CN109271735B - Array directional diagram synthesis method based on quantum heuristic gravity search algorithm - Google Patents
Array directional diagram synthesis method based on quantum heuristic gravity search algorithm Download PDFInfo
- Publication number
- CN109271735B CN109271735B CN201811185156.6A CN201811185156A CN109271735B CN 109271735 B CN109271735 B CN 109271735B CN 201811185156 A CN201811185156 A CN 201811185156A CN 109271735 B CN109271735 B CN 109271735B
- Authority
- CN
- China
- Prior art keywords
- array
- directional diagram
- quantum
- calculating
- fitness
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
- G06N3/00—Computing arrangements based on biological models
- G06N3/004—Artificial life, i.e. computing arrangements simulating life
- G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Evolutionary Computation (AREA)
- General Engineering & Computer Science (AREA)
- Artificial Intelligence (AREA)
- Computational Linguistics (AREA)
- Health & Medical Sciences (AREA)
- Life Sciences & Earth Sciences (AREA)
- Computer Hardware Design (AREA)
- Biomedical Technology (AREA)
- Biophysics (AREA)
- Geometry (AREA)
- Data Mining & Analysis (AREA)
- General Health & Medical Sciences (AREA)
- Molecular Biology (AREA)
- Computing Systems (AREA)
- Mathematical Physics (AREA)
- Software Systems (AREA)
- Variable-Direction Aerials And Aerial Arrays (AREA)
Abstract
The invention discloses an array directional diagram synthesis method based on a quantum heuristic gravity search algorithm, which comprises the following steps: collecting information of an array to be optimized, and determining the requirement that a directional diagram needs to be formed by the array antenna; performing population initialization according to the array information; calculating a directional diagram; calculating a fitness value; updating the candidate solution set; selecting quantum potential wells and updating population positions; and if the fitness value meets the precision requirement or reaches the maximum iteration times, outputting the amplitude and the phase of the array element excitation determined according to the expected directional diagram. The method of the invention only has one control parameter: compared with the traditional intelligent algorithm, the compression-expansion coefficient has the characteristics of less control parameters and easiness in debugging.
Description
Technical Field
The invention relates to an array antenna technology, in particular to an array directional diagram synthesis method based on a quantum heuristic gravity search algorithm.
Background
Array antennas are widely used in the fields of radar, communication, electronic countermeasure and the like, and different application requirements require that the array antennas can form a special directional diagram. For example: the guard search radar requires to form a cosecant square wave beam, so that the intensity of a received signal is only related to the height of a target and is not related to the distance of the target; the tracking radar generally adopts a pencil-shaped wave beam with narrow main lobe and high gain; an electronic countermeasure system and a satellite communication system are required to form a multi-beam directional diagram in order to achieve multi-target and omnibearing effective interference of enemies and improve communication capacity and spectrum utilization rate.
Array synthesis is a process of determining array parameters (including array element excitation, array element number, array element arrangement and the like) according to an array radiation pattern. However, with the complication of the application requirements of the array antenna, the traditional array synthesis technology, such as an analytic method like the chebyshev method and a numerical method like the conjugate gradient method, is very weak; compared with the former, the method is inspired by phenomena such as natural law, species population habit and the like to find the optimal solution, and the intelligent algorithm is rapidly developed by virtue of the advantages of no dependence on related gradient information, no need of an accurate mathematical model, randomness, robustness and the like, and is widely used for solving the complex high-dimensional nonlinear optimization problems such as array synthesis and the like. Typical intelligent algorithms include genetic algorithms, particle swarm algorithms, gravity search algorithms, and the like. But the problems of population diversity attenuation and premature convergence exist in the optimization process; in addition, the basic intelligent optimization algorithms have the problem of low calculation speed when the comprehensive problem of the directional diagram of a large area array is processed.
Therefore, it is necessary to establish an intelligent algorithm with stronger diversity and global search capability, and apply array synthesis and design. Aiming at the challenge, the invention provides an array directional diagram comprehensive technology based on a quantum heuristic gravity search algorithm, which can accurately obtain the amplitude and the phase of the excitation of a comprehensive array element according to an expected directional diagram and guide the design of an array antenna.
Disclosure of Invention
The invention aims to solve the technical problem of providing an array directional diagram comprehensive method based on a quantum heuristic gravity search algorithm aiming at the defects in the prior art.
The technical scheme adopted by the invention for solving the technical problem is as follows: an array directional diagram synthesis method based on a quantum heuristic gravity search algorithm comprises the following steps:
1) Collecting information of an array to be optimized, wherein the information comprises the number of units, the unit interval and the array type; the requirements for defining the directional diagram of the array antenna comprise: shape, main lobe width, side lobe level, scanning direction;
2) Population initialization: randomly generating particles X in N search spaces according to the array information i ＝(x i1 ,x i2 ,…x ij …,x iD ) I =1,2,.., N, each dimensional component x ij All satisfy x ij ∈[x min ,x max ]J =1,2,3, … D; wherein, N is the size of the population, namely the number of candidate solutions; d is a spatial dimension related to the number of cells; x is the number of ij The position coordinates of the particles correspond to the excitation amplitude phase of the jth unit;
3) Calculating directional diagram
If the target array is a small array (the number of units is less than 100), calculating a directional diagram according to a basic formula;
if the target array is a large area array, adopting an IFFT-based directional diagram fast calculation method to calculate a directional diagram:
in the above formula, the first and second carbon atoms are,
wherein, floor represents a rounding operation; m and N are sampling points in the x direction and the y direction respectively, for a K multiplied by L area array, M > K, N > L is required, and the data shortage part is filled with zero; dx and dy are unit distances in the x direction and the y direction respectively; λ is the wavelength; theta and
pitch angle and azimuth angle, respectively; i (m, n) is the complex excitation of the (m, n) th cell; AF is an array factor of the array;
the formula shows that the directional diagram of the array and the complex excitation have an inverse Fourier transform relation, so that the array direction can be quickly calculated by directly calling the self-carried IFFT function of matlab. The above equation is for a two-dimensional planar array, and for a one-dimensional linear array, a one-dimensional IFFT can be used to increase the calculation speed in the same manner.
3) Calculating a fitness value fitness, designing a proper fitness function according to the directional diagram requirement, and calculating a fitness function value;
fitness＝c 1 E 1 +c 2 E 2 (4)
wherein E is 1 And E 2 Mean square error of main lobe and side lobe of directional diagram, c 1 And c 2 Is the corresponding weight coefficient;
4) Updating candidate solution set K best : selecting K individuals with better fitness as an optimal candidate set;
5) Selecting quantum potential wells and updating population positions: set the candidate solution K best Is provided with a Delta potential well center, and each particle randomly selects K according to the roulette rule best As a quantum well, and the update formula is as follows
X i (k+1)＝P i +α·|P i -X i (k)|·ln(1/u)ifS＞0.5
X i (k+1)＝P i -α·|P i -X i (k)|ln(1/u)ifS＜0.5 (5)
Wherein, P i A quantum well selected for the ith particle; u and S are random numbers between 0 and 1; alpha is called the compression-expansion coefficient and is also the only control parameter of the algorithm;
k is the current number of iterations, X i (k) Is the current position of the ith particle, P i A quantum well selected for the ith particle; u and S are random numbers between 0 and 1; alpha is a compression-expansion coefficient and is also the only control parameter of the algorithm, and the existing numerical test shows that alpha belongs to the 0.5,1.3 if the convergence of the algorithm is ensured]；X i (k) Is an updated position;
6) And (4) judging termination conditions: if the fitness value meets the precision requirement or reaches the maximum iteration times, outputting the amplitude and the phase of array element excitation determined according to the expected directional diagram; otherwise, repeating the steps 3) to 6).
The invention has the following beneficial effects:
1. compared with the traditional intelligent algorithm, the method has stronger randomness and global optimization capability, and can effectively synthesize array excitation according to the directional diagram requirement;
2. the method only has one control parameter (compression-expansion coefficient), and compared with the traditional intelligent algorithm, the method has the characteristics of few control parameters and easiness in debugging.
3. The invention integrates the fast directional diagram calculation technology based on IFFT, has high calculation efficiency and can be used for the directional diagram synthesis of large area array
Drawings
The invention will be further described with reference to the accompanying drawings and examples, in which:
fig. 1 is a cosecant square pattern of 20-element equidistant linear arrays of an embodiment of the present invention;
FIG. 2 is a 20-wire array optimized convergence curve according to an embodiment of the present invention;
FIG. 3 is a 9X 9 area array layout of an embodiment of the present invention;
FIG. 4 is a 9X 9 area array pencil pattern (two-dimensional) of an embodiment of the present invention
FIG. 5 is a 9X 9 area array pencil pattern (cut-plane) of an embodiment of the present invention;
FIG. 6 is a 9 × 9 area array optimized convergence curve of an embodiment of the present invention;
FIG. 7 is a layout diagram of a rectangular grid circular aperture Taylor array according to an embodiment of the present invention;
FIG. 8 is an excitation amplitude versus circular aperture Taylor excitation (main and side lobe level ratio of 30 dB) for an embodiment of the present invention;
fig. 9 is a rectangular grid circular aperture taylor area array multi-beam pattern of an embodiment of the present invention;
fig. 10 is a rectangular grid circular aperture taylor area array multi-beam pattern (top view) of an embodiment of the present invention;
FIG. 11 is an optimized excitation phase for an embodiment of the present invention;
FIG. 12 is a circular aperture Taylor area array optimized convergence curve according to an embodiment of the present invention;
FIG. 13 is a method flow diagram of an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
As shown in fig. 1, an array pattern synthesis method based on quantum heuristic gravity search algorithm includes the following steps:
the method comprises the following steps:
1) Collecting information of an array to be optimized, wherein the information comprises unit number, unit spacing, array type (linear array or area array) and the like; defining directional pattern requirements such as shape, main lobe width, side lobe level, scan direction, etc
2) Population initialization: randomly generating particles X in N search spaces according to array information i ＝(x i1 ,x i2 ,…x ij …,x iD ) I =1,2,.., N, each dimensional component x ij All satisfy x ij ∈[x min ,x max ]. Wherein, N is the size of the population, namely the number of candidate solutions; d is a spatial dimension related to the number of cells; x is the number of ij The position coordinates of the particles correspond to the excitation amplitude phase of the jth unit;
3) Calculating directional diagram
For the array with a small number of units (less than 100), calculating a directional diagram according to a basic formula;
for the array with a large number of units (more than 100), an IFFT-based rapid directional diagram calculation method is adopted:
in the above formula
Wherein floor represents a rounding operation; m and N are the number of sampling points in the x direction and the y direction respectively, and the sampling points are corresponding to the K multiplied by L surfaceArray, require M > K, N > L, the data deficiency part is filled with zero; dx and dy are unit distances in the x direction and the y direction respectively; λ is the wavelength; theta and
pitch angle and azimuth angle, respectively; i (m, n) is the complex excitation of the (m, n) th cell; AF is the array factor of the array.
The formula shows that the directional diagram of the array and the complex excitation have an inverse Fourier transform relation, so that the array direction can be quickly calculated by directly calling the self-carried IFFT function of matlab. The above equation is for a two-dimensional planar array, and for a one-dimensional linear array, a one-dimensional IFFT can be used to increase the calculation speed in the same manner.
4) Calculating a fitness value: designing a proper fitness function according to the requirements of the directional diagram, and calculating the fitness function value
fitness＝c 1 E 1 +c 2 E 2 (4)
Wherein E is 1 And E 2 Mean square error of main lobe and side lobe of directional diagram, c 1 And c 2 Is the corresponding weight coefficient;
it should be noted that the pattern requirements are different and the form of the fitness function is also different. Therefore, the above formula is only an example, and the present invention does not require any special form of the fitness function.
5) Selecting an optimal candidate solution set K best : selecting K individuals with better fitness as an optimal candidate set;
6) Selecting quantum potential wells and updating population positions: set the optimal candidate solution K best Is set to the Delta potential well center, and each particle randomly selects K according to the roulette rule best As a quantum well, and the update formula is as follows
Where k is the current iteration number, X i (k) Is the ith granuleCurrent position of child, P i A quantum well selected for the ith particle; u and S are random numbers between 0 and 1; alpha is called compression-expansion coefficient and is the only control parameter of the algorithm, and the existing numerical tests show that alpha belongs to 0.5,1.3 if the convergence of the algorithm is ensured]；X i (k) Is the updated position.
7) And (4) judging termination conditions: if the fitness value meets the precision requirement or reaches the maximum iteration times, outputting a result, namely the array excitation corresponding to the expected directional diagram; otherwise, repeating the steps 3) to 6).
The effect of the invention is described below by combining with a specific simulation experiment, which is specifically as follows:
1) The number of the array elements is 20, the spacing between the array elements is lambda/2, the excitation amplitude and the phase are optimized, the cosecant square wave beam is required to be formed in theta in the shape of being equal to [90 degrees ] and 125 degrees ], the main lobe is reduced by 10dB, and the level of the side lobe is not higher than-25 dB;
the optimized parameter settings are as follows:
population size popsize =200; the number of iterations max _ N =3000; the excitation amplitude optimization space is set to (0,1), and the excitation phase optimization space is set to (0,2 pi);
K best in a linearly descending manner, i.e.
Kbest＝popsize+(1-popsize)·t/max_N (6)
The compression-expansion coefficient alpha is in a value range of [0.5,1.3] according to the corresponding numerical test result, and the change form adopts linear reduction, namely
α＝0.8·(max_N-t)/max_N+0.5 (7)
As can be seen from fig. 1 and fig. 2, the excitation pattern synthesized by the technique meets the expected requirements, and the algorithm approaches to the global optimal solution at about 2500 th iteration;
2) A 9 × 9 rectangular area array, the layout is shown in fig. 3, the array element spacing is λ/2, the excitation amplitude and phase are optimized, a pen-shaped directional pattern is required to be formed, and the wave beam is directed
The main lobe width is 15 degrees, the level of the side lobe is not higher than-25 dB, and the optimization parameters are set as follows:
the number of iterations max _ N =1000, the excitation amplitude ratio was set to 10, and the remainder of the same example (1)
The result is shown in fig. 4, 5 and 6, the main lobe width error obtained by optimization is less than 1 degree, and the highest side lobe level error is less than 0.5dB, so that the effectiveness of the invention is proved.
3) The rectangular grid circular aperture taylor area array is a common array form in engineering, and for the circular aperture taylor area array (316 array elements) with the aperture radius of 5 lambda, as shown in fig. 7; amplitude is fixed to the Taylor excitation as shown in FIG. 8; optimization of excitation phase, as required
The four directions form a constant-amplitude multi-beam, and the level of the side lobe is not higher than-25 dB; the optimized parameter settings are as follows:
the iteration number max _ N =3000, the excitation phase optimization space is set to (-pi, pi), and the rest of the same example (1)
The results are shown in FIGS. 9, 10, 11 and 12, in the u-v coordinate system
The ideal beam pointing direction would be (0.5), (-0.5,0.5), (-0.5 ), (0.5, -0.5); the actually optimized beam directions (0.51,0.5), (-0.505, -0.51), (-0.5 ), (0.5, -0.495) have normalized main lobe peaks of-0.6776 dB, 0dB, -0.9819dB, -0.9187dB respectively. It can be seen that the pointing deviation is smaller compared to the expected beam, and the main lobe deviation of each beam is smaller than 1dB, which proves the effectiveness of the invention.
It will be understood that modifications and variations can be made by persons skilled in the art in light of the above teachings and all such modifications and variations are intended to be included within the scope of the invention as defined in the appended claims.
Claims (3)
1. An array directional diagram synthesis method based on a quantum heuristic gravity search algorithm is characterized by comprising the following steps:
1) Collecting information of an array to be optimized, comprising: number of cells, cell pitch, array type; the requirements for defining the directional diagram of the array antenna comprise: shape, main lobe width, side lobe level, scanning direction;
2) And according to the array information, performing population initialization: randomly generating particles X in N search spaces according to the array information i ＝(x i1 ,x i2 ,…x ij …,x iD ) I =1,2,.., N, each dimensional component x ij All satisfy x ij ∈[x min ,x max ]J =1,2,3, … D; wherein, N is the size of the population, namely the number of candidate solutions; d is a spatial dimension related to the number of cells; x is the number of ij The position coordinates of the particles correspond to the excitation amplitude phase of the jth unit;
3) Calculating directional diagram
If the target array is a small array, calculating a directional diagram according to a basic formula; the small array is an array with the number of units less than 100;
if the target array is a large area array, adopting an IFFT-based directional diagram fast calculation method to calculate a directional diagram:
in the above-mentioned formula, the compound has the following structure,
wherein, floor represents a rounding operation; m and N are sampling points in the x direction and the y direction respectively, for a K multiplied by L area array, M > K, N > L is required, and the data shortage part is filled with zero; dx and dy are unit distances in the x direction and the y direction respectively; λ is the wavelength; theta and
pitch angle and azimuth angle, respectively; i (m, n) is the complex excitation of the (m, n) th unit; AF is an array factor of the array;
4) Calculating a fitness value fitness, designing a proper fitness function according to the directional diagram requirement, and calculating a fitness function value;
5) Updating candidate solution set K best : selecting K individuals with better fitness as an optimal candidate set;
6) Selecting quantum potential wells and updating population positions: collecting the candidate solution K best Is positioned with the Delta potential well center, and each particle randomly selects K according to the roulette rule best As a quantum well, and the update formula is as follows
X i (k+1)＝P i +α·|P i -X i (k)|·ln(1/u)ifS＞0.5
X i (k+1)＝P i -α·|P i -X i (k)|·ln(1/u)ifS＜0.5
Wherein, P i A quantum well selected for the ith particle; u and S are random numbers between 0 and 1; alpha is called the compression-expansion coefficient and is also the only control parameter of the algorithm;
k is the current number of iterations, X i (k) Is the current position of the ith particle, P i A quantum well selected for the ith particle; u and S are random numbers between 0 and 1; alpha is a compression-expansion coefficient and is also the only control parameter of the algorithm; x i (k) Is an updated position;
7) And (4) judging termination conditions: if the fitness value meets the precision requirement or reaches the maximum iteration times, outputting the amplitude and the phase of array element excitation determined according to the expected directional diagram; otherwise, repeating the steps 3) to 6).
2. The array pattern synthesis method based on the quantum heuristic gravity search algorithm according to claim 1, wherein in the step 4), the following formula is adopted for calculating the fitness function value:
fitness＝c 1 E 1 +c 2 E 2
wherein E is 1 And E 2 Mean square error of main lobe and side lobe of directional diagram, c 1 And c 2 Are the corresponding weight coefficients.
3. The method for synthesizing the array pattern based on the quantum heuristic gravity search algorithm according to claim 1, wherein the compression-expansion coefficient α e [0.5,1.3] in the step 6).
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811185156.6A CN109271735B (en) | 2018-10-11 | 2018-10-11 | Array directional diagram synthesis method based on quantum heuristic gravity search algorithm |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201811185156.6A CN109271735B (en) | 2018-10-11 | 2018-10-11 | Array directional diagram synthesis method based on quantum heuristic gravity search algorithm |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN109271735A CN109271735A (en) | 2019-01-25 |
| CN109271735B true CN109271735B (en) | 2022-11-25 |
Family
ID=65195779
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201811185156.6A Active CN109271735B (en) | 2018-10-11 | 2018-10-11 | Array directional diagram synthesis method based on quantum heuristic gravity search algorithm |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN109271735B (en) |
Families Citing this family (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111128315B (en) * | 2019-12-13 | 2023-08-11 | 桂林理工大学 | Geopolymer concrete mixing proportion method based on gravity search algorithm |
| CN111914045B (en) * | 2020-07-09 | 2023-06-30 | 珠海云洲智能科技股份有限公司 | Data compression method, device, terminal equipment and storage medium |
| CN113328263B (en) * | 2021-05-28 | 2022-04-19 | 北京邮电大学 | Shaping method and system for realizing null-free beam falling of linear array antenna |
Family Cites Families (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5081463A (en) * | 1989-04-13 | 1992-01-14 | Mitsubishi Denki Kabushiki Kaisha | Method and system for forming desired radiation pattern with array antenna |
| CN104901734B (en) * | 2015-06-26 | 2018-08-03 | 中国船舶重工集团公司第七二四研究所 | A kind of form-giving array antennas beams method |
| CN107294589B (en) * | 2017-08-03 | 2020-10-02 | 哈尔滨工业大学 | Multi-beam satellite array antenna directional pattern comprehensive method based on particle swarm optimization algorithm |
-
2018
- 2018-10-11 CN CN201811185156.6A patent/CN109271735B/en active Active
Also Published As
| Publication number | Publication date |
|---|---|
| CN109271735A (en) | 2019-01-25 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Pappula et al. | Linear antenna array synthesis using cat swarm optimization | |
| Ma et al. | Pattern synthesis of 4-D irregular antenna arrays based on maximum-entropy model | |
| Li et al. | An improved particle swarm optimization algorithm for pattern synthesis of phased arrays | |
| Bucci et al. | Plane-wave generators: Design guidelines, achievable performances and effective synthesis | |
| CN109271735B (en) | Array directional diagram synthesis method based on quantum heuristic gravity search algorithm | |
| CN106407723B (en) | The determination method of sparse arrangement array antenna exciting current amplitude towards Sidelobe | |
| CN104615854B (en) | A kind of beam-broadening and side lobe suppression method based on sparse constraint | |
| CN111160556B (en) | Array sparse optimization method based on adaptive genetic algorithm | |
| Liu et al. | Synthesis of large unequally spaced planar arrays utilizing differential evolution with new encoding mechanism and Cauchy mutation | |
| Koziel et al. | Rapid multi-objective optimization of antennas using nested kriging surrogates and single-fidelity EM simulation models | |
| Li et al. | Improved GA and PSO culled hybrid algorithm for antenna array pattern synthesis | |
| Xu et al. | Grating lobe suppression of non-uniform arrays based on position gradient and sigmoid function | |
| CN112100701A (en) | Two-dimensional distributed antenna subarray position optimization method based on genetic algorithm | |
| Oliveri et al. | Synthesis of monopulse sub-arrayed linear and planar array antennas with optimized sidelobes | |
| CN110232228B (en) | Multi-split domino irregular subarray array surface optimal selection design method | |
| Rocca et al. | Polyomino subarraying through genetic algorithms | |
| CN114371447A (en) | Subarray-level distributed frequency control array sidelobe suppression method based on improved genetic algorithm | |
| CN108446504A (en) | Near-field array Antenna measuring table method based on convex optimization | |
| CN112016662A (en) | Array directional diagram synthesis method based on mixed differential evolution algorithm and weighted total least square method | |
| CN116911162A (en) | Method and system for synthesizing phase-only satellite-borne phased array antenna based on improved dayfish algorithm | |
| CN115133291A (en) | Irregular antenna subarray, phased array antenna and design method of phased array antenna | |
| CN115374695A (en) | Sparrow search algorithm and array weighting-based sparse array antenna optimization method | |
| Li et al. | Unequally spaced linear antenna arrays synthesis based on genetic algorithm | |
| CN115146544A (en) | Array antenna design method adopting knowledge and data hybrid driving | |
| CN114239380B (en) | Rectangular sparse array optimization method based on self-adjusting mapping rule |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |