Abstract
We propose a jam-then-harvest protocol for dual-hop cooperative networks with an untrusted relay, where an external friendly jammer helps keep information secret from the untrusted relay by transmitting a priori jamming signal for the destination. In particular, the wireless powered jammer scavenges energy from the received forwarded signal and recovers its initial energy to perform jamming in next time slot. We analytically derive an exact expression of the probability of nonzero secrecy rate (PNSR) for the proposed jam-then-harvest protocol. For performance comparison, cooperative jamming with the constant power supply is provided as a lower bound benchmark. Our results show that the proposed protocol not only can achieve the secure communication but also can harvest the enough energy without a loss of performance in the low jamming power region.
1. Introduction
With the wide deployment of cellular mobile network and Internet as well as the emergence and development of various wireless networks, wireless communications have become an integral part in our daily life for enabling ubiquitous access and different service demand. However, due to the openness and shared nature of the wireless channel, the security of information transmission is a critical issue for wireless networks. Traditionally, the secrecy is guaranteed mostly relying on the cryptographic techniques and protocols at the upper layers of wireless networks [1]. One main drawback of these existing techniques is their heavy dependence on a complex mathematics computation in the secret key generation and distribution and management, which is impractical for wireless networks due to resource constraints and the lack of the infrastructure support. Recently, cooperation-based physical layer security has emerged as an attractive solution to improve the secrecy of low-power single-antenna wireless systems [2, 3]. In addition, node cooperation is also beneficial to enhance the spectral efficiency and power utilization.
One of the most common cooperative schemes in physical layer security is cooperative jamming (CJ) (see [4–6] and the references therein), where external friendly jammers are employed to collaboratively transmit interfering signals when source is transmitting, so as to degrade the wiretap channel for greatly enhancing the secrecy rate. However, additional energy consumption to transmit jamming signals at the helpers brings about the following two major challenges. First, low-power jammers with limited battery supplies would likely prefer saving energy for their own communication to aiding the others; thus, the benefits of CJ would be quite compromised. Second, the energy imbalance among users may lead to the creation of energy holes and even shorten the network lifetime.
Recently, radiofrequency- (RF-) enabled wireless energy harvesting (WEH) has attracted an upsurge of interest due to its great potential to provide the power supply in a cost-effective and reliable way for energy-constrained wireless nodes and networks [7, 8]. In fact, WEH potentially offers new opportunities to replenish the extra energy requirements at the jammers to overcome the critical challenges above. In [9, 10], a wireless powered jammer was employed to enable secure direct communication between source and destination in the presence of an eavesdropper and yet not to add extra power cost. As to the relay systems, a harvest-and-jam protocol was presented where multiantenna jammers were powered by the source to secure two-hop networks in [11]. While in [12], by using a set of single-antenna WEH-enabled self-sustaining AF relays/jammers, a mixed cooperative beamforming-CJ approach was proposed to improve security. In [13], the best wireless powered relay/jammer with a random jammer/relay selection schemes was investigated for two-hop relay networks. While in [14], the power allocation is optimized to maximize the secrecy sum rate of a decode-and-forward two-way relay network by using artificial noise and WEH-enabled jammers. In these models, relays are assumed to be trusted; however, from a robust perspective, the relay could be a potential eavesdropper. For example, all users of practical applications in defence and financial networks do not have the same rights to access the information [15]. With the constant power supply, in [16, 17], the secure transmission schemes were presented to hinder the untrusted relay from deciphering the source messages. By using energy harvesting, in [18], the secrecy performance of two-hop networks via a WEH-enabled untrusted relay was investigated, where the destination-assisted jamming signal helps confuse the untrusted relay as well as acts as a potential energy source. To the best of our knowledge, for the untrusted relay system, how to enable two-hop secure communication by using a WEH-enabled jammer has not been addressed in the literature.
Motivated by reaping the benefits from WEH and pressing demands for secure communication in untrusted relay networks, in this paper, we focus on a wireless powered jammer-assisted secure dual-hop cooperative communication. Our main contributions can be summarized as follows:(i)We propose a newly designed jam-then-harvest (JH) protocol to enable secure communication for dual-hop cooperative networks with an untrusted relay.(ii)We theoretically discuss the secrecy performance of the proposed JH and then derive an exact analytical expression for its probability of nonzero secrecy rate (PNSR).(iii)The conventional cooperative jamming (CJ) scheme with the constant power supply is provided as a lower bound benchmark. We show that the proposed JH can achieve a similar secrecy performance as CJ in the low initial jamming power region.
2. System Model and Secure Protocol
As depicted in Figure 1, we consider a cooperative dual-hop relay system where the source S tries to transfer information to the destination D located out of its communication range via one untrusted relay R. To help keep information secret from R, a friendly jammer J is employed to jam the untrusted relay; however, J is an energy-constrained node only with the initial power but without conventional energy supply. A simple RF circuit for harvesting energy is equipped at J to harvest energy from external RF signals. The harvested energy is assumed able to recharge the jammer’s battery with infinite capacity. All nodes only have one omnidirectional antenna operating in a half-duplex mode. The complex channel coefficient between nodes i () and j (, ) is denoted by , which is modeled as a zero-mean, independent, circularly symmetric complex Gaussian random variable with a variance , where in meters (m) is the Euclidean distance between nodes i and j and φ is the path loss exponent. Additionally, the noise at all nodes is assumed to be additive white Gaussian with zero mean and variance .
Since the direct link between S and D is not available, a jam-then-harvest protocol based on two time slots of equal length is adopted, as shown in Figure 2. Without loss of generality, each transmit time slot is normalized to be 1 so that at each time slot the numerical values of energy are identical to power. The jam-then-harvest protocol consists of two parts: (1) transmitting and jamming phase: in the first time slot, S broadcasts information signal to the untrusted relay R, while J simultaneously emits a unit-power jamming signal z to create interference at R; (2) relay and energy-harvesting phase: during the second time slot, after amplifying the received mixture signals from S and J, R forwards the resulting signal to D with the transmit power P. Meanwhile, J is capable of harvesting energy from the signals sent by R to store and recover the initial energy .
In phase 1, to protect information from being eavesdropped by untrusted R, the friendly jammer J performs jamming while S transmits unit-power signal , so the received superposition signal at R can be expressed as follows:where denotes the transmit power by S and represents the narrow-band Gaussian noise at R. Then during phase 2, R broadcasts the mixture signals based on the amplify-and-forward protocol to D, as such the received signal at D and J can be, respectively, written aswhere is the power normalization factor given by . The signal-to-interference-plus-noise ratio (SINR) at D and R to decode is thus, respectively, given bywhere and . Note that we assume the jamming signal z is a priori known to D, which will just hurt the untrusted relay’s listening but not cause any harm to the destinations; therefore, the jamming signal has been perfectly cancelled in . To perfectly eliminate the jamming signals at D, such signals should be confidently shared between J and D before jamming. This can be practically implemented as in [19]. First, the same pseudo-random generators with finite states and seed tables are pre-stored at both J and D (but not available at R). Next, before each transmission phase, one seed is randomly chosen from the seed table and the index of this seed is shared between J and D. In particular, the seed index can be shared by using the two-step phase-shift modulation-based method [19]. Accordingly with (3), the achievable rate at the destination D and R in bits/sec/Hertz (bps/Hz) can be, respectively, given by
From (3) and (4), we can see that both and are increasing function of γ but decreasing function of . However, if increases (decreases) slower than as () increases, the difference between and may increase.
On the other hand, from (2), the harvested energy at the jammer J can be calculated aswhere denotes the energy-harvesting efficiency of the jammer. Similarly, it can be observed from (5) that the harvested energy also increases with or .
3. Secrecy Performance
The friendly external jammer helps prevent source confidential information leakage to the untrusted relay and achieve the secure communication; thus, the probability of achieving strictly nonzero secrecy rate is an important performance metric to evaluate the system secrecy performance. In this section, we analyze the PNSR of the proposed jam-then-harvest scheme (denoted as “JH”). Additionally, for performance comparison, the secrecy performance for conventional cooperative jamming relying on the constant power supply (denoted as “CJ”) is provided as a lower bound benchmark.
3.1. JH Scheme
For the proposed jam-then-harvest scheme, the amount of scavenged energy must satisfy the lowest requirement, i.e., . If the harvested energy E is less than the given threshold , the power received by the jammer is not sufficient to transmit the jamming signal in next time slot, and thus the power outage occurs. Meanwhile, it can be easily obtained from (3) that when , is greater than with probability 1, which means a secrecy outage will occur with probability 1 when the power outage happens. If the power received by the friendly jammer J is not smaller than the given initial threshold , the secure outage occurs when the achievable rate is not more than . Thus, the overall achieved PNSR can be formulated as follows:where denotes the probability.
Substituting from (3) and E from (5) and after simplification, (6) can be rewritten aswhere is the root greater than of the equation and . Note that when , , so the corresponding . When , and , so the corresponding . , and are all exponentially distributed random variables with mean . Further, we can express in (7) analytically as given in Proposition 1.
Proposition 1. The achieved PSNR for the jam-then-harvest scheme is given bywith
Proof. See Appendix A.
3.2. Benchmark CJ Scheme
In contrast, for the conventional cooperative jamming scheme without employing wireless powered technique, the friendly jammer has a constant power supply. The secrecy outage event occurs only when the achievable rate is not more than ; thus, the PNSR can be expressed as
Proposition 2. An analytical expression for the achieved PNSR for “CJ” scheme can be given bywithwhere is the modified Bessel function of the second kind with ordern defined in [20].
Proof. See Appendix B.
4. Numerical Results
In this section, the PNSR of the proposed “JH” scheme given by (8) is compared with that of the conventional “CJ” scheme in (11). The simulation parameters are set up as follows: the noise variance ; average signal power attenuation at a reference distance is 80 dB; the path loss factor ; S, R, and D are lying on one straight line and the distance between S and D, . Besides, we assume that the distance from J to R is 1 m.
First, we set the location of R as the midpoint of the line segment from S to D. Figure 3 demonstrates the analytical results for the PNSR versus the different transmit power P and the initial jamming power . It can be seen that the proposed “JH” scheme achieves a similar secrecy performance as “CJ” scheme in the low initial jamming power region. However, in the high region, the PNSR remains almost unchanged for “CJ” while increases for “JH” similar to the power outage probability (POP). This is because as increases, the PNSR for “JH” is dominated by the power outage. The higher the is set, the more it becomes difficult to replenish the initial power. In addition, the PNSR is observed to decrease as the transmit power P increases for both schemes. Figure 4 further shows that analytical results are in excellent agreement with simulation results as or . It can also be observed that the proposed JH scheme can achieve the secure communication without a loss of performance in the low jamming power region.
(a)
(b)
Next, the coordinate of R is set to move from to . Figure 5 plots the PNSR versus the distance () between S and R. It is observed that the PNSR for both schemes decreases as R moves close to D. This is because the closer the R is to D, the smaller the achievable rate at R is, while the rate at D will increase. It is worth noting that as expected for “JH,” the PNSR is not less than the power outage probability.
5. Conclusion
In this paper, the secrecy performance of the cooperative dual-hop network via an untrusted relay is investigated. Specifically, we first propose a jam-then-harvest protocol for the cooperative dual-hop relay system with the help of an external friendly WEH-enabled jammer. Then, we derive the explicit expression for the probability of nonzero secrecy rate (PNSR). Numerical results show that the exact expression for the PNSR is matched well with the simulation results. It can also be observed from the numerical results in the low initial jamming power region that the proposed protocol is capable of achieving the secure communication but also replenishing the initial jamming energy without a loss of performance.
Appendix
A. Proof of Proposition 1
We start with the probability as follows:
Now, we have
Similarly, we can also obtain the probability in (7) as follows:
Now, we can easily obtain
Let us denote the second term on the right-hand side (RHS) of (A.5) and the first and second terms on the RHS of (A.6) as , and respectively, then after some algebraic manipulation, we obtainwhere and , thus yielding the proposition.
B. Proof of Proposition 2
According to (10), we have
Now, we havewhere
So, we get Proposition 2.
Data Availability
The data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that there are no conflicts of interest regarding the publication of this paper.
Acknowledgments
This work was partly supported by National Natural Science Foundation of China (Nos. 41504026 and 61362009), Natural Science Foundation of Jiangxi (No. 20152ACB21003), Foundation for Distinguished Young Talents Training Programme of Jiangxi (No. 20171BCB23006), and the Innovation Fund Designated for Graduate Students of Nanchang University (No. cx2016277).