Method for obtaining phase distribution of plane reflection array antenna based on multi-target algorithm

Abstract

The invention discloses a method for obtaining phase distribution of a plane reflection array antenna based on a multi-target algorithm. The method comprises the following steps: designing a plane reflection array; establishing a near-field electric field calculation model through the parameters of the plane reflection array, and defining a forming target area and a limiting target area; respectively establishing a first target loss function and a second target loss function according to the forming target and the limiting target; an NSGA-III multi-objective optimization algorithm is adopted to carry out optimization solution, a contradictory relation between a forming objective and a limiting objective in a solution set is analyzed based on a Pareto graph, the range of a limiting area is adjusted, and an optimized second objective loss function is obtained; and solving the optimized second target loss function, selecting a Pareto optimal phase distribution scheme in an optimal solution set, designing a reflective array antenna, and verifying a near-field rectangular focal spot generation effect. According to the method, the target is adjusted through a method of improving the loss function, so that a better shaping effect is obtained.

Description

Technical Field

[0001] This invention relates to the field of near-field focusing technology, and in particular to a method for obtaining the phase distribution of a planar reflective array antenna based on a multi-target algorithm. Background Technology

[0002] Near-field focusing (NFF) technology plays a crucial role in fields such as microwave wireless power transfer (MWPT) and medical hyperthermia. NFF technology effectively focuses microwave energy onto a receiving antenna or device, creating a maximum radiation field at the target area. Furthermore, depending on the application scenario, the electric field energy emitted by the antenna can be shaped, causing the electric field energy to be concentrated on the receiving antenna in a specific shape.

[0003] Near-field focusing can be achieved using various antennas, such as parabolic reflector antennas, planar Fresnel arrays, and planar microstrip arrays. Among these, planar reflector array antennas combine the advantages of parabolic antennas and phased array antennas, offering low cost and high gain in near-field focusing and shaping. A planar reflector array consists of hundreds or thousands of reflective elements. Each element has the ability to adjust its phase, meaning the phase compensation of the electromagnetic wave varies with the element's topology. The electromagnetic waves reflected by these elements collectively form the transmitted beam of the planar reflector array, giving it different antenna characteristics. Therefore, obtaining a suitable element phase distribution is crucial for achieving near-field focusing and shaping, which is typically achieved through optimization algorithms.

[0004] In existing articles on near-field focusing and beamforming, optimization algorithms for single targets, such as convex optimization algorithms and IA algorithms, can quickly determine the phase distribution of simple targets. The loss function, based on the least squares method, constrains the electric field in the target region and the electric field in other regions. Specifically, the loss function is the sum of the objective function (constraining the electric field at the beamforming focus or with a specific shape) and the function constraining the external electric field (minimizing the electric field in other regions).

[0005] In complex optimization tasks, the appropriateness of the constraint function setting directly impacts the final optimization result. In traditional optimization methods, since the loss function is a summation function, changes in the loss function as optimization progresses do not significantly reflect the optimization status of the objective and constraint functions. Experimenters can only roughly adjust the objective or constraint functions based on the quality of the final algorithm output. However, multi-objective optimization algorithms, such as NSGA-III, offer a new approach to near-field focusing and beamforming. By setting multiple objective functions, the constraint function is relatively independent. Pareto plots allow for a direct observation of the constraint function's impact on beamforming, enabling improvements to the objective or constraint functions based on Pareto plot trends, or the adoption of the relatively better solution from the solution set. Therefore, for complex objectives, multi-objective optimization algorithms help experimenters quickly obtain suitable antenna design solutions. Summary of the Invention

[0006] To address the technical problems existing in the prior art, this invention proposes a method for obtaining the phase distribution of a planar reflective array antenna based on a multi-objective algorithm, in order to generate better shaping effects.

[0007] To achieve the above objectives, this invention provides a method for obtaining the phase distribution of a planar reflective array antenna based on a multi-objective algorithm, comprising:

[0008] Design a planar reflective array;

[0009] A near-field electric field calculation model is established using the parameters of the planar reflective array, and the shaping target region and the confinement target region are defined.

[0010] A first target loss function and a second target loss function are established based on the shaping target and the constraint target, respectively. The first target loss function is used to maximize the electric field intensity in the target region, and the second target loss function is used to minimize the electric field intensity in the constraint region.

[0011] The NSGA-III multi-objective optimization algorithm is used to optimize the loss function of the first objective and the loss function of the second objective respectively. Based on the Pareto chart analysis, the contradiction between the shaping objective and the constraint objective in the solution set is analyzed, and the range of the constraint region is adjusted to obtain the optimized second objective loss function.

[0012] The optimized second objective loss function is solved, the Pareto optimal phase distribution scheme in the optimized solution set is selected, the reflective array antenna is designed, and the near-field rectangular focal spot generation effect is verified.

[0013] Preferably, the planar reflective array is composed of a plurality of planar reflective elements, wherein the planar reflective elements provide phase tuning by changing the size of the element patches;

[0014] The planar reflective unit includes a double-layer structure, wherein the upper layer is a metal patch layer and the lower layer is a dielectric substrate layer. The metal patch layer is composed of a square and two intersecting square rings of the same width.

[0015] Preferably, the near-field electric field calculation model is established based on the Fresnel diffraction formula, specifically as follows:

[0016]

[0017] In the formula, Represents a two-dimensional Fourier transform. This represents the two-dimensional inverse Fourier transform, where E(x, y, z) is the field distribution of the beam on the plane at distance z, E(x, y, 0) is the electric field intensity in the time domain, and H... F (f x f y , z) is the transfer function.

[0018] Preferably, the shaping target area is a rectangular area, and the limiting target area is an extended rectangular area surrounding the shaping target area.

[0019] Preferably, the first target loss function is:

[0020]

[0021] In the formula, F1 represents the set target electric field region, m1 is a fixed coefficient, E0(i,j) is the normalized electric field, and f1 is the first target loss function;

[0022] The second objective loss function is:

[0023]

[0024] In the formula, F2 represents the electric field region of the confined target, m2 is a fixed coefficient, and f2 is the second target loss function.

[0025] Preferably, adjusting the range of the restricted area includes:

[0026] Keep the boundaries of the shaping target region unchanged;

[0027] The outer boundary of the restricted area is contracted towards the shaping target area to form a new ring-shaped restricted area.

[0028] Preferably, the optimized second objective loss function is:

[0029]

[0030] In the formula, F3 represents the new restricted region, E0(i,j) is the normalized electric field, m2 is a fixed coefficient, and f2' is the optimized second objective loss function.

[0031] Compared with the prior art, the present invention has the following advantages and technical effects:

[0032] This invention designs antennas based on optimization results, ultimately achieving an antenna design method for near-field rectangular region shaping. A multi-objective algorithm distinguishes the shaping target from the constraint target, different loss functions are set for optimization, Pareto charts are used to observe the relationships between different targets, and the target is adjusted by improving the loss function, thereby obtaining a better shaping effect. Attached Figure Description

[0033] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments and descriptions of this application are used to explain this application and do not constitute an undue limitation of this application. In the drawings:

[0034] Figure 1 This is a schematic diagram of a planar reflective array antenna according to an embodiment of the present invention;

[0035] Figure 2 The diagram shows a planar reflection unit model and its phase characteristic curve according to an embodiment of the present invention, wherein (a) is the unit model and (b) is the phase characteristic curve.

[0036] Figure 3 This is a flowchart of the NSGA-III optimization process according to an embodiment of the present invention;

[0037] Figure 4 This is a schematic diagram of the xoz planar electric field model and the optimization target region according to an embodiment of the present invention;

[0038] Figure 5 This is a Pareto chart representing an embodiment of the present invention;

[0039] Figure 6 This is a normalized electric field distribution diagram of the xoz surface in Example A of this invention;

[0040] Figure 7 This is a normalized electric field distribution diagram of the xoz surface in Example B of this embodiment of the invention;

[0041] Figure 8 This is a schematic diagram of the xoz planar electric field model and the new optimization target region in an embodiment of the present invention;

[0042] Figure 9 This is an optimized Pareto chart according to an embodiment of the present invention;

[0043] Figure 10 This is a normalized electric field distribution diagram of the xoz surface in Example C of this embodiment of the invention;

[0044] Figure 11 This is a schematic diagram of the simulation results of the normalized electric field on the xoz surface in Example C of this invention.

[0045] Figure 12 This is a flowchart of a method for obtaining the phase distribution of a planar reflective array antenna based on a multi-target algorithm, according to an embodiment of the present invention. Detailed Implementation

[0046] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0047] It should be noted that the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0048] This embodiment proposes a method for obtaining the phase distribution of a planar reflective array antenna based on a multi-objective algorithm, such as... Figure 12 ,include:

[0049] Design a planar reflective element array;

[0050] A near-field electric field calculation model is established using the parameters of the planar reflective unit array, and the shaping target region and the confinement target region are defined.

[0051] A first target loss function and a second target loss function are established based on the shaping target and the constraint target, respectively. The first target loss function is used to maximize the electric field intensity in the target region, and the second target loss function is used to minimize the electric field intensity in the constraint region.

[0052] The NSGA-III multi-objective optimization algorithm is used to optimize the loss function of the first objective and the loss function of the second objective respectively. Based on the Pareto chart analysis, the contradiction between the shaping objective and the constraint objective in the solution set is analyzed, and the range of the constraint region is adjusted to obtain the optimized second objective loss function.

[0053] The optimized second objective loss function is solved, the Pareto optimal phase distribution scheme in the optimized solution set is selected, the reflective array antenna is designed, and the near-field rectangular focal spot generation effect is verified.

[0054] Specifically, this embodiment takes the shaping of a square electric field as an example. NSGA-III optimization is used to obtain the solution set of the antenna element phase distribution. The constraint function is improved based on the Pareto diagram and the electric field distribution of the solution. A new solution set is then obtained again using NSGA-III and compared with the previous solution. The comparison results show that the electric field strength outside the target area is proportional to the electric field strength within the target area. When the electric field outside the target is overly constrained, the shaping target cannot be achieved. Based on this, a solution with better performance is selected for antenna design. The near-field electric field of the antenna is analyzed using the simulation software CST, and the results prove the feasibility of the antenna design scheme.

[0055] Furthermore, the planar reflective array is composed of several planar reflective elements, and the planar reflective elements provide phase tuning by changing the size of the element patches;

[0056] The planar reflective unit includes a double-layer structure, wherein the upper layer is a metal patch layer and the lower layer is a dielectric substrate layer. The metal patch layer is composed of a square and two intersecting square rings of the same width.

[0057] Specifically, a planar reflective array is composed of planar reflective units, such as... Figure 1 As shown, the feed emits electromagnetic waves that reach each planar reflector element, compensating for the phase of each element in the antenna array. This ensures that the emitted beam from the array forms the maximum electric field at the target location, thus achieving beam shaping. This embodiment designs a planar reflector element that provides phase tuning by changing the size of the element patches, using a plane wave as the feed. Furthermore, to expand the phase tuning range and obtain a phase characteristic curve with relatively low linearity, the designed element employs a double-layer structure.

[0058] like Figure 2 As shown in (a), the planar reflective unit consists of a single-layer metal patch and two dielectric substrates. The side length of the unit is a = b = 20 mm, the center frequency is 5.8 GHz, the height of the dielectric substrate is h1 = 1.5 mm, the height of the air layer is h2 = 2 mm, the material of the dielectric substrate is Arlon 350A, and the corresponding ε r =3.5.

[0059] The patch employs a classic structure consisting of a square and two intersecting square rings of equal width. Similar structures have been proven in existing technologies to have a good phase change range. The outer square ring has a fixed position and size, while the square and inner square ring are treated as a whole, with their corresponding dimensions varying. Figure 2In (a), the position of the outer square ring is determined by x1 and x2, x1 = 18mm and x2 = 17mm; the position of the inner square ring is determined by x3 and x4, the side length of the square is x5, and x3 = x4 + 1mm and x5 = x4 - 4mm are set, with x4 varying from 6 to 15mm.

[0060] By varying x4, under y-polarization conditions, an S-curve describing the relationship between the reflection characteristics and the size / length of a planar reflecting unit was obtained, as shown below. Figure 2 As shown in (b), it can be seen that x4 achieves a phase tuning range of 420° within a variation of 6-15mm. Based on this, a variation range of 8-15mm for x4 is selected, within which the phase tuning reaches a variation range of approximately 360°.

[0061] Furthermore, the near-field electric field calculation model is established based on the Fresnel diffraction formula, specifically as follows:

[0062]

[0063] In the formula, Represents a two-dimensional Fourier transform. This represents the two-dimensional inverse Fourier transform, where E(x, y, z) is the field distribution of the beam on the plane at distance z, E(x, y, 0) is the electric field intensity in the time domain, and H... F (f x f y , z) is the transfer function.

[0064] Specifically, the Fresnel diffraction formula takes into account the curvature and wave effect of the wavefront during near-field propagation, and can calculate the electric field formed in the near-field space after being emitted from the feed and reflected by the reflecting surface.

[0065] The field distribution of the beam in the plane at a distance z can be expressed as:

[0066]

[0067] In the formula, E(x',y',0) represents the initial wave field on the array element; λ is the wavelength; k is the wave number, k=2π / λ, j is the imaginary part, z is the Z-axis coordinate, x′ is the reciprocal of x, and y′ is the reciprocal of y.

[0068] Equation (2) can be written in the form of a convolution integral:

[0069]

[0070] The convolution kernel is:

[0071]

[0072] In the formula, hF (x, y) is the convolution kernel.

[0073] Therefore, equation (2) can be expressed as:

[0074]

[0075] The transfer function is:

[0076]

[0077] In the formula, f x and f y Representing two-dimensional frequency domain coordinates, Represents a two-dimensional Fourier transform. This represents the two-dimensional inverse Fourier transform.

[0078] In the near-field shaping problem of planar reflective array, given the center frequency (5.8GHz in this embodiment), array structure (a 39*39 array with a unit perimeter p = 20mm in this embodiment), and scattering parameters (phase characteristics and amplitude characteristics) of each unit, the near-field electric field in a certain area can be calculated using equations (5) and (6).

[0079] Furthermore, the shaping target region is a rectangular region, and the limiting target region is an extended rectangular region surrounding the shaping target region.

[0080] Furthermore, the first objective loss function is:

[0081]

[0082] In the formula, F1 represents the set target electric field region, m1 is a fixed coefficient, E0(i,j) is the normalized electric field, and f1 is the first target loss function;

[0083] The second objective loss function is:

[0084]

[0085] In the formula, F2 represents the electric field region of the confined target, m2 is a fixed coefficient, and f2 is the second target loss function.

[0086] Specifically, this embodiment uses a 39×39 planar reflective array antenna (unit period p = 20mm) for shaping. The shaping objective is to generate the maximum electric field within a square area set in the near field and to confine the electric field outside the area. The side length of the planar reflective unit used in the array is 20mm, and the center frequency is 5.8GHz.

[0087] Establish the electric field model of the antenna's near-field xoz plane, such as... Figure 4As shown. The center of the antenna array is at x = 0, y = 0, z = 0. The near-field region involved in the calculation is x = -380:380 mm, z = 0:1000 mm, y = 0 mm. Under plane wave incident conditions, the discrete electric field E in this region is calculated using the Fresnel diffraction formula. xoz Among them, E xoz For N x ×N z The matrix, where each element represents the electric field E(i,j) (i=1:N) in the divided grid. x j = 1:N z ). Figure 4 The black box in the image shows the shaped target, which is the region where the emitted beam is expected to generate the maximum electric field. The target region has the range of x = 0:200 mm, z = 300:450 mm, and y = 0 mm. Figure 4 The white box in the diagram represents the limiting objective, which is to minimize the electric field in the area between the black box and the white box. The area within the white box has the following dimensions: x = -200:380 mm, z = 100:650 mm, and y = 0 mm.

[0088] Establish a loss function based on the shaping objective and the constraint objective.

[0089] First, the calculated electric field is normalized:

[0090]

[0091] Among them, E max This represents the maximum value of the electric field in the near-field calculation region.

[0092] Establish the loss function corresponding to the shaping target, i.e., the first target loss function:

[0093]

[0094] F1 represents the electric field region within the black box, m1 is a fixed coefficient, E0(i,j) is the normalized electric field, and f1 is the first objective loss function.

[0095] Establish the loss function corresponding to the constraint objective, i.e., the second objective loss function:

[0096]

[0097] In the formula, F2 represents the electric field region inside the white box and outside the black box, m2 is a fixed coefficient, and f2 is the second objective loss function.

[0098] The established loss function is then substituted into the NSGA-III algorithm to obtain the optimization results.

[0099] Specifically, the NSGA-III algorithm is introduced as follows:

[0100] The Non-dominated Sorting Genetic Algorithm (NSGA), proposed by Kalyanmoy Deb's team in 1995, evolved into NSGA-III after two improvements. NSGA-III introduces a high-dimensional reference point search strategy to handle multi-objective problems in high-dimensional target spaces, thereby increasing search capabilities.

[0101] The basic steps of the NSGA-III algorithm are as follows:

[0102] 1) Initialize parameters: Set the population size N, problem dimension M, number of iterations, mutation rate and crossover rate, number of reference point segments H, and various objective loss functions, etc.

[0103] 2) Generate reference points: Calculate the normalized spatial distribution of reference points by initializing parameters, so that solutions can be selected later;

[0104] 3) Initial sorting: Generate an initial population (containing N individuals) and substitute it into the loss function for calculation. Based on the calculation results, perform the initial sorting of the individuals in the population, including non-dominated sorting and reference point sorting. The former divides the non-dominated layer, and the latter further sorts the individuals in the non-dominated layer.

[0105] 4) Generate offspring: Based on the previous sorting results, perform crossover and mutation operations on the best individuals in the population to generate offspring (the number of offspring is N);

[0106] 5) Re-sort to generate a new population and update the reference point: Mix the parent and offspring (number of which is 2N), and select N individuals to form a new population after sorting by non-dominant sort and reference point. Update the reference point according to the new population.

[0107] 6) Repeat step 4) until the termination condition is met.

[0108] In conjunction with the near-field shaping target in this embodiment, the mathematical model of the near-field electric field is incorporated into the scoring process. That is, the near-field electric field of an individual is calculated, substituted into the loss function, and then the selection is performed based on the result of the loss function. Figure 3 The main optimization steps are introduced, including the sorting process and the scoring process.

[0109] Furthermore, adjusting the scope of the restricted area includes:

[0110] Keep the boundaries of the shaping target region unchanged;

[0111] The outer boundary of the restricted area is contracted towards the shaping target area to form a new ring-shaped restricted area.

[0112] Specifically, in the NSGA-III iteration process, the population size was set to 300, the number of segments to 20, and the number of iterations to 1000. After iteration, 300 solutions were obtained, and the Pareto plot can reflect the magnitude of the loss function for different solutions. Each solution represents a 39*39 phase distribution matrix.

[0113] Pareto chart Figure 5 As shown, the horizontal and vertical axes represent the first target loss function f1 and the second target loss function f2, respectively.

[0114] Depend on Figure 5 It can be seen that in the optimization results, f1 and f2 are approximately inversely proportional, meaning that the larger the electric field value in the target region, the larger the electric field value in the confined region, and the smaller f1 is, the greater the upward trend of f2. At this point, the minimum value of f1 only reaches 16.68. Taking the solution with f1 = 16.68 and f2 = 25.90 as Example A for analysis, the corresponding electric field model is calculated using the Fresnel diffraction formula, as follows... Figure 6 As shown, the electric field values ​​have been normalized.

[0115] In Example A, the near-field electric field forms a large, approximately square radiating electric field in the shaped target region at x = 0:200 mm and z = 300:450 mm. The maximum normalized electric field value in this region is 1, located at x = 125 mm and z = 350 mm. Due to the influence of the confining target, a significant inward shift of the boundary of the square electric field can be observed near x = 0, z = 300:450, and x = 200, z = 300:450. Conversely, the confining target electric field has only a normalized electric field value of approximately 0.4 in the region 10 mm outside the square boundary, and the electric field value continues to decrease with distance from the shaped region until it reaches approximately 0.

[0116] When the experimenter's design goal focuses more on confining the electric field outside the target region, a solution with a smaller f2 can be chosen, such as f1 = 26.21 and f2 = 20.68, which can be used as Example B for analysis. The near-field electric field corresponding to Example B is calculated as follows: Figure 7 As shown, as f2 decreases, f1 increases significantly, corresponding to... Figure 7 The square area and Figure 6 Compared to a significant reduction, for example Figure 6 The normalized electric field value at the boundary points x = 20 mm and y = 350 mm of the square is 0.70, while... Figure 7 The value is only 0.59. In contrast, Figure 7 The electric field value decreases rapidly in the confined region near the square. Figure 6 The normalized electric field value at the boundary points x = -20 mm and y = 350 mm of the restricted region is 0.21, while... Figure 7 The value is only 0.18.

[0117] However, when the experimenter's design goal focuses more on shaping, hoping that the square region will more closely resemble the target, the optimization results cannot provide a better choice due to the limitation of the minimum f1 value. Therefore, the loss function is improved based on this optimization.

[0118] Furthermore, given the known conflict between the shaping objective and the constraint objective, reducing the constraint objective can effectively improve the shaping result. For example... Figure 8 As shown, to improve the shaping effect, the constraint range is reduced to between the white and brown boxes, and the loss function is reconstructed. The positions and sizes of the white box (the outer boundary of the constraint region) and the black box (the shaping region) remain unchanged from the previous optimization. The new brown box positions are x = -100:300mm, y = 200:550mm, and z = 0mm.

[0119] The optimized second objective loss function is:

[0120]

[0121] In the formula, F3 represents the new restricted region, E0(i,j) is the normalized electric field, m2 is a fixed coefficient, and f2' is the optimized second objective loss function.

[0122] Similarly, in the NSGA-III iteration process, the population size was set to 300, the number of segments to 20, and the number of iterations to 1000. The new Pareto graph is obtained as follows: Figure 9 As shown, the horizontal and vertical axes represent the loss function f1 and the loss function f2, respectively.

[0123] Although f1 and f2 are still approximately inversely proportional in the optimization results, their changing trend is relatively small. This proves that the contradiction between the shaping objective and the constraint objective is relatively mitigated after the loss function is improved. Because the loss function of the constraint region has changed, it is impossible to compare f2 from the two optimizations. This embodiment only compares f1 with the one in the previous section. At this time, with the loss function f1 unchanged, f1 can achieve a minimum value of 14.8, further proving the feasibility of the improvement scheme.

[0124] Taking the solutions f1 = 14.8 and f2' = 10.85 as example C, the near-field electric field is calculated and analyzed using the Fresnel diffraction formula. The normalized electric field distribution on the xoz plane is shown below. Figure 10 As shown.

[0125] and Figure 6 compared to, Figure 10 This more closely approximates the shape of a square. For example, at the vertices of a square, x = 0 mm, z = 300 mm. Figure 10 The corresponding normalized electric field value is 0.45, while Figure 6 The value is only 0.35. The electric field value outside the shaping region is... Figure 10 The middle also generally increases, for example Figure 6 The normalized electric field value at the boundary points x = -20 mm and y = 350 mm of the restricted region is 0.21, while... Figure 10 The value is 0.26. The comparative results show that improving the loss function to reduce the restricted area can effectively increase the electric field value in the target area, achieving better shaping results.

[0126] Using the unit phase distribution and phase characteristic curve from Example C, a planar reflective array antenna is designed, a corresponding array model is established, and full-wave simulation is performed using CST. Figure 11 As shown in the figure, the maximum value of the simulation result occurs at x = 95 mm and z = 380 mm, while the electric field distribution calculated by Fresnel's formula is different. Figure 10 In the above, this value appears at x = 70 mm and z = 380 mm. Figure 11 and Figure 10 Compared to the relatively consistent electric field distribution in the shaped target region, the numerical differences from the mathematical model may be due to the inconsistency between the actual phase and the design phase.

[0127] This embodiment designs an antenna based on the optimization results, ultimately achieving a near-field square region shaping antenna design method. A multi-objective algorithm distinguishes the shaping target from the constraint target, different loss functions are set for optimization, Pareto charts are used to observe the relationships between different targets, and the target is adjusted by improving the loss function, thereby obtaining a better shaping effect.

[0128] The above are merely preferred embodiments of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for obtaining the phase distribution of a planar reflective array antenna based on a multi-objective algorithm, characterized in that, include: Design a planar reflective array; A near-field electric field calculation model is established using the parameters of the planar reflective array, and the shaping target region and the confinement target region are defined. A first target loss function and a second target loss function are established based on the shaping target and the constraint target, respectively. The first target loss function is used to maximize the electric field intensity in the target region, and the second target loss function is used to minimize the electric field intensity in the constraint region. The NSGA-III multi-objective optimization algorithm is used to optimize the loss function of the first objective and the loss function of the second objective respectively. Based on the Pareto chart analysis, the contradiction between the shaping objective and the constraint objective in the solution set is analyzed, and the range of the constraint region is adjusted to obtain the optimized second objective loss function. The optimized second objective loss function is solved, the Pareto optimal phase distribution scheme in the optimized solution set is selected, the reflective array antenna is designed, and the near-field rectangular focal spot generation effect is verified.

2. The method for obtaining the phase distribution of a planar reflective array antenna based on a multi-objective algorithm according to claim 1, characterized in that, The planar reflective array is composed of several planar reflective elements, and the planar reflective elements provide phase tuning by changing the size of the element patches; The planar reflective unit includes a double-layer structure, wherein the upper layer is a metal patch layer and the lower layer is a dielectric substrate layer. The metal patch layer is composed of a square and two intersecting square rings of the same width.

3. The method for obtaining the phase distribution of a planar reflective array antenna based on a multi-objective algorithm according to claim 1, characterized in that, The near-field electric field calculation model is based on the Fresnel diffraction formula, specifically: In the formula, Represents a two-dimensional Fourier transform. This represents the two-dimensional inverse Fourier transform, where E(x, y, z) is the field distribution of the beam on the plane at distance z, E(x, y, 0) is the electric field intensity in the time domain, and H... F (f x f y , z) is the transfer function.

4. The method for obtaining the phase distribution of a planar reflective array antenna based on a multi-objective algorithm according to claim 3, characterized in that, The shaping target area is a rectangular area, and the limiting target area is an extended rectangular area that surrounds the shaping target area.

5. The method for obtaining the phase distribution of a planar reflective array antenna based on a multi-objective algorithm according to claim 1, characterized in that, The first objective loss function is: In the formula, F1 represents the set target electric field region, m1 is a fixed coefficient, E0(i,j) is the normalized electric field, and f1 is the first target loss function; The second objective loss function is: In the formula, F2 represents the electric field region of the confined target, m2 is a fixed coefficient, and f2 is the second target loss function.

6. The method for obtaining the phase distribution of a planar reflective array antenna based on a multi-objective algorithm according to claim 1, characterized in that, Adjusting the range of the restricted area includes: Keep the boundaries of the shaping target region unchanged; The outer boundary of the restricted area is contracted towards the shaping target area to form a new ring-shaped restricted area.

7. The method for obtaining the phase distribution of a planar reflective array antenna based on a multi-objective algorithm according to claim 6, characterized in that, The optimized second objective loss function is: In the formula, F3 represents the new restricted region, E0(i,j) is the normalized electric field, m2 is a fixed coefficient, and f2' is the optimized second objective loss function.

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