Unit rotation and mutual coupling considered sparse linear array beam forming method and system

Abstract

The invention relates to the technical field of array antennas, in particular to a sparse linear array beam forming method and system with unit rotation and mutual coupling considered. Array elements are obtained, Euler angle derivation is carried out on rotation of the array elements around the z axis, and a radiation electric field after rotation is obtained; setting a beam forming target according to the electric field of the radiation field; according to a beam forming target, optimizing the position, the rotation angle and the excitation phase of an array element by adopting a random optimization algorithm, and generating an initial beam scheme; an active directional diagram is extracted from the initial beam scheme according to full-wave simulation, the active directional diagram is combined with a CAL-SAPSO algorithm to optimize the array element position, the rotation angle and the excitation phase, and a final array element directional diagram is generated; according to the invention, by introducing array element rotation and considering a mutual coupling effect, efficient beamforming of the sparse wiring array is realized, the radiation characteristic of the antenna array can be adjusted more finely, the peak side lobe level and the cross polarization level are effectively reduced, and the overall performance of the system is improved.

Description

Technical Field

[0001] This invention relates to the field of array antenna technology, and more specifically to a method and system for beamforming sparse wire arrays with element rotation and mutual coupling consideration. Background Technology

[0002] Antennas are essential equipment in various civilian and military radio systems, including radio communication, broadcasting, navigation, radar, telemetry and control, microwave remote sensing, radio astronomy, and electronic countermeasures. They are also devices that enable the reception and transmission of electromagnetic waves.

[0003] An antenna array is created by arranging and exciting multiple antenna elements with identical radiation characteristics at specified locations. Utilizing the principles of electromagnetic wave interference and superposition, the electromagnetic waves radiated by all elements form a specific beam in free space, resulting in a specific radiation pattern. Generally, antenna arrays can be broadly categorized into uniformly spaced arrays and non-uniformly spaced arrays. Non-uniformly spaced arrays, through optimization of element positions, can achieve lower peak sidelobe levels (PSL) than uniformly spaced arrays.

[0004] Optimization of the positions of array elements in a non-uniform array is collectively referred to as sparse optimization design, including analytical methods, matrix beamforming methods, convex optimization methods, compressed sensing techniques, and stochastic optimization methods. These methods typically involve adjusting the element positions, excitation amplitudes, and phases to create a specific radiation pattern for the array antenna—a process known as beamforming.

[0005] Traditional beamforming methods are typically limited to adjusting the position, excitation amplitude, and phase of array elements to form the desired radiation pattern. While this simplifies the design process to some extent, for antenna arrays with high-density elements, such as those used in 5G millimeter-wave base stations or satellite communication systems, the mutual coupling effect between elements becomes particularly important, significantly impacting the overall performance of the antenna array. Furthermore, existing array antenna beamforming designs often neglect the impact of element rotation on the radiation pattern. In fact, rotating elements can alter their contribution to various angles of the synthesized radiation pattern, enabling finer pattern control. However, currently, there is a lack of methods to effectively integrate the element rotational degrees of freedom into the beamforming process, especially when mutual coupling effects need to be considered simultaneously. Moreover, existing technologies do not fully consider the impact of element mutual coupling during beamforming, particularly in sparsely distributed arrays with closely packed elements, where mutual coupling can lead to radiation pattern distortion, increased sidelobe levels, and increased cross-polarization levels. Summary of the Invention

[0006] To address the problems mentioned in the prior art, this invention proposes a method and system for beamforming sparse wire arrays with rotating elements and considering mutual coupling. The method employs a stochastic optimization algorithm to solve the beamforming problem of the array antenna and uses a surrogate-assisted particle swarm optimization algorithm based on committee active learning to obtain a rotating array antenna layout scheme that considers coupling and meets the beamforming requirements.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] This invention discloses a beamforming method for sparse wire arrays with element rotation and mutual coupling, comprising the following steps:

[0009] Obtain the array elements, derive the Euler angle by rotating the array elements around the z-axis, and obtain the radiated electric field after rotation;

[0010] Beamforming targets are set based on the electric field of the radiation field.

[0011] Based on the beamforming target, a stochastic optimization algorithm is used to optimize the position, rotation angle and excitation phase of the array elements to generate an initial beam scheme;

[0012] The active radiation pattern is extracted from the initial beam pattern based on full-wave simulation. The active radiation pattern is then combined with the CAL-SAPSO algorithm to optimize the element position, rotation angle, and excitation phase, generating the final element radiation pattern.

[0013] As a further improvement to the present invention, Euler angles are derived for the rotation of the antenna array elements around the z-axis to obtain the radiated electric field after rotation, including:

[0014] The radiated electric field after the antenna is rotated is:

[0015]

[0016] As a further improvement of the present invention, setting the beamforming target based on the radiation field electric field includes:

[0017] Define the user's desired main polarization direction

[0018] Calculate the projection of the principal polarization direction perpendicular to the propagation direction based on the principal polarization direction.

[0019] Cross-polarization direction calculated based on projection.

[0020] As a further improvement to the present invention, it also includes constraining the beamforming target:

[0021] Assume peak sidelobe level ≤ -13dB;

[0022] Assume the expected value of the cross-polarization level is ≤ -15dB.

[0023] As a further improvement of the present invention, based on the beamforming target, a stochastic optimization algorithm is used to optimize the position, rotation angle, and excitation phase of the array elements to generate an initial beam scheme, including:

[0024] Set optimization variables: element position, rotation angle, and excitation phase.

[0025] By using a mapping function to transform the positions of the array elements, the discrete spacing constraint is converted into a continuous domain optimization problem, which is then solved as follows:

[0026]

[0027] After solving for P and K, construct the values ​​of two matrices C and G, in which all elements follow a uniform distribution in the interval (0,1), to obtain the positions of the array elements.

[0028] The array element positions, rotation angles, and excitation phases are used as input vectors, and the SHADE algorithm is employed to optimize and generate the initial beam pattern.

[0029] As a further improvement to this invention, the element position, rotation angle, and excitation phase are used as input vectors, and the SHADE algorithm is employed for optimization, including:

[0030] Initialization parameters, including the historical storage space M for initializing the mutation factor and crossover probability. F and M CR and the length of historical storage space;

[0031] First, an iterative process is performed to generate F. i and CR i Its expression is as follows:

[0032] CR i =randn i (M CRri ,0.1)

[0033] F i =randc i (M Fri ,0.1)

[0034] In the formula: ri is the index number randomly generated in the sequence {1,2,...,H};

[0035] randn(μ,σ 2 ) and randc(μ,σ 2 Let μ and σ represent random values ​​from the Cauchy and normal distributions, respectively. 2 These represent its mean and variance, respectively.

[0036] Set constraints: When the generated CRi If it does not belong to [0,1], then it is truncated to the interval [0,1]; if the generated F i If it is greater than 1, then set it to 1; if the generated F i If it is less than 0, then regenerate F. i Until F is satisfied i ∈[0,1];

[0037] Perform a mutation operation to obtain a mutation vector, the expression of which is as follows:

[0038]

[0039] In the formula: r1 and r2 are index values ​​randomly selected from the sets {1,2,...,NP} and {1,2,...,H+NP}, respectively, and are integers that are distinct from i; It is an external storage file and the current population P G The selected individuals; This refers to an individual randomly selected from the individuals with the highest fitness ranking in the current population; It is a mutation vector;

[0040] Crossover and mutation are performed to obtain the experimental vector, whose expression is as follows:

[0041]

[0042] In the formula: randb(j) represents the j-th estimate of the random number generator between [0, 1];

[0043] rnbr(i)∈(1,2,…,D) represents a randomly selected sequence, used to ensure At least from Obtain a parameter; CR represents the crossover operator, and its value range is [0, 1].

[0044] experimental vector With the current population vector The comparison is achieved by calculating the fitness function. When the fitness function is minimized, the vector with the smaller fitness function will appear in the next generation of the population.

[0045] Each time generation is successful, the corresponding parameter CR is set. i and F i To store and update historical data, the expression is as follows:

[0046]

[0047]

[0048] The index k in the above formula is updated using the weighted Lehmer mean.

[0049] As a further improvement of the present invention, the expression for the fitness function is:

[0050]

[0051] In the formula: P d (θ,φ) represents the desired shaped COP power pattern; Γ SL Indicates the sidelobe level of the desired shaped beam; Γ X The desired XPL value for beamforming is represented, and W3 is introduced to influence its importance in the optimization process, thereby controlling the final array orientation. Figure X PL size; M, S, and Q represent the main lobe region and side lobe region Ω in the main polarization pattern, respectively. SL and cross-polarization pattern angular domain Ω X The number of sampling points.

[0052] This invention proposes a sparse wire array beamforming system with element rotation and mutual coupling consideration, comprising:

[0053] The rotation module is used to acquire array elements, derive the Euler angle for the rotation of array elements around the z-axis, and obtain the radiated electric field after rotation.

[0054] The setting module is used to set the beamforming target based on the radiation field and electric field.

[0055] The generation module uses a stochastic optimization algorithm to optimize the position, rotation angle and excitation phase of the array elements based on the beamforming target, and generates an initial beam scheme.

[0056] The optimization module is used to extract the active radiation pattern of the initial beam scheme based on the full-wave simulation, and combine the active radiation pattern with the CAL-SAPSO algorithm to optimize the array element position, rotation angle and excitation phase, and generate the final array element radiation pattern.

[0057] This invention proposes a beamforming device for a sparse wire array with rotating elements and considering mutual coupling, comprising a processor and a memory, wherein the processor executes a computer program stored in the memory to implement the beamforming method for a sparse wire array with rotating elements and considering mutual coupling as described above.

[0058] This invention proposes a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the sparse wire array beamforming method with element rotation and mutual coupling as described above.

[0059] Compared with the prior art, the present invention achieves the following technical effects:

[0060] This invention achieves efficient beamforming for sparse wire arrays by introducing element rotation and considering mutual coupling effects. Compared to traditional methods, it allows for more precise adjustment of the antenna array's radiation characteristics, effectively reducing peak sidelobe levels and cross-polarization levels, and improving the overall system performance. Specifically, by optimizing element positions, rotation angles, and excitation phases, it not only precisely controls the primary polarization direction but also significantly improves secondary polarization performance, enabling the antenna array to maintain stable communication capabilities even in complex electromagnetic environments. Furthermore, this method considers the mutual coupling effects between elements, resulting in an array design that better reflects actual conditions, further improving design accuracy and reliability. Attached Figure Description

[0061] Figure 1 This is a schematic diagram of the antenna element of the present invention;

[0062] Figure 2 This is the 3D total electric field pattern of the antenna element of the present invention;

[0063] Figure 3 The antenna element of this invention is shown in the main polarization and cross polarization pattern in the xoz plane;

[0064] Figure 4 This invention does not consider the radiation pattern of mutually coupled arrays and the radiation pattern of full-wave simulated arrays;

[0065] Figure 5 This invention does not consider the radiation pattern of mutually coupled arrays and the radiation pattern of full-wave simulated arrays;

[0066] Figure 6 This is a two-dimensional radiation pattern shaped for the full-wave simulation of the array antenna of the present invention;

[0067] Figure 7 Normalized shaping pattern for 11-element full-wave simulation;

[0068] Figure 8 This is a physical image of the antenna of the present invention;

[0069] Figure 9 This is a test diagram of the antenna S-parameters of the present invention;

[0070] Figure 10 This is a schematic diagram of the antenna test of the present invention;

[0071] Figure 11 This is the power supply excitation setting interface for the present invention;

[0072] Figure 12 This is the antenna measurement pattern of the present invention;

[0073] Figure 13 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0074] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0075] See Figure 13 This invention proposes a beamforming method for sparse wire arrays with element rotation and mutual coupling, characterized by the following steps:

[0076] Obtain the array elements, derive the Euler angle by rotating the array elements around the z-axis, and obtain the radiated electric field after rotation;

[0077] Beamforming targets are set based on the electric field of the radiation field.

[0078] Based on the beamforming target, a stochastic optimization algorithm is used to optimize the position, rotation angle and excitation phase of the array elements to generate an initial beam scheme;

[0079] The active radiation pattern is extracted from the initial beam pattern based on full-wave simulation. The active radiation pattern is then combined with the CAL-SAPSO algorithm to optimize the element position, rotation angle, and excitation phase, generating the final element radiation pattern.

[0080] The present invention will be further explained below with reference to the accompanying drawings and specific embodiments:

[0081] Step 1: Obtain the microstrip antenna as an array element. In this embodiment, the antenna can be obtained through full-wave simulation.

[0082] The derivation of the Euler angle for the rotation of the pair around the z-axis is as follows:

[0083] Assume that the relationship between the pitch angle (θ, φ) of array element ANT and the pitch angle (θ′, φ′) of the rotated array element Ant′ satisfies:

[0084] cosθ=cosθ′cosβ+sinθ′sinβcos(φ′-α)

[0085]

[0086] The radiated electric field of the array element Ant is:

[0087]

[0088] In the formula: and Let θ and φ be the polarization components of the radiated electric field along the directions θ and φ, respectively. and These are unit vectors along the directions θ and φ, respectively.

[0089] If Ant′ and Ant are fed by the same power source, then the radiated electric field of the rotated array element Ant′ is:

[0090]

[0091]

[0092]

[0093] The above formula can determine the relationship of the radiated electric field after the array element is rotated. It can also be seen that the rotation of the array element does not change the position of the array element center. By optimizing θ and φ, we can obtain the rotation angle we want.

[0094] Because the translational placement of the antenna will generate a phase difference in the radiated electric field, the spatial path difference between the two is dsinθ, where d is the distance between the two antenna elements. In addition, the radiation field of the array element also needs to consider the feed amplitude and phase of the antenna.

[0095] Therefore, based on the above derivation, without considering element mutual coupling, if all antennas use equal-amplitude feeding, then the antennas placed... The N array elements on the array are polarized in electric fields θ and φ respectively.

[0096]

[0097]

[0098] In the formula: k = 2π / λ represents the wave number in free space, λ is the wavelength, and αn and These represent the rotation angle and excitation phase of the nth antenna element, respectively. It is a unit vector representing the direction of electromagnetic wave propagation.

[0099] Step 2: Assume the user's desired main polarization direction Defined expected principal polarization direction Perpendicular to the direction of propagation The projection of the wavefront onto the wavefront plane can be expressed as:

[0100]

[0101] In the formula: ||·||2 represents the modulo operation of the vector.

[0102] Based on the achievable cross-polarization direction and The relationship between them is perpendicular to each other. It can be represented as

[0103] Set the maximum expected values ​​for Peak Sidelobe Level (PSL) and Cross-Polarization Level (XPL). A lower PSL value is better, generally required to be below -13dB; a lower XPL value is also better, generally required to be below -15dB.

[0104] Therefore, the main polarization electric field pattern and the cross-polarization electric field pattern of the antenna are as follows:

[0105]

[0106] in:

[0107]

[0108] Step 3: Use the SHADE algorithm to find suitable array element positions, rotation angles and excitation phases to synthesize the initial beam scheme. Generally, the initial position setting is between 0.5 wavelengths and 1 wavelength between the elements.

[0109] Two different mapping functions, T1 and T2, are used to generate the element positions that satisfy the minimum element spacing, thus transforming the constrained optimization problem with restricted areas into a constrained optimization problem in the continuous domain.

[0110] Given a rectangular region of 2L×2H, solve the following problem:

[0111]

[0112] P and K are obtained by solving the above equation, and then two matrices C and G (C∈R) are constructed, in which all elements are uniformly distributed in the interval (0,1). P×(K+1) ,G∈R( P+1)×K The value of ) is used to obtain the position of the array elements of the two-dimensional sparsely distributed planar array.

[0113] Matrices C and G can be represented as T1(C) and T2(G), where:

[0114]

[0115]

[0116] All elements in the above two equations belong to the interval [0,1]. Therefore, the array antenna position distribution of the desired beam can be obtained by optimizing the elements in matrices C and G.

[0117] The array element positions, rotation angles, and excitation phases are used as input vectors, and the SHADE algorithm is employed for optimization. The process is as follows:

[0118] Construct historical storage space M for F and CR F and M CR Both have a length of H. The values ​​of F and CR are randomly generated based on the constructed historical storage space.

[0119] CR i =randn i (M CRri ,0.1)

[0120] F i =randc i (M Fri ,0.1)

[0121] In the formula: ri is a randomly generated index in the sequence {1,2,...,H}, randn(μ,σ) 2 ) and randc(μ,σ 2 Let μ and σ represent random values ​​from the Cauchy and normal distributions, respectively. 2 These represent its mean and variance, respectively.

[0122] Additionally, if the generated CR is not in the range [0,1], it is truncated to the interval [0,1]. If the generated F is greater than 1, it is set to 1, but if it is less than 0, F is regenerated until it is within the interval [0,1].

[0123] Perform mutation operations to obtain mutation vectors. The mutation strategy is as follows:

[0124]

[0125] In the formula: r1 and r2 are index values ​​randomly selected from the sets {1,2,...,NP} and {1,2,...,H+NP}, respectively, and are integers that are distinct from i. It is an external storage file and the current population P G The selected individuals, where the external storage archive is composed of each successful solution generated and solutions in the archive space are randomly deleted to ensure that there is enough space to store new successful solutions. This refers to the current population P G (When combined with the SRPG framework, it can also guide the population GP) Individuals randomly selected from the top pi·NP individuals in terms of fitness ranking, where p i Randomly generated within the interval [2 / NP, 0.2].

[0126] After performing crossover mutation, each experimental vector is:

[0127]

[0128]

[0129] In the formula: randb(j) represents the j-th estimate of the random number generator between [0, 1]; rnbr(i) ∈ (1, 2, ..., D) represents a randomly selected sequence used to ensure At least from Obtain a parameter; CR represents the crossover operator, and its value range is [0, 1].

[0130] To determine the test vector Whether it will become a member of the next generation depends on whether, like the differential evolution algorithm, the experimental vector is compared with the target vector in the current population according to the greedy criterion. A selection comparison is performed. Optimization is achieved by calculating the fitness function; when the fitness function is minimized, vectors with smaller fitness functions will appear in the next generation of the population.

[0131] This ensures that all individuals in the next generation are better or at least as good as their counterparts in the current population. Note: In the selection process, the trial vector is compared with only one individual, not with all individuals in the existing population.

[0132] Each time a successful solution is generated, the corresponding parameters CRi and Fi should be stored in SCR and SF respectively.

[0133] MCR and MF are updated via stored SCR and SF:

[0134]

[0135]

[0136] In the formula, the index k (1≤k≤H) represents the location where the updated data is stored. It is initialized to 1 and gradually incremented when inserting elements, returning to 1 when the index exceeds H. WL (·) and mean WA (·) is the weighted Lehmer mean, calculated as follows:

[0137]

[0138]

[0139] w in calculating the mean k :

[0140]

[0141] The expression for constructing the fitness function is as follows:

[0142]

[0143] The fitness function Y S and Z q for:

[0144]

[0145] In the formula: P d (θ,φ) represents the desired shaped COP power pattern; Γ SL Indicates the sidelobe level of the desired shaped beam; Γ X The desired XPL value for beamforming is represented, and W3 is introduced to influence its importance in the optimization process, thereby controlling the final array orientation. Figure X PL size; M, S, and Q represent the main lobe region and side lobe region Ω in the main polarization pattern, respectively. SL and cross-polarization pattern angular domain Ω X The number of sampling points.

[0146] In this embodiment, the maximum number of iterations G is set. max Generally, the number should be set below 2000; the maximum fitness evaluation count (MaxGen) is set to Dim × 4 × G. max .

[0147] Step 4: Use the Dim×4 individuals obtained by the SHADE algorithm as the initial training samples. The fitness of the individuals is recalculated based on the radiation pattern obtained from the full-wave simulation. The execution of HFSS is controlled by the HFSSScript interface in Matlab to realize the fitness evaluation process when considering the element coupling of the rotating array antenna layout scheme.

[0148] The agent-assisted particle swarm optimization algorithm based on committee active learning is used to solve the problem of time-consuming fitness function evaluation in solving optimization problems, and to perform beamforming on a sparse array with coupling to obtain the final array element pattern.

[0149] This invention proposes a specific process for a beamforming method for sparse wire arrays considering mutual coupling:

[0150] This embodiment designs a flat-top beamforming array antenna. Its one-dimensional linear array uses a microstrip antenna with a U-shaped slot loading, coaxial feed, and a center frequency of 10 GHz as array elements. Its schematic diagram is shown below. Figure 1 As shown.

[0151] The specific dimensions of the antenna are shown in Table 1:

[0152] Table 1 Antenna Element Structure Parameters

[0153]

[0154] The dielectric substrate material used is Rogers 5880, with a relative permittivity εr = 2.2.

[0155] The direction of the total electric field of the antenna element in 3D is as follows Figure 2 As shown, the maximum electric field strength in the far-field region is 25.11 V / m. The main polarization electric field pattern and the cross-polarization electric field pattern of the antenna are shown below. Figure 3 As shown.

[0156] For the calculation of the beamforming value, a center frequency of 10 GHz was selected as the design frequency point, and beamforming of the array pattern was performed on a one-dimensional linear array of 11 elements. Similarly, the spacing constraint between the elements was set as: 0.5λ≤di,j≤λ, (i,j)∈{1,2,…,N},i≠j, where di,j represents the distance between element i and element j.

[0157] By optimizing the position xn of 11 array elements (N=11), the element rotation angle αn, and the excitation phase... A total of 32 variables (Dim=32) are used to obtain the initial beam pattern.

[0158] Assuming the user's desired main polarization direction is According to the equation in step two, we can obtain: on the xoz plane, the principal polarization... and cross-polarization The directions are φ and θ, respectively.

[0159] The flat-top main lobe region is set to θm∈[-15°,15°], and the sidelobe region is set to θs∈[-90°,-20°]∪[20°,90°]. Furthermore, in this array beamforming, the desired maximum peak sidelobe level and cross-polarization level are set to ΓSL=-13dB and ΓX=-15dB, respectively.

[0160] The parameters for constructing the fitness function are: W1 = 1.2, W2 = 1, W3 = 1.

[0161] Furthermore, the parameters of the SHADE algorithm are set as follows: MF = {0.7}, MCR = {0.5}, NP = 128, H = NP, Q = 64, R = 0.2, u = 16. The maximum number of iterations is set to Gmax = 500, i.e., the maximum number of fitness evaluations MaxGen = Dim × 4 × 500. The parameters of CAL-SAPSO are those in its original literature, with the maximum number of fitness evaluations MaxGenSA = Dim × 8.

[0162] First, the vector array element radiation pattern is obtained by simulating a U-shaped slot loaded with a microstrip antenna with periodic boundaries. Then, without considering mutual coupling changes, the SHADE algorithm is used to find suitable array element positions, rotation angles, and excitation phases to synthesize the flat-top array element radiation pattern. The optimal synthesized xoz plane radiation pattern obtained by running the SHADE algorithm is shown below. Figure 4 As shown, the radiation pattern obtained without considering the mutual coupling between array elements differs from that obtained from the full-wave simulation. The full-wave simulation, including mutual coupling, significantly degrades the cross-polarization, increasing the cross-polarization level from -14.13 dB to -10.45 dB. Although the influence of mutual coupling on the array element radiation pattern is not taken into account, leading to some differences from the full-wave simulation results, the overall radiation pattern shapes of the two are highly similar. This is the premise for optimizing the beamforming of the mutually coupled array antenna as two independent parts separately.

[0163] Figure 4 As can be seen, the desired main lobe region of the optimal array antenna obtained by the SHADE algorithm is close to a flat-top shape, but the side lobe region has not yet reached the design requirements. Therefore, it can be considered that the array antenna arrangement excitation scheme that is relatively close to the desired beam was obtained through the SHADE algorithm. In order to improve the performance of the array pattern considering mutual coupling, the Dim×4 individuals obtained by the SHADE algorithm are used as the initial training samples. The fitness of the individuals is re-solved based on the pattern obtained by the full-wave simulation. The execution of HFSS is controlled by the Script interface in Matlab to realize the fitness evaluation process when considering the element coupling of the rotating array antenna layout scheme. Beamforming of the sparse array including coupling is realized by running CAL-SAPSO. It is worth noting that for each feasible layout scheme, it takes 4 seconds to solve the fitness value of the array pattern without considering coupling, and 6 minutes to solve the fitness value of the array pattern considering coupling (i.e., full-wave simulation).

[0164] By optimizing the radiation pattern without considering the coupled array, and then solving a small number of the resulting NP layout schemes using the CLA-SAPSO algorithm, this optimization process saves a significant amount of time compared to directly optimizing the coupled array using the SHADE algorithm.

[0165] Figure 5 The full-wave simulation model obtained by using the Script interface in HFSS in Matlab under the optimal layout excitation scheme is shown. Figure 6 The diagram shows the main polarization and cross-plan radiation patterns of the obtained radiation pattern after the program runs, considering coupling. As can be seen from the diagram, the obtained radiation pattern basically meets the shaping requirements. Table 2 shows the final element positions, excitation phases, and rotation angles of the obtained flat-top radiation pattern. The element position coordinates can be converted to actual physical dimensions by multiplying the free-space wavelength corresponding to the center frequency.

[0166] Table 2 shows the element positions, excitation phases, and rotation angles obtained from beamforming the flat-top pattern of the antenna array.

[0167]

[0168] Based on the modeling and simulation analysis in the preceding sections, a flat-top pattern array was designed. This invention demonstrates the results of fabrication and testing of the array antenna. Figure 8 The image shows a physical diagram of the rotating array antenna. As can be seen, the entire antenna array is approximately 22cm long. Each element of the rotating array is then welded with a 50-ohm SMA coaxial connector. The reflection coefficient of each port of the fabricated antenna with optimized rotating angle was tested using a vector network analyzer.

[0169] Figure 9 The S11 parameters of the antenna array elements are shown. It can be seen that the lowest point of the S-parameters is around 9.8 GHz, and S11 is less than -10 dB at 10 GHz, which is consistent with the simulation results. Furthermore, by measuring the S-parameters of each element in the array one by one, not only can the manufacturing quality be effectively evaluated, but the soldering integrity of each SMA interface can also be detected, thus laying the foundation for subsequent testing of the array antenna pattern.

[0170] The structural principle of this invention is as follows: a stochastic optimization algorithm is used to solve the beamforming problem of an array antenna, wherein the radiation field of the array antenna is synthesized using AEP (Automatic Emission Programming). Full-wave simulation is used to obtain the difference between the optimal scheme population in the stochastic optimization and the desired beam, and this difference is used as initial training data to run a surrogate-assisted particle swarm optimization algorithm based on committee active learning to obtain a rotating array antenna layout scheme that considers coupling and satisfies the beamforming requirements. The technical effects of this invention are explained below in conjunction with fabrication and testing.

[0171] 1. Test content and results:

[0172] The optimized rotating angle array antenna design was tested in practice. Figure 8 As shown.

[0173] The S11 parameters of a single antenna were tested, and the test results are as follows: Figure 9 As shown.

[0174] The radiation pattern of the 11-element array antenna with optimized rotation angle is shown in the following figure. Figure 12 As shown.

[0175] Test Result Analysis:

[0176] Reference Figure 9The S11 parameters of the antenna array elements show that the lowest point of the S parameters is around 9.8 GHz, and S11 is less than -10 dB at the 10 GHz frequency point, which is consistent with the simulation results.

[0177] In addition, by measuring the S-parameters of each element in the array one by one, we can not only effectively evaluate the manufacturing quality, but also detect the welding integrity of each SMA interface, thus laying the foundation for subsequent testing of the array antenna pattern.

[0178] Figure 11 Interface for setting up power supply excitation; Figure 12 The comparison between the test and simulation results of the antenna measurement pattern and radiation pattern shows that, by adopting an optimized excitation distribution design, the proposed array antenna with optimized rotation angle successfully achieved the expected flat-top pattern characteristics. At the same time, under the condition of element rotation, its cross-polarization level was effectively controlled and kept within an acceptable range. The obtained antenna array obtained the desired radiation pattern under different phase feeds, proving that incorporating element rotation into the beamforming of the array antenna is an effective method, while avoiding unequal feeds.

[0179] Based on the same inventive concept, this embodiment of the invention also provides a beamforming system for a sparse wire array with rotating units and considering mutual coupling. Since the principle of solving the problem by this beamforming system for a sparse wire array with rotating units and considering mutual coupling is similar to that of the aforementioned beamforming method for a sparse wire array with rotating units and considering mutual coupling, the implementation of this beamforming system for a sparse wire array with rotating units and considering mutual coupling can refer to the implementation of the beamforming method for a sparse wire array with rotating units and considering mutual coupling. Repeated details will not be repeated.

[0180] In specific implementation, the sparse wire array beamforming system with unit rotation and mutual coupling provided in the embodiments of the present invention specifically includes:

[0181] The rotation module is used to acquire array elements, derive the Euler angle for the rotation of array elements around the z-axis, and obtain the radiated electric field after rotation.

[0182] The setting module is used to set the beamforming target based on the radiation field and electric field.

[0183] The generation module uses a stochastic optimization algorithm to optimize the position, rotation angle and excitation phase of the array elements based on the beamforming target, and generates an initial beam scheme.

[0184] The optimization module is used to extract the active radiation pattern of the initial beam scheme based on the full-wave simulation, and combine the active radiation pattern with the CAL-SAPSO algorithm to optimize the array element position, rotation angle and excitation phase, and generate the final array element radiation pattern.

[0185] Accordingly, embodiments of the present invention also provide a beamforming device for a sparse wire array with rotating elements and considering mutual coupling, including a processor and a memory, wherein the processor executes a computer program stored in the memory to implement the beamforming method for a sparse wire array with rotating elements and considering mutual coupling as provided in embodiments of the present invention.

[0186] For more detailed information on the above methods, please refer to the relevant content disclosed in the foregoing embodiments, which will not be repeated here.

[0187] Accordingly, embodiments of the present invention also provide a computer-readable storage medium for storing a computer program, wherein the computer program, when executed by a processor, implements the sparse wire array beamforming method with unit rotation and mutual coupling as described in the embodiments of the present invention.

[0188] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the systems, devices, and storage media disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple; relevant parts can be referred to the method section.

[0189] Those skilled in the art will further recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of the various examples have been generally described in terms of functionality in the foregoing description. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0190] The steps of the methods or algorithms described in conjunction with the embodiments disclosed herein can be implemented directly by hardware, a software module executed by a processor, or a combination of both. The software module can be located in random access memory (RAM), main memory, read-only memory (ROM), electrically programmable ROM, electrically erasable programmable ROM, registers, hard disk, removable disk, CD-ROM, or any other form of storage medium known in the art.

[0191] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0192] The present invention has provided a detailed description of the beamforming method, system, device, and storage medium for sparse wire arrays with unit rotation and mutual coupling. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A beamforming method for sparse wire arrays with element rotation and considering mutual coupling, characterized in that, Includes the following steps: Obtain the array elements, derive the Euler angle by rotating the array elements around the z-axis, and obtain the radiated electric field after rotation; Beamforming targets are set based on the electric field of the radiation field. Based on the beamforming target, a stochastic optimization algorithm is used to optimize the position, rotation angle and excitation phase of the array elements to generate an initial beam scheme; The active radiation pattern is extracted from the initial beam pattern based on full-wave simulation. The active radiation pattern is then combined with the CAL-SAPSO algorithm to optimize the element position, rotation angle, and excitation phase, generating the final element radiation pattern.

2. The beamforming method for a sparse wire array considering unit rotation and mutual coupling according to claim 1, characterized in that, The Euler angle is derived for the rotation of the antenna array elements around the z-axis to obtain the radiated electric field after rotation, including: The radiated electric field after the antenna is rotated is:

3. The beamforming method for a sparse wire array considering unit rotation and mutual coupling according to claim 1, characterized in that, Setting beamforming targets based on the radiation field's electric field includes: Define the user's desired main polarization direction Calculate the projection of the principal polarization direction perpendicular to the propagation direction based on the principal polarization direction. Cross-polarization direction calculated based on projection.

4. The beamforming method for a sparse wire array considering unit rotation and mutual coupling according to claim 3, characterized in that, It also includes constraints on beamforming targets: Assume peak sidelobe level ≤ -13dB; Assume the expected value of the cross-polarization level is ≤ -15dB.

5. The beamforming method for a sparse wire array considering unit rotation and mutual coupling according to claim 1, characterized in that, Based on the beamforming objective, a stochastic optimization algorithm is used to optimize the position, rotation angle, and excitation phase of the array elements to generate an initial beamforming scheme, including: Set optimization variables: element position, rotation angle, and excitation phase. By using a mapping function to transform the positions of the array elements, the discrete spacing constraint is converted into a continuous domain optimization problem, which is then solved as follows: After solving for P and K, construct the values ​​of two matrices C and G, in which all elements follow a uniform distribution in the interval (0,1), to obtain the positions of the array elements. The array element positions, rotation angles, and excitation phases are used as input vectors, and the SHADE algorithm is employed to optimize and generate the initial beam pattern.

6. The beamforming method for a sparse wire array considering unit rotation and mutual coupling according to claim 5, characterized in that, The array element positions, rotation angles, and excitation phases are used as input vectors, and the SHADE algorithm is employed for optimization, including: Initialization parameters, including the historical storage space M for initializing the mutation factor and crossover probability. F and M CR and the length of historical storage space; First, an iterative process is performed to generate F. i and CR i Its expression is as follows: CR i =randn i (M CRri ,0.1) F i =randc i (M Fri ,0.1) In the formula: ri is the index number randomly generated in the sequence {1,2,...,H}; randn(μ,σ 2 ) and randc(μ,σ 2 Let μ and σ represent random values ​​from the Cauchy and normal distributions, respectively. 2 These represent its mean and variance, respectively. Set constraints: When the generated CR i If it does not belong to [0,1], then it is truncated to the interval [0,1]; if the generated F i If it is greater than 1, then set it to 1; if the generated F i If the value is less than 0, then F is regenerated. i Until F is satisfied i ∈[0,1]; Perform a mutation operation to obtain a mutation vector, the expression of which is as follows: In the formula: r1 and r2 are index values ​​randomly selected from the sets {1,2,...,NP} and {1,2,...,H+NP}, respectively, and are integers that are distinct from i; It is an external storage file and the current population P G The selected individuals; This refers to an individual randomly selected from the individuals with the highest fitness ranking in the current population; It is a mutation vector; Crossover and mutation are performed to obtain the experimental vector, whose expression is as follows: In the formula: randb(j) represents the j-th estimate of the random number generator between [0, 1]; rnbr(i)∈(1,2,…,D) represents a randomly selected sequence, used to ensure At least from Obtain a parameter; CR represents the crossover operator, and its value range is [0, 1]. experimental vector With the current population vector The comparison is achieved by calculating the fitness function. When the fitness function is minimized, the vector with the smaller fitness function will appear in the next generation of the population. Each time generation is successful, the corresponding parameter CR is set. i and F i To store and update historical data, the expression is as follows: The index k in the above formula is updated using the weighted Lehmer mean.

7. The beamforming method for a sparse wire array considering unit rotation and mutual coupling according to claim 6, characterized in that, The expression for the fitness function is: In the formula: P d (θ,φ) represents the desired shaped COP power pattern; Γ SL Indicates the sidelobe level of the desired shaped beam; Γ X The desired XPL size for beamforming is represented by W3, which influences its importance in the optimization process and thus controls the final array pattern XPL size; M, S, and Q represent the values ​​of Ω in the main lobe region and side lobe region of the main polarization pattern, respectively. SL and cross-polarization pattern angular domain Ω X The number of sampling points.

8. A sparse wire array beamforming system with element rotation and mutual coupling consideration, characterized in that, include: The rotation module is used to acquire array elements, derive the Euler angle for the rotation of array elements around the z-axis, and obtain the radiated electric field after rotation. The setting module is used to set the beamforming target based on the radiation field and electric field. The generation module uses a stochastic optimization algorithm to optimize the position, rotation angle and excitation phase of the array elements based on the beamforming target, and generates an initial beam scheme. The optimization module is used to extract the active radiation pattern of the initial beam scheme based on the full-wave simulation, and combine the active radiation pattern with the CAL-SAPSO algorithm to optimize the array element position, rotation angle and excitation phase, and generate the final array element radiation pattern.

9. A sparse wire array beamforming device with unit rotation and considering mutual coupling, characterized in that, It includes a processor and a memory, wherein the processor executes a computer program stored in the memory to implement the sparse wire array beamforming method with element rotation and mutual coupling as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, Used to store a computer program, wherein the computer program, when executed by a processor, implements the sparse wire array beamforming method with element rotation and mutual coupling as described in any one of claims 1 to 7.

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