Introduction

As electronic devices become more efficient, according to Koomey’s law1, a common belief has been established that future consumer electronics will require 1000 times less energy compared to their present counterparts. Besides, there are trillions of Internet of Things (IoT) devices deployed yearly. Such a large number urgently demands to develop a new charging network for these low-power devices. Considering that the current battery-powered methods are not long-lifetime and eco-friendly, the wireless power transfer (WPT) is a promising solution, which possesses the advantages of being contactless, compact, and controllable. The development of wireless power will spawn a myriad of new wireless applications, such as wireless-powered edge computing2, wireless-powered sensing3,4, and biomedical sciences5. Thus, it will become a fundamental building block for future wireless networks.

At present, electromagnetic inductive-type WPT has been widely deployed (e.g., wireless charging of smartphones), and gains a considerable market value. Its advantage lies in the convenience and non-contact. However, due to a lack of adaptive tunability, the transmission distance of conventional inductive-type WPT is short, and the devices under charging are needed to fix their locations for maximum transfer efficiency. This seems to weaken the benefits of contactless WPT. By contrast, the radiative-type WPT is an emerging and flexible solution, that can cover from the near field to the far field. To this end, there are numerous researches reported in academia and industry6,7,8. For instance, explored the microstrip patch array to focus the wireless power in Fresnel region9,10,11; carried out theoretical analyses and experimental validations for the near-field and far-field WPT12,13; and expanded from single device to multiple devices14,15. Further, to realize the point-to-point directional WPT, the phased array system has obtained widespread attentions16,17,18, due to its flexible beamforming capability. In fact, phased array opened up a wide imagination of WPT researches and applications. Subsequently, the new wireless communication architecture of simultaneous wireless information and power transfer (SWIPT)19,20 was reported, which provides new ideas of communication and power supply for IoT devices in future. Besides, the studies21,22 found that large-scale phased arrays are expected to break through long-distance and high-power wireless charging. However, the phased array requires complex feeding networks (e.g., phase shifters and power amplifiers), making them costly and bulky to widely apply. Hence the low-cost beamforming technique urgently is needed to be studied and developed.

Recently, the rise of programmable metasurface (PMS) provides a promising solution for flexible beam focusing23,24,25. Developed from the passive metasurface, the PMS can dynamically switch the wavefront phase by loading electric-tunable devices, such as varactors and positive-intrinsic-negative (PIN) diodes26,27,28,29,30. It is a low-cost alternative to the expensive phase shifters. Although generally speaking, PMS performs a rough 1-bit or 2-bit quantization for the wavefront phase of electromagnetic (EM) wave31,32,33,34, and there is a gap in the efficiency of power focusing. However, this deficiency can be remedied by designing a larger aperture. In fact, the potentials of PMS have been widely appreciated and explored, such as wireless communication35,36,37, microwave imaging33,38,39, radar detection40,41,42, and vital signs monitor43,44. However, the majority of PMS applications were controlled in a manual manner, and they concentrated on the verification of pre-designed functions. But in terms of the WPT system, we are considering expanding the PMS to intelligent PMS, and realizing the adaptive beamforming by tracking the locations of terminals. Hence it is necessary to integrate the positioning function on PMS. For instance, introduced the compressive sensing to achieve the direction of arrival (DoA) estimation based on a single channel PMS40,45; combined the space-time-coding (STC) technique to estimate multiple targets46,47, etc. Yet, they are half duplex, and cannot estimate the distance of targets. Besides, the intelligent metasurface systems for automatic tracking of moving targets were presents32,48, relying on the fast development of computer vision technology. Yet this solution requires an additional vision sensor, whose accuracy was affected by light and weather.

Currently, the majority of current research on WPT remains confined to theoretical studies. Indeed, owing to the significant reduction in power consumption of electronic devices8,49, wireless power-based sensing, processing, and communication are ripe for exploration and implementation, thus fostering the further advancement of WPT. Consequently, we propose to construct an adaptive wireless-powered network (AWPN) based on PMS to power for terminal devices, enabling data sensing and processing. Then it uploads the perceived data to the user in a wireless manner, enabling a battery-free sensing system. Considering the movement of terminal devices, the dynamic power focusing based on target positions will become increasingly important.

In comparison to visual positioning, we prefer wireless positioning based on EM wave, since it can work around the clock, and the system is more integrated. Thus, we aim to design a dual-band metasurface to realize simultaneous target positioning and power focusing, which is innovative for metasurface research. Besides, a specially designed terminal device also plays a vital role. Consider that the rectification process from alternating current (AC) to direct current (DC) is a nonlinear process, which generates high-order harmonics. We utilize these harmonics as positioning signals fed back to the dual-band metasurfaces to achieve full-duplex localization. As the terminal device resides in the near field of the metasurface, it enables to estimate both direction and distance, and makes up the shortcomings of previous methods that cannot capture the distance32,50. Additionally, by combining the STC technique and convolutional neural network (CNN), this study realizes high-accuracy positioning on a single-input single-output (SISO) hardware architecture. It only requires to collect the training datasets and train CNN model in the initial stage, so that the CNN allows the quick near-field positioning (NFP), and there is no need for huge computing overhead. Therefore, the proposed AWPN is a multifunctional and highly integrated system that fully utilizes the advantages of the metasurface in full-duplex beam steering and sensing, advancing the evolution of PMS towards intelligent PMS.

Results

Framework of the proposed AWPN

Based on a dual-band metasurface, we propose an AWPN for real-time wireless charging, enabling wireless-powered sensing, processing, and communication, as shown in Fig. 1. In contrast to the conventional metasurface, the designed dual-band metasurface consists of two band meta-atoms for transmitting and receiving EM wave in full-duplex mode. They are a 16 × 16 low-band array at 5.8 GHz and an L-shaped high-band array at 11.6 GHz, working for focusing wireless power and collecting NFP signals, simultaneously. This design can focus more attention to optimize low-band meta-atoms with low insertion loss and high phase accuracy, thereby improving the WPT efficiency. Besides, this L-shaped array is more like an add-on device that does not change the structure of the existing metasurface device. As a solution with strong compatibility, it has potential to be widely installed on single-function equipment to enrich their functions.

Fig. 1: Concept view of the proposed AWPN for wireless-powered sensing, processing, and communication.
figure 1

Based on the dual-band metasurfaces, AWPN can track targets and dynamically focus wireless energy onto a moving receiving terminal in real-time. The receiving terminal rectifies the RF power into DC output to power sensors, microprocessors, communication modules, etc. Besides, it feeds back the harmonics to the metasurface for positioning.

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For the receiving terminal, it efficiently harvests radio frequency (RF) power and rectifies them into DC output, thereby powering for electron devices. In contrast to the assumption that the terminals are stationary, we fully exploit the beam-scanning capabilities of the metasurface to enable charging for moving terminals. Therefore, the accurate NFP is more important. Consider that the Schottky diode used for rectification is a nonlinear device, and the process of rectification generates high-order harmonics, with the 2nd harmonic at 11.6 GHz being particularly prominent. Therefore, we leverage it to function as the positioning signal, which is fed back to the metasurfaces for response.

In order to locate the receiving terminal, the high-band meta-atoms on the metasurface modulate this 11.6 GHz positioning signal by STC technique, and the accompanying STC harmonics will be extracted and analyzed. STC harmnics bring multidimensional feature information, and enhance differentiation between different positions. Due to these feedback signals are modeled as spherical waves, making them possible to estimate both the direction and distance. The CNN model serves as the feature extractor for the NFP. The whole process only requires to extract the amplitudes of STC harmonics, and avoids the high computational complexity and expensive hardware of conventional methods.

Dual-band metasurface and the power focusing

The meta-atoms of the designed dual-band metasurface are shown in Fig. 2a. They are 1-bit reflective coding elements. The big one is responsible for transmitting and focusing wireless power, while the small one is for receiving and modulating the feedback positioning signals. As can be seen, there are two metallic patches and a PIN diode at their top structures. Controlled by the DC bias voltages, the on and off states of this PIN diode correspond to two phase states of the 1-bit meta-atoms, respectively. The geometric parameters of these two meta-atoms are detailed in Supplementary Note 1. The simulated phase responses of these two meta-atoms are shown in Fig. 2b and Fig. 2c. From the simulated results, their center frequencies are 5.8 GHz and 11.6 GHz respectively, at which the phase switching from 0° to 180° can be realized.

Fig. 2: Design of the dual-band metasurface and the simulation results.
figure 2

a Side views of two frequencies meta-atoms. b The phase responses under ON and OFF states of low-band meta-atoms, whose center frequency is 5.8 GHz. c The phase responses under ON and OFF states of high-band meta-atoms, whose center frequency is 11.6 GHz. d Calculated three different coding matrixes on metasurface for power focusing at (0, 0, 50)cm, (0, −10, 50) cm, and (−10, 0, 50) cm. e Simulated electric field distributions at z = 50 cm, they present different focal spots.

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One of the most exciting features of the PMSs is the excellent EM-wave manipulation enabled by adjusting the coding matrix. For the designed metasurfaces with 16 × 16 meta-atoms, it enable flexible near-field focusing for power transmission. The corresponding coding matrixes can be derived numerically (see “Methods” for details). We simulate the E-field distributions under different coding matrixes. As shown in Fig. 2d, three coding matrixes are calculated to generate focal spots at different positions. From the simulated results plotted in Fig. 2e, there are three distinct focal spots appear in positions of (0, 0, 50) cm, (0, −10, 50) cm, and (−10, 0, 50) cm, which is consistent with the expected results. They have verified that the designed 16 × 16 metasurface has the ability to power focusing, and can intelligently manipulate beams to the area of interest (AoI), which is vital for our adaptive power transmission.

Design and evaluation of the receiving terminal

The explosive view of the well-thought-out receiving terminal is illustrated in Fig. 3a, which is a two-layer structure. The upper layer is a dual-port antenna designed for harvesting energy and radiating positioning signal, while the bottom layer converts the RF energy into DC voltage through a rectifier. These two layers are interconnected via coaxial connectors. Since this receiving terminal is battery-free and can realize environmental sensing, it can be called wireless-powered sensor. According to the previous reports51, temperature is a crucial index of battery safety during charging. Therefore, our proposed AWPN will illustrate to sense environmental temperature as an example. Then, the perceived data is sent to users by wireless communication, thereby demonstrating the ability of safety alerts for future high-power wireless charging. For instance, notify the transmitter to reduce transmission power when charging temperatures exceed a certain threshold, or increase transmission power to maintain a constant power supply.

Fig. 3: Design of the receiving terminal.
figure 3

a Explosive view of the receiving terminal, which is a two-layer structure. b Harmonic feedback rectifier, which rectifies a 5.8 GHz high-power signal to DC output and generates an 11.6 GHz feedback signal. c S-parameter of the designed antenna array. d Realized gain under two frequency bands. e Reflection coefficient and DC output of the rectifier versus input power. f The 2nd harmonic power and rectification efficiency of the rectifier versus input power.

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In Fig. 3b, the layout of the rectifier is depicted. As can be seen, after passing through an impedance matching network, the RF power at 5.8 GHz is input into a Schottky diode (MA4E1317, MACOM, Inc.) for rectification. Accompanying the AC-to-DC conversion, this nonlinear process generates multiple high-order harmonic components, with the 2nd harmonic being prominent. It will be transmitted into the other port and re-radiated by the antenna for wireless positioning. Thus, different from the conventional rectifiers, our design is the harmonic feedback rectifier. The derivation of harmonic generation is detailed in Supplementary Note 2.

The antenna array adopts a dual-band co-aperture design, thereby enhancing the system integration. The outer square loop is used to receive RF energy at 5.8 GHz, while the inner dumbbell-shaped structure is utilized for radiating the 11.6 GHz positioning signal. Under the bottom surface, this 4 × 4 array is synthesized into two ports through two power combiners. The measured reflection coefficients of these two ports are shown in Fig. 3c, which illustrates the good matching at their respective operating frequencies, ensuring efficient energy reception and radiation. Additionally, their maximum radiation gains are 10.3 dBi and 12.2 dBi, as depicted in Fig. 3d.

For the design of the harmonic feedback rectifier, we aim to extract its 2nd harmonic while not obviously reducing the rectification efficiency. This requires a well-thought-out filter design that allows the 2nd harmonic to pass through with small insertion loss and reflects the fundamental component. The simulated reflection coefficient of the input port is presented in Fig. 3e, which illustrates that the RF power can be efficiently rectified with slight reflection loss. When input power is enhanced to 14 dBm, the maximum DC output is 17.7 mW, as shown in the green curve. Besides, Fig. 3f presents the measured results of the designed rectifier. It can be observed that the 61% maximum rectification efficiency from RF to DC is achieved when the input power is 14 dBm. At this point, the generated 2nd harmonic power is close to −10 dBm, which is high enough for positioning purposes. As the supplementary, the details of this receiving terminal are presented in Supplementary Note 3.

In the designed receiving terminal, the sensor collects the environmental temperature, and the microprocessor processes the analog signal into digital signals. Then, the perceived results or feedback instructions are sent to users via a Bluetooth module for a closed-loop operation. Thus, the DC output from the rectifier simultaneously powers the sensor and Bluetooth. Since the measured result that the average power consumption of the sensor and Bluetooth does not exceed 7 mW, the designed rectifier can cover the power requirements. Importantly, considering that the output voltage of the rectifier varies with input power, a low dropout regulator (LDO TPS63900, Texas Instruments, Inc.) with a wide input range is used to stabilize the output voltage at 3.3 V. Besides, to observe the dynamic change of the input power, an analog-to-digital converter (ADC) module is used to record the real-time DC output. As an additional component, this ADC is powered through an external port.

STC harmonic analysis

For the smart AWPN, it is important to locate the receiving terminal. Here, our designed dual-band metasurface receives the feedback signal from the rectifier for realizing positioning. Rather than far-field plane waves, we prefer to model the feedback signal using near-field spherical waves, which enables to estimate both the distance and angles. The L-shaped array composed of 24 high-band meta-atoms plays a key role. Its array aperture is 275 × 275 mm2. According to the definition of the near field52, r < 2D2/λ, the near field of this L-shaped array is within 5.8 m, which is large enough and ensures that the receiving terminal is located at the near field.

The traditional NFP methods based on multiple-input multiple-output (MIMO) arrays require cost RF channels to collect the signals, and the used 2-D super-resolution algorithms have high computational complexity. Therefore, it is a challenge and innovation that achieve NFP on the metasurface-based SISO systems. The STC technology provides a promising approach to simplify the hardware architecture. The harmonic generated during the STC are, to some extent, intended to be equivalent to traditional multi-channel data, thereby providing the potential for accurate positioning. For this purpose, the feedback signals will be STC modulated by the high-band meta-atoms, and then received by the same horn antenna of the metasurface.

For illustrating the near-field model and STC process, we first consider the 12 high-band meta-atoms along the y-axis. As shown in Fig. 4a, in the spherical coordinate system, the position of the terminal can be expressed as p(θ, φ, r) = ru(θ, φ), where u(θ, φ) = [sinθcosφ, sinθsinφ, cosθ]T is the unit direction vector. Then, the distance from the terminal to the nth meta-atom is given by

$${r}_{n}^{y}(\theta,\varphi,r)=\sqrt{{r}^{2}+\Vert {{{{\bf{q}}}}}_{n}^{y}\Vert -2r{{{\bf{u}}}}(\theta,\varphi )\cdot {{{{\bf{q}}}}}_{n}^{y}}$$
(1)

where \({{{{\bf{q}}}}}_{n}^{y}\) is the position vector of nth meta-atom, and ||⋅|| denotes the modulo operation. The phase difference between two adjacent meta-atoms can be expressed when a feedback signal is incident

$${\delta }_{y}(\theta,\varphi,r)={k}_{2}[{r}_{n+1}^{y}(\theta,\varphi,r)-{r}_{n}^{y}(\theta,\varphi,r)]$$
(2)

where k2 is the spatial wavenumber of the feedback signal at 11.6 GHz. This phase difference is the function of θ, φ, and r, when the terminal is located near field. It demonstrates that different meta-atoms will experience varying arrival angles and propagation distances when receiving signals from the same terminal53, resulting in different propagation phases. If we consider the far field, it can be simplified as δy(θ, φ)=k2dsinθsinφ, but cannot capture the distance information.

Fig. 4: CNN-based near-field positioning.
figure 4

a Concept view of the NFP, where the incident signal is modeled as spherical waves. b STC matrix optimized by BPSO. c Harmonic distributions under three positions, and they show remarkable differences. d Constructed CNN model serves as a feature extractor. e Classification accuracy and loss of the CNN model.

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To realize the target positioning on a SISO system, each meta-atom will periodically modulate the feedback signal. The used STC matrix is shown in Fig. 4b, where its horizontal and vertical axes represent time-coding sequences and coding elements, respectively. (The optimization process of this STC matrix is presented in Supplementary Note 4). In each sequence, it has 12 intervals and totally takes 1 ms, which means the STC modulation frequency fp is 1 KHz, and the duration of each interval is 1/(12 × fp). Accordingly, the receiving signal R(θ,φ,r,t) modulated by this STC will be synthesized to the horn antenna, and it concludes many STC harmonics (see “Methods” for detailed derivation). Especially, each harmonic in value simultaneously depends on directions and distances of the receiving terminal, given by Rq(θ,φ,r,t), which provides the possibility for target localization. To illustrate, we numerically calculate the harmonics from -8th to 8th orders under three different coordinates at (0°, 0, 0.5 m), (45°, 0, 0.5 m) and (45°, 0, 0.7 m). As shown in Fig. 4c(i) and Fig. 4c(ii), the influence of angels on the harmonic distribution is evident, which is consistent with previous research findings43,50. Especially, compared with Fig. 4c(ii) and Fig. 4c(iii), the distance also affects their amplitude distribution, which is attributed to the near-field advantages. Thus, the amplitude distribution corresponds to a specific coordinate, not just the directional angles, and we can utilize them as the feature information. In fact, these harmonics generated by STC modulation enhance differentiation between different positions, and the more harmonic orders, the better. In other words, STC harmonics bring multidimensional information for target positioning, enabling the CNN-based classification for high-accuracy NFP.

CNN-based positioning

Based on the unique feature information, the data-driven positioning can be realized. The CNN is a powerful tool for data analysis. It can be trained on large datasets to learn complex hierarchical representations of data for classification and clustering. The learned features can then be used for target positioning, where the CNN serves as the feature extractor. Compared with conventional analytical methods, CNN offers significant speed advantages. Once the network has been trained in the initial phase, subsequent data classification and matching can be performed rapidly with minimal additional computational resources, which is particularly crucial for real-time scenarios.

Here, we divide the whole AoI into multiple grids, and the CNN model is used to classify the receiving terminal into the correct grids for positioning. Consider the power focusing capability of the designed 16×16 metasurface, and the 1-dB fade of the focal spot is about a circle with a diameter of 3 cm, as shown in Fig. 2e. This dimension can be used as a reference for positioning accuracy. Thus, we divide the AoI into multiple 3 × 3 × 3 cm3 grids, which ensures that the main power of the focal spot adequately covers each grid. In each grid, the harmonic amplitude distributions at different positions are marked by the same label. Then, a CNN model is established by training on these labeled datasets, where each input is associated with a corresponding class label. This network learns to map the raw input data to these class labels by adjusting its parameters.

For the data collections, we adopt a full-duplex SISO architecture, and collect time-domain data through a universal software radio peripheral (USRP). The system architecture diagram is detailed in Supplementary Note 5. After fast fourier transformation (FFT) for the collected data, the harmonic components can be extracted in the spectrum by spectral peak searching. Here, we extract the harmonic amplitudes from −Q to Q orders, and write them in vector form, given by

$${{{\bf{h}}}}(\theta,\varphi,r)={\left[\big|{R}^{-Q}(\theta,\varphi,r)\big|,\big|{R}^{-Q+1}(\theta,\varphi,r)|,\cdots,\big|{R}^{Q}(\theta,\varphi,r)\big|\right]}^{{{{\rm{T}}}}}$$
(3)

where h(θ,φ,r) is a harmonic vector with the dimension of 2Q × 1, Rq(θ,φ,r) is the qth harmonic component of the receiving signal, and \(\left|\cdot \right|\) denotes the magnitude of complex numbers. Considering the direct leakage between the receiving terminal and the horn antenna, the fundamental component at 11.6 GHz is excluded. Besides, since the power of feedback signals is varying, the vectors h(θ, φ, r) are required to be normalized as \(\hat{{{{\bf{h}}}}\,}(\theta,\varphi,r)\), which is rather important. Further, before the CNN training, convert this one-dimension vector to matrix form as

$${{{\bf{H}}}}=\hat{{{{\bf{h}}}}}(\theta,\varphi,r){\hat{{{{\bf{h}}}}}}^{{{{\rm{T}}}}}(\theta,\varphi,r)$$
(4)

where H is a matrix with the dimension of 2Q×2Q, which functions as the input of CNN. In each divided grid, all the matrixes H are marked with the same label.

For verifying our proposed CNN-based NFP, we extract harmonics from −8 to 8 orders for numerical simulations. The whole AoI (x∈[−6, 12] cm, y ∈ [−12, 12] cm, and z ∈ [48, 63] cm) is divided into 240 grids with the dimension of 3 × 3 × 3 cm3. The dataset is built with the step of 5 mm, and a total of 51,840 positions were sampled. The constructed CNN is shown in Fig. 4d, which is composed of 2 convolutional layers. The convolutional layer within the CNN captures local patterns by a 2 × 2 convolutional kernel, which allows the network to learn complex relationships and dependencies within the harmonic amplitude distributions. The ReLU activation function introduces nonlinearity into the network, enabling it to learn and approximate complex functions that cannot be represented by linear models. Besides, for ensuring the network to capture both local and global features, pooling layers further reduce the spatial dimensions of the data. Finally, the output layer of this network converts extracted features into categorical predictions using softmax activation.

This CNN model is trained with the Adam optimizer with a learning rate of 1 × 10−3 and a batch size of 200. The training processing is depicted in Fig. 4e. As can be seen, the validation dataset reaches 97.8% classification accuracy after 500 epochs, which is highly accurate for our proposed AWPN and verifies the feasibility of the CNN model. Based on the trained CNN, the receiving terminal can be accurately classified into themselves grids, which will direct to compute corresponding coding matrix of the metasurface, thereby focusing the power to the center of their grids.

Dynamic demonstrations of the AWPN

We implement experiments to verify the full-duplex power focusing and positioning. The experimental environment and setups are depicted in Fig. 5a. As can be seen, the high-power RF power is first fed by a wide-band horn antenna, and then it will be focused on a spot by the designed dual-band metasurface. The receiving terminal is mounted on a scanning shelf for equivalent to its dynamic movement. The feedback signal from this terminal will be modulated and reflected into the horn antenna again for NFP. Thus, this horn antenna works in the transmitting and receiving states, simultaneously, by connecting with a duplexer. The system architecture diagram is detailed in Supplementary Note 5. Besides, we place a heat source in the normal direction, and the receiving terminal continuously measures the environmental temperature during movement. The temperature data is then transmitted to users by Bluetooth, enabling safety monitoring and adaptive feedback adjustment.

Fig. 5: Experimental results of simultaneous target positioning and power focusing.
figure 5

a Photograph of the experimental setup. b Receiving RF power and DC output under fixed focus. c Comparison between tracking focus and fixed focus. d CDF of classification error at different transmitting powers. e Moving trajectories of the receiving terminal, which display the letters ‘X’, ‘D’, and ‘U’, respectively. f Statistical results of receiving power and DC output under different trajectories. g Temperature data collected by wireless-powered sensor.

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To demonstrate the advantages of adaptive power focusing, the received RF power and DC output of the rectifier are compared under two scenarios: fixed focus and tracking focus. To this end, we fix the scanning shelf at z = 50 cm and allow the terminal to move along the y-axis. First considering the fixed focus, when the focal spot is fixed at (0, 0, 50) cm and the transmitting power is 33 dBm, the measured results are depicted in Fig. 5b. The horizontal axis represents the offset distance from the terminal to focal spot, while the vertical axis shows the received RF power and DC output. It can be observed that as the receiving terminal deviates from the center, the received RF power and DC output of the rectifier decreases radidly. Especially, the voltage drops to 1.5 V and the received power is reduced by 8.9 dB when the terminal only offsets by 7 cm. Besides, the 1-dB fade range shown in the blue background is about 3 cm, in which the variation of DC output remains within 0.2 V. This reduction is acceptable and reflects the reasonability of the 3 cm classification resolution. Further, we extend the experimental range and put these two scenarios in the same figure for comparison, as shown in Fig. 5c. Unlike the rapid drop of the dashed line, the tracking focus represented by the solid orange line can maintain high RF power over a larger range. Expecially, in certain areas, the improvement is more than 10 dB. Correspondingly, the DC output keeps above 1.9 V even though the terminal offsets by 20 cm, as shown in solid blue line. In contrast, the fixed focus decreases to close to 0 V after extending the experimental range, as seen in dashed blue line. Compared with Fig. 5b and Fig. 5c, although they both show a convex trend, tracking focus in Fig. 5c receives higher power in a larger range. Thus, on the one hand, these results highlight the advantages of metasurface in flexible beam manipulation. On the other hand, it shows the potential of metasurface in adaptive WPT. It is urgent to develop the intelligent metasurface for simultaneous target positioning and power focusing. (The dynamic presentation is shown in Supplementary Movie 1.).

Similar to the numerical simulation, the whole AoI is 18 × 24 × 15 cm3, and is divided into 240 grids. we sample the harmonic amplitudes with 1 cm steps, and establish the training dataset from 6480 different coordinates in total. They will be classified into 240 categories and applied to train the CNN model. The training dataset is built by automatic collection based on MATLAB scripts, and the whole process takes no more than 4 h. After the CNN training, we collect the testing datasets under different transmitting powers to validate the accuracy of this model. The cumulative distribution function (CDF) of the classification error is plotted in Fig. 5d. As can be seen, more than 92% of the samples are classified correctly, and at most 98% of them are classified correctly when the transmitting power is 30 dBm. The existing errors can be ascribed to the abnormal fluctuations of data and the limited signal-to-noise ratios (SNRs). Importantly, the transmitting power does not obviously affect the classification accuracy, which indicates our proposed AWPN is different from the conventional positioning methods based on the received signal strength indicator (RSSI). We leverage the relative amplitude distribution of harmonics, but not the received harmonic strength. In fact, this is more suitable for our positioning requirement, because the power of the feedback signal is not constant.

Using the trained CNN model, we further demonstrate the adaptive power focusing based on the target localization. Since the constraints of the 2-D scanning shelf, this shelf is manually moved to three discrete distances, z = 50, 56, and 62 cm. In each distance, the terminal moves along different trajectories, which display the letters “X”, “D”, and “U”, respectively, as can be seen in Fig. 5e. These trajectories will be localized by the CNN-based NFP, which directs the laptop to calculate coding matrixes, enabling to maintain a high-power delivery. Subsequently, the terminal realizes the wireless-powered sensing and communication. The dynamic demonstrations are shown in Supplementary Movies 2, 3, and 4. As can be seen, when the terminal deviates from the center of focal spots, the DC output obviously decreases. Meanwhile, the metasurface receives feedback signals lasting 2 s and extracts their harmonic components by the FFT. It should be emphasized that this 2 s sampling time is considered to obtain a better harmonic SNR and higher spectral resolution. Otherwise, increasing the transmitting power allows for faster target localization with the same accuracy, thereby enhancing the system efficiency. Based on the collected amplitudes distribution of harmonics, the CNN reclassifies the terminal into the correct grid. Then, the metasurface adjusts the coding matrix to focus the power on the center of the new grid, thereby enhancing the DC output again. Under the transmitting power of 33 dBm, we count the received power for these three trajectories, and plot the statistical results in Fig. 5f, where the horizontal axis marks the respective trajectories. As observed, attributed to the metasurface-based tracking focus, the received RF power along the same trajectory maintains relatively stable. By comparing these three trajectories, the received power shows obvious fluctuation on the X trajectory, which can be explained by the strong standing waves produced by the superposition of incident waves from the horn antenna and scattered waves from the metasurface. Besides, the received power decreases with increasing distance. The DC output consistently keeps above 2.8 V, which is adequate for the minimum input of LDO. Based on the wireless transimitted power, the sensor is activated successfully and works normally. The perceived environmental temperatures are plotted in Fig. 5g. As can be seen, since the U trajectory is closest to the heat source, it perceives the highest temperature. In contrast, the X-trajectory data is close to room temperature. From the presented results, the designed terminal successfully realizes wireless-powered sensing, processing, and communication.

It is worth emphasizing that the training datasets of the CNN was collected in real environments, accounting for multipath effects and environmental scattering. In practice applications, the terminal (such as the multifunctional robot) can automatically collect training datasets in real environments through trajectory planning. This approach is common in fingerprint-based positioning methods, where real-environment data better captures the complex features of signal propagation. Here, we investigate the impact of environment change on the classification accuracy of a trained CNN, and instruct a person to sit at different distances from the metasurface to simulate this change. The experimental details are shown in Supplementary Note 6. The results indicate that our method can well tolerate environment variations within a certain range. However, when substantial environmental changes occur, it requires to re-collect the training datasets.

Furthermore, to simulate scenarios of battery overheating during high-power wireless charging in the future, we dynamically adjust the temperature of the heat source. When the temperature exceeds a certain threshold, such as 50 °C, the terminal realizes a safety warning. Subsequently, the AWPN adaptively adjusts the transmitting power to reduce the charging speed, thus safeguarding the battery equipment. Additionally, after the temperature decreases, the high-power signals are realigned towards the terminal. This dynamic presentation is shown in Supplementary Movie 5. From this perspective, the proposed AWPN not only enables wireless-powered sensing and communication, but also will serve as safety warnings during high-power wireless charging in the future.

Discussion

we propose a novel AWPN to achieve sensing and communication in wireless charging. The superiority of this SISO system manifests in its ability to accurately locate the receiving terminal and adaptively focus the energy beam onto the terminal. Consequently, a stable power supply can be provided for moving terminals. To this end, we design a dual-band metasurface to realize simultaneous target positioning and beam focusing, which is the first attempt for intelligent PMS and obviously enhances the system integration. During operation of the AWPN, the 2nd harmonic of the rectifier is fully utilized as feedback signals for positioning. This 2nd harmonic is naturally generated during the rectification process, which is the passive behavior and does not require additional signal sources. Thus, unlike traditional MIMO array and camera-based positioning systems, this solution optimizes the hardware architecture and achieves full-duplex operation. Additionally, the STC harmonics serve as the feature information of terminal positions, and their amplitude distributions are extracted for training the CNN model. We only need to collect the training datasets and train CNN model in the initial stage, so that the CNN allows the quick classification during positioning, and there is no need for huge computing overhead. Besides, compared with traditional radar positioning, the advantages of our method are highlighted in Supplementary Note 7.

In anticipation of the heat generation in future high-power wireless charging scenarios, we use temperature sensor as an example to illustrate the AWPN, and design a terminal to realize wireless-power sensing, processing, and communications. This terminal monitors the environmental temperature in real time and uploads the perceived data. When the environmental temperature exceeds a preset threshold, the transmitter adaptively adjusts the transmission power or deflects the beam spot away from the terminal, to achieve security warnings and protection. Moreover, experiments demonstrate that the proposed CNN-based NFP achieves a classification accuracy of over 98%. Based on the precise target positions, the metasurface adaptively adjusts its coding matrix to ensure efficient power transmission.

In the future, radiative WPT will offer significant conveniences, such as contactless and battery-free operation, greening of energy based on the solar power satellite station21,54,55, and remote energy supply. However, it currently faces a deficiency of low efficiency, which is a challenge that requires to be overcome for all researchers. For our proposed AWPN, for further enhancing the system efficiency, the promising solutions include utilizing high-bit meta-atoms, and designing larger-aperture metasurfaces and antennas. Indeed, the application of WPT also requires substantial exploration and development. In this paper, our contribution lies in exploring an innovative solution to achieve adaptive wireless charging, and realizing wireless-powered sensing, processing, and communication.

Methods

Coding matrix of digital reconfigurable metasurfaces

Consider a wideband horn antenna as a feed source and incident a 5.8 GHz RF power toward the metasurface. The tangential E-field Et(xm, yn) of (m, n)th meta-atom can be expressed as

$${E}_{{{{\rm{t}}}}}({x}_{m},{y}_{n}) =\\ {A}_{mn}\exp (j{\phi }_{mn})\cdot {E}_{0}({x}_{m},{y}_{n})\cdot \exp \left(j{k}_{1}\sqrt{{({x}_{{{{\rm{s}}}}}-{x}_{m})}^{2}+{({y}_{{{{\rm{s}}}}}-{y}_{n})}^{2}+{z}_{{{{\rm{s}}}}}^{2}}\right)$$
(5)

where Amn and ϕmn are reflective amplitude and phase of (m, n)th meta-atom, E0(xm, yn) is tangential E-field incident from the feed source, k1 denotes the spatial wavenumber at 5.8 GHz, and (xs, ys, zs) is the position coordinate of the feed source. To produce a focal spot at (xf, yf, zf), the reflective waves from each meta-atom should be in-phase at this spot. Thereby, ϕmn is given by

$${\phi }_{mn}=-{k}_{1}\sqrt{{({x}_{{{{\rm{s}}}}}-{x}_{m})}^{2}+{({y}_{{{{\rm{s}}}}}-{y}_{n})}^{2}+{z}_{{{{\rm{s}}}}}^{2}}\\ -{k}_{1}\sqrt{{({x}_{{{{\rm{f}}}}}-{x}_{m})}^{2}+{({y}_{{{{\rm{f}}}}}-{y}_{n})}^{2}+{z}_{{{{\rm{f}}}}}^{2}}$$
(6)

Since the metasurface is 1-bit digital coding, the reflection phase ϕmn is required to be quantized by

$${\phi }_{mn}^{{{{\rm{q}}}}}=\left\lfloor \frac{{\phi }_{mn}}{\pi }\right\rfloor \cdot \pi$$
(7)

where \({\phi }_{{mn}}^{{\mbox{q}}}\) is the quantized phase, and \(\left\lfloor \cdot \right\rfloor\) is the round down operator. Based on Eqs. (6) and (7), a 16×16 coding matrix can be obtained.

Signal model of STC harmonics in near field

The receiving signal modulated by y-axis meta-atoms is given by

$${R}_{y}(\theta,\varphi,r,t)=\exp (j2\pi {f}_{2}t){\sum}_{n=1}^{12}{{{{\boldsymbol{\Gamma }}}}}_{n}(t){W}_{n}^{y}\exp \left[-j{k}_{2}{r}_{n}^{y}(\theta,\varphi,r)\right]$$
(8)

where f2 = 11.6 GHz, \({W}_{n}^{{y}}\) denotes the spatial response between nth meta-atom and horn antenna, and \({\varGamma }_{n}(t)\) is the periodic time-coding sequence of nth meta-atom, written as

$${{{{\boldsymbol{\Gamma }}}}}_{n}(t)={\sum}_{l=1}^{L}{{{{\boldsymbol{\Gamma }}}}}_{l}^{n}{U}_{l}(t)$$
(9)

where \({\varGamma }_{n}(t)\) is divided into L intervals in a period, \({\varGamma }_{l}^{{n}}\) denotes the reflection coefficient of l th interval, Ul (t) is a periodic pulse function with period Tp. In each cycle, Ul (t) is given by

$${U}_{l}(t)=\left\{\begin{array}{c}1,(l-1)\tau \le t < l\tau \\ 0,{{{\rm{otherwise}}}}\hfill\end{array}\right.$$
(10)

where τ = Tp / L is the pulsewidth. Decompose Ul (t) into Fourier series as

$${U}_{l}(t)={\sum}_{q=-\infty }^{\infty }{c}_{l}^{q}\exp (j2\pi q{f}_{{{{\rm{p}}}}}t)$$
(11)

where fp = 1/Tp, and \({c}_{l}^{q}\) is the Fourier coefficients. Therefore, Eq. (8) can be rewritten as

$${R}_{y}(\theta,\varphi,r,t)={\sum}_{q=-\infty }^{\infty }{\sum}_{n=1}^{12}{\alpha }_{n}^{q}{W}_{n}^{y}\exp [j2\pi ({f}_{2}+q{f}_{{{{\rm{p}}}}})t]\exp [-j{k}_{2}{r}_{n}^{y}(\theta,\varphi,r)]$$
(12)

where

$${\alpha }_{n}^{q}={\sum}_{l=1}^{L}{{{{\boldsymbol{\Gamma }}}}}_{l}^{n}{c}_{l}^{q}={\sum}_{l=1}^{L}\frac{{{{{\boldsymbol{\Gamma }}}}}_{l}^{n}}{L}{{{\rm{sinc}}}}\left(\frac{\pi q}{L}\right)\exp \left[\frac{-j\pi q(2l-1)}{L}\right]$$
(13)

Furthermore, consider all meta-atoms in the L-shaped array along both x and y axes, and the receiving signal can be expressed as R(θ, φ, r, t)=Rx(θ, φ, r, t)+Ry(θ, φ, r, t), which is consisted of numerous STC harmonics at frequencies of f2±fp, f2±2fp, etc. For instance, the qth harmonic in the frequency domain can be extracted as

$${R}^{q}(\theta,\varphi,r)={\sum}_{n=1}^{12}{\alpha }_{n}^{q}\left[{W}_{n}^{x}\exp (-j{k}_{2}{r}_{n}^{x}(\theta,\varphi,r))+{W}_{n}^{y}\exp (-j{k}_{2}{r}_{n}^{y}(\theta,\varphi,r))\right]$$
(14)

Equation (14) shows that the amplitudes of harmonics are determined by positions of the receiving terminal.

Simulations

In this paper, the full-wave simulations for the dual-band metasurface and antenna are performed by HFSS of Ansys Electronics Desktop 2022. For the rectifier design, to analyze the nonlinear characteristics of Schottky diodes, we employed Advanced Designed System 2020 for large-signal model simulation. Then, the EM and circuit co-simulation is performed using its Momentum plugin. The rest of the numerical computations and simulations are conducted using MATLAB 2022a.

CNN model training

We train the CNN model using the Deep Network Designer in MATLAB 2022a toolbox. The system is implemented on a computer with NVIDIA GeForce GTX 1650 GPU and 64 GB RAM. The CNN model is trained with the Adam optimizer with a learning rate of 1 × 10−3 and a batch size of 200. It contains 11 layers and 370.6 k trainable parameters.

Experimental validation

For obtaining the operation frequency of the antenna and rectifier, their S parameters are first measured by a vector network analyzer (Agilent N9918A), and the harmonic power from the rectifier is measured by the spectrum analyzer (Ceyear 4051F). In the step of dataset collection, we use MATLAB script to control the movement of the scanning shelf. At the same time, a universal software radio peripheral (USPR B210, ETTUS Research Corporation) is applied to data sampling. The whole process is automatic. The experimental equipment contains a signal generator, a power amplifier (PA), a duplexer, a wide-band horn antenna, a low noise amplifier, a mixer module, and a USRP. The 5.8 GHz signal transmitted from the signal generator is enhanced to more than 2 W by the PA. The duplexer ensures that the wide-band horn antenna works in full-duplex mode. Considering that the USRP operates at frequencies below 6 GHz, we used an external mixer to down convert the 11.6 GHz feedback signal to below 6 GHz. The system architecture of the transceiver is detailed in Supplementary Note 5. Besides, the perceived data sent by the terminal is received by another Bluetooth module on the laptop.