Discrete phase optimal beamforming method and system for dynamic metasurface antenna

Abstract

This invention discloses a discrete-phase optimal beamforming method and system for dynamic metasurface antennas. The method includes: establishing a phase optimization problem for each microstrip in the dynamic metasurface antenna; the phase optimization problem aims to maximize the transmitted signal amplitude of the microstrip, using the phase of each element within the microstrip as the optimization variable; solving the phase optimization problem for each microstrip under Lorentz constraints and phase discretization constraints to obtain the phase of each element in each microstrip; calculating the configurable weights of each element based on its phase to complete beamforming. This invention can achieve optimal beamforming under discrete-phase and Lorentz constraints, improving the received signal-to-noise ratio and system capacity of downlink single-user communication systems, while reducing the computational complexity of beamforming.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and more specifically, relates to a discrete phase optimal beamforming method and system for dynamic metasurface antennas. Background Technology

[0002] With the full commercialization of fifth-generation (5G) mobile communication technology and the in-depth research on sixth-generation (6G) mobile communication technology, the requirements for spectral efficiency, energy efficiency, and system capacity of wireless communication systems are constantly increasing. Massive MIMO technology significantly improves system performance by achieving spatial multiplexing and beamforming on a massive number of antenna elements. However, traditional phased array-based antenna systems suffer from high hardware complexity, high power consumption, and high cost, which limits their further widespread application.

[0003] Over the past few years, metamaterials have garnered significant attention as a powerful technology with broad application potential, including in wireless communications. Metamaterials are a class of artificial materials whose physical properties, particularly their dielectric constant and magnetic permeability, can be custom-modified to meet various needs. When metamaterials are deployed in planar structures (i.e., metasurfaces), their effective parameters can be altered to achieve the desired transformations of transmitted, received, or reflected electromagnetic waves.

[0004] As a promising alternative, Dynamic Metasurface Antennas (DMA) have attracted widespread attention in academia. DMA consists of a large number of subwavelength metamaterial radiating elements whose electromagnetic properties can be precisely tunable. Compared to traditional antenna arrays, DMA flexibly processes signals in the analog domain through simplified transceiver hardware, eliminating the need for complex feed networks and active phase shifters, thus significantly reducing cost, power consumption, and hardware complexity. This ability to implement flexible antenna architectures at large scale, low cost, low hardware complexity, and low power consumption makes DMA a highly attractive technology for implementing ultra-large-scale MIMO transceivers in 6G wireless networks. Metasurface antennas (DMA) are primarily used for transmitter beamforming. Current optimization methods for DMA beamforming mainly fall into two categories: (1) Continuous Domain Relaxation Method: To simplify the problem, existing studies often relax the discrete phase shift constraint to a continuous domain and ignore the Lorentz constraint, assuming that the unit weight is a complex number of unit magnitude (i.e., only the phase is optimized). After solving, the continuous solution is quantized to the discrete domain using methods such as Closest Point Projection (CPP). Although this method is computationally simple, it leads to significant performance loss due to ignoring the physical constraints of the hardware, especially in low quantization bit scenarios (such as 1-bit).

[0005] (2) Random search or heuristic algorithm: Another type of method is to search randomly in the discrete domain or use heuristic methods such as genetic algorithms to find a better solution. Although these methods can directly handle discrete constraints, they lack theoretical optimality guarantees, and have high computational complexity and slow convergence speed, making it difficult to meet real-time requirements.

[0006] In summary, finding the beamforming coefficients that can globally optimize system performance while strictly satisfying the discrete phase shift and Lorentz physical constraints of DMA units is an urgent technical problem to be solved. Existing methods either have poor performance due to relaxed constraints or are too complex and impractical. Summary of the Invention

[0007] To address the shortcomings and improvement needs of existing technologies, this invention provides a discrete-phase optimal beamforming method and system for dynamic metasurface antennas. The aim is to achieve optimal beamforming under discrete-phase constraints and Lorentz constraints, thereby improving the received signal-to-noise ratio and system capacity of downlink single-user communication systems, and reducing the computational complexity of beamforming.

[0008] To achieve the above objectives, according to one aspect of the present invention, a discrete phase optimal beamforming method for dynamic metasurface antennas is provided, comprising: A phase optimization problem is established for each microstrip in the dynamic metasurface antenna; the phase optimization problem aims to maximize the signal amplitude transmitted by the microstrip, and uses the phase of each element in the microstrip as the optimization variable; The phase optimization problem of each microstrip is solved under Lorentz constraints and phase discretization constraints to obtain the phase of each element in each microstrip; The configurable weights of each element are calculated based on its phase to complete beamforming.

[0009] Furthermore, for the first For each microstrip, the objective function for the phase optimization problem is:

[0010] in, , , This indicates the number of microstrips in a dynamic metasurface antenna. This indicates the number of cells in each microstrip; ; Indicates the first The first microstrip The phase of each unit, Represents the phase set of the unit cell. Indicates the number of discrete phases; , , and They represent the real part and the imaginary part, respectively. Indicates the first The first microstrip Path loss and phase change from unit to user Indicates the first From the starting position of the first microstrip to the second The first microstrip The changes in amplitude and phase caused by the propagation of each unit It represents the imaginary unit, and the superscript "T" indicates transpose; ; and They represent and Direction angle; Represents a unit vector Direction angle; Represents the magnitude of a vector.

[0011] Furthermore, for the first Solve the phase optimization problem of a microstrip under Lorentz constraints and phase discretization constraints, including: according to Calculation interval Inside The point where the value changes abruptly yields the set. ; For sets After deduplicating and sorting the points in the array, the interval is then divided using these points. Divide into multiple sub-intervals; After merging the first and last sub-intervals obtained from the division into a single continuous sub-interval, in each sub-interval... In China, according to Solve extreme points ,like Then determine In subinterval The optimal value is Otherwise, confirm. In subinterval The optimal value is such that The endpoints of the interval with larger values; Will The optimal value in each sub-interval is used as a candidate point, and the corresponding value for each candidate point is calculated. This will make The candidate point with the largest value is selected as the global optimal solution. Calculate the first based on the global optimal solution. Phase of each unit in each microstrip ; in, ; This indicates the modulo operation.

[0012] Furthermore, the phase optimization problem for each microstrip is solved in parallel.

[0013] Furthermore, the discrete phase optimal beamforming method for dynamic metasurface antennas provided by the present invention further includes: sending the phase and configurable weights of each element obtained by solution to the controller of the dynamic metasurface antenna, so that the controller configures each element.

[0014] According to another aspect of the present invention, a computer program product is provided, characterized in that it includes a computer program; when the computer program is executed by a processor, it implements the discrete phase optimal beamforming method for dynamic metasurface antennas provided by the present invention.

[0015] According to another aspect of the present invention, a computer-readable storage medium is provided, including a stored computer program that, when executed by a processor, implements the discrete phase optimal beamforming method for dynamic metasurface antennas provided by the present invention.

[0016] According to another aspect of the present invention, a discrete phase-optimal beamforming apparatus for a dynamic metasurface antenna is provided, characterized in that it comprises: A computer-readable storage medium for storing computer programs; And a processor for reading a computer program in a computer-readable storage medium to implement the discrete phase optimal beamforming method for dynamic metasurface antennas provided by the present invention.

[0017] According to another aspect of the present invention, a data transmitter is provided, characterized in that it includes: a dynamic metasurface antenna; the phase and configurable weight of each element in the dynamic metasurface antenna are obtained by the discrete phase optimal beamforming method for dynamic metasurface antennas provided by the present invention.

[0018] According to another aspect of the present invention, a dynamic metasurface antenna-assisted wireless communication system is provided, including the data transmitter provided by the present invention.

[0019] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects: (1) This invention decomposes the traditional beamforming optimization problem aimed at maximizing the signal-to-noise ratio into... Each subproblem corresponds to the phase optimization of a microstrip, thus transforming the original high-dimensional non-convex optimization problem into a series of low-dimensional subproblems, effectively reducing the complexity of solving the optimization problem. Furthermore, by solving the phase optimization problem corresponding to each microstrip under discrete phase constraints and Lorentz constraints, optimal beamforming can be achieved under discrete phase constraints and Lorentz constraints, thereby improving the received signal-to-noise ratio and system capacity of the downlink single-user communication system.

[0020] (2) By separating the real and imaginary parts of the objective function and introducing auxiliary vectors, the objective function corresponding to each microstrip is reconstructed into an angle-dependent function of the unit vector, which further reduces the difficulty of solving the optimization problem.

[0021] (3) When solving the optimization problem corresponding to each microstrip, the present invention uses the angle search and critical point analysis method to transform the problem into a problem that can be searched in a finite number of candidate solutions, and uses geometric and algebraic properties to greatly reduce the search space, further reducing the computational complexity.

[0022] (4) Based on the decomposition of the problem into multiple independent sub-problems, the present invention solves these sub-problems in parallel, which can further improve the efficiency of beamforming. Attached Figure Description

[0023] Figure 1 This is a schematic diagram of the existing dynamic metasurface antenna communication system architecture.

[0024] Figure 2 This is a schematic diagram of the existing Lorentz constraint.

[0025] Figure 3 This is a flowchart of a discrete phase optimal beamforming method for dynamic metasurface antennas provided in an embodiment of the present invention.

[0026] Figure 4 The cumulative signal-to-noise ratio distribution function of different algorithms under 1-bit beamforming conditions provided by this invention.

[0027] Figure 5 The average SNR provided by this invention varies with the number of microstrips. Changes ( ).

[0028] Figure 6 The average SNR provided by this invention varies with the number of microstrip units. Changes ( ).

[0029] Figure 7 The average SNR provided by this invention varies with base station-user distance. L Changes ( , ). Detailed Implementation

[0030] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0031] In this invention, the terms "first," "second," etc. (if present) in the invention and the accompanying drawings are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence.

[0032] Before beamforming a dynamic metasurface antenna, it is necessary to analyze and model the metasurface antenna-assisted wireless communication system, as follows: Consider a DMA-assisted downlink single-user communication system, where the base station is equipped with a DMA-assisted downlink single-user communication system. DMA is composed of metamaterial radiation units, among which Indicates the number of microstrips. This indicates the number of radiative units contained in each microstrip.

[0033] DMA system architecture such as Figure 1 As shown, the input signal first passes through a digital baseband pre-encoder. The data is processed and then fed into each microstrip via a dedicated RF chain, ultimately being emitted through multiple radiating elements on the microstrip. The frequency response of each radiating element can be externally controlled by adjusting its local electrical characteristics, thus reconstructing the antenna radiation pattern. In narrowband systems, it is typically assumed that the frequency response of each element is flat. Figure 2 As shown, the Lorentz model is used to describe the configurable weights of the radiating elements. The first microstrip Weight of each unit It can be represented as:

[0034] in, Indicates the first The first microstrip Adjustable phase of each unit; It represents the imaginary unit.

[0035] In practical DMA architectures, due to hardware limitations (such as the use of PIN diodes or varactor diodes), the adjustable phase of each cell is limited. It can only take a finite number of discrete values, and adopts a general quantization strategy, namely phase. Constrained within an arbitrary discrete set, i.e.:

[0036] in, Represents the number of quantification levels; without loss of generality, assume .

[0037] The propagation characteristics of a signal within a microstrip are described by the following equation:

[0038] in, Indicates the first From the starting position of the first microstrip to the second The first microstrip The amplitude and phase changes brought about by the propagation of each unit; , and Represent the waveguide attenuation coefficient, wave number, and wave number respectively. i The first microstrip l The position of each cell. For a uniform DMA array, there are ,in D This indicates the spacing between cells within the microstrip.

[0039] make This represents the baseband input vector for all microstrip lines. The overall radiated signal emitted by the DMA. It can be written as:

[0040] in This is a diagonal matrix describing the propagation effect within each microstrip, with the following diagonal elements:

[0041] also, This is a block diagonal matrix representing the configurable weights of a DMA unit, and its elements are defined as follows:

[0042] It should be noted that the above model... The diagonal assumption neglects the mutual coupling effect between the waveguide and the metasurface elements. While mutual coupling does affect system performance and model accuracy, this simplification is commonly used in cases of weak coupling between the metasurface elements and the guided wave modes. To further reduce mutual coupling, physical design techniques can be employed, such as offsetting the elements towards the waveguide edge and arranging them in an alternating left-right pattern. In practice, it is assumed that the element spacing within each microstrip is not less than half a wavelength, which helps ensure that the elements do not significantly interfere with the waveguide modes, thus making the interactions between elements negligible.

[0043] Consider a single-user wireless communication system where the base station employs a... A DMA architecture for radiative metasurface units is designed to transmit unity-power symbols. Serving users, using pre-encoders and transmission power Therefore, the transmit signal for the input DMA is .

[0044] Based on the above signal model, the user receives the signal at [location]. y Represented as:

[0045] in, This represents the channel between the base station and the user. It is additive white Gaussian noise (AWGN) at the user's location. This indicates the signal transmission power.

[0046] Since the distance between the DMA and the user is much larger than the physical size of the DMA, it is assumed that the path loss from each metasurface unit to the user is approximately the same. Therefore, the channel vector Modeled as a Ricean fading channel:

[0047] in This represents the distance-related path loss between the base station and the user. Rice K factor, and Let represent the deterministic line-of-sight (LoS) component and the random non-line-of-sight (NLoS) component, respectively. The NLoS component is modeled as follows: .

[0048] For a given system, the signal-to-noise ratio at the user end is defined as:

[0049] in It is the received power at the user's location.

[0050] Traditional beamforming methods aim to maximize the receiver's signal-to-noise ratio (SNR). To maximize the receiver's SNR, the pre-encoder needs to be jointly optimized under the following constraints. and DMA coefficient : 1. Power constraints ensure that the transmit power remains within permissible limits; 2. Lorentz constraint requires the matrix Maintain the predefined Lorentz structure; 3. Phase discretization constraints restrict the phase of each element to take values ​​in the discrete set.

[0051] Therefore, remove the constant factor from the SNR expression. and The optimization problem is then formulated as follows:

[0052] For a given coefficient matrix The optimal precoder that maximizes the objective function is given by the maximum ratio transmission (MRT):

[0053] Therefore, the problem simplifies to about Single-variable optimization problem:

[0054] The superscript "H" indicates conjugate transpose.

[0055] The constraints of the optimization problem P2 are phase discretization constraint and Lorentz constraint.

[0056] The above system model will include digital precoders and DMA configuration matrix The joint optimization problem is formalized, and practical constraints such as discrete phase shift and Lorentz coupling amplitude-phase relationship are taken into account.

[0057] Based on the optimization problem P2 mentioned above, existing optimization methods for DMA beamforming are mainly divided into two categories: continuous domain relaxation methods and random search or heuristic algorithms. The former has poor performance due to the relaxation of constraints, while the latter is not practical due to its high complexity.

[0058] To address the aforementioned technical problems in existing technologies, this invention provides a discrete phase optimal beamforming method and system for dynamic metasurface antennas. The basic concept lies in transforming the original high-dimensional non-convex optimization problem into a series of low-dimensional sub-problems through ingenious problem reconstruction and decomposition. Then, using angle search and critical point analysis techniques, the global optimal solution is found in polynomial time, thereby significantly improving system performance. The invention will be explained in detail below.

[0059] This invention first utilizes the block diagonal property of the DMA structure to decompose the original optimization problem under Lorentz constraints. There are three independent subproblems, each corresponding to a microstrip. Taking the first microstrip as an example, the objective function can be reconstructed as:

[0060] The constraints of the reconstructed objective function are: .

[0061] The objective function reconstructed above reflects the core characteristics of the DMA system: the first term This represents the fixed phase contribution of all elements, derived from the fixed terms in the Lorentz constraints. The second term... This is achieved by adjusting the phase of each unit. The controllable part. This invention, through reconstruction, transforms the optimization objective into maximizing the amplitude of the synthesized signal by selecting a suitable phase configuration to superimpose these two parts in the same direction on the complex plane.

[0062] To obtain a more manageable form, this embodiment further separates the real and imaginary parts of the objective function. The purpose of this separation is to transform the complex complex optimization problem into a real-domain optimization problem, facilitating the application of traditional optimization techniques. Specifically, a vector is defined... for:

[0063] in, ; and They represent the real part and the imaginary part, respectively. Indicates the first microstrip Path loss and phase change from unit to user This indicates the position from the start of the first microstrip to the position of the first microstrip. The changes in amplitude and phase caused by the propagation of each unit.

[0064] Further introduce rotation matrix :

[0065] Based on the introduced vector and and rotation matrix The problem shown in equation (13) can be reformulated in the following compact form:

[0066] To further explore this optimization problem, an auxiliary vector is introduced. Auxiliary vector It is a unit vector, that is By applying the Cauchy-Schwarz inequality, the objective function shown in equation (16) can be restated as follows:

[0067] in, This represents the inner product operation. For a given... The inner product term in the above equation depends on The maximum value of this inner product is defined as:

[0068] Therefore, the original problem is equivalent to maximizing the inner product:

[0069] in," " indicates that it is equivalent to.

[0070] because It is a unit vector, which can be expressed through angle variables. Parameterization:

[0071] Similarly, each vector In polar coordinates, it is represented as:

[0072] in, Representing vectors The direction angle.

[0073] According to the geometric definition of the inner product, the objective function becomes Functions:

[0074] in:

[0075] Based on the above derivation process, it can be seen that by maximizing This maximizes the amplitude of the signal transmitted by the first microstrip. Equation (22) is the objective function that this invention ultimately solves.

[0076] Further analysis of this invention reveals that, given the discreteness of the phase shift, for the first microstrip... Units, Is to make and The value with the smallest angular difference between them. Obviously, when In the interval During internal changes, The value in Changes occur at these points. These points are not differentiable. They form a new set:

[0077] The modulo operation ensures Constrained in interval Inside.

[0078] gather The key angles corresponding to the points in the equation divide the domain into the most... There are several different intervals, within each interval It is differentiable.

[0079] Finally, a global optimal solution search is performed. To identify the optimal phase shift configuration, the angle parameters are... Perform a full search on top. By removing sets After identifying any duplicate angles and sorting the remaining angles in ascending order, a set can be used. Construct a series of intervals from the remaining angles:

[0080] First interval and the last interval They are considered connected, forming a continuous interval.

[0081] In each interval Inside, The derivative is given by the following formula:

[0082] Setting the derivative to zero, we can obtain the extreme points:

[0083] For the extreme points obtained ,like Then keep As In subinterval The optimal value; otherwise, it indicates... In the interval If the trend is monotonically increasing or monotonically decreasing, then remove it. and the interval At the endpoints of the interval, such that Take the endpoints of the interval with larger values ​​as In subinterval The optimal value. The optimal value in each sub-interval is used as a candidate point. By evaluating all candidate points (key angles and internal extreme points), it is guaranteed that a solution can be found in polynomial time. The global maximum value, the corresponding global maximum value The value is the result of the optimization solution of the objective function (22). Based on equation (22), the corresponding element phase can be further determined. After optimizing the phase of each element in the microstrip, the configurable weights of each element can be calculated according to the Lorentz constraint shown in equation (1). .

[0084] The optimization methods for the phase and configurable weights of the cells in the remaining microstrips are the same as those for the first microstrip.

[0085] In practical applications, the physical parameters of DMA are known, including the number of microstrips. Number of microstrip units Element spacing, waveguide attenuation coefficient and wave number Furthermore, the phase shift quantization level of the DMA unit. and its discrete sets It is known that the system can acquire or estimate the channel vector between the user and the DMA. .

[0086] The following is an example.

[0087] Example 1: A discrete phase optimal beamforming method for dynamic metasurface antennas, such as Figure 1 As shown, it includes: A phase optimization problem is established for each microstrip in the dynamic metasurface antenna; the phase optimization problem aims to maximize the signal amplitude transmitted by the microstrip, and uses the phase of each element in the microstrip as the optimization variable; The phase optimization problem of each microstrip is solved under Lorentz constraints and phase discretization constraints to obtain the phase of each element in each microstrip; The configurable weights of each element are calculated based on its phase to complete beamforming.

[0088] Based on the above analysis, it can be seen that in this embodiment, for the first... For a microstrip, the objective function for the phase optimization problem is:

[0089] For the The phase optimization problem of a microstrip is solved under Lorentz constraints and phase discretization constraints, specifically including: according to Calculation interval Inside The point where the value changes abruptly yields the set. ; For sets After deduplicating and sorting the points in the array, the interval is then divided using these points. Divide into multiple sub-intervals; After merging the first and last sub-intervals obtained from the division into a single continuous sub-interval, in each sub-interval... In China, according to Solve extreme points ,like Then determine In subinterval The optimal value is Otherwise, confirm. In subinterval The optimal value is such that The endpoints of the interval with larger values; Will The optimal value in each sub-interval is used as a candidate point, and the corresponding value for each candidate point is calculated. This will make The candidate point with the largest value is selected as the global optimal solution. Calculate the first based on the global optimal solution. Phase of each unit in each microstrip .

[0090] After optimizing and obtaining the phase and configurable weights of each element in each microstrip, this embodiment may further include: sending the solved phase and configurable weights of each element to the controller of the dynamic metasurface antenna, so that the controller can configure each element.

[0091] In a preferred embodiment, the optimization solutions for the phase optimization problems corresponding to each microstrip are executed in parallel to further improve the efficiency of beamforming.

[0092] Based on the above analysis, it can be seen that this embodiment decomposes the traditional optimization problem of maximizing the signal-to-noise ratio at the receiver into... Each subproblem corresponds to a phase optimization of a microstrip; and through clever mathematical transformations, each subproblem is transformed into a problem that can be searched among a finite number of candidate solutions, and the search space is greatly reduced by utilizing geometric and algebraic properties.

[0093] The time complexity analysis of this embodiment is as follows: For each subproblem, the set of key perspectives... Maximum contents Sorting n elements has a time complexity of O(n). For each element, the algorithm determines the optimal phase shift by evaluating candidate points. This process involves evaluating the set... A linear scan of size M results in a computational cost of O(m) for each interval. This operation. Given a subproblem, there are... Given intervals, the total complexity of solving a subproblem is... Consider all The algorithm has a total computational complexity of O(n sub-problems). Compared to the exponential complexity of exhaustive search... In comparison, this embodiment can find the global optimal solution in polynomial time, which has a significant advantage in computational efficiency.

[0094] Overall, this embodiment achieves optimal beamforming under discrete phase constraints and Lorentz constraints, improving the received signal-to-noise ratio and system capacity of the downlink single-user communication system, while reducing the computational complexity of beamforming.

[0095] Example 2: A computer program product, characterized in that it includes a computer program; when the computer program is executed by a processor, it implements the discrete phase optimal beamforming method for dynamic metasurface antennas provided in Embodiment 1 above.

[0096] Example 3: A computer-readable storage medium includes a stored computer program that, when executed by a processor, implements the discrete phase optimal beamforming method for dynamic metasurface antennas provided in Embodiment 1 above.

[0097] Example 4: A discrete phase-optimal beamforming apparatus for dynamic metasurface antennas, characterized in that it comprises: A computer-readable storage medium for storing computer programs; And a processor for reading a computer program in a computer-readable storage medium to implement the discrete phase optimal beamforming method for dynamic metasurface antennas provided in Embodiment 1 above.

[0098] Example 5: A data transmitter, characterized in that it includes: a dynamic metasurface antenna; the phase and configurable weight of each element in the dynamic metasurface antenna are obtained by the discrete phase optimal beamforming method for dynamic metasurface antennas provided in Embodiment 1 above.

[0099] Example 6: A dynamic metasurface antenna-assisted wireless communication system includes the data transmitter provided in Embodiment 5 above.

[0100] The following analysis further verifies the beneficial effects of this invention based on specific simulation results.

[0101] The simulation parameters are as follows: System model: Single-user MISO downlink system, base station equipped with DMA, operating frequency 28 GHz.

[0102] DMA parameter: number of microstrips and number of microstrip units It is variable, with both the unit spacing and the microstrip spacing being half a wavelength.

[0103] Channel model: Ricean fading channel, Ricean factor .

[0104] Waveguide parameters: attenuation coefficient , wave number .

[0105] Power parameters: Transmit power noise power .

[0106] Path loss: ,in The distance between the base station and the user (in meters).

[0107] For ease of description, the discrete phase optimal beamforming method for dynamic metasurface antennas provided by this invention will be abbreviated as OMPB. This invention has undergone extensive Monte Carlo simulations and has been compared with existing methods, including: Closest Point Projection (CPP) algorithm: First, solve for the optimal solution of continuous phase, and then project it onto the discrete domain.

[0108] Relaxation algorithm: Ignore the Lorentz constraint, optimize only the phase, and then perform quantization.

[0109] Randomized algorithm: Randomly generate 100 sets of discrete phase shift coefficients and select the set with the best performance.

[0110] Upper bound of continuous phase: The theoretical upper limit of performance when the phase is continuously adjustable.

[0111] All simulations were performed in the MATLAB R2023a environment. To ensure the statistical significance and reliability of the results, each data point was averaged based on 100 independent channel implementations, which effectively eliminated the fluctuations caused by random channel fading and enabled the simulation results to truly reflect the long-term average performance of the algorithm.

[0112] To more comprehensively evaluate the robustness and stability of the algorithm under different channel conditions, the cumulative distribution function (CDF) of signal-to-noise ratio under 1-bit beamforming conditions was plotted. Figure 4 The results visually demonstrate the performance levels achievable by different algorithms under various channel implementations. The results show that the CDF curve of OMPB is consistently on the far right, meaning it has the highest probability of successfully reaching or exceeding any given SNR threshold. The CPP algorithm follows closely behind, with its curve almost parallel to OMPB, but shifted to the left by approximately 0.7 dB, indicating that while its performance is excellent, it still has a measurable gap from the globally optimal solution. Notably, in the low SNR region, the random algorithm even outperforms the relaxation method. This is because, with a small number of cells, random search has a high probability of finding a good phase configuration. However, as the array size increases, its performance deteriorates sharply, highlighting the necessity of optimizing the OMPB algorithm.

[0113] In evaluating the scalability and engineering value of beamforming methods, this invention systematically studies the impact of array size on performance. This is achieved by increasing the number of microstrips... ( Figure 5 ) and number of microstrip units ( Figure 6 It can be concluded that the performance advantage of OMPB provided by this invention remains stable across all array sizes.

[0114] based on Figure 5 and Figure 6 The simulation results shown in this invention demonstrate that increasing the number of units per microstrip... The resulting performance gain far outweighs the increase in the number of microstrips. Specifically, in the 1-bit OMPB algorithm, when hour, Increasing from 4 to 40 can result in a 17 dB improvement in SNR; while when hour, Increasing the cell density from 4 to 40 only yields a gain of 10.1 dB. This result indicates that, given limited hardware resources, prioritizing increased cell density within the microstrip is a more effective performance enhancement strategy. However, simulations also reveal the marginal effect of performance improvements: when... When the value is too large, the rate of performance improvement will slow down significantly due to the signal propagation attenuation inside the waveguide. This indicates that in actual system design, it is necessary to find the optimal balance between performance, cost and power consumption.

[0115] To simulate real-world scenarios of user movement or network changes, this invention further examines the performance of the beamforming method at different communication distances. The simulation results are as follows: Figure 7 As shown. According to Figure 7 The results show that as the distance L between the base station and the user increases from 200 meters to 400 meters, the average SNR of all algorithms decreases linearly due to the increased path loss. However, most importantly, the relative performance ranking among the algorithms remains unchanged throughout this process. Under 1-bit conditions, the OMPB algorithm consistently outperforms the relaxation algorithm by approximately 1.3 dB and the CPP algorithm by approximately 0.4 dB. This result strongly demonstrates the robustness of the invention: its performance advantage is independent of specific channel conditions or path loss levels, and it can continuously provide optimal or near-optimal beamforming performance in dynamically changing wireless environments, which is crucial for ensuring a superior user experience in future 6G networks.

[0116] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A discrete-phase optimal beamforming method for dynamic metasurface antennas, characterized in that, include: A phase optimization problem is established for each microstrip in the dynamic metasurface antenna; The phase optimization problem aims to maximize the signal amplitude transmitted by the microstrip, with the phase of each unit within the microstrip as the optimization variable. The phase optimization problem of each microstrip is solved under Lorentz constraints and phase discretization constraints to obtain the phase of each element in each microstrip; The configurable weights of each element are calculated based on its phase to complete beamforming; for the first element... For each microstrip, the objective function for the phase optimization problem is: in, , , This indicates the number of microstrips in the dynamic metasurface antenna. This indicates the number of cells in each microstrip; ; Indicates the first The first microstrip The phase of each unit, Represents the phase set of the unit, Indicates the number of discrete phases; , , and They represent the real part and the imaginary part, respectively. Indicates the first The first microstrip Path loss and phase change from unit to user Indicates the first From the start position of the first microstrip to the second The first microstrip The changes in amplitude and phase caused by the propagation of each unit It represents the imaginary unit, and the superscript "T" indicates transpose; ; and They represent and Direction angle; Represents a unit vector Direction angle; Represents the magnitude of a vector; For the Solve the phase optimization problem of a microstrip under Lorentz constraints and phase discretization constraints, including: according to Calculation interval Inside The point where the value changes abruptly yields the set. ; For sets After deduplicating and sorting the points in the array, the interval is then divided using these points. Divide into multiple sub-intervals; After merging the first and last sub-intervals obtained from the division into a single continuous sub-interval, in each sub-interval... In China, according to Solve extreme points ,like Then determine In subinterval The optimal value is Otherwise, confirm. In subinterval The optimal value is such that The endpoints of the interval with larger values; Will The optimal value in each sub-interval is used as a candidate point, and the corresponding value for each candidate point is calculated. This will make The candidate point with the largest value is selected as the global optimal solution. Calculate the first based on the global optimal solution. Phase of each unit in each microstrip ; in, ; This indicates the modulo operation.

2. The discrete phase optimal beamforming method for dynamic metasurface antennas as described in claim 1, characterized in that, The phase optimization problem for each microstrip is solved in parallel.

3. The discrete phase optimal beamforming method for dynamic metasurface antennas as described in claim 1, characterized in that, It also includes: sending the phase and configurable weights of each element obtained from the solution to the controller of the dynamic metasurface antenna, so that the controller can configure each element.

4. A computer program product, characterized in that, It includes a computer program; when the computer program is executed by a processor, it implements the discrete phase optimal beamforming method for dynamic metasurface antennas as described in any one of claims 1 to 3.

5. A computer-readable storage medium, characterized in that, The method includes a stored computer program, which, when executed by a processor, implements the discrete phase optimal beamforming method for dynamic metasurface antennas as described in any one of claims 1 to 3.

6. A discrete-phase optimal beamforming apparatus for dynamic metasurface antennas, characterized in that, include: A computer-readable storage medium for storing computer programs; And a processor for reading a computer program in the computer-readable storage medium to implement the discrete phase optimal beamforming method for dynamic metasurface antennas as described in any one of claims 1 to 3.

7. A data transmitter, characterized in that, include: Dynamic metasurface antenna; The phase and configurable weights of each element in the dynamic metasurface antenna are obtained by the discrete phase optimal beamforming method for dynamic metasurface antennas as described in any one of claims 1 to 3.

8. A wireless communication system assisted by a dynamic metasurface antenna, characterized in that, Includes the data transmitter as described in claim 7.

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