Wireless heterogeneous networks are capable of increasing the efficiency and flexibility of wireless systems, which are composed of various independent subsystems[1-2]. In a heterogeneous wireless network, various subsystems may be allowed to perform their respective wireless transmissions simultaneously. However, due to the broadcast nature of radio propagation[3], and the open system architecture of heterogeneous wireless networks[4], the confidential messages may be vulnerable to eavesdropping attacks when they are transmitted by heterogeneous wireless systems independently. Thus, the risk of confidential messages being successfully eavesdropped upon will be increased significantly. As a result, more research efforts should be devoted to protecting wireless transmissions transmitted by heterogeneous wireless networks against malicious eavesdropping.
Physical-layer security (PLS) [5-6] emerges as an effective method to guard against wiretapping with the aid of its ability to exploit the physical characteristics of wireless channels. Recently, PLS has also been designed for spectrum-sharing aided heterogeneous networks[7-8]. Jamming schemes were investigated in Ref.[9]. To be specific, in order to impose an interference on the eavesdroppers, the jammers were invoked to transmit jamming signals, whereas the amount of the interference imposed on the scheduled users was considered to be below a threshold. Single-input multiple-output (SIMO) and multiple-input multiple-output (MIMO) techniques[10-11] have been investigated to decrease the secrecy outage probability of wireless transmissions. In Ref.[12], the antenna selection was conceived to improve the PLS of wireless transmissions in the presence of an eavesdropper.
In this paper, we investigate the PLS of a heterogeneous wireless network consisting of multiple SD pairs in the presence of an eavesdropper. Differing from Refs.[7-12], the cooperation between various SD pairs has been explored to defend against malicious eavesdropping relying on a conceived cooperative framework. Moreover, we propose an SD pair scheduling scheme to improve the PLS of wireless transmissions. The main contributions of this paper can be summarized as follows. First, a heterogeneous cooperative framework is conceived to protect wireless transmissions against eavesdropping with the aid of two stages. Secondly, we propose a specific SD pair scheduling scheme, called the TAS-OSDS. In the TAS-OSDS scheme, one antenna of the chosen SD will be selected to transmit the repacked data to enhance the PLS of the transmitted data. Finally, it is shown that the IP of TAS-OSDS scheme will be beneficially reduced by increasing the number of SD transmission pairs.
1 System Model and Opportunistic SD Scheduling
1.1 System model
As shown in Fig.1, we investigate a wireless system consisting of M source-destination (SD) pairs in the presence of an eavesdropper E, where an source node (SN) Sm has the ability to communicate both with its corresponding destination node (DN) Dm,m∈{1,2,…,M}, and with other SNs at different transmission stages. For notational convenience, the set of SD pairs is assumed to be denoted as Φ. E with the aid of a wide-band receiver is deployed to wiretap the signal transmitted by the legitimate SD pairs. Moreover, we also assume that all DNs are connected with each other through the core network, and thus, each DN has the ability to forward the received data to other DNs. Furthermore, Rayleigh fading is used to characterize both the main links (spanning from the legitimate transmitters to the legitimate receivers) and the wiretap links (spanning from the legitimate transmitters to the eavesdropper).
Fig.1 A heterogeneous wireless network with M multiple source-destination pairs in the presence of an eavesdropper
In order to improve the PLS of wireless transmissions of the multiple SD pairs, a heterogeneous cooperative framework is invoked with the aid of two stages. More specifically, at the beginning of the first stage, an SD pair will be chosen to be a transmitting node relying on the criterions of the RSDS and the TAS-OSDS schemes. Then, in order to help other SNs to forward their data, the chosen SD pair will receive the data of other SNs through a high-reliability low-power interface, and then repack the received data and its own data. At the second stage, the specifically selected SN may forward the repacked packet to its DN. After decoding the packet, the DN will send the sub-packets to the other DNs relying on the index of the pair in the sub-packet via the core network.
1.2 Signal model
Without loss of generality, Sm is assumed to be the selected transmitting node in the first stage. As mentioned above, other SNs will transmit their signal to Sm. Moreover, we also assume that only one antenna of Sk is chosen to transmit its data to Sm, which is represented by antenna i. Hence, the signal received at Sm transmitted by Sk, k∈Φ-{m}, can be shown as
(1)
where Ps, xk, hskismj and nsm are the transmit power of Sk, the transmit signal of Sk, the instantaneous channel gain of the Ski-Smj link, and the thermal noise received at Sm, respectively. Moreover, NT is the number of antennas of Sm. Meanwhile, since the broadcast nature of radio propagation, E may also overhear the signal transmitted by Sk, which can be given as
(2)
where ne represents the thermal noise encountered at E, and hskieldenotes the channel gain of Ski-El link.
From Eq.(2), and using maximal-ratio combining (MRC), we can obtain the channel capacity of the Sk-E link as
(3)
where 
denotes the received signal-to-noise (SNR) at E of the Sk-E link; N0 denotes the variance of thermal noise of Dm and E; and NE denote the number of antennas of E.
In the second stage, we also assume that one antenna of Sm is invoked for forwarding the received data to Dm. Without loss of generality, we assume that the antenna i of Sm, i∈{1,2,…,NT}, is chosen to transmit packet xs to Dm. Hence, the signal received at Dm can be expressed as
(4)
where hsmidmj and ndm denote the channel gain of the Smi-Dmj link, and the thermal noise encountered at Sm, respectively. Moreover, NR denotes the number of antennas of Dm, and Pt represents the transmit power of Sm.
Similarly to Eq.(2), E may overhear the signal transmitted by Sm, which is
(5)
where hsmieldenotes the channel gain of the Smi-El link.
With the aid of Eq.(4) and MRC, the instantaneous channel capacity of the Sm-Dm link can be obtained as
Csmdm=log2(1+γsmdm)
(6)
Utilizing Eq.(5) and MRC, we can obtain the instantaneous channel capacity of the Sm-E link as
(7)
From Eq.(3) and Eq.(7), and utilizing the maximum of individual channel capacity of the Sm-E and Sk-E links in the first and second stages, we can obtain the overall capacity of the signal from Sk as
(8)
In contrast, since the signal from Sm is only transmitted at the second stage, the overall capacity of the signal of Sm can still be given as
(9)
Noting that given the chosen transmission pair, the signal of the chosen SD will only be overheard by E once, due to the fact that it is only transmitted at the second stage. Differing from the chosen SD, the signal of other SDs will be overheard both in the first state and in the second stage, which are represented by Eq.(2) and Eq.(5), respectively.
1.3 TAS assisted opportunistic SD scheduling scheme
In this subsection, a TAS assisted opportunistic SD scheduling (TAS-OSDS) scheme is proposed. Specifically, in order to enhance the PLS of wireless transmissions of multiple SD pairs, an SN with the maximal channel capacity in set Φ will be chosen to be as the transmitting node at the given time slot, which will help other SNs to forward their data to their DNs. Hence, relying on Eq.(6), the SD pair scheduling criterion of the TAS-OSDS scheme can be shown as
(10)
where o represents the index of the chosen SD pair in the TAS-OSDS scheme, and a denotes the index of the selected antenna of the chosen So. Moreover, Eq.(10) can be rewritten as
(11)
which can be performed in a distributed manner. The processing procedure of the TAS-OSDS scheme is shown as follows:
1) Assume that the number of SD pairs is M, and each SN is required to maintain NT timers.
2) At the beginning of the first stage, the TAS-OSDS scheme will be triggered.
3) Each SD estimates the instantaneous channel state information, and the initial value of each timer is set inversely proportionally to 
Thus, o and a can be determined, according to which the timer becomes zero first.
4) So will notify other SNs that it is the optimal node via broadcasting a notification. Then, other SNs transmit their data to So, which will repack the received data and their own data.
5) At the second stage, So will forward the repacked data to its corresponding DN relying on a-th antenna of So. Once the transmission is finished, Do will send other SNs’ data to their corresponding DNs relying on the core network.
2 Intercept Probability Analysis over Rayleigh Fading Channels
In this section, we analyze the intercept probability of the RSDS and TAS-OSDS schemes over Rayleigh fading channels.
2.1 Conventional RSDS scheme
As a benchmarking scheme, we present the IP analysis of the traditional RSDS scheme. With the conventional RSDS scheme, each SD pair in set Φ has the same chance to be chosen to transmit at the given time slot. Based on the definition of the IP[12], the IP of the signal from Sm and Sk in the first and second stages for the RSDS scheme relying on the Sm-Dm pair can be shown as
(12)
and
(13)
Combining Eqs.(6), (8) and (9), we can obtain
(14)
and
(15)
where Δ1=Pt/Ps. Additionally, from Eqs.(14) and (15), we can see that SD pairs are selected without taking the random variables (RVs) 
for i∈{1,2,…,NT}, j∈{1,2,…,NR}, are independent and identically distributed (i.i.d.) RVs having the same mean 
Similarly, the fading coefficients of the wiretap links |hsmiel|2 for i∈{1,2,…,NT}, l∈{1,2,…,NE}, are also assumed to be i.i.d RVs with the same average channel gain 
Then, denoting 
due to RVs 
can be shown as
FU(x1)fX1(x1)dx1
(16)
=
(17)
respectively, where FU(u) is the cumulative distribution function (CDF) of RV U, and fX1(x1) and fX2(x2) are the probability density function (PDF) of RVs X1 and X2, respectively. Based on Ref.[8], they can be given by
(18)
(19)
(20)
Substituting Eqs. (18) and (19) into Eq. (16) yields
(21)
Substituting Eqs.(18), (19) and (20) into Eq.(17) yields
(22)
where
dkd=
ckm=
We assume that each SD has the same weighting coefficient. Hence, the IP of the investigated system relying on Sm can be defined as
(23)
As previously mentioned, each SD pair can be selected to transmit with equal opportunity in the RSDS scheme. Moreover, relying on the law of total probability[13], the IP of the multiple SD pairs in the RSDS scheme can be given by
(24)
2.2 Proposed TAS-OSDS scheme
This subsection presents the IP analysis of the TAS-OSDS scheme. As shown in Eq.(10), the index of the chosen SD pair is denoted by o in the scheme. Hence, with the aid of the TAS-OSDS scheme, the IP of the signal transmitted by So and Sk can be formulated as
(25)
and
(26)
Using Eqs.(6) to (9), Eqs.(25) and (26) can be rewritten as
(27)
and
(28)
respectively, where Λ1=Pt/Ps. Based on Eq.(11), we can obtain
(29)
(30)
Moreover, denoting 
due to RVs Q, W1 and W2 being independent of each other, 
can be formulated as
(31)
(32)
Based on Ref.[10], FQ(w), fW1(w1) and fW2(w2) can be given as
(33)
(34)
(35)
Using Ref.[11] and substituting Eqs. (33) and (34) into Eq.(31) yields
(36)
Using Eqs.(33), (34) and (35), Eq.(32) can be obtained as
(37)
Then, with the aid of the definition in Eq.(23), the IP of the multiple SD pairs aided by the proposed TAS-OSDS scheme can be given by
(38)
From Eq.(38), we can not only evaluate the PLS of wireless transmissions, but also investigate the effects of the channel gain, the number of antennas, and the number of source-destination (SD) pairs on the attainable PLS level of wireless transmissions.
3 Numerical Results
In this section, we evaluate the IP of the proposed TAS-OSDS by comparing this scheme with the conventional RSDS scheme. In this evaluation, the analytic IP of the RSDS and TAS-OSDS schemes are evaluated by plotting Eq.(24) and Eq.(38), respectively. Moreover, we assume that the main-to-eavesdropper ratio (MER) 
For comparison purposes, the traditional non-cooperation (non-coop) transmission scheme is also presented, wherein the SD pairs work independently. For the sake of fair comparison of the above mentioned schemes, we assume that each pair only occupies 1/M times bandwidth of the whole spectrum. In contrast, the transmission SD pair can occupy the total shared spectrum due to only one SD pair being selected to perform transmission at the given transmission slot in the investigated cooperative method. Hence, the IP of the non-coop scheme is shown as
(39)
Similarly to Eq. (36), 
can be obtained as
=
(40)
Fig.2 shows the IP vs. MER of the traditional RSDS, non-coop as well as of the proposed TAS-OSDS schemes for different (NT,NR,NE) by plotting Eq.(24), Eq.(40) and Eq.(38), as a function of the MER. It is shown in Fig.2 that as the number of antennas (NT,NR,NE) increases from (NT,NR,NE)=(1,1,1) to (2,2,2), the IP of the RSDS, non-coop and TAS-OSDS schemes will be reduced correspondingly, which confirms that the PLS of wireless transmissions can be enhanced by increasing the number of antennas of the SD pairs. Moreover, Fig.2 also shows that although the IP of all schemes will be decreased as the MER increases from -10 to 15 dB, the proposed TAS-OSDS schemes can still achieve the lowest IP among the RSDS, non-coop, and TAS-OSDS schemes. Hence, at a given IP constraint, the proposed TAS-OSDS scheme can be used to guarantee the PLS of wireless transmission in a lower MER case.
Fig.2 Comparison of intercept probabilities under different MERs
Fig.3 illustrates the IP vs. the number of source-destination pairs M of the traditional RSDS, non-coop and the TAS-OSDS schemes for different numbers of antennas of E. As shown in Fig.3, increasing the number of antennas of E will increase the risk of the wireless transmission being eavesdropped upon successfully in the traditional RSDS, non-coop and the TAS-OSDS schemes, whereas the IP of the TAS-OSDS is lower than that of both the RSDS and non-coop schemes. Furthermore, it can be seen from Fig.3 that although the PLS of wireless transmissions will be degraded, the IP of wireless transmissions will be significantly decreased relying on increasing the number of SD pairs in the proposed scheme, demonstrating the superiority of the proposed TAS-OSDS scheme. This is due to the fact that the cooperation between SD pairs will be more beneficial for increasing the PLS of wireless transmissions in the proposed TAS-OSDS scheme, whereas no benefit can be achieved in either the RSDS or non-coop schemes.
Fig.3 Intercept probability with respect to the number of SD pairs M
4 Conclusion
1) In this paper, we study PLS for a heterogeneous wireless network including multiple SD pairs in the presence of an eavesdropper, where the SD pairs access the shared spectrum in a dynamic manner.
2) We explore a cooperation framework for SD pairs to protect against eavesdropping attacks. Specifically, an SD pair is chosen as the transmitting pair at the beginning of the given transmission slot, then it participates in collaborative transmitting among the SD pairs. Moreover, the IPs of the proposed TAS-OSDS as well as the conventional RSDS schemes are analyzed for comparison purposes.
3) It is shown that the TAS-OSDS scheme achieves a better IP performance than that of the RSDS and conventional non-cooperation schemes, where each source communicates with its corresponding destination without co-operating with other SD pairs in the non-cooperation scheme. Furthermore, with an increasing number of the SD pairs, the IP of the TAS-OSDS scheme will be reduced clearly.
[1] Kibria M G, Nguyen K, Villardi G P, et al. A stochastic geometry analysis of multiconnectivity in heterogeneous wireless networks[J]. IEEE Transactions on Vehicular Technology, 2018, 67(10): 9734-9746. DOI:10.1109/tvt.2018.2863280.
[2] Sharma D, Bhondekar A P. Traffic and energy aware routing for heterogeneous wireless sensor networks[J]. IEEE Communications Letters, 2018, 22(8): 1608-1611. DOI:10.1109/lcomm.2018.2841911.
[3] Zou Y L, Sun M, Zhu J, et al. Security-reliability tradeoff for distributed antenna systems in heterogeneous cellular networks[J]. IEEE Transactions on Wireless Communications, 2018, 17(12): 8444-8456. DOI:10.1109/twc.2018.2877610.
[4] Lv T, Gao H, Yang S S. Secrecy transmit beamforming for heterogeneous networks[J]. IEEE Journal on Selected Areas in Communications, 2015, 33(6): 1154-1170. DOI:10.1109/jsac.2015.2416984.
[5] Wyner A D. The wire-tap channel[J]. Bell System Technical Journal, 1975, 54(8): 1355-1387. DOI:10.1002/j.1538-7305.1975.tb02040.x.
[6] Leung-Yan-Cheong S K, Hellman M E. The Gaussian wiretap channel [J]. IEEE Transactions on Information Theory, 1978, 24(4): 451-456. DOI:10.1109/tit.1978.1055917.
[7] Xu L, Cai L, Gao Y S, et al. Security-aware proportional fairness resource allocation for cognitive heterogeneous networks[J]. IEEE Transactions on Vehicular Technology, 2018, 67(12): 11694-11704. DOI:10.1109/tvt.2018.2873139.
[8] Zou Y L. Physical-layer security for spectrum sharing systems[J]. IEEE Transactions on Wireless Communications, 2017, 16(2): 1319-1329. DOI:10.1109/twc.2016.2645200.
[9] Tang W J, Feng S L, Ding Y H, et al. Physical layer security in heterogeneous networks with jammer selection and full-duplex users[J]. IEEE Transactions on Wireless Communications, 2017, 16(12): 7982-7995. DOI:10.1109/twc.2017.2755640.
[10] Bang I, Kim S M, Sung D K. Artificial noise-aided user scheduling from the perspective of secrecy outage probability[J]. IEEE Transactions on Vehicular Technology, 2018, 67(8): 7816-7820. DOI:10.1109/tvt.2018.2834562.
[11] Lei H J, Xu M, Ansari I S, et al. On secure underlay MIMO cognitive radio networks with energy harvesting and transmit antenna selection[J]. IEEE Transactions on Green Communications and Networking, 2017, 1(2): 192-203. DOI:10.1109/tgcn.2017.2684827.
[12] He D X, Liu C X, Quek T Q S, et al. Transmit antenna selection in MIMO wiretap channels: A machine learning approach[J]. IEEE Wireless Communications Letters, 2018, 7(4): 634-637. DOI:10.1109/lwc.2018.2805902.
[13] Zou Y L, Zhu J, Zheng B Y, et al. An adaptive cooperation diversity scheme with best-relay selection in cognitive radio networks[J]. IEEE Transactions on Signal Processing, 2010, 58(10): 5438-5445. DOI:10.1109/tsp.2010.2053708.