High-performance cost efficient simultaneous wireless information and power transfers deploying jointly modulated amplifying programmable metasurface

Programmable metasurfaces present significant capabilities in manipulating electromagnetic waves, making them a promising candidate for simultaneous wireless information and power transfer (SWIPT), which has the potential to enable sustainable wireless communication in complex electromagnetic environments. However, challenges remain in terms of maximum power transmission distance and stable phase manipulation with high-power scattered waves. Additionally, waveform limitations restrict average scattered power and rectifier conversion efficiency, affecting data transmission rates and energy transmission distance. Here we show an amplifying programmable metasurface (APM) and a joint modulation method to address these challenges. The APM mitigates the peak-to-average power ratio and improves maximum power, phase response stability, average output power, and rectifier conversion efficiency. Through experimental validation, we demonstrate the feasibility of the SWIPT system, showcasing simultaneous LED array powering and movie video transmission. This innovative SWIPT system holds promise for diverse applications, including 6 G wireless communications, IoT, implanted devices, and cognitive radio networks.


{ } ( ) ( ) ( ) ( )
{ }} where k is the wavenumber in free space, and C and S are the Fresnel integral.The tangential electric intensity x y m n E x y of each unit cell can be obtained from co-simulation results and expressed as We assume a function ( ) ( ) It is worth noting that the magnitude of the coefficient should fulfill the relation ( ) because unilateral power amplifiers are embedded with each unit cell.Herein, the scattering electric field is readily obtained by extracting the electric field of the feed horn at each unit cell and the scattering parameters from the co-simulation results.Based on the aforementioned method, we calculate the y-polarized electric field along the z direction (Supplementary Fig. 1b) under three distinct phase distributions (Supplementary Fig. 1c).
improve energy harvesting efficiency.The underline theory of joint modulation can be expressed as follow.The total harvested energy is a sum of baseband and continuous waves, denoted by where ( ) i , P PAPR η is conversion efficiency which is a function of average power a P and denotes the transmission channel from the transmitter to the receiver with Nth antenna equipped on the receiver and Mth antenna equipped on the transmitter, ( ) denotes random baseband signal at the nth symbol interval, and Pc is the average energy of continuous wave.And the baseband transmission from the APM to the receiver can be modeled as where ( ) represents the received baseband signal at the nth symbol, and ( ) n z denotes the receiver noise vector.Since only one physical channel in the proposed system uses a high-directional beam and one antenna equipped on the receiver (M=1, N=1), the total harvested energy can be written as because the frequency of a continuous wave is different from the modulated baseband signals, where Pn is the average energy of the receiver noise.We suppose that the ratio of the continuous wave to the baseband signal energy is α .
Hence, we can adjust α to improve the total harvested energy while keeping the baseband energy for high-quality data transmission.Furthermore, the PAPR of the total transmitted signal can be readily reduced by increasing the ratio α .According to the field calculation in equation S1 in Supplementary information, the transmission coefficient in the Fresnel Zone is proportional to the scattered energy . Hence, we can adjust the code distribution on the APM to form an arbitrary high-directional beam for energy and information transmission.

Supplementary Note 3. Theoretical analysis of the converter circuit
The DC output power is time-average energy which is a constant value in a transmitted signal.
The peak amplitude of transmitted signals only determines the peak voltage across the diode, which is not the main factor for DC output power if the peak amplitude takes little proportion of the transmitted signals.Besides, a signal with a larger PAPR drives a larger current through the diode than a CW signal.This larger current results in a higher energy loss on the series resistance.And the waveform of a larger PAPR signal may over the reverse breakdown voltage and be clipped.Therefore, a transmitted signal with a low PAPR and suitable energy level will be helpful to a converter for providing DC output power.Since DC output power is timeinvariant, the maximum DC output power is identical to the DC output power.We can theoretically explain the generation of DC output power from a single-diode converter under a joint modulated signal.An ideal energy-harvesting circuit model extracted from the converter circuit (Supplementary Fig. 2a) is considered to analyze the DC output power, as shown in Supplementary Fig. 2b.We ignore the package and all other diode parasitics for theoretical analysis simplicity.The current through junction capacitance CJ is negligible due to that capacitance is very small.Similar to the analysis of energy-harvesting circuits 2 , the DC output power is a function of the time-average energy of the converted signals, which can be denoted where Vdc,d is the voltage across the diode, Rs is the series resistance, RL is the load resistance.
For an input signal in the time T, the DC output voltage of the diode is the time-average voltage across the diode, which can be written as The voltage across the diode under the input signal s(t) is related to the threshold voltage and the transient voltage of signals s(t).When the input signal is larger than the reverse breakdown voltage Vr, the voltage across the diode is -Vr.When the diode turns off or the input signal is less than the threshold, the diode voltage Vd is equal to the signals.When the signal is larger than the threshold, the diode voltage Vd is equal to the threshold voltage Vt.The diode voltage can be denoted as r d , ( ) Based on the joint modulation method, the input signal to the energy-harvesting circuit is the sum of the modulated baseband signals ( ) m j t x t e ω and continuous signal c ω .Since we employ the APM to generate a high-directional beam for wireless energy and information transmission, the modulated signal arriving at the receiver can be expressed as where b c , h h ∈  represent the equivalent complex channel, and x(t) is the baseband signal.
Here, we take three cases (Supplementary Fig. 2c) as examples for demonstrating the DC output power performance.The peak amplitude of the three cases is normalized to the reverse breakdown voltage.Case I is the converter circuit under input modulated signals with a high PAPR.Case II is an input signal with a middle PAPR, and Case III is continuous waves.
According to the characteristics of diode BAT15-03w from Infineon, the threshold voltage is set to 0.224V, the series impedance is set to 5Ω, and the reverse breakdown voltage is set to 4.2V.
The envelope of three modulated signals is depicted in Fig. R5c the amplification coefficient of the electric field under q-bit status.The electric field is the tangential incident field at the center of each unit cell.The Fresnel integral in equation (S1) is defined as follows: are the transmission coefficiency of the physical channel of baseband signals and continuous wave, respectively, which depends on the scattered energy by the proposed APM, and Pe is the energy of continuous wave feeding to the APM.The maximum rate can be denoted ( ) ( ) ω .Note that the angular frequency of modulated baseband m ω is different with the continuous signal c . The PAPR distributions of signals of Case I and Case II are shown in Supplementary Fig. 2d.Since any CW signal has a zero PAPR value, we have not calculated the PAPR distribution of Case III in Fig. R5d.Based on the above theory, we can observe that the DC output power of the converted circuit increases as the PAPR value decreases, as depicted in Supplementary Fig. 2e.