Outage Analysis and Optimization of SWIPT in Network-Coded Two-Way Relay Networks

This paper investigates the outage performance of simultaneous wireless information and power transfer (SWIPT) in networkcoded two-way relay systems, where a relay first harvests energy from the signals transmitted by two sources and then uses the harvested energy to forward the received information to the two sources. We consider two transmission protocols, power splitting two-way relay (PS-TWR) and time switching two-way relay (TS-TWR) protocols.We present two explicit expressions for the system outage probability of the two protocols and further derive approximate expressions for them in high and low SNR cases. To explore the system performance limits, two optimization problems are formulated to minimize the system outage probability. Since the problems are nonconvex and have no known solutionmethods, a genetic algorithm(GA-) based algorithm is designed. Numerical and simulation results validate our theoretical analysis. It is shown that, by jointly optimizing the time assignment and SWIPT receiver parameters, a great performance gain can be achieved for both PS-TWR and TS-TWR. Moreover, the optimized PS-TWR always outperforms the optimized TS-TWR in terms of outage performance. Additionally, the effects of parameters including relay location and transmit powers are also discussed, which provide some insights for the SWIPT-enabled two-way relay networks.


Introduction
1.1.Background.One of the main challenges in energyconstrained wireless communication networks, for example, the battery-powered wireless sensor networks, is the limited lifetime due to the fixed energy-supplying devices with finite service life.In order to provide a perpetual energy supply to maintain reliable wireless communications, harvesting energy from the surrounding environment is considered as an effective solution [1][2][3][4][5][6][7][8][9].Traditional energy harvesting (EH) harvests energy from the external energy sources including solar, wind, and vibration, which are greatly affected and limited by environment or climate, and cannot provide stable energy supply for wireless communication networks [10,11], while harvesting energy from ambient radiofrequency (RF) signals [12], especially from dedicated radiofrequency radiation, is regarded as a stable and promising energy source for future energy-constrained wireless networks that cannot be offered by conventional battery or grid power-operated wireless communication networks.Because RF signals are independent with the external conditions of the environment and climate and can be easily designed and controlled.Since RF signals can carry energy as well as information at the same time, energy and information can be delivered simultaneously via RF signals, which is known as the simultaneous information and power transfer (SWIPT) advocated in [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28].

Related Work.
A number of works on SWIPT, thus far, can be found in the literature.In [14], the authors proposed two SWIPT receiver architectures, where energy harvesting and information detection are operated in either power splitting (PS) architecture or time switching (TS) architecture at the receiver, making it possible to realize 2 Mobile Information Systems SWIPT in practical wireless communication systems.In the past few years, the two receiver architectures have been widely adopted to various wireless communication systems.In [15], the PS and TS architectures were investigated in pointto-point communication systems with SWIPT technology.Later, they were studied in more SWIPT-enabled complex network systems such as nonrelaying two-way transmission systems (see, e.g., [16]), two-hop transmissions (see, e.g., [17]), MIMO communication systems (see, e.g., [18]), and nonregenerative MIMO-OFDM relaying systems (see, e.g., [19]).Besides, SWIPT is also be benefit to the relay networks, so that some existing works focused on the system design and performance analysis for SWIPT-enabled relay networks, see for example, [20][21][22][23], where one-way two-hop relay systems with amplify-and-forward (AF) or decode-and-forward (DF) relaying operation were studied.
As is known, the two-way relay network, where two sources exchange their information with a helping relay node, is able to greatly improve system spectral efficiency and throughput by employing some advanced coding technologies such as network coding (NC) [29][30][31] and the twoway relay transmission has wide applications in various wireless networks, so some recent works began to investigate SWIPT in two-way relay networks; see, for example, [24][25][26][27][28]. Specifically, the work in [24] investigated SWIPT in an AF energy harvesting two-way relay system with TS receiver, where however, only the system bit error rate (BER) performance was analyzed.In [25], the authors studied the outage performance for an asymmetric two-way relaying system with PS receiver architecture, where however, only AF relaying protocol was considered.In [26], the authors analyzed and optimized the system outage performance for two-way relay system, where however, just traditional four-phase two-way EH relay system was considered and NC transmission was not considered.In [27], the authors studied the network-coded two-way relay network from an information theoretical viewpoint, where their goal was to explore the system throughput limit with data rate fairness and the system outage probability was not analyzed, although, in [28], the authors considered SWIPT for a network-coded two-way relay system by using DF relaying and derived the outage probability for the system, where only TS receiver architecture was considered and the time allocation for the two-way relay information transmission was not involved.

Motivations and Contributions.
In this paper, we also study a network-coded two-way relay system with SWIPT and DF relaying operation, where two sources with sufficient energy supply desire to exchange their individual information through an EH relay node.Due to the shadowing of the obstacles like high buildings or the long distance, the direct link between two sources is unavailable.
Compared with previous works, two main differences in our work are stressed as follows.Firstly, both TS and PS receiver architectures are took into account in our work, where the power splitting factor for the energy receiver and the time assignment factor for the transmission phases are jointly optimized for PS-TWR, and the time switching factor for the energy receiver and the time assignment factor for the transmission phases are jointly optimized for TS-TWR.Secondly, our goal is to explore the system outage performance limits for the PS-TWR and TS-TWR, where network coding is involved in our work.
The main contributions of this paper are summarized as follows.First, we derive the closed-form expression of the outage probability for PS-TWR as well as the TS-TWR.Second, to explore the system performance limits, two optimization problems are formulated to minimize the outage probability for PS-TWR and TS-TWR, where the power splitting factor for the energy receiver and the time assignment factor for the transmission phases are jointly optimized for PS-TWR, and the time switching factor for the energy receiver and the time assignment factor for the transmission phases are jointly optimized for TS-TWR.Third, since two optimization problems are nonconvex and cannot be solved by directly using traditional solution methods, a genetic algorithm (GA)-based scheme is designed to solve them.Fourth, in order to achieve simplicity, two approximate expressions of the system outage probabilities of PS-TWR and TS-TWR are derived at the high and low SNR regions, respectively.Finally, we provide some numerical and simulation results demonstrate our theoretical analysis associated with the PS-TWR and TS-TWR systems.It is shown that by jointly optimizing the time assignment and the SWIPT receiver parameters, a great performance gain can be achieved for both PS-TWR and TS-TWR.It is also shown that the optimized PS-TWR always outperforms the optimized TS-TWR in terms of outage performance.In addition, the effects of various system parameters including the relay location, the transmit power of the two sources are also discussed, which provide some insights for the SWIPTenabled two-way relay networks.

Organization.
The rest of the paper is organized as follows.Section 2 describes the system model and the PS-TWR and TS-TWR protocols.Sections 3 and 4 analyze the system outage probability for the two protocols, respectively, where the exact and approximate outage probability expressions of for PS-TWR and TS-TWR are presented.Section 6 formulates two optimization problems to minimize the outage probabilities of PS-TWR and TS-TWR and then designs a GA-based optimization algorithm to solve the problems.Section 7 provides some numerical and simulation results and, finally, Section 8 summarizes the paper with some conclusions.

System Model and Protocols
2.1.Network Model.Consider a SWIPT-enabled two-way relay system as shown in Figure 1, where node 1 and node 2, namely, S 1 and S 2 , are with sufficient energy supply and desire to exchange their individual information with each other.However, due to the shadowing of some obstacles like the high buildings or the long distance, the direct link between S 1 and S 2 is nonexistent, so that the information exchange between S 1 and S 2 has to be helped by an intermediate node, node 3 (also referred to as node R).It is assumed that node 3 is an energy-selfish/energy contained node, which is not willing to/has no power to help node 1 and node 2 to exchange Figure 1: System model.their information.By employing RF-EH technique, node 3 is able to harvest energy from the RF signals transmitted by node 1 and node 2 and then use the harvested energy to help the information transmission.All three nodes are equipped with single antenna.It is worth noting that such an energyconstrained two-way relay model can be applied to many different wireless scenarios, for example, the wireless sensor network (WSN) in a toxic environments and the wireless body area network (WBAN).
Quasi-block fading channel is considered, which means that all channel coefficients associated with the links can be regarded to be constant in each fading block and then change independently from one fading block to the next following Rayleigh distribution.The channel gains of the links from S  to R and from R to S  are denoted by ℎ  and   , respectively, and the distances from S  to R are denoted as  S, , where  = 1, 2.
Moreover, S 1 and S 2 have large amount of data to be exchanged and R is with a capacity-limited rechargeable battery buffer, which means that all harvested energy at R in a fading block must be used for the information transmission in the same fading block.
Based on the system mode described above, we shall present the two protocols, PS-TWR and TS-TWR, for the SWIPT-enabled two-way relay system in the following two subsections.

PS-TWR Protocol.
Figure 2(a) illustrates the transmission framework of PS-TWR.Let  be the time period of each fading block.In PS-TWR,  is divided into three parts by the time assignment factors   , that is,  1 ,  2  and (1− 1 − 2 ), where 0 <   < 1 and 0 <  1 +  2 < 1.In the    parts, S  transmits information to R and, in the (1 −  1 −  2 ) part, R forwards the network-coded information to the two sources.
In first two transmission parts (i.e., source transmission phases), S  transmits its information to R, where (1 −   ) R, power is used for the information transmission to R, and the rest    R, power is for energy harvested by R.Here 0 <   < 1 denotes the power splitting factor of the energy harvesting receiver, and  R, is the power of the received signal transmitted from S  at R, which can be expressed as where  is the path loss exponent and   is the S  transmit power.
In the third phase (R forwarding phase), R first decodes the received information transmitted from S  in first two transmission phases and mixes the two flows of the received information with NC, and then broadcasts the mixed information to S 1 and S 2 using all the harvested energy ∑ 2 =1    R, , simultaneously.Since S 1 and S 2 know their own prior knowledge, they can decode the desired information from the mixed information once they receive the broadcasted information from R.
The receiver architecture of R for PS-TWR is depicted in Figure 2(b), where the received signal  R is split into two parts for information processing and energy harvesting by a power splitter in   : 1−  proportion.So, a part of the received signal √    R is allocated to the EH receiver, the other part √1 −    R is for the information receiver.And, the received signal  R at R is interfered by two noises,  R, and  R, , where  R, ∼ CN(0,  2 R, ) is the receiving antenna noise at the relay node R and  2 R, denotes the noise power. R, ∼ CN(0,  2 R, ) is the sampled AWGN introduced by the RF-band to baseband signal conversion at the information receiver as shown in Figure 2(b) and  2 R, is the noise power.
2.3.TS-TWR Protocol.Figure 3(a) shows the transmission framework of TS-TWR, where  is also divided into three phases by the time assignment factors   as those defined in PS-TWR.However, in TS-TWR, the first two    time intervals are further divided into two subphases by the time switching ratio   of the TS receiver architecture, where 0 <   < 1 and  = 1, 2.
In the first two phases (i.e., source transmission phases),      is assigned to R for harvesting energy from the received signals transmitted by S  and the remaining part (1 −   )   is used for R to receive information from S  during the first two subphases.In the third phase (R forwarding phase), R first decodes the received information from S  and mixes the two flows of information with NC, and then broadcasts the mixed information to S 1 and S 2 simultaneously by using all the harvested energy.
The block diagram of TS-TWR the receiver architecture at R is shown in Figure 3(b), where the received RF signal,  R , at R is input into the energy harvesting receiver in the      subphase, and then input into to the information receiver for information decoding during the (1 −   )   subphase. R, and  R, are AWGNs received at R, similar to those defined in PS-TWR.

Exact Expression of the Outage Probability for PS-TWR.
As depicted in Figure 2, the individual information is transmitted from S  to R in the th source transmission phase, and after the processing of the relay information receiver, the sampled baseband signal  (PS)  R, at R can be given by Phase 1:  1 T Phase 2:  2 T Energy harvesting at R Energy harvesting at R  1 P R,1 ) 2 P R,2 ) R broadcasting using the Energy harvesting receive Information receiver

RF to baseband conversion
Baseband processing R broadcasting using the harvested energy  where   is the sampled and normalized information signal from S  ; that is, E{|  | 2 } = 1.E{⋅} = 1 is the expectation operator and |⋅| is the absolute value operator.ℎ  is the channel gain of the link S  to R.  R,  and  R,  are the AWGNs with the variances  2 R,  and  2 R,  , respectively.Based on (1), the data rate  (PS)  R, at R from S  can be given by where R,  is the overall AWGNs at R in the first two transmission phases.
Meanwhile, using (1), the RF-band energy  (PS) R, harvested by R from S  at the relay energy harvesting receiver can be given by where 0 <  ≤ 1 is used to describe the energy conversion efficiency, and we assume  = 1 in this paper.
After the first two transmission phases, the total energy may be harvested by R from S 1 and S 2 can be expressed as , which is consumed by R to forward the received information in the third relay forwarding phase.As the fact that R communicates with S  for the time (1 −  1 −  2 ) as shown in Figure 2(a) and using  (PS) R, in (4), the transmit power of the relay,  (PS)  R , in the third phase can be given by At the end of R forwarding phase, the received signal  (PS) S, at S  from R can be given by where  = 1, 2 and  ̸ = .  is the channel gain of the link R to S  . S,  is the baseband AWGN with variance  2 S,  and  S,  is the sampled AWGN with variance  2 S,  .The achievable date rate at S  from R can be given by where  S, ≜  S,  +  S,  with  2 S, ≜  2 S,  +  2 S,  .Due to the impact of channel   and the employed NC, the broadcast data rate of R is limited in the third phase.Therefore, the actual achievable broadcast rate,  (PS)  SR , at S  from R can be given by where ).As is known, in traditional one-way relay networks, an outage occurs if either link's rate of two hops falls below the given target rate  sr .Comparatively, the two-way relay networks have two communication tasks which refer to three transmission links: S 1 to R link, S 2 to R link and R forwarding link.Unfortunately, any link's transmission failure can result in system outage.So, we define the system outage probability in terms of the analysis in [32,33] as follows: where Theorem 1.For PS-TWR protocol, given a predetermined transmission rate   , the system outage probability can be calculated as (11) in terms of   ,   ,   , , and  , , where Proof.See the Appendix.

Approximate Expressions of the Outage Probability for PS-TWR.
Since the theoretical analysis expression of the system outage probability  (PS)  out in ( 11) is complicated with the modified Bessel functions, it is difficult to obtain an analytic solution of  (PS) out by using traditional methods.For the sake of simplicity, the approximate expressions of  (PS)  out at extremely high and low SNR regions are formulated in the following theorems.
Theorem 2. At high SNR region, the approximate expression of the system outage probability  ()   in (11) for PS-TWR protocol can be formulated as Proof.If 0 <  ≤ √ V + 1, the modified Bessel function of the second kind follows from the approximation [34] given by where Γ(V) is the Gamma function.Therefore, we can obtain the approximate expressions of  1 (⋅) and  2 (⋅) as At high SNR region, the variables in  1 (⋅) and  2 (⋅) of the system outage probability  (PS)  out are very close to zero with the relatively high variables  and , which are contained in the denominators of the variables in  1 (⋅) and  2 (⋅).Substituting ( 14) into (11), the approximate expression for  (PS)  out at high SNR region can be calculated as (12).Theorem 3. At low SNR region, the approximate expression of the system outage probability  ()   in (11) for PS-TWR protocol can be formulated as Proof.If  > |V 2 − 1/4|, the modified Bessel function of the second kind follows from the approximation [34] as At low SNR region, the denominators of the variables in  1 (⋅) and  2 (⋅) are either  or , which is relatively low leading to the variables in  1 (⋅) and  2 (⋅) of the system outage probability  (PS)  out are very close to infinity.Thus, substituting ( 16) into (11), the approximate expression of  (PS)  out at low SNR region can be achieved as (15).

Exact Expression of the Outage Probability for TS-TWR.
As shown in Figure 3(b), the RF received signal  R is first sent to the energy harvesting receiver to collect energy by R over the      time in the S  transmission phase.Thus, the received RF signal  (TS)  R, at R for harvesting energy can be given by where   , , ℎ  ,  ,  , and  ,  are defined as (2).
Using (1), the achieved data rate  (TS) R, at R from S  in the (1 −   )   subphase can be given by where During the first two transmission phases, the harvested RF-band energy  (TS) R, by R from S  in the      subphase can be given by where  is the energy conversion efficiency.
At the end of the first two S  transmission phases, the total energy may be harvested by R from S 1 and S 2 can be expressed as  (TS)  R,1 + (TS) R,2 , which is used by R for forwarding the received information to S 1 and S 2 simultaneously in the third relay forwarding phase.Using  (TS) R, in (19), the transmit power of R broadcasting in the third phase can be given by At the end of the third R forwarding phase, the sampled received signal at S  from R can be given by where  = 1, 2 and  ̸ =  and   ,  S,  , and  S,  are defined as (6).
Finally, the achievable data rate at S  from R is given by where  S, ≜  S,  +  S,  with  2 S, ≜  2 S,  +  2 S,  .In the third relay forwarding phase, the broadcast data rate of R is limited by the effect of the channel   and the employed digital NC, so that the actual achievable broadcast rate at S  from R is where As described above for PS-TWR, we also define the system outage probability based on the analysis in [32,33] as follows: where Theorem 4. For TS-TWR protocol, given a predetermined transmission rate   , the system outage probability also can be calculated as (26) in terms of variants   ,   ,   , , and  , , where 1 (⋅),  2 (⋅),   1 , and   2 are set to be similar to PS-TWR protocol.
Proof.The detailed derivation of the system outage probability  (TS) out for TS-TWR is skipped here, because it follows the same steps as given in the Appendix.

Approximating Expressions of the Outage Probability for TS-TWR.
Due to the theoretical analysis expression of the system outage probability  (TS)  out in ( 26) is complicated containing the modified Bessel functions, it is difficult to obtain an analytic solution of  (TS)  out by using traditional methods.For the sake of simplicity, the approximate expressions of  (TS)  out at extremely high and low SNR regions are formulated in the following theorems.
Theorem 5.For TS-TWR protocol, the approximate expression of the system outage probability  ()  in (26) at high SNR region can be formulated as Mobile Information Systems Proof.The detailed derivation of  (high) TS for TS-TWR protocol is omitted here because it follows the same steps as given in Theorem 2 for PS-TWR protocol.Theorem 6.For TS-TWR protocol, the approximate expression of the system outage probability  ()   in ( 26) at low SNR region can be formulated as  ()    in Proof.The detailed derivation of  (low)

TS
for TS-TWR protocol is also omitted here because it follows the same steps as given in Theorem 3 for PS-TWR protocol.

Theoretical Comparison of PS-TWR and TS-TWR
As mentioned previously, it can be obtained that the expressions of the harvested RF energy  (PS/TS) R, by R in the first two phases and the corresponding transmit power of the relay broadcasting  (PS/TS) R in the third phase in PS-TWR and TS-TWR systems, respectively.In order to compare the two systems, we list the terms  (PS/TS) R , that is, ( 5) and (20), in Table 1 with the only difference   and   .For the two systems, PS-TWR and TS-TWR, the system outage probabilities can be given by ( 9) and ( 24
Based on the above analysis, it can be also achieved that the approximating outage probabilities of TS-TWR are higher than that of PS-TWR even at high and low SNR regions.

Optimization Problem Formulation for PS-TWR.
From the description in Section 3, it can be seen that for PS-TWR, the transmit power   of S  and all channel parameters are known, while the rest parameters such as the conversion efficiency  for the energy harvesting, the power splitting factor   , the time assignment factor   and the distance  S, between S 1 and S 2 are all required to be determined and configured.Besides, all the parameters maybe effect on the system outage performance so that jointly designing them for achieving the minimal system outage probability is meaningful and necessary.In this subsection, we formulate an optimization problem to minimize the outage performance of PS-TWR by jointly optimizing   and   , which can be expressed as min Table 1: PS-TWR versus TS-TWR.

Optimization Problem Formulation for TS-TWR.
For TS-TWR protocol, we also formulate an optimization problem to explore its minimal outage probability by jointly optimizing the time switching factor   of the energy receiver and the time assignment factor   .The optimization problem can be expressed by min (30) 6.3.GA-Based Algorithm.Since both problems in ( 29) and ( 30) are nonconvex and not easy to derive closed-form solutions by using conventional solution methods, to solve the two problems, we present a GA-based algorithm as follows.
GA-based algorithm is a metaheuristic, which iteratively refines an initial population of candidate solution until some termination criterions are satisfied; it starts with randomly creating an initial population of individuals, which is a group of chromosomes.Then each individual is evaluated using a fitness function and a fitness value is allocated to each individual indicating how to close a candidate solution is to an ideal solution.Based on the survival of the fittest, individuals with better fitness will be selected for evolution, or abandoned.The common genetic operations are selection, crossover and mutation.Selection is used to select parents to create new offsprings including tournament selection, roulette wheel selection and rank selection.Crossover varies the programming of an individual or individuals from one generation to the next including one-point crossover, twopoint crossover, and "cut and splice."Mutation causes a certain level of an organism's genes to change at a certain probability so that the problem of local extreme value can be avoided with proper perturbation introduced by mutation including mut, mutate, and mutbga.Finally, once the termination conditions are satisfied, the process of evolution is stopped [26,28,35].
In our work, the main steps of GA-based algorithm are simply described in Algorithm 1 for PS-TWR and TS-TWR.

Numerical Results
In this section, some simulation and numerical results are presented to validate our analysis and discuss the performance of the proposed PS-TWR and TS-TWR protocols.In our simulations, we consider a typical three-node relaying network as shown in Figure 4, in which there is an obstacle between S 1 and S 2 .The relay R is located on the top of the obstacle to help the information exchanging between S 1 and S 2 .Note that the height of the obstacle is varied according to the different environment conditions.
The distance between S 1 and S 1 is denoted as  S, , which is regarded as a reference distance.The variable, 0 <  < 1, is applied to describe the ratio of the distance from S 1 to the obstacle.And ℎ is the height of the obstacle, where we define it as the setting height of R. Therefore, the distance from S  to R can be given by Note that, if ℎ = 0, R is located on the direct line S 1 -to-S 2 , which is generally considered as a model to discuss that R is moving along the direct S 1 -to-S 2 link.If ℎ ̸ = 0, R is located on the top of the obstacle hindering S 1 and S 2 communication, which is common in our real life as shown in Figure 1.The power spectral density of the receiving noise at S  is set to be −100 dBm as well as at R. Besides, the path loss effect is also considered, where the path loss exponent is 3, and the distance of the direct S 1 -to-S 2 link,  S, , is set to be 100 m.

Number Scenarios 1
Fixed Based on the simulation network model as presented in Figure 4, we consider five different system configurations (or scenarios) for comparison, as shown in Table 2 for PS-TWR and Table 3 for TS-TWR, respectively.Besides, unless specifically stated, we set  sr = 1 bit/sec/Hz,  = 1.For simplicity, all the mean values of the exponential random variables

Verification of Analytical Results
. In this subsection, some simulation results are presented to verify our analytical expressions of the system outage probability and the effectiveness of our designed GA-based algorithm, where the Monte Carlo simulation is adopted by using up to 10 5 simples.In Figure 5, we present the system outage performances of both PS-TWR and TS-TWR versus the available S 1 transmit power  1 for  = 0.2 with  2 =  1 and ℎ = 0 based on the 5th scenario as shown in Tables 2 and 3, respectively.

Number Scenarios 1
Fixed system outage probability and GA-based algorithm.Moreover, it shows that the two protocols can achieve lower system outage probability with the increment of  1 .The reason is that more  1 will lead to higher SNR.It is also shown that the system outage performance of TS-TWR is higher than that of PS-TWR, because in the same channel conditions, the system outage performances of PS-TWR and TS-TWR rely on the information received and energy harvested by R. To well balance information transmission and energy harvesting, for TS-TWR, except for the system transmission time assignment and the power allocation, information PS-TWR: GA (optimal  1 ,  2 ,  1 , and  2 ) decoding and energy harvesting processed by TS receiver at R are sequenced over the S  transmission phase with the different time switching factor.But for PS-TWR, except for the system transmission time assignment and the power allocation, information decoding and energy harvesting are indeed processed simultaneously by PS receiver at R over the S  transmission phase with the different power splitting factor.PS-TWR comparing with TS-TWR is more intelligent to allocate the system resources, so it may greatly improve the system outage performance compared with TS-TWR as shown in Figure 5.

Effect of 𝑆 𝑖 's Transmit Power on System Performance.
Figures 6 and 7 depict the system outage performances of both PS-TWR and TS-TWR versus  1 for  = 0.5 and  = 0.2 with  2 =  1 and ℎ = 0, respectively, which mean that in Figure 6, R is placed on the middle of the straight line S 1 -to-S 2 , and in Figure 7, R is closer to S 1 than S 2 .
From Figure 6, it can be observed that the optimal system outage probabilities of the five scenarios as shown in Table 2 decrease as the increment of  1 , and the system outage performance of the 1st scenario is much higher than that of the other four scenarios, which demonstrates that jointly optimizing the flexible power splitting factor and time assignment factor is superior to only optimizing the fixed power splitting factor and time assignment factor.The curves of the 2nd and the 4th scenarios are almost coincident with each other by only optimizing the power splitting factor   with fixed time assignment factor   = 1/3.And the curves of the 3rd and the 5th scenarios are also almost coincident with each other with jointly optimizing the power splitting factor   and the time assignment factor   .But the system outage performances of the 3rd and the 5th scenarios outperform that of the 2nd and the 4th scenarios.In other words, the system outage performance obtained by jointly optimizing the power splitting factor   and the time assignment factor PS-TWR: GA (optimal , with  1 =  2 = 1/3 and  1 =  2 ) PS-TWR: GA (optimal ,  1 , and  2 with  1 =  2 ) PS-TWR: GA (optimal  1 ,  2 with  1 =  2 = 1/3) PS-TWR: GA (optimal  1 ,  2 ,  1 , and  2 )   is better than by only optimizing the power splitting factor   with fixed time assignment factor   = 1/3, or the time assignment factor   can greatly affect the system outage performance with jointly optimizing the power splitting factor   .
The similar results can also be seen in Figure 7, but the curves of the 3rd and the 5th scenarios are close to each other when  1 is within the interval of 0 dBm to 25 dBm and almost coincident when  1 goes to the rest of the value, because more harvested energy should be allocated to  1 in order to reduce the growing path loss firstly with  = 0.2, and then  1 is large enough to meet the system requirements.Besides, the system outage performance gain between the 3rd, 5th scenarios and the 2nd, 4th scenarios is larger than that in Figure 6, which mean that no matter whether R is placed in the middle position of S 1 and S 2 or not, jointly optimizing the power splitting factor   and the time assignment factor   on the system outage performance outperforms only optimizing the power splitting factor   with the fixed time assignment factor   = 1/3.Thus, depending on those different influences, we can reasonably configure system parameters in practice.
Figure 8 shows the system outage probability versus  1 and  for PS-TWR based on the 5th scenario as shown in Table 2, where it shows that the system outage probability achieves its minimum at R deployed closer to source nodes with better channel quality.Figure 9 plots the optimal region of  1 and  for system outage probability, which may guide us to select a proper  1 and  pair to obtain the optimal system outage probability.

Effect of Relay Location on System Outage Probability.
In this subsection, we shall discuss the system performances of PS-TWR and TS-TWR by varying the location of R with different ℎ.As shown in Figure 4, the relay location is described by the ratio  changing in (0, 1), so that we set it   varies from 0.1 to 0.9 with ℎ = 0 and ℎ = 50 m in Figures 10  and 11, respectively.
From Figure 10, we can see that the optimal system outage probabilities of the five scenarios as shown in Table 2 first increase and then decrease with the increment of  and achieve their maximums at  = 0.5, that is, when R is positioned on the middle of the direct link S 1 -to-S 2 .It is noteworthy that the system outage probability is differ from the traditional case where EH is not considered at the relay and the minimal outage probability is achieved when R is deployed in the middle of S  and S 2 .
While, in Figure 11, the system outage probabilities of the five scenarios first decrease and then increase with the increment of  and achieve their minimums at  = 0.5, these results are opposite to that in Figure 10 but similar to the traditional case.The reason may be that when  is small, R is closer to S 1 , a higher energy harvesting efficiency can be yielded at R from S 1 and S 2 .When  is 0.5, R is placed on the middle of the direct link S  -to-S 2 and now lower energy harvesting efficiency can be obtained at R, which may have effect on the system outage problem.When  is large, R is closer to S 2 , which leading to the result is opposite for the symmetric channel model.Besides, from Figures 10 and 11, we can also find that PS-TWR can greatly improve the system outage performance compared with TS-TWR.
To further investigate the effect of the relay location on the system outage performance, we set the height ℎ to be 0 m and 100 m, and the distance ratio  to vary from 0.1 to 0.9. Figure 12 plots the system outage probability when  1 =  2 = 50 dBm and  S, = 100 m.It can be observed that, as ℎ increasing, the optimal outage probability is significantly different.The curve of the optimal system outage probability is convex when ℎ varies from 0 m to 40 m.However, when ℎ changes in (40, 100), the curve is concave.As a result, the maximum outage probability is achieved when the relay is deployed in the middle of the two sources with ℎ changing in (0, 40) as shown in Figure 10, so that, in order to make the system outage performance better, the relay node should be deployed closer to the source node with better channel quality, whereas, when ℎ changes in (40, 100), the result is exactly the opposite when ℎ changes in (0, 40) as shown in Figure 11.
Besides, Figure 13 plots the optimal region of the relay location versus  1 and  for system outage probability corresponding to Figure 12, where the obtained results may guide us to select a suitable location for the relay to achieve the optimal outage probability.

Convergence
Behavior of GA-Based Algorithm.Figure 14 plots the convergence behaviors of the system outage probability by using the GA-based algorithm during 25 generations from the 2nd to the 5th scenarios as shown in Table 2.It can been seen that since the number of optimized parameters is different, the curve of the 5th scenario converges slower than the other three scenarios.For the 2nd and 4th scenarios, the convergence point is found within 5 runs, and the predefined precision of the 3rd and the 5th scenarios is achieved after almost 15 generations.

Comparison of the Exact and the Approximate Outage
Probabilities.The approximate versus the theoretical analysis system outage probabilities based on the 5th scenario as shown in Table 2 for PS-TWR and Table 3 for TS-TWR are plotted in Figures 15(a

Conclusion
This paper investigated SWIPT in a network-coded two-way relay system with exploring the system outage performance.For such a system, we presented two protocols, PS-TWR and TS-TWR to analyze the system outage performance.Besides, we also derived the corresponding approximate expressions of the system outage probability at the high and low SNR regions, respectively.In order to explore effects of the relay position and the sources transmit power on the system outage performance, we formulated two optimization problems to minimize the system outage probability by jointly optimizing the power splitting factor of the energy harvesting receiver and the time assignment factor of transmission phase for PS-TWR, and by jointly optimizing the time splitting factor of the energy harvesting receiver and the time assignment factor of transmission phase for TS-TWR.To solve the problems, we designed GA-based algorithm for them.Numerical and simulation results validated our theoretical analysis.It is shown that by jointly optimizing the time assignment and the SWIPT receiver parameters, a great performance gain can be achieved for both PS-TWR and TS-TWR.It is also shown that the optimized PS-TWR always outperforms the

Figure 2 :
Figure 2: (a) The framework of PS-TWR.(b) Architecture of the relay (R) receiver for PS-TWR.

Figure 3 :
Figure 3: (a) The framework of TS-TWR.(b) Architecture of the relay (R) receiver for TS-TWR.

Figure 4 :
Figure 4: The graph of experimental scene for PS-TWR and TS-TWR.
) and 15(b), respectively.It can be seen that all approximate outage probability results obtained by our analytical expressions in Theorems 2, 3, 5, and 6 are very close to those of the exact ones obtained in Theorems 1 and 4, respectively, which validate our analytical results for the approximate outage operability of PS-TWR and TS-TWR.