## 1. Introduction

Wireless Sensor Networks (WSN) is a rapidly emerging field and is driven by a wealth of research. In the WSN, sensor nodes collect and process environmental information. Then, the sensor nodes transmit sensed information to a base station. However, data rate of the transmission is limited at low power sensor nodes for a longer battery lifetime. Relaying is a significant technique to increase the data rate for WSN under the power constraint [

1,

2,

3]. Idle sensor nodes with no information to transmit can assist the network by performing as relay nodes. However, the sensor nodes must able to communicate with others sensor nodes. The fifth generation (5G) wireless network, which supports device-to-device communication, will address the demand of inter-sensor communication [

4].

Following the broadcast nature of wireless channels, transmission between sensor nodes and base station can be easily overheard and possibly extracted by an eavesdropper. This makes WSN highly susceptible to eavesdropping. In order to achieve a confidential and secure wireless communication, existing systems rely on cryptographic techniques at upper layers [

5,

6]. However, the cryptographic techniques such as encryption rely on the assumption that the eavesdropper has limited computational capability and is therefore not likely to decipher the key in finite time. Recently, physical layer security has been identified as a promising strategy to provide additional protection against eavesdropping.

Unlike the cryptographic techniques, physical layer security techniques do not rely on computational complexity and will not be compromised by eavesdropper with powerful computational capability. Physical layer security uses wiretap channel coding to achieve the information-theoretic perfect secrecy, where the eavesdropper gains no information about the legitimate information [

7,

8,

9,

10]. Physical-layer security exploits the characteristics of the wireless channel to improve transmission security. The secrecy of wireless transmission can be quantified by the secrecy capacity, which is defined as the maximum secrecy rate which can be conveyed to legitimate receiver while the eavesdropper gaining no information about the secrecy message [

11]. On the other hand, an intercept event occurs and transmission becomes insecure when the secrecy rate falls below zero. The transmission with lower probability of occurrence of an intercept event,

i.e., intercept probability, is more secure and robust against eavesdropping. However, the achievable secrecy rate and intercept probability are severely degraded due to the fading effect of wireless communication. To overcome this limitation, extra cooperative node can be used to improve the secrecy [

12,

13].

A cooperative node injecting jamming signal to interfere the eavesdropper can improve the secrecy rate. However, the jamming signal may deteriorate the desired legitimate transmission as well. This can be avoided by performing beamforming to minimize the adverse effect of the jamming signal towards the desired data transmission [

14]. As a result, the jamming signal consumes additional power resource and the design of beamformer increases the complexity. On the other hand, the cooperative relaying has been identified as a promising technique which not only improves reliability and data rate but also can be further utilized to ensure the secrecy of wireless transmission [

15,

16,

17,

18,

19,

20].

Conventionally, a half-duplex relay cannot perform simultaneous transmission and reception of signal within the same frequency channel. Therefore, when the half-duplex relay is transmitting a signal, the source has to stop transmission. As a result, the spectral efficiency of conventional half-duplex relay is at most half of the spectral efficiency of direct transmission. In order to improve the spectral efficiency of cooperative relaying transmission, a full-duplex relay which can perform simultaneous transmission and reception in the same frequency channel has been proposed. However, in practice, the transmission of the full-duplex relay is interfering its own reception. This self-interference is the main detrimental factor in full-duplex relaying. Since the transmit and receive antennas of full-duplex relay are co-located, the self-interference is much stronger (

i.e., 99 dB as reported in [

21]) than the intended received signal. The self-interference saturates the analog-to-digital converter (ADC) at the receiver and making it challenging for the cancellation of known self-interference. The suppression of self-interference requires sophisticated hardware and/or advanced signal processing which significantly increase the cost and complexity of relays [

22,

23,

24]. In fact, for full-duplex relaying, the combination of propagation domain, analog domain and digital domain cancellation techniques are needed to achieve good suppression of self interference [

25,

26]. In [

27], full-duplex and full-duplex jamming secrecy network are proposed. Full-duplex relay improves achievable secrecy rate and secrecy outage probability by providing higher spectral efficiency than conventional half-duplex relay. In full-duplex jamming secrecy network, the full-duplex relay transmits jamming signal towards the eavesdroppers while concurrently receives source message, in order to achieve lower secrecy outage probability [

27].

Compared to full-duplex relay, the implementation of a half-duplex relay is much simpler and cheaper. Two-path successive relaying (TPSR) has been proposed as an alternative to achieve the full-duplex spectral efficiency by scheduling a pair of half-duplex relays to assist the source transmission alternately [

28]. In TPSR, since the two relays are physically separated, the separation distance between relays is able to attenuate the inter-relay interference due to the distance path loss effect. Since the inter-relay interference is much weaker than the self-interference encountered in full-duplex relay with co-located transmit and receive antennas, simple interference management techniques, such as treating the interference as noise or successive interference cancellation, is effective [

29,

30]. Existing literature mainly considers the TPSR in conventional scenarios without eavesdroppers [

31,

32,

33,

34,

35]. The performance of TPSR in secrecy communication remains unexplored.

In this paper, we propose a secure TPSR protocol that can provide full-duplex spectral efficiency. Two half-duplex relays are used to forward messages from source to destination alternately, the source transmits new messages continuously, and full-duplex spectral efficiency can be achieved. We evaluate the performance of the proposed protocol in terms of ergodic achievable secrecy rate, intercept probability and secrecy outage probability. The performance is compared with half-duplex relaying, full-duplex relaying and full-duplex jamming schemes in [

27]. We also analyze the intercept probability of the proposed scheme and full-duplex relaying.

The contributions of this paper are listed as follows. Firstly, we propose secrecy TPSR which is still unexplored by any existing literature. We evaluate the achievable performance of the proposed secrecy TPSR in terms of ergodic achievable secrecy rate, intercept probability and secrecy outage probability. Secondly, we compare the achievable performance of proposed schemes with the existing half-duplex relaying, full-duplex relaying and full-duplex jamming schemes. Finally, the lower bound intercept probabilities of proposed scheme and existing full-duplex relaying are derived and verified with simulations.

The remaining of the paper is organized as follows. In

Section 2, the system model and transmission protocol of TPSR are explained and the intercept probability of TPSR is analyzed in

Section 3. In

Section 4, the achievable secrecy rate of comparison schemes are presented. In

Section 5, the numerical simulations are presented to verify the analysis. Finally, the conclusions is given in

Section 6.

## 5. Numerical Results

In this section, several Monte Carlo simulation results of the proposed two-path successive relaying (TPSR) and existing half-duplex relaying (HDR), full-duplex relaying (FDR) and full-duplex jamming (FDJ) schemes are presented. In the simulations, the transmit power of source and relay,

P is fixed to unity and the SNR for channel from node

i to node

j is defined as

${\gamma}_{{}_{ij}}=1/{\sigma}_{j}^{2}$. There are

$T=1000$ independent codewords transmitted from the source in all schemes. In this paper, we assume that the self-interference is the residual self-interference [

27] after the self-interference suppression, which has the same level as the receiver noise. For fair comparison, we assume that the inter-relay interference is at noise level, which can be achieved through physical separation between the relays, relay selection, other techniques,

etc.

Figure 2 shows the ergodic achievable secrecy rate

versus SNR of various schemes when

${\gamma}_{sr}={\gamma}_{rd}$,

${\gamma}_{se}={\gamma}_{re}=10\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$ and the inter-relay interference or residual self-interference,

${\gamma}_{rr}=0\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$. It is obvious that TPSR and FDR achieved the same ergodic achievable secrecy rate. This means that the TPSR has the same bandwidth efficiency as the FDR. The TPSR and FDR also achieved

$95.4\phantom{\rule{0.166667em}{0ex}}\%$ and

$63.3\phantom{\rule{0.166667em}{0ex}}\%$ ergodic secrecy rate gain compared to HDR and FDJ, respectively, when

$\mathrm{SNR}=40\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$. This is because the higher bandwidth efficiency of TPSR and FDR compared to the HDR and FDJ. The FDJ employs jamming technique to interfere the eavesdropper. As a result, the FDJ achieves higher ergodic achievable secrecy rate than the HDR. However, FDJ achieves a lower ergodic achievable secrecy rate than TPSR and FDR because half of the bandwidth is used to transmit jamming signals.

Figure 3 shows the intercept probability of various schemes

versus SNR when

${\gamma}_{sr}={\gamma}_{rd}$,

${\gamma}_{se}={\gamma}_{re}=10\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$ and the inter-relay interference or residual self-interference,

${\gamma}_{rr}=0\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$. We observe that the FDR has higher probability of interception compared to the HDR. This is because of the residual self-interference of full-duplex relay in FDR. By transmitting jamming signal to the eavesdropper, the FDJ achieves lower probability of interception compared to the FDR and HDR. The intercept probability of TPSR is lower bounded by theoretical result. Meanwhile, the theoretical result of FDR are well matched to the simulation result. This verifies that the lower bound intercept probability of TPSR and FDR in Equations (

20) and (

26), respectively. TPSR also achieves the lowest probability of interception compared to all the other schemes at high SNR,

i.e.,

$\mathrm{SNR}\ge 30\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$. This is because the two mutually independent assisted link of

${\mathrm{R}}_{1}$ and

${\mathrm{R}}_{2}$ contribute lower intercept probability to the TPSR compared to the other schemes equipped with only one relay.

Figure 4 shows the intercept probability

versus inter-relay interference or residual self-interference,

${\gamma}_{rr}$ for various schemes when

${\gamma}_{sr}={\gamma}_{rd}=40\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$ and

${\gamma}_{se}={\gamma}_{re}=10\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$. The FDR has the highest probability of interception compared to the other schemes even when

${\gamma}_{rr}=0\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$. The residual self-interference decreases the data transmission rate of the FDR. Therefore, the FDR has higher probability of interception compared to the HDR. However, by employing jamming technique, the FDJ with low residual self-interference can achieve lower probability of interception compared to the HDR. On the other hand, when the inter-relay interference

${\gamma}_{rr}<15\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$, the TPSR has the lowest probability of interception compared to the other schemes. This shows that the operating requirement for inter-relay interference level in TPSR is much lower and practical if compared to the self interference level in FDR.

Figure 5 shows the secrecy outage probability

versus target secrecy rate,

r of various schemes when

${\gamma}_{sr}={\gamma}_{rd}=40\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$,

${\gamma}_{se}={\gamma}_{re}=10\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$ and the inter-relay interference or residual self-interference,

${\gamma}_{rr}=0\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$. The probability of secrecy outage of all the schemes is increasing when the target secrecy rate,

r is increased. The TPSR has the lowest probability of secrecy outage compared to the other schemes and it is lower bounded by the FDR. This is due to the use of two relays in TPSR which provide additional diversity and full-duplex bandwidth efficiency. In contrast to previous results in

Figure 3, where the FDR has lower probability of secrecy outage than the HDR and FDJ. This is because the “1/2” pre-log factor in achievable secrecy rate of HDR and FDJ in Equations (

24) and (

28). The jamming technique benefits the FDJ by delivering lower probability of secrecy outage than HDR.

Figure 6 shows the secrecy outage probability

versus inter-relay interference or self-interference,

${\gamma}_{rr}$ for various schemes when target secrecy rate,

$r=2\phantom{\rule{0.166667em}{0ex}}\mathrm{bits}/\mathrm{s}/\mathrm{Hz}$,

${\gamma}_{se}={\gamma}_{re}=10\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$ and

${\gamma}_{sr}={\gamma}_{rd}=40\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$. The TPSR has the lowest probability of secrecy outage compared to the FDR and FDJ. In other words, with the same

${\gamma}_{rr}$, TPSR is more secure than the FDR and FDJ. By considering the HDR as baseline scheme, when

${\gamma}_{rr}=10\phantom{\rule{0.166667em}{0ex}}\mathrm{dB}$, the TPSR has lower probability of secrecy outage, whereas the FDR and FDJ have higher probability of secrecy outage. This shows that the FDR and FDJ require much lower

${\gamma}_{rr}$ compared to the TPSR to achieve lower probability of secrecy outage than the HDR. As a result, the FDR and FDJ have a stricter requirement on residual interference compared to the TPSR.