I Introduction
The limited battery lifetime is a crucial factor affecting the performance of wireless communications. Wireless devices (WDs) need to replace/recharge battery when the energy is exhausted, which leads to frequent interruption to normal communication process and severe degradation of the quality of communication service. Alternatively, thanks to the recent advance of radio frequency (RF) based wireless energy transfer (WET) technology, the WDs can continuously harvest energy without interrupting their normal operation. The newly emerged wireless powered communication network (WPCN) integrates WET into conventional wireless communication system [1, 2, 3, 4, 5, 6, 7], which has shown its advantages in lowering the operating cost and improving the robustness of communication service in low power applications, such as sensing devices in internet of things (IoT) networks. There have been extensive studies on the design and optimization in WPCN. For instance, [3] presented a harvestthentransmit strategy in WPCN, where WDs first harvest RF energy from a single antenna hybrid access point (HAP) in the downlink (DL), and then use the harvested energy to transmit information to the HAP in a timedivisionmultipleaccess (TDMA) manner in the uplink (UL). Besides, [3] revealed an inherent doubly nearfar problem in WPCN, where the near user from the HAP achieves much higher transmission rate than the farther user as it harvests more energy from and consumes less energy to transmit information to the HAP. To improve the user fairness, [9, 10, 11, 12] have proposed several different user cooperation methods. For example, a twouser cooperation WPCN was presented in [9], where the near user with more abundant energy helps relay the far user’s information to the HAP. Besides, [10] allowed two cooperating users to form a distributed virtual antenna array and transmit jointly to the information access point. [11] considered optimal transceiver design and relay selection for simultaneous wireless information and power transfer (SWIPT) in a twohop cooperative network with energy harvesting constraints at the receiver. Further, the authors in [12] proposed a clusterbased user cooperation method, where one of a cluster of users is designated as the cluster head to relay the other users’ information. To supplement the higher energy consumption of the cluster head, the multiantenna HAP applies the energy beamforming technique [1] to achieve directional energy transfer.
A major concern in the design of user cooperation in WPCN is the time and energy consumption on exchanging individual information among the collaborating users. Recently, ambient backscatter (AB) communication technology has emerged as a promising method to reduce the cooperation overhead [13, 16, 15, 14]. Specifically, with AB communication, a WD can backscatter the RF signal (e.g., WiFi and cellular signals) to transmit its information to another WD in a passive manner [17], thus saving the device battery on generating and transmitting carrier signals as in conventional active information transmissions. Several recent works have studied signal detection methods [18] and communication circuit design [19] to improve the throughput of AB communication. In practice, the performance of AB communication has been evaluated in various wireless scenarios, where [20] showed that AB communication achieves high transmission rates over relatively short distances, e.g., less than meters. [21] developed a BackFi backscatter system that improves communication rates up to 5Mbps within 1m and 1Mbps within 5m in the backscatter communication link using ambient WiFi signals, [22] employed the highorder (PSK) modulation for AB communication and devised the corresponding maximum likelihood detector, [23] analyzed the achievable rate and capacity for AB communication with the instantaneous channel state information (CSI). In addition, [24] presented a network architecture for a largescale backscatter communication network, modeled and analyzed the communication performance using stochastic geometry.
The integration of AB communication technique in modern communication network leads to many new technological innovations and networking paradigms. However, a major performance limitation is the timevarying ambient RF signal source, whose randomness in both strength and time availability renders AB communication performance uncontrollable. The combination of WET technology and AB communication effectively mitigates such problem, where the fully controllable energy signal is used as the carrier of AB communication [25, 26, 27, 28]. For instance, [25]
optimized the energy beamforming from a multiantenna energy transmitter to multiple energy receivers with limited channel estimations at destined receivers in a backscatter communication system.
[26] and [27] introduced AB communication into RFpowered cognitive radio networks, and showed the improved throughput performance of the secondary system. Further, [28] investigated a hybrid wireless powered backscatter communication scheme in heterogeneous wireless networks. Overall, the combination of WPT and AB communications provides more robust and energyconserving communication service in lowpower applications.Recently, several works have also examined the use of AB communication for cooperative transmissions in WPCN [29, 30, 31]. For instance, a backscatter relay communication system powered by an energy beacon station was first studied in [29], where each backscatter radio harvests energy to sustain batteryless transmissions, while the other radios serve as relays to realize cooperative transmission. [30] proposed a relay selection scheme for backscatter communications which enables the outofcoverage device to communicate with the HAP via backscatter relay devices, in which the HAP adopts energy beamforming to power the backscatter devices to carry out their operations. [31] presented two user cooperation schemes in a WPCN with backscatter communication, where one device operates in backscatter mode and the other device operates in harvestthentransmit mode. The authors considered two cases in which either one of the two devices serves as the relay node for the other device in forwarding information to the AP to improve the overall throughput performance. However, most of the existing works that adopt AB communication for cooperation consider a collaborating device transmitting information in either active RF communication mode or passive backscatter communication mode. In practice, however, a device can harvest energy and receive information backscattered from the other device simultaneously during the wireless power transfer stage. Meanwhile, the harvested energy can be used to transmit information actively in later stage. Therefore, it is promising to implement cooperative transmissions in a WPCN by allowing a device to transmit both in active and passive communication. In this case, a joint design of system resource allocation on both active and passive communications is needed to achieve the maximum energy and communication efficiency. However, to the best of our knowledge, this important research topic is currently lacking of concrete study.
In this paper, we consider realizing efficient user cooperation in WPCN using both active RF communication and ABassisted passive communication. In this system, WD can be either in the active communication mode or the backscatter communication mode to transmit information to WD. As shown in Fig. 1, we consider that an HAP broadcasts wireless energy to two WDs in the downlink and receives information transmission from the WDs in the uplink. Specifically, during the WET stage ( time slot), the weaker user (WD) backscatters the received energy signal to transmit its information to the relay user (WD) in a passive manner. Meanwhile, the relay user can reuse the energy signal for simultaneous energy harvesting and information decoding using a noncoherent information decoder, e.g., energy detector. Such signal reuse effectively reduces the collaborating overhead compared to when conventional active information transmission is used.
The detailed contributions of this paper are summarized as follows:

The proposed user cooperation scheme exploits the use of AB communication during the WET stage, which enables the relay user to harvest energy from the HAP and receive the other user’s information simultaneously. Compared to existing cooperation scheme without backscatter communication, the considered backscatterassisted cooperation method reduces the collaborating overhead (transmission time and energy consumption) in the WPCN, and thus has the potential to improve the overall communication performance.

With the considered ABassisted cooperation scheme, we first analyze the achievable data rates of the two users. Then, we jointly optimize the system time and power allocations on wireless energy and information transmissions to maximize the common throughput, which is an important metric of user fairness in WPCN. We derive the semiclosedform expressions of the optimal solution and propose an efficient algorithm to solve the optimization problem.

We simulate under extensive network setups to evaluate the performance of the proposed backscatterassisted cooperation method. By comparing with conventional user cooperation method based on active communication, we show that the proposed passive cooperation can effectively enhance the throughput performance of energyconstrained devices in WPCN, especially when the weaker user is unable to harvest sufficient energy for efficient active information transmission.
The rest of the paper is organized as follows: In Section II, we present the system model of the proposed backscatterassisted relaying in WPCN. We formulate the maxmin throughput optimization problem in Section III and propose an efficient algorithm to solve it in Section IV. In Section V, we perform simulations to evaluate the performance of the proposed cooperation method. Finally, Section VI concludes this paper.
Ii System Model
Iia Channel Model
As shown in Fig. 1. we consider a WPCN where the HAP broadcasts RF energy to the two WDs in the DL and receives the WDs’ information in the UL. The HAP and the two WDs are assumed to be equipped with one antenna each. We assume that all devices operate over the same frequency band. For simplicity of expression, it is assumed that the channel reciprocity holds for the communication links. We denote and as the channel coefficient and the channel power gain between the HAP and WD. Besides, the channel coefficient between WD and WD is and the corresponding channel power gain is . Without loss of generality, we assume that WD is closer to the HAP and has a better channel condition, such that it helps relay WD’s information to the HAP.
The two users can perform information transmissions in two modes: active RF communication mode and passive backscatter communication mode. We illustrate the circuit block diagram of two WDs in Fig. 2. The two users can switch flexibly among the following three operating modes with the two switches and .

RF Communication Mode (): the active communication mode is activated when the RF communication circuit connects to the antenna. In this case, the WDs apply traditional RF wireless communication techniques to transmit and receive information, e.g., using QAM encoder and coherent detector. The energy consumption of active transmission is powered by an onchip rechargeable battery.

Energyharvesting Mode ( and is open): in this mode, the antenna is connected to the energy harvesting circuit, such that the received RF signal is converted into direct current energy and stored in a rechargeable battery, which supplies the power consumptions of the other circuits.

Backscatter Mode ( and is closed): when the passive communication mode is used, energy harvesting and backscatter communication circuits are both connected to the antenna. Further, when setting the switch , the circuit operates in the reflecting state to transmit “1”. Otherwise, when , the circuit switches to the absorbing state and “0” is transmitted. Accordingly, the backscatter receiver decodes the 1bit information using a noncoherent detection method, e.g., energy detector[32]. Notice that the energy harvesting circuit can harvest a small amount of energy during the backscatter mode especially when transmitting “0”. The harvested energy is sufficient to power the backscatter circuit, thus we neglect the energy consumption when performing backscatter communication (such as in [26]).
IiB Protocol Description
The time allocation of the proposed backscatterassisted relaying is shown in Fig. 1. Initially, channel estimation (CE) occupies the first time block of length , from which the HAP (or a central control point) has the knowledge of channel coefficients , e.g., via channel sounding. Subsequently, the backscatterassisted relaying communication consists of four operation phases. In the first phase, the HAP transfers wireless energy to the WDs in the DL for amount of time. In the second phase, WD backscatters the received energy signal to transmit its information to WD for amount of time. Notice that WD can decode the backscattered information from the WD and simultaneously harvest wireless power transfer from the HAP, which will be detailed in Section III. We assume that the HAP is only equipped with conventional active RF communication circuit such that it does not decode the reflected signal from WD. The case that the HAP also decodes from the reflected signal will be investigated in future study.
In the third phase of duration , WD uses the harvested energy to transmit its information to WD in conventional active communication mode. Note that RF transmission of WD can be overheard by the HAP during this phase. In the last phase of duration , the WD transmits information to the HAP. In particular, is divided into two parts. In the first part of duration , WD acts as a relay to transmit WD’s information to the HAP. In the second part of duration , WD conveys its own message to the HAP, where . Accordingly, the total time constraint is
(1) 
Without loss of generality, it is assumed that is a fixed parameter. In the following section, we derive the optimal throughput performance of the considered backscatterassisted cooperation in WPCN.
Iii Throughput Performance Analysis
Iiia Phase I: Energy Transfer
In the first stage of length , the HAP transfers wireless energy to WD and WD with fixed transmit power . We denote as the baseband equivalent energy signal transmitted from the HAP, which is a pseudorandom sequence with [1]. Then, the two WDs receive
(2) 
where denotes the receiver noise power. It is assumed that the energy received from the receiver noise is negligible, where WD and WD harvest the following amount of energy in the first phase [33]
(3) 
Here, denotes the fixed energy harvesting efficiency.^{1}^{1}1Although a single energy harvesting circuit exhibits nonlinear energy harvesting property due to the saturation effect of circuit, it is shown that the nonlinear effect can be effectively rectified by using multiple energy harvesting circuits concatenated in parallel, resulting in a sufficiently large linear conversion region in practice [35, 36].
IiiB Phase II: Backscatter Information Transmission
In the backscattering phase, WD backscatters the received energy signal to transmit its information to WD for amount of time. We denote the baseband equivalent pseudorandom energy signal transmitted by the HAP as with . We assume that the backscattering transmission rate is bits/second, which is a fixed parameter determined by the backscatter circuit, thus it takes second to transmit one bit information. Specially, when a symbol “0” is transmitted by WD, the WD receives only the energy signal from the HAP, which is expressed as
(4) 
Otherwise, when a symbol “1” is transmitted, WD receives the energy signal and WD’s reflected signal, i.e.,
(5) 
where is the receiver noise at WD with power , and denotes the complex signal attenuation parameter of the reflection at WD with .
We consider implementing a power splitting receiver at WD in Fig. 3, where it can split the received RF signal into two parts. Specifically, of the signal power is harvested and stored in the battery, and the rest of the signal power is used for information decoding (ID), where is the splitting factor. For convenience, we assume that is a constant in the following sections, and the impact of to the overall system performance will be investigated numerically in simulation. The information decoding circuit introduces an additional independent noise with power [34]. Thus, the energy and information signals at the WD are
(6) 
(7) 
where when transmitting “0” and when transmitting “1”. Therefore, WD harvests the following average signal power during phase II,
(8)  
where
denotes the probability of transmitting “0”. Without loss of generality, we consider
in the following analysis. Because a large number of i.i.d. random bits are sent during the backscattering stage (e.g., more than several thousand bits in practice), the amount of energy harvested by WD, denoted by , can be well characterized by the following scaled average harvest energy,(9) 
where denotes a power margin parameter to ensure that
by the central limit theorem and
is a small parameter. In other words, WD can harvest more than with sufficiently high probability, thus we can safely use to represent the energy harvested by the WD during phase II in the following. Meanwhile, it is assumed that WD keeps its battery level unchanged during this phase, where the small amount of harvested energy is used for powering the backscatter transmit circuit [18].We denote the sampling rate of backscatter receiver at WD as , i.e., the number of samples in the transmission of a bit information is . We consider using an optimal energy detector to decode the onebit information, where the bit error rate (BER) is shown in the following lemma.
Lemma 3.1: The bit error rate (BER) of the optimal energy detector is
(10) 
where erfc() is the complementary error function defined as
(11) 
Proof: Please refer to Appendix 1.
With the optimal energy detector, the backscatter communication is equivalent to a binary symmetric communication channel with a cross error probability . Thus, we can express the channel capacity as
(12) 
Accordingly, the date rate of WD transmitting to WD is
(13) 
Remark 1: Given a fixed sampling rate , a larger leads to a smaller , thus higher BER in (10). Consider an extreme case that , we have and . Accordingly, the channel capacity , resulting a zero data rate in (13). Therefore, a higher backscatter rate does not directly translate to a higher effective data rate due to the higher decoding error probability.
IiiC Phase III: Active Information Transmission
After the backscattering communication phase, WD continues to transmit information in active communication mode in Phase III, which exhausts the energy harvested in phase I. Accordingly, the transmit power of WD is
(14) 
We denote the complex baseband signal transmitted by WD in Phase III as with , such that WD and the HAP respectively receive
(15) 
(16) 
where and denote the independent Gaussian receiver noises both with power . Thus, the achievable rates from WD to WD and WD to the HAP in phase III are
(17) 
(18) 
where denotes the system bandwidth and it is assumed without loss of generality that , such that is not present in (17) and (18) as well as the data rate expressions in the remainder of this paper.
IiiD Phase IV: Information Relaying
In the last phase of duration , WD first relays WD’s message with transmit power for amount of time, then transmits its own message to the HAP with power and duration . Thus, the total energy consumption on WD is restricted by the total energy harvested in the first two phases, i.e.,
(19) 
We denote the time and power allocations as and , respectively. Then, the transmission rate of WD relaying WD’s information to the HAP is
(20) 
Note that the HAP can jointly decode WD’s active information transmission in the rd and th phases. Therefore, the achievable rate of WD in the time period of duration is[9]
(21)  
and WD’s achievable rate is
(22) 
Remark 2: The proposed backscatterassisted relaying reduces to the conventional active twouser cooperation in WPCN (e.g., in [9]) when phase II is eliminated (i.e., ). Further, if we set , the proposed method reduces to the case that the two users transmit each independent message to the HAP without cooperation [3]. In other words, they are both special cases of ours.
IiiE Problem Formulation
In this paper, we jointly optimize the time allocation and power allocation on wireless energy and information transmissions to maximize the minimum (maxmin) throughput of the two users. The optimal solution is often referred to as the common throughput, which directly reflects the user fairness in the network. Mathematically, the maxmin throughput optimization problem is
(23)  
s. t.  
In the next section, we propose an effective optimization algorithm to solve (P1). It is worth mentioning that the proposed solution algorithm can also be extended to solve the weighted sum rate (WSR) maximization problem of the two users, i.e., maximizing given two fixed positive weighting parameters and (). The detailed solution methods are omitted for brevity, while the WSR performance will be demonstrated in Simulations when discussing the achievable rate region.
Iv Optimal Solution to (P1)
Iva Problem Reformulation
We observe that problem (P1) is nonconvex because of the multiplicative terms in (19). By introducing two auxiliary variables and , (P1) is transformed into a convex problem. With in (14), we can express , and in (17), (18) and (20) as functions of . Meanwhile, and in (21) and (22) are reformulated as functions of and , i.e.,
(24) 
(25) 
(26) 
(27)  
(28) 
where , , are constant parameters.
Consequently, we introduce another auxiliary variable and transform problem (P1) into the following equivalent problem (P2):
(29)  
s. t.  
The following lemma shows that (P2) is a convex optimization problem. Therefore, it can be solved using classic convex optimization algorithms (such as interior point method [37]). When the optimal and are obtained, the optimal power allocation in (P1) can be easily obtained as and .
Lemma 4.1: and are concave functions.
Proof: Please refer to Appendix 2.
IvB Alternative Solution Method
To obtain some insights on the optimal solution structure and further reduce the complexity of general convex optimization algorithms for solving (P2), we derive in this subsection an alternative method to solve (P2). Specifically, a partial Lagrangian of (P2) is given by
(30)  
where denotes the Lagrange multipliers associated with the corresponding constraints in (29). We can express the dual function of (P2) as
(31)  
and the dual problem is
(32)  
The optimal solution can be obtained if the optimal dual solution is found by solving the dual problem of (P2). We first investigate the optimal solution of the dual function in (31) given a set of dual variables. The firstorder necessary conditions for maximizing the dual function are
(33) 
(34) 
(35) 
(36) 
(37) 
From (33) and (35), we see that the dual variables must satisfy the two equalities for the dual function to be bounded above. Suppose that (33) and (35) are satisfied, we derive the optimal solution of (31) as follows. By introducing a new variable , (34) can be expressed in the form of , where
(38) 
(39) 
(40) 
Since hold at the optimum, we only select the positive solution to the quadratic equality, where
(41) 
Similarly, by changing variables as and in (36) and (37), we have the following equations
(42) 
(43) 
Define , which is a monotonically increasing function when . Therefore, given the dual variables, we can obtain unique and as the solutions of and in (42) and (43), e.g., using the Newton’s method. The following Lemma establishes the relation between and ( and ) at the optimum of (P2).
Lemma 4.2: The unique optimal , are expressed as
(44) 
(45) 
where denotes the LambertW function, which is the inverse function of , i.e., . Accordingly, the optimal power allocation and are .
Proof: Please refer to Appendix 3.
Remark 3: It can be easily verified from (44) and (45) that must hold, which indicates the corresponding constraints of (P2) are active. Using (44) as an example, as when , if , the optimal solution , and if , the optimal . Both cases obviously will not hold at the optimum, therefore . Similar argument also leads to the result that .
Then, the optimal solution to dual function (31) can be obtained as follows. Notice that any solution satisfying (41), (46) and (47) is optimal to problem (31), thus there are infinite number of equally optimal solutions. We therefore only need to find one particular solution that satisfies the three equalities. For example, we can easily find a set of that satisfies the total time constraint (1) in addition to (41), (46) and (47). Then, we substitute the optimal to (27) and (28) to compute . This will lead a set of optimal solutions of (31).
After solving the dual function, We update the dual variables by using the projected subgradient method. By substituting the obtained to the corresponding terms, we obtain the subgradient of the dual variables in , denoted as
(48) 
(49) 
(50) 
(51) 
(52) 
Because the total time constraint in (1) is satisfied with equality in the design of dual function optimal solution, the subgradient to is always . Suppose that an initial feasible is given, the dual variable is updated in the th iteration by the following projection to the feasible region of , denoted by , i.e.,
(53) 
where is a small learning rate. Specifically, the above projection is calculated from the following convex problem,
(54) 
which could be easily solved using a bisection search over the line connecting and .
After obtaining the updated dual variables , we can further update the optimal solution to (P2). Such iteration proceeds until a stopping criterion is met. Notice that the purpose of the algorithm is to obtain the optimal dual variables , from which we can obtain the optimal , and . After substituting into (P2), we transform (P2) into a simple linear programming problem, which can be efficiently solved by the simplex method[37]. Because (14) is convex, the KKT conditions are sufficient for optimality. Once the optimal solution , are obtained, the optimal power allocation at WD is obtained as and . The pseudocode of the optimal solution algorithm to (P2) is summarized in Algorithm 1.
IvC Benchmark Methods
In this subsection, we select two representative benchmark methods for performance comparison. For both methods, it is assumed that CE occupies the same amount of time as the proposed ABassisted relaying method.

User cooperation without AB: This corresponds to the method in [9]. In this case, WD does not backscatter during the WET phase, and WD relays WD’s active information transmission to the HAP. We jointly optimize the system time duration and user transmit power allocations to maximize the minimum throughput.

User cooperation with information exchange: This corresponds to the method in [10]. In this case, the two WDs are allowed to share their harvested energy to transmit each other’s information. The two cooperating WDs first exchange their independent information with each other as to form a virtual antenna array and then transmit jointly to the HAP. We implement the cooperation scheme and maximize the common throughput by optimizing the transmit time allocation on wireless energy and information transmissions. The detailed expressions are omitted here due to the page limit.

Independent transmission without cooperation: The noncooperation method follows the harvestthentransmit protocol in [3]. Specifically, WD and WD first harvest energy from the HAP and then transmit independently their information to the HAP, the achievable rates of WD and WD are
(55) (56) Thus, the corresponding maxmin throughput optimization problem is
(57) s. t.
V Simulation Results
Parameter  Description  Value 

Transmission power of HAP  W  
Energy harvesting efficiency  
Noise power at receiver antenna  W  
Noise power at ID circuit  W  
Carrier frequency  MHz  
Pathloss factor  
Antenna power gain  dB  
Sampling rate  MHz  
System bandwidth  kHz  
Power margin  
Channel estimation time  
Backscatter reflection coefficient 
In this section, we provide simulation results to evaluate the performance of the proposed backscatterassisted cooperation scheme. In all simulations, we use the parameters of Powercast TX915011W transmitter with W as the energy transmitter at the HAP, and P2110 Powerharvester as the energy receiver at each WD with energy harvesting efficiency. Unless otherwise stated, the parameters used in the simulations are listed in Table I, which correspond to a typical outdoor wireless powered sensor network similar to the setups in [6] and [9]. In addition, we denote