Design method of conformal transmit array combining spatial mapping algorithm and swarm intelligence algorithm

Abstract

The application discloses a kind of high-efficiency accurate conformal transmission array design methods, comprising: setting fine model and coarse model;Using swarm intelligence algorithm optimization to obtain coarse model optimal solution, and as fine model initial parameter;Using swarm intelligence algorithm extracts coarse model parameter corresponding to fine model parameter;According to the principle of space mapping, update mapping matrix, predict next step fine model parameter;Repeat the last two steps until the design result of fine model meets the requirement or mapping converges.The application proposes to combine space mapping algorithm and swarm intelligence algorithm to optimize the phase distribution of transmission array surface, designs conformal transmission array based on considering actual amplitude and phase error, and realizes excellent conformal transmission array.The method converts the full-wave simulation process (fine model) of transmission array into efficient array factor (coarse model) optimization process through parameter extraction, so that complex transmission array optimization can be successfully realized.

Description

Technical Field

[0001] This invention belongs to the field of antenna technology, specifically a shaped transmission array design method that combines spatial mapping algorithm and swarm intelligence algorithm. Background Technology

[0002] Beamforming is an important antenna technology with wide applications in wireless communication, radar detection, and other fields. There are generally two methods for achieving antenna beamforming. The first method is analytical, such as Fourier transform, Taylor synthesis, Chebyshev synthesis, and Woodward-Lawson methods. These methods find a direct correspondence between the radiation pattern and the amplitude and phase distribution of the antenna aperture, resulting in high beamforming efficiency. However, the radiation patterns generated by these analytical methods are not fully controllable, and it is difficult to achieve radiation pattern synthesis with limited amplitude and phase dynamic range, making the design less flexible. The second method is global optimization, which utilizes swarm intelligence algorithms, including genetic algorithms, particle swarm optimization, and artificial bee colony optimization, to globally search within the solution domain to obtain design parameters that meet performance conditions. It has advantages such as the ability to specify the solution domain and perform multi-objective optimization, making it suitable for multi-objective optimization problems of beamforming patterns. For the transmission phase optimization problem in beamforming transmission array design, swarm intelligence algorithms are often used.

[0003] Transmissive array antennas combine optical theory and antenna array theory, possessing numerous advantages such as low loss, high gain, planar structure, and simple fabrication. However, current research on transmissive array antennas mainly focuses on achieving high gain and high efficiency, with relatively little research on beamforming aspects.

[0004] Beamforming in transmission array antennas primarily relies on phase synthesis alone, i.e., altering the transmission phase distribution of the transmission array surface to obtain the target radiation pattern. In reality, transmission arrays are quasi-periodic structures, and the transmission phase of each transmission element varies with the oblique incidence angle and structural changes in neighboring elements, resulting in a certain amplitude-phase deviation compared to the expected transmission performance obtained under ideal periodic boundary conditions. These amplitude-phase errors cause the actual radiation pattern to deviate from the theoretically expected pattern, which is particularly significant in shaped transmission arrays. To achieve better beamforming, it is essential to research shaped transmission array design methods that consider actual amplitude-phase errors. Summary of the Invention

[0005] The purpose of this invention is to provide an efficient and accurate method for designing shaped transmission arrays. By combining spatial mapping algorithms and swarm intelligence algorithms to optimize the phase distribution of the transmission array surface, and considering actual amplitude and phase errors, a shaped transmission array with excellent performance is designed.

[0006] The technical solution to achieve the objective of this invention is: a method for designing a shaped transmission array combining a spatial mapping algorithm and a swarm intelligence algorithm, the method comprising: optimizing the phase distribution of the transmission array surface by combining the spatial mapping algorithm and the swarm intelligence algorithm; including the following steps:

[0007] Step 1: Set up the detailed model and the coarse model;

[0008] Step 2: Use a swarm intelligence algorithm to optimize and obtain the optimal solution of the coarse model; set the initial parameters of the fine model to be equal to the optimal solution of the coarse model.

[0009] Step 3: Use swarm intelligence algorithms to optimize and extract coarse model parameters corresponding to fine model parameters;

[0010] Step 4: Based on the principle of spatial mapping, update the mapping matrix to obtain the predicted parameters for the next detailed model step.

[0011] Step 5: Repeat steps 3 and 4 until the design results of the detailed model meet the design requirements or the mapping converges.

[0012] Furthermore, in step 1, the array factor of the feed radiation field illumination is used as the coarse model and the full-wave simulation model is used as the fine model.

[0013] Furthermore, suppose the transmission array includes M×M phase-modulated transmission elements, and the feed antenna array includes p×p microstrip patches, with each microstrip patch being equivalent to two slot antennas;

[0014] The coarse model is:

[0015]

[0016] in, Let E1(x) be the array factor of the feed radiation field illumination. m ,y n )for:

[0017] E1(x m y n )=-jωA(x m y n )

[0018] in,

[0019] ω=2πf

[0020]

[0021]

[0022] In the formula, f is the resonant frequency of the feed antenna array, and x m y nLet x and y be the x and y coordinates of the phase-modulated transmission unit in the m-th row and n-th column, respectively, and k be the phase constant in free space. Let be the azimuth vector from the slot antenna to the phase-modulated transmission element in the m-th row and n-th column. This is the position vector from the array center to the transmission array element. Let |Τ be a unit vector at any position in the coordinate system. mn | represents the amplitude of the transmission coefficient of the phase-modulated transmission unit in the m-th row and n-th column, ψ mn Let ω be the phase of the transmission coefficient of the transmission element in the m-th row and n-th column, ω be the angular frequency, and A be the magnetic vector potential distribution. These are the unit vectors for the x-axis, y-axis, and z-axis, respectively, where x, y, and z are the three-dimensional coordinates of the charge distribution of the slot antenna.

[0023] Further, step 2, which involves using a swarm intelligence algorithm to optimize and obtain the optimal solution for the coarse model, specifically involves: combining the coarse model, setting a target radiation pattern, and using a swarm intelligence algorithm to optimize and obtain the optimal design parameters of the coarse model as the initial phase distribution of the transmission array. The specific process includes:

[0024] The flat-top target pattern is divided into three regions: the main lobe region, the side lobe region, and the transition region. The target pattern in the main lobe region presents a flat-top beam. In the side lobe region, all side lobes of the target pattern are below the upper limit of the side lobe constraint. In the transition region, no side lobes appear in the target pattern. This region is located between the main lobe region and the side lobe region.

[0025] Based on the above regional division, and according to different optimization objectives, different objective functions are set, resulting in the following three stages:

[0026] Phase 1: Aiming at the sidelobe level, obtain a transmission array phase distribution lower than the set sidelobe level. The objective function for this phase is:

[0027] f = α + SIL if SIL ≥ Thr0

[0028] Where α is a set positive real number, SIL is the maximum sidelobe value in the sidelobe region, and Thr0 is the threshold of SIL;

[0029] Second stage: Based on the first stage, with the E-plane main lobe condition as the objective, the phase distribution of the transmission array that satisfies the set flat-top condition is obtained. The objective function for this stage is:

[0030] f = β + ξ1 if ξ1 ≥ Thr1

[0031] Where β is a set positive real constant, ξ1 is the second norm of the pattern vector of the main lobe region on the E plane, i.e., the xoz coordinate plane, and Thr1 is the threshold of ξ1.

[0032] The third stage: Based on the first two stages, with the main lobe condition of the H-plane (i.e., the yoz coordinate plane) as the objective, the phase distribution of the transmission array that satisfies the set flat-top condition is obtained. The objective function for this stage is:

[0033] f = γ + ξ² if ξ² ≥ Thr²

[0034] Where γ is a set positive real constant, ξ2 is the second norm of the pattern vector of the main lobe region on the H plane, and Thr2 is the threshold of ξ2;

[0035] The swarm intelligence algorithm adopts the artificial bee colony algorithm, and the optimization objective is to obtain the minimum value of the above objective function, thereby obtaining the optimal solution of the coarse model; in the above formula, the relationship between α, β, and γ is (α+Δ)>(β+Δ)>(γ+Δ), where Δ is the difference threshold between the three positive real numbers.

[0036] Further, step 3, extracting the coarse model parameters corresponding to the fine model parameters, specifically involves: using the orientation pattern obtained from the fine model as the target, optimizing the coarse model design parameters, and calling a swarm intelligence algorithm to extract the coarse model design parameters corresponding to the fine model design parameters.

[0037] With detailed model Using the direction pattern as the target, the artificial bee colony algorithm is called to optimize the coarse model design parameters, thus obtaining the fine model design parameters. The corresponding coarse model design parameter X c 0 The process specifically includes:

[0038] Based on the shaping requirements of different regions of the radiation pattern, the radiation pattern is set into several parameter extraction regions; the following description focuses on parameter extraction region I and parameter extraction region II:

[0039] Phase 1: In the coarse model, extract the design parameters X that satisfy the sidelobe requirements for the radiation pattern in parameter extraction region I of the E-plane and H-plane. c 0 ;

[0040] Phase Two: Building upon Phase One, extract the orientation pattern and the fine model from the parameter extraction region II of surface E within the coarse model. The coarse model design parameter X, which approximates the radiation pattern in parameter extraction region II. c 0 The objective function for this stage is:

[0041] f = β + ε1 if ε1 ≥ Thres1

[0042] Where ε1 is the coarse model X on the E surface. c 0 Radiation pattern and detailed model The L2 norm of the difference vector of the orientation pattern in parameter extraction region II, Thrs1 is the threshold of ε1;

[0043] The third stage: Based on the previous two stages, extract the orientation pattern and the fine model from the H-plane parameter extraction region II in the coarse model. Coarse model design parameter X in the radiation pattern approximation of parameter extraction region II c 0 The objective function for this stage is:

[0044] f = γ + ε² if ε² ≥ Thrs²

[0045] Where ε2 is the coarse model X on the H surface. c 0 Radiation pattern and detailed model The L2 norm of the difference vector in region II of the orientation pattern is extracted, and Thrs2 is the threshold of ε2.

[0046] The swarm intelligence algorithm employs the artificial bee colony algorithm, and its optimization objective is to obtain the minimum value of the aforementioned objective function, thereby acquiring the detailed model design parameters. The corresponding coarse model design parameter X c 0 .

[0047] Furthermore, step 4 involves updating the fine model parameters based on the principle of spatial mapping. The specific process includes:

[0048] After the first parameter extraction in step 3, the detailed model design parameters are obtained. The corresponding coarse model design parameter X c 0 The residual vectors of both are calculated as follows:

[0049]

[0050] If the model is detailed The orientation pattern meets the design requirements or is consistent with the rough model X. c 0 The residual vector satisfies the convergence requirement ||ΔX c 0 ||≤η, where η is a real number, thus establishing and X c 0 The mapping relationship is as follows:

[0051] Otherwise, the obtained residual vector ΔX c 0 Substitute these parameters into the detailed model design parameters for the next iteration. The update formula for the Jacobian matrix B1 is:

[0052]

[0053]

[0054] in, The calculation formula is:

[0055]

[0056] In the formula, B0 = [I], that is, B0 is the identity matrix.

[0057] Furthermore, step 5 specifically includes:

[0058] The design parameters obtained from the i-th update Substitute the parameters into the detailed model for full-wave simulation, and then perform step 3 to extract the parameters for the next step, thus obtaining the design parameters of the detailed model. Corresponding coarse model design parameters

[0059] Determine if it satisfies Or detailed model design parameters If the radiation pattern meets the target radiation pattern setting, the mapping ends; otherwise, repeat steps 3 and 4 until it meets the target. until.

[0060] Compared with the prior art, the significant advantages of this invention are:

[0061] (1) The amplitude and phase distribution of the electric field irradiated onto the transmission array by the antenna radiation field calculation method is calculated, and then the phase of the transmission array surface is optimized to obtain a transmission array design that meets the specified radiation pattern index. This scheme takes the illumination field more accurately, and the initial phase distribution of the transmission array obtained is itself more accurate than the phase distribution of the transmission array designed by the traditional scheme.

[0062] (2) Based on the initial design of the transmission array, the spatial mapping algorithm was used to further optimize the design of the transmission array, taking into account the phase error in the actual structure, and finally the shaped pattern closer to the target was achieved.

[0063] (3) The spatial mapping algorithm is used to optimize the design of the transmission array. The full-wave simulation process (fine model) of the transmission array is transformed into an efficient array factor (coarse model) optimization process through parameter extraction, so that the complex transmission array optimization can be successfully realized.

[0064] The present invention will now be described in further detail with reference to the accompanying drawings. Attached Figure Description

[0065] Figure 1This is a flowchart illustrating the shaped transmission array design method combining spatial mapping algorithm and swarm intelligence algorithm proposed in this invention.

[0066] Figure 2 This is a schematic diagram of the transmission array antenna used in the embodiments of the present invention, used to derive the coarse model.

[0067] Figure 3 This is a simulation model of the actual structure of the transmission array antenna built in HFSS software, serving as a detailed model.

[0068] Figure 4 The images show the phase distribution (a) and amplitude distribution (b) of the feed illumination field on the transmission array surface calculated in the new fine model of this invention.

[0069] Figure 5 This is a region division map of the target orientation map in an embodiment of the present invention.

[0070] Figure 6 The optimal solution X of the coarse model obtained by the artificial bee colony algorithm in this embodiment of the invention is... c That is, the initial phase distribution of the transmission array.

[0071] Figure 7 The initial values ​​for the fine model in this embodiment of the invention The radiation pattern and the optimal solution X of the coarse model obtained from the simulation were analyzed. c The diagrams are shown in comparison, where (a) is the radiation pattern of the E plane (xoz coordinate plane) and (b) is the radiation pattern of the H plane (yoz coordinate plane).

[0072] Figure 8 The fine model parameters obtained through two iterations of spatial mapping in this embodiment of the invention are... Schematic diagram.

[0073] Figure 9 This is the final optimized fine model obtained in the embodiments of the present invention. The radiation pattern and the optimal solution X of the coarse model obtained from the simulation were analyzed. c The diagrams are shown in comparison, with Figure (a) showing the radiation pattern in the E plane (xoz coordinate plane) and Figure (b) showing the radiation pattern in the H plane (yoz coordinate plane). Detailed Implementation

[0074] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description, in conjunction with the accompanying drawings and embodiments, is provided. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0075] This invention proposes a shaped transmission array design method combining spatial mapping algorithms and swarm intelligence algorithms. Specifically, it optimizes the phase distribution of the transmission array surface using both algorithms. The array factor illuminated by the feed radiation field is used as the coarse model, and the full-wave simulation model is used as the fine model. First, the optimal design parameters of the coarse model are obtained using the swarm intelligence algorithm, and the initial parameters of the fine model are set equal to the optimal solution of the coarse model. Then, if the initial results of the fine model do not meet the design requirements, the swarm intelligence algorithm is invoked to extract parameters, obtaining the coarse model design parameters corresponding to the fine model design parameters. Next, the mapping matrix and fine model parameters are updated according to the spatial mapping algorithm process, iterating multiple times until the design results of the fine model meet the requirements or the mapping converges.

[0076] The spatial mapping algorithm uses a coarse model to accurately calculate the amplitude and phase distribution of the electric field irradiated onto the transmission array by the antenna's radiation field calculation method. This is more accurate than the conventional transmission array pattern calculation method. The coarse model itself reduces the error in the transmission array pattern calculation and is closer to the fine model.

[0077] The swarm intelligence algorithm has two important functions: first, it is used for initial value solving in the spatial mapping algorithm to find the initial optimal solution of the coarse model, i.e., the initial phase distribution of the transmission array; second, it is used for parameter extraction in the spatial mapping algorithm. When solving for the initial optimal solution of the coarse model (i.e., designing the initial phase distribution of the transmission array), the proposed more accurate coarse model is used, a target radiation pattern is set, and the optimal design parameters of the coarse model are obtained by optimization using the swarm intelligence algorithm, which serve as the initial phase distribution of the transmission array. When extracting parameters, the radiation pattern obtained from the fine model is used as the target, and the design parameters of the coarse model are optimized to obtain the coarse model design parameters corresponding to the fine model design parameters, thus completing the parameter extraction of the spatial mapping algorithm.

[0078] In one embodiment, the target radiation pattern is a flat-top beam with ±30° on both the E-plane (xoz coordinate plane) and the H-plane (yoz coordinate plane), and sidelobes below -12dB. Combined with... Figure 1 The specific process of the shaped transmission array design method combining spatial mapping algorithm and swarm intelligence algorithm of this invention includes the following steps:

[0079] 1. Define the detailed model and the coarse model;

[0080] 2. The optimal solution of the coarse model is obtained by using a swarm intelligence algorithm; the initial parameters of the fine model are set to be equal to the optimal solution of the coarse model.

[0081] 3. Employ swarm intelligence algorithms to optimize the extraction of coarse model parameters corresponding to fine model parameters;

[0082] 4. Based on the principle of spatial mapping, update the mapping matrix to obtain the predicted parameters for the next detailed model step;

[0083] 5. Repeat steps 3 to 4 until the design results of the detailed model meet the design requirements or the mapping converges.

[0084] 1. Define the detailed model and the coarse model

[0085] Combination Figure 2 The schematic diagram of the transmission array antenna in this example is used to derive the rough model. For example... Figure 2 As shown, the center frequency of the transmission array antenna is f = 10 GHz. The feed array consists of 2×2 microstrip patches, and the feed antenna is designed on an F4BM220 dielectric substrate with a dielectric constant of ε = 2.2. The element antenna size is 6.6 mm × 6.6 mm, and the element spacing is d = 24 mm, which is 0.8 wavelengths of the center frequency. Based on the empirical design method of transmission arrays, the focal length and dimensions of the transmission array are set according to an edge level of approximately -10 dB. The length and width of the transmission array are set to L = D = 216 mm, the focal length F = 180 mm, and the focal diameter ratio F / D = 0.83. The transmission array consists of 18×18 transmission elements, and the length and width of each transmission element are set to P = 12 mm.

[0086] Figure 3 This is a simulation model of the actual structure of the transmission array antenna built in HFSS software, serving as a detailed model.

[0087] The coarse model is a novel array model proposed in this invention for calculating the radiation pattern of a transmission array. This new array model uses antenna radiation field calculation methods to accurately calculate the amplitude and phase distribution of the electric field irradiated onto the transmission array from the feed source. This is then added to the phase distribution vector of the transmission array surface to obtain the amplitude and phase distribution of the entire transmission array aperture. The radiation pattern is then calculated based on traditional array antenna theory. Conventional array models used for calculating transmission array radiation patterns typically fit the feed radiation pattern to a cosine wave. Q (θ) simplifies the theoretical calculation of the transmission array, but this feed pattern approximation introduces errors in the transmission array pattern calculation. Because it more accurately considers the actual illumination field, this array model is more accurate than the traditional model, and the calculation results are closer to the actual pattern, meaning the coarse and fine models have better consistency.

[0088] In this example, a 2×2 microstrip patch array is used. Based on the basic principle of patch antennas, each microstrip patch can be equivalent to two slot antennas. Then, based on the principle of vector superposition, the amplitude and phase distribution of each element on the transmission array surface illuminated by the eight slot antennas can be calculated.

[0089] When a slotted antenna illuminates a transmission array, the resulting electric field vector distribution E1 can be obtained from the magnetic vector potential distribution A on the transmission array, where the resonant frequency of the feed antenna is f = 10 GHz.

[0090] E1(x m y n)=-jωA(x m y n (1.1)

[0091] ω=2πf (1.2)

[0092] The magnetic vector potential distribution A on the transmission array surface illuminated by the slot antenna can be obtained using the following formula:

[0093]

[0094]

[0095] Combination Figure 2 In the coordinate system setting, in the above formula, x m y n Let x and y be the x and y coordinates of the phase-modulated transmission unit in the m-th row and n-th column, respectively, and k be the phase constant in free space. Let ω be the azimuth vector from the slot antenna to the phase-modulated transmission element in the m-th row and n-th column, where ω is the angular frequency and A is the magnetic vector potential distribution. These are the unit vectors for the x-axis, y-axis, and z-axis, respectively, where x, y, and z are the three-dimensional coordinates of the charge distribution of the slot antenna.

[0096] Figure 4 Let E1(x) be the feed illumination field on the transmission array surface obtained according to the above calculation method. m ,y n Phase distribution (a) and excitation amplitude distribution (b).

[0097] After obtaining the feed illumination field, it is added to the phase distribution vector of the transmission array surface to obtain the amplitude and phase distribution of the entire transmission array aperture. The radiation pattern is then calculated based on traditional array antenna theory. The theoretical formula for the far-field radiation of a transmission array antenna is:

[0098]

[0099] Combination Figure 2 The coordinate settings are as follows: In the above formula, E1(x) m ,y n () is the feed illumination field calculated above. This is the position vector from the array center to the transmission array element. Let |Τ be a unit vector at any position in the coordinate system. mn | represents the amplitude of the transmission coefficient of the phase-modulated transmission unit in the m-th row and n-th column, ψ mn Let |Τ| be the phase of the transmission coefficient of the transmission element in the m-th row and n-th column. When performing full-wave simulation on each transmission element individually, the transmission coefficients of all elements are close to 1, so |Τ| is set to |Τ|. mn | is 1.

[0100] 2. The optimal solution of the coarse model is obtained by using a swarm intelligence algorithm.

[0101] Combination Figure 5 The flat-top target pattern is divided into three regions: the main lobe region, the side lobe region, and the transition region. In this example, within the main lobe region, θ∈(-30°, 30°), the target pattern is required to have minimal fluctuations, with the overall waveform close to the normalized maximum value, exhibiting a flat-top beam. Within the side lobe region, θ∈(-90°, -45°)∪(45°, 90°), all side lobes of the target pattern are required to be below the upper limit of the side lobe constraint. Within the transition region, θ∈(-45°, -30°)∪(30°, 45°), the target pattern is required to have no side lobes; this region lies between the main lobe region and the side lobe region.

[0102] Based on the above regional division, and according to different optimization objectives, different objective functions are set. Specifically, it can be divided into the following three stages:

[0103] The first stage aims to obtain a transmission array phase distribution lower than the set sidelobe level, with the objective function shown in formula (1.6). Here, α is a set positive real constant, and SIL is the maximum sidelobe value in the sidelobe region θ∈(-90°,-45°)∪(45°,90°). α is set to satisfy the constraint that the objective function in the optimization algorithm must be positive. The sidelobe values ​​in the two planes are constrained by the SIL threshold Thr0. Based on the target radiation pattern, Thr0 = -12 is set.

[0104] f=α+SIL if SIL≥Thr0 (1.6)

[0105] The second stage: Based on the first stage, with the main lobe condition of the E-plane (xoz coordinate plane) as the objective, the phase distribution of the transmission array that satisfies the set flat-top condition is obtained. The objective function of this stage is shown in formula (1.7), where β is a set positive real constant, and ξ1 is the L2 norm of the pattern vector of the main lobe region on the E-plane (xoz coordinate plane). β is set to satisfy the constraint that the objective function in the optimization algorithm must be positive. The main lobe oscillation of the E-plane (xoz coordinate plane) is constrained by the threshold Thr1 of ξ1. Based on experience, the threshold Thr1 of ξ1 is set to Thr1 = 15.

[0106] f=β+ξ1 if ξ1≥Thr1 (1.7)

[0107] The third stage: Based on the first two stages, with the main lobe condition of the H-plane (yoz coordinate plane) as the objective, the phase distribution of the transmission array that satisfies the set flat-top condition is obtained. The objective function of this stage is shown in (1.8), where γ is a set positive real constant, and ξ2 is the L2 norm of the pattern vector of the main lobe region on the H-plane (yoz coordinate plane). γ is set to satisfy the constraint that the objective function in the optimization algorithm must be positive. The main lobe oscillation of the H-plane (yoz coordinate plane) is constrained by the threshold Thr2 of ξ2. Based on experience, the threshold Thr2 of ξ2 is set to Thr2 = 15.

[0108] f=γ+ξ2 if ξ2≥Thr2 (1.8)

[0109] Furthermore, the optimization logic of the swarm intelligence algorithm in this invention is to obtain the minimum value of the objective function. That is, the smaller the objective function value of the model parameter being solved, the closer the parameter is to the solution objective in this example. Therefore, α, β, and γ in the above formula also have a magnitude relationship, that is, (α+Δ)>(β+Δ)>(γ+Δ), where Δ is the threshold of the difference between the three positive real numbers. Based on experience, Δ is set to 1000 in this example.

[0110] In this embodiment, the transmission array consists of 18×18 transmission elements. Due to the symmetry of the target radiation pattern and the feed illumination field, 81 transmission phases of 9×9 elements on a quarter-array surface are selected for optimization. Furthermore, the normal operation of the transmission elements requires the transmission array to exhibit a quasi-periodic distribution. Therefore, in this example, the initial phase range of all transmission elements is solved as (0, 0.5π). Within this range, the element structure sizes are similar, exhibiting a quasi-periodic distribution.

[0111] Combination Figure 6 The initial phase distribution of the transmission array, optimized by the artificial bee colony algorithm described above, is shown in this embodiment. The initial phase distribution is a row vector with 81 dimensions, X... c =[x c 1 ,x c 2 ,x c 3 ,…,x c 81 According to the initial value assignment rules for the fine model in the spatial mapping algorithm, let...

[0112] Following the spatial mapping algorithm process, for the detailed model Perform full-wave simulation. Figure 7 Detailed model in the embodiments of the present invention The optimal solution X of the radiation pattern and coarse model cA comparison of radiation patterns, where (a) is the radiation pattern of the E-plane (xoz coordinate plane) and (b) is the radiation pattern of the H-plane (yoz coordinate plane). Figure 7 It can be seen that, compared to the coarse model X c Direction pattern, detailed model The main lobe region of the radiation pattern shows increased fluctuations, and the beam also exhibits dips in the transition region. This is due to deviations between the amplitude and phase distribution of the transmission array and the theoretical values; in this invention, we only consider phase errors.

[0113] 3. Employ swarm intelligence algorithms to extract coarse model parameters corresponding to fine model parameters.

[0114] Following the spatial mapping algorithm process, a detailed model is obtained. If the radiation pattern does not meet the design requirements or convergence requirements, parameter extraction is required to obtain the detailed model design parameters. The corresponding coarse model design parameter X c 0 and update X f Domain and X c Mapping between domains.

[0115] The specific operation for parameter extraction is as follows: using a fine model Using the direction pattern as the target, the artificial bee colony algorithm is called to optimize the coarse model design parameters, thus obtaining the fine model design parameters. The corresponding coarse model design parameter X c 0 This process is similar to step 2, which involves finding the optimal solution for the coarse model.

[0116] Based on the shaping requirements of different regions of the radiation pattern, in this example, the radiation pattern is set into two parameter extraction regions: Parameter Extraction Region I (θ∈(-90°,-50°)∪(50°,90°)) and Parameter Extraction Region II (θ∈(-50°,50°)). In this example, in Parameter Extraction Region I (θ∈(-90°,-50°)∪(50°,90°)), the coarse model design parameter X... c 0 The sidelobes of the radiation pattern only need to be below the set target sidelobe threshold (-12dB); in parameter extraction region II (θ∈(-50°,50°)), the coarse model radiation pattern needs to be consistent with the fine model design parameters. The high degree of similarity is the key area for shaping in this example. Specifically, it can be divided into the following three stages:

[0117] Phase 1: Combining formula (1.6), extract the design parameters X from the coarse model that satisfy the sidelobe requirements for the radiation pattern in parameter extraction region I (θ∈(-90°,-50°)∪(50°,90°)) on the E-plane (xoz coordinate plane) and H-plane (yoz coordinate plane). c0 .

[0118] Second stage: Based on the first stage, extract the orientation pattern and refine the model from the parameter extraction region II (θ∈(-50°,50°)) on the E plane (xoz coordinate plane) in the coarse model. The coarse model design parameter X approximating the radiation pattern in parameter extraction region II (θ∈(-50°,50°)) c 0 The degree of convergence is determined by ε1, where ε1 is the coarse model X on the E surface. c 0 Radiation pattern and detailed model The L2 norm of the difference vector of the orientation pattern in parameter extraction region II (θ∈(-50°,50°)). The threshold of ε1 is set empirically to Thrs1, Thrs1=10. See formula (1.9) for details.

[0119] f=β+ε1 if ε1≥Thrs1 (1.9)

[0120] The third stage: Based on the previous two stages, extract the orientation pattern and the fine model from the parameter extraction region II (θ∈(-50°,50°)) in the H-plane (yoz coordinate plane) of the coarse model. The coarse model design parameter X in the parameter extraction region II (θ∈(-50°,50°)) approximates the radiation pattern. c 0 The degree of convergence is determined by ε2, where ε2 is the coarse model X on the H surface. c 0 Radiation pattern and detailed model The L2 norm of the difference vector in the parameter extraction region II (θ∈(-50°,50°)) of the orientation pattern is calculated. Based on experience, the threshold for ε2 is set to Thrs2, Thrs2=10, as detailed in formula (1.10).

[0121] f=γ+ε2 if ε2≥Thrs2 (1.10)

[0122] During parameter extraction, to avoid obtaining multiple solutions with significant differences from the initial phase, a neighborhood interval is introduced (a suitable neighborhood interval for parameter extraction is set based on the initial phase distribution of the coarse model). The neighborhood interval means that the design parameters of the optimized coarse model are limited to the range of ±t0 of the optimal solution Xc of the coarse model during parameter extraction, thereby avoiding multiple solutions and establishing a reasonable mapping. In this embodiment, the neighborhood interval parameter t0 is set to 0.1π based on experience.

[0123] 4. Based on the principle of spatial mapping, update the mapping matrix and update the detailed model parameters.

[0124] After the first parameter extraction, the detailed model design parameters can be obtained. The corresponding coarse model design parameter X c 0 Their residual vectors are calculated as follows:

[0125]

[0126] If the detailed model The orientation pattern meets the design requirements or is consistent with the rough model X. c 0 The residual vector satisfies the convergence requirement (mapping termination condition): ||ΔX| ... c 0 ‖≤η, where η is a very small real number, set to 5 in this example. Therefore, the established mapping relationship is:

[0127]

[0128] Otherwise, the obtained residual vector ΔX c 0 Substitute these parameters into the next iteration. Since the first parameter extraction did not meet the mapping termination condition, another iteration is needed. The detailed model parameters for the next iteration... The update method for the two variables of the Jacobian matrix B1 adopts the Broyden formula update method, which is as follows:

[0129]

[0130]

[0131] in, The calculation formula is:

[0132]

[0133] B0 = [I], meaning B0 is the identity matrix.

[0134] The above optimization result is equivalent to making the residual vector ΔX c 0 The mathematical process of approximating 0.

[0135] 5. Repeat steps 3-4 until the detailed model meets the design requirements or the mapping converges.

[0136] The updated Substituting these parameters into the full-wave simulation of the detailed model and continuing with the next parameter extraction, we can obtain the design parameters of the detailed model. Corresponding coarse model design parameters Check again to see if it meets the requirements. Or detailed model design parameters If the radiation pattern meets the target radiation pattern setting, the mapping ends; otherwise, repeat steps 3-4 until it meets the target. until.

[0137] According to the above spatial mapping design, in this embodiment, the active spatial mapping undergoes two iterations to obtain... X c 1 , X c 2 Once the mapping termination condition is met, the final determination is made. The phase distribution is set to satisfy the target radiation pattern for the fine model. Figure 8 The phase distribution of the transmission array in this embodiment of the invention is obtained through two iterations of spatial mapping and final optimization.

[0138] Detailed model in the embodiments of the present invention And the optimal solution X of the coarse model c Direction pattern comparison chart as follows Figure 9 As shown, (a) is the radiation pattern in the E-plane (xoz coordinate plane), and (b) is the radiation pattern in the H-plane (yoz coordinate plane). Figure 9 As can be seen, after spatial mapping optimization, the ripple in the main lobe region of both the E-plane (xoz coordinate plane) and the H-plane (yoz coordinate plane) is reduced: before optimization, the main lobe region fluctuated between 0 and -3 dB, while after optimization, the main lobe ranged from 0 to -1.5 dB, a reduction of approximately 1.5 dB. Furthermore, after spatial mapping optimization, the original fine model... The depression in the intermediate transition region has been corrected, and the optimized fine model has been improved. The radiation pattern is also closer to the target radiation pattern in the coarse model. This demonstrates that the spatial mapping method can optimize the phase distribution of the transmission array and achieve a better shaped radiation pattern, taking into account phase errors in the actual structure.

[0139] In summary, this invention proposes to combine spatial mapping algorithm and swarm intelligence algorithm to optimize the phase distribution of the transmission array. Based on the actual amplitude and phase error, a shaped transmission array is designed, which can achieve a high-performance shaped transmission array.

[0140] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the claimed invention.

Claims

1. A method for designing a shaped transmission array combining spatial mapping algorithms and swarm intelligence algorithms, characterized in that, The method combines spatial mapping algorithms and swarm intelligence algorithms to optimize the phase distribution of the transmission array, and includes the following steps: Step 1: Set up the detailed model and the coarse model; Step 2: Use a swarm intelligence algorithm to optimize and obtain the optimal solution of the coarse model; set the initial parameters of the fine model to be equal to the optimal solution of the coarse model; Step 3: Use swarm intelligence algorithms to optimize and extract coarse model parameters corresponding to fine model parameters; Step 4: Based on the principle of spatial mapping, update the mapping matrix to obtain the predicted parameters for the next detailed model step. Step 5: Repeat steps 3 and 4 until the design results of the detailed model meet the design requirements or the mapping converges; Step 1 uses the array factor of the feed radiation field illumination as the coarse model and the full-wave simulation model as the fine model; Assume the transmission array includes Each phase-modulated transmission element and the feed antenna array includes p×p microstrip patches, with each microstrip patch equivalent to two slot antennas; The coarse model is: in, The array factor of the feed radiation field is the radiation field of the feed. for: in, In the formula, x is the resonant frequency of the feed antenna array. m y n Let x and y be the x and y coordinates of the phase-modulated transmission unit in the m-th row and n-th column, respectively, and k be the phase constant in free space. The azimuth vector from the slot antenna to the phase-modulated transmission element in the m-th row and n-th column. is the position vector from the transmission array element in the array. Let |Τ be a unit vector at any position in the coordinate system. mn | represents the amplitude of the transmission coefficient of the phase-modulated transmission unit in the m-th row and n-th column, ψ mn Let ω be the phase of the transmission coefficient of the transmission element in the m-th row and n-th column, ω be the angular frequency, and A be the magnetic vector potential distribution. , , These are the unit vectors for the x-axis, y-axis, and z-axis, respectively, where x, y, and z are the coordinates of the charge distribution of the slot antenna.

2. The shaped transmission array design method combining spatial mapping algorithm and swarm intelligence algorithm according to claim 1, characterized in that, Step 2, which involves using a swarm intelligence algorithm to optimize and obtain the optimal solution for the coarse model, specifically involves: combining the coarse model, setting a target radiation pattern, and using a swarm intelligence algorithm to optimize and obtain the optimal design parameters of the coarse model, which are then used as the initial phase distribution of the transmission array.

3. The shaped transmission array design method combining spatial mapping algorithm and swarm intelligence algorithm according to claim 1, characterized in that, The steps following step 2 and before step 3 include: The optimal solution X of the coarse model c The initial value X, used as a parameter for detailed model design. f 0 , that is, X f 0 =X c ; Based on the spatial mapping algorithm, design parameters X for the detailed model are... f 0 Perform full-wave simulation to obtain the radiation pattern corresponding to the parameters of the fine model; Determine whether the radiation pattern meets the design requirements or convergence requirements. If it does, exit the entire process; otherwise, proceed to step 3.

4. The shaped transmission array design method combining spatial mapping algorithm and swarm intelligence algorithm according to claim 1, characterized in that, Step 3, which involves extracting the coarse model parameters corresponding to the fine model parameters, specifically involves: taking the orientation pattern obtained from the fine model as the target, optimizing the coarse model design parameters, and calling a swarm intelligence algorithm to extract the coarse model design parameters corresponding to the fine model design parameters.

5. The shaped transmission array design method combining spatial mapping algorithm and swarm intelligence algorithm according to claim 4, characterized in that, In the process of extracting the coarse model design parameters corresponding to the fine model design parameters, a neighborhood interval is introduced. Within the neighborhood interval, a swarm intelligence algorithm is called to extract the parameters. The neighborhood interval refers to the range of ±t0 of the optimal solution Xc of the coarse model during parameter extraction.

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