A method for generating reconfigurable metasurface beams based on the branch-bound method

Abstract

This invention discloses a reconfigurable metasurface beamforming method based on the branch-and-bound method. The method includes: constructing a fundamental beamforming problem and calculating its initial solution; progressively optimizing the phase distribution of the metasurface based on the search and branching steps of the branch-and-bound method; discarding non-optimal branches using a pruning strategy to reduce computational complexity; and obtaining the beamforming result based on the final discrete phase of each element. This invention is the first to introduce the branch-and-bound method into metasurface beamforming, enabling rapid and accurate generation of the digitally encoded sequence corresponding to the target beam. Compared with traditional analytical methods, this invention has advantages such as high computational efficiency and ease of operation, and is suitable for high-precision beam control and signal optimization systems in 6G wireless communication scenarios.

Description

Technical Field

[0001] This invention belongs to the field of beam control in wireless communication, specifically relating to a reconfigurable metasurface beam generation method based on the branch-bound method. This method, combining the flexible controllability of reconfigurable metasurfaces, introduces the branch-bound method into beamforming for the first time, aiming to solve the problems of high computational complexity and low efficiency of traditional methods. Background Technology

[0002] As wireless communication technology evolves towards the sixth generation, the demand for high-performance beamforming is becoming increasingly urgent. Beamforming technology can effectively improve system spectral efficiency, expand coverage, and suppress interference, and has become a core technology for large-scale MIMO systems. Reconfigurable smart metasurfaces (RIS), as an emerging artificial electromagnetic material, can flexibly control the phase, amplitude, and other characteristics of electromagnetic waves through programming, providing an ideal platform for realizing complex beamforming scenarios. However, most existing RIS-based beamforming schemes rely on traditional optimization methods such as genetic algorithms and particle swarm optimization. These methods often face inherent limitations such as high computational complexity and slow convergence speed, making it difficult to meet the real-time and large-scale deployment requirements of future communication systems.

[0003] Therefore, achieving fast and accurate beam generation while maintaining low computational complexity has become a major challenge in the field of wireless communication. To address this, this invention proposes for the first time a reconfigurable metasurface beam generation method based on the branch-and-bound approach, aiming to overcome the shortcomings of existing optimization algorithms and provide a feasible technical path for achieving high-efficiency, low-cost beam generation. Summary of the Invention

[0004] This invention aims to overcome the shortcomings of existing beam generation methods, such as high computational complexity and slow convergence speed, and proposes for the first time a reconfigurable metasurface beam generation method based on the branch-and-bound method. This method, through the efficient optimization framework of the branch-and-bound method, fully utilizes the flexible phase modulation capability of RIS (Reconfigurable Metasurface Beam Generation System) to achieve high-efficiency and high-precision beam generation in large-scale MIMO systems, effectively meeting the dual requirements of 6G communication for real-time performance and complexity.

[0005] Technical solution:

[0006] The technical solution of the present invention is achieved through the following steps:

[0007] A method for generating reconfigurable metasurface beams based on the branch-bound method includes the following steps:

[0008] S1: Based on the array information of RIS and the target beam characteristics, the initial continuous phase distribution of each element is calculated using analytical methods;

[0009] S2: Based on the initial continuous phase distribution, a target optimization function is constructed using the mask method. The mask method constrains the far-field radiation pattern by setting the gain boundaries between the main lobe region and the side lobe region, and sets the target function value corresponding to the initial continuous phase distribution as the global upper bound of the optimization process.

[0010] S3: The search branching strategy based on the branch and bound method discretizes the continuous phase of each unit of the metasurface: rounds up and down to the nearest discrete phase value to form two branches, and calculates the objective function value under the two branches respectively, and defines the better value as the lower bound of the branch node.

[0011] S4: By comparing the numerical relationship between the lower bound of each branch node and the current global upper bound, a pruning strategy is executed: if the lower bound of a branch is worse than the current global upper bound, then the branch is pruned; otherwise, the global upper bound is updated to the lower bound, and the phase of the cell is fixed to the discrete value that generated the lower bound.

[0012] S5: Iterate through steps S3 and S4 until all unit phases are discretized, and generate beamforming results based on the obtained optimal discrete phase distribution.

[0013] Preferably, in step S1, for the RIS... Each unit, its initial continuous phase The calculation formula is:

[0014]

[0015] in, It is a fixed phase shift caused by the path difference from the feed source to the metasurface element. It is the target beam direction. It is the first The position vector of each element relative to the array center is the free space wavenumber.

[0016] Preferably, in step S2, the objective optimization function is a loss function, the expression of which is:

[0017]

[0018] in, The far-field pattern representing RIS. and These represent the upper boundary of the main lobe region and the lower boundary of the side lobe region of the mask, respectively. and These are coefficients used to adjust the relative weights of the main lobe and side lobe terms. , and These are the pitch angle and the azimuth angle, respectively.

[0019] Preferably, the far-field pattern The calculation formula is:

[0020]

[0021] in, Indicates that the feed is applied to the first The fixed amplitude and phase of each unit, It is the spacing between RIS cells. This indicates the total number of rows in the RIS array. This represents the total number of columns in the RIS array. is the free space wavenumber.

[0022] Preferably, the array information includes: operating frequency, array size, number of unit phase control bits, element spacing, beam type, beamwidth, and beam direction.

[0023] Preferably, the method further includes setting a convergence criterion: defining a global upper bound. and branch lower bound The relative difference between them is The optimization process is terminated when the calculated GAP is less than the preset GAP.

[0024] Preferably, the minimum difference GAP is set to 0.5%.

[0025] Preferably, in step S3, the search branch strategy is a two-branch strategy.

[0026] Preferably, after step S5, the beamforming result is further verified by at least one of numerical simulation, full-wave simulation, and experimental measurement.

[0027] Preferably, the target beam is a single beam.

[0028] Beneficial Effects: Traditional beam generation methods, such as particle swarm optimization and genetic algorithms, while capable of beam optimization, suffer from heavy computational burdens and slow convergence speeds in large-scale systems, making it difficult to meet real-time requirements. The beneficial effects of this invention are mainly reflected in the following aspects:

[0029] 1. Reduced computational complexity: This invention introduces the branch-and-bound method into metasurface beamforming for the first time. It can effectively eliminate a large number of non-optimal solutions while ensuring the global optimal solution, avoiding unnecessary calculations. It is particularly suitable for real-time beam control under large-scale antenna arrays, greatly reducing the computational burden of the system.

[0030] 2. Improved beam generation efficiency and accuracy: By combining the flexible beam control capability of RIS with the efficient global search capability of the branch and bound method, this invention can quickly converge within limited computing resources, generate more accurate complex beams that meet the requirements, and achieve higher overall efficiency.

[0031] 3. High practicality and deployability: The solution of this invention does not rely on complex mathematical models or high hardware computing power. The process is clear and easy to implement. It has low implementation costs and high engineering practical value, which is conducive to large-scale promotion and application in future communication networks.

[0032] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0033] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the following description of the embodiments taken in conjunction with the accompanying drawings, wherein:

[0034] Figure 1 This is a basic schematic diagram of the branch-and-bound method provided in the embodiments of the present invention;

[0035] Figure 2 The single-beam generation results provided in this embodiment of the invention are shown in (a) and (b) respectively, where (a) is a comparison of the results of numerical simulation, full-wave simulation and experimental measurement, and (b) is the corresponding digital encoding diagram. Represents discrete 2-bit phase ;

[0036] Figure 3 The beam scanning results of the numerical simulation provided in the embodiments of the present invention include a far-field radiation pattern and a corresponding digitally encoded pattern.

[0037] Figure 4 The beam scanning results of full-wave simulation and experimental measurement provided in the embodiments of the present invention are shown, where (a) is the E-plane and (b) is the H-plane;

[0038] Figure 5 This is a performance comparison between the method provided in the embodiments of the present invention and traditional optimization methods;

[0039] Figure 6 This is a schematic diagram of the structure of the present invention. Detailed Implementation

[0040] The specific embodiments of the present invention will be further illustrated below with reference to the accompanying drawings and specific examples. It should be understood that these examples are only for illustrating the principles and applications of the present invention and are not intended to limit the scope of the claims. After reading this invention, those skilled in the art can make modifications to various equivalent forms of the present invention, all of which fall within the scope defined by the appended claims.

[0041] The core of this embodiment lies in constructing the beam generation problem of reconfigurable metasurfaces (RIS) as an integer programming problem, and introducing the branch and bound method for efficient solution for the first time. The branch and bound method is a classic integer programming optimization algorithm that systematically explores the solution space through a tree-like search structure, and has the advantages of fast convergence speed and clear steps.

[0042] This embodiment uses a specific single-beam generation example to illustrate the implementation process of this method in detail. The key system parameters set in this embodiment are as follows: operating frequency of 11 GHz, corresponding to a wavelength of approximately 2.73 cm; RIS array size of 8 rows × 8 columns (i.e., M=8, N=8), totaling 64 units; unit spacing of half a wavelength; phase modulation capability of each unit of 2 bits, meaning the phase can be adjusted from a discrete set... Selected from the options. The beam type is a single directional beam; the target beam direction (i.e., the beam direction) is the normal direction, i.e., the elevation angle. Azimuth Based on the array size and operating frequency, the expected half-power beamwidth (i.e. beamwidth) of the beam designed in this embodiment is approximately 14.1°.

[0043] First, the objective optimization function is constructed based on the mask method. Let... and These represent the upper boundary of the main lobe region and the lower boundary of the side lobe region of the mask, respectively. The difference between the actual result of each iteration and the mask is quantified by a loss function, as shown in the following expression:

[0044]

[0045] in The far-field radiation pattern representing RIS is expressed as follows:

[0046]

[0047] in, It is the wavenumber in free space. Indicates that the feed is applied to the first Each unit has a fixed amplitude and phase. It is the spacing between RIS cells. It is a constant that simplifies the equation. For the first The phase of each element. The first term in the loss function constrains the performance of the main beam, including directivity, beamwidth, and gain; the second term constrains the sidelobe level (SLL) of the far-field pattern. and In this embodiment, to adjust the relative weights of these two items, and Take values ​​of 0.2 and 0.8 respectively.

[0048] The phase to be optimized is stored in a discrete set. In this context, the optimization problem can be expressed as:

[0049]

[0050] Next, the continuous phase is optimized into discrete values ​​suitable for RIS using the branch and bound method. Specifically, this method includes three steps: initial solution calculation, search and branching, and pruning optimization.

[0051] Specifically, taking the generation of a single beam as an example, the RIS... The continuous phase of each unit can be expressed as:

[0052]

[0053] in, It is a fixed phase shift caused by the path difference from the feed source to the metasurface element. It is the target beam direction. It is the first The position vectors of each element relative to the array center. After calculating the initial continuous solution, the far-field pattern of the RIS can be obtained. The corresponding initial loss function is calculated according to formula (1.1) and defined as the upper bound. .

[0054] Further steps involve search and branching, which will optimize the set of variables. The phase is rounded up and down to two distinct discrete values. Then, the loss function value corresponding to this phase distribution under each branch is calculated, expressed as follows: and .

[0055] After the search is complete, the optimization problem needs to be branched. Since too many branches significantly reduce the algorithm's efficiency, this embodiment of the invention employs a two-branch strategy, and... This is defined as the lower bound of the branch, i.e., the potential optimal feasible solution. Then, by comparison... and Decide whether to retain the result of this branch: If Less than This means that the potential optimal solution does not meet the requirements, so the optimization of that element is skipped and the continuous phase of that element is retained; if Greater than Then the upper bound is replaced with the lower bound, and the continuous phase is discretized, such as Figure 1 As shown in the green section.

[0056] Finally, pruning optimization is performed. This embodiment of the invention applies the dominance rule, that is, pruning subproblems with poor performance. Although the dominance rule may not be applicable to all problems, it is the strategy that can converge to the solution fastest while maintaining reliable performance. Figure 1 As shown in red in the diagram, all branches except the adopted ones will be pruned. Specifically, the current lower bound will be... With the current global upper bound Comparison:

[0057] like If the lower bound is inferior to the upper bound, then this branch is determined to be unable to produce a better solution, and a pruning strategy is implemented to discard the branch.

[0058] like If the lower bound is better than the upper bound, then this branch has the potential to produce a better solution. Update the global upper bound. And fix the phase of the unit to generate The discrete phase value. This branch is retained and continues to optimize the next element.

[0059] Repeat the above three steps until all RIS units have been processed. Furthermore, the convergence criterion of the algorithm must be considered: the relative difference between the upper and lower bounds is defined as:

[0060]

[0061] if If the value is less than 0.5%, the upper bound is considered to be the globally optimal solution, and the algorithm terminates at this point.

[0062] Finally, the algorithm outputs a set of loss functions. The optimal discrete phase distribution is minimized. This phase distribution is applied to RIS, and the beamforming results are verified through numerical simulation, full-wave simulation, and experimental measurements.

[0063] The operating frequency was set to 11 GHz, corresponding to a wavelength of approximately 2.73 cm. The metasurface unit spacing was fixed at half a wavelength. The array size was 8×8, and the unit control degree of freedom was 2 bits, i.e., 4 different discrete phase states. The target beam was a single beam.

[0064] Numerical simulation, full-wave simulation and experimental results are as follows Figure 2 As shown in the figure. First, it can be seen that the numerical results are as follows... Figure 2 As shown by the red solid line in (a), the main beam pointing and sidelobe electrical averages meet the expected requirements; the full-wave simulation results are as follows. Figure 2 As shown by the blue dashed line in (a), the main beam is largely consistent with the numerical calculation, but the sidelobe level is slightly higher than expected. Experimental measurement results are as follows: Figure 2 As shown by the black star-shaped line in (a), the main beam is basically consistent with the simulation results, but the sidelobe level is slightly higher than expected. The corresponding digital coding diagram is shown below. Figure 2 As shown in (b). Overall, the numerical simulation, full-wave simulation, and experimental measurement results all verify the feasibility of the method proposed in this invention.

[0065] Beam scanning performance in numerical simulation, such as Figure 3 As shown, this result demonstrates that the method proposed in this invention can effectively reduce the sidelobe level of the far-field pattern of the metasurface. The beam scanning performance, as shown in the full-wave simulation and experimental measurements, is as follows: Figure 4 As shown, the main beam at different angles is roughly the same as theoretically expected, and the sidelobe level remains below -6 dB.

[0066] To fully illustrate the advantages of this invention, in embodiments of this invention, the branch and bound method (B&B) is compared with the single-beam results of particle swarm optimization (PSO) and genetic algorithm (GA), such as... Figure 5 As shown, its detailed performance indicators are as follows:

[0067] Table 1 Comparison results with traditional methods

[0068]

[0069] It can be seen that the main beamwidth and sidelobe level of these three methods are not significantly different, but the branch-bound method proposed in this embodiment of the invention has a much shorter computation time than the other two traditional methods. The results show that the beam optimization method proposed in this invention can achieve better beamforming performance in a short time.

[0070] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of different embodiments or examples.

[0071] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "N" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0072] Any process or method description in the flowchart or otherwise herein can be understood as representing a module, segment, or portion of code comprising one or N executable instructions for implementing custom logic functions or processes, and the scope of preferred embodiments of the invention includes additional implementations in which functions may be performed not in the order shown or discussed, including substantially simultaneously or in reverse order depending on the functions involved, as will be understood by those skilled in the art to which embodiments of the invention pertain.

[0073] The above description is only a partial embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for generating reconfigurable metasurface beams based on the branch-bound method, characterized in that, Includes the following steps: S1: Based on the array information of RIS and the target beam characteristics, the initial continuous phase distribution of each element is calculated using analytical methods; S2: Based on the initial continuous phase distribution, a target optimization function is constructed using the mask method. The mask method constrains the far-field radiation pattern by setting the gain boundaries between the main lobe region and the side lobe region, and sets the target function value corresponding to the initial continuous phase distribution as the global upper bound of the optimization process. S3: The search branching strategy based on the branch and bound method discretizes the continuous phase of each unit of the metasurface: rounds up and down to the nearest discrete phase value to form two branches, and calculates the objective function value under the two branches respectively, and defines the better value as the lower bound of the branch node. S4: By comparing the numerical relationship between the lower bound of each branch node and the current global upper bound, execute the pruning strategy: if the lower bound of a branch is worse than the current global upper bound, then prune that branch. Otherwise, update the global upper bound to the lower bound and fix the phase of the cell to the discrete value that generated the lower bound; S5: Iterate through steps S3 and S4 until all unit phases are discretized, and generate beamforming results based on the obtained optimal discrete phase distribution. In step S2, the objective optimization function is a loss function, and its expression is: ； in, The far-field pattern representing RIS. and These represent the upper and lower boundaries of the mask, respectively. and These are coefficients used to adjust the relative weights of the main lobe and side lobe terms. , and These are the elevation angle and the azimuth angle, respectively. The far-field pattern The calculation formula is: ； in, Indicates that the feed is applied to the first The fixed amplitude and phase of each unit, It is the spacing between RIS cells. This indicates the total number of rows in the RIS array. This represents the total number of columns in the RIS array. is the free space wavenumber.

2. The method according to claim 1, characterized in that, In step S1, for RIS... Each unit, its initial continuous phase The calculation formula is: ； in, It is a fixed phase shift caused by the path difference from the feed source to the metasurface element. It is the target beam direction. It is the first The position vector of each element relative to the array center is the free space wavenumber.

3. The method according to claim 1, characterized in that, The array information includes: operating frequency, array size, number of unit phase control bits, element spacing, beam type, beamwidth, and beam direction.

4. The method according to claim 1, characterized in that, The method also includes setting a convergence criterion: defining a global upper bound. and branch lower bound The relative difference between them is The optimization process is terminated when the calculated GAP is less than the preset GAP.

5. The method according to claim 4, characterized in that, The minimum difference GAP is set to 0.5%.

6. The method according to claim 1, characterized in that, In step S3, the search branch strategy is a two-branch strategy.

7. The method according to claim 1, characterized in that, Following step S5, the beamforming results are further verified through at least one of numerical simulation, full-wave simulation, and experimental measurement.

8. The method according to claim 1, characterized in that, The target beam is a single beam.

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