# Optimal Resource Allocation in Full-Duplex Ambient Backscatter Communication Networks for Green IoT

Ambient backscatter communication (AmBC) enables wireless-powered backscatter devices (BDs) to transmit information over ambient radio-frequency (RF) carriers without using an RF transmitter, and thus has emerged as a promising technology for green Internet-of-Things. This paper considers an AmBC network in which a full-duplex access point (FAP) simultaneously transmits downlink orthogonal frequency division multiplexing (OFDM) signals to its legacy user (LU) and receives uplink signals backscattered from multiple BDs in a time-division-multiple-access manner. To enhance the system performance from multiple design dimensions and ensure fairness, we maximize the minimum throughput among all BDs by jointly optimizing the BDs' backscatter time portions, the BDs' power reflection coefficients, and the FAP's subcarrier power allocation, subject to the LU's throughput constraint, the BDs' harvested-energy constraints, and other practical constraints. As such, we propose an efficient iterative algorithm for solving the formulated non-convex problem by leveraging the block coordinated decent and successive convex optimization techniques. We further show the convergence of the proposed algorithm, and analyze its complexity. Finally, extensive simulation results show that the proposed joint design achieves significant throughput gains as compared to the benchmark scheme with equal resource allocation.

## Authors

• 12 publications
• 2 publications
• 38 publications
• ### Optimal Resource Allocation in Full-Duplex Ambient Backscatter Communication Networks for Wireless-Powered IoT

This paper considers an ambient backscatter communication (AmBC) network...
06/18/2018 ∙ by Gang Yang, et al. ∙ 0

• ### Resource Allocation of Dual-Hop VLC/RF Systems with Light Energy Harvesting

In this paper, we study the time allocation optimization problem to maxi...
11/15/2020 ∙ by Shayan Zargari, et al. ∙ 0

• ### Novel Sparse-Coded Ambient Backscatter Communication for Massive IoT Connectivity

Low-power ambient backscatter communication (AmBC) relying on radio-freq...
06/08/2018 ∙ by Tae Yeong Kim, et al. ∙ 0

• ### Energy-Efficient UAV Backscatter Communication with Joint Trajectory Design and Resource Optimization

Backscatter communication which enables wireless-powered backscatter dev...
11/13/2019 ∙ by Gang Yang, et al. ∙ 0

• ### D2D Communications Underlaying Wireless Powered Communication Networks

In this paper, we investigate the resource allocation problem for D2D co...
05/29/2018 ∙ by Haichao Wang, et al. ∙ 0

• ### Optimal Time Scheduling Scheme for Wireless Powered Ambient Backscatter Communication in IoT Network

In this paper, we investigate optimal scheme to manage time scheduling o...
10/13/2018 ∙ by Xiaolan Liu, et al. ∙ 0

• ### Joint Allocation Strategies of Power and Spreading Factors with Imperfect Orthogonality in LoRa Networks

The LoRa physical layer is one of the most promising Low Power Wide-Area...
04/25/2019 ∙ by Licia Amichi, et al. ∙ 0

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## I Introduction

Internet of Things (IoT) is a key application scenario for the fifth generation (5G) and future mobile communication systems, and various IoT devices typically have strict limitations on energy, cost, and complexity. Recently, ambient backscatter communication (AmBC) which enables backscatter devices (BDs) to modulate their information symbols over the ambient RF carriers (e.g., WiFi, TV, or cellular signals) without using a complex and power-hungry RF transmitter [1], has emerged as a promising technology for energy-efficient and cost-efficient IoT communications.

Recently, there are a few literature on performance analysis and optimization for AmBC systems. In [10], the ergodic capacity for backscatter communication is maximized for a standard AmBC system. In [8], the transmit beamforming is optimized for a cooperative AmBC system with multiple antennas at the ambient transmitter. In [11], for an ambient-backscatter assisted cognitive radio network, the secondary transmitter’s rate is maximized by optimizing the time resource.

In this paper, we consider a full-duplex AmBC network (ABCN) over ambient OFDM carriers as shown in Fig. 1, consisting of a full-duplex access point (FAP), a legacy user (LU), and multiple BDs. We optimize the throughput performance for such an ABCN, which has not been studied in the literature to our best knowledge. The main contributions of this paper are summarized as follows:

• First, by employing an FAP, we propose a new model to enable simultaneous downlink information transmission (energy transfer) to the LU (multiple BDs) and uplink information transmission from multiple BDs. We characterize the corresponding throughput and energy transfer performances of the BDs, as well as the throughput performance of the LU.

• Second, to ensure fairness, we formulate a problem to maximize the minimum throughput among all BDs by jointly optimizing three blocks of variables including the BDs’ backscatter time portions, the BDs’ power reflection coefficients, and the FAP’s subcarrier power allocation. Through joint optimization, the system performance can benefit from multiple design dimensions.

• Third, to solve the formulated non-convex problem, we propose an iterative algorithm by leveraging the block coordinated decent (BCD) and successive convex optimization (SCO) techniques, in each iteration of which the three blocks of variables are alternately optimized. Also, we show the convergence of the proposed algorithm and analyze its complexity.

• Finally, numerical results show that significant throughput gains are achieved by our proposed joint design, as compared to the benchmark scheme with equal resource allocation. Also, the BD-LU throughput tradeoff and the BDs’ throughput-energy tradeoff are revealed.

The rest of this paper is organized as follows. Section II presents the system model for a full-duplex ABCN over ambient OFDM carriers. Section III formulates the minimum-throughput maximization problem. Section IV proposes an efficient iterative algorithm by applying the BCD and SCO techniques. Section V presents the numerical results. Finally, Section VI concludes this paper.

## Ii System Model

In this section, we present the system model for a full-duplex ABCN. As illustrated in Fig. 1, we consider two co-existing communication systems: the legacy communication system which consists of an FAP with two antennas for simultaneous information transmission and reception, respectively, and its dedicated LU111We consider the case of a single LU, since the FAP typically transmits to an LU in a short period for practical OFDM systems like WiFi system. The analyses and results can be extended to the multiple-LU case., and the AmBC system which consists of the FAP and BDs. The FAP transmits OFDM signals to the LU. We are interested in the AmBC system in which each BD transmits its modulated signal back to the FAP over its received ambient OFDM carrier. Each BD contains a backscatter antenna, a switched load impedance, a micro-controller, a signal processor, an energy harvester, and other modules (e.g., battery, memory, sensing). The BD modulates its received ambient OFDM carrier by intentionally switching the load impedance to vary the amplitude and/or phase of its backscattered signal, and the backscattered signal is received and finally decoded by the FAP. The energy harvester collects energy from ambient OFDM signals and uses it to replenish the battery which provides power for all modules of the BD.

The block fading channel model is assumed. As shown in Fig. 1, let be the -path forward channel response from the FAP to the -th BD, for , be the -path backward channel response from the -th BD to the FAP, be the -path direct-link channel response from the FAP to the LU, and be the -path interference channel response from the -BD to the LU. Let be the number of subcarriers of the transmitted OFDM signals. For each channel, define the frequency response at the -th subcarrier as , , , , for .

We consider frame-based transmission, and the frame structure is shown in Fig. 2. In each frame of time duration (seconds) consisting of slots, the FAP simultaneously transmits downlink OFDM signals to the LU, and receives uplink signals backscattered from all BDs in a time-division-multiple-access (TDMA) manner. The -th slot of time duration (with time portion ()) is assigned to the

-th BD. Denote the backscatter time portion vector

. In the -th slot, BD reflects back a portion of its incident signal for transmitting information to the FAP and harvests energy from the remaining incident signal, and all other BDs only harvest energy from their received OFDM signals.

Let be the FAP’s information symbol at the -th subcarrier, , in the -th OFDM symbol period of the

-th slot. After inverse discrete Fourier transform at the FAP, a cyclic-prefix (CP) of length

is added at the beginning of each OFDM symbol. The transmitted time-domain signal in each OFDM symbol period is

 sm,t(n)=1NN−1∑k=0√Pm,kSm,k(n)ej2πktN, (1)

for the time index , where is the allocated power at the -th subcarrier in the -th slot. The subcarrier power values are subject to the average power constraint , where is the total transmission power in all slots. Denote the subcarrier power allocation matrix , where is the subcarrier power allocation vector in the -th slot.

In the -th slot, the incident signal at BD is , where means the convolution operation. Let () be the -th BD’s power reflection coefficient, and denote the vector . Let () be the energy-harvesting efficiency for all BDs. From the aforementioned system model and [12], the total harvested energy by BD in all slots is thus

 Em(τ,αm,P)= ηN−1∑k=0|Fm,k|2[τmPm,k(1−αm)+M∑r=1,≠mτrPr,k]. (2)

Let be the -th BD’s information symbol, whose duration is designed to be the same as the OFDM symbol period. We assume each BD can align the transmission of its own symbol with its received OFDM symbol222

BD can practically estimate the arrival time of OFDM signal by some methods like the scheme that utilizes the repeating structure of CP

[3].. In the -th slot, the backscattered signal from the -th BD is thus .

The transmitted downlink signal is known by the FAP’s receiving chain. Thus, this signal can be reconstructed and subtracted from the received signals. Therefore, the self-interference can be cancelled by using existing digital or analog cancellation techniques. For this reason, we assume perfect self-interference cancellation (SIC) at the FAP in this paper. After performing SIC, the received signal backscattered from the -th BD is given by

 ym,t(n)= (3) √Pm,k√αmsm,t(n)⊗fm,l⊗gm,lXm(n)+wm,t(n),

where the additive white Gaussian noise (AWGN) is assumed, i.e., .

After CP removal and discrete Fourier transform operation at the FAP, the received frequency-domain signal is

 Ym,k(n)= (4) √Pm,k√αmFm,kGm,kSm,k(n)Xm(n)+Wm,k(n),

where the frequency-domain noise .

The FAP performs maximum-ratio-combining (MRC) to recover the BD symbol as follows

 ˆXm(n)=1NN−1∑k=0Ym,k(n)√Pm,k√αmFm,kGm,kSm,k, (5)

and the resulting decoding signal-to-noise-ratio (SNR) is

 γm(αm,P)=αmσ2N−1∑k=0|Fm,k|2|Gm,k|2Pm,k. (6)

Hence, the -th BD’s throughput333This paper adopts normalized throughput with unit of bps/Hz. normalized to is

 Rm(τm,αm,pm)= τmNlog(1+αmσ2N−1∑k=0|Fm,k|2|Gm,k|2Pm,k). (7)

Similar to (4), the received frequency-domain signal at the LU can be written as follows

 Zm,k(n)=√Pm,kHkSm,k(n)+... (8) √Pm,k√αmFm,kVm,kSm,k(n)Xm(n)+˜Wm,k(n),∀k,m

where the frequency-domain noise .

Similar to (II), treating backscatter-link signal as interference, the total throughput of the LU is given by

 ˜R(τ,α,P)= (9) 1NM∑m=1τmN−1∑k=0log(1+|Hk|2Pm,kαm|Fm,kVm,k|2Pm,k+σ2).

## Iii Problem Formulation

In this section, we formulate the optimization problem. The objective is to maximize the minimum throughput among all BDs, by jointly optimizing the BDs’ backscatter time portions (i.e., ), the BD’s power reflection coefficients (i.e., ), and the FAP’s subcarrier power allocation (i.e., ). We consider the following constraints: the total throughput of the LU needs to be larger than a given minimum throughput , i.e., ; each BD has a minimum energy requirement , i.e., ; the total power consumed by the FAP needs to be less than a given maximum power , i.e., ; the sum of backscatter time portions for all BDs should be no larger than 1, i.e., , with non-negative time portion for each BD ; the peak power value for each subcarrier is , i.e., ; the power reflection coefficients are positive numbers and no larger than 1, i.e., . The optimization problem is thus formulated as follows

 maxQ,τ,α,PQ (10a) s.t.τmNlog(1+ αmσ2N−1∑k=0|Fm,k|2|Gm,k|2Pm,k)≥Q,∀m (10b) 1NM∑m=1τmN−1∑k=0log(1+|Hk|2Pm,kαm|Fm,kVm,k|2Pm,k+σ2)≥D (10c) ηN−1∑k=0|Fm,k|2[τmPm,k(1−αm)+M∑r=1,≠mτrPr,k] ≥Emin,m,∀m (10d) M∑m=1N−1∑k=0τmPm,k≤¯P (10e) M∑m=1τm≤1 (10f) 0≤Pm,k≤Ppeak,∀m, k (10g) τm≥0,∀m (10h) 0≤αm≤1,∀m. (10i)

Notice that problem (10) is non-convex and challenging to solve in general, since the variables are all coupled and the constraint function in (10c) is non-convex over ’s.

## Iv Proposed Algorithm

In this section, we propose an efficient iterative algorithm for the problem (10) by applying the block coordinate descent (BCD) [13] and successive convex optimization (SCO) techniques [14]. Then, we show the convergence of the proposed algorithm and analyze its complexity.

### Iv-a Backscatter Time Allocation Optimization

In iteration , for given power reflection coefficients and subcarrier power allocation , the backscatter time portions can be optimized by solving the problem

 maxQ,τQ (11a) s.t.(???),(???),(???),(???),(???),(???), (11b)

where the variables ’s and ’s are replaced by given ’s and ’s, respectively, in all the constraints. Notice that problem (11

) is a standard linear programming (LP), it can be solved efficiently by existing optimization tools such as CVX

[15].

### Iv-B Reflection Power Allocation Optimization

For given backscatter time portions and subcarrier power allocation , the power reflection coefficients can be optimized by solving the following problem

 maxQ,αQ (12a) s.t.(???),(???),(???),(???), (12b)

where the variables ’s and ’s are replaced by given ’s and ’s, respectively. Since the left-hand-side of the constraint (10c) with given and is a decreasing and convex function of , the constraint is convex. Hence, problem (12) is a convex optimization problem that can also be efficiently solved by CVX [15].

### Iv-C Subcarrier Power Allocation Optimization

For given backscatter time portions and power reflection coefficients , the subcarrier power allocation can be optimized by solving the following problem

 maxQ,PQ (13a) s.t.1NM∑m=1τ{j}m (13b) N−1∑k=0log⎛⎝1+|Hk|2Pm,kα{j}m|Fm,kVm,k|2Pm,k+σ2⎞⎠≥D (13c)

where the variables ’s and ’s are replaced by given values ’s and ’s, respectively. Since the constraint function in (13b) is non-convex with respect to , problem (13) is non-convex. Notice that the constraint function can be rewritten as

 ˜R(P)|τ{j},α{j} =M∑m=1τ{j}mNN−1∑k=0[−log(αm|Fm,kVm,k|2Pm,k+σ2)+... log((α{j}m|Fm,kVm,k|2+|Hk|2)Pm,k+σ2)]. (14)

To handle the non-convex constraint (13b), we exploit the SCO technique [14] to approximate the second logarithm function in (IV-C). Recall that any concave function can be globally upper-bounded by its first-order Taylor expansion at any point. Specifically, let denote the subcarrier power allocation in the last iteration. We have the following concave lower bound at the local point

 ˜R(P)|τ{j},α{j},P{j}≥ (15) M∑m=1τ{j}mNN−1∑k=0[log((α|Fm,kVm,k|2+|Hk|2)Pm,k+σ2)−... log(α|Fm,kVm,k|2P{i,j}m,k+σ2)− α|Fm,kVm,k|2(Pm,k−P{i,j}m,k)α|Fm,kVm,k|2P{i,j}m,k+σ2]≜˜Rlb(P)|τ{j},α{j},P{j}.

With given local points and lower bound in (15), by introducing the lower-bound minimum-throughput , problem (13) is approximated as the following problem

 maxQlbtpa,PQlbtpa (16a) s.t.˜Rlb(P)|τ{j},α{j},P{j}≥D (16b) (16c)

where the variables ’s and ’s are replaced by given ’s and ’s, respectively. Problem (16) is a convex optimization problem which can also be efficiently solved by CVX [15]. It is noticed that the lower bound adopted in (16b) implies that the feasible set of problem (16) is always a subset of that of problem (13). As a result, the optimal objective value obtained from problem (16) is in general a lower bound of that of problem (13).

### Iv-D Overall Algorithm

We propose an overall iterative algorithm for problem (10) by applying the BCD technique [13]. Specifically, the entire variables in original problem (10) are partitioned into three blocks, i.e., , and , which are alternately optimized by solving problem (11), (12), and (16) correspondingly in each iteration, while keeping the other two blocks of variables fixed. Furthermore, the obtained solution in each iteration is used as the input of the next iteration. The details are summarized in Algorithm 1.

### Iv-E Convergence and Complexity Analysis

Notice that in our case, for subcarrier power allocation problem (13), we only solve its approximate problem (16) optimally. Thus, the convergence analysis for the classical BCD technique cannot be directly applied [13], and the convergence of Algorithm 1 needs to be proved, as follows.

###### Theorem 1.

Algorithm 1 is guaranteed to converge.

###### Proof.

First, in step 3 of Algorithm 1, since the optimal solution is obtained for given and , we have the following inequality on the minimum throughput

 Q(τ{j},α{j},P{j})≤Q(τ{j+1},α{j},P{j}). (17)

Second, in step 4, since the optimal solution is obtained for given and , it holds that

 Q(τ{j+1},α{j},P{j})≤Q(τ{j+1},α{j+1},P{j}). (18)

Third, in step 5, it follows that

 Q(τ{j+1},α{j+1},P{j}) (a)=Qlb,{j}tpa(τ{j+1},α{j+1},P{j}) (b)≤Qlb,{j}tpa(τ{j+1},α{j+1},P{j+1}) (c)≤Q(τ{j+1},α{j+1},P{j+1}), (19)

where (a) holds since the Taylor expansion in (15) is tight at given local point, which implies problem (16) at has the same objective function as that of problem (13); (b) is because is the optimal solution to problem (16); (c) holds since the objective value of problem (16) is a lower bound of that of its original problem (13).

From (17), (18), and (19), we have

 Q(τ{j},α{j},P{j})≤Q(τ{j+1},α{j+1},P{j+1}), (20)

which implies that the objective value of problem (10) is non-decreasing after each iteration in Algorithm 1. Since the objective value of problem (10) is a finite positive value, the proposed Algorithm 1 is guaranteed to converge to the optimal objective value and solutions. This completes the convergence proof. ∎

The complexity of Algorithm 1 is polynomial, since only three convex optimization problems need to be solved in each iteration. Hence, the proposed Algorithm 1 can be practically implemented with fast convergence for full-duplex ABCNs with a moderate number of BDs and LU(s).

## V Numerical Results

In this section, we provide simulation results to evaluate the performance of the proposed joint design. We consider an ABCN with

BDs. Suppose that the FAP-to-BD1 distance and FAP-to-BD2 distance are 2.5 m and 4 m, respectively, the FAP (BD1, BD2)-to-LU distances are all 15 m. We assume independent Rayleigh fading channels, i.e., the channel coefficient of each path is a circularly symmetric complex Gaussian prandom variable, and the power gains of multiple paths are exponentially distributed. For each channel link, its first-path channel power gain is assumed to be

, where is the distance with unit of meter. Let the number of pathes , , and . Other parameters are set as . Define the average receive SNR at the FAP as . Let . For performance comparison, we consider a benchmark scheme in which the backscatter time portion and subcarrier power are equally allocated, i.e., , and all BDs adopt a common power reflection coefficient that is optimized via CVX. The following results are obtainepd based on 100 random channel realizations.

Fig. 3 plots the max-min throughput of all BDs versus the LU’s throughput requirement for different SNRs ’s. We fix and J. As expected, the max-min throughput decreases as increases, which reveals the throughput tradeoff between the BDs and the LU. We further observe that the max-min throughput performance is significantly enhanced by using the proposed joint design, compared to the benchmark scheme. Also, higher max-min throughput is achieved when the SNR at the FAP is higher.

Fig. 4 compares the max-min throughput under different BDs’ energy requirements ’s and subcarrier peak-power values ’s, for both the proposed joint design and the benchmark scheme. We fix bps/Hz. In general, the max-min throughput increases as the SNR increases. We have three further observations. First and foremost, the proposed joint design achieves significant max-min throughput gains as compared to the benchmark scheme. Second, higher max-min throughput is achieved for lower harvested-energy requirement with given , which reveals the BDs’ throughput-energy tradeoff. This observation can be specifically obtained from the three red solid curves for our proposed joint design and the three blue dotted curves for the benchmark scheme, given . Third, higher max-min throughput is obtained for higher peak-power value with given , which is demonstrated in the red and black solid curves with triangle marker for our proposed joint design.

## Vi Conclusion

This paper has investigated a full-duplex AmBC network over ambient OFDM carriers. The minimum throughput among all BDs is maximized by jointly optimizing the BDs’ backscatter time portions, the BDs’ power reflection coefficients, and the FAP’s subcarrier power allocation. By utilizing the block coordinated decent and successive convex optimization techniques, an efficient iterative algorithm is proposed, which is guaranteed to converge. Numerical results show that significant throughput gains are achieved as compared to the benchmark scheme with equal resource allocation, benefitting from multiple design dimensions of the proposed joint optimization. The interesting BDs’ throughput-energy tradeoff and the throughput tradeoff between the BDs and the LU are also revealed.

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