# Power Control for Passive QAM Multisensor Backscatter Communication Systems

Authors: Shengbo Hu; Jinrong Mo; Tingting Yan; Yanfeng Shi
Journal: Journal of Sensors
 (2017)

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## Abstract

To achieve good quality of service level such as throughput, power control is of great importance to passive quadrature amplitude modulation (QAM) multisensor backscatter communication systems. First, we established the RF energy harvesting model and gave the energy condition. In order to minimize the interference of subcarriers and increase the spectral efficiency, then, the colocated passive QAM backscatter communication signal model is presented and the nonlinear optimization problems of power control are solved for passive QAM backscatter communication systems. Solutions include maximum and minimum access interval, the maximum and minimum duty cycle, and the minimal RF-harvested energy under the energy condition for node operating. Using the solutions above, the maximum throughput of passive QAM backscatter communication systems is analyzed and numerical calculation is made finally. Numerical calculation shows that the maximal throughput decreases with the consumed power and the number of sensors, and the maximum throughput is decreased quickly with the increase of the number of sensors. Especially, for a given consumed power of sensor, it can be seen that the throughput decreases with the duty cycle and the number of sensors has little effect on the throughput.


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## Body

## 1. Introduction

Since the advent of backscatter communication, it has been widely used in the passive RFID (radio frequency identification) system due to its low cost and low power [1, 2]. Similarly, using the principle of the backscatter communication, the passive sensor node transmitter can be simplified into a transistor connected to the antenna. This will greatly reduce the cost and power consumption of wireless communication systems. For example, scholars from the University of Washington [3] researched the WISP (wireless identification and sensing platform) wireless smart sensor systems which can harvest RF energy based on backscatter communication. Now, PBC (passive backscatter communication) has been applied in these fields of smart car, wireless temperature measurement, the biological signal acquisition [4–9], and so forth. Undoubtedly, the study and application of passive backscatter communication will attract more and more attention.In passive backscatter communication systems, sensor nodes need to harvest RF energy from the transceivers or reader and use it to recharge their finite energy storage capacity as shown in Figure1. However, the unpredictable environments such as the channel, the number of sensors, and challenges of the RF energy harvesting make the activities of the sensors difficult, including sensing, processing, and communicating by nodes with a given rate. So, an efficient energy management is necessary in order to guarantee sensors’ activities and a QoS (quality of service) of backscatter communication [10–12].Figure 1
Passive backscatter sensor node.In fact, the mode using RF energy harvesting as a supplement to the finite energy storage capacity is called energy neutral operation [13]. In this mode, for such RF energy harvesting nodes with ideal finite energy storage capacity, the condition for energy neutral operation should be satisfied for all nonnegative values of τ:
(1)∫0τPctdt≤∫0τPRFtdt+B0,where PRFt is the harvested RF power at time t, Pct is the consumed power by nodes at that time, B0 is the initial energy stored in the ideal capacity, and τ is the runtime. So, the goal of power control for passive backscatter communication is to maximize QoS level under condition of energy neutral operation.For implementing multisensor backscatter communication systems, subcarrier modulation can be used for each sensor [14]. This leads to interference among sensors. In order to minimize such interference and increase spectral efficiency, modulations including QAM are used to improve data throughput [15–17]. It shows that it is feasible to use load-dependent scattering for yielding a simple QAM backscatter [15, 17]. In this paper, we focus on colocated multisensor QAM backscatter communication, showing that power control is important for the backscatter communication systems to achieve good QoS level via analysis and simulation. We introduce a related work in Section 2 and describe a system model in Section 3. In Section 4, we present the performance of the backscatter communication systems. And we analyze the impact of power control on the throughput of systems in Section 5. Finally, we provide some concluding remarks in Section 6.


## 2. Related Work

Several papers have mainly proposed power control on nodes using energy harvesting, because power control of energy harvesting determines the level of connectivity of backscatter communication as well as the achievable QoS of the systems. An RF-powered transmitter that supports 915 MHz downlink and 2.45 GHz uplink bands is designed in [18]. In [19], the paper computes the minimal number of sinks required to keep the network connected and to satisfy the required constraints.There exist attractive applications of the RF-powered devices such as wireless body networks. Benefiting from RF energy harvesting, some low-power devices can achieve real-time work-on-demand power from RF sources, which further enables a battery-free circuit with reduced size [20]. The body devices that implement high efficiency can be found in [21, 22]. For the multisensor system, we can refer [23]. The authors address the problem of developing energy-efficient transmission strategies for body sensor networks with energy harvesting [24]. And the authors evaluate the impact of transmit power control on the usefulness of a multisink WSN-Heap using energy harvesting, deployed in uniform string topology for railway track monitoring [25].


## 3. System Models

### 3.1. RF Energy-Harvesting Model

The RF energy harvester is composed of an antenna, impedance matching circuit, rectifier, and voltage multiplier as shown in Figure2. The efficiency η of the RF energy harvester is defined as follows:
(2)η=η1η2η3=PehPin,where η1, η2, and η3 are the efficiencies of the receiving antenna, impedance transformation network, and the rectifier, respectively, Peh is the output DC power and the meaning of eh is energy harvesting, and Pin is the input RF power.Figure 2
RF energy-harvesting model.
(a)
(b)In Figure2, Y-stage voltage multiplier circuits are used to promote the output voltage. So, the upper limit of the steady-state output voltage Vdd is increased by a factor Y and can be written as [26]
(3)Vdd=2YVpeak−Von,where Vpeak is the peak voltage of the signal at the input of the view of the Y-stage voltage multiplier circuits and Von is the turn-on voltage of the diode.Now, let us consider the minimum voltage for nodes to operate. Assuming, the harvesting power from the transceivers or reader isPeht and the consumed power by nodes at that time is Pct. When the power made available by the transceivers or reader is insufficient for continuous operation, that is, Peht<Pct, a capacity must be used to store RF energy until enough RF energy exists to complete an access. This affects the backscatter communication QoS level. Under these circumstances, the capacitor must be charged unless the stored energy Estored is greater than or equal to the access energy Eaccess, where Eaccess is the energy required for each access.The stored energyEstored can be written as
(4)Estored=12CVdd2−Vnode2,where C is the value of energy harvesting circuit output capacity and Vnode is the voltage level at which the node operates. And the access energy Eaccess can be written as
(5)Eaccess=∫T0T0+TaccessPcdt=Vnode∫T0T0+TaccessIaccessdt,where T0,T0+Taccess is the access interval and Iaccess is the time-varying current draw of the node during each access.Hence, the minimum voltage for nodes to operate is solved as(6)Vddmin=2EaccessC+Vnode2.OnceVdd<Vddmin, the node can not operate.


### 3.2. Energy Condition for Node Operating

Backscatter communication links include forward link and backscatter link. While accessing, the node harvests RF energy from the transceivers or reader firstly by forward link. OnceVdd≥Vddmin, that is, Estored≥Eaccess, the node draws power to carry out its operation and sends the sensor data to the transceivers or reader by backscatter link. These can be defined as an energy model as given in Figure 2. Each access interval comprises a charging phase and backscatter communication phase. In Figure 2, while accessing at time T0, the capacitor C charges unless the stored energy is Estored≥Eaccess at time T0+Tc. Then, the node sends data by backscatter link. Once Estored<Eaccess at time T0+Tc+Td, the node stops operating and waits next access. Let Eeh=B0+η∫T0T0+TcPeht−Pct+dt, the condition for energy neutral operation should be satisfied in the access interval T0,T0+Taccess:
(7)Eeh−∫T0+TcT0+Tc+TdPct−Peht+dt≥0,where η∈0,1 is the charging rate, B0 is the initial energy stored in the capacity, and the rectifier function x+ is defined as follows:
(8)x+=x,x≥0,0,x<0.Meanwhile, the limitation of capacity size requires the constraint to be satisfied as follows:(9)Eeh−∫T0+TcT0+Tc+TdPct−Peht+dt≤B,where B is the maximum energy that can be stored in the capacitor.Hence, the energy conditions for the node operating include (7), (9), and (10). And (10) is given as follows:
(10)B0+η∫T0T0+TcPeht−Pct+dt≥Etask,where Etask is the minimum energy required for the node to operate.For simplicity, assuming the consumed power by the node with forward link isPfc, the consumed power by the sensor with backscatter link is PbcPfc<Pbc and P is the harvested power, then the energy condition for node operating is given as follows:
(11)B0+ηTcP−Pfc−TdPbc≥0,B0+ηTcP−Pfc−TdPbc≤B,B0+ηTcP−Pfc≥Eaccess.


## 3.1. RF Energy-Harvesting Model

The RF energy harvester is composed of an antenna, impedance matching circuit, rectifier, and voltage multiplier as shown in Figure2. The efficiency η of the RF energy harvester is defined as follows:
(2)η=η1η2η3=PehPin,where η1, η2, and η3 are the efficiencies of the receiving antenna, impedance transformation network, and the rectifier, respectively, Peh is the output DC power and the meaning of eh is energy harvesting, and Pin is the input RF power.Figure 2
RF energy-harvesting model.
(a)
(b)In Figure2, Y-stage voltage multiplier circuits are used to promote the output voltage. So, the upper limit of the steady-state output voltage Vdd is increased by a factor Y and can be written as [26]
(3)Vdd=2YVpeak−Von,where Vpeak is the peak voltage of the signal at the input of the view of the Y-stage voltage multiplier circuits and Von is the turn-on voltage of the diode.Now, let us consider the minimum voltage for nodes to operate. Assuming, the harvesting power from the transceivers or reader isPeht and the consumed power by nodes at that time is Pct. When the power made available by the transceivers or reader is insufficient for continuous operation, that is, Peht<Pct, a capacity must be used to store RF energy until enough RF energy exists to complete an access. This affects the backscatter communication QoS level. Under these circumstances, the capacitor must be charged unless the stored energy Estored is greater than or equal to the access energy Eaccess, where Eaccess is the energy required for each access.The stored energyEstored can be written as
(4)Estored=12CVdd2−Vnode2,where C is the value of energy harvesting circuit output capacity and Vnode is the voltage level at which the node operates. And the access energy Eaccess can be written as
(5)Eaccess=∫T0T0+TaccessPcdt=Vnode∫T0T0+TaccessIaccessdt,where T0,T0+Taccess is the access interval and Iaccess is the time-varying current draw of the node during each access.Hence, the minimum voltage for nodes to operate is solved as(6)Vddmin=2EaccessC+Vnode2.OnceVdd<Vddmin, the node can not operate.


## 3.2. Energy Condition for Node Operating

Backscatter communication links include forward link and backscatter link. While accessing, the node harvests RF energy from the transceivers or reader firstly by forward link. OnceVdd≥Vddmin, that is, Estored≥Eaccess, the node draws power to carry out its operation and sends the sensor data to the transceivers or reader by backscatter link. These can be defined as an energy model as given in Figure 2. Each access interval comprises a charging phase and backscatter communication phase. In Figure 2, while accessing at time T0, the capacitor C charges unless the stored energy is Estored≥Eaccess at time T0+Tc. Then, the node sends data by backscatter link. Once Estored<Eaccess at time T0+Tc+Td, the node stops operating and waits next access. Let Eeh=B0+η∫T0T0+TcPeht−Pct+dt, the condition for energy neutral operation should be satisfied in the access interval T0,T0+Taccess:
(7)Eeh−∫T0+TcT0+Tc+TdPct−Peht+dt≥0,where η∈0,1 is the charging rate, B0 is the initial energy stored in the capacity, and the rectifier function x+ is defined as follows:
(8)x+=x,x≥0,0,x<0.Meanwhile, the limitation of capacity size requires the constraint to be satisfied as follows:(9)Eeh−∫T0+TcT0+Tc+TdPct−Peht+dt≤B,where B is the maximum energy that can be stored in the capacitor.Hence, the energy conditions for the node operating include (7), (9), and (10). And (10) is given as follows:
(10)B0+η∫T0T0+TcPeht−Pct+dt≥Etask,where Etask is the minimum energy required for the node to operate.For simplicity, assuming the consumed power by the node with forward link isPfc, the consumed power by the sensor with backscatter link is PbcPfc<Pbc and P is the harvested power, then the energy condition for node operating is given as follows:
(11)B0+ηTcP−Pfc−TdPbc≥0,B0+ηTcP−Pfc−TdPbc≤B,B0+ηTcP−Pfc≥Eaccess.


## 4. Performance Analysis

### 4.1. Colocated QAM Multisensor Backscatter Signal

Typically, backscatter communication systems use single-frequency continuous wave transmission waveforms for accessing. The resulting complex signal from the node received at the transceivers or reader is given as(12)rt=2Eαmtexpjωct+φ+nt,where E, ωc, and φ are the peak power, the angular frequency, and the phase of the carrier signal, respectively, nt is AWGN (additive white Gaussian noise), and mt is the message signal to be transmitted.To improve spectral efficiency, the use of QAM opens up many new avenues for backscatter communication systems. It has been shown recently that it is feasible to build backscatter systems supporting QAM using node load selection methodology [17, 27]. However, improved spectral efficiency means that the node’s impedance is mismatched and the power harvested or the efficiency of impedance transformation network η2 is reduced.What is more,mt can be given as
(13)mt=∑k=−∞∞akgt−kT,where gt is the rectangle pulse with width T and ak is the sequence of symbols with L levels. If the number of phases φ is K in (12), the number of the carrier states is K×L. And when K=L=2, the modulation is 4QAM, that is, to design and implement 4QAM backscatter modulator, four RC lumped impedances are connected to an antenna port through RF 4-1 Mux, each lumped impedance corresponding to different reflection coefficients. The design of 4QAM colocated backscatter communication systems with this procedure is given in Figure 3. In Figure 3, serial/parallel converts sensor data into 2 bits for controlling the 4-1 Mux.Figure 3
Passive QAM backscatter multisensor communication systems.To make the structure of the backscatter multisensor nodes simple, we put forward an access scheme with different subcarrier modulations for each sensor; namely, each sensor has different pulse width. So, the cumulative colocated QAM multisensor backscatter signal at the transceivers or reader is a sum of all complex signals from sensors with additive white noise, resulting in(14)rt=2Piαimitexpjωct+φ+∑k≠i2Pkαkmktexpjωct+φ+nt.


### 4.2. Throughput Maximization for Colocated QAM Multisensor under the RF Energy-Harvesting Constraints

The goal of power control for passive multisensor random interrogating is to meet some QoS criteria, for example, throughput.In Figure3, each sensor has different subcarrier frequencies; however, the information leak of one sensor interferes other sensors. The amount of such interference depends on the power spectrum of the chosen subcarrier modulation and the number of sensors. According to the constraint of the correlated short-range wireless communication spectrum, the power spectrum of QAM modulation of the ith sensor can be approximated as [28]
(15)Sf≈1f−fi4,where fi=1/Ti and Ti is the pulse width of the ith sensor data.Under the lognormal channel, signal-to-interference-and-noise ratio (SINR) at the transceivers or reader in Figure3 is written as
(16)Γi=2EihiW0/Ti+∑j=1,≠iN2EjhjSfj−fi,where Ei is the transmitted bit energy, W0 is the power spectrum density, hi=liΩi, li is the path loss, Ωi is the shadow fading of logarithmic normal distribution, and Ωi=ex. x follows normal distribution Gμ,σ2.In this paper, the multiple sensors are colocation and share a transmitter and transceiver, so it can be assumed thathi=hj and Ei=Ej. Consequently, (16) can be rewritten as
(17)Γi=1ΓN−1+ΓI−1,where ΓN=2EiTi⋅liγi⋅10xi/10/W0 and ΓI=∑j=1,≠iN10xi−xj/10⋅li/ljγ⋅1/Sfj−fi.Now, we characterize the performance of backscatter communication. We start by defining the concept of the throughput.Definition 1.
The data delivery ratioDr of backscatter communication systems is a ratio of successful data packet received to attempted data packet transmitted.Definition 2.
The throughputTh of backscatter communication systems is the probability that a packet is successfully received during a data interrogation interval.For a packet to be received successfully, the SINR at the transceivers or reader must exceed some thresholdλth. Using the definitions above, the data delivery ratio Dri and the throughput Thi in the access interval Taccess of the ith sensor can be written, respectively, as
(18)Dri=PΓi≥λth,Thi=PΓi≥λthTaccess.So, the average data delivery ratio and throughput of the backscatter communication systems can be written as follows:(19)Dr=∑i=1NDriN,Th=∑i=1NThiN,where N is the number of sensors.Generally, obtaining throughput in a closed form is not always possible and remains analytically challenging; because of the cumulative distribution function of random variable,Γi remains difficult. Thanks to nodes colocating, this problem can be solved easily. In this case, xi=xj, li=lj, and (16) can be rewritten as
(20)Γi=1ΓN−1+∑j=1,≠iNSfj−fi.Let(21)ki=10logW02EiTiliγi⋅λth1−λth∑j=1,≠iNSfj−fi,then,
(22)Dri=PΓi≥λth=Pxi≥ki=1−Pxi<ki=1−∫−∞ki12πσie−xi2/2σi2dx.Hence, the average data throughputTh can be rewritten as
(23)Th=∑i=1NDriNTaccess=∑i=1N1−∫−∞ki1/2πσie−xi2/2σi2dxNTaccess.Assuming duty cycleρ=T¯d/T¯c+T¯d=T¯d/T¯task,ρ∈0,1, the nonlinear optimization problems of power control for passive QAM backscatter communication systems with N nodes can be expressed as
(24)maxTh=∑i=1NDriNTaccess,subject to
(25)B0m+η1−ρT¯taskP−NPfc−ρNT¯taskPbc≥0,B0m+η1−ρT¯taskP−NPfc−ρNT¯taskPbc≤B,B0m+η1−ρT¯taskP−NPfc≥Etask,B0≤B.


## 4.1. Colocated QAM Multisensor Backscatter Signal

Typically, backscatter communication systems use single-frequency continuous wave transmission waveforms for accessing. The resulting complex signal from the node received at the transceivers or reader is given as(12)rt=2Eαmtexpjωct+φ+nt,where E, ωc, and φ are the peak power, the angular frequency, and the phase of the carrier signal, respectively, nt is AWGN (additive white Gaussian noise), and mt is the message signal to be transmitted.To improve spectral efficiency, the use of QAM opens up many new avenues for backscatter communication systems. It has been shown recently that it is feasible to build backscatter systems supporting QAM using node load selection methodology [17, 27]. However, improved spectral efficiency means that the node’s impedance is mismatched and the power harvested or the efficiency of impedance transformation network η2 is reduced.What is more,mt can be given as
(13)mt=∑k=−∞∞akgt−kT,where gt is the rectangle pulse with width T and ak is the sequence of symbols with L levels. If the number of phases φ is K in (12), the number of the carrier states is K×L. And when K=L=2, the modulation is 4QAM, that is, to design and implement 4QAM backscatter modulator, four RC lumped impedances are connected to an antenna port through RF 4-1 Mux, each lumped impedance corresponding to different reflection coefficients. The design of 4QAM colocated backscatter communication systems with this procedure is given in Figure 3. In Figure 3, serial/parallel converts sensor data into 2 bits for controlling the 4-1 Mux.Figure 3
Passive QAM backscatter multisensor communication systems.To make the structure of the backscatter multisensor nodes simple, we put forward an access scheme with different subcarrier modulations for each sensor; namely, each sensor has different pulse width. So, the cumulative colocated QAM multisensor backscatter signal at the transceivers or reader is a sum of all complex signals from sensors with additive white noise, resulting in(14)rt=2Piαimitexpjωct+φ+∑k≠i2Pkαkmktexpjωct+φ+nt.


## 4.2. Throughput Maximization for Colocated QAM Multisensor under the RF Energy-Harvesting Constraints

The goal of power control for passive multisensor random interrogating is to meet some QoS criteria, for example, throughput.In Figure3, each sensor has different subcarrier frequencies; however, the information leak of one sensor interferes other sensors. The amount of such interference depends on the power spectrum of the chosen subcarrier modulation and the number of sensors. According to the constraint of the correlated short-range wireless communication spectrum, the power spectrum of QAM modulation of the ith sensor can be approximated as [28]
(15)Sf≈1f−fi4,where fi=1/Ti and Ti is the pulse width of the ith sensor data.Under the lognormal channel, signal-to-interference-and-noise ratio (SINR) at the transceivers or reader in Figure3 is written as
(16)Γi=2EihiW0/Ti+∑j=1,≠iN2EjhjSfj−fi,where Ei is the transmitted bit energy, W0 is the power spectrum density, hi=liΩi, li is the path loss, Ωi is the shadow fading of logarithmic normal distribution, and Ωi=ex. x follows normal distribution Gμ,σ2.In this paper, the multiple sensors are colocation and share a transmitter and transceiver, so it can be assumed thathi=hj and Ei=Ej. Consequently, (16) can be rewritten as
(17)Γi=1ΓN−1+ΓI−1,where ΓN=2EiTi⋅liγi⋅10xi/10/W0 and ΓI=∑j=1,≠iN10xi−xj/10⋅li/ljγ⋅1/Sfj−fi.Now, we characterize the performance of backscatter communication. We start by defining the concept of the throughput.Definition 1.
The data delivery ratioDr of backscatter communication systems is a ratio of successful data packet received to attempted data packet transmitted.Definition 2.
The throughputTh of backscatter communication systems is the probability that a packet is successfully received during a data interrogation interval.For a packet to be received successfully, the SINR at the transceivers or reader must exceed some thresholdλth. Using the definitions above, the data delivery ratio Dri and the throughput Thi in the access interval Taccess of the ith sensor can be written, respectively, as
(18)Dri=PΓi≥λth,Thi=PΓi≥λthTaccess.So, the average data delivery ratio and throughput of the backscatter communication systems can be written as follows:(19)Dr=∑i=1NDriN,Th=∑i=1NThiN,where N is the number of sensors.Generally, obtaining throughput in a closed form is not always possible and remains analytically challenging; because of the cumulative distribution function of random variable,Γi remains difficult. Thanks to nodes colocating, this problem can be solved easily. In this case, xi=xj, li=lj, and (16) can be rewritten as
(20)Γi=1ΓN−1+∑j=1,≠iNSfj−fi.Let(21)ki=10logW02EiTiliγi⋅λth1−λth∑j=1,≠iNSfj−fi,then,
(22)Dri=PΓi≥λth=Pxi≥ki=1−Pxi<ki=1−∫−∞ki12πσie−xi2/2σi2dx.Hence, the average data throughputTh can be rewritten as
(23)Th=∑i=1NDriNTaccess=∑i=1N1−∫−∞ki1/2πσie−xi2/2σi2dxNTaccess.Assuming duty cycleρ=T¯d/T¯c+T¯d=T¯d/T¯task,ρ∈0,1, the nonlinear optimization problems of power control for passive QAM backscatter communication systems with N nodes can be expressed as
(24)maxTh=∑i=1NDriNTaccess,subject to
(25)B0m+η1−ρT¯taskP−NPfc−ρNT¯taskPbc≥0,B0m+η1−ρT¯taskP−NPfc−ρNT¯taskPbc≤B,B0m+η1−ρT¯taskP−NPfc≥Etask,B0≤B.


## 5. Numerical Results and Discussions

We evaluate the performance of the power control using numerical analysis. The analysis includes the impact ofPbc on the throughput and the harvested power.


### 5.1. Parameters for Numerical Analysis

Referring to the relation between bit error rate and SINR for 4QAM under AWGN channel, the thresholdλth can be chosen as 3.0156 corresponding to the data delivery ratio ranging from 1 to 1×10−5. Meanwhile, the given transmission data rate is 40 kbps, the data packet size is 64 bits, and the duration of a data packet transmission is Tdm=1.6sec. All parameters used are listed in Table 1 [29].Table 1
Parameters for numerical analysis.
Parameter
Value
W
0
−
1.0779
d
B
w
/
H
z
l
i
−
1
d
B
λ
t
h
3.0156
T
d
m
1.6 sec
P
f
c
68.9 nW
B
0.0125 J
η
0.65


### 5.2. Impact ofPbc on Throughput Th

In this section, we first investigate the choice ofPbc to achieve maximal throughput.Under the energy condition for node operating in (11) and solving the inequality group, it can be shown that the maximum and minimum access interval Taccess is given by
(26)Taccessmin=ηTdP−NPfc+NTdPbcηP−NPfc,Taccessmax=ηTdP−NPfc+NTdPbc+BηP−NPfc.The access intervalTaccess is a function of Pbc. When P=189μW, N=2, N=4, and N=8, the minimum and maximum access intervals of sensor node1 with subcarrier f1=50000 Hz are plotted in Figures 4 and 5. The subcarriers of other nodes are 50,002 Hz, 50,010 Hz, 50,100 Hz, 50,110 Hz, 50,120 Hz, 50,150 Hz, and 50,200 Hz (the same below). According to these frequencies and the value of Taccess, we can deduce the corresponding value of the throughput using (20), (23), and (24). And the throughput changes by varying of Taccess.Figure 4
The minimum access interval versus the consumed power by sensor with scatter link.Figure 5
The maximum access interval versus the consumed power by sensor with scatter link.It is observed that the maximum and minimum access intervalsTaccess increase with Pbc in Figures 4 and 5. It is easy to understand, because the greater the Pbc, the longer the charge time to meet the energy condition for node operating. It is worthwhile to note that the maximum and minimum access interval Taccess increases more with the increase of N.Hence, the maximum throughput as a function ofPbc is plotted under the condition of the minimum access interval Taccess in Figure 6. It is found that the maximal throughput decreases with the increase of Pbc. And the maximum throughput is decreased quickly with the increase of N.Figure 6
The maximum throughput versus the consumed power by sensor with scatter link.


### 5.3. Impact of Duty Cycleρ on Throughput Th

Next, we investigate the impact of varying duty cycleρ on the throughput Th.Similar to Section4.2, the maximum and minimum duty cycle ρ under the energy condition for node operating is given as follows:
(27)ρmax=ηTdP−NPfcηTdP−NPfc+NTdPbc,ρmin=ηTdP−NPfcB+ηTdP−NPfc+NTdPbc.For a givenPbc=0.524μW and a given Pfc=0.0689μW, the throughput Th as a function of duty cycle ρ is shown in Figure 7. It can be seen that the throughput Th decreases with the increase of duty cycle ρ. Because decreasing duty cycle ρ leads to the increasing of the access interval Taccess.Figure 7
The throughput versus the duty cycleρ.It should be noted thatN has little effect on the throughput in Figure 7, because duty cycle ρ is insensitive to N. Especially, N has almost no effect on the minimum duty cycle ρ. We can analyze this using parameter sensitivity.Taking the partial derivative, the sensitivity ofρmax and ρmin is given as
(28)Sρmax=∂ρmax∂N=ηTd2PPbcηTdP−NPfc+NTdPbc2,Sρmin=∂ρmin∂N=ηTd2PPbc+TdBPfcB+ηTdP−NPfc+NTdPbc2.Hence, theSρmax and Sρmin as functions of N are shown in Figure 8. In Figure 8, Sρmax and Sρmin are very small. Especially, N has almost no effect on the minimum duty cycle ρ, because of using the large stored capacity. This can be also seen from the relation between duty cycle ρ and N shown in Figure 9.Figure 8
The sensitivity of duty cycle aboutN.Figure 9
The relation between the duty cycleρ and N.


### 5.4. Impact ofPbc on the Minimum Harvested Energy Pmin

Finally, we analyze the choice ofPbc to achieve the minimal RF-harvested energy under the energy condition for node operating.In the same way, we can derive that the minimal RF-harvested energy is given by(29)Pmin=NPbc+Etaskη1−ρTtask.ThePmin as a function of Pbc is plotted in Figure 10. In Figure 10, as the Pbc and N increase, the Pmin increases. This conclusion is obvious. Similar to Section 5.2, the number of sensors has larger effect on the minimum RF-harvested power.Figure 10
The minimum RF-harvested power versus the consumed power by sensor with scatter link.


## 5.1. Parameters for Numerical Analysis

Referring to the relation between bit error rate and SINR for 4QAM under AWGN channel, the thresholdλth can be chosen as 3.0156 corresponding to the data delivery ratio ranging from 1 to 1×10−5. Meanwhile, the given transmission data rate is 40 kbps, the data packet size is 64 bits, and the duration of a data packet transmission is Tdm=1.6sec. All parameters used are listed in Table 1 [29].Table 1
Parameters for numerical analysis.
Parameter
Value
W
0
−
1.0779
d
B
w
/
H
z
l
i
−
1
d
B
λ
t
h
3.0156
T
d
m
1.6 sec
P
f
c
68.9 nW
B
0.0125 J
η
0.65


## 5.2. Impact ofPbc on Throughput Th

In this section, we first investigate the choice ofPbc to achieve maximal throughput.Under the energy condition for node operating in (11) and solving the inequality group, it can be shown that the maximum and minimum access interval Taccess is given by
(26)Taccessmin=ηTdP−NPfc+NTdPbcηP−NPfc,Taccessmax=ηTdP−NPfc+NTdPbc+BηP−NPfc.The access intervalTaccess is a function of Pbc. When P=189μW, N=2, N=4, and N=8, the minimum and maximum access intervals of sensor node1 with subcarrier f1=50000 Hz are plotted in Figures 4 and 5. The subcarriers of other nodes are 50,002 Hz, 50,010 Hz, 50,100 Hz, 50,110 Hz, 50,120 Hz, 50,150 Hz, and 50,200 Hz (the same below). According to these frequencies and the value of Taccess, we can deduce the corresponding value of the throughput using (20), (23), and (24). And the throughput changes by varying of Taccess.Figure 4
The minimum access interval versus the consumed power by sensor with scatter link.Figure 5
The maximum access interval versus the consumed power by sensor with scatter link.It is observed that the maximum and minimum access intervalsTaccess increase with Pbc in Figures 4 and 5. It is easy to understand, because the greater the Pbc, the longer the charge time to meet the energy condition for node operating. It is worthwhile to note that the maximum and minimum access interval Taccess increases more with the increase of N.Hence, the maximum throughput as a function ofPbc is plotted under the condition of the minimum access interval Taccess in Figure 6. It is found that the maximal throughput decreases with the increase of Pbc. And the maximum throughput is decreased quickly with the increase of N.Figure 6
The maximum throughput versus the consumed power by sensor with scatter link.


## 5.3. Impact of Duty Cycleρ on Throughput Th

Next, we investigate the impact of varying duty cycleρ on the throughput Th.Similar to Section4.2, the maximum and minimum duty cycle ρ under the energy condition for node operating is given as follows:
(27)ρmax=ηTdP−NPfcηTdP−NPfc+NTdPbc,ρmin=ηTdP−NPfcB+ηTdP−NPfc+NTdPbc.For a givenPbc=0.524μW and a given Pfc=0.0689μW, the throughput Th as a function of duty cycle ρ is shown in Figure 7. It can be seen that the throughput Th decreases with the increase of duty cycle ρ. Because decreasing duty cycle ρ leads to the increasing of the access interval Taccess.Figure 7
The throughput versus the duty cycleρ.It should be noted thatN has little effect on the throughput in Figure 7, because duty cycle ρ is insensitive to N. Especially, N has almost no effect on the minimum duty cycle ρ. We can analyze this using parameter sensitivity.Taking the partial derivative, the sensitivity ofρmax and ρmin is given as
(28)Sρmax=∂ρmax∂N=ηTd2PPbcηTdP−NPfc+NTdPbc2,Sρmin=∂ρmin∂N=ηTd2PPbc+TdBPfcB+ηTdP−NPfc+NTdPbc2.Hence, theSρmax and Sρmin as functions of N are shown in Figure 8. In Figure 8, Sρmax and Sρmin are very small. Especially, N has almost no effect on the minimum duty cycle ρ, because of using the large stored capacity. This can be also seen from the relation between duty cycle ρ and N shown in Figure 9.Figure 8
The sensitivity of duty cycle aboutN.Figure 9
The relation between the duty cycleρ and N.


## 5.4. Impact ofPbc on the Minimum Harvested Energy Pmin

Finally, we analyze the choice ofPbc to achieve the minimal RF-harvested energy under the energy condition for node operating.In the same way, we can derive that the minimal RF-harvested energy is given by(29)Pmin=NPbc+Etaskη1−ρTtask.ThePmin as a function of Pbc is plotted in Figure 10. In Figure 10, as the Pbc and N increase, the Pmin increases. This conclusion is obvious. Similar to Section 5.2, the number of sensors has larger effect on the minimum RF-harvested power.Figure 10
The minimum RF-harvested power versus the consumed power by sensor with scatter link.


## 6. Conclusion

To achieve good QoS level such as throughput, power control is of great importance to passive QAM multisensor backscatter communication systems. This paper presents the RF energy-harvesting model and gives the energy condition for node operating. In order to minimize interference resulted from multisensors and increase spectral efficiency, we propose the colocated passive QAM backscatter communication signal model, give the closed-form solution of the throughput under log-normal channel, and put forward the nonlinear optimization problems of power control for passive QAM backscatter communication systems. Solving the nonlinear optimization problems, we obtain the maximum and minimum access intervals, the maximum and minimum duty cycle, and the minimal RF harvested energy under the condition of node operating. Based on the solutions above, we analyze the maximum throughput of passive QAM backscatter communication systems and make numerical calculation. Finally, we make the conclusion as follows:(i)
The energy condition for node operating is a prerequisite for designing and optimizing the passive backscatter communication systems, and the goal of power control is to maximize the QoS of the systems.(ii)
Under the energy condition for node operating, the consumed powerPbc of the sensor with backscatter link and the number of sensors has large effect on the throughput of systems. It is found that the maximal throughput decreases with the increase of Pbc and N and the maximum throughput is decreased quickly with the increase of N.(iii)
Especially, for a givenPbc and a given Pfc, it can be seen that the throughput Th decreases with the increase of duty cycle ρ and the number of sensors has little effect on the throughput.(iv)
There also exists a further improvement in this paper. For the next phase work, we will try to establish an actual model for data measurement and we will consider the WCDMA or LTE signals substituting for QAM signals.



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*Source: 4319709-2017-12-27.xml*