Backscatter-Aided Relaying for Next-Generation Wireless Communications with SWIPT

In this paper, we analyze a backscatter network that implements simultaneous wireless information and power transfer. The backscatter devices (BDs) in the network work as relays that receive RF signals from the source, harvests the energy and uses it to reflect the signal to the receiver. We assume a non-linear energy harvesting (EH) circuit that takes into account the sensitivity and non-linearity of the electronic components. We formulate an optimization problem to maximize the achievable rate at the receiver of this network. By considering both amplify-and-forward and decode-and-forward modes, we propose algorithms to jointly optimize the power-splitting ratio and the reflection coefficient of the BDs. Simulation results demonstrate the effectiveness of the proposed algorithms with respect to baseline relay networks. In particular, the impact of the number of BDs, source transmit power, and distance of the BDs from the source and destination on the average rate and energy efficiency of the network are illustrated.


I. INTRODUCTION
The recent introduction of fifth-generation (5G) standards has brought forward the prospects of massive connectivity in the field of wireless communications and networks [1]. Accordingly, the number of connected devices is expected to increase quite significantly and reach 100 billion by the year 2030 [2]. However, large amounts of transmit power will be required to support the abounding number of devices, which will inevitably lead to high energy costs [3] and increase greenhouse gas emissions [4], [5].
Because of the above, in recent years, energy efficiency has been considered as one of the key metrics due to its commercial and ecological impact [6]. There are several ways in which energy efficiency can be achieved in a wireless communication system, such as efficient resource allocation [7]- [9], optimal network planning [7]- [9], etc. Accordingly, several techniques have been proposed to control the power consumption in wireless communications systems, while also achieving very high capacities. One such technique to improve energy efficiency, while delivering high capacity and better coverage in wireless networks is cooperative communication (CC) [10]. In a cooperative wireless network, messages from the source are relayed to the destination by other devices (users) that act as relay nodes. For example, idle users can use their energy to assist the active users in conveying messages more reliably and effectively. Cooperative networks allow the effective distribution of users to imitate an array of antennas thus achieving spatial diversity gains which include improvements in reliability and capacity. These gains emulate those seen in multiple-input multipleoutput (MIMO) systems [11].
A relay is often deployed in either Amplify-and-forward (AF) or decode-and-forward (DF) mode and they can outperform each other depending on the channel conditions from both source to relay and relay to destination, [12]. While relays are often seen as coverage extenders, there are instances when they have also been deployed to primarily reduce the transmit power of base stations (BSs) [13]. In particular, besides increasing spectral efficiency, capacity, and coverage, they also offer energy conservation for the BS in that they allow the BS to go into an idle mode more often as users within close proximity communicate with each other without having to route traffic via the network infrastructure [4]. They also enable the users at the edge of the network to receive signals without the BS having to use very high power for transmission since other users can relay the messages from the BS to the edge users [14]. However, since the users utilize their own energy to relay messages, this may lead to decreased battery life and up-time for the users' devices that act as relays. This calls for the use of systems that require very little energy to operate or devices with very high energy efficiencies.
One such technology is backscatter-aided communication that is seen as a promising technique for data transmissions without the need for a conventional energy supply from a battery or power outlet [15]- [22]. In such a system, a backscatter device (BD), which is passive in nature receives an RF signal from an active device, modulates it, and then reflects it to the receiver without having to generate its RF signals. The modulation of the information is performed by varying the reflection coefficient of the antenna. Since the BD does not transmit its RF signals, it consumes orders of magnitude less power than that of other active devices. Hence, such devices can be powered by just harvesting radio frequency (RF) energy from ambient active cellular transmitters. Accordingly, in this paper, we study the concept of a hybrid communication framework that employs backscatter aided relays to perform simultaneous wireless information and power transfer (SWIPT).

A. LITERATURE REVIEW
While several works have shown the utility of wireless backscatter and RF-EH communications (SWIPT in particular) as individual technologies, only a handful of articles have explored them in conjunction with each other. In this sub-section, we first review these two techniques as the basis for self-sustainable RF networks. We then present the works that consider the two technologies in conjunction with each other.
Conventional backscatter communications have been used in many useful applications such as radio-frequency identification (RFID), remote switches, medical telemetry, tracking devices, and low-cost sensor networks to name a few [23], [24]. Nevertheless, several works on backscatter-assisted wireless communication systems have recently been studied [18]- [22]. In [19] the authors proposed a relay cooperation strategy in a backscatter-assisted communication system for IoT to enhance the throughput of the system. Similarly, in [21] a backscatter technology was proposed for wireless communications on high-speed rails which outperforms the direct wireless communication strategy. An iterative algorithm was proposed in [22] for maximizing the energy efficiency for non-orthogonal multiple access (NOMA)-enabled backscatter-assisted communication system.
Next, in cooperative relaying networks, SWIPT has emerged as one of the most promising technologies to extend the lifespan of the network [25]- [29]. In particular, in [25], the outage probability and secrecy outage probability were studied for a SWIPT-enabled full-duplex (FD) jamming system. The authors in [27] proposed user pairing and resource allocation algorithms to maximize the sum rate of a SWIPT-enabled cooperative non-orthogonal multiple access (NOMA) system. Similarly, in [28], the authors considered a dual-hop DF multicasting MIMO relaying system with SWIPT and designed transceivers under both power splitting (PS) based protocol and time switching (TS) based protocols. Further, the SWIPT technology was also investigated for cellfree massive MIMO systems in [28].
Finally, with regards to the two technologies complementing each other, recently, RF-enabled SWIPT has been explored in backscatter-assisted communication system [30]- [35]. In [30], the authors considered a multi-antenna energy transmitter that transmits energy to multiple energy receivers in a backscatter-assisted communication system. The authors then proposed a resource allocation scheme in order to maximize the total utility of the harvested energy by all the receivers. In [31], a backscatter-assisted wireless sensor network with a single hybrid access point and multiple users which operate in both harvest-then-transmit and backscatter modes, was considered. Moreover, an optimal transmission strategy was investigated in [31] to improve the sum-throughput of the network. Next, while the authors in [34] designed a beamforming scheme to maximize the minimum achievable rate in a backscatter-assisted multi-user communication network, a study on the comparison between backscatter communication and RF-EH was presented in [35] for massive IoT networks. Furthermore, in [18], a hybrid harvest-then-transmit backscatter communication mode was proposed for Internet-of-Things (IoT) applications in a wireless powered cognitive radio network. However, to the best of the authors' knowledge, none of the existing works in [30]- [35] have investigated backscatter-assisted relaying schemes with SWIPT. In Table 1, we highlight the differences among conventional relays, backscatter aided communication and the recently evolving intelligent reflecting surface (IRS) aided communication.
The role of a BD can be categorized into two parts: i) the BD can function conventionally by modulating its information with the received RF signal sent from the primary node [36], [37] and then reflect it to the receiver. ii) Alternatively, it may be used purely as a relay in the mold of a conventional cooperative communication method [38], [39], whereby it retransmits the information received from the source. For the purpose of this study, we consider an ambient backscatter communication system, which acts purely as a relay. We find the best average rate configuration of the backscattering network and compare it with a conventional relay setup. The primary distinctions of this work are summarized below.
• We consider a backscatter wireless communication system wherein a source sends data to a destination with the aid of multiple BDs. The direct link between source and destination is also taken into account, which is a more general assumption than the one without it. • The BDs are considered to have wireless energy harvesting capability. Accordingly, the BDs do not need an internal power supply to support their operations. In particular, the BDs receive RF signals from the source, harvests the energy, and use it to reflect the signal to the receiver node. We assume a non-linear energy harvesting circuit that takes into account the sensitivity and non-linearity of components such as inductors, capacitors, and diodes found in the EH circuits. Moreover, the considered model also takes into account the sensitivity power (defined as the minimum power with which the circuit can operate) and the maximum output power. • We assume that the BDs operate in both AF and DF mode. For each operation, we find the optimal power splitting ratio and the dynamic reflection coefficient to maximize the end-to-end communication achievable rate. We evaluate the system performance (in terms of average rate and energy efficiency) with respect to a baseline system, wherein the BDs are replaced by conventional relays. • For BDs operating in DF mode, we propose a BD selection scheme to further enhance the end-to-end average rate. The key idea behind this selection is to balance the average rate between the source-to-BDs and BDsto-destination links. Paper structure: The paper is structured as follows. Section II describes the system model. The problem formulation for the BD network and corresponding solutions are depicted in Section III and Section IV, respectively. Conventional AF and DF relaying protocols are presented in Section V. Numerical results are provided in Section VI and concluding remarks along with future research directions are provided in Section VII.

II. SYSTEM MODEL
Consider a communication system comprising of a single source (S), which transmits a signal to a destination (D) with the aid of M back-scatter devices (BDs) as shown in Fig.  1. All devices are equipped with a single antenna and all channels experience block Rayleigh fading. Let us define the channels from S to D, S to BDs, and BDs to D as f ∈ C 1 , h ∈ C M ×1 , and g ∈ C M ×1 , respectively. The corresponding distances from S to D, S to BD, and BD to D are d f , d hm , and d gm , respectively. The signal received by D is expressed as y where x is the transmitted symbol with E |x| 2 = 1 and P s is the source transmit power. w d indicates the additive white Gaussian noise (AWGN) with covariance σ 2 d . The corresponding SNR can be expressed as Note that in this work, we consider two modes of operation for the BDs, namely AF and DF, whereby we assume the availability of perfect channel state information (CSI) in both AF and DF communication.

A. BD IN AF MODE (BD-AF)
Here, we consider all the BDs to operate in AF mode i.e., all the BDs simply reflect the received signal from S to the destination D. As a consequence, there is no significant signal processing at the BDs and S − BD − D path of transmission is accomplished within one time slot [40] only. The signal arriving 1 at the m-th BD is expressed as [38] y AF m = P s h m x , where P s is the transmit power for the source node S. Inside the m-th BD, the signal is split into two fractions based on the power-splitting coefficient β. The fraction √ β is absorbed by the BD for its operation and √ 1 − β is scattered towards D. The value of √ β should be adjusted such that it is sufficient to complement the power requirement for the BD's internal circuit operation, P c . In practise, a RF energy harvesting circuit does not behave linearly. There are various models to find a closed-form relation between the output and input power of such circuits [41], [42]. In this paper, we adopt the model proposed in [42], which is given as 1 Since the BDs only reflect the signals with particular phase adjustments and do not perform any decoding, interference from the reflected signal to the destination will not affect the incoming signal from the source.  Here, P sen is the energy harvesting circuit sensitivity , P max is the maximum power output of the energy harvesting circuit, and ν and τ are parameters obtained from regression for given dataset pairs of P in and P out . The requirement for the BD's operation is that P out > P c . If P in β m P s |h m | 2 is too low, implying that P out < P c even for β m = 1, then the BD's circuit will not have sufficient power to operate and hence it will not be able to backscatter the incoming signal towards D. On the other hand, if P out = P c , then the BD's circuit will work but there will be no power left for backscattering. The reflected signal from the m-th BD is thus expressed as where Γ m is the complex reflection coefficient of m-th BD and defined as is an index set of BDs that can backscatter the signal. The cumulative received signal from the S −D and the S −BD − D links is expressed as where w d is the AWGN at D with zero mean and variance σ 2 d . Then, the end-to-end achievable rate for the system in Fig. 1 with AF backscatter relays is expressed as

B. BD IN DF MODE (BD-DF)
Here, we consider all the BDs to operate in DF mode 2 . Among them, only certain BDs decode the received signal from S in the first time slot. Since BDs do not have a power supply (battery or capacitor to store energy), the operation of all the BDs depend on the RF harvesting power [40].
The incident signal at the m-th BD in the first time slot is expressed as where w BD,m is the AWGN at the m-th BD. The BDs which fail to backscatter the signal due to bad channel conditions are called inactive BDs. LetM denote the set of BDs that successfully decode the signal. Consequently, the SNR for the link between S to them-th BD is expressed as We redefine and rearrange the elements inM such that γ DF s,1 ≥ γ DF s,2 ≥ · · · ≥ γ DF s,M . Signal decoding is successfully performed by active BDs if the achievable rate is greater than the predefined threshold R (1) m as given below Here, C (1) m = 1 2 log 2 1 + γ DF s,m . Suppose we choose the bestM ≤M BDs to decode and forward the signal. Then, the rate at the selected BDs is equal to or greater than the rate of the worst performing BD, i.e., C DF,1 ≥ C (1) M . This is to ensure successful decoding of the signal from S by all the active BDs, which is to say that SNR of the first time slot γ DF s,bd ≥ γ s,M . In the second time slot, allM selected BDs transmit the signal to D. Thus, the received signal at D can be expressed as where gm is the channel from themth selected BD to D and Γm = |Γm| e jθm . The received SNR based on (12) is expressed as The end-to-end achievable rate for the system in Fig. 1 with DF backscatter relays is expressed as Note: The fraction 1/2 in (11) and (14) comes from the fact that the transmission requires two time-slots under DF mode.

III. BD-AF: PROBLEM FORMULATION AND SOLUTION
In this section, we formulate the optimization problem for maximizing the end-to-end achievable rate for the BD-AF scenario.

A. PROBLEM FORMULATION
Using (8), the rate maximization problem for the joint design of power-splitting coefficient β m and phase shift θ m under BD-AF scenario is formulated as where P out is the harvested power output as a function of P in and is defined in (4). The constraint (C.1) ensures that the output of the energy harvesting circuits of BDs must be enough to run the circuits of BDs, while the constraint (C.2) guarantees that the phase offset of each BD is fully controlled through load modulation [43]. Finally, the constraint (C.3) ensures that the value of the power-splitting coefficient β m lies between 0 and 1. Now, the problem of maximizing the achievable rate can be reformulated to maximizing the end-to-end SNR as follows.
The joint optimization problem (16) is non-convex in the variables β m and θ m due to coupling of the variables and thus, it is difficult to solve. Therefore, we adopt an alternating optimization approach where we optimize one variable while keeping the other as a constant.

B. SOLUTION AND PROPOSED ALGORITHM
For a given power-splitting coefficient β m , the optimization problem (16) can be reformulated as Since Γ m = |Γ m | e jθm , we observe that the phase θ m is a critical design variable for the channel enhancement, while |Γ m | can simply be set to its maximum value in order to increase the reflected signal power [38]. The objective of the problem (17) is to achieve the maximum rate w.r.t. θ m , if allM + 1 complex scalar terms in the numerator, i.e., f and g m Γ m √ 1 − β m h m , ∀m = 1, · · · ,M are aligned in the same direction. Note that all the phases can be adjusted except for the first one i.e., f . Accordingly, the values of all θ m are set such that the term g m Γ m √ 1 − β m h m should align in the direction of f . Thus, the optimal θ m can be obtained as Now, substituting (18) into the objective function of (17) yields Using (19) and θ opt m , the optimization problem (16) can be written as It can seen that the objective function in (20) monotonically decreases with respect to increasing values of β m within the range 0 < β m < 1. Thus, the optimal β opt m is set as low as possible while satisfying the harvested energy requirement for the BDs to operate. In other words, β opt m , ∀m ∈M are the values that lead to P out (β m ) = P c . Now, rearranging the terms in (4) such that P in is kept in the left-hand-side, we obtain the following expression Since P in = β m P s |h m | 2 and by taking into account that 0 < β m ≤ 1, we obtain If β opt m = 1, the corresponding term in the numerator of the objective function in (20), i.e. |g m | |Γ m | √ 1 − β m |h m |, is zero, leading to the conclusion that the m-th BD fails to backscatter the incident signal to D. The rate maximization procedure for the BD-AF scenario is summarized in Algorithm 1.

IV. BD-DF: PROBLEM FORMULATION AND SOLUTION
In this section, we formulate the optimization problem for maximizing the achievable rate for the BD-DF scenario. VOLUME 4, 2016 Algorithm 1: Rate maximization for BD-AF scenario Input: f , h, g, P S , P C , P sen , ν, τ . Output: C AF . 1 Calculate β opt m by using (22). 2 Obtain γ AF s,d using (19) or calculate (18) and then substitute it into the objective of (17). 3 Compute C AF using the objective of (15).

A. PROBLEM FORMULATION
Using (14), the optimization problem for maximizing the achievable rate in the BD-DF network can be formulated as In the above, C.1 -C.3 are the same as defined for (16), while the constraint C.4 indicates the number of selected BDs. The formulated problem (23) is non-convex due to the coupling of variables βm and θm, and thus cannot be solved in a straightforward way.

B. SOLUTION AND PROPOSED ALGORITHM
Due to the fact that γ DF bd,d is the only term arising due to the reflected signal, it is the only term in the objective function (23) that depends on θ opt m . Now, for givenM and βm, the optimization problem (23) is reformulated to find the optimal θ opt m as The objective of the problem (24) is to achieve the maximum rate w.r.t. θm if allM complex scalar terms in the numerator, i.e., gmΓm √ 1 − βm √ P s hm, are aligned in the same direction. Since all the terms' phases can be adjusted, the value of θm for ∀m, is set such that these terms are perfectly aligned to 0 o . Hence, the optimal θm is obtained as Substituting (25) into the objective function of the problem (24), the optimal SNR of the link from BD-to-D under the BD-DF case is expressed as For given θ opt m andM , the optimization problem (23) with βm as the variable of interest turns into a problem of maximizing (26) with the constraints as expressed in (23) that have correlation with βm. This can mathematically be given as This problem is similar to (20), where the objective function in (27) is also monotonically decreasing with respect to increasing values of βm within the range 0 < βm < 1. Thus, the solution to (27) with βm as the variable of interest is the same as that expressed in (22). Now, with the optimal θ opt m and β opt m , ∀m ∈M, the problem (23) Note that γ DF s,bd and γ DF bd,d in (28) are dependent ofM and γ DF s,bd is a monotonically decreasing function with respect to the increment inM since γ DF s,bd is equal to the bestM link from S to BD after sorting the channel in a descending order, i.e. γ DF s,bd = γ s,M . Moreover, the best γ DF s,bd is obtained whenM = 1, which means that the best link from S to D is chosen. On the contrary, γ DF bd,d , as expressed in (26), is a monotonically increasing increasing function with respect to the increment inM based on the fact that for all non-negative Furthermore, the best γ DF bd,d is obtained whenM =M , which means that all the active BDs participate in backscattering the signal towards D.
The rate maximization procedure for the BD-DF scenario is summarized in Algorithm 2, where the optimalM opt is obtained by setting its increment from 1 to the maximumM . At the beginning, γ DF s,bd has the best value and γ DF bd,d has the worst value, leading to C DF (M ) having a low value due to the min operation. As we incrementM , the value of γ DF s,bd decreases and γ DF bd,d increases, leading to an improvement in C DF (M ). At a particular value ofM , γ DF s,bd < γ DF bd,d , leading to a decrease in C DF (M ), which is when the iteration is stopped. This particular value ofM is set asM opt . Additionally, we solve the problems (24) and (27) outside the loop since θ opt m and β opt m , ∀m ∈M are independent ofM . Since the problem (24) and (27) are executed only once, the execution time of Algorithm 2 is quite fast.

V. COMPLEXITY ANALYSIS
For the BDs operating in AF mode, there are two variables to be optimized, namely θ m and β m , ∀m, where the solution of each is obtained by the closed-form solution (18) and (22), respectively. Since β opt m does not depend on θ m , ∀m and vice versa, the joint optimal solution is obtained by once executing (22) and (18), respectively. Since β opt m does not depend on θ m , ∀m and vice versa, the joint optimal solution Algorithm 2: Rate Maximization for BD-DF Case Input: f , h, g, P S , P C , P sen , ν, τ . Output: C DF . 1 Get θm and βm, ∀m ∈M by solving (24) and (27) IncrementM . 5 Get C DF (M ) by calculating the objective in (28). 6 end is obtained by once executing (22) followed by (18). In (22), the variable related to each BD is only h m which appears in the denominator, while the numerator in (22) consists of constants that are independent of m and thus must be computed once. In terms of M , the complexity of (22) is O (M ) since (22) needs to be computed M times. In (18), the number of multiplication and angle operator are fixed and independent of M , but the computation of (18) needs to be repeatedM -times for the active BDs. Hence, the complexity in calculating (18) is O M . Thus, the overall complexity 3 of the proposed algorithm for BD-AF network is O M +M . Now, for the BDs operating in DF mode, there are three variables to be optimized, namely β m , θ m , ∀m, andM , where the solution is obtained by (22), (25), and line 3-6 of Alg. 2. Since β opt m does not depend on θ m , ∀m and vice versa, the jointly optimal solution is obtained by once executing (22) followed by (25). As discussed before, the complexity of (22) in terms of M is O (M ). Similar to (18), the number of multiplication and angle operator in (25) are fixed and independent of M , but (25) needs to be executedM times for the active BDs. Hence, the complexity of (25)

VI. NUMERICAL RESULTS
In this section, we analyze the performance of the optimized backscatter network through extensive computer simulations for varying system parameters.

A. SIMULATION SETUP
Unless otherwise stated, the system parameters are chosen as follows. Each entry of f , h m , and g m , ∀m ∈ M is the realization of the zero-mean and unit variance complex Normal random variable. The distance between S, D, and 3 Note that the number of active BDs is less than or equal to the total number of BDs in the network, i.e.,M ≤ M . BDs are normalized to one. The constants concerning the harvesting energy circuit are set to be τ = 274, ν = 0.29, P max = 4.927 × 10 −3 W, P sen = 6.4 × 10 −5 W, and P c = 8.9 · 10 −6 W [44], [45]. The noise power at BDs and D are −15 dBm. The amplitude of the dynamic reflection coefficient |Γ m | for all BDs is set to 0.7. Any other parameters used will be explicitly mentioned when and wherever used. Next, results from [11], [46] will be used as baseline for comparison of the BD assisted system with conventional relay assisted ones.

B. CSI ACQUISITION
Since the BDs have limited radio resources and signal processing capabilities to send or receive pilot symbols for channel estimation, the source has to estimate all the channels and use them to compute the transmit power allocation as well as the reflection coefficients. The source then provides information on the required reflection configuration (i.e. Γ) to either a micro-controller connected to the BDs or the BDs themselves if they have built-in circuitry. The information can be provided in the form of an index of a predefined quantized codebook shared by the source and microcontroller, that contains the various reflection configurations possible at the BDs. Further, techniques such as blind channel estimation [47] and machine learning [48] can also be used to obtain the CSI in such BD-assisted systems.

C. AVERAGE RATE VERSUS NUMBER OF BDs
In Fig. 2, we show the achievable average rate versus the number of BDs in the network. This figure demonstrates that as the number of BDs increases in the network, the achievable rate of the system also increases for both AF and DF cases due to diversity gain. However, the BD-AF case always outperforms the BD-DF case. Further, the average rate increases more rapidly in the region with lower BDs. While the increase in capacity saturates early for the BD- DF case, for the BD-AF case, the growth is consistent with respect to the increasing number of BDs, albeit in a slow manner. Fig. 3 shows the average rate versus the transmit power at the source (P s ) for different number of BDs. It can be seen from the figure that the average rate of the system increases as the the value of P s increases. However, the slopes of the curves are somewhat restrained when compared to the increase in transmit power. The increase in average rate with respect to the number of BDs has already been illustrated in Fig. 2 and is further validated here. In particular this figure suggests that average rate of the network can be increased by adding more BDs. In particular this figure suggests that average rate of the network can be increased by adding more BDs, which is an alternative to increasing the transmit power in the network. This result is further validated in 4, which shows that increasing the number of BDs has substantial effect on  5 shows the input power P in versus output power P out for the non-linear EH model. The signal power that enters the energy harvesting circuit is not linearly related to the output power of the circuit due to the sensitivity and non-linear performance of components such as diodes, inductors and capacitors [49]. However, from the figure, we can observe that for low values of P in , P out linearly increases with P in before saturating beyond 15 mW. Fig. 6 shows the variation of average rate with respect to the normalized distance between the source and the BD. In particular, the normalized S-BD distance is defined as the S-BD distance divided by the S-D distance. The values 0 and 1 in the x-axis of the figure indicates that the BD is placed at the S and D, respectively. It can be seen from the figure that as the separation between the source and the BDs increase, the performance of the system degrades for both the AF and DF case. The degradation is more significant when the normalized distance is small.

F. AVERAGE RATE VERSUS SOURCE TO BD DISTANCE
To understand the effect of the distance on the performance of the system better we formulate an example by considering that the BDs are operating in DF mode only. In particular, within a square area of varying sides, we place 1000 BDs in a uniform but random manner such that they would only be able to decode and forward the signal if they are within a certain distance from the source. We then plot curves using the diagonal of the square for the x-axis and the number of BDs that are active in the y-axis. This is illustrated in Fig. 7, where we can observe that as the size of the square increases, a fewer number of BDs can decode and forward the signal to the destination.   Fig. 8 shows the effect of the source transmit power on the EE of the network for varying number of BDs. It can be seen that the EE decreases much faster with the increase in transmit power at the source for BD-AF as compared to BD-DF. However, for the BD-AF case, increasing the number of BDs results in higher efficiency, which indicates that BD aided transmission is indeed energy-efficient. Similar but minuscule effects are also seen for the BD-DF case.

H. COMPARISON OF BD-AF/BD-DF WITH CONVENTIONAL AF/DF RELAY NETWORKS
In this subsection, we compare the average rate performance of the proposed BD-AF and BD-DF networks with respect to baseline AF and DF relay networks. For fair comparison, the total power budget, noise power at the relays and at the destination D are kept the same.

1) AF Relaying Scheme
For the system as depicted in Fig. 1 by replacing the BDs with AF relays, the amplifying factor for the m-th relay is given by [11], [46] α m = a where P r is the total transmission power of the relays and a is a constant to satisfy the total relay power constraint. The achievable rate of the system with α m is given by whereγ s,m = P s |h m | 2 /σ 2 m andγ m,d = P r |g m | 2 /σ 2 d . Furthermore, the power allocation between S and R can be considered similar [11] to improve the system throughput by introducing a variable ζ such that 0 ≤ ζ ≤ 1. Then, P r = ζP tot , P S = (1 − ζ)P tot , and the optimal ζ is obtained as where b m = P tot |h m | 2 |g m | 2 /σ 2 m σ 2 d . With the above generalization, we now compare the BDaided system to a conventional AF relay system with respect to the number of BDs/relays and source transmit power in Fig. 9 and Fig. 10. It can seen from the figures that the BDaided system significantly outperforms the conventional relay based one. For example for equivalent number of BDs/relays, the increase in the average rate of the BD aided system is VOLUME 4, 2016 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication.  higher than the relay aided one when the source transmit power increases. Similarly, for fixed source transmit power the increase in the number of BDs produces far better average rate than the relay aided system when equivalent number of relays are increased in the network.

2) DF Relaying Scheme
Next, consider a system as depicted in Fig. 1, where the BDs are now replaced by DF relays. Here, in the first time slot, S transmits the signal to both R and D with the rate R DF,1 . In the second time slot, the set of relays that successfully decode the message, i.e.,M = {m : log 2 (1 + γ s,m ) ≥ 2R} helps in forwarding the source's message to D. It is shown in [11], [50] that the effective SNR at the destination after combining the signal both from the first and second-time slot using maximum ratio combining is given by [50] γ eff = P S |f | 2 σ 2 Note that [11] did not consider the design of source transmission rate R DF,1 , that affects the set of relaysM that successfully decode the message with an effective SNR γ eff . Hence, we implement the design ofM by incorporating Algorithm 2 into the framework of [11] for a fair comparison. The work in [11] also did not consider the power allocation between S and R. For comparison, we set P S = P r = 0.5P tot . The above generalization is now used to compare the BDaided system to a conventional DF relay system with respect to the number of BDs/relays and source transmit power in Fig. 11 and Fig. 12. Similar to the AF case, the BD-assisted system consistently outperforms the conventional DF-based system. However, unlike the AF case, the gap in performance between the BD and relay-based systems for the DF case is smaller.

VII. CONCLUSION AND FUTURE WORK
We considered a backscatter relay network implementing SWIPT at the BDs. By considering a non-linear EH circuit at the BDs, we formulated an optimization problem to maximize the average rate at the receiver. Both AF and DF modes were considered and algorithms were proposed to jointly optimize the power-splitting ratio and the reflection coefficient of the BDs. Simulation results were performed to assess the impact of the number of BDs and source transmit power on the performance of the network.
This study provides a reference concerning the use of BDs for achieving high throughput with minimal energy in wireless networks. It can act as a cornerstone to accelerate their implementation in next-generation in future cooperative communications. Nevertheless, certain aspects remain beyond the scope of this paper that may further improve the performance of the system. One such facet is adaptive switching between AF and DF among the BDs, whereby the BDs will always attempt to decode the transmitted data stream from the source. The BDs that can successfully decode the data stream will proceed with the DF operation, while the rest will switch to the AF operation. The above hybrid method will be explored in our future work.