Energy Efficiency Maximization in the Wireless-Powered Backscatter Communication Networks with DF Relaying

This paper focuses on the design of an optimal resource allocation scheme to maximize the energy e ﬃ ciency (EE) in the wireless-powered backscatter communication networks (WPBCN) with decode and forward (DF) relaying. The two di ﬀ erent devices are supported to operate in di ﬀ erent modes, the harvest-then-transmit (HTT) mode and backscatter communication (BackCom) mode, respectively. In particular, we formulate an optimization problem to maximize system EE by jointly optimizing the transmit power of hybrid access point (H-AP) and the system time resource allocation. To deal with the nonconvex problem, we investigate the characteristics of the EE expression and a variable substitution approach. Then, the optimal power allocation scheme and iterative optimization algorithm were derived for achieving maximum EE. Extensive simulation results have demonstrated that the system EE can be improved about 10% because the proposed scheme provides more ﬂ exibility to utilize the resource e ﬃ ciently by employing the proposed scheme.


Introduction
With the development of the Internet of Things (IoT), numerous wireless devices (WDs) have been deployed widely in the world to provide ubiquitous connectivity, which improves human being's life greatly in all aspects [1,2]. However, the sustainable energy supply is a major challenge for the evolvable IoT networks. Fortunately, a new technology named as wireless power transfer (WPT) has been deemed as an attractive promising approach to power WDs conveniently and steadily [3][4][5][6][7][8]. Wireless-powered communication network (WPCN) is a novel communication solution for IoT that using WPT techniques solves the problem of sustainable energy supply for the tiny WDs. Consequently, WPCN has been widely studied in recent years, especially in [5][6][7][8][9]. A well-known protocol for WPCN is named as "harvest-then-transmit (HTT)" protocol proposed in [8]. Following the HTT protocol, hybrid access point (H-AP) first broadcasts the wireless energy to its served users for energy harvesting, and then, users transmit their information actively to H-AP by utilizing the harvested energy.
Recently, ambient backscatter communication (Back-Com) [10] has been emerging as a promising technology for low-energy communication systems that was designed to communicate with WDs nearby without resorting to any existing energy supply or storage device. Different from the devices using the HTT mode, the BackCom devices transmit information by modulating and reflecting the instantaneous incident signals passively [11,12]. Hence, the active RF components are not required at all, which can significantly decrease the circuit energy consumption and meet the low-power requirement of IoT devices. Furthermore, the dedicated energy harvesting (EH) time is also not necessary, and then, the information transmission time can be extended.
Essentially, there exist some different tradeoffs between EH time and data transmission time for HTT protocol and BackCom. They may complement each other for increasing the data rates and energy utilization while they are used in IoT. Hence, applying BackCom in WPCNs and wirelesspowered backscatter communication networks (WPBCNs) is a very efficient way to exploit the advantages of the HTT mode and the BackCom mode, which have gained extensive attention in academic field, especially in [12][13][14][15][16]. The authors in [12] presented an optimal time resource allocation method to achieve the maximal throughput for WPBCNs. The literatures [13][14][15][16] played an emphasis on optimizing the EE performance of WPBCNs.
It is to be noted that EE is a crucial performance metric in IoT to achieve a better tradeoff between data rates and the overall energy consumption. Due to the characteristics of WPT, the energy cost of WPCNs, especially the energy consumption of the dedicated energy source devices, has drawn a great deal of attention [14,15]. In [17], the authors proposed an EE resource allocation scheme which employed a Dinkelbach-based iterative algorithm to obtain the optimal time allocation, reflection coefficient, and transmit power of the dedicated RF energy source in BackCom networks. The literature [18] utilized energy beamforming communication and ambient BackCom to overcome the energy problem of network, and a EE cooperative communication scheme was presented. The EE maximum problem was investigated in cooperative sensor networks with bidirectional wireless information and power transfer [19]. By studying the derivative properties of the objective function, the authors derived the optimal power allocation and time allocation. The authors in [20] studied the EE performances for an unmanned aerial vehicle-(UAV-) assisted backscatter communication network. They maximized the EE of the network by jointly optimizing the UAV trajectory, the backscatter device scheduling, and the carrier emitter transmit power. The literature [14] studied the EE of WPBCNs which consist of two types of WDs that operate in different modes, the HTT mode and BackCom mode, respectively. The authors in [14] study the network which includes two different types WDs. One device named as HD, operating in the HTT mode, transmits its information directly to the access point (AP), and the other device named as BD, operating in the BackCom mode, backscatters its information directly to AP. By jointly optimizing the energy beamforming vector, power allocation, and time allocation, the system maximum EE is achieved. Obviously, the researchers have done many works in improving the EE of WPCNs and a lot of valuable achievements have been obtained. However, the EE optimization of WPBCNs that consists of two types of WDs has not been sufficiently exploited by the existing works.
The authors in [12] proposed a new network structure in which HTT mode is adopted in the last hop and BackCom mode is used in the other hops. They assumed that the devices could only consume the energy harvested within the current time block. Therefore, based on the above assumption, the nodes do not harvest the energy after they finish the information forwarding in one time block, which leads to the reduction of harvested energy and the inefficient energy utilization. Both in [19,21], the authors think that the devices can store the harvested energy in their battery and do not consume all the energy harvested in the current time block. Especially in [19], the remote device is designed to harvest the energy from the relay during the phase of relay transmitting information to the base station. Inspired by the literatures [19,21], we develop a new network model and the corresponding communication protocol which improve the EE and throughput of new model.
In this paper, we investigate a new WPBCN with DF relaying (WPB-R-CN) which is more suitable to the realistic IoT application scenario. WPB-R-CN consists of one hybrid access point (H-AP), one relay, and one backscatter user (SU) which is shown in Figure 1. Following the literature [12], SU operates in BackCom mode and relay transmits the information by operating in HTT mode. Different from [12], SU is required to harvest energy from RF signal transmitted by a relay device during the phase of relay transmitting information to H-AP. The energy harvested during this time by SU will be stored in its battery for use in the next time block. Obviously, the proposed new model can improve system EE further.
Obviously, WPB-R-CN is a new network model which is different with the existing models, such as the models of literatures [12,14], which are more similar to our proposed model. In [12,14], BackCom mode and HTT mode are used simultaneously in the models. However, in [14], the device named as HD, operating in the HTT mode, transmits its information directly to access point (AP) and the other device named as BD, operating in the BackCom mode, backscatters its information directly to AP. The authors in [14] only study one-hop link performane for two different types WDs. Different from the model of [14], the authors in [12] study multihop hybrid backscatter communication network. However, the other nodes do not harvest the energy transmitted by the node operating in HTT mode which leads to the reduction of harvested energy and the inefficient energy utilization. Therefore, the model we studied in this paper is a new one. No existing algorithms can achieve the maximum EE of WPB-R-CN.
We aim at WPB-R-CN EE maximization by optimizing its resource allocation and H-AP transmit power. To obtain the optimal parameters, we formulate a nonconvex system EE maximization problem. To make the optimization problem tractable, we investigate the characteristics of the EE expression. Then, the optimal power allocation scheme and iterative optimization algorithm were derived for solving the nonconvex optimal problem and achieving maximum EE. Our contribution can provide a useful insight for optimizing system performance in both system throughput and EE in WPBCN.
The main contributions of our work are summarized as follows: (iii) We formulate a system EE maximization problem and obtain the joint power allocation scheme for the proposed model. By investigating the characteristics of the EE expression, the optimal power allocation scheme and iterative optimization algorithm were derived for achieving maximum EE (iv) We investigate the performances of the optimal power allocation scheme and the proposed iterative optimization algorithm. Comparing their performances with the other two schemes, our proposed scheme is proved to be efficient in improving system EE performance The remainder of the paper is organized as follows. System model and communication protocol are described in Section 2. The problem of jointly optimizing H-AP transmit power and time resource allocation scheme is formulated to maximize the system EE in Section 3. Section 4 gives the optimal time allocation and power allocation schemes for maximizing the system EE. Simulation experiments are conducted to verify the effectiveness of the proposed strategies in Section 5. Finally, we conclude the paper in Section 6.

System Model and Communication Protocol
2.1. System Model. We consider a WPB-R-CN illustrated in Figure 1, which consists of one H-AP, one relay, and one SU. Each device is equipped with one antenna. H-AP is assumed to have sustainable power supply acting as a wireless power provider and information receiver. Relay and SU operate in the HTT mode and the BackCom mode, respectively. They do not have embedded energy supplies. Both relay and SU can harvest the energy from RF signal using their EH circuit and store the energy into a rechargeable battery. The stored energy can be consumed while relay and SU transmit their information. Moreover, by using the existing energy in SU battery, the information transmission can be initialized before energy harvesting and SU can consume all the harvested energy during the frame [19]. Each channel among nodes is assumed to be undergoing independent identically distributed (i.i.d) quasistatic block fading [22]. And the channels are reciprocal in two directions [19,22]. Assume that no direct link exists between nodes H-AP and SU due to severe path loss and/or shadowing. Therefore, relay node has the obligation to relay the data of SU to H-AP.
Let h 0 , h 1 , h 2 denote the channel response of the relay-SU link, the H-AP-relay link, and the H-AP-SU link, respectively. Similarly, d 0 , d 1 , d 2 are the distance of relay and SU, H-AP and relay, and H-AP and SU. Let n 1 , n 2 , n 3 denote the additive white Gaussian noise at the receiver of SU, relay, and H-AP, respectively, n i~C N ð0, σ 2 Þ, i ∈ f1, 2, 3g. Without loss of generality, relay is closer to H-AP than SU in the system which means d 1 < d 2 , resulting in jh 1 j 2 > jh 2 j 2 . The duration of each frame T f is one second, and the system bandwidth is B Hz. P cr is the circuit power consumed while the H-AP and relay work as the receiver. P ct is denoted as the circuit power consumed while SU and relay work as the transmitter. Figure 2, one time-frame duration T f is divided into three time phases that are denoted by τ 0 , τ 1 , and τ 2 , respectively. During the first time phase τ 0 , H-AP transfers its wireless energy to relay and SU by transmitting the modulated signal sðtÞ = ffiffiffiffiffiffi P H p xðtÞ, where P H denotes the transmit power of H-AP and xðtÞ is a known signal with E½jxðtÞj 2 = 1. Correspondingly, both relay and SU work as the energy harvester and harvest the energy from the ambient RF signal using their EH circuit and store the energy into a rechargeable

Proposed New Communication Protocol. As shown in
where η ∈ ð0, 1 denotes the energy harvesting efficiency. The harvested energy of relay is split into two parts. One part energy is used to maintain the circuit consumption of the relay during the time τ 1 , and the other part is used to transmit information during the time τ 2 . The harvested energy of SU is used to maintain its circuit consumption while SU backscatters the information during the time τ 1 . During the second time phase τ 1 , H-AP continues to transmit the modulated signal sðtÞ. SU enters the active state to backscatter its information to relay by utilizing incident signals from H-AP, and relay also enters the active state to decode the information of SU. The received signal y 1 ðtÞ by SU is given by Then, SU modulates its own signal c 1 ðtÞ on the received signal y 1 ðtÞ and c 1 ðtÞ satisfies E½jc 1 ðtÞj 2 = 1. Therefore, the backscattered signal y 2 ðtÞ by SU is written as The signal received by relay is denoted as y 3 ðtÞ which is expressed as Obviously, The first term of y 3 ðtÞ is the received desired signal by relay. The second term of y 3 ðtÞ is the noise caused by backscattering process. The third term of y 3 ðtÞ is the interference from the H-AP, the power of which is typically larger than that of the desired signal. Following the literatures [23,24], successive interference cancellation (SIC) technique is used to remove it from the y 3 ðtÞ since relay has known the information sðtÞ well. Thus, the signal-noise-ratio (SNR) at relay during the second time phase τ 1 is given by While jh 0 j 2 < <1, then equation (6) can be written as During the third time phase τ 2 , H-AP stops transmitting the modulated signal sðtÞ and acts as a information receiver. Relay operates in HTT mode and transmits the information decoded during the time τ 1 . SU enters sleep state and acts as energy harvester. It harvests the RF energy transmitted by relay. Let P R denote the transmit power of relay which is written as Relay transmits the information c 2 ðtÞ to H-AP, and c 2 ðtÞ satisfies E½jc 2 ðtÞj 2 = 1. The received signal of H-AP y 4 ðtÞ and SNR γ 2 at H-AP is, respectively, given by The harvested energy E U 1 by SU is expressed as Thus, the total energy harvested E U by SU is written as Consequently, the SU-relay link and relay-H-AP link throughput are, respectively, calculated as H-AP broadcasts modulated signal to transfers energy; Relay and SU 1 works as a energy harvester.
H-AP broadcasts modulated signal; SU 1 backscatters its information to relay; Relay decodes the information.
Relay transmits SU 1 information to H-AP; H-AP decodes SU 1 information transmitted by Relay; SU 1 works as a energy harvester.
Following the literature [19], the system throughput R is given by Obviously, since both SU and relay are powered by harvested energy, only H-AP device consumes the energy in the system. Therefore, the total energy consumption of the whole system is also the energy consumption of H-AP which consists of two parts: the energy consumed in H-AP transmitting RF signal phase and the energy consumed in H-AP decoding information phase. Then, the total energy consumption of the whole system is written as where ζ ∈ ð0, 1 is the power amplifier efficiency.

Problem Formulation and Analysis
In this section, we formulate an optimization problem to maximize the system EE by jointly optimizing time resource allocation and H-AP transmit power. The system EE ψðP H , τ 0 , τ 1 , τ 2 Þ is defined as the ratio of the achievable system throughput to the total energy consumption [14,16], which is given by Then, the optimization problem is formulated as In problem P1, C1 indicates that the summation of three time variables equals to the duration of one frame T f . C2 limits that each time variables must be nonnegative. C3 constrains the transmit power range of H-AP. C4 and C5 guarantee that the total energy consumed does not exceed the total energy harvested for SU and relay, respectively. Notice that the WPB-R-CN is a new network which is distinguished from the conventional relaying and the main difference can be found in Section 2. These differences make the formulated EE problem noticeably different from that of the conventional relaying network.
Obviously, the above-formulated EE optimization problem is appealing in practice. For one thing, the time resource allocation can be exploited to satisfy the maximum system throughput requirement. For another, the EE can be further improved by optimizing the transmit power of H-AP. However, problem P1 cannot be solved directly for the following two main challenges. First, both the nominator and denominator of problem P1 include the variables fτ 0 , τ 1 , τ 2 g, P H . Second, the optimization variables fτ 0 , τ 1 , τ 2 g, P H are coupled in both objective function and the constrains C4 and C5. Consequently, P1 is a nonconvex problem which cannot be solved directly. In general, there are no standard methods to solve the nonconvex optimization problems efficiently. Note that when P H remains unchanged, the bigger nominator of objective function leads to the bigger EE. Then, the original problem P1 can be written as Obviously, the problem P2 is also nonconvex optimization problem which is too difficult to obtain a globally optimal solution.

Energy Efficiency Maximization Resource Allocation
To solve problem P2 for obtaining its optimal solution fτ * 0 , τ * 1 , τ * 2 , P * H g, we decompose the problem P2 into two subproblems to make it more tractable according to reference [19].

Optimal Resource Allocation Scheme.
First, we formulate one subproblem to achieve the maximum system throughput by optimizing the resource allocation while P H is considered as remaining unchanged. The optimal resource allocation is denoted as fτ * 0 , τ * 1 , τ * 2 g. Let R * denote the system throughput which corresponds to the optimal resource allocation fτ * 0 , τ * 1 , τ * 2 g. It means that R * > R + , ∀ fτ + 0 , τ + 1 , τ + 2 g ≠ fτ * 0 , τ * 1 , τ * 2 g when P H remains unchanged, where R + denotes the system throughput which corresponds to the resource allocation fτ + 0 , τ + 1 , τ + 2 g. Therefore, the first subproblem denoted as P2a is formulated as Accordingly, P2a is still a nonconvex problem because there are coupling relationships among different optimization variables. In order to solve it, we present the following lemmas. Lemma 1. R 1 = R 2 is a necessary but insufficient condition for problem P2a obtaining the optimal solution.
We apply Lemma 1 to the problem P2a. Then, the new optimization problem P3 is formulated as Similar to problem P2a, problem P3 is also a nonconvex problem. To tackle this problem, we first divide the problem P3 into two subproblems and solve two subproblems sequently. Finally, We use the optimal solutions of the two subproblems to obtain the optimal solution of problem P3 by iterative optimization and proportional compression algorithm.
At first, we relax the variable τ 2 and make τ 2 = 0. Correspondingly, the constrain C1 becomes the new constrain τ 0 + τ 1 = T f . Let τ 0 = αT f and τ 1 = ð1 − αÞT f , where 0 < α < 1 is the factor of SU transmission time. The first subproblem P3a is formulated as According to the references [4,17,22], P cr ≤ P ct is always satisfied in WPCN. Obviously, E R 0 > E U is always satisfied according to the system model. Thus, the constrain C5 can be satisfied while the constrain C4 is satisfied. Based on the above conclusion, we formulate problem P4 as follows: Obviously, P4 is a more tractable problem. By use of the optimization method in [12,17], P4 can obtain the maximum throughput while the constrain C4 satisfies E U = P ct τ 1 . Substituting τ 0 = αT f , τ 1 = ð1 − αÞT f and equation (2) into E U = P ct τ 1 , the following equation can be obtained shown as follows: The optimal solution α * can be easily calculated from equation (16) which is given by Substituting the optimal solution α * into the objective function, the maximum throughputR 1 of problem P3a is achieved which is written aŝ Secondly, we relax the variable τ 1 to satisfy τ 1 = 0 and relax the variable T f to satisfy T f = T R , where 0 < T R < T f denotes the transmission cycle time of relay. Additionally, to simplify the optimization process, we make τ 0 = βT R and τ 2 = ð1 − βÞT R , where 0 < β < 1 is the factor of relay transmission cycle time. Thus, another subproblem P3b of problem P3 is formulated as Substituting τ 0 = βT R , τ 2 = ð1 − βÞT R and equation (7) into equation (12), R 2 can be written as Let c = ðηP H jh 1 j 4 Þ/σ 2 and b = 1 − ðP ct jh 1 j 2 Þ/σ 2 . Then, the objective function R 2 can be rewritten as Lemma 2. The optimization problem P3b is convex, and the optimal parameter β * = ðx * − bÞ/ðx * − b + cÞ and x * is the solution of equation Proof. See the appendix. Substituting the optimal solution β * into the objective function of P3b, the maximum throughputR 2 of problem P3b is achieved which is given bŷ In order to solve problem P3, we makeR 2 =R 1 to obtain T R which is expressed as Wireless Communications and Mobile Computing According to our model, we can easily get 0 < T R < T f for the cause of jh 1 j 2 > jh 2 j 2 . To find the optimal solution f τ * 0 , τ * 1 , τ * 2 g, we define τ 01 = α * T f , τ 11 = ð1 − α * ÞT f , τ 02 = β * T R , and τ 22 = ð1 − β * ÞT R . Obviously, we select τ 00 = max f τ 01 , τ 02 g which can satisfy R 1 = R 2 . Then, we devise a iterative optimization algorithm to obtain the optimal solution fτ * 0 , τ * 1 , τ * 2 g of problem P3 which is given in Algorithm 1 with an error ε.
where P + H is the unique solution satisfying gðP + H Þ = 0. To solve the optimal solution P * H , we devise a power allocation algorithm which is described in Algorithm 2 with the given error δ.

Simulation Results
In this section, the performance of WPB-R-CN is evaluated by the system-level simulation. The following parameters are used for simulation unless stated otherwise. The simulation duration is ten time frames, and the channel model between arbitrary nodes is modeled as jh i j 2 = jg i j 2 d −3 i [22], where g ĩ CN ð0, 1Þ denotes the channel coefficient between two nodes and is set as g i =1 for simplicity [14]; d i is the distance between adjacent nodes. System bandwidth is set B =100 Hz. The distance between relay and SU is set d 0 =20 m, the distance between H-AP and relay is set d 1 =14 m, and the distance between H-AP and SU is set d 2 =30 m. P max =30 dBm [14], σ 2 = −70 dBm, η = 0:6 [12], T f = 1:0 s, P ct = −16:5 dBm [12], and P cr = −20:5 dBm [12].
Assume that fτ * 0 , τ * 1 , τ * 2 , P * H g is an optimal solution for achieving maximum EE of the system. According to Algorithm 1, if the energy E U 0 harvested by SU during the time τ * 0 is greater than the energy consumed by SU maintaining the circuit normal operation during the time τ * 1 , SU does not require to harvest the energy from the relay during the time τ * 2 . Therefore, it does not need to execute iteration. This scenario is not considered in this section. We mainly play an emphasis on the other scenario that includes E U 0 < P ct τ * 1 and the energy E R 0 harvested by relay during the time τ * 0 being enough to transmit the required data to H-AP. Therefore, SU needs to harvest the energy from the relay during the time τ * 2 to store it into the rechargeable battery for use in the next frame. Figure 3 depicts the EE of the proposed Algorithm 1 versus the number of iterations under different H-AP transmit powers P H . It can be seen that Algorithm 1 converges after only three iterations, which demonstrate the efficiency of Algorithm 1. Simultaneously, Figure 3 shows that system EE increases while H-AP transmit power P H increases from 19 dBm to 23 dBm. It shows that the optimal H-AP transmit power P * H is greater than 23 dBm. Figure 4 shows the system EE performance versus H-AP maximum transmit power P max . Four different schemes have been simulated to verify the predominance of the proposed scheme. "Proposed scheme with iteration" denotes as "the proposed Algorithm 1" and the optimal H-AP transmit power P * H is obtained by use of Algorithm 2. "Proposed scheme without iteration" denotes as the "scheme 2" that the optimal τ * 0 equals to the maximal value of τ 01 and τ 02 in the proposed Algorithm 1, and the optimal H-AP transmit power P * H is obtained by the use of Algorithm 2. "Throughput maximization" denotes "scheme 3" that fτ * 0 , τ * 1 , τ * 2 g are solved by the use of the proposed Algorithm 1, and P * H is set to P max for achieving the maximal system throughput. To show the superiority of the framework design and proposed scheme, we have simulated the performance of the existing scheme proposed in reference [12], which is denoted as "scheme 4." In "scheme 4," we aim at the maximum EE by solving for the optimal H-AP transmitting power. It can be seen from Figure 4 that the system EE of four schemes is increasing with the increasing P max while P max ≤ P * H . "The proposed Algorithm 1," "scheme 3," and "scheme 4" behave exactly the same in system EE when P max ≤ P * H . However, the system EE of "scheme 3" decreases sharply and the other two schemes keep unchangeable while P max ≥ P * H . We conclude that the throughput maximization scheme may achieve the lower EE than "the proposed Algorithm 1" due to the fact that the optimal resource allocation for throughput maximization is not energy efficient. It illustrates the importance of maximizing the EE. It also can be observed that "the proposed Algorithm 1" always achieves the better system EE than that of the other three schemes, because SU can harvest energy from the relay during the time τ * 2 and the τ * 0 is reduced by the iteration process. In addition, we have also simulated the system throughput performance of four different schemes shown in Figure 5, which shows the system throughput performance versus H-AP maximum transmit power P max . "The proposed Algorithm 1," "scheme 2," and "scheme 4" behave similarly in the system throughput. Their system throughput is increasing when P max ≤ P * H and kept unchanged when P max ≥ P * H , whereas the system throughput of "scheme 3" always increases with the increasing P max . The reason is that 1: Let P 1 = 0, P 2 = P max and δ > 0 2: Calculate v = gðP max Þ based on Eq.(32). 3: ifv < 0 then 4: whilejP 2 − P 1 j > δdo 5: Let P + H = P 1 + P 2 /2 6: Calculate u = gðP + H Þ 7: ifu ≥ 0then 8: Let P 1 = P 1 + P 2 /2 9: else 10: Let P 2 = P 1 + P 2 /2 11: end if 12: end while 13: P * H = P +