I. INTRODUCTION
Microwave wireless power transfer is suitable for supplying energy to IoT devices or sensors that are placed indoors or inside machines. Although distance attenuation is large and supplied energy is small, the wireless power transfer has at least two merits: stable electric power supply regardless of time and environment, compared to energy harvesting tech- nologies, and the possibility of utilizing wireless access points for data communication. In particular, many researchers in wireless communication are starting to work on the integration of wireless power transmission and information transmission Fig. 1: Single antenna wire- [1]–[10]. We believe that simultaneous wireless information and power transfer (SWIPT) will be a key technology in the IoT era. This paper addresses the efficiency of wireless power trans- mission by radio waves while aiming at the future imple- mentation of SWIPT. Wireless power transfer using a single antenna causes an energy shortage problem because an IoT device distant from the antenna obtains less energy. Figure 1 shows an example of power transfer using a single antenna. Some IoT devices may have an energy shortage because of distance attenuation of radio waves. Using distributed multiple antennas efficiently supplies en- ergy because the relative distance between antennas and IoT devices becomes less than using a single antenna. There are two types of research in wireless power transfer using multiple antennas: one is for a single IoT device [11]–[14] and the other is for multiple IoT devices [15], [16]. Our study focuses on power transfer using multiple antennas for multiple IoT devices. It is known that the use of distributed multiple antennas for multiple IoT devices causes a standing wave problem [16]. Figure 2 shows an example of the standing wave problem. Constructive and destructive standing waves arise when mul¬ tiple antennas emit radio waves simultaneously. IoT devices located on destructive standing waves cannot obtain sufficient energy. To solve the standing wave problem, [16] proposes carrier shift diversity (CSD) power transfer. Figure 3 shows an example of CSD power transfer. CSD power transfer enables uniform energy delivery, in space, by continuously changing the phases of radio waves. The received energy on each IoT device is averaged because the continuous phase change alternates destructive and constructive interference in a brief period. However, while decreasing the amount of destructive interference, CSD power transfer also decreases the amount of constructive interference. Therefore this paper proposes phase-controlled cooperative power transfer (PC-CPT). PC-CPT improves power transfer efficiency under the condition of distributed multiple antennas and multiple IoT devices. The proposed PC-CPT controls the phase of emitted radio waves from each antenna to increase the amount of constructive interference at each IoT device. Additionally, switching the phase optimization for individual IoT devices improves the equitable distribution of supplied energy among all IoT devices. Figure 2 and Figure 4 show examples of PC-CPT. The example shows the switching of phase sets Θ 1 and Θ 2 , in time-division manner, to change the pattern of constructive interference. We have evaluated the proposed method compared to existing methods, such as CSD, and the evaluation results show the proposed method outperforms existing methods. The remainder of this paper is organized as follows: Section II introduces the proposed system model which includes a network model and an IoT device model, and shows a received signal strength indicator (RSSI) feedback problem in the model. Section III describes the proposed algorithm to solve the RSSI feedback problem. Section IV discusses the evalu- ation of the proposed method by computer simulations and experimental micro benchmarks. Finally, Section V concludes the paper.
II.  S YSTEM M ODEL
A. Preliminaries
Figure 5 shows the network model of PC-CPT. Several TX antennas and IoT devices are deployed in a network. The positions of the TX antennas and the IoT devices are fixed. Each TX antenna is connected to a wireless power transmitter and TX antennas transmit the same frequency radio waves while sharing a local oscillator. The wireless power transmitter controls each phase of the radio wave from each TX antenna by a phase controller. Here the set of phases at all TX antennas is called a phase set Θ = θ 1 ,θ 2 , · · · ,θ m where m is the number of TX antennas. TX antennas switch phase sets Ψ = Θ 1 , Θ 2 , ･ ･ · , Θ p in time- division manner to supply energy for all IoT devices equitably, where p is the number of phase sets. The wireless power transmitter centrally controls the phase of a radio wave from the TX antenna, according to RSSI feedback from IoT devices. Figure 6 shows the IoT device model. We assume that each IoT device has a backscatter module, an energy har- vest module, and a low power data decoder module. The backscatter module performs data transmission by reflecting and absorbing radio waves from access points. Backscatter communication consumes much less power than conventional wireless communication using an external access point's waves as carrier waves [17]–[19]. The energy harvest module absorbs energy from radio waves, via a rectenna, and stores the energy in a capacitor. The capacitor supplies energy to a main control unit (MCU), a low-power data decoder, and a backscatter module. The data decoder module decodes a data signal from the wireless power transmitter, using very low energy, and an energy detector as described in [20], [21]. Additionally, the IoT device can measure RSSI using the data decoder.
B.  RSSI  Feedback  Problem
In the system model in Section II.A, the optimal power transfer with multiple antennas and IoT devices can be repre- sented as: minimize subject to
where k represents the number of phase sets, C j is the possible stored energy in the capacitor on an IoT device j , and T i represents transmission duration on phase set i . The equation W i j = Energy(Θ i , j ) represents power supplied to the IoT device j when Θ j = θ j,1,θ j,2, . . . ,θ j,m where m is the number of TX antennas. For example, θ 3.5 represents a phase which is emitted by a 5th TX antenna using a 3rd phase set 03. The equation (1) is an objective function. The optimal time allocation is the smallest total power transmission duration satisfying the constraint equations (2)–(4). The equation (2) requires that the supplied energy must be smaller than or equal to the possible stored energy of the capacitor on each IoT device. The equation (3) represents the supplied energy at each IoT device. The amount of supplied energy on an IoT device E is expressed by the product T i of the transmission duration of a phase set Θ i and W i,j , which is the amount of power supply per second. The equation (4) represents the amount of power supply per second for each IoT device. Solving equations (1)–(4) derives optimal power transfer. However, pnr™ , RSSI feedback packets, which indicates the power supplied to an IoT device on a phase set, are a problem. The Energy(Θ i , j ) function returns energy supplied to an IoT device j by one RSSI feedback when TX antennas emit a continuous wave using a phase set Θ i . We need one RSSI feedback packets to acquire the energy supplied to one IoT device. Therefore, we need pnr™ feedback packets to calculate phase sets Ψ because the supplied energy on each phase set must be measured for each IoT device. The number of IoT devices n is usually 128 or 256; r is the resolution of the digital phase controller; and p , which can be infinite, is the number of phase sets.
III.  Proposed Approach: Phase-controlled
Cooperative Power Transfer
To solve the RSSI feedback problem, this paper proposes phase-controlled cooperative power transfer (PC-CPT). First, PC-CPT reduces the number of feedback packets from infinite to finite by assuming p = n . When the number of phase sets is limited to n , a linear programming solver can solve equations (1)–(4). However, we still need n 2 r m RSSI feedback packets when executing Energy(Θ i, j ). To further reduce the number of RSSI feedback packets from n²r™ to nrm , PC-CPT uses the following: 1) Reduce the number of feedback packets from n ² r m to nr™ by maximizing the power supplied to only one IoT device per phase set. 2) Reduce the number of feedback packets from nrm to nrm by sequentially determining each phase from AP 1 to AP m when estimating the phase set which maximizes the power supplied to an IoT device. 3) Calculate the duration of transmission on each phase set using the approximate reciprocal ratio of the supplied power of each IoT device. 4) Calculate the approximate reciprocal ratio using one RSSI feedback per phase set. Algorithm 1 shows how to estimate phase sets. In the Algorithm 1 , i , j , k are variables for iteration, t and a are temporary variables, n is the number of IoT devices, m is the number of TX antennas, r is the resolution of the digital phase controller, startRF( j, k ) is a function that lets a TX antenna j start emitting a continuous wave on setting k to the digital phase controller, stopRF( j ) is a function such that TX antenna j stops emitting a continuous wave, getRSSI(i) is a function that gets RSSI feedback from IoT device i , and stopAllRF() is a function that stops all TX antennas' emissions of a continuous wave. Algorithm 1 Phases estimation 1:  for i = 1 to n do startRF(1,0) 2:
Algorithm 1 estimates n phase sets for each IoT device sequentially. In lines 1–2 of Algorithm 1 , TX antenna 1 starts emitting a continuous wave, with phase 0, when estimating the phase set of the sensor i . Next, Algorithm 1 controls the phases of signals from TX antenna 2 to m for IoT device i . In lines 3–12 of Algorithm 1, the phase, which maximizes the received power of IoT device i of a signal from TX antenna j , is estimated by acquiring RSSI feedback from IoT device i . In line 14 of Algorithm 1 , after estimating the phase of the signal from TX antenna j , the TX antenna j starts emitting a continuous wave with the estimated phase. In line 16 of Algorithm 1 , all TX antennas stop emission of a continuous wave after all phases of the signals from TX antennas for the IoT device i are estimated. The ratio of the duration of transmission R i , using a phase set i and the entire transmission time, is determined by:
TX antennas deliver energy to each IoT device uniformly by calculating the power transmission duration of each phase set as the approximate reciprocal ratio of each supplied power. As can be seen in equation (5), the approximate reciprocal ratio only uses each supplied power Wa.b , where a = b , to reduce the number of RSSI feedback packets.
IV.  EVALUATION
We evaluated the proposed method using computer simula- tions and experimental micro benchmarks:
A. Computer Simulations
1) Evaluation settings: Figure 7 shows environmental set- tings. We assume that the TX antennas are embedded in the ceiling lights, and the room size is 15 m by 15 m by 2.5 m. There are 64 TX antennas and each antenna is 2 m away from a neighboring antenna. Each antenna transmits a 10-mW continuous non-modulated sine wave at 2.4 GHz, and the path loss is assumed to follow the Friis equation. The number of IoT devices varies from 1 to 100 and the position of the IoT devices are random. To evaluate the proposed PC-CPT we compare the following three methods: 1) uncontrolled power transmission (no control), 2)  carrier shift diversity (CSD) [16], and 3)  PC-CPT (proposed). 2) Average Received Power:  We evaluated average received power per IoT device, without changing the number of IoT devices in a network. The received power is the average of 100 trials. Figure 8 shows the evaluation result. The horizontal axis denotes the number of IoT devices and the vertical axis denotes the average received power from each IoT device. As shown in Figure 8, the proposed approach outperforms other methods, especially when the number of IoT devices is small. For example, when the number of IoT devices equals 1, 10 or 100, the average received power is approximately 481.4 μW, 54.5 µW, and 14.2 µW, which are approximately 49.8 times, 5.6 times, and 1.5 times the performance of CSD, respectively. As the number of IoT devices increases, the difference between the proposed method and the existing method becomes smaller. 3) Fairness: To evaluate the fairness of the proposed ap- proach, we evaluated the standard deviation of the received power of IoT devices while changing the number of IoT devices. Figure 9 shows the evaluation result. The horizontal axis denotes the number of IoT devices, and the vertical axis denotes the standard deviation of received power for each IoT device. In Figure 9, smaller standard deviations correspond to higher performances. As shown in Figure 9, the proposed approach realizes higher fairness when the number of IoT devices is large. For example, when the number of IoT devices is 100, the standard deviation of received power is about 2.1 μW, which is about 40 percent of CSD. When the number of IoT devices is small, the standard deviation of the proposed approach is higher than CSD's, because the proposed approach delivers much higher energy compared to CSD, and there is no control as described in Section IV-A2. For example, when the number of IoT devices equals 1 or 10, the standard deviations of received power are about 114.3 μW and 5.9 μW, which are 21.2 times and 1.1 times the standard deviations of CSD, respectively. To understand the relation between the average received power and the fairness in detail, we evaluated the cumulative distribution function of the received power per IoT device in all trials. Figure 10 shows the cumulative distribution function versus received power when the number of IoT devices is 100. As shown in Figure 10, the proposed method achieves the highest received power. In particular, 100 % of the IoT devices receive power greater than about 8.4 μW and there is a quick drop-off above that point. We can also see CSD has higher received power than with no control and has a steeper drop-off than with no control. Figure 11 shows the cumulative distribution function of the received power when the number of IoT devices is 1. In Figure 11, the drop-off is gentler than CSD's with no control, because the standard deviation of the proposed method is much larger than CSD with no control, when the number of IoT devices is 1, as described above in Figure 9. However, Figure 11 shows that the received power is much higher than CSD's with no control.
B. Experimental Micro Benchmarks
To verify the feasibility of the proposed method, we have conducted experimental micro benchmarks. Figure 12 shows an experimental configuration. There are four TX antennas and three RX antennas as IoT devices. TX antennas and RX antennas are Inventek Systems W24-SSMA-M which is a monopole antenna whose gain is 2.15 dBi. In this paper, we represent the transmitting antenna i as TXi and the receiving antenna i as RX i . The four TX antennas are connected to a 2.4 GHz non-modulated sine wave transmitting Texas Instruments CC2531 through a phase shifter Analog Device, HMC928 LP5E, for each TX antenna. Each phase shifter is controlled by an Atmel ATMEGA128L-8MU MCU, connected to a Panasonic Let's Note CF-SZ6 laptop through a USB with a Future Technology Devices International (FTDI) FT245RL. The transmission power from each antenna is approximately 25 μ W because the transmission power of the transmitter is 1 mW, and the transmit signal is divided between 4 antennas, and the power loss of each phase shifter is approximately 10 dB. Each RX antenna is connected to a power sensor, Analog Device LT5534, and the output analog voltage of the power sensor is converted to a digital value using an AD converter on Silicon Labs C8051F360 MCUs. The three MCUs are connected to a PC, through a USB, with an FTDI FT232HL. A PC processes the proposed PC-CPT described in Section III. We measured results in an anechoic chamber to cut off external radio waves. Figure 13 and Figure 14 show the layout of the TX and RX antennas. Four TX antennas and three RX antennas were placed on the 5 × 5 grid. Each grid size is 12.5 cm. The TX antennas are placed in a 39.5 cm by 39.5 cm square. Figure 13 and Figure 14 show placement A and placement B, respectively. The RX antennas are placed according to the following criteria: First, RX1 is placed in the center of the grid, which is equidistant from the TX antennas. The position of RX1 is fixed in all experiments for reference to other RX antennas throughout the experiments. And second, RX2 is placed inside the square surrounded by the TX antennas. RX2 is placed adjacent to a TX antenna and that placement is susceptible to interference from other TX antennas. And third, RX3 is placed outside the square surrounded by the TX antennas. RX3 is placed adjacent to a TX antenna and that placement is less susceptible to interference as compared to RX2. Table I and Table II list the experimental results of place- ment A and placement B. From Table I and Table II, we can see the following two things: First, the proposed CP-CPT outperforms CSD in both placements A and B. In placement A, the proposed CP-CPT has about 1.7 times higher performance than CSD because the average received powers of the proposed CP-CPT and CSD are 37.5 and 21.6, respectively. In placement B, the proposed CP-CPT also has about 1.7 times higher performance than CSD based on average received powers of the proposed CP-CPT and CSD of 30.5 and 18.3, respectively. TABLE I: Received power, transmission time ratio, and stan- dard deviation in placement A
TABLE II: Received power, transmission time ratio, and standard deviation in placement B
And second, the proposed CP-CPT does not always achieve higher fairness than CSD: CP-CPT has a smaller standard deviation than CSD in placement A, but CP-CPT has a larger standard deviation than CSD in placement B. The reason why the proposed CP-CPT sometimes has a larger standard deviation is related to equation (5). The proposed CP-CPT only uses W α,b , where α = b , to calculate R i with reducing the number of RSSI feedback packets. It is desirable to calculate R i using the received power at all antennas for all phase sets. For example, in Table II, R 2 should be smaller because the received power of RX2 is larger when the phase set is Θ 3 .
V.  CONCLUSION
Here we have proposed a phase-controlled cooperative power transmission with distributed multiple antennas for multiple IoT devices. The key ideas of our approach are RSSI feedback-based phase control and a heuristic feedback reduction algorithm. We have evaluated our approach by computer simulations and experimental micro benchmarks. The evaluation shows our approach is better than existing methods such as CSD and an uncontrolled approach.
ACKNOWLEDGMENT
We acknowledge the support received by JSPS Science Research Grants (JP16H01718, JP17J02859, JP17KT0042, and JP16K16044) and the NTT Access Network Service Laboratories and Panasonic Corporation.