Abstract
When direct source-destination communications are in outage, relay selection is a preferable solution to improve reliability for this communications. However, such a relay selection makes the eavesdropper better overhear source data through both source-relay and relay-destination communication hops, losing data security. To improve both reliability and security, this paper proposes a relay selection-and-jamming (RaJ) scheme to select one intermediate node as a conventional relay and another node as a jammer. To enhance energy efficiency, all intermediate nodes harvest radio frequency energy in source signals for their operations with nonlinear energy harvesting (NL-EH). The security and reliability of the RaJ scheme are assessed through suggested rigorous/asymptotic expressions and are significantly better than two benchmark schemes without neither jamming nor both relay selection and jamming. Additionally, they can be optimized with reasonable selection of specifications. Moreover, the NL property of the energy harvesters dramatically affects the reliability but negligibly degrades the security for the RaJ scheme. Furthermore, the linear EH (L-EH) is more reliable but less secure than the NL-EH.
1. Introduction
1.1. Background
Radio frequency energy harvesting (RF EH), which exploits available RF signals to power communication devices, can solve problems of energy efficiency, energy shortage, and green communications in modern wireless systems [1–4]. RF EH is efficiently implemented through power-splitting (PS) and time-switching (TS) protocols in which the former carries out EH and data decoding in the same duration while the latter performs them separately in different durations (i.e., the latter requires lower circuitry implementation than the former) [5]. For performance analysis, EH has been modelled as linear (L) [6] or NL [7]. The linear EH (L-EH) model represents the linear increase of the scavenged energy with the input RF power. Nonetheless, nonlinear (NL) behaviors of EH circuit elements (e.g., diodes and inductors) induce the NL-EH model more realistic and precise than the L-EH one. As such, this paper is interested in the NL-EH model for practical-and-exact performance analysis.
When direct source-destination communications are in outage due to severe propagation conditions (strong path-loss, heavy shadowing, and deep fading), relay selection in which only one intermediate node among all available nodes between the source-destination pair is selected to satisfy a preset criterion is regarded as a technique that is efficient in improving communication reliability and reducing complexity as well as economical in bandwidth and power [8]. Nonetheless, such a relay selection offers the eavesdropper more chances to overhear source message through both source-relay and relay-destination communication hops instead of merely one hop in direct source-destination communications, threatening data security. To conceal legitimate data, the jamming technique where jamming signals (or artificial noises) are purposively generated to impair solely the eavesdropper has been popularly exploited [9].
This paper assumes two intermediate nodes, which are self-powered by scavenging RF energy in source signals with the practical NL-EH, are willing to ameliorate both reliability and security for data transmission between the source-destination pair. The question is which node plays a role as a traditional relay to enhance communication reliability and as a jammer to protect secret data over both hops. Our solution, relay selection-and-jamming (RaJ) scheme, solves this question.
1.2. Previous Works
Our proposed RaJ scheme differs [7, 10–22] which investigated problems of security and/or reliability for the NL-EH (References which studied the L-EH with/without relaying (e.g., [5, 6, 9]) or the NL-EH without relaying (e.g., [23–35]) must not be surveyed because this paper considers simultaneously the NL-EH, relaying, and jamming.) with relaying. More specifically, [7, 10] analyzed the reliability of the pure relaying (namely, the nonrelay selection nonjamming (nRnJ)) scheme in terms of outage probability (OP). In the nRnJ scheme in [7, 10], the relay performs the amplify-and-forward (AF) operation on source signals with energy harvested by the TS protocol. Reconsidering the nRnJ scheme and the AF relay in [7, 10], the authors in [11, 12] analyzed and simulated the reliability in terms of bit error rate and throughput, respectively. Additionally, both [11, 12] utilized the PS protocol for scavenging energy in source signals. Secrecy performance quantified by secrecy outage probability was simulated in [13], and the OP was analyzed in [14–20] for the same nRnJ scheme as [7]. Notwithstanding, all the works in [13–20] investigated the decode-and-forward (DF) relay, which is also a research object of this paper. As compared to the AF relay, the DF relay is advantageous in preventing noise enhancement, probably improving the overall system performance. In [21], the throughput was simulated for the nonrelay selection-and-jamming (nRaJ) scheme where one relay capable of EH is appointed as a conventional relay and another user is dedicated as an energy supplier as well as a jammer. Instead of dedicating an intermediate node as a jammer in [21], the authors in [22] availed the destination as a jammer. Further, [22] considered the AF relay and the energy harvesting based on the PS protocol. However, the performance analysis on the ergodic secrecy capacity and the total harvested energy was not included in [22].
1.3. Contributions
Beside proposing the RaJ scheme with the NL-EH, this paper suggests the rigourous/asymptotic formulas of the OP and the intercept probability (IP) to quickly assess both reliability and security. These expressions are then simplified to obtain the OP/IP of the nRnJ and RnJ (relay selection nonjamming) schemes for performance comparison and highlighting the efficacy of simultaneous relay selection and jamming. Moreover, the OP/IP of the RaJ scheme with the L-EH is derived. Monte-Carlo simulations validate these analyses and shed insights into the reliability/security of the considered schemes and the feature of the NL-EH in comparison to the L-EH.
1.4. Structure
The remainder of this paper is structured as follows. Part 2 describes the investigated system. Next, part 3 provides detailed derivations of reliability and security of the proposed RaJ scheme. Then, two (nRnJ and RnJ) benchmark schemes are discussed in part 4. Subsequently, some useful remarks are withdrawn in part 5, especially the remark on the L-EH. Finally, part 6 presents simulated/theoretical results, and part 7 closes the paper.
2. System Description
Figure 1 sketches the considered RaJ scheme where the source fails to convey secret messages directly to the destination owing to bad propagation conditions (e.g., severe fading and strong shadowing). Therefore, two intermediate nodes, and , are exploited with different roles as a traditional relay to heal communications and as a jammer to protect secret data against the eavesdropper . To improve energy efficiency, and scavenge RF energy in source signals through the TS protocol and utilize scavenged energy for relaying and jamming operations. Accordingly, secret data reaches in three stages with an entire duration of .
In stage I with (Stage I is just for energy harvesting. Consequently, transmits an arbitrary signal, which carries RF energy, not necessarily the secret information or a deterministic signal.) a duration of , the nonlinear energy harvester of , , generates the power [7]:where ; is energy converting efficiency; is a time fraction; is the transmission power of ; is the saturation threshold; is the channel gain. Flat block Rayleigh fading channels are considered, and hence, is modelled ( notates a zero-mean -variance complex Gaussian random variable. Therefore, obeys exponential distribution with mean , shortly denoted as , resulting in its cumulative distribution function (CDF) and the probability density function (PDF) as and , respectively, where .) as and is unchanged during but changes independently in the next . To guarantee ’s messages to be restored correctly at the intermediate nodes with the highest possibility, ultimately limiting error propagation as much as possible, and with are selected as the conventional relay and the jammer, respectively, if (i.e., the channel is better than the channel).
In stage II with a duration of , transmits secret data while jams for securing ’s data. Therefore, signals received at and have an unique form aswhere ; and are the unit-power transmit symbols of and , correspondingly; and are the and channel gains, respectively; is the additive noise at the receiver .
The jamming signal created by is deliberate to impair solely the wire-tapping of without degrading signal reception of desired users ( and ). Such a special characteristic of can come from pseudo-random signal generators whose seeds are securely shared only among , , and [9, 21, 36–44]. Consequently, and can regenerate exactly and entirely eliminate it, ultimately creating the signal received at in stage II asfrom which the signal-to-noise ratio (SNR) at is established as
Generating is solely known at , , and for hiding but is blind with it. As such, the signal-to-interference plus noise ratio (SINR) which obtains for restoring in stage II is calculated from (2) to be
In stage III with a duration of , decodes and forwards ’s data while interrupts for securing ’s transmission. Accordingly, signals received at and have an unique form aswhere ; is the unit-power transmit symbol of ; and are the and channel gains, correspondingly; is the additive noise at the receiver .
Thanks to the property of the jamming signal and processing it similarly as stage II, the SNR at and the SINR at in stage III are correspondingly given by
The decode-and-forward operation of results in aggregated SINR at for restoring as
Since receives signals in both stages, it can perform selection-combining them for higher intercept possibility [45], yielding the aggregated SINR as
The channel capacity available at for restoring is represented to be
3. The Proposed RaJ Scheme
Communication reliability and data security can be measured through the OP at and the IP at , respectively. These probability expressions of the proposed RaJ scheme are first derived in this part to quickly evaluate both reliability and security without exhaustive simulations. Then, by simplifying them, the OP and the IP of two benchmark RnJ and nRnJ schemes are inferred in the next part to facilitate performance comparison and show the efficacy of simultaneous relay selection and jamming.
3.1. Intercept Probability
The IP is addressed as the probability which restores successfully. According to information theory, given a preset transmission rate , the IP is the probability that is smaller than , namely,where and is the probability operator.
Inserting (10) into (12), one obtainswhere follows the total probability law and the event means as a conventional relay while as a jammer.
Let , , and . Then, plugging (5) and (8) into in (13) results inwhere is the expectation operator.
in (14) is expressed in closed-form as
Based on (1), four combinations of are considered when deriving (14) as follows.
Combination 1:
This combination holds when and . Incorporating these conditions with in (14) results in existence region of as and . By averaging in (15) over this region, one obtains for this combination aswhere
Invoking in (15) with and after some simplifications, the integral in (17) is solved aswhere with is the exponential integral [46].
Combination 2:
This combination holds when and . Incorporating these conditions with in (14) results in empty region of . Therefore, one obtains for this combination as
Combination 3:
This combination holds when and . Incorporating these conditions with in (14) results in existence region of as and . By averaging in (15) over this region, one obtains for this combination aswhere and is expressed in closed-form as follows after invoking in (15), substituting with and executing simplifications:
Combination 4:
This combination holds when and . Incorporating these conditions with in (14) results in existence region of as and . By averaging in (15) over this region, one obtains for this combination aswhere is in (15) with , which is a constant.
Now it is ready to simplify (13) using the total probability law as
The asymptotic IP, , is obtained when approaches infinity. In the asymptotic region, only the combination 4 happens and hence,which indicates a complete insecurity.
3.2. Outage Probability
The OP is addressed as the probability which restores unsuccessfully. Consequently, the OP is the probability that is greater than , namely,
Given in (9), one rewrites (25) as
Plugging (4) and (7) into in (26) results in
Based on (1), two cases of are considered when deriving (27) as follows.
Case 1.
This case holds when . Incorporating this condition with and in (27) results in existence region of . More specifically, if , then the existence region is empty and hence, in (27) becomes . Otherwise, the existence region is and . By averaging in (27) over this region, one obtains for this case aswhere is given in (A.1) in Appendix A.
Case 2.
This case holds when . Incorporating this condition with and in (27) results in existence region of as and where . By averaging in (27) over this region, one obtains for this case asNow it is ready to simplify (26) using the total probability law asThe asymptotic OP, , is obtained when approaches infinity. In the asymptotic region, only the case 2 happens and hence,which indicates joint impact of three involved channels (, , and ) on communication reliability.
3.3. Comment
Both and in (23) and (30) are expressed in novel-and-exact forms, facilitating in evaluating swiftly both security and reliability of the proposed RaJ scheme with the NL-EH without exhaustive simulations. In addition, they are leveraged to derive performance measures for benchmark schemes as well as linear energy harvesters.
4. Benchmark Schemes (RnJ and nRnJ)
4.1. The RnJ Scheme
To evaluate the efficacy of the jamming operation in our scheme, we compare it with the only relay selection scheme (e.g., [6, 47]) which lets be idle in our scheme, namely, the RnJ scheme. The OP of the RnJ scheme is the same as that of ours (i.e., ) but the IP of the former is different from that of the latter. Following the derivation of in (30) with the note that , one obtains the IP of the RnJ scheme aswhere is given in (B.1) in Appendix B.
The asymptotic OP of the RnJ scheme iswhich indicates a complete insecurity.
4.2. The nRnJ Scheme
To evaluate the efficacy of simultaneous relay selection and jamming in our scheme, we compare it with the nRnJ scheme (e.g., [7]) which lets always relay the source data and be idle in our scheme (i.e., pure relaying). Then, the IP of the nRnJ scheme is
By considering two cases of as for deriving in (30), one obtains the IP of the nRnJ scheme asfrom which the asymptotic IP of the nRnJ scheme is given bywhich indicates a complete insecurity.
The OP of the nRnJ scheme is expressed to be
By considering two cases of as for deriving in (30), one obtains the OP of the nRnJ scheme asfrom which the asymptotic OP of the nRnJ scheme is given bywhich indicates the dependence of communication reliability on only the channel.
5. Remarks
Remark 1. Three (RaJ, RnJ, and nRnJ) schemes are completely insecure as (please refer to (24), (33), and (36)). This is reasonable since receives strong signals from as , making decode successfully source data.
Remark 2. For the L-EH (i.e., in (1) is infinite), the IP and the OP of the RaJ scheme are, respectively, addressed aswhere is expressed in (A.4) in Appendix B.
6. Demonstrative Results
This part illustrates theoretical/simulated results to evaluate both reliability and security of the considered schemes via pivotal parameters. Monte-Carlo simulations produce simulated results while the derived expressions in parts 3–5 are calculated to achieve theoretical ones. Path-loss is accounted by modelling fading power of channel as where is the distance. For illustration purpose, users are located on a 2-dimension plane where at , at , at , at , and at ; , ; bits/s/Hz. Since both RaJ and RnJ schemes achieve the same OP (i.e., ), the following results only expose .
Results in Figures 2–4 show coincidences between theory and simulation and between asymptote and theory at large , validating both rigorous and asymptotic analyses. Moreover, these figures demonstrate that without jamming, two (RnJ and nRnJ) benchmark schemes suffer a complete insecurity () since secret data is not protected in both stages (II and III) as in the proposed RaJ scheme which is drastically secured (i.e., ). Furthermore, with relay selection, both (RaJ and RnJ) schemes achieve significantly better reliability than the nRnJ scheme (i.e., ). Therefore, the proposed RaJ scheme, which exploits simultaneous jamming and relay selection, considerably outperforms the (RnJ and nRnJ) benchmark schemes in terms of security as well as reliability.
Figure 2 unveils the OP/IP via for dB and . It is observed that decreases with increasing , which makes senses because of increasing the harvested energy. Nevertheless, is minimum (i.e., the security reaches the peak) at a certain value of . This implies that increasing does not always improve security because also benefits from receiving strong signals from and , eventually wire-tapping more source data. Interestingly, the minimum happens at the asymptotic OP , and hence, can be optimized to obtain the best reliability and security performances. Compared to the NL-EH, the L-EH apparently offers considerably better reliability (). However, the security of the former () fluctuates around that of the latter () with increasing .
Figure 3 plots the IP/OP versus for dB. It is noted that is proportional to the EH time but inversely proportional to the signal processing time (stages II and III). Accordingly, should be optimally adopted to balance these times for optimum reliability. Figure 3 shows that the RaJ and nRnJ schemes reach the lowest OP at and , respectively. Interestingly, the security of the proposed RaJ scheme is considerably enhanced (i.e., significantly decreases) with increasing . Some reasons lead to this observation as follows. Firstly, increasing reduces the channel capacity at because of the factor before the logarithm in (11), causing the decrease of . Secondly, although increasing helps and collect more energy, suffers the increase of the jamming power from , eventually reducing . Compared to the NL-EH, the L-EH is drastically more reliable () but less secure ().
Figure 4 exposes the IP/OP versus for dB and . The reliability-and-security trade-off of the proposed RaJ scheme is observed in this figure. Nonetheless, the reliability gain increases faster than the security loss with increasing the saturation threshold of the NL energy scavenger , exposing the advantage of both relay selection and jamming in our scheme in ensuring high reliability with affordable security threat. Such a trade-off with increasing is reasonable since the NL-EH operates in the linear mode with higher harvested energy more frequently in the range of large . Indeed, the performances of the NL-EH, and , reach those of the L-EH, and , at large .
7. Conclusions
The current paper recommended the relay selection-and-jamming scheme for radio frequency energy harvesting networks with the nonlinear energy harvester. Its security and reliability were also analyzed via the intercept and outage probabilities. Thanks to selecting the relay with the highest probability of decoding the source data and jamming the eavesdropper in both signal transmission stages, the proposed RaJ scheme achieved better reliability and security than the (RnJ and nRnJ) benchmark schemes without neither jamming nor both relay selection and jamming. Additionally, the best performance of the recommended scheme is achievable with choosing properly the source power and the time fraction, respectively. Moreover, the nonlinearity property of the energy harvesters significantly affects the reliability yet slightly degrades the security for the proposed scheme. Furthermore, the nonlinear energy harvester is less reliable yet more secure than the linear energy harvester.
Appendix
A. Derivation of in (28)
in (28) iswhere
Invoking the series expansion for , one rewrites (A.2) as
Using [46] (Equation (3.381.6)), the last integral in (A.3) is numerically evaluated as where is the Whittaker’s function. Plugging this result into (A.3), one obtains
By plugging (A.4) into (A.1), one represents in (28) in a precise closed form.
B. Derivation of in (32)
in (32) iswhere is expressed in (A.4).
Availing [46] (Equation (3.471.9)), in (B.1) is solved as where is the modified Bessel function of the second kind. Plugging this result into (B.1), one obtains
Data Availability
The authors declare that all data used to support the findings of this study are included within the article.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
This study/work/research was fully funded by the Tra Vinh University under grant contract number 181/HD.HDKH&DT-DHTV. The other supports Khuong Ho-Van who would like to thank Ho Chi Minh City University of Technology (HCMUT), VNU-HCM for the support of time and facilities for this study.