1. Introduction
Prolonging the lifetime of a wireless network with fixed energy-supplying devices has become a critical issue [1-11]. Generally, those fixed energy- supplying such as batteries has limited service life. To solve this problem, one solution is to replace or recharge batteries, but it may cost a lot and usually inconvenient, particularly for devices deployed in dangerous environment or embedded in structures. Another way is using the energy harvesting (EH) technology which allows devices to collect energy from the surrounding environment.
Recently, EH has attracted extensive attention and has been considered as a promising approach to realize green communications [1-11]. Conventional EH sources such as solar, wind, vibration, thermoelectric effects or other physical phenomena (see [1-4]), rely on external energy sources that are not components of communication networks. However, these EH techniques require the deployment of peripheral equipment to take advantage of external energy sources. Most recently, a new operation of EH which collects energy from ambient radio-frequency (RF) signals has been proposed, which is based on the fact that RF signals can carry energy and information at the same time [5].
For wireless EH from RF signals, a few works can be found in the literature [5-11]. The idea of simultaneous wireless information and energy transfer (SWIET) was first proposed in [5], where the performance tradeoff between the energy and information rate was investigated. However, the receivers in [5] were assumed to be ideal and able to detect data and extract energy from the wireless signal at the same time. Later, this assumption was proved to be hard to realize in practical systems [6], where the authors proposed a practically realizable receiver architecture design, in which EH and signal detection could be operated in time switching or power splitting patterns, and this architecture has been widely used for various wireless systems [6-11]. Among these works, some of them focused on point-to-point communications (see e.g., [7-8]), while the others considered the relaying systems with SWIET (see e.g., [9-11]). Specifically, in [9], the outage and throughput performances were developed for the one-way transmission model composed of one source-destination pair and an amplify- and-forward (AF) EH relay. In [10], different power allocation strategies were investigated for the scenario where multiple source-destination pairs communicated via the help of a common EH relay. In [11], the outage probability and diversity gain were studied for different EH relaying strategies, where the spatial randomness of the relay locations was first taken into consideration.
As is known, the two-way relay system is a widely model which has been deeply investigated in recent years [12-17]. However, to the best of our knowledge, only a few works investigated the two-way relay system with EH technology [16-17]. Among these works, only one of them considered the SWIET in a two-way relay system with an EH relay node [17]. Specifically, in [17], the outage probability and the ergodic capacity for the two-way relay network were analyzed, where AF relaying protocol was considered.
In this paper, we also focus on SWIET for the two-way relay network with an EH relay node. We consider a scenario where two sources with sufficient energy supply want to exchange their information with the help of an energy-constrained relay. Due to the deep fading over their direct link or the shadowing of the barrier, the direct link between the two sources is unavailable. Compared with previous work, some differences of our work are deserved to be stressed as follows. Firstly, the decode-and-forward (DF) relaying protocol is adopted in our work rather than AF considered in [17], because the DF protocol can ensure better link reliability by blocking noise propagation to the subsequent stages in a multi-hop communication scenario, and the DF analysis is more complicated due to the decoding and re-encoding operation of the relay. Secondly, in [11], the authors investigated the one-way DF relaying transmission with direct link, where the impact of relay’s random locations was first studied. But, in this paper, we focus on the two-way DF relaying transmission. We assume that the relay is located on the line between the two sources, and for such a system, we aim to optimize the system configuration parameters to minimize the system outage probability.
Note that, in the two-way relay system, there are several different transmission strategies. For example, four-phase transmission, three-phase transmission with digital network coding (NC), and two-phase transmission with physical NC. Although applying NC can improve the system spectral efficiency and capacity, four-phase two-way relaying is relatively simpler than two-phase NC and three-phase NC. Because in three-phase NC, dynamic data buffer management is required at the relay, and in two-phase NC, strict synchronization control is necessary at the relay, which make them much more complicated than four-phase two-way relaying to be deployed. Thus, many works still investigated the four-phase two-way relay transmission model because of its wide existence in current wireless communication systems and its easy implementation in practical systems [12][14]. As the first paper investigating the SWIET in two-way relay transmission, we focus on the practically realizable four-phase transmission in this paper. Our main contributions can be summarized as follows:
The rest of the paper is organized as follows. In Section 2, we present the system model and the proposed PSTWR protocol. In Section 3, we describe the process of two-way transmission and analysis the system outage performance. In Section 4, an optimization algorithm is proposed to find the optimal system parameters to achieve the minimum system outage probability. In Section 5, we provide numerical results. Finally, the conclusion is followed in Section 6.
2. System Model
2.1 Assumptions and Notations
Consider a two-way wireless relay network which has two sources (namely, u1 and u2 respectively) and an EH relay R . The two sources want to exchange their information with each other via the relay through orthogonal channels such as different time slots or non-overlapping frequency bands. In this paper, we assume that each node transmits in different time slots. Let f1, g1, f2, g2 denote the channel gain of u1 to R channel, u2 to R channel, R to u1 channel and R to u2 channel respectively. All the channel coefficients are assumed to be independent complex circular symmetric Gaussian random variables, following a Rayleigh distribution. The distance from u1 to R and from u2 to R are denoted as d1 and d2 , respectively.
In this paper, the sources transfer both information and energy to R through its own transmitted RF signals simultaneously. The delivered energy can be obtained by R from the recipients, and used for the following communications. We assume that the energy constrained relay recharges its battery only by using the energy of its observations from u1 and u2 , and the battery of the relay is assumed to be sufficiently large, so no energy overflow is required to be considered. The harvested energy from u1 and u2 is exhausted to relay the information for the two users in the following phases. We also assume that R employs the DF relaying strategy and operates in a half-duplex mode. All the nodes are equipped with a single antenna. Based on these, we shall describe the proposed PSTWR protocol in the following subsection.
2.2 Proposed PSTWR Protocol
Fig. 1 illustrates the transmission process and the architecture of the relay receiver in the PSTWR protocol. Let Pu1 and denote the power of the received signal from u1 and u2 respectively, and T denotes the total time period of each round of two-way transmission. By adopting the equal time division strategy, T is equally divided into four phases, thus each phase lasts for a time duration of T/4. During the first phase, u1 transmits its information to R , in which part of power is used for the information transmission from u1 to relay, and the other part of power is used for energy harvesting, where 0≤α≤1 denotes the power splitting ratio. During the second phase, similar to phase 1, u2 transmits its information to R , among which part is used for the information transmission from u2 to relay, and the other part is used for energy harvesting. After the first two phases, R has already harvested power from u1 and u2 . Then, in the third phase, R decodes and re-encodes the signal it received, and uses part of the harvested energy for the information transmission from R to u1 . In the fourth phase, similar to phase 3, the remaining energy is used for the information transmission from R to u2 . For convenience, we assume the same α for u1 and u2 , and the analysis of the system outage performance can be easily extended to different α for u1 and u2 .
Fig. 1.PSTWR protocol and architecture of relay receiver.
Fig. 1 also describes the architecture of the relay receiver in the PSTWR protocol. As is shown, the received signal yr at the relay antenna is split by the power splitter in α:1-α proportion, in which part of power is sent to the EH receiver, and the remaining part is input into the information receiver. Note that yr is corrupted by two noises, where nr,a is introduced by the receiving antenna which is modeled as a narrowband Gaussian noise, and nr,c is the sampled additive noise due to the RF band to baseband signal conversion. The details of the EH receiver and the information receiver can be found in [6].
3. Outage Probability Analysis
In this section, we shall first describe the process of the two-way transmission, and then analysis the explicit expression for the system outage probability.
As illustrated in Fig. 1, ui (i=1,2) transmits its information to the relay during the i-th phase, and at the end of the i-th phase, after the processing of the relay receiver, the sampled baseband signal at the relay is given as follows
where 0≤α≤1 denotes the power splitting ratio, Pi is the transmit power of ui , m denotes the path loss exponent, si denotes the sampled and normalized information signal from ui . hi denotes the channel from ui to R , and hi=f1 for i=1 and hi=g1 for i=2 . denote the baseband additive white Gaussian noise (AWGN) with variance due to the relay’s receiving antenna and the sampled AWGN with variance due to the conversion from RF band signal to baseband signal, respectively.
The energy that R harvests from ui is given by
where 0<η≤1 is used to describe energy conversion efficiency. So, the relay’s transmit power harvested from ui is given by
The data rate from ui at R is given by
Defining as the overall AWGN at the relay in the first two phases, so
After the first two phases, the relay has already harvested Pr,1+Pr,2 transmit power from u1 and u2 in total. Then, R decodes and re-encodes the received signals and redistributes the harvested power in θ:1-θ portion, such that θ(Pr,1+Pr,2) part is used for the information transmission to u1 in the third phase, and the remaining part (1-θ)(Pr,1+Pr,2) is for the information relaying to u2 in the fourth phase.
Therefore, at the end of the k-th phase (k=3,4) , the sampled received signal at ui(i=1,2) is given by
where j=1,2 and j≠i , k=3 for i=1 and k=4 for i=2 , respectively. θ* = θ for i=1 and θ* = 1-θ for i=2 , respectively, 0≤θ≤1 is the transmit power redistribution factor, nu,ai and nu,ci are the baseband AWGN with variance σ2u,ai and the sampled AWGN with variance σ2u,ai at ui , respectively. hk denotes the channel from the relay to ui , and hk=f2 for k=3 and hk=g2 for k=4 . The date rate at ui is given by
Defining nu,i=nu,ai + nc,ai as the overall AWGN at ui , we have that
In traditional one-way relay network, an outage occurs if either link’s rate of two hops falls below the targeted rate R0 . Comparatively, the two-way relay network has two communication tasks which refer to four transmission links. Any link failure over the four links may result in system outage. So, the outage probability Pout for the four phase two-way relay transmission can be calculated as
Theorem 1: Given a target transmission rate R0 , the outage probability for the two-way relay network with an EH relay is given by (8) in the next page, where are the mean value of the exponential random variables ｜f1｜2 ｜f2｜2 ｜g1｜2 and ｜g2｜2 , respectively. K1(·) and K2(·) denote the first-order and second-order modified Bessel function of the second kind respectively.
Proof: See the appendix.
Since the exact expression of Pout is complicated, we derive its approximation expression at high SNR in the following corollary.
Corollary 1: The outage probability in (8) can be approximated by (9) at high SNR as follows
Proof: For , the modified Bessel function of the second kind has the approximate expression [21] as follows
where Γ(ν) denotes the Gamma function. At high SNR, a, b, c and d contained in the denominators of the variables in K1(·) and K2(·) are relatively high, which makes the variables in K1(·) and K2(·) in (8) are very close to zero. So the approximation in (10) can be used. Substituting K1(x)=1/x and K2(x)=2/x2 into (8), the approximation expression of Pout at high SNR can be obtained.
Remark 1: With the system outage probability obtained in (8), the system spectral efficiency of the proposed PSTWR protocol for such a two-way relay network can be given by
where B denotes the system bandwidth, and the coefficient 1/2 is due to the fact that four equal phases are used to transmit two new signals.
4. Outage-Minimal System Design
4.1 Optimization Problem Formulation
In a practical system with specific parameters, that is, channels distribution and source-relay distance, it is desirable to obtain the optimal configuration pair of α and θ to achieve the minimum system outage probability. The system optimization problem can be formulated as follows:
Because of the Bessel functions involved in the analytical expressions of Pout shown in (8), it is difficult to obtain an analytic solution of α and θ. To solve this problem, in the following subsection, we shall design a genetic algorithm (GA) based optimization algorithm to obtain the optimal solution of α and θ to achieve the optimal outage performance.
4.2 GA-Based Algorithm
Genetic algorithm is a global random search and optimization method which imitates the natural evolution mechanism. It is a general optimization algorithm which can be applied to most of the function optimization problems and has been widely used to a lot of optimization applications [18].
GA starts with the generation of a random population, which is a group of chromosomes. Each chromosome has a fitness which is evaluated against the objective function. According to the survivor selection criterion based on survival of the fittest, chromosomes with better fitness will survive for evolution while chromosomes with less fitness will be discarded. The evolution includes three operations: mate selection, crossover and mutation. Mate selection selects chromosome mates with better fitness from the survivors to create new offspring. Crossover is then executed over the selected chromosome mates to reproduce new offspring. Crossover is a process of gene recombination which can transfer partial genes from parents to offspring. Mutation is implemented to alter partial genes of offspring, which can avoid converging into local optimal solution fast. That is to say, new genes are generated after mutation, which leads to searching solutions in distinct area of solution space. The evolution process repeats until the termination conditions are satisfied. In this work, α and θ can be regarded as genes respectively, and the combination of α and θ compose a chromosome. Objective function in (12) is used to calculate each chromosome’s fitness. Qmin(t) denotes the optimal solution of the t-th generation, and δ is the predefined precision of GA. Main steps of the GA-based optimization algorithm are as follows:
The computational complexity of the proposed GA-based algorithm depends on the number of iterations Nite in GA, the number of chromosomes Kini in each iteration, and the complexity in evaluating the fitness value in (8), which has the computational complexity of O(1) . Therefore, the total complexity of our proposed method is O(Nite·Kini) . To the best of our knowledge, the convergence of GA for the case of finite iteration number is still an open problem [19]. So in this paper, instead of giving theoretical analysis, we shall investigate the convergence of GA-based optimization algorithm by simulations in Section 5.
5. Numerical Results
In this section, we provide some numerical results to verify our theoretical analysis on the system outage probability and the effectiveness of the proposed GA-based algorithm. Besides, we also discuss the effects of various system parameters including power splitting ratio α, transmit power redistribution factor θ, and source-relay distance: d1 and d2 on the system outage performance by simulations.
Unless specifically stated, we set R0=1bit/sec/Hz, η=1, P1=P2=1Watt, B=1Hz, and m=2.7 (which corresponds to urban cellular network). All the mean values of the exponential random variables ｜f1｜2, ｜f2｜2, ｜g1｜2 and ｜g2｜2 are set to be 1. For simplicity, we assume that And in GA, Kini=100, ε=0.5, μ=0.05 and δ=10-5.
5.1 Verification of the Analytical Outage Probability
In this subsection, simulation results are obtained through the Monte Carlo simulation using (7) to justify our analytical expression for the system outage probability in (8). The antenna noise variance and the conversion noise variance are set to be 10-5 , θ is set to be 0.51.
From Fig. 2, it can be seen that, the analytical and the simulation results match well for all α (0≤α≤1), this verifies the analytical expression for Pout presented in Theorem 1.
Fig. 2.Outage probability: numerical vs simulation.
5.2 Effect of α and θ on System Outage Probability
Fig. 3 (a) plots the optimal system outage probability for different α . The optimal outage probability means that, for each particular α, we calculate all the possible outage probabilities obtained against different θ , and choose the lowest outage probability as the optimal one. It can be observed that, no matter what value of θ is, the optimal outage probability decreases as α increases from 0 to the optimal value (α=0.67), and start increasing as α increases from the optimal value. The reason is that, the relay obtains less transmit power (Pr,1+Pr,2) from energy harvesting for smaller α than the optimal α , which incurs more outages in phases 3 and 4. On the other hand, when α gets higher, the relay may obtain more transmit power than the optimal value. Thus, less power is left for the users to transmit their own information to the relay. Consequently, poor signal strength is observed at the relay, which makes the relay hard to decode the signal correctly and results in higher outage probability.
Fig. 3.(a) Optimal system outage probability for different α (b) optimal system outage probability for different θ.
Fig. 3 (b) plots the optimal system outage probability for different θ. Similarly, the optimal outage probability means that, for each particular θ, we calculate all the possible outage probabilities obtained against different α , and choose the lowest outage probability as the optimal one. It can be observed that, no matter what value of α is, the optimal outage probability is achieved when θ=0.5 . This is due to the fact that, when the system is symmetric (where P1=P2, d1=d2 and independent identically distributed channels fi and gi , i=1,2), the optimal transmit power redistribution strategy is to equally distribute the relay power to the two users.
5.3 Optimal Region of α and θ for Optimal Outage Probability
Let P*out denote the minimal system outage probability. It is assumed that if Pout-P*out ≤ 10-5 , Pout □ P*out . With this assumption, the corresponding α and θ of Pout can be considered as the α* and θ* .
Fig. 4 (a) shows the outage probability versus α and θ , where it shows that P*out=0.3%. Fig. 4 (b) plots the optimal region of α and θ , and all the pairs of α and θ within the gray area lead to Pout-P*out ≤ 10-5 . It shows that the optimal region is Pout={Pout(α,β): α∈[0.64,0.70], β∈ [0.45,0.54]} . The Pout may guide us to select a proper α and θ pair to obtain the optimal outage probability.
Fig. 4.(a) 3-dimensional graph for system outage probability (b) optimal region of α and θ for optimal outage probability.
5.4 Effect of Relay Location on System Outage Probability
To investigate the influence of the relay location on the system outage probability, the distance from relay to u2 is set to be d2=2-d1. Fig. 5 (a) plots the optimal system outage probability for different d1. It can be observed that the optimal outage probability increases as d1 increases, and achieve its maximum when d1=d2=1 , i.e., the relay is deployed in the middle of the two sources. It is noteworthy that the system outage probability is different from the traditional case where EH is not considered at the relay and the minimal outage probability is achieved when the relay is deployed in the middle of the two sources.
Fig. 5.(a) Optimal system outage probability for different d1 (b) optimal α and θ vs d1.
Fig. 5 (b) plots the optimal α and θ versus d1. It can be observed that θ increases as d1 increases, which can be easily understood: more harvested energy should be allocated to u1 in order to combat the growing path loss. As for α, it increases as d1 increases, and achieve its maximum when d1=1, and later, it starts decreasing as d1 increases. We also note that when d1=d2=1, θ=0.5 and α=0.67 , which corresponds to our previous analysis of Fig. 3.
5.5 System Spectral Efficiency of the Proposed PSTWR Protocol
To explore more system performance limit for such a two-way relay network with an EH relay, we also plot the system spectral efficiency of the proposed PSTWR protocol in this subsection. Fig. 6 (a) plots the system spectral efficiency for different d1 and Fig. 6 (b) shows the effects of two sources’ transmit power P1 and P2 on the system spectral efficiency, where we set P1=1, and let P2 vary from 0.5 to 1.5. It can be seen that, as P2/P1 increases, the system spectral efficiency also increases, which is due to the fact that, the system outage probability decreases as P2/P1 increases.
Fig. 6.(a) System spectral efficiency for different d1 (b) for different P2/P1.
5.6 Convergence Behavior of the Proposed GA-Based Algorithm
For an arbitrary two-way relay system with given parameters, the proposed GA-based optimization algorithm can be used to obtain the optimal α and θ to achieve the optimal outage performance. Fig. 7 illustrates the convergence behavior of the proposed GA-based algorithm. It can be seen that the algorithm converges fast, and the predefined precision is achieved within 20 runs.
Fig. 7.Convergence behavior of the GA-based algorithm
6. Conclusion
In this paper, a two-way transmission network with an EH relay was considered. By adopting the power splitting receiver architecture, we proposed a PSTWR protocol to enable the simultaneous information processing and energy harvesting at the relay for the two-way transmission. Then, the explicit expression for the system outage probability was presented, based on which, we discussed the effects of various system parameters on the system outage performance. Additionally, a GA-based algorithm was proposed to find the optimal pair of system parameters to achieve the minimal outage probability. Extensive numerical results demonstrated the accuracy of the analytical results and revealed that the GA-based algorithm is effective and converges fast.
For future work, we intend to extend the performance analysis of SWIET to the model of two-way relay network with network coding technology employed, and investigate the performance gain brought by the combination of network coding and energy harvesting.
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