Power Control for Passive QAM Multisensor Backscatter Communication Systems

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.


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][5][6][7][8][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 Figure 1.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][11][12].
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: where P RF t is the harvested RF power at time t, P c t is the consumed power by nodes at that time, B 0 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][16][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.

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].

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 Figure 2. The efficiency η of the RF energy harvester is defined as follows: where η 1 , η 2 , and η 3 are the efficiencies of the receiving antenna, impedance transformation network, and the rectifier, respectively, P eh is the output DC power and the meaning of eh is energy harvesting, and P in is the input RF power.
In Figure 2, Y-stage voltage multiplier circuits are used to promote the output voltage.So, the upper limit of the steadystate output voltage V dd is increased by a factor Y and can be written as [26] where V peak is the peak voltage of the signal at the input of the view of the Y-stage voltage multiplier circuits and V on 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 is P eh t and the consumed power by nodes at that time is P c t .When the power made available by the transceivers or reader is insufficient for continuous operation, that is, P eh t < P c t , 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 E stored is greater than or equal to the access energy E access , where E access is the energy required for each access.
The stored energy E stored can be written as where C is the value of energy harvesting circuit output capacity and V node is the voltage level at which the node operates.And the access energy E access can be written as where T 0 , T 0 + T access is the access interval and I access is the time-varying current draw of the node during each access.Hence, the minimum voltage for nodes to operate is solved as Once V dd < V min dd , the node can not operate.

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.Once V dd ≥ V min dd , that is, E stored ≥ E access , 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 T 0 , the capacitor C charges unless the stored energy is E stored ≥ E access at time T 0 + T c .Then, the node sends data by backscatter link.Once E stored < E access at time T 0 + T c + T d , the node stops operating and waits next access.Let E eh = B 0 + η T 0 +T c T 0 P eh t − P c t + dt, the condition for energy neutral operation should be satisfied in the access interval T 0 , T 0 + T access : where η ∈ 0, 1 is the charging rate, B 0 is the initial energy stored in the capacity, and the rectifier function x + is defined as follows: Meanwhile, the limitation of capacity size requires the constraint to be satisfied as follows: 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: where E task is the minimum energy required for the node to operate.For simplicity, assuming the consumed power by the node with forward link is P fc , the consumed power by the sensor with backscatter link is P bc P fc < P bc and P is Typically, backscatter communication systems use singlefrequency continuous wave transmission waveforms for accessing.The resulting complex signal from the node received at the transceivers or reader is given as where E, ω c , and φ are the peak power, the angular frequency, and the phase of the carrier signal, respectively, n t is AWGN (additive white Gaussian noise), and m t 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 η 2 is reduced.
What is more, m t can be given as where g t is the rectangle pulse with width T and a k 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.
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 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 Figure 3, 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] S f ≈ 1 where f i = 1/T i and T i is the pulse width of the ith sensor data.4

RF oscillator Power amplifier
Journal of Sensors Under the lognormal channel, signal-to-interferenceand-noise ratio (SINR) at the transceivers or reader in Figure 3 is written as where E i is the transmitted bit energy, W 0 is the power spectrum density, h i = l i Ω i , l i is the path loss, Ω i is the shadow fading of logarithmic normal distribution, and In this paper, the multiple sensors are colocation and share a transmitter and transceiver, so it can be assumed that h i = h j and E i = E j .Consequently, ( 16) can be rewritten as where Now, we characterize the performance of backscatter communication.We start by defining the concept of the throughput.Definition 1.The data delivery ratio D r of backscatter communication systems is a ratio of successful data packet received to attempted data packet transmitted.Definition 2. The throughput T h 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 threshold λ th .Using the definitions above, the data delivery ratio D ri and the throughput T hi in the access interval T access of the ith sensor can be written, respectively, as So, average data delivery ratio and throughput of the backscatter communication systems can be written as follows: 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, Γ i remains difficult.Thanks to nodes colocating, this problem can be solved easily.In this case, x i = x j , l i = l j , and ( 16) can be rewritten as then, Hence, the average data throughput T h can be rewritten as Assuming duty cycle ρ = 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

Numerical Results and Discussions
We evaluate the performance of the power control using numerical analysis.The analysis includes the impact of P bc on the throughput and the harvested power.

Parameters for Numerical Analysis.
Referring to the relation between bit error rate and SINR for 4QAM under AWGN channel, the threshold λ th 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 T dm = 1 6 sec.All parameters used are listed in Table 1 [29].
5.2.Impact of P bc on Throughput T h .In this section, we first investigate the choice of P bc 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 T access is given by The access interval T access is a function of P bc .When P = 189 μW, N = 2, N = 4, and N = 8, the minimum and maximum access intervals of sensor node1 with subcarrier f 1 = 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 T access , we can deduce the corresponding value of the throughput using (20), (23), and (24).And the throughput changes by varying of T access .
It is observed that the maximum and minimum access intervals T access increase with P bc in Figures 4 and 5.It is easy to understand, because the greater the P bc , 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 T access increases more with the increase of N.
Hence, the maximum throughput as a function of P bc is plotted under the condition of the minimum access interval T access in Figure 6.It is found that the maximal throughput decreases with the increase of P bc .And the maximum throughput is decreased quickly with the increase of N. It should be noted that N 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.The minimum access interval (s)    Hence, the S ρ max and S ρ min as functions of N are shown in Figure 8.In Figure 8, S ρ max and S ρ min 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.In the same way, we can derive that the minimal RF-harvested energy is given by The P min as a function of P bc is plotted in Figure 10.In Figure 10, as the P bc and N increase, the P min increases.This conclusion is obvious.Similar to Section 5.2, the number of sensors has larger effect on the minimum RFharvested power.

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 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 power P bc 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 P bc and N and the maximum throughput is decreased quickly with the increase of N.
(iii) Especially, for a given P bc and a given P fc , it can be seen that the throughput T h 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.

5. 3 .Figure 7 .
Figure 7.It can be seen that the throughput T h decreases with the increase of duty cycle ρ.Because decreasing duty cycle ρ leads to the increasing of the access interval T access .It should be noted that N has little effect on the throughput in Figure7, 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.

Figure 4 :
Figure 4: The minimum access interval versus the consumed power by sensor with scatter link.

Figure 5 :
Figure 5: The maximum access interval versus the consumed power by sensor with scatter link.

5. 4 .
Impact of P bc on the Minimum Harvested Energy P min .Finally, we analyze the choice of P bc to achieve

Figure 6 :
Figure 6: The maximum throughput versus the consumed power by sensor with scatter link.

Figure 7 :
Figure 7: The throughput versus the duty cycle ρ.

Figure 8 :
Figure 8: The sensitivity of duty cycle about N.

Figure 9 :
Figure 9: The relation between the duty cycle ρ and N.

Figure 10 :
Figure 10: The minimum RF-harvested power versus the consumed power by sensor with scatter link.

Table 1 :
Parameters for numerical analysis.