**2. Retro-reflective beamforming scheme and numerical modeling**

The proposed retro-reflective beamforming scheme is illustrated in a typical indoor environ‐ ment shown in **Figure 1**. The wireless power transmitter consists of a base station and multiple charging panels. The charging panels are mounted over the ceiling or walls. Each charging panel includes an array of planar antenna elements. The base station and charging panels are connected through cables. Mobile/portable devices in the room receive wireless power from the wireless power transmitter through the following two steps.

Step (1) One or more than one device(s) broadcast pilot signals.

Step (2) In response to the pilot signals, the charging panels jointly construct focused (that is, dedicated) microwave power beam(s) onto the target device(s).

When the mobile/portable devices are in motion, the microwave power beams would follow the devices' locations dynamically as long as the devices broadcast pilot signals periodically. A charging panel transmits power only if it has line-of-sight interaction with the target

**Figure 1.** Depiction of wireless power transmission based on retro-reflective beamforming.

device(s); if the line-of-sight path is blocked by any obstacle, the charging panel is deactivated such that the obstacle, which might be human being, is not illuminated by power beams directly.

The underlying theory of retro-reflective beamforming is "time-reversal," which takes advantage of channel reciprocity to accomplish a space-time matched filter [22]. Specifically, propagation of pilot signals follows the "channel from target devices to charging panels," whereas propagation of microwave power beams follows the "channel from charging panels to target devices." If these two channels are reciprocal to each other and if the microwave power transmission is tailored to be the retro-reflected version of pilot signals, microwave power is spatially focused onto the locations from which the pilot signals stem, that is, locations of the target devices. Furthermore, spatial focusing due to retro-reflection/time-reversal does not suffer from multipath environments [23–27].

The timing sequence of the retro-reflective beamforming scheme is depicted by a flow chart in **Figure 2**. Interactions between the wireless power transmitter and wireless power receiver are toggled among three modes: communication mode, radar mode, and charging mode. The process in **Figure 2** starts when a wireless power receiver (a mobile device, for instance) communicates a "charging request" signal to the wireless power transmitter. Once the wireless power transmitter acknowledges "charging request," the system enters the radar mode in Microwave Power Transmission Based on Retro-reflective Beamforming http://dx.doi.org/10.5772/62855 93

**Figure 2.** Timing sequence in the retro-reflective beamforming scheme.

device(s); if the line-of-sight path is blocked by any obstacle, the charging panel is deactivated such that the obstacle, which might be human being, is not illuminated by power beams

**Figure 1.** Depiction of wireless power transmission based on retro-reflective beamforming.

The underlying theory of retro-reflective beamforming is "time-reversal," which takes advantage of channel reciprocity to accomplish a space-time matched filter [22]. Specifically, propagation of pilot signals follows the "channel from target devices to charging panels," whereas propagation of microwave power beams follows the "channel from charging panels to target devices." If these two channels are reciprocal to each other and if the microwave power transmission is tailored to be the retro-reflected version of pilot signals, microwave power is spatially focused onto the locations from which the pilot signals stem, that is, locations of the target devices. Furthermore, spatial focusing due to retro-reflection/time-reversal does

The timing sequence of the retro-reflective beamforming scheme is depicted by a flow chart in **Figure 2**. Interactions between the wireless power transmitter and wireless power receiver are toggled among three modes: communication mode, radar mode, and charging mode. The process in **Figure 2** starts when a wireless power receiver (a mobile device, for instance) communicates a "charging request" signal to the wireless power transmitter. Once the wireless power transmitter acknowledges "charging request," the system enters the radar mode in

directly.

not suffer from multipath environments [23–27].

92 Wireless Power Transfer - Fundamentals and Technologies

which the wireless power receiver transmits pilot signal and the wireless power transmitter prepares for beamforming through analyzing the pilot signal. When the wireless power transmitter is ready, both the wireless power transmitter and wireless power receiver march into the charging mode and power is delivered to the receiver through spatially focused beams. In practice, the environment may change during the charging process; for examples, the wireless power receiver may move and/or another wireless power receiver may request for charging. As a result, the beamforming plan must be adjusted accordingly. To accommodate these situations, the system is periodically switched from the charging mode to the commu‐ nication mode and the radar mode such that the system would be reconfigured in reaction to the environmental changes.

A system block diagram of the retro-reflective beamforming scheme is plotted in **Figure 3**. The wireless power receiver is assumed to be a mobile/portable device, and thus, it is imperative to minimize its size, weight, and cost. To this end, the wireless power receiver only includes one antenna and two simple circuit blocks. The "pilot signal generator" block in the wireless power receiver is an impulse generator, which generates a periodic train of narrow impulses as the pilot signal. The other block in the wireless power receiver, "microwave-to-DC con‐ verter," converts microwave power received from the wireless power transmitter to DC. The wireless power transmitter is composed of multiple antenna elements coordinated by a base station. Behind each antenna element, there are two circuit blocks: a "pilot signal analyzer" and a "microwave power generator." The "pilot signal analyzer" analyzes the pilot signal received from the wireless power receiver, and the "microwave power generator" generates microwave power based on the outcome of analyzing pilot signal. Since the pilot signal is composed of an impulses train, its spectrum covers multiple discrete spectral lines. The wireless power transmitter selects some of these discrete frequencies to analyze the pilot signal and transmit microwave power. At any discrete frequency, if the pilot signal has phase *ϕ*, microwave power is generated with phase −*ϕ*; in other words, microwave power is configured to be the conjugate version of pilot signal because "phase conjugation in frequency domain" is equivalent to "reversal in time domain" [19].

**Figure 3.** System block diagram of the retro-reflective beamforming scheme [20].

Employing narrow impulses as the pilot signal constitutes one of the major merits of the proposed retro-reflective beamforming scheme. In prior research efforts on retro-reflective beamforming, pilot signals are always generated by a microwave oscillator [28, 29]. Compared with microwave oscillators, impulse generators can be realized using relatively low-complex‐ ity and low-power circuitries [30] and hence is more suitable for mobile/portable devices. Because periodic impulses include information over multiple discrete frequencies, the wireless power transmitter has the flexibility of selecting multiple frequencies to transmit microwave power; in contrast, if the pilot signal is a continuous wave, the flexibility is limited to the pilot signal's frequency and its high-order harmonics. Moreover, employing multiple frequencies to carry wireless power would result in better performance in spatial focusing, as demon‐ strated by some numerical results below.

**Figures 4**–**6** show some numerical results for the retro-reflective beamforming scheme described above. The numerical model is illustrated in **Figure 4**. Eight charging panels are assumed to be deployed over a circular region with radius 3 m in the *x*–*y* plane. Each charging panel includes an antenna array with 5 by 5 elements equal spaced by 12 cm. Two devices reside in the region. The antennas over the charging panels and devices are all *z*-oriented dipoles. The devices transmit short impulses as pilot signals, which cover frequency band [4

**Figure 4.** Numerical model of the retro-reflective beamforming scheme [19].

wireless power transmitter selects some of these discrete frequencies to analyze the pilot signal and transmit microwave power. At any discrete frequency, if the pilot signal has phase *ϕ*, microwave power is generated with phase −*ϕ*; in other words, microwave power is configured to be the conjugate version of pilot signal because "phase conjugation in frequency domain"

Employing narrow impulses as the pilot signal constitutes one of the major merits of the proposed retro-reflective beamforming scheme. In prior research efforts on retro-reflective beamforming, pilot signals are always generated by a microwave oscillator [28, 29]. Compared with microwave oscillators, impulse generators can be realized using relatively low-complex‐ ity and low-power circuitries [30] and hence is more suitable for mobile/portable devices. Because periodic impulses include information over multiple discrete frequencies, the wireless power transmitter has the flexibility of selecting multiple frequencies to transmit microwave power; in contrast, if the pilot signal is a continuous wave, the flexibility is limited to the pilot signal's frequency and its high-order harmonics. Moreover, employing multiple frequencies to carry wireless power would result in better performance in spatial focusing, as demon‐

**Figures 4**–**6** show some numerical results for the retro-reflective beamforming scheme described above. The numerical model is illustrated in **Figure 4**. Eight charging panels are assumed to be deployed over a circular region with radius 3 m in the *x*–*y* plane. Each charging panel includes an antenna array with 5 by 5 elements equal spaced by 12 cm. Two devices reside in the region. The antennas over the charging panels and devices are all *z*-oriented dipoles. The devices transmit short impulses as pilot signals, which cover frequency band [4

is equivalent to "reversal in time domain" [19].

94 Wireless Power Transfer - Fundamentals and Technologies

**Figure 3.** System block diagram of the retro-reflective beamforming scheme [20].

strated by some numerical results below.

GHz, 6 GHz]. Charging power is allocated to *N* discrete frequencies in this band. To represent more realistic scenarios, a metallic plate with length 1 m and height 0.6 m is placed to block the line-of-sight path between the devices and one charging panel, which is Charging Panel B in **Figure 4**.

The model in **Figure 4** is simulated by a full-wave solver based on the Method of Moments [19]. Simulated *Ez* field distributions in a 2 m by 2 m region around the two devices are presented in **Figure 5**. When one device (the one at the center) sends pilot signals to the charging panels with the absence of obstacle, all the eight charging panels are active. If the charging panels only transmit power at one frequency 4.09 GHz (i.e., *N* = 1), the field distribution is shown in **Figure 5(a)**. Apparently, field is focused at many locations other than the device (the undesired focal points resemble side lobes of regular phased beamforming [31]). When *N* is chosen to be 30, only one focal point remains, which coincides with the device's location, as shown in **Figure 5(b)**. When both devices send pilot signals, the field is automatically focused onto the two devices (**Figure 5(c)**). In **Figure 5(d)**, the obstacle is assumed to be present, and Charging Panel B is blocked and turned off (the other seven charging panels are active). Field focusing does not rely on the obstacle's presence and the number of active charging panels, as shown in **Figure 5(d)**. With the presence of obstacle, which charging panels should be deactivated can be determined through analyzing the pilot signals. Two charging panels, Charging Panel A and Charging Panel B, are used as examples. After these two charging panels receive pilot signals from one device, phase differences between two local antenna elements are plotted in **Figure 6**; one of the two local elements is at the center and the other at the corner in the 5 by 5 array. As expected, since Charging Panel A has line-of-sight interaction with the device, its

**Figure 5.** Simulated field distributions of the model in **Figure 4** (with |*Ez*| represented by colors) [19]. (a) One device, 1 frequency, no obstacle. (b) One device, 30 frequencies, no obstacle. (c) Two devices, 30 frequencies, no obstacle. (d) One device, 30 frequencies, with obstacle

phase difference follows a straight line proportional to the frequency (corresponding to a time delay), whereas such a pattern does not appear at Charging Panel B.

### **3. Experimental verification of retro-reflective beamforming scheme**

We have conducted a range of experimental studies to verify the retro-reflective beamforming scheme described in the previous section [20] [21]. Some of the experimental results are presented in this section.

One of the experimental setup is depicted in **Figure 7**. The wireless power transmitter includes one charging panel, which further includes four microstrip antenna elements. The wireless power receiver has one microstrip antenna. The power transmitter is stationary, whereas the wireless power receiver moves along the *x* axis in the experiments and it emulates a mobile/ portable device. "*x* = 0" denotes the location over the *x* axis right in front of the charging panel. The distance between "*x* = 0" and the wireless power transmitter is 50 cm.

Microwave Power Transmission Based on Retro-reflective Beamforming http://dx.doi.org/10.5772/62855 97

**Figure 6.** Numerical results of phase difference with the presence of obstacle [19]. (a) Phase difference at Charging Pan‐ el A. (b) Phase difference at Charging Panel B.

**Figure 7.** Depiction of an experimental setup with one charging panel [21]. (a) Power receiver broadcasts pilot signal to power transmitter. (b) Power transmitter transmits microwave power to power receiver.

The experimental procedure has the following two steps.

phase difference follows a straight line proportional to the frequency (corresponding to a time

**Figure 5.** Simulated field distributions of the model in **Figure 4** (with |*Ez*| represented by colors) [19]. (a) One device, 1 frequency, no obstacle. (b) One device, 30 frequencies, no obstacle. (c) Two devices, 30 frequencies, no obstacle. (d) One

We have conducted a range of experimental studies to verify the retro-reflective beamforming scheme described in the previous section [20] [21]. Some of the experimental results are

One of the experimental setup is depicted in **Figure 7**. The wireless power transmitter includes one charging panel, which further includes four microstrip antenna elements. The wireless power receiver has one microstrip antenna. The power transmitter is stationary, whereas the wireless power receiver moves along the *x* axis in the experiments and it emulates a mobile/ portable device. "*x* = 0" denotes the location over the *x* axis right in front of the charging panel.

**3. Experimental verification of retro-reflective beamforming scheme**

delay), whereas such a pattern does not appear at Charging Panel B.

The distance between "*x* = 0" and the wireless power transmitter is 50 cm.

presented in this section.

device, 30 frequencies, with obstacle

96 Wireless Power Transfer - Fundamentals and Technologies

Step (1): Power receiver transmits pilot signal to power transmitter (**Figure 7(a)**). The power receiver's antenna is connected to an impulse generator. The impulses transmitted by the power receiver's antenna behave as the pilot signal. In our implementation, the impulses are generated through amplitude modulating a continuous wave at 2.08 GHz by periodic square impulses with a pulse width of 25 ns and a pulse repetition rate of 4 MHz (its waveform is illustrated in **Figure 8**). The pilot signal is received by the four antennas of the power trans‐ mitter and then analyzed by the "pilot signal analyzers."

Step (2): Power transmitter transmits wireless power to power receiver (**Figure 7(b)**). In this step, the power transmitter's four antennas are fed by microwave power generators. The microwave power generators are configured according to the outcome of Step (1) so that a focused power beam is constructed toward the location from which the pilot signal is emitted. Wireless power collected by the power receiver's antenna is detected by either a power meter or a rectifier. The rectifier is implemented by following a voltage multiplier design in [32] and optimized around 2.1 GHz.

A photo of the experimental setup is shown in **Figure 9**: in Step (2), wireless power is delivered from the power transmitter to power receiver and wireless power reception is indicated by a light emitting diode (LED) on the power receiver.

The four antenna elements in the power transmitter are identical to one another. Each is a regular rectangular microstrip patch with dimensions 31.4 mm by 46 mm over FR4 substrate. The four antenna elements are equispaced with the distance between two adjacent elements 7

**Figure 8.** Illustration of the impulse pilot signal.

**Figure 9.** A photo of the experimental setup with one charging panel [21].

cm. Each antenna element's "−10 dB return loss frequency band" is roughly from 2.055 to 2.155 GHz. Each antenna element has a gain value of 3.8 dBi and half-power beamwidth of 136°. The microstrip antenna in the power receiver is the same as those in the power transmitter. All the antennas in **Figure 9** are linearly polarized, and the electric field is polarized along the *x* direction marked in **Figure 9**.

Step (2): Power transmitter transmits wireless power to power receiver (**Figure 7(b)**). In this step, the power transmitter's four antennas are fed by microwave power generators. The microwave power generators are configured according to the outcome of Step (1) so that a focused power beam is constructed toward the location from which the pilot signal is emitted. Wireless power collected by the power receiver's antenna is detected by either a power meter or a rectifier. The rectifier is implemented by following a voltage multiplier design in [32] and

A photo of the experimental setup is shown in **Figure 9**: in Step (2), wireless power is delivered from the power transmitter to power receiver and wireless power reception is indicated by a

The four antenna elements in the power transmitter are identical to one another. Each is a regular rectangular microstrip patch with dimensions 31.4 mm by 46 mm over FR4 substrate. The four antenna elements are equispaced with the distance between two adjacent elements 7

optimized around 2.1 GHz.

light emitting diode (LED) on the power receiver.

98 Wireless Power Transfer - Fundamentals and Technologies

**Figure 8.** Illustration of the impulse pilot signal.

**Figure 9.** A photo of the experimental setup with one charging panel [21].

The two vital blocks in **Figure 7**, "pilot signal analyzers" and "microwave power generators," are illustrated in **Figures 10** and **11**, respectively. In **Figure 10**, the pilot signals received by the four antennas are amplified by four low-noise amplifiers, down-converted through four mixers and a local oscillator at frequency *fLO*, and then converted to the digital format by a fourchannel analog-to-digital converter (ADC). The digital signals are stored within the memory of a personal computer and read by a signal processing program developed in the C++ language. The signal processing program calculates the phases of the four digital signals using short-time (20 μs, to be specific) discrete Fourier transform at the frequency *fIF*. With the calculated phases (denoted as *ϕ*1, *ϕ*2, *ϕ*3, and *ϕ*4), a system control program operates a digitalto-analog converter (DAC), which provides four DC bias voltages (denoted as *V*1, *V*2, *V*3, and *V*4) to control the phase shifters in **Figure 11**. The DAC also outputs a control signal *V*CTRL that is used to turn on/off the oscillator in the microwave power generators. In **Figure 11**, a continuous wave generated by an oscillator at frequency *ft* is split into four channels first; next, each channel goes through a phase shifter and power amplification before reaching the antenna. The retro-reflective beamforming is achieved by properly controlling the state of the four phase shifters so that the transmitting array is fed with phases − *ϕ*1, − *ϕ*2, − *ϕ*3, and − *ϕ*4, respectively. This is done by the system control program that determines the output DC bias voltages of the DAC based on the characteristics of the four phase shifters. The system control program is also responsible for controlling the operation sequence of the entire system. Specifically, in Step (1) of the experiment, the system control program activates the ADC and calls the signal processing program to analyze the pilot signal. In the meantime, the oscillator in the microwave power generators is turned off by the control signal *V*CTRL to avoid the interference of microwave power to the pilot signal analyzers. In Step (2), the system control program deactivates the ADC and reset *V*CTRL to turn on the oscillator so that the wireless power is transmitted.

The pilot signal analyzers and microwave power generators are implemented using commer‐ cial off-the-shelf components with model numbers listed in **Figures 10** and **11**. The mixers, amplifiers, and the oscillators are made by Analog Devices Inc. The four phase shifters are made by Beijing Tianhua Zhongwei Technology. The 1:4 power splitters are made by Mini-Circuits. The ADC and DAC are made by Beijing Art Technology Development Co. The ADC PCI8502 provides four synchronized channels with a sampling rate of 40 MHz and 12-bit resolution. The DAC PCI8250 provides eight synchronized channels with 16-bit resolution.

Employing impulses as the pilot signal leads to the flexibility of configuring *ft* . The pilot signal's spectrum is centered at 2.08 GHz and contains discrete spectral lines with separation of 4 MHz. In one of the implementations, *ft* = 2.08 GHz with *fLO* = 2.079 GHz and *fIF* = 1 MHz. *ft* can be reconfigured to other frequencies straightforwardly; for instance in another implementation, *ft* is reconfigured to be 2.108 GHz with *fLO* = 2.1 GHz and *fIF* = 8 MHz.

**Figure 10.** Block diagram of "pilot signal analyzers."

**Figure 11.** Block diagram of "microwave power generators."

**Figure 12.** Received microwave power at frequency 2.08GHz [21].

**Figure 10.** Block diagram of "pilot signal analyzers."

100 Wireless Power Transfer - Fundamentals and Technologies

**Figure 11.** Block diagram of "microwave power generators."

In the experiments, a pilot signal is broadcasted by the power receiver at a location denoted as *x*0, and the pilot signal is received and analyzed by the power transmitter; then after the power transmitter is configured by the outcome of analyzing the pilot signal, the power receiver moves along *x* axis to detect the wireless power. In all the experiments, the total power transmitted by the power transmitter is roughly 1 Watt (that is, 250 mW from each of its four antennas).

In **Figure 12**, microwave power measured by a power meter is plotted when *ft* = 2.08 GHz. The four subplots in **Figure 12** correspond to "*x*0 = 0," "*x*0 = − 10 cm," "*x*0 = − 20 cm," and "*x*0 = − 30 cm," respectively. The calculated curves in **Figure 12** are obtained using the Friis transmission equation [31]

$$P\_r = P\_l \left(\frac{\lambda}{4\pi d}\right)^2 G\_l G\_r$$

When *x*0 = 0 and *x* = 0, the transmitted power *Pt* = 1 Watt, wavelength *λ* = *c*/*ft* , *c* is the speed of light in free space, the transmitter–receiver distance *d* = 50 cm, the transmitting antenna's gain *Gt* = 9.8 dBi, the receiving antenna's gain *Gr* = 3.8 dBi, and the received power *Pr* is calculated to be 12 mW. In **Figure 12**, the measured data and calculated data generally match each other. The measured data in reaction to "*x*0 = 0" have a peak at "*x* = 0," with peak value of the received power about 14 mW. The measured value (14 mW) is slightly larger than the calculated value (12 mW); we believe it is because the power receiver does not reside in the power transmitter's far-zone, which makes Friis equation not very precise. When *x*<sup>0</sup> changes to −10, −20, and −30 cm, the power beam is steered and the beam center tracks *x*0. In our experiments, the beam cannot be steered beyond −30 cm due to the limitation of individual microstrip antennas' radiation patterns. When *x*0 takes positive values, the power beam is steered and the beam center tracks *x*<sup>0</sup> as well; beam steering for positive *x*<sup>0</sup> values is not demonstrated because it is symmetric to the negative *x*0 values. Similar sets of results are displayed in **Figure 13**, after the power meter is replaced by the rectifier. The vertical axis in **Figure 13** represents the DC voltage measured over a 1.8-kΩ load resistor in the rectifier. Beams in reaction to four *x*0 values are clearly shown. When *x*0 = 0, the peak voltage 3.5 V corresponds to (3.5)<sup>2</sup> /(1.8 k) ≅ 7 mW.

After *ft* is reconfigured to 2.108 GHz, curves similar to those in **Figure 12** are plotted in **Figure 14**. The beamforming phenomena exhibited in **Figure 14** are basically the same as those in **Figure 12**.

On the basis of the experimental setup in **Figure 7**, another set of experiments are carried out as illustrated in **Figure 15**. As a progress with respect to **Figure 7**, the wireless power trans‐ mitter in **Figure 15** includes two charging panels, each consisting of four antenna elements. The two charging panels are placed over *x* axis and *y* axis, respectively. The wireless power receiver moves within a certain region in the *x*–*y* plane. **Figure 16** shows a photo of the

**Figure 13.** Received DC voltage at frequency 2.08GHz [21].

**Figure 14.** Received microwave power at frequency 2.108 GHz [21].

The measured data in reaction to "*x*0 = 0" have a peak at "*x* = 0," with peak value of the received power about 14 mW. The measured value (14 mW) is slightly larger than the calculated value (12 mW); we believe it is because the power receiver does not reside in the power transmitter's far-zone, which makes Friis equation not very precise. When *x*<sup>0</sup> changes to −10, −20, and −30 cm, the power beam is steered and the beam center tracks *x*0. In our experiments, the beam cannot be steered beyond −30 cm due to the limitation of individual microstrip antennas' radiation patterns. When *x*0 takes positive values, the power beam is steered and the beam center tracks *x*<sup>0</sup> as well; beam steering for positive *x*<sup>0</sup> values is not demonstrated because it is symmetric to the negative *x*0 values. Similar sets of results are displayed in **Figure 13**, after the power meter is replaced by the rectifier. The vertical axis in **Figure 13** represents the DC voltage measured over a 1.8-kΩ load resistor in the rectifier. Beams in reaction to four *x*0 values are

is reconfigured to 2.108 GHz, curves similar to those in **Figure 12** are plotted in

**Figure 14**. The beamforming phenomena exhibited in **Figure 14** are basically the same as those

On the basis of the experimental setup in **Figure 7**, another set of experiments are carried out as illustrated in **Figure 15**. As a progress with respect to **Figure 7**, the wireless power trans‐ mitter in **Figure 15** includes two charging panels, each consisting of four antenna elements. The two charging panels are placed over *x* axis and *y* axis, respectively. The wireless power receiver moves within a certain region in the *x*–*y* plane. **Figure 16** shows a photo of the

/(1.8 k) ≅ 7 mW.

clearly shown. When *x*0 = 0, the peak voltage 3.5 V corresponds to (3.5)<sup>2</sup>

102 Wireless Power Transfer - Fundamentals and Technologies

**Figure 13.** Received DC voltage at frequency 2.08GHz [21].

After *ft*

in **Figure 12**.

**Figure 15.** Illustration of an experimental setup with two charging panels [20].

experimental setup corresponding to **Figure 15**. The antennas of the wireless power transmitter are microstrip antennas polarized along *z* direction; the antenna of the receiver is a monopole antenna, with omni-directional radiation pattern in the *x*–*y* plane.

Some results measured with the configuration in **Figures 15** and **16** are shown in **Figure 17**. The microwave power transmitted by each antenna element of the wireless power transmitter is roughly 175 mW, with a total of 175 mW × 8 = 1.4 Watt. A power meter is connected to the wireless power receiver's antenna, and the measured microwave power is plotted in **Fig‐ ure 17**. The two plots in **Figure 17(a)** and **(b)** are obtained when the pilot signal is broadcasted from (*x* = 60 cm, *y* = 60 cm) and (*x* = 70 cm, *y* = 70 cm), respectively. **Figure 17** clearly demon‐ strates that the microwave power is focused onto the location from which the pilot signal is broadcasted as a result of retro-reflective beamforming.

## **4. Conclusion**

This chapter presents a retro-reflective beamforming scheme aiming to supply microwave power to portable/mobile electronic devices over long distances (several meters or longer) efficiently. The preliminary numerical and experimental results demonstrate that the proposed retro-reflective beamforming scheme is capable of focusing microwave power onto target devices' locations through analyzing pilot signals broadcasted by the target devices. We are currently conducting research to verify the retro-reflective beamforming scheme more comprehensively.

experimental setup corresponding to **Figure 15**. The antennas of the wireless power transmitter are microstrip antennas polarized along *z* direction; the antenna of the receiver is a monopole

Some results measured with the configuration in **Figures 15** and **16** are shown in **Figure 17**. The microwave power transmitted by each antenna element of the wireless power transmitter is roughly 175 mW, with a total of 175 mW × 8 = 1.4 Watt. A power meter is connected to the wireless power receiver's antenna, and the measured microwave power is plotted in **Fig‐ ure 17**. The two plots in **Figure 17(a)** and **(b)** are obtained when the pilot signal is broadcasted from (*x* = 60 cm, *y* = 60 cm) and (*x* = 70 cm, *y* = 70 cm), respectively. **Figure 17** clearly demon‐ strates that the microwave power is focused onto the location from which the pilot signal is

This chapter presents a retro-reflective beamforming scheme aiming to supply microwave power to portable/mobile electronic devices over long distances (several meters or longer) efficiently. The preliminary numerical and experimental results demonstrate that the proposed retro-reflective beamforming scheme is capable of focusing microwave power onto target devices' locations through analyzing pilot signals broadcasted by the target devices. We are currently conducting research to verify the retro-reflective beamforming scheme more

antenna, with omni-directional radiation pattern in the *x*–*y* plane.

**Figure 16.** A photo of the experimental setup with two charging panels [20].

104 Wireless Power Transfer - Fundamentals and Technologies

broadcasted as a result of retro-reflective beamforming.

**4. Conclusion**

comprehensively.

**Figure 17.** Microwave power distribution measured with the configuration in **Figures 15** and **16** [20]. (a) Pilot signal from (*x* = 60 cm, *y* = 60 cm). (b) Pilot signal from (*x* = 70 cm, *y* = 70 cm).

### **Acknowledgements**

This work was supported in part by National Science Foundation Grant ECCS 1303142, National Science Foundation Grant ECCS 1503600, and National Natural Science Foundation of China Grant 61471195
