A programmable metasurface design method for assisting broadband wireless communication

Abstract

The application discloses a programmable intelligent metasurface design method for assisting broadband wireless communication, and comprises the following steps: designing an electromagnetic model of a broadband intelligent metasurface, outputting an amplitude correlation of the design model through electromagnetic simulation software, and fitting the amplitude correlation into a mathematical expression; setting a broadband wireless communication experimental prototype of an intelligent metasurface assisting single-in single-out orthogonal frequency division multiplexing based on the fitted amplitude correlation, and through joint optimization of power distribution of each subcarrier and beamforming of each RIS small element until convergence, the maximum average subcarrier rate of the system is obtained; and the performance of the algorithm is evaluated through setting different simulation indexes, and the influence of different factors on the transmission quality in the field test prototype is further evaluated by considering the simplified conditions of the field test.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to the research on system prototype design and beamforming in intelligent metasurface-assisted broadband wireless communication in the 5th generation (5G) mobile communication system. Background Technology

[0002] The explosive growth of mobile data and the ever-increasing demand for higher data rates are driving advancements in wireless communication technologies. In the upcoming fifth-generation (5G) wireless networks, network capacity is expected to increase a thousandfold, and energy efficiency is projected to improve by several orders of magnitude.

[0003] However, the key technologies of 5G—massive MIMO and millimeter wave (mmWave)—have very high requirements for signal processing solutions and hardware facilities.

[0004] Therefore, in order to achieve higher data rates and efficiency in wireless networks, a low-cost, simple-to-process, and sustainable improvement solution is crucial, and reconfigurable intelligent surfaces have emerged in response to this trend.

[0005] It can reshape the amplitude and phase shift of impact signals using a large number of low-cost passive components, thereby enabling the reconfiguration of the wireless propagation environment and significantly improving wireless communication coverage, network throughput, and energy efficiency. Furthermore, RIS operates in full-duplex (FD) mode, without any antenna noise amplification or self-interference, thus outperforming traditional active relays.

[0006] Because of RIS's significant performance advantages, many researchers have made major contributions to building and testing RIS proof-of-concept and prototype designs.

[0007] In terms of theoretical analysis, the research work includes channel modeling, precoding / beamforming, channel estimation, resource allocation, and coordinated deployment of multiple RIS.

[0008] In terms of prototype design, teams have already designed mature RIS manufacturing board prototypes and conducted different types of test experiments, such as compact field tests, standard far field tests, and backscattering tests, and used different indicators for quantitative analysis, such as transmission rate, power gain, and spectral efficiency.

[0009] Broadband communication features large system capacity, flexible coverage, and high service rate support. Broadband RIS access wireless communication systems can not only assist high-bandwidth communication applications and significantly improve system throughput, but also encompass intelligent reflector design schemes that need to operate in multiple different frequency bands, simplifying deployment and saving costs.

[0010] However, most theoretical analyses and field experiments are limited to very narrow frequency bandwidths because the frequency-varying amplitude and phase characteristics of RIS units make the RIS channel model more complex, and it is difficult for reconfigurable scatterer surface units to generate stable phase differences as the frequency changes. Therefore, the field of RIS-assisted broadband communication is a research direction that urgently needs to be explored.

[0011] Existing solutions—In the theoretical analysis of broadband RIS, many studies have conducted precoding design and beamforming analysis under the assumption of RIS-assisted OFDM communication systems. In the field experimental research of broadband RIS, some teams have designed prototypes that can use the state switching of PIN diodes to control the distribution of surface current in scatterer units, thereby achieving a stable reflection coefficient phase curve under a 600MHz bandwidth.

[0012] While the existing schemes described above are closer to broadband wireless communication systems in terms of design and experimental results compared to traditional RIS algorithms, few theoretical analyses assign amplitude and phase relationships to the actual RIS unit model. Most of the analyses rely on simple ideal states and simplified equivalent circuits to make assumptions about the RIS phase control unit.

[0013] Furthermore, while the PIN diode control scheme reduces charging and discharging time, it cannot achieve continuous phase modulation and introduces complex and redundant bias circuit designs. Therefore, there is a need to improve the existing scheme. Summary of the Invention

[0014] This invention proposes an electromagnetic model of a broadband smart metasurface, verifies the amplitude-phase relationship of the design model using electromagnetic simulation software, and fits it into a mathematical expression.

[0015] This invention sets up a broadband wireless communication experimental prototype of RIS-assisted SISO-OFDM based on the proposed electromagnetic model, and maximizes the average subcarrier rate of the system output through beamforming and power allocation methods.

[0016] This invention simplifies the field test settings in the algorithm simulation, thereby further evaluating the impact of different factors on transmission quality in the field test prototype.

[0017] This invention provides the following technical solutions:

[0018] A design method for broadband smart metasurface models includes:

[0019] By introducing the design concept of fixed metasurfaces and the design method of frequency-selective surfaces, a basic prototype is selected as the foundational structure for subsequent applications.

[0020] By introducing existing smart metasurface small unit loading varactor diodes and combining them with the basic structure, the amplitude and phase of the reflection coefficient can be controlled by different bias voltages.

[0021] A method for fitting the amplitude-phase relationship of a practical electromagnetic model into a mathematical expression includes:

[0022] A unified mathematical fitting function is used to correlate the amplitude and phase at the same frequency through mathematical expressions.

[0023] A method for beamforming using actual amplitude-phase correlation includes:

[0024] By simulating a smart reflector-assisted broadband orthogonal frequency division multiplexing (OFDM) single-input single-output (SISO) communication system, where the OFDM system has K subcarriers and the RIS board has M small cells, a beamforming algorithm is designed.

[0025] In practice, the maximum average subcarrier rate of the system is obtained by jointly optimizing the power allocation of each subcarrier and the beamforming of each RIS small element.

[0026] In practice, the non-convexity of the joint optimization problem is addressed by iterating until convergence.

[0027] A simulation method incorporating the concept of field testing errors includes:

[0028] In practice, to evaluate the advantages of using actual models for beamforming methods, different models were used as benchmarks for simulation comparison.

[0029] In particular, in order to align with the theme of applying algorithm analysis to practical models, simplifications are made in the simulation to consider actual on-site factors, and the conclusions are compared with those of the ideal state.

[0030] Beneficial effects

[0031] The broadband varactor diode phase-modulating programmable smart metasurface model implemented in this invention can achieve a smooth phase shift profile within an 800MHz bandwidth, and the phase difference between adjacent phase curves remains almost constant as the frequency changes.

[0032] The bias voltage of the varactor diode is controlled to achieve a phase difference of 180 degrees over the bandwidth, while the normalized reflection coefficient exceeds 0.75.

[0033] The simulation results of the intelligent reflector-assisted broadband orthogonal frequency division multiplexing single-input single-output communication system based on this invention show that, after beamforming and precoding matrix design, the average subcarrier rate is significantly improved compared to all baseline models. Attached Figure Description

[0034] Figure 1 This is a topological schematic diagram of the broadband smart metasurface designed in this invention;

[0035] Figure 2 This is a side view schematic diagram of the broadband smart metasurface designed in this invention;

[0036] Figure 3 This is a top view schematic diagram of the broadband smart metasurface designed in this invention;

[0037] Figure 4 This is a graph showing the normalized amplitude of the reflection coefficient of the broadband smart metasurface designed in this invention as a function of frequency.

[0038] Figure 5 This is a trend diagram of the phase variation of the reflectance coefficient of the broadband smart metasurface designed in this invention as a function of frequency;

[0039] Figure 6 This is a schematic diagram of a scenario simulating an intelligent metasurface-assisted broadband orthogonal frequency division multiplexing single-input single-output communication system according to the present invention.

[0040] Figure 7 This is a flowchart of the beam amplitude and phase algorithm design of the present invention;

[0041] Figure 8 It compares the model of this invention with existing models, ideal models, and direct-link models without intelligent reflectors under different input power conditions.

[0042] Figure 9 This paper compares the model of this invention with the simplified control model, the ideal model, and the direct link model without intelligent metasurfaces, considering the influence of actual field test factors under different input power conditions. Detailed Implementation

[0043] The system architecture or scenario in which this invention is applied

[0044] The main application scenario of this invention is in B5G / 6G next-generation wireless communication networks. In order to cope with the deployment of large-scale active nodes and enhance network coverage and capacity, the invention solves the fading and interference problems by reconstructing wireless channels through intelligent metasurfaces.

[0045] High-bandwidth smart metasurfaces can not only further improve network throughput, but also encompass multiple narrowband metasurface deployments, saving costs and simplifying the design process.

[0046] Detailed description of the broadband intelligent metasurface model of the present invention

[0047] The intelligent metasurface is composed of a large number of periodic passive reflective metasurface units. To obtain the expression for the reflection coefficient of the elements, this invention, following the framework of the document "An Accurate Method for Synthesis of Reflecting Elements to Design Wideband Reflectarray Antenna," assumes that the surface impedance of each element in each reflective unit can be expressed as Z. in =jX in Material loss is ignored.

[0048] Therefore, the metasurface unit will have a reflection coefficient of the following form:

[0049]

[0050] Where Φ is the reflection coefficient, G(f) is the amplitude component of the reflection coefficient, F(f) is the phase component of the reflection coefficient, Z0 is the characteristic impedance, f is the frequency, and X... in It is the imaginary part of the surface impedance.

[0051] The objective of this invention is to design a RIS element that exhibits linear phase characteristics under periodic boundary conditions and has specific slopes and nodes within the operating frequency band. Therefore, the phase of the aforementioned reflection coefficient can be further expressed as:

[0052] F(f) = -2tan -1 (X in / Z0)=180(deg)-T0f (2)

[0053] Where T0 represents the slope of the linear phase curve, the present invention reconstructs the above expression as follows:

[0054]

[0055] Where s = jf, Y in Y0 is the input admittance, and Y0 is the free-space characteristic admittance. Applying the above expression to the continued fraction expansion theorem, we obtain:

[0056]

[0057] The circuit model corresponding to formula (4) is low-pass, where the inductor (L) is in the parallel branch and the capacitor (C) is in the series branch.

[0058] Therefore, we use the equation for low-pass to band-pass filter conversion to convert it to the desired frequency band. The band-pass circuit model has parallel LC slots in the series branch and series LC slots in the parallel branch.

[0059] Finally, in order to implement the bandpass circuit model using reflective radiation elements, this invention replaces the parallel LC slots in the series branch with the series LC slots in the parallel branch between the two admittance inverters.

[0060] The simplest form of an admittance inverter can be a quarter-wavelength transmission line (TL) with characteristic admittance (denoted as J), equivalent to Z0.

[0061] Therefore, the present invention can implement the circuit model using a frequency selective surface (FSS) configuration. The series LC circuit in each parallel branch is formed using an FSS structure with suitable printed components.

[0062] According to the literature "An Overview of Equivalent Circuit Modeling Techniques of Frequency Selective Surfaces and Metasurfaces", the equivalent circuit under single resonance can be represented as a series LC circuit patch with a frequency-selective surface model resembling a dog bone. Therefore, this invention selects the dog bone patch as the basic model for designing broadband metasurface units.

[0063] Based on the equivalent circuit model (ECM) proposed in the literature "Equivalent Circuit Models for Metasurfaces Using Floquet Modal Expansion of Surface Current Distributions", this invention suggests that if a change in load does not completely reconstruct the surface current distribution of the frequency-selective surface, then the reconfigurable amplitude and phase response of the metasurface can be controllably varied with the change in load.

[0064] Therefore, the present invention loads a varactor diode in the middle of the dog bone patch, thereby controlling the reflective properties of the metasurface through this loading method.

[0065] Each broadband unit structure of this invention consists of a three-layer dielectric substrate and a three-layer metal patch, the topology of which is shown in the appendix. Figure 1 See attached top view. Figure 2 See attached side view. Figure 3 The specific parameters of the metasurface unit are shown in the table below.

[0066]

[0067] The top layer of the designed metasurface unit is a dog-bone shaped copper patch supported by substrate 1, with a MAVR-011020-1411 varactor diode loaded in the middle to change the surface current of the metal patch, thereby controlling the reflection characteristics.

[0068] The design unit places a metal ground plane between substrate 2 and substrate 3 that can capture reflected electromagnetic waves.

[0069] The bottom layer of the design contains two bias lines for adjusting the junction capacitance of the varactor diode.

[0070] The two vias of the design unit run through the entire model, bridging the two ends of the varactor diode and the two bias lines at the bottom. Therefore, an external control module can be connected through the bias lines to adjust the model's reflection coefficient.

[0071] Note that the through hole should be separated from the ground plate by a certain gap to prevent accidental electrical contact.

[0072] To facilitate subsequent design, this invention selects four typical bias voltages, which correspond to different states of the varactor diode, and thus correspond to four amplitude-phase-frequency relationships.

[0073] This invention simultaneously encodes the four sets of curves into 2-bit digital symbols c, and enables this encoding method to be used for QPSK modulation. The correspondence between the encoding and the bias voltage is shown in the table below.

[0074]

[0075] This invention describes the fitting function for the amplitude-phase relationship.

[0076] The bandwidth of the broadband reflector unit designed in this invention is sufficient to support most algorithm designs and field broadband wireless communication transmission applications that require a large bandwidth. Therefore, amplitude-frequency curves and phase shift-frequency curves were extracted from the metasurface unit. The curves at different frequencies do not show significant differences, so a unified fitting function can be used for different frequencies.

[0077] The relationship between the frequency and phase of a RIS element can be approximately fitted to a straight line, and the relationship between the amplitude and phase shift at different frequencies can be considered a quadratic function. When the bias voltage supplied to a RIS element changes, i.e., when the encoding method changes, the slope and intercept of the phase-frequency curve will change accordingly. The fitting function used in this invention is:

[0078] F c,m (f)=a c,1 f+a c,2 (1.a)

[0079]

[0080] For a broadband smart metasurface with a total of M reflective units, the reflection phase of the m-th unit encoded as c is represented by formula (1.a), and the reflection amplitude of the m-th unit encoded as c is represented by formula (1.b).

[0081] Where f represents the input frequency, F c,m (f) represents the reflection phase at f, G c,m (f) represents the reflection amplitude at f.

[0082] The fitting coefficients for each encoding method are shown in the table below:

[0083]

[0084] Description of iterative beamforming algorithm in this invention

[0085] In the algorithm design of this invention, a RIS-assisted wideband multi-carrier orthogonal frequency division multiplexing communication system is considered, wherein a single wireless network access point (AP) and a single user are configured, as shown in the attached figure. Figure 6 .

[0086] Furthermore, the RIS control board of this system is configured with M small unit components, and under OFDM technology, the frequency domain is divided into K subcarriers with a center frequency of f. c =5.9GHz, the center frequency of the kth sub-channel is:

[0087]

[0088] This invention sets H k Let F be the direct channel matrix from the AP to the user under the k-th subcarrier. k Let G be the channel matrix from AP to RIS under the k-th subcarrier. k Let be the channel matrix from the RIS point to the user under the k-th subcarrier.

[0089] This invention makes Let G represent the reflection coefficient of the m-th RIS element under the k-th subcarrier, where G c,m (f k F represents the reflection amplitude under the k-th subcarrier. c,m (f) represents the reflection phase under the k-th subcarrier.

[0090] Therefore, let the reflection matrix of the RIS board be represented as Θ. k =diag(Φ c,k,1 ,...,Φ c,k,m ), where diag represents a diagonal matrix.

[0091] In this invention, the total wireless transmission channels include the direct channel from the AP point to the user and the cascaded channel from the AP point to the RIS board and from the RIS board to the user.

[0092] Therefore, this invention allows h k The total channel under the k-th subcarrier can be represented as:

[0093]

[0094] In this invention, the equivalent baseband signal received by the user from the AP point under the k-th carrier can be expressed as:

[0095]

[0096] p k This represents the power of the signal transmitted under the k-th carrier, s k This represents the transmitted signal at point AP under the k-th carrier, n k This indicates that the additional mean is zero and the variance is σ under the k-th carrier. 2 Gaussian white noise.

[0097] Because the quality of OFDM transmission communication systems can be judged by the average subcarrier rate R, the higher the average achievable subcarrier rate, the higher the upper limit of the system's transmission performance.

[0098] To achieve the goal of maximizing R, we define R as:

[0099]

[0100] The optimization objective of this invention can be expressed as:

[0101] R

[0102] st

[0103]

[0104] Where Λ={00,01,10,11} represents a two-bit code.

[0105] This invention addresses the non-convexity and complexity of optimization problems through iterative calculation.

[0106] We assume p k Given, the optimization problem can be expressed as:

[0107] R

[0108] st

[0109] c∈Λ, (7)

[0110] The design flow of the beam reflection coefficient algorithm of this invention is attached. Figure 7 The algorithm obtains the reflection coefficient vector Φ that maximizes the average subcarrier rate R. c .

[0111] After completing the above steps, the present invention designs a precoding matrix, i.e. a power allocation algorithm, after a given reflection vector, using the classic water-filling algorithm.

[0112] This invention sets Let K be the channel gain-to-noise ratio for the k-th sub-channel, and initialize the number of available sub-channels K. * =K.

[0113] This invention defines the value of the water injection constant as follows: Where P is the total power of the input system. Γ represents the signal-to-noise ratio interval.

[0114] This invention calculates the Nth * The power allocated to each sub-channel is if Let K * =K * -1, and recalculate the injection constant ζ, repeating until...

[0115] After completing the above steps, the present invention finally calculates the final power allocation vector as p. k =ζ-Γ / g k Where k = 1,...,K * .

[0116] After obtaining the optimal allocation vector by using the water-filling algorithm for power allocation, the beam reflection coefficient vector and power allocation vector are repeatedly iterated and optimized until the results converge.

[0117] Simulation setup and performance analysis of the present invention

[0118] This invention sets up a RIS-assisted SISO-OFDM communication scenario, wherein the center frequency f c =5.9GHz, the number of small cells on the RIS board is M=100.

[0119] The amplitude-phase relationship extracted from the broadband electromagnetic metasurface model is substituted into the reflection coefficient matrix of the algorithm design. The coding scheme and power allocation are iteratively optimized, and finally the average subcarrier rate R is obtained.

[0120] Let d IP =50m represents the distance from RIS to AP, d uP=50m represents the distance from the user to the AP point, d uI =2m represents the distance from the user to the RIS.

[0121] The road loss model can be expressed as:

[0122]

[0123] Where κ0 represents the path attenuation at a distance of 1m, and is set to -30dB.

[0124] The path loss coefficients from RIS to AP, user to AP, and user to RIS are set to ε, respectively. IP =2.2, ε uP =3.5 and ε uI =2.8.

[0125] Based on the above settings, we consider a Rissen fading model to simulate small-scale fading across three links, with the noise power set to σ. 2 = -70dBm.

[0126] The channel from the user to the AP point is set as follows:

[0127]

[0128] Where ω represents the Rissen factor, H LOS and H NLOS This indicates a LOS direct channel and a Rayleigh fading channel.

[0129] The channel settings for channel F from RIS to AP and channel G from user to RIS are similar to those for channel H from user to AP.

[0130] The Risen factor for each of the three links is set to ω. Pu =0, ω IP →∞,ω Iu =0.

[0131] To highlight the superiority of the algorithm design model, two sets of simulation diagrams are provided in this invention, as shown in the appendix. Figure 8 and attached Figure 9 .

[0132] In the appendix Figure 8 In addition to the proposed algorithm result curve, this invention also establishes three sets of baselines: "circuit model", "ideal model" and "RIS-free model".

[0133] The "circuit model" represents a simple representation of the RIS cell topology using circuits, resistors, and inductors connected in series and parallel. The reference is from "Practical Modeling and Beamforming for Intelligent Reflecting Surface Aided Wideband Systems". The relationship between the reflection coefficient and frequency is extracted through full-wave simulation using simulation software and then input into the beamforming algorithm used in this invention to obtain the resulting curve.

[0134] The “ideal model” represents the ideal phase model of the reflection coefficient in the RIS cell. The amplitude model is the same as the amplitude model in the electromagnetic simulation of this invention. The curve is obtained by inputting the relationship between the reflection coefficient and the frequency into the beamforming algorithm used in this invention.

[0135] The "RIS-free model" refers to a communication system that does not use a RIS board to improve the communication link, and only sets up one user, resulting in the average subcarrier rate curve.

[0136] In the appendix Figure 9 In this invention, based on the appendix Figure 8 The results take into account additional factors to illustrate the impact of various constraints on field test performance, namely “simplified control”, “simplified coding”, and “simplified board fabrication”.

[0137] Since it is difficult for the RIS control device to generate a large number of parallel bias voltages to accurately adjust the reflection coefficient of each component, this invention considers using a "simplified control" model, that is, connecting every five small components of the RIS control board together with the bias line, and testing the impact of the control method on the simulation results.

[0138] Complex encoding methods increase the difficulty of optimization iteration and also greatly prolong the actual algorithm execution response time. Therefore, this invention considers a "simplified encoding" model, which simplifies the encoding method to 1 bit and tests the impact of the encoding method on the simulation results.

[0139] The more RIS boards there are, the more complex the iterative optimization becomes, and the greater the error in board manufacturing will be. Therefore, this invention considers a "simplified board manufacturing" model, halving the number of small units, and tests the impact of board size on simulation results.

[0140] This invention sets two bandwidths in the simulation settings: one with a frequency domain subcarrier number K=256 under a 400M bandwidth (see appendix). Figure 8 and attached Figure 9 (Solid line curve in the image) and the number of frequency domain subcarriers K=512 under 800M bandwidth (see appendix) Figure 8 and attached Figure 9 (The dashed curve in the middle).

[0141] Appendix Figure 8 and attached Figure 9 All solid curves in the diagram show greater performance improvements than their corresponding dashed curves because, for a given subcarrier spacing, a wider bandwidth leads to phase and amplitude distortion, making beamforming more difficult.

[0142] Appendix Figure 8 Among all baselines, the proposed beam assignment method using a real model performs significantly better.

[0143] For example, when the transmission power P = -2dBW and K = 256, the average subcarrier rate increased from 0.1534 to 0.8926, achieving a gain of 4.81 times.

[0144] Meanwhile, the results of this invention are significantly better than those of the "circuit model" and the "ideal model", proving the non-adaptive defects of the circuit model and the superiority of the amplitude-phase coupling design.

[0145] In addition, Figure 9 In this example, keeping the same parameters as before, we can conclude that all simplification methods lead to performance losses. This result allows us to make trade-offs based on measured factors in subsequent system physical design.

[0146] Future Prospects of the Invention

[0147] This invention provides pioneering insights for future researchers in the prototype design and simulation setup of broadband intelligent reflective surfaces. Clearly, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A broadband intelligent metasurface unit, characterized in that, Each metasurface unit structure consists of three layers of dielectric substrate and three layers of metal patch; The top layer of the designed metasurface unit is a dog-bone shaped copper patch supported by substrate 1, with a varactor diode loaded in the middle to change the surface current of the metal patch, thereby controlling the reflection characteristics. A metal ground plane capable of capturing reflected electromagnetic waves is provided between substrates 2 and 3; the bottom layer contains two bias lines for adjusting the junction capacitance of varactor diodes. Two through holes run through the entire model, bridging the two ends of the varactor diode and the two bias lines at the bottom. The bias lines are connected to an external control module to adjust the model's reflection coefficient. The amplitude and phase relationship of the reflection coefficient at different frequencies were calculated using simulation software.

2. The broadband intelligent metasurface unit according to claim 1, characterized in that, The amplitude and phase relationship of the reflection coefficient at different frequencies specifically includes: The fitting function is expressed as: F c,m (f)=a c,1 f+a c,2 Where f represents the input frequency, F c,m (f) represents the reflection phase, G c,m (f) represents the reflection amplitude, a c,1 a c,2 b c,1 b c,2 b c,3 This represents the fitted parameters.

3. A beamforming method, characterized in that, This method uses the amplitude and phase relationship of the reflection coefficient at different frequencies as described in claim 2 to design a method that maximizes the average subcarrier rate, specifically including: Set up a broadband OFDM communication scenario, in which there is a wireless access point, a user, and a smart metasurface. The smart metasurface is composed of multiple metasurface units as described in claim 1. The channel consists of a direct link from the wireless access point to the user and a cascaded link from the wireless access point to the metasurface and then to the user. Specifically, the OFDM communication scenario has K subcarriers and the smart metasurface has M metasurface units. Given a pre-encoding matrix, design the phase-optimal reflection coefficient matrix for each metasurface unit; Given the reflection coefficient matrix, the optimal precoding matrix is ​​designed using the classic water-filling algorithm; The non-convexity of the joint optimization problem is addressed by jointly optimizing the power allocation of each subcarrier and the beamforming of each metasurface unit, and by iteratively solving the problem until convergence.

Images