect interference cancellation [27]. XD is the interference signal sent by D, and hDD is the loopback interference channel, which can be also modeled as a Rayleigh fading channel [22]. ED = ρηPs |hSD,p |2 T is the energy harvested from S and stored in battery in the previous symbol duration (current harvested energy will be stored in the battery for transmitting interference in the following symbol duration) at D, where T denotes the symbol duration, η is the conversion efficiency of the energy harvester at D, and hSD,p is the channel coefficient for S-D link in the previous symbol duration. PD = ETD = ρηPs |hSD,p |2 is the transmitted power at D. The received signal at E is p p (2) yE = Ps hSE Xs + PD hDE XD + nE where hSE and hDE are the channel coefficients for S-E and D-E links, respectively; and nE is the AWGN with 2. zero mean and a variance of σE

DD

and γE ≈ ρη|h |hSE|2||h |2 . SD,p DE The received signal at PU Rx is p p yP = Ps hSP Xs + PD hDP XD + nP

(5)

where hSP and hDP are the channel coefficients for S-PU Rx and D-PU Rx links, and nP is the AWGN with zero mean and a variance of σP2 . The instantaneous interference plus AWGN power at PU Rx is PI = Ps |hSP |2 + ρηPs |hSD,p |2 |hDP |2 + σP2 .

(6)

Since all channel coefficients are independent and identical Rayleigh-fading variables, |hb |2 (the subscript, b, can represent the terms of SD, SE, DD, DE, SD,p, SP, and DP, respectively) has exponential distribution with the probability density function (PDF) and cumulative distribution function (CDF) denoted as [29] f|hb |2 (x) =

1 x exp(− ) gb gb

and F|hb |2 (x) = 1 − exp(−

(7)

x ) gb

(8)

respectively, and gb is the expectation of channel power gain. III. P ROBABILITY OF S TRICTLY P OSITIVE S ECRECY C APACITY The instantaneous achievable rates at D and E are RD = log2 (1 + γD )

(9)

RE = log2 (1 + γE )

(10)

and



respectively. Thus, the instantaneous achievable secrecy capacity for S-D link is Cs = max{RD − RE , 0}.

(11)

In non-CRNs systems, SPSC is defined as the probability of the secrecy capacity Cs is greater than zero. While under CRNs systems, S can only transmit its confidential information to D when the total interference at PU Rx is smaller than Γ (i.e., PI ≤ Γ), where Γ is the interference temperature limit. Thus, SPSC under CRNs systems is PSP SC = P r(Cs > 0)P r(PI ≤ Γ).

(12)

Assuming γD > γE , the secrecy rate in (11) can be re-expressed as 1 + γD Cs = log2 1 + γE 1 + (1−ρ)|hSD |2 (13) ρη|hSD,p |2 |hDD |2 = log2 . 2 1 + ρη|h |hSE|2||h |2 SD,p

DE

Therefore, the expression of P r(Cs > 0) can be written as 1 + γD >0 P r(Cs > 0) = P r log2 1 + γE ! 1 + (1−ρ)|hSD |2 ρη|hSD,p |2 |hDD |2 =P r log2 >0 2 1 + ρη|h |hSE|2||h |2 SD,p DE Y1 =P r X > Y 2 Y1 =1 − P r X ≤ Y2 (14) where X = (1 − ρ)|hSD |2 , Y1 = |hDD |2 |hSE |2 , and Y2 = |hDE |2 . Hence, one has the PDF and CDF of X as fX (x) = λ1 exp(−λ1 x) (15) and FX (x) = 1 − exp(−λ1 x)

(16)

1 where λ1 = (1−ρ)g . SD Making use of Eqs. (3.471.9) (i.e., set v = 0 and β =λ2 y in Eq. (3.471.9)) and (3.324.1) in [30], the PDF and CDF of Y1 is obtained as Z ∞ 1 y 2 (x)dx fY1 (y) = f|hSE |2 f x x |hDD | 0 Z ∞ λ2 y 1 =λ2 λ3 exp − − λ3 x dx (17) x x 0 p =2λ2 λ3 K0 2 λ2 λ3 y

and Z

∞Z

y x

FY1 (y) =

f|hSE |2 (z)f|hDD |2 (x)dxdz Z y = F|hSE |2 f|hDD |2 (x)dx x 0 ! Z ∞ λ2 y = 1 − exp − x 0 0 ∞

0

× λ3 exp(−λ3 x)dx

Z =

∞

λ3 exp(−λ3 x)dx 0 Z ∞ λ2 y − λ3 exp − exp(−λ3 x)dx x 0 ! Z ∞ λ2 y exp − − λ3 x dx =1 − λ3 x 0 p p =1 − 2 λ2 λ3 yK1 2 λ2 λ3 y

(18)

1 1 where λ2 = gSE , λ3 = gDD , and Kv (·) is the modified Bessel function of the second kind defined in Eq. (8.432) of [30]. 3 Using Eq. √ (6.643.3) (i.e., set µ = 2 , α = λ4 , v = 0, and β = λ2 λ3 y in Eq. (6.643.3)) in [30], the PDF of Y = YY12 is given by Z ∞ fY (y) = xfY1 (yx)fY2 (x)dx 0 Z ∞ p =2λ2 λ3 λ4 x exp(−λ4 x)K0 2 λ2 λ3 yx dx 0 r λ2 λ3 − 1 λ2 λ3 λ2 λ3 2 y exp y W− 3 ,0 y = 2 λ4 2λ4 λ4 (19) 1 where λ4 = gDE and Wλ,µ (·) is Whittaker function defined in Eq. (9.22) of [30]. Substituting (15) and (19) into (14), we have

P r(Cs > 0) Z ∞Z y =1 − fX (x)fY (y)dxdy 0 0 Z ∞ =1 − 1 − exp(−λ1 y) fY (y)dy 0 Z ∞ (20) = exp(−λ1 y)fY (y)dy r0 Z 1 λ2 λ3 ∞ = exp(−λ1 y)y − 2 λ4 0 λ2 λ3 λ2 λ3 × exp y W− 3 ,0 y dy. 2 2λ4 λ4

Using Eq. (7.621.3) in [30], this integration can be



solved to give

P r(Cs > 0) =

λ2 λ3 λ2 λ3 F 1, 2; 3; 1 − 2λ1 λ4 λ1 λ4

(21)

where F (α, β; γ; z) is Hypergeometric function defined in Eq. (9.14) of [30]. Define U = |hSP |2 and V = ρη|hSD,p |2 |hDP |2 . It is easy to have the PDF of U as fU (x) = λ5 exp(−λ5 x), 1 . Using (17), the PDF of V is given by where λ5 = gSP p fV (x) = 2λ6 λ7 K0 2 λ6 λ7 x (22) 1 ρηgSD,p

and λ7 = where λ6 = (7), and (22), one has

1 gDP

. Making use of (6),

From (15), (18) and Eq. (6.643.3) in [30], we have s s ! λ6 λ7 (Γ − σP2 ) λ6 λ7 (Γ − σP2 ) I1 = 1 − 2 K1 2 , 2Ps 2Ps (26) λ5 (Γ − σP2 ) (27) , I3 = 1 − exp − 2Ps and Z

∞Z u

I2 =

fV (v)fU (u)dvdu 0 Z ∞

=

0

p ! p 1 − 2 λ6 λ7 uK1 2 λ6 λ7 u

0

P r(PI ≤ Γ) =P r(Ps |hSP |2 + ρηPs |hSD,p |2 |hDP |2 + σP2 ≤ Γ) Γ − σP2 =P r U + V ≤ Ps Z Γ−σP2 Z Γ−σP2 −v Ps Ps = fU (u)fV (v)dudv 0

0 2 Γ−σP

Z

Ps

=

1 − exp −λ5

0

Γ − σP2 −v Ps

Z =

fV (v)dv − exp −λ5

0

×

Γ − σP2 Ps

2 Γ−σP Ps

(28)

0

=1 − exp

× exp(−λ5 u)du λ6 λ7 λ6 λ7 1 W−1, . 2 2λ5 λ5

IV. N UMERICAL R ESULTS AND D ISCUSSIONS

Z

× λ5 exp(−λ5 u)du p Z ∞ 1 λ6 λ7 u 2 K1 2 λ6 λ7 u

Finally, substituting (21), (24), and (25) into (12), the upper and lower bounds of SPSC can be obtained.

× fV (v)dv 2 Γ−σP Ps

=1 − 2λ5

p

exp(λ5 v)fV (v)dv

0

(23) Clearly, it is difficult to solve the second integration operation in (23) as no closed form expressions can be obtianed. Thus, instead of deriving the closed-form expression of P r(PI ≤ Γ), we derive the upper and lower bounds of P r(PI ≤ Γ). Note that U + V is upper and lower bounded by 2 max{U, V } and 2 min{U, V }, respectively, i.e., 2 min{U, V } ≤ U +V ≤ 2 max{U, V }. 2 P Therefore, the probability P r(U + V ≤ Γ−σ Ps ) is upper 2 P and lower bounded by P r(2 min{U, V } ≤ Γ−σ Ps ) and 2 P P r(2 max{U, V } ≤ Γ−σ Ps ), respectively. Thus, one has the upper and lower bounds as P r(PI ≤ Γ)U = I1 I2 + I3 (1 − I2 )

(24)

and (25) P r(PI ≤ Γ)L = I3 I2 + I1 (1 − I2 ) 2 P , I2 = P r(U ≥ V ), and where I1 = P r 2V ≤ Γ−σ Ps 2 P I3 = P r 2U ≤ Γ−σ . Ps

In this section, numerical results are presented. Unless otherwise explicitly specified, the parameters are set as 2 = 20 dB , g = 1, η = 0.9, ρ = 0.1, Γ/P = Ps /σD s b 2 = σ 2 = σ 2 , and α = g 10 dB , σD /g . SD SE E P In Fig. 2, we present analytical and simulation results for SPSC vs. α under various Γ/Ps . Upper and lower bounds analytical results are obtained according to (24) and (25), respectively. One can see that simulation results are bounded by the upper and lower bounded analytical results, which validates the accuracy of those two bounded analytical expressions derived. We can also observe that the upper and lower bounded curves merge together to be the real one at high Γ values. This is because when Γ is high, the probability that PI exceeds Γ is very low, which results in the values of (24) and (25) close to one. Moreover, SPSC can be improved as α increases, because a higher α means a better channel condition for S-D link compared to S-E link. As depicted in Fig. 3, SPSC with a lower gDD is superior to the one with a higher gDD . It is because a lower gDD value represents a worse loopback interference channel. Therefore, the residual loopback interference at D due to FD operation will be smaller, which means D has a better interference cancellation capability. In Fig. 4, one can see that SPSC can be improved by increasing gDE . It can be explained by the fact that a



0

0

10

SPSC

SPSC

10

Γ/Ps = 8 dB, 5 dB, and 2 dB −1

−1

10

gDE = 1, 0.8, 0.6, 0.4, and 0.2

10

Analytical_Upper Bound Analytical_Lower Bound Simulation Results

Analytical_Upper Bound Analytical_Lower Bound Simulation Results −2

−20

−15

−10

−5

0 α (dB)

5

10

15

10 −20

20

Fig. 2: SPSC under various Γ/Ps .

−15

−10

−5

0 α (dB)

5

10

15

20

Fig. 4: SPSC under various gDE .

higher gDE value means a better channel condition for D-E link, which results in a higher interference power arrived at E to degrade its decoding capacity.

0

10

0

SPSC

SPSC

10

−1

10

ρ = 0.5, 0.7, and 0.9

Analytical_Upper Bound Analytical_Lower Bound Simulation Results

−2

gDD = 0.2, 0.4, 0.6, 0.8, and 1

10

−1

10

−20 Analytical_Upper Bound Analytical_Lower Bound Simulation Results −20

−15

−10

−5

0 α (dB)

5

10

15

−15

−10

−5

0 α (dB)

5

10

15

20

Fig. 5: SPSC for various ρ. 20

Fig. 3: SPSC for various gDD . As shown in Fig. 5, SPSC with a higher ρ is outperformed by that with a lower ρ. It is clear that a higher ρ means a lower portion of the received power is split for information decoding and more power is for EH. Thus, a low received SINR is resulted at D, which leads to a lower capacity at D. V. C ONCLUSION This paper has studied the secrecy performance in underlay cognitive radio networks with full-duplex

wireless-powered secondary system. By considering that the destination node in the secondary system equipped with two isolated antennas to enable full-duplex operation and the receiving antenna can simultaneously receive information and energy from the source through power splitting protocol, the probability of strictly secrecy capacity has been studied. Upper and lower bounds of probability of strictly positive secrecy capacity have been derived. Numerical results show that under the condition that the interference at primary user’s receiver is smaller than its interference temperature limit, the upper and lower bounds merge together to become the exact probability of strictly positive secrecy capacity.



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