Improved differential evolution depositions optimization method based on virtual interference pattern

Abstract

An improved differential evolutionary sparse distribution optimization method based on virtual interference patterns is proposed. This invention relates to sparse distribution optimization methods for spaceborne antennas. The purpose of this invention is to solve the problem that the limited number of uniform phased array elements due to the limited load of spaceborne antennas restricts the antenna performance. The process is as follows: 1. Create an initial population, with each population having N... p An individual represents one of the M radii corresponding to the antenna array ring; the population represents the N radii corresponding to the antenna array ring. p ×M radii; N p For all individuals in a population; 2. Calculate the fitness value of each individual; Fitness value F(d1,d2,...,d...) N The value is defined as the average of the main lobe and side lobe gain ratios on the plane and the θ = 0° plane; III. Repeat step II to obtain N. p The population is analyzed by first determining the fitness value of each individual, then retaining the individual with the optimal fitness value; fourth, a differential operation is performed on the population to obtain the optimal individual, which is the optimal antenna array. This invention is applicable to the field of aerospace technology.

Description

Technical Field

[0001] This invention relates to a method for optimizing the sparse distribution of spaceborne antennas, and relates to the field of aerospace technology. Background Technology

[0002] As terrestrial mobile communication technology matures, the future direction of communication technology is gradually shifting towards satellite communication. Compared to geosynchronous orbit satellites (GEO), low earth orbit satellites (LEO) have advantages such as faster launch speed, mass production, lower cost, and lower link loss.

[0003] The rapid development of low-Earth orbit (LEO) satellite constellations has placed higher demands on satellite communication technology. Among these, onboard antenna technology plays a crucial role in both feeder and user links, influencing transmission rates, link capacity, and the satellite's Earth coverage range. Due to the relatively short distance and high speed of LEO satellites relative to the ground, they often employ multi-beam antennas to achieve ground coverage. By using spatial division multiplexing to reuse spectrum, system capacity can be significantly increased without increasing spectrum usage or power costs.

[0004] A multi-beam antenna is a spaceborne antenna that uses a single antenna array to generate multiple parallel beams, each covering a specific service area, collectively achieving the goal of covering the target within that service area. Multi-beam antennas come in three basic forms: reflector type, lens type, and phased array type. Among these, phased array antennas can flexibly control the beam shape by adjusting the phase and amplitude of the array elements, and they also have a smaller size and lighter weight. Therefore, phased array antennas are frequently used in low-Earth orbit satellites for signal transmission.

[0005] Low-Earth orbit (LEO) satellites move at high speeds relative to the ground and are relatively close to the ground. This requires LEO satellite phased array antennas to have better pointing capabilities, i.e., a smaller main lobe width and a higher main-side lobe gain ratio. The main lobe width is inversely proportional to the antenna aperture; a smaller main lobe width means a larger antenna aperture, i.e., more antenna elements. This will lead to a significant increase in the size, weight, and production cost of the spaceborne antenna.

[0006] To address the aforementioned issues, it is necessary to study array antennas with sparse distribution characteristics. Compared to a periodic full array with the same aperture, a sparse array, although exhibiting a lower antenna gain, maintains almost the same main beamwidth. Furthermore, the reduced number of array elements significantly lowers the production cost of the antenna system, making the feeding system easier to implement and reducing the failure rate. For sparse arrays, it is essential to study the element arrangement of sparse phased array antennas, finding the optimal element position distribution for a given aperture size. This requires developing a sparse synthesis algorithm that can achieve the optimal element position distribution for antenna performance. Summary of the Invention

[0007] The purpose of this invention is to solve the problem that the limited number of uniform phased array elements caused by the limited load of spaceborne antennas leads to the limitation of antenna performance, and proposes an improved differential evolution sparse distribution optimization method based on virtual interference patterns.

[0008] The specific process of the improved differential evolution sparse distribution optimization method based on virtual interference pattern is as follows:

[0009] Step 1: Create an initial population, with N cells per population. p Individual;

[0010] Individuals represent the M radii [ρ1, ρ2, ..., ρ] corresponding to the antenna array ring. i ,…,ρ M ];

[0011] The population represents N corresponding to the circular ring of the antenna array. p ×M radii;

[0012] N p For all individuals in a population;

[0013] Step 2: Calculate the individual fitness value;

[0014] Fitness value F(d1,d2,...,d N ) is defined as The average value of the main lobe and side lobe gain ratios on the plane and the θ = 0° plane;

[0015] in, Let θ be the angle between the projection of a point in the space containing the xyz rectangular coordinate axes onto the xOy plane and the x-axis, and let θ be the pitch angle of the point in the space containing the xyz rectangular coordinate axes onto the xOy plane. N The position of the antenna array element;

[0016] Step 3: Repeat step 2 to obtain N. p For each individual fitness value, retain the individual corresponding to the optimal fitness value;

[0017] Step 4: Perform differential operations on the population to obtain the optimal individual in the population, which is the optimal antenna array.

[0018] The beneficial effects of this invention are as follows:

[0019] This invention realizes the sparse distribution optimization of a circular planar sparse distribution array. Compared with the traditional sparse distribution optimization algorithm, the sparse distribution array obtained by this algorithm has a better main lobe-side lobe gain ratio.

[0020] This invention addresses the issue of poor performance of uniform arrays due to limited payload in spaceborne antennas. It investigates a sparse array optimization algorithm for planar sparse arrays, aiming to generate array element arrangements with superior antenna performance within a given number of elements. This invention employs an improved differential evolution algorithm, using differential evolution preprocessing and post-processing before and after the algorithm to ensure the newly generated population meets the minimum spacing requirement. In the fitness calculation within the differential evolution algorithm, this invention uses a virtual interference beamforming algorithm, unlike traditional amplitude-weighted and adaptive beamforming algorithms. This beamforming algorithm calculates antenna element weights by setting virtual interference sources and using a minimum variance distortion-free response, resulting in an antenna pattern with a superior main-sidelobe gain ratio.

[0021] This invention employs an improved differential evolution algorithm to optimize the sparse distribution of a circular planar array. Unlike traditional differential evolution algorithms, the improved algorithm performs a pre-operation before population mutation, processing the radius vectors corresponding to individuals in the population to obtain indirect radius vectors. Subsequent mutations and crossovers are performed on these indirect radius vectors. After crossover, a post-operation is performed, processing the indirect radius vectors to obtain the actual radius vectors, which are then used as the basis for selecting between the new and original populations. Through these pre- and post-operations, it is ensured that the radius vectors corresponding to individuals in the newly generated population still satisfy the minimum spacing constraint.

[0022] In this invention, the beamforming algorithm used to calculate the fitness function during differential evolution is a virtual interference beamforming algorithm. Conventional weighted beamforming algorithms reduce array sidelobes by lowering the main lobe gain, but this doesn't significantly improve the main-sidelobe gain ratio. Adaptive beamforming algorithms, on the other hand, require using received signal errors for beamforming. The virtual interference beamforming algorithm proposed in this invention sets virtual interference sources in the array's sidelobe regions, uses a minimum variance distortion-free response algorithm to obtain array weights, and employs a digital beamforming architecture. This significantly improves the main lobe gain of the obtained antenna pattern, solving the problem of limited antenna performance caused by the limited number of elements in a uniform phased array due to spaceborne antenna load constraints. Attached Figure Description

[0023] Figure 1 An optimized model for a circular ring-shaped sparsely distributed planar array;

[0024] Figure 2 The flowchart of the improved differential evolution algorithm;

[0025] Figure 3 Here is the flowchart of the virtual interference beamforming algorithm;

[0026] Figure 4 The optimal array element arrangement is obtained by using an improved differential evolution sparse distribution optimization algorithm based on virtual interference pattern synthesis;

[0027] Figure 5 The three-dimensional pattern of the obtained optimal array;

[0028] Figure 6 The radiation pattern of the plane at θ = 0° for the obtained optimal array.

[0029] Figure 7 To obtain the optimal array A planar orientation diagram. Detailed Implementation

[0030] Specific Implementation Method 1: This implementation method is based on the improved differential evolution sparse distribution optimization method of virtual interference pattern. The specific process is as follows:

[0031] Step 1: Create an initial population suitable for differential evolution, with each population having N... p Individual;

[0032] Individuals represent the M radii [ρ1, ρ2, ..., ρ] corresponding to the antenna array ring. i ,…,ρ M ];

[0033] The population represents N corresponding to the circular ring of the antenna array. p ×M radii;

[0034] N p For all individuals in a population;

[0035] Step 2: Calculate the individual fitness value;

[0036] Calculating the fitness function provides a measure of population evolution;

[0037] Fitness value F(d1,d2,...,d N ) is defined as The average value of the main lobe and side lobe gain ratios on the plane and the θ = 0° plane;

[0038] in, Let θ be the angle between the projection of a point in the space containing the xyz rectangular coordinate axes onto the xOy plane and the x-axis, and let θ be the pitch angle of the point in the space containing the xyz rectangular coordinate axes onto the xOy plane. N The positions of the antenna array elements can be calculated from individual populations;

[0039] Step 3: Repeat step 2 to obtain N. p For each individual fitness value, retain the individual with the best fitness value (the one with the largest fitness value);

[0040] Step 4: Perform differential operations on the population to obtain the optimal individual in the population, which is the optimal antenna array.

[0041] Specific Implementation Method Two: This implementation method differs from Specific Implementation Method One in that: in step one, an initial population suitable for differential evolution is created, and each population has N... p Individual;

[0042] Individuals represent the M radii [ρ1, ρ2, ..., ρ] corresponding to the antenna array ring. i ,…,ρ M ];

[0043] The population represents N corresponding to the circular ring of the antenna array. p ×M radii;

[0044] The specific process is as follows:

[0045] Step 11: The research object is a planar concentric ring array with unequal spacing between the rings and the array elements are randomly distributed on the rings;

[0046] Assume the antenna aperture is R, the number of rings is M, and the number of array elements in one quadrant is N;

[0047] The angles of each array element are The radii of each array element are [ρ1, ρ2, ..., ρ i ,…,ρ M ];

[0048] in, For the i-th ring, the th The angle of each array element, ρ i Let be the radius of the i-th annular array element;

[0049] To prevent mutual coupling between array elements, the distance between each concentric ring should not be less than d. c d c Distance threshold;

[0050] Step 1 and 2: Randomly generate [0, S] ρ The M indirect radii [x1, x2, ..., x] i ,…xM ];

[0051] Among them, S ρ S is the remaining radius length. ρ =R-(M-1)×d c ;

[0052] Step 13: Calculate the obtained indirect radius x i Sort by ascending order, then by ρ i =x i +(i-1)×d c Generate radius vector [ρ1,ρ2,…,ρ i ,…,ρ M (The element positions are represented in polar coordinates). This yields the radius vector that satisfies the minimum spacing requirement, which serves as the radius for an individual in the initial population. Each population has N elements. p Individual.

[0053] The other steps and parameters are the same as in Specific Implementation Method 1.

[0054] Specific Implementation Method Three: This implementation method differs from Specific Implementation Method One or Two in that: in step two, the individual fitness value is calculated;

[0055] Calculating the fitness function provides a measure of population evolution;

[0056] Fitness value F(d1,d2,...d) N ) is defined as The average value of the main lobe and side lobe gain ratios on the plane and the θ = 0° plane;

[0057] in, Let θ be the angle between the projection of a point in the space containing the xyz rectangular coordinate axes onto the xOy plane and the x-axis, and let θ be the pitch angle of the point in the space containing the xyz rectangular coordinate axes onto the xOy plane. N The positions of the antenna array elements can be calculated from individual populations;

[0058] The specific process is as follows:

[0059] The process for determining the main lobe and sidelobe gain ratio is as follows:

[0060] Step 21: Obtain the coordinates of the array element positions based on the radius corresponding to the current population;

[0061] Step 22: The virtual interference pattern synthesis method is used to process the position coordinates of the array elements to generate an antenna pattern. Each antenna pattern obtains a main lobe-side lobe gain ratio, which is an individual fitness value.

[0062] Other steps and parameters are the same as in specific implementation method one or two.

[0063] Specific Implementation Method Four: This implementation method differs from Specific Implementation Methods One to Three in that: in step two-one, the coordinates of the array element positions are obtained based on the radius corresponding to the current population; the specific process is as follows:

[0064] To ensure a reasonable number of array elements on each ring, the array elements are allocated according to the radius of each ring, that is, according to the ratio of the ring's circumference. The formula for calculating the number of array elements on the i-th ring is as follows:

[0065]

[0066] Where, N i Let N be the number of array elements on the i-th ring, and N be the number of array elements in one quadrant.

[0067] Subsequently, to prevent mutual coupling between array elements on the ring, the arc length between array elements should be greater than d. c ;

[0068] The angular difference between array elements on the same ring is calculated based on the radius of each ring.

[0069] ang_interval i =d c / ρ i

[0070] Among them, ang_interval i Let be the angular difference between the array elements on the i-th ring;

[0071] After obtaining the angular difference between the array elements, calculate the angle difference on the i-th ring. The angle of each array element; the specific process is as follows:

[0072] Based on ang_interval i Calculate the remaining angle S on the i-th ring. αi =π / 2-(N) i -1)×ang_interval i ;

[0073] In [0, S αi Randomly generate N intervals i An indirect angle [ang1, ang2, ... ang] Ni ];

[0074] [ang1,ang2,…ang] Ni Sort in ascending order;

[0075] Based on ang_interval i And the indirect angles after sorting [ang1,ang2,…ang]Ni Calculate the i-th ring on the i-th ring. The angle of each array element, i.e.

[0076]

[0077] in, N i The total number of array elements in the i-th ring;

[0078] Calculate the angles of all array elements on the i-th ring, and calculate the angles of all array elements on the M rings. This gives us the result that makes the arc length between array elements greater than d. c The array element angles (polar coordinates);

[0079] The rectangular coordinates of the array elements are obtained based on the conversion relationship between polar coordinates and rectangular coordinates, and are used for array pattern calculation.

[0080] The other steps and parameters are the same as those in one of the specific implementation methods one to three.

[0081] Specific Implementation Method Five: This implementation method differs from Specific Implementation Methods One through Four in that the rectangular coordinates of the array elements are calculated using the following formula:

[0082]

[0083] in, For the i-th ring, the th The angle of each array element, ρ i Let be the radius of the i-th annular array element; The coordinates of the array elements are rectangular coordinates.

[0084] The other steps and parameters are the same as those in specific implementation methods one through four.

[0085] Specific Implementation Method Six: This implementation method differs from Specific Implementation Methods One to Five in that: in step two, a virtual interference pattern synthesis method is used to process the coordinates of the array elements to generate an antenna pattern. Each antenna pattern obtains a main lobe-side lobe gain ratio, which is an individual fitness value; the specific process is as follows:

[0086] The basic idea of ​​virtual interference is to set Z interferences in the sidelobe region. The number Z should be large enough to form a zero limit and only achieve the effect of suppressing the sidelobes. Since the fitness function only considers... The average value of the main lobe and side lobe gain ratios on the plane and the θ = 0° plane, therefore in Z interference sources are set on both the plane and the plane where θ = 0°;

[0087] set up The angles of the interference sources on the plane are [θ1, θ2, ... θ ZThe angle of the interference source on the plane θ = 0° is...

[0088] Based on the intensity of the interference source power and noise power, as well as the direction of interference, the array pattern is obtained using the Minimum Variance Distortion-Free Response (MVDR) algorithm.

[0089] Calculate the main lobe range of the antenna based on the radiation pattern, and assign the interference value within the main lobe range to 0;

[0090] Regarding interference in the sidelobe region, if the voltage level at the interference point is higher than the set voltage level, the interference is amplified; if the voltage level at the interference point is lower than the set voltage level, the interference is weakened.

[0091] The process is iterated until the optimal main lobe-side lobe gain ratio is obtained and output as the fitness function.

[0092] Step 22A, in A targets are set on the plane and the plane where θ = 0°;

[0093] set up The target on the plane points at an angle of [θ] 01 ,θ 02 ,…,θ 0p ,…,θ 0A The target pointing angle on the plane θ = 0° is...

[0094] Calculate the target pointing angle and [θ 01 ,θ 02 ,…,θ 0p ,…,θ 0A The guiding vector and the weighting vector are initialized;

[0095] The specific process is as follows:

[0096] Target pointing angle and [θ 01 ,θ 02 ,…,θ 0p ,…,θ 0A The method for calculating the guiding vector is shown in the following formula:

[0097]

[0098] in, The directional vector; j is the imaginary unit, j 2 =-1; k is the wave number, k = 2π / λ, λ is the wavelength. The coordinates of the array elements are rectangular.

[0099] For the plane where θ = 0°, θ takes zero in the guiding vector, while Then take the corresponding target pointing angle.

[0100] for Plane, guiding vector Take zero, while θ takes the corresponding target pointing angle [θ 01 ,θ 02 ,…,θ 0p ,…,θ 0A ];

[0101] Direct each target and [θ 01 ,θ 02 ,…,θ 0p ,…,θ 0A The target guiding vector a0 is obtained by adding the guiding vectors of the two vectors. The target guiding vector a0 is used to initialize the weighting vector W.

[0102] Since this paper studies multibeamforming, the target pointing on the θ = 0° plane is... The target on the plane points to [θ] 01 ,θ 02 ,…,θ 0p ,…,θ 0A Therefore, the target pointing guidance vector used when calculating the value should also be the sum of the guidance vectors of each target.

[0103] The sum of the guiding vectors on the plane θ = 0° is shown in the following formula:

[0104]

[0105] The sum of the guiding vectors on the plane is shown in the following equation:

[0106]

[0107] The sum of the steering vectors of the target beams on the two planes is shown in the following equation:

[0108]

[0109] The formula for initializing the weighted vector is shown below:

[0110]

[0111] Step 22B: Set the location of the interference source and initialize the interference power; the specific process is as follows:

[0112] There are Z interference sources on each research plane, with one interference source set at every 0.5 degrees.

[0113] set up The angles of the interference sources on the plane are [θ1=-90°, θ2=-89.5°,…θ Z =90°], while the angle of the interference source on the plane θ=0° is Z is 361;

[0114] The power of each interference source on the plane is

[0115] The power of each interference source on the θ=0° plane is

[0116] Initialize the interference power of each interference source on the θ = 0° plane Set to 0, initialize Interference power of each interference source on the plane It is 0; that is:

[0117]

[0118]

[0119] Step 2.2C: Begin iteration. Based on the weight vector W(k) obtained from the initialization, solve for the antenna patterns on the two planes respectively; the specific process is as follows:

[0120]

[0121]

[0122] Where, W(k) H is the conjugate of W(k), where W(k) is the weighted vector for the k-th iteration;

[0123] After obtaining the antenna pattern, the zero-power main lobe interval of the antenna pattern is calculated for subsequent updates of the interference power value.

[0124] Since this paper studies multibeamforming, the target pointing on the θ = 0° plane is... There are multiple main lobe regions on each plane; therefore, it is necessary to solve for the interval of each main lobe separately. A represents the number of main lobes on the study plane. The target on the plane points to [θ] 01 ,θ 02 ,…θ 0A There are multiple main lobe regions on each plane, therefore, it is necessary to solve for the interval of each main lobe separately, i.e., [θ]. L1 ,θ R1 ]、[θ L2 ,θ R2 ]…[θ LA ,θ RAA represents the number of main lobes on the research plane.

[0125] Step 22D: Update the interference power based on the main lobe interval; the specific process is as follows:

[0126] The method for updating the interference power is as follows:

[0127]

[0128]

[0129] For the interference source where θ = 0°:

[0130]

[0131] For, for Interference source:

[0132]

[0133] The decimal value of the expected sidelobe level yes The decimal value of the desired sidelobe level d(θ) q )yes

[0134] in, Let be the left boundary of the p-th main lobe interval on the plane where θ = 0°. Let θ be the right boundary of the p-th main lobe interval on the plane where θ = 0°. Lp (k) is The left boundary of the p-th main lobe interval on the plane, θ Rp (k) is The right boundary of the p-th main lobe interval on the plane. for The update power of the q-th interference source on the plane. Let be the update power of the q-th interference source on the plane θ = 0°. for The current power of the q-th interference source on the plane. Let θ be the current power of the q-th interference source on the plane where θ = 0°. q for The q-th interference source on the plane, Let η0 be the q-th interference source on the plane where θ = 0°, and let η0 be the iteration gain. yes d(θ q )for

[0135] Step 2.2E: Calculate the covariance matrix based on the magnitude of the interference power; the specific process is as follows:

[0136] The covariance matrix is ​​calculated as shown in the following formula:

[0137]

[0138] Among them, R xx (k+1) is the covariance matrix corresponding to the (k+1)th iteration, σ 2 Let I be the noise power, and I be the identity matrix. for The power magnitude of the q-th interference source in the plane at the (k+1)th iteration. Let be the power magnitude corresponding to the (k+1)th iteration of the q-th interference source on the θ=0° plane. Planar guiding vector for θ=θ q The guiding vector a(θ) on the plane q )for for The conjugate of a H (θ q ) is a(θ q The conjugate of ) and Z is the number of interference sources on a plane;

[0139] Step 2.2F: Update the weighted vector for the (k+1)th iteration based on the covariance matrix and the target guidance vector a0; the specific process is as follows:

[0140] The weighted vector for the (k+1)th iteration is calculated as follows:

[0141]

[0142] Step 22G, iterating from step 22C to step 22G (total) Next, get For each antenna pattern, a main-sidelobe gain ratio is obtained, and the optimal main-sidelobe gain ratio (the largest gain ratio) is taken as an individual fitness value.

[0143] The other steps and parameters are the same as those in specific implementation methods one through five.

[0144] Specific Implementation Method Seven: This implementation method differs from Specific Implementation Methods One through Six in that: in step four, a differential operation is performed on the population to obtain the optimal individual in the population, which is the optimal antenna array; the specific process is as follows:

[0145] Step 41: Preprocess all individuals in the population; the expression is:

[0146] x i =ρi -(i-1)×d c

[0147] Step 42: Perform mutation operations on the individual: The specific process is as follows:

[0148] To ensure that differentially mutated individuals still meet the minimum distance requirement, the differential evolution algorithm is improved; preprocessing with differential operations is required, which involves transforming the radius vector [ρ1, ρ2, ..., ρ] of the population individuals. i ,…,ρ M The process yields the indirect radius vector [x1, x2, ..., x]. i ,…,x M ], using indirect radius vectors to perform differential mutation operations;

[0149] For x i To perform a mutation operation, the expression is:

[0150]

[0151] in, These are the differentially mutated individuals generated. and These are two randomly selected individuals used for difference analysis. These are randomly selected individuals used for summation, and r1, r2, r3, and... They are all different; F is the mutation operator, a real constant value used to control the degree to which the difference variables are amplified; r1, r2, and r3 take values ​​ranging from 1 to N. p , For the first Individual, It is the number of iterations;

[0152] Step 4.3: Perform cross-operations on individuals: The specific process is as follows:

[0153] The crossover operation still uses the indirect radius vector;

[0154] The differentially mutated population obtained from the indirect radius vector is cross-crossed with the original indirect radius vector with a certain probability to generate a crossover population; that is, differentially mutated individuals... and target individual x i Crossover occurs at certain positions according to the crossover probability; after the crossover operation is completed, a difference operation is required for post-processing to process the resulting crossover population and obtain the actual radius vector from the indirect radius vector.

[0155] Step 4: Perform differencing on the individual data and then process it; the expression is:

[0156]

[0157] in, The target individual after the cross-operation; The radius is ;

[0158] After the crossover operation is completed, a difference operation post-processing is required to process the resulting crossover population and obtain the actual radius vector from the indirect radius vector.

[0159] Steps four and five involve selecting individuals; the specific process is as follows:

[0160] For the radius of step four And the radius ρ in step four one i Make a selection; the process is as follows:

[0161] Calculate the radius in step four. fitness value;

[0162] Calculate the radius ρ in step four. i fitness value;

[0163] The radius corresponding to the maximum fitness value is retained in the population.

[0164] Step 46: Repeat steps 2 to 4 until the maximum number of iterations is reached. Take the radius corresponding to the maximum fitness value in the population in the last iteration as the optimal individual in the population, which is the optimal antenna array obtained by the improved differential evolution sparse distribution optimization algorithm based on virtual interference pattern synthesis.

[0165] The other steps and parameters are the same as those in one of the specific implementation methods one to six.

[0166] This invention may have other embodiments. Without departing from the spirit and essence of this invention, those skilled in the art can make various corresponding changes and modifications according to this invention, but these corresponding changes and modifications should all fall within the protection scope of the appended claims.

Claims

1. An improved differential evolutionary sparse distribution optimization method based on virtual interference patterns, characterized in that: The specific process of the method is as follows: Step 1: Create the initial population. Each population has... Individual; Each individual represents one of the M radii corresponding to the antenna array ring. ; Population represents the antenna array ring corresponding to One radius; For all individuals in a population; Step 2: Calculate the individual fitness value; fitness value Defined as plane and The average value of the main lobe and side lobe gain ratio on the plane; in, for A point in the space containing the rectangular coordinate axes Projection on a plane and The included angle of the axis, for A point in the space containing the rectangular coordinate axes The pitch angle of the plane, The position of the antenna array element; Step 3: Repeat step 2 to obtain... For each individual fitness value, retain the individual corresponding to the optimal fitness value; Step 4: Perform differential operations on the population to obtain the optimal individual in the population, which is the optimal antenna array; In step two, the individual fitness value is calculated; fitness value Defined as plane and The average value of the main lobe and side lobe gain ratio on the plane; in, for A point in the space containing the rectangular coordinate axes Projection on a plane and The included angle of the axis, for A point in the space containing the rectangular coordinate axes The pitch angle of a plane, The position of the antenna array element; The specific process is as follows: The process for determining the main lobe and sidelobe gain ratio is as follows: Step 21: Obtain the coordinates of the array element positions based on the radius corresponding to the current population; Step 22: The virtual interference pattern synthesis method is used to process the position coordinates of the array elements to generate an antenna pattern. Each antenna pattern obtains a main lobe-side lobe gain ratio, which is an individual fitness value. In step four, the population is subjected to a differential operation to obtain the optimal individual in the population, which is the optimal antenna array; the specific process is as follows: Step 41: Preprocess all individuals in the population; the expression is: Step 42: Perform mutation operations on the individual: The specific process is as follows: right To perform a mutation operation, the expression is: （14） in, These are the differentially mutated individuals generated. and These are two randomly selected individuals used for difference analysis. These are randomly selected individuals used for summation, and... , , and They are all distinct, and F is the mutation operator; , , The value range is 1- , For the first Individual, ; It is the number of iterations; Step 4.3: Perform cross-operations on individuals: The specific process is as follows: Individuals with differential mutation and target individuals Crossing occurs at certain positions according to crossover probability; Step 4: Perform differencing on the individual data and then process it; the expression is: in, The target individual after the cross-operation; The radius is ; Steps four and five involve selecting individuals; the specific process is as follows: For the radius of step four and the radius of step four. Make a selection; the process is as follows: Calculate the radius in step four. fitness value; Calculate the radius in step four. fitness value; The radius corresponding to the maximum fitness value is retained in the population. Step 46: Repeat steps 2 to 4 until the maximum number of iterations is reached. Take the radius corresponding to the maximum fitness value in the population in the last iteration as the optimal individual in the population, which is the optimal antenna array.

2. The improved differential evolution sparse distribution optimization method based on virtual interference pattern according to claim 1, characterized in that: In step one, an initial population is created, and each population has... Individual; Each individual represents one of the M radii corresponding to the antenna array ring. ; Population represents the antenna array ring corresponding to One radius; The specific process is as follows: Step 11: The object is a planar concentric ring array with unequal spacing between the rings and the array elements are randomly distributed on the rings. Assume the antenna aperture is R, the number of rings is M, and the number of array elements in one quadrant is N; To prevent mutual coupling between array elements, the distance between each concentric ring should not be less than [amount missing]. , Distance threshold; Steps 1 and 2: Randomly generate [0, ... M indirect radii ; in, The remaining radius length, ; Step 13: Obtain the indirect radius Sort in ascending order, then sort by Generate radius vector This yields the radius vector that satisfies the minimum spacing requirement, which serves as the radius corresponding to an individual in the initial population. Each population has... Individual.

3. The improved differential evolution sparse distribution optimization method based on virtual interference pattern according to claim 2, characterized in that: In step two, the coordinates of the array element positions are obtained based on the radius corresponding to the current population; the specific process is as follows: The array elements are allocated according to the radius of each ring, that is, according to the ratio of the ring's circumference. The formula for calculating the number of array elements on the i-th ring is as follows: in, Let be the number of array elements on the i-th ring. The number of array elements in one quadrant; To prevent mutual coupling between array elements on the ring, the arc length between array elements should be greater than [missing information]. ; The angular difference between array elements on the same ring is calculated based on the radius of each ring. in, Let be the angular difference between the array elements on the i-th ring; After obtaining the angular difference between the array elements, calculate the angle difference on the i-th ring. The angle of each array element; the specific process is as follows: based on Calculate the remaining angle on the i-th ring. ; In [0, Randomly generated intervals An indirect perspective ; Will Sort in ascending order; based on and indirect angles after sorting Calculate the i-th ring on the i-th ring. The angle of each array element, i.e. in, , The total number of array elements in the i-th ring; Calculate the angles of all array elements on the i-th ring, and calculate the angles of all array elements on the M rings. This gives us the result that makes the arc length between array elements greater than 1. The angle of the array elements; The rectangular coordinates of the array elements are obtained by converting between polar coordinates and rectangular coordinates.

4. The improved differential evolution sparse distribution optimization method based on virtual interference pattern according to claim 3, characterized in that: The rectangular coordinates of the array elements are calculated using the following formula: （4） in, For the i-th ring, the th From the perspective of each array element, Let be the radius of the i-th annular array element; The coordinates of the array elements are rectangular coordinates.

5. The improved differential evolution sparse distribution optimization method based on virtual interference pattern according to claim 4, characterized in that: In step two, the virtual interference pattern synthesis method is used to process the position coordinates of the array elements to generate an antenna pattern. Each antenna pattern obtains a main lobe-side lobe gain ratio, which is an individual fitness value. The specific process is as follows: Step 22A, in plane and A targets are set on each plane; set up The target pointing angle on the plane is , The target pointing angle on the plane is ; Calculate the target pointing angle and The guiding vector and the weighting vector are initialized; The specific process is as follows: Target pointing angle and The method for calculating the guiding vector is shown in the following formula: （5） in, As the guiding vector; The imaginary unit, ; For wave number, , For wavelength, The coordinates of the array elements are rectangular. for Plane, guiding vector Take zero, and Then take the corresponding target pointing angle. ; for Plane, guiding vector Take zero, and Then take the corresponding target pointing angle. ; Direct each target and The target guidance vector is obtained by adding the guidance vectors together. Target guidance vector Used to initialize the weighted vector ; The sum of the guiding vectors on the plane is shown in the following equation: The sum of the guiding vectors on the plane is shown in the following equation: The sum of the steering vectors of the target beams on the two planes is shown in the following equation: The formula for initializing the weighted vector is shown below: Step 22B: Set the location of the interference source and initialize the interference power; the specific process is as follows: set up The angle of the interference source on the plane is ,and The angle of the interference source on the plane is Z is 361; The power of each interference source on the plane is ; The power of each interference source on the plane is ; initialization Interference power of each interference source on the plane Set to 0, initialize Interference power of each interference source on the plane It is 0; that is: Step 2.2C: Based on the weight vector obtained from initialization Solve for the antenna radiation patterns on the two planes separately; the specific process is as follows: in, for conjugate, Let be the weighted vector for the k-th iteration; After obtaining the antenna pattern, calculate the zero-power main lobe interval of the antenna pattern; Step 22D: Update the interference power based on the main lobe interval; the specific process is as follows: The method for updating the interference power is as follows: Among them, for Interference source: For, for Interference source: The decimal value of the expected sidelobe level yes The decimal value of the expected sidelobe level yes ; in, for The left boundary of the p-th main lobe interval on the plane. for The right boundary of the p-th main lobe interval on the plane. for The left boundary of the p-th main lobe interval on the plane. for The right boundary of the p-th main lobe interval on the plane. for The update power of the q-th interference source on the plane. for The update power of the q-th interference source on the plane. for The current power of the q-th interference source on the plane. for The current power of the q-th interference source on the plane. for The q-th interference source on the plane, for The q-th interference source on the plane, For iterative gain, yes , for ; Step 2.2E: Calculate the covariance matrix based on the magnitude of the interference power; the specific process is as follows: The covariance matrix is ​​calculated as shown in the following formula: in, for The covariance matrix corresponding to the next iteration For noise power, It is the identity matrix. for The q-th interference source on the plane The power level corresponding to the next iteration. for The q-th interference source on the plane The power level corresponding to the next iteration. Planar guiding vector for , Planar guiding vector for , for conjugate, for The conjugate of , where Z is the number of interference sources on a plane; Step 2F: Based on the covariance matrix and the target guidance vector Update # The weighted vector for the next iteration; the specific process is as follows: No. The weighted vector for the next iteration is calculated as follows: Step 22G, iterating from step 22C to step 22G (total) Next, get For each antenna pattern, a main lobe and side lobe gain ratio are obtained. The gain ratio with the largest main lobe and side lobe gain ratio is taken as the individual fitness value.

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