Jammer against eavesdropper in half-duplex energy harvesting cooperative relaying networks: secrecy outage probability analysis

Phu Tran Tin1, Duy Hung Ha2, Minh Tran3, Tran Thanh Trang4 1 Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Vietnam 2 Wireless Communications Research Group, Faculty of Electrical and Electronics Engineering, Ton Duc Thang University, Ho Chi Minh City, Vietnam 3 Optoelectronics Research Group, Ton Duc Thang University, Vietnam 4 National Key Laboratory of Digital Control and System Engineering, Vietnam

system performance in terms of the integral form expression of secrecy outage probability. In addition, we have investigated the effect of source rate, time switching factor, energy coefficient, and the ratio P s /N 0 on the system performance. Finally, all the mathematical, analytical expressions are verified by Monte Carlo simulation, and the analytical results match well with the simulation ones to convince the correctness of the analytical expression. The main contribution of this research can be formulated as the following a. The integral form of expression of secrecy outage probability is derived. b. The effect of source rate, time switching factor, energy coefficient, and the ratio Ps/N0 on the system performance is demonstrated. c. The Monte Carlo simulation is conducted to verify the correctness of the analytical expressions.

SYSTEM MODEL
We consider a communication scenario with the help of a friendly jammer (J), as illustrated in Figure 1. The EH and IT processing are proposed in Figure 2. In this scheme, T is the block time in which the source fully transmits the information data to the destination. In the first interval time (αT), the R and J harvest energy from the S signal, where α is the time switching factor α ∈ (0, 1) In the two remaining intervals time (1-α)T/2, the S and R node transfer information to the D node [5][6][7][16][17][18][19][20][21][22][23][24]. Figure 2. The EH and IT phases.

Energy harvesting phase
In the first phase, the source will supply the energy for both jammer and relay nodes. Hence, the harvested energy at the jammer and relay can be given as, respectively The average transmitted power at the jammer and relay nodes can be obtained from (1) and (2), respectively

Information transmission phase
In the second phase, the received signal at the relay can be rewritten as Where h SR is the channel gain of S-R link, x s is the transmitted signal from source and n r is additive white Gaussian noise (AWGN) with variance N 0 and {| | 2 } = which {•} is expectation operator. In the third phase, the received signal at the destination can be given by = ℎ +

881
Where h RD is the channel gain of R-D link, x r is the transmitted signal from relay and n d is (AWGN) with variance N 0 and {| | 2 } = Here, we consider amplify and forward (AF) mode at the relay. Hence, the amplify factor can be given as Substituting (7) into (6), we have: From (8), the end to end signal to noise ratio (SNR) of S-R-D link can be calculated as After doing some algebra and using the fact that N 0 <<P R , (9) can be rewritten as Substituting (3) and (4) into (10), the end to end SNR can be reformulated as

OUTAGE PROBABILITY (OP)
The received signal at the eavesdropper can be given by Where h SE is the channel gain of S-E link and n E is AWGN with variance N 0 and �� � 2 � = To protect information from being eavesdropped by E, the friendly jammer J performs jamming. Hence, the SNR at the eavesdropper can be expressed as Substituting (3) and (4) into (13), we have: Where = |ℎ | 2 , = �ℎ � 2 �ℎ � 2 Next, the channel capacity of S-R-D and of eavesdropper can be obtained as, respectively Utilizing the result in [25], the CDF of X and Y can be shown as the below (18) where (•)is the modified Bessel function of the second kind and v th order and , are mean of random variables (RVs) �ℎ � 2 , �ℎ � 2 , respectively. From (18), the probability density function (PDF) of V can be calculated as, after applying the following formula

Secrecy Outage probability (SOP)
The Secrecy capacity of the system can be defined as Where [ ] + = (0, ) The SOP can be formulated by Where = 2 and is source rate. In order to calculate the probability in (21), we have to find ( ) and ( ) At first, we have: Substituting (11) into (22), (22) can be rewritten as Where , are the mean of RVs|ℎ | 2 , |ℎ | 2 , respectively. Apply equation [3.324,1] of the table of integral, we can obtain as followings Next, combine with (14), the CDF of can be given by Where is the mean of RV|ℎ | 2 Applying Taylor series as follows (27) Substituting (27) into (26), we have: By changing variable = � and then applying equation [6.561,16] of table of integral, equation (28) can be reformulated as From (30), the PDF of can be obtained as Applying results from (23) and (30) for (21), finally the SOP can be claimed by

NUMERICAL RESULTS AND DISCUSSION
In this section, the effect of source rate, time switching factor, energy coefficient, and the ratio P s /N 0 on the system performance is investigated. The SOP versus the source rate R S is plotted in Figure 3 with the main system parameters as ϕ= 5 Db, η=0.8 and α=0.25, 0.5, 0.85. As shown in Figure 3, the SOP significantly increases while the source rate increases from 0 to 6 bps/Hz. Figure 4 presents the influence of ϕ on the system SOP. In Figure 4, we set η=0.8, α=0.5 and R S = 0.5, 1.0, 1.5 bps/Hz, respectively. From the results, we can see that the system SOP crucially falls down with the rising of ϕ from 0 to 30 dB. In Figure 3 and Figure 4, the simulation results match well with the analytical ones for verifying the correctness of the system performance analysis.
The effect of the energy efficiency coefficient on the system SOP is illustrated in Figure 5, in which we set α=0.5, R S =0.5 bps/Hz, ϕ=1, 5,10 dB, respectively. Here, we can state that the system SOP has fallen down when η varies from 0 to 1. Furthermore, the system SOP versus time switching factor α is drawn in Figure 6. We set ϕ=5 dB, R S =0.5 bps/Hz, and η=0.25, 0.5, 1, respectively. The same as the above case, the system SOP decreases massively with the rising of α from 0 to 1. As shown in Figure 5 and Figure 6, the analytical and the simulation results are the same to convince the analytical system performance analysis.    Figure 6. SOP versus α.

CONCLUSION
In this paper, we have investigated the HD EH Cooperative Relaying Networks in the presence of the Jammer Against Eavesdropper. We have analyzed the system performance in terms of the integral form expression of secrecy outage probability. In addition, we have investigated the effect of source rate, time switching factor, energy coefficient, and the ratio P s /N 0 on the system performance. Finally, all the mathematical, analytical expressions are verified by Monte Carlo simulation, and the analytical results match well with the simulation ones to convince the correctness of the analytical expression.