Lower and upper bound form of outage probability in one-way AF full-duplex relaying network under impact of direct link

This paper proposed and investigated the one-way amplify-and-forward (AF) full-duplex relaying network under impact of direct link. For the system performance analysis, the exact and lower and upper bound form of the system outage probability (OP) are investigated and derived. In this system model, authors assume that the E uses the maximal ratio combining (MRC) technique. Finally, we can see that the analytical and the simulation values overlap to verify the analytical section using the Monte Carlo simulation. Also, we investigate the influence of the system primary parameters on the proposed system OP.


SISTEM MODEL
In Figure 1, we illustrated the system model of the peoposed system and the energy harvesting (EH) and information processing (IT) phases are illustrated in Figure 2 as in [19]- [25]. In this model, all of the channels are Rayleigh fading. Then the CDF of the channel gains 2 SR h , 2 RD || h and 2 SD || h can be formulated as (1).
Finally, the PDFs of 2 SR h , 2 RD h and 2 f can be given as the follows

Energy harvesting and Information transmission
The received signal at the relay can be expressed as The average transmitted power at the relay can be computed as the following where 1 The received signal at the destination can be given by  (7) and combining with (5), we can obtain: After doing some algebra, the end-to-end signal to interference noise (SINR) can be obtained as (9), . Next, the destination will also receive the information directly from the source. Therefore, the SINR in this phase can be obtained by (10).

SYSTEM PERFORMANCE ANALYSIS 3.1. Exact analysis
The System OP at the source destination can be defined as (12), where th  is the predetermined threshold of the system. To find the probability in (12), we have to calculate the cumulative distribution function (CDF) of X and the probability density function (PDF) of Y. So, the CDF of X can be found as (13).
By denoting 22
TELKOMNIKA Telecommun Comput El Control From (10), the CDF of random variables (RVs) T can be computed by (15).
Next, the CDF of Y can be found as (18).

Lower and upper bound analysis
From (11), we can compute as (21).
Substituting (23) and (24) into (22), we have: Similar to the above, the upper bound OP of the system can be computed as (26).

NUMERICAL RESULTS AND DISCUSSION
The system OP versus α is shown in Figure 3 with η=1, γth =1, and Φ =7 dB. The results show that the OP of the model system has a massive decrease with the rising of α from 0 to 0.45 and the has a considerable increase when α rises to 1 in three cases with exact, lower and upper bound analysis. The maximal value of the system OP can be obtained with α=0.45. Furthermore, the OP is considered as the function of γth, as shown in Figure 4. Here we set η=0.8, α=0.25, and Φ =5 dB. Here, γth increases from 0 to 6, as shown in Figure 4. As shown in Figure 4, the system OP increases significantly when β rises in three cases with exact, lower, and upper bound analysis. From Figures 4 and 5, the analytical and the simulation curves overlap each others as shown in the analytical section.  Tran Tin) 1167 Furthermore, the system OP versus η and Φ are investigated in Figures 5 and 6, respectively. In Figure 5, the main system parameters are set as α=0.75, γth =1 and Φ =5 dB, and in Figure 6, we set α=0.5, γth =1, and η=1 respectively. From Figures 5 and 6, it can be observed that the system OP has a slight increase with rising η from 0 to 1 and has a massive decrease when Φ varies from -5 to 15 dB, respectively. Also, the simulation and analytical values agree to justify the analytical section. Figure 5. OP versus η Figure 6. OP versus Φ

CONCLUSION
This paper proposed and investigated the one-way AF full-duplex relaying network under impact of direct link. For the system performance analysis, the exact and lower and upper bound form of the system outage probability (OP) are investigated and derived. In this system model, authors assume that the E uses the MRC (maximal ratio combining) technique. Finally, we can see that the analytical and the simulation values overlap to verify the analytical section using the Monte Carlo Simulation. Also, we investigate the influence of the system primary parameters on the proposed system OP.