Hybrid decode-amplify and forward protocol of FD EH relaying network: outage probability analysis

Nowadays, many research papers focus on the WPCN problem and how to improve its efficiency. In this research, we propose and investigate Hybrid Decode-Amplify and Forward Protocol (HDAF) of the Full-Duplex (FD) Energy Harvesting (EH) Relaying Network with the Time Switching (TS) protocol. In the beginning stage, we present the HDAF mode, which can be work like a Decode-and-Amplify (DF) or Amplify-and-Forward (AF) modes based on the best of its performance in the FD EH relaying network. Furthermore, the closed-form expression of the outage probability (OT) is analyzed and derived in connection with the primary system parameters. Besides, the comparison of the system performance in the AF, DF, and HDAF is proposed and investigated. Finally, all the results are convinced by the Monte Carlo simulation for all cases.


Introduction
Remotely powering wireless communication device is an innate tendency in modern wireless networks, especially when a user or communication device has limited access to battery power or the resources necessary to regularly replace the batteries.Recently, wireless-powered communication has gained considerable interest because of its capability to deal with the energy scarcity in energy-constrained wireless networks.The energy-constrained communication systems have a limited operational lifetime, and to maintain network connectivity, periodical battery replacement or recharging is performed, which is nevertheless costly, inconvenient, and sometimes impossible.As such, energy harvesting, which scavenges energy from external natural resources such as solar, wind or vibration, has gained a great deal of interest, since it provides a cost-effective solution to prolong the lifetime of wireless communications systems.However, the amount of energy harvested from natural resources is random and highly depends on some uncontrollable factors such as the weather conditions, which makes reliable communication difficult.An attractive solution that overcomes the above limitation is to harvest energy from human-made radio frequency (RF) electromagnetic radiation (also known as wireless power transfer) [1][2][3][4][5][6].In the last decade, many research papers focused on WPCN and how to improve its efficiency.This concept of a tradeoff between EH and information transmission in WPCN was proposed and investigated in [7] and extended in [8].Moreover, the concept of partial network-level cooperation for EH networks was presented in detail in [9], and in [10] wireless EH and information transfer in cognitive relay networks was intensely analyzed.In WPCN, the two traditional time switching (TSP) and power splitting (PSP) protocols have been intensively studied in the literature, and many from these studies have compared the system performance of the two protocols under different scenarios [11][12][13][14][15].

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In this research, we propose and investigate hybrid decode-amplify and forward protocol (HDAF) of the full-duplex (FD) energy harvesting (EH) relaying network with the time switching (TS) protocol.In the beginning stage, we present the HDAF mode, which can be work like a decode-and-amplify (DF) or amplify-and-forward (AF) modes based on the best of its performance in the FD EH relaying network.Furthermore, the closed-form expression of the outage probability (OT) is analyzed and derived in connection with the primary system parameters.In addition, the comparison of the system performance in the AF, DF, and HDAF is proposed and investigated.Finally, all the results are convinced by the Monte Carlo simulation for all cases.The main contribution of this paper can be drawn as the follows: − The HDAF of the FD EH relaying network is proposed and investigated.− The closed-form expression of the system OP is derived and investigated in connection with the primary system parameters.− The comparison of the system performance in the AF, DF, and HDAF is proposed and investigated.− The Monte Carlo simulation convinces all the results.
The remaining part of this research can be drawn like the below sections.We propose the system model network in sections 2, and the outage probability analysis is provided in section 3. Section 4 gives the research results and discussions, and some conclusions are written in the last section.

System Model
In this section, Figure 1 presents the HDAF of the FD EH relaying network in the TS Protocol.In this model system, the information is transferred from the source (S) to the destination (D), through an energy-constrained intermediate relay (R).The energy harvesting (EH) and information transferring (IT) phases of the system model are drawn in Figure 2. In this scheme, T is the block time of the proposed system.In the first interval time (αT), where α is the TS factor α ∈ (0, 1), the R harvests energy from the S. Here; we consider the interference noise at the relay node which the factor f. In the remaining interval time (1-α) T, the information is transferred from the S to R and D, as shown in Figure 2. All the fading channels from S to R and R to D are proposed as the Raleigh fading channels [16][17][18][19][20].

Information transmission (IT)
Figure 2. The EH and IT phases

System Performance Analysis
The received signal at the relay can be expressed as denotes the expectation operation, r n is the zero-mean additive white Gaussian noise (AWGN) with variance N0, f is the loopback interference.Moreover, the energy harvesting in the relay can be computed as (1 ) 1 where we denote 1 . The received signal at the destination can be given as where RD h is the channel coefficient and d n is the zero-mean AWGN with variance N0.In this paper, we consider the hybrid Decode-Amplify and forward (HDAF) protocol.In the AF protocol, the relay amplifies the input signal by a factor  which is given by substituting ( 4) into (3).Finally, we have Moreover, then substituting (1) into ( 5), the received signal at the destination can be rewritten as   = ℎ    +   = ℎ  (ℎ    +   +   ) +   = ℎ  ℎ    ⏟  ℎ    + ℎ    +   ⏟  (6) after doing some algebra, the end to end signal to interference noise (SINR) can be obtained as in [21]  substituting ( 2) into (7), the end to end SINR at the destination can be reformulated as where we denote 0 s P N = .

DF
In the DF protocol, from (1) the SINR at the relay can be given as

Outage Probability (OP)
In HDAF protocol, the OP can be defined as follows where DF OP and AF OP are the outage probabilities in case of DF and AF modes, respectively, and 2 21 R  =− is the threshold of the system and R is the source rate.
The first term in (11) where we denote  f .Similar to the above case, we have the probability of operating in DF mode is given by ( ) using the law of conditional probability, ( 14) can be reformulated as ) Since, from ( 9) and ( 10), R SINR and D SINR are independent of each other, ( 15) can be obtained as

Remark
The cumulative density function (CDF) of 1  can be derived as ( ) ( ) where sr  and rd  are the mean of RV where () v K • is the modified Bessel function of the second kind and v th order.Applying (18) and replace x k , equation ( 16) can be obtained as Next, we will find the probability to operate in AF mode.The OP of AF mode can be given as where ( ) 8) and ( 9), we have ( ) substituting (13), (19) and ( 21) into (11), the OP of HDAF protocol can be claimed as

Numerical Results and Discussion
In this section, we investigate the influence of the primary system parameters such as α, ψ, η, and RFro on the OP of the proposed model system and the comparison of the AF, DF, and HDAF modes on the system performance [22][23][24][25].In Figure 3, the effect of η on the system OP is plotted.In this case, we consider three cases of AF, DF, and HADF modes and set the main system parameters as α = 0.8, ψ = 1 dB, and R = 0.5 bps/Hz.In this figure, we can see that the OP of AF and DF modes have a slight decrease the increases with rising α, but the OP of the HDAF mode has a tendency decrease with rising α.It can be observed that the HDAF mode has a better system performance in comparison with the both AF and DF modes.Furthermore, the influence of ψ on the system OP is illustrated in Figure 4 for the AF, DF, and HDAF modes.Here we set η = 0.8, α = 0.5, and R = 0.5 bps/Hz for this model system.Again, the system OP of all three modes significant decrease when ψ rises from 0 to 50 dB and the system OP in HDAF mode is better than other cases.In Figures 3 and 4, all simulation results using Monte Carlo simulation is the same with the analytical results.
Moreover, the influence of R and α on the system OP is dawn in Figures 5 and 6, respectively.In these Figures., we investigate all AF, DF, and HDAF cases with the main parameters are set as α = 0.8, η = 0.8, ψ = 1 dB, and R = 0.5 bps/Hz.From the results, we can see that the system OP in HDAF mode is a lot of better than in AF and DF modes.Then, the system OP increases with rising R from 0 to 7 and decreases with rising α from 0 to 1, respectively.All the analytical results agree with the simulation results using Monte Carlo simulation.

Conclusion
In this research, we propose and investigate hybrid Decode-Amplify And Forward Protocol (HDAF) of the Full-Duplex (FD) Energy Harvesting (EH) Relaying Network with the Time Switching (TS) protocol.In the beginning stage, we present the HDAF mode, which can be work like a Decode-and-Amplify (DF) or Amplify-and-Forward (AF) modes based on the best of its performance in the FD EH relaying network.Furthermore, the closed-form expression of the outage probability (OT) is analyzed and derived in connection with the primary system parameters.Also, the comparison of the system performance in the AF, DF, and HDAF is proposed and investigated.Finally, all the results are convinced by the Monte Carlo simulation for all cases.The results can provide the novel recommendation for the wireless relaying communication network shortly.


is the mean of the random variable(RV)

Figure 3 .Figure 5 .
Figure 3. OP versus η Figure 4. OP versus ψ defines that the signal at the relay is successfully decoded and operates in DF mode.The terns