Sub-array-level aperiodic medium-and-small-scale array antenna and design method

Abstract

The invention belongs to the technical field of array antennas, and particularly relates to a sub-array level aperiodic medium and small scale array antenna and a design method. In order to solve the problems that a conventional multi-arm helix is high in optimization dimension, poor in optimization effect and the like, an Archimedes helix is used as a mother helix to sequentially rotate to obtain the multi-arm helix, the multi-arm helix is formed by alternately distributing two sub-array helixes, array elements are framed on the two sub-array helixes, and different array element numbers and adjacent array element distances are used, so that the multi-arm helix is obtained. The distances between all the sub-array spirals and the original point are equal, the spiral growth rates of the two sub-array spirals are the same, and the sub-array level aperiodic medium and small scale array antenna is optimized by using a bat algorithm to determine an optimal solution.

Description

Technical Field

[0001] This invention belongs to the field of array antenna technology, specifically relating to a subarray-level non-periodic small-scale array antenna and its design method. Background Technology

[0002] The theoretical framework for array antennas was gradually established as early as the 20th century. Among them, uniformly distributed antenna arrays were the first to enter the public eye and received extensive research. In uniform array antennas, the array elements are equally spaced, and the spacing is usually set to be greater than or equal to half the source wavelength to avoid antenna mutual coupling caused by the close proximity of the array elements. However, under uniform arrangement, to achieve the required antenna performance, increasing the array aperture and placing more antenna elements becomes the only option, which undoubtedly requires more funding. Moreover, the periodicity of the uniform arrangement inevitably leads to the appearance of grating lobes, which in turn causes the energy of the main lobe to be dispersed. To address this problem, breaking the periodicity of the array antenna arrangement is imperative, and non-uniform array antennas have begun to attract increasing attention from scholars. Compared with uniform array antennas, non-uniform array antennas have more freedom in the position of array elements, can achieve lower peak sidelobe levels with fewer array elements, and have advantages such as small size, low manufacturing cost, and low system power consumption. They are widely used in phased arrays, radar, and wireless communication.

[0003] Due to its unique geometry, the helical structure can significantly disrupt the periodicity of uniform arrangements and, compared to other arrays, boasts a larger bandwidth and maintains stability over a wider frequency range. The helix facilitates the search for optimal solutions to non-periodic arrangements, thus attracting increasing attention. A Nordborg et al. simulated various single-arm helical microphone array configurations, observing the strong anti-interference capabilities of helical arrays. Doughenty RP reduced array spacing redundancy by arranging microphones with equal arc lengths along a logarithmic helix, achieving a low sidelobe design over a wider frequency range. While single-arm helical arrays can largely overcome array spacing redundancy, they inherently suffer from insufficient utilization of array space. Multi-arm helical arrays can further improve the anti-interference and sidelobe suppression capabilities of helical structures.

[0004] The Archimedean spiral, also known as the Archimedean concentric spiral or constant-velocity spiral, is a curve formed on a plane by a point moving at a constant velocity along a ray while that ray rotates around the origin at a constant angular velocity. Furthermore, the Archimedean spiral exhibits equidistant properties, meaning the distance between two adjacent spiral turns is constant. This regularity helps reduce space utilization issues during array element optimization, thereby improving optimization potential. Chen Rilin et al. used particle swarm optimization with an equiangular distribution, aiming to minimize the maximum sidelobe level, to search for the optimal array configuration within the Archimedean spiral. Summary of the Invention

[0005] To address the optimization problem of planar multi-arm spiral arrays, this invention employs the Archimedean spiral as the parent spiral to construct a multi-arm spiral, providing a subarray-level aperiodic small-scale array antenna design method based on the Archimedean spiral. With the objective of minimizing peak sidelobe level (PSLL), it utilizes two subarray spiral interleaved distributions. The optimal solution for the multi-arm spiral array structure is obtained by optimizing the intercept parameter from the spiral's starting point to the pole, the spiral growth rate, and the spacing between adjacent elements on each subarray spiral using the Bat algorithm. Examples demonstrate that this method reduces the complexity of adjusting element spacing and exhibits fast convergence speed and good optimization effect, effectively reducing the PSLL of the antenna array.

[0006] To achieve the above objectives, the present invention employs the following technical solution:

[0007] This invention provides a subarray-level aperiodic small-scale array antenna, comprising:

[0008] A multi-armed spiral is obtained by rotating the Archimedes spiral as the parent spiral in sequence.

[0009] The multi-arm spiral is composed of two types of sub-array spirals interspersed with each other. Each type of sub-array spiral has array elements defined on it, and different numbers of array elements and spacing between adjacent array elements are used. All sub-array spirals are equidistant from the origin, and the spiral growth rate of the two types of sub-array spirals is the same.

[0010] The Bat Algorithm is used to optimize small-scale, non-periodic array antennas at the subarray level and determine the optimal solution.

[0011] Furthermore, the two types of subarray spirals are uniformly distributed in the azimuth angle within the plane.

[0012] Furthermore, the optimal solution for the spacing between adjacent array elements is determined by the bat algorithm, and the polar angle is determined by the optimal spacing between adjacent array elements, thereby determining the arrangement position of the array elements.

[0013] Furthermore, the optimal solution includes the intercept parameter between the starting point of the subarray spiral and the pole, the spiral growth rate, and the spacing between adjacent elements on different subarray spirals.

[0014] This invention also provides a design method for a subarray-level non-periodic small-scale array antenna, comprising the following steps:

[0015] S1. Determine the number of spiral arms in a multi-armed spiral;

[0016] S2. By assigning different numbers of array elements to different subarray spirals, the number of each subarray spiral is determined;

[0017] S3. Generate random initialization data;

[0018] S4. Establish a reference model of the multi-armed spiral structure, determine the arrangement position of the array elements and calculate the initial fitness function according to the different positions searched by each bat in the random initialization data.

[0019] S5. Start the iteration. After each iteration, the distance between the positions searched by each bat will be judged. If the distance requirement is met, proceed directly to S6; otherwise, adjust the search position until the distance requirement is met, and then proceed to S6.

[0020] S6. Calculate the orientation pattern of the arrangement of each bat, determine the fitness function of the corresponding arrangement position, and store the relevant data;

[0021] S7. If the bat algorithm has not reached the maximum number of iterations, proceed to S5 for the next iteration search; otherwise, obtain the bat search position corresponding to the current best fitness function, which corresponds to the best array element arrangement position.

[0022] Furthermore, S1 specifically refers to:

[0023] After placing an array element at the center of the origin, determine the number of spiral arms of subarray spiral 1 and subarray spiral 2 respectively. and ,have .

[0024] Furthermore, S2 specifically refers to:

[0025] The number of array elements allocated to each single spiral arm of subarray spiral 1 and subarray spiral 2 are determined as follows: The total number of array elements is ,have .

[0026] Furthermore, S3 specifically refers to:

[0027] The intercept parameter a from the starting point of the spiral to the pole, the spiral growth rate b, and the spacing between adjacent elements on the two types of subarray spirals ( ~ (), ~ Initialize.

[0028] Among them, the total optimization dimension .

[0029] Specifically, step S4 is as follows:

[0030] Since this invention does not address amplitude and phase excitation, the array factor of this spiral array can be expressed as:

[0031] ;

[0032] in, , Representing the first subarray spiral 1 The first spiral arm The polar radius and polar angle corresponding to the position of each array element; , Representing the first of subarray spiral 2 The first spiral arm The polar radius and polar angle corresponding to each array element position.

[0033] The specific methods for calculating the polar radius and polar angle are as follows:

[0034] First, determine the first polar angle of each spiral arm of each spiral subarray. Taking subarray spiral 1 as an example, the first polar angle of subarray spiral 1 is... The polar angle corresponding to the first element on the spiral arm is:

[0035] , ( =0, 1, 2, ..., );

[0036] in, This represents the counter-clockwise rotation offset of the first subarray spiral. Since subarray 1 does not require any rotation, therefore... .

[0037] The polar angle can be used to determine the first subarray spiral. The polar radius corresponding to the first element on the spiral arm is:

[0038] , ( =0, 1, 2, ..., );

[0039] Next, determine the subsequent polar angles on the n1th spiral arm of subarray spiral 1.

[0040] Starting from the current position of the polar angle of the array element, increase the polar angle by 0.01, calculate the rectangular coordinate position of the array element after the increase, and compare it with the position before the increase. The Euclidean distance between the later array element and the previous array element satisfies the following formula:

[0041] , ( =0, 1, 2, ..., );

[0042] At this point, the polar angle of the next array element is determined to be the polar angle that continues to increase from the current position. In the above formula, and Representing the first subarray spiral respectively The first spiral arm Each element and the first The planar coordinate positions represented by each array element This indicates the calculation of the Euclidean distance.

[0043] After successively determining the polar angle of each element on each spiral arm, the formula can be used to... The corresponding polar radius is obtained. The above method can be used to obtain the radius of subarray spiral 1. The positions of all array elements on the spiral arm are distributed as an image obtained by rotating the mother spiral counterclockwise by the same angle with the origin as the center.

[0044] The methods for determining the polar angle and polar radius of subarray spiral 2 are similar to those for subarray spiral 1. The difference is that, since it is desirable for the spiral arms of subarray spiral 2 to be interspersed among the spiral arms of subarray spiral 1, therefore... .

[0045] At this point, the initial fitness function can be determined as follows:

[0046] , ;

[0047] in, This represents the maximum value of the matrix factor modulus; This indicates the first null trap of the matrix factor.

[0048] Furthermore, step S5 specifically involves:

[0049] The spacing requirements are as follows: the spacing between adjacent elements on the subarray spiral is greater than half a wavelength, and the spacing between any elements in the entire multi-arm spiral arrangement is also greater than half a wavelength.

[0050] The spacing determination:

[0051] After obtaining the arrangement positions of all array elements, store the Euclidean distance between any two array elements in matrix form. Since the distance between array elements does not need to be considered, fill the diagonal elements in the matrix with infinity. Then, check if there is an Euclidean distance between two array elements that is less than half a wavelength. Return True (adjustment is performed) otherwise return False (no adjustment is performed).

[0052] When the spacing condition first returns True:

[0053] Verify whether the intercept parameter 'a' between the starting point of the subarray spiral and the pole found by the bat population is greater than half a wavelength. If 'a' is less than half a wavelength, first set it directly equal to half a wavelength and a random small perturbation greater than 0 and less than 0.1 times the wavelength. At this time, the distance between the starting point of the spiral arm and the origin must meet the requirements. Then, re-evaluate the reassigned position. If it still returns True, increase the size of the spiral growth rate 'b' found in the bat population by 0.01 each time until the Euclidean distance between any two array elements is greater than half a wavelength, i.e., when the spacing judgment returns False, stop increasing.

[0054] If a is greater than half the wavelength, it means that the distance between the starting point and the origin of the spiral arm meets the requirements. At this time, if the spacing does not meet the requirements, it must be because the distance between the array elements between the spiral arms is too close. At this time, directly increase the size of the spiral growth rate b found in the bat population, increasing it by 0.01 each time, until the spacing judgment returns False, then stop increasing.

[0055] When the spacing check first returns False:

[0056] This indicates that the distance between any array elements is greater than half a wavelength, which meets the spacing requirement, so no adjustment is needed.

[0057] Furthermore, S6 specifically refers to:

[0058] When the array elements meet the spacing requirements, the orientation pattern of the arrangement of each bat in the bat population is obtained according to the above calculation formulas for array factor and fitness function, and the fitness function of the corresponding arrangement position is determined; the current iteration number, fitness function, intercept parameter a, spiral growth rate b, and the corresponding adjacent array element spacing parameters on the two subarray spirals are stored and printed.

[0059] Furthermore, S7 specifically refers to:

[0060] If the bat algorithm does not reach the maximum number of iterations, it proceeds to S5 for the next iteration search. If and only if the fitness function in this iteration is less than the previously stored optimal fitness function, the global optimal fitness function is modified to the fitness function of this iteration, and the position of the globally optimal bat individual is adjusted to the position found by the bat in this iteration; otherwise, no modification is made. When the bat algorithm reaches the maximum number of iterations, the current best fitness function and the corresponding bat search position are obtained, which corresponds to the optimal array element arrangement position.

[0061] This scheme is a multi-constraint problem. The fitness function is the peak sidelobe level. The minimum element spacing is constrained to half a wavelength and the maximum polar radius is fixed for the solution.

[0062] Compared with the prior art, the present invention has the following advantages:

[0063] This invention employs a spiral array configuration with two subarrays interspersed in a spiral pattern. By optimizing the intercept parameter between the starting point and the pole of the spiral, the spiral growth rate, and the spacing between adjacent array elements on each subarray spiral using the bat algorithm, the optimal solution for the multi-arm spiral array structure is obtained. This significantly suppresses the peak sidelobe level of small-to-medium scale array antennas with fewer array elements, providing an effective solution for the current poor optimization effect and lack of design ideas in multi-arm spiral arrays. This invention is of great significance for the practical application of antenna systems.

[0064] This invention can significantly reduce peak sidelobe levels, making the selection of the number of array elements in multi-arm spiral arrays more flexible. This invention is not limited to a fixed number of array elements and can be used to expand small and medium-sized array antennas of different scales. Attached Figure Description

[0065] Figure 1 This is a flowchart of the design method of the present invention.

[0066] Figure 2 This is a schematic diagram of the structure of the invented array antenna.

[0067] Figures 3(a) and 3(b) show the two-dimensional planar radiation pattern and the three-dimensional radiation pattern of the preferred embodiment of the 37-element array antenna after optimization in the simulation experiment of the present invention, respectively. Figure 3(c) shows the three-dimensional radiation pattern of this preferred embodiment. Two-dimensional slices on a plane.

[0068] Figure 4 The convergence curves of the structure of this invention using the bat algorithm with a population size of 100 and an iteration count of 500 are shown in the figure. The average convergence curve is the total average convergence curve of the ten independent experiments.

[0069] Figure 5 The results of the psll test of the array structure of the present invention in multiple independent repeated experiments are shown.

[0070] Figure 6 This is a schematic diagram of the array antenna structure when the number of array elements is 16.

[0071] Figure 7 This is a schematic diagram of the array antenna structure when the number of array elements is 92. Detailed Implementation

[0072] To further illustrate the technical solution of the present invention, the present invention will be further described below through embodiments.

[0073] This embodiment of a subarray-level aperiodic small-scale array antenna includes:

[0074] A multi-armed spiral is obtained by rotating the Archimedes spiral as the parent spiral in sequence.

[0075] The multi-arm spiral is composed of two types of sub-array spirals interspersed with each other. Each type of sub-array spiral has array elements defined on it, and different numbers of array elements and spacing between adjacent array elements are used. All sub-array spirals are equidistant from the origin, and the spiral growth rate of the two types of sub-array spirals is the same.

[0076] The Bat Algorithm is used to optimize small-scale, non-periodic array antennas at the subarray level and determine the optimal solution.

[0077] Among them, the two types of subarray spirals are evenly distributed in the azimuth angle within the plane.

[0078] The optimal spacing between adjacent array elements is determined by the bat algorithm. The polar angle is then determined by the optimal spacing between adjacent array elements, thereby determining the arrangement position of the array elements.

[0079] The optimal solution includes the intercept parameter between the starting point of the subarray spiral and the pole, the spiral growth rate, and the spacing between adjacent elements on different subarray spirals.

[0080] This embodiment presents a design method for a subarray-level aperiodic small-scale array antenna, such as... Figure 1 As shown, it includes the following steps:

[0081] S1. Determine the number of spiral arms in a multi-armed spiral;

[0082] S2. By assigning different numbers of array elements to different subarray spirals, the number of each subarray spiral is determined;

[0083] S3. Generate random initialization data;

[0084] S4. Establish a reference model of the multi-armed spiral structure, determine the arrangement position of the array elements and calculate the initial fitness function according to the different positions searched by each bat in the random initialization data.

[0085] S5. Start the iteration. After each iteration, the distance between the positions searched by each bat will be judged. If the distance requirement is met, proceed directly to S6; otherwise, adjust the search position until the distance requirement is met, and then proceed to S6.

[0086] S6. Calculate the orientation pattern of the arrangement of each bat, determine the fitness function of the corresponding arrangement position, and store the relevant data;

[0087] S7. If the bat algorithm has not reached the maximum number of iterations, proceed to S5 for the next iteration search; otherwise, obtain the bat search position corresponding to the current best fitness function, which corresponds to the best array element arrangement position.

[0088] Specifically, the spacing requirement is as follows: the spacing between adjacent array elements on the subarray spiral is greater than half a wavelength, and the spacing between any array elements in the entire multi-arm spiral arrangement is also greater than half a wavelength.

[0089] The spacing determination is specifically as follows: after obtaining the arrangement positions of all array elements, the Euclidean distance between any two array elements is stored in matrix form. The elements on the diagonal of the matrix are filled with infinity, and then a determination is made. If there is an Euclidean distance between two array elements that is less than half a wavelength, then an adjustment is made; otherwise, no adjustment is made.

[0090] If the Euclidean distance between two array elements is less than half a wavelength: verify whether the intercept parameter 'a' between the starting point of the subarray spiral and the pole found by the bat population is greater than half a wavelength; if 'a' is less than half a wavelength, first set it directly equal to half a wavelength plus a random small perturbation greater than 0 and less than 0.1 times the wavelength. At this time, the distance between the starting point of the spiral arm and the origin must meet the requirements. Then, re-evaluate the reassigned position. If there are still two array elements with an Euclidean distance less than half a wavelength, increase the spiral growth rate 'b' found in the bat population by 0.01 each time until the Euclidean distance between any two array elements is greater than half a wavelength, then stop increasing; if 'a' is greater than half a wavelength, directly increase the spiral growth rate 'b' found in the bat population by 0.01 each time until there are no two array elements with an Euclidean distance less than half a wavelength, then stop increasing.

[0091] In this embodiment, the fitness function is defined as the peak sidelobe level, while the minimum element spacing is constrained to half a wavelength and the maximum polar radius is fixed for the solution.

[0092] Example 1

[0093] This embodiment uses a 37-element array antenna as an example to further explain the above method.

[0094] like Figure 2As shown, this embodiment uses the designed heterogeneous subarray spiral structure to optimize the 37-element array antenna. The specific steps are as follows:

[0095] Step 1: First, place an array element at the origin. Then, based on the total number of array elements, determine that the number of spiral arms of the multi-armed spiral is 6. Sub-array spiral 1 and sub-array spiral 2 each have three spiral arms.

[0096] Step 2: Determine the number of array elements allocated on a single spiral arm of subarray spiral 1 and subarray spiral 2 to be 5 and 7 respectively.

[0097] Step 3: Calculate the intercept parameter 'a' from the starting point of the spiral to the pole, the spiral growth rate 'b', and the spacing between adjacent elements on the two types of subarray spirals (…). ~ (), ~ A total of 12 optimization dimensions were initialized.

[0098] Step 4: Establish a reference model for the heterogeneous subarray spiral structure. Based on the different positions searched by each bat in the initial data, determine the arrangement of array elements and calculate the initial fitness function.

[0099] The array factor of this spiral array can be expressed as:

[0100] ;

[0101] Subarray Spiral 1 The polar angle corresponding to the first element on the spiral arm is:

[0102] , ( =0, 1, 2);

[0103] Next, determine the subsequent polar angles on the n1th spiral arm of subarray spiral 1.

[0104] Starting from the current position of the polar angle of the array element, increase the polar angle by 0.01, calculate the rectangular coordinate position of the array element after the increase, and compare it with the position before the increase. The Euclidean distance between the later array element and the previous array element satisfies the following formula:

[0105] , ( =0, 1, 2, 3);

[0106] At this point, the polar angle of the next array element is determined to be the polar angle that continues to increase from the current position.

[0107] After successively determining the polar angle of each element on each spiral arm, the formula can be used to... Find the corresponding polar radius.

[0108] Since it is desired that the spiral arms of subarray spiral 2 can be interspersed among the spiral arms of subarray spiral 1, therefore:

[0109] Subarray Spiral 2nd The polar angle corresponding to the first element on the spiral arm is:

[0110] , ( =0, 1, 2);

[0111] The subsequent methods for calculating the polar angle and polar radius are similar to those for subarray spiral 1. Starting from the current polar angle position of the array element, the polar angle is increased by 0.01. The rectangular coordinate position of the array element after the increase is calculated and compared with that before the increase. The Euclidean distance between the later array element and the previous array element satisfies the following equation:

[0112] , ( =0, 1, 2, 3, 4, 5);

[0113] At this point, the polar angle of the next array element is determined to be the polar angle that continues to increase from the current position. Among these, and Representing the second subarray spiral respectively The first spiral arm Each element and the first The planar coordinate positions represented by each array element.

[0114] Step 5: Start iteration. After each iteration, the distance between the positions searched by each bat will be judged (including initialization). If the distance requirement is met, proceed directly to S6; otherwise, adjust the search position until the requirement is met, and then proceed to S6.

[0115] Step 6: Calculate the orientation pattern of the arrangement of each bat, determine the fitness function of the corresponding arrangement position, and store the relevant data;

[0116] Step 7: If the bat algorithm has not reached the maximum number of iterations, proceed to S5 for the next iteration search; otherwise, obtain the current best fitness function and the corresponding bat search position, which corresponds to the best array element arrangement position.

[0117] The effectiveness of this embodiment can be further illustrated by the following simulation:

[0118] Experimental platform: Intel Core i5-1135G7 processor, 64-bit operating system Windows 11 Home Chinese Edition with a base frequency of 2.40GHz, Python 3.11, PyCharm Community Edition 2024.3.5.

[0119] (1) Simulation parameters

[0120] Bat population Maximum number of iterations Loudness parameter Pulse emission rate .

[0121] Simulation conditions: Total number of array elements The spacing between array elements must not be less than half a wavelength, and the maximum polarization is fixed at 2.00. 2.15 2.30 2.45 2.60 .

[0122] (2) Simulation content

[0123] Experimental Results: Figures 3(a) and 3(b) show the two-dimensional and three-dimensional radiation patterns of the optimized 37-element array antenna in the simulation experiment, respectively. Figure 3(c) shows the three-dimensional radiation pattern of this optimized example. Two-dimensional slices on a plane. Figure 4 The structure of this invention, when the population size is 100, the number of iterations is 500, the number of array elements is fixed at 37, and different maximum polar diameters are fixed, differs from traditional multi-armed spirals with different arm numbers. Comparing the line graphs, Arm2 represents a two-armed helix, Arm3 represents a three-armed helix, and so on. Figure 5 This is a convergence curve diagram of ten independent experiments conducted on the structure of the present invention with the maximum radius constraint fixed at 2.45 times the wavelength. The average convergence curve is the total average convergence curve of the ten independent experiments. Table 1 shows the correspondence between different array structures and their corresponding number of independent baselines and redundancy when the number of array elements is 37.

[0124] Table 1. Correspondence between the number of independent baselines and redundancy.

[0125] Arm2 Arm3 Arm4 Arm6 Arm9 Arm12 My Construction Number of independent baselines 342 666 342 324 666 324 654 Redundancy 1.95 1.00 1.95 2.06 1.00 2.06 1.02

[0126] (3) Analysis

[0127] Depend on Figure 4 It is evident that when the maximum polarity is greater than 2.15 times the wavelength, the array structure described in this invention exhibits superior PSLL optimization potential compared to other conventional multi-arm spiral array structures. Based on the suppression effect on peak sidelobe levels, this invention > conventional multi-arm spiral with an odd number of arms > conventional multi-arm spiral with an even number of arms. This is because an even number of arms inevitably introduces baseline redundancy, while selecting an odd number of arms breaks this symmetry, resulting in a non-redundant array.

[0128] Referring to Table 1, it can be seen that even when choosing an even number of arms, if the number of arms is appropriate, space utilization can be guaranteed, and even with higher redundancy, there is still good optimization potential. For example, for a 37-element multi-arm spiral, when the number of spiral arms is selected as 6, although the redundancy is high, the optimization result is only 1.08 dB worse than the optimal result with an odd number of arms. Considering that in some cases, forcibly choosing an odd number of arms to achieve a lower peak sidelobe level may not yield ideal results, the heterogeneous subarray multi-arm spiral array proposed in this invention allows the array to convert the traditional even-numbered multi-arm spiral into a combination of two different odd-numbered multi-arm spirals while selecting an even number of arms, thereby obtaining a better PSL. Among the five fixed apertures, when the fixed maximum aperture is 2.45... At that time, the array structure described in this invention has the lowest psll, reaching -22.60dB.

[0129] according to Figure 5 In multiple independent repeated experiments, the worst PSLL result of the array structure described in this invention was -19.79dB, the best PSLL result was -22.98dB, and the average PSLL result was -22.26dB. It can be found that the average PSLL iterative image is closely related to the best result image. In 500 iterations, the average PSLL is only 0.72dB lower than the best PSLL, indicating that the worst PSLL is only an extreme case. This fully demonstrates that the array structure has great optimization potential and strong optimization stability.

[0130] Figure 6 and Figure 7 For example, when the number of array elements is selected as 16 and 92, the preferred examples of the extended application of the method described in this invention are -18.52dB and -25.24dB, respectively. Specifically, when the number of array elements is selected as 92, more array elements can be placed at the center of the array structure, reducing the optimization dimensionality of the algorithm while obtaining better optimization results.

[0131] The foregoing has shown and described the main features and advantages of the present invention. It will be apparent to those skilled in the art that the present invention is not limited to the details of the exemplary embodiments described above, and that the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, it is intended that all variations falling within the meaning and scope of equivalents of the claims be included within the present invention.

[0132] Furthermore, it should be understood that although this specification describes embodiments, not every embodiment contains only one independent technical solution. This narrative style is merely for clarity. Those skilled in the art should consider the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A subarray-level aperiodic small-scale array antenna, characterized in that, include: A multi-armed spiral is obtained by rotating the Archimedes spiral as the parent spiral in sequence. The multi-arm spiral is composed of two types of sub-array spirals interspersed with each other. Each type of sub-array spiral has array elements defined on it, and different numbers of array elements and spacing between adjacent array elements are used. All sub-array spirals are equidistant from the origin, and the spiral growth rate of the two types of sub-array spirals is the same. The Bat Algorithm is used to optimize small-scale, non-periodic array antennas at the subarray level and determine the optimal solution.

2. The subarray-level aperiodic small-scale array antenna according to claim 1, characterized in that, The two types of subarray spirals are uniformly distributed in the azimuth angle within the plane.

3. The subarray-level aperiodic small-scale array antenna according to claim 1, characterized in that, The optimal solution for the spacing between adjacent array elements is determined by the bat algorithm. The polar angle is then determined by the optimal spacing between adjacent array elements, thereby determining the arrangement position of the array elements.

4. The subarray-level aperiodic small-scale array antenna according to claim 1, characterized in that, The optimal solution includes the intercept parameter between the starting point of the subarray spiral and the pole, the spiral growth rate, and the spacing between adjacent elements on different subarray spirals.

5. A design method for a subarray-level aperiodic small-scale array antenna according to any one of claims 1-4, characterized in that, Includes the following steps: S1. Determine the number of spiral arms in a multi-armed spiral; S2. By assigning different numbers of array elements to different subarray spirals, the number of each subarray spiral is determined; S3. Generate random initialization data; S4. Establish a reference model of the multi-armed spiral structure, determine the arrangement position of the array elements and calculate the initial fitness function according to the different positions searched by each bat in the random initialization data. S5. Start the iteration. After each iteration, the distance between the positions searched by each bat will be judged. If the distance requirement is met, proceed directly to S6; otherwise, adjust the search position until the distance requirement is met, and then proceed to S6. S6. Calculate the orientation pattern of the arrangement of each bat, determine the fitness function of the corresponding arrangement position, and store the relevant data; S7. If the bat algorithm has not reached the maximum number of iterations, proceed to S5 for the next iteration search; otherwise, obtain the bat search position corresponding to the current best fitness function, which corresponds to the best array element arrangement position.

6. The design method for a subarray-level aperiodic small-scale array antenna according to claim 5, characterized in that, The spacing requirement is specifically as follows: the spacing between adjacent array elements on the subarray spiral is greater than half a wavelength, and the spacing between any array elements in the entire multi-arm spiral arrangement is also greater than half a wavelength.

7. The design method for a subarray-level aperiodic small-scale array antenna according to claim 6, characterized in that, The spacing determination is specifically as follows: After obtaining the arrangement positions of all array elements, store the Euclidean distance between any two array elements in matrix form, fill the diagonal elements of the matrix with infinity, and then make a judgment. If there is an Euclidean distance between two array elements that is less than half a wavelength, make an adjustment; otherwise, do not make any adjustment. If the Euclidean distance between two array elements is less than half a wavelength: verify whether the intercept parameter 'a' between the starting point of the subarray spiral and the pole found by the bat population is greater than half a wavelength. If 'a' is less than half the wavelength, first set it directly equal to the sum of half the wavelength and a random small perturbation greater than 0 and less than 0.1 times the wavelength. At this point, the distance between the starting point of the spiral arm and the origin will definitely meet the requirements. Then, re-evaluate the reassigned position. If there are still two array elements whose Euclidean distance is less than half the wavelength, increase the size of the spiral growth rate 'b' found in the bat population by 0.01 each time until the Euclidean distance between any two array elements is greater than half the wavelength, then stop increasing. If 'a' is greater than half the wavelength, directly increase the size of the spiral growth rate 'b' found in the bat population by 0.01 each time until there are no two array elements whose Euclidean distance is less than half the wavelength, then stop increasing.

8. A design method for a subarray-level aperiodic small-scale array antenna according to any one of claims 5-7, characterized in that, The fitness function is defined by using the peak sidelobe level as the fitness function, while constraining the minimum element spacing to half a wavelength and fixing the maximum polar radius for the solution.

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