Performance analysis for three cases of outage probability in one-way DF full-duplex relaying network with presence of direct link

In this paper, the one-way decode-and-forward (DF) full-duplex relaying network system with presence of direct link is investigated. In the analysis section, we derived the exact, lower, and upper bound for outage probability (OP) with maximal ratio combining (MRC) at the receiver. Furthermore, the system performance's analytical expressions are verified by using the Monte Carlo simulation. In addition, we investigated the effect of the main parameters on the OP of the proposed system. Finally, we can sate that the simulation curves overlap the analytical curves to convince the analysis section. This research can provide a novel recommendation for the communication network.

for outage probability (OP) with maximal ratio combining (MRC) at the receiver. Furthermore, the system performance's analytical expressions are verified by using the Monte Carlo simulation. In addition, we investigated the effect of the main parameters on the OP of the proposed system. Finally, we can sate that the simulation curves overlap the analytical curves to convince the analysis section.

SYSTEM MODEL
In this section, Figure 1 proposed the system model. The energy harvesting (EH) and information transferring (IT) phases are drawn in Figure 2 [16]- [20]. Assume that all of the channels are Rayleigh fading, hence the channel gains 2 To take path-loss into account, we can model the parameters as follows: The CDF is expressed as; Then, the PDFs of |ℎ | 2 , |ℎ | 2 , |ℎ | 2 and | | 2 are expressed, respectively as; The received signal at the relay can be expressed as; The average transmitted power at the relay can be given as; where 01  : energy conversion efficiency (which takes into account the energy loss by harvesting circuits and also by decoding and processing circuits). The received signal at the destination in the first phase can be given by; where D n is the AWGN with variance N0.
Here, in our model, we adopt the decode-and-forward (DF) protocol. Hence, the signal to interference noise (SINR) at the relay node from (5) can be given by; Substituting (6) into (8) and using the fact that N0<<PS, we have: (7), the SINR at the destination can be obtained by; where 0 s P N = Next, the destination will also receive the information directly from the source. Therefore, the SINR in this phase can be expressed by; Finally, using the MRC technique at the receiver, the overall SINR of the system can be claimed as; where = ( 1− | | 2 , |ℎ | 2 |ℎ | 2 ) and = |ℎ | 2

OUTAGE PROBABILITY (OP) ANALYSIS 3.1. Exact analysis
The OP of the system at the source destination can be defined as; where th  is the predetermined threshold of the system. To find the probability in (13), 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;  (15) From (3), 1 I can be calculated as; By applying equation (3.324,1) of [21], in (17) can be reformulated by; where () v K • is the modified Bessel function of the second kind and v th order. Substituting (17) and (18) into (15), we obtain: Next, the CDF of Y can be found by; From (20), the PDF of Y can be obtained by; Substituting (19) and (21) where ( ) = √

Lower and upper bound analysis
It is easy to observe that (22) is very difficult to calculate in a closed-form expression. Hence, in this section, we will perform the OP of the system in lower and upper bound forms. From (12), we can compute as; Therefore, the OP of the system in lower bound form can be given by; From (19), P1 can be calculated as; Next, P2 can be found by; 2 1 Pr exp 22 Substituting (25) and (26) into (24), we claim: Similar to the above, the upper bound OP of the system can be computed as;

NUMERICAL RESULTS AND DISCUSSION
The model system's system performance is investigated using Monte Carlo simulation, as shown in [22]- [27]. The OP as a function of the energy coefficient η is drawn in Figure 3 with the main system parameters as γth=1, ψ= 3dB, and ρ=0.3. In this figure, we considered the exact, upper, and lower bound analysis of the system OP. The results show that the system OP decrease with the increase of the energy coefficient. In the same way, the system OP versus γth is illustrated in Figure 4, and we set η=0.8, Φ=7dB, and ρ=0.8. The system OP has a significant rise while γth varies from 0 to 6 as shown in Figure 4 for all cases with exact, lower, and upper bound. From Figures 3 and 4, the simulation and the analytical values agree well. Moreover, the system OP versus Φ and ρ are presented in Figures 5 and 6, respectively. We set γth=1, η=1, and ρ-0.5 for Figure 4, Φ=5 dB for Figure 5, respectively. From Figure 6, it can be stated that the system OP falls while ψ rises from 0 dB to 20 dB. The system OP has a slight fall with ρ varies from 0 to 0.5 and then has a rise with the remaining values of ρ. The maximum value of the system OP can be obtained with ρ=0.5, as shown in Figure 6. Once again, the simulation results agree with the mathematical, analytical results, as in Figures 5 and 6.

CONCLUSION
In this paper, the one-way DF full-duplex relaying network system with presence of direct link is investigated. In the analysis section, we derived the exact, lower, and upper bound for outage probability (OP) with maximal ratio combining (MRC) at the receiver. Furthermore, the system performance's analytical expressions are verified by using the Monte Carlo simulation. In addition, we investigated the effect of the main parameters on the OP of the proposed system. Finally, we can sate that the simulation curves overlap the analytical curves to convince the analysis section. This research can provide a novel recommendation for the communication network.