Thin cloth array antenna design method based on improved pelican optimization algorithm

Abstract

The invention discloses a thin cloth array antenna design method based on an improved pelican optimization algorithm. The thin cloth array antenna design method comprises the step of obtaining an optimal solution of an array antenna directional diagram comprehensive design model under a design target by using an improved POA. By utilizing the advantage of balancing global and local search of a triangular migration strategy, the triangular migration strategy is added after a prey moving stage (an exploration stage) and a water wing spreading stage (a development stage) of the POA, so that after the development stage of the algorithm, a development stage is created again by utilizing the triangular migration strategy; therefore, the problem of imbalance between exploration and development can be effectively solved, the local search precision of the algorithm is improved, local optimum is jumped out, the convergence speed is increased, and the optimal solution is found. According to the design method, on the premise that the width of the main lobe of the sparse antenna array is not broadened, the side lobe level of the sparse antenna array is effectively restrained, a deep zero point is formed in the direction of a designated position, and a required array antenna directional diagram is achieved.

Description

Technical Field

[0001] The invention belongs to the technical field of mobile communication antenna design, and in particular relates to a sparse array antenna design method based on an improved Pelican optimization algorithm. Background Art

[0002] With the development of science and technology, the requirements for antenna performance are increasing. In traditional uniform linear arrays, the spacing between array elements is fixed. Although this can achieve functions such as directional signal reception and transmission to a certain extent, it also has limitations. For example, the sidelobe level of the uniform linear array is relatively high, which will lead to increased interference. When receiving signals, in addition to the useful signals in the direction of the main lobe, the side lobes will also receive interference signals from other directions; when transmitting signals, the side lobes will also cause energy waste and may cause unnecessary interference in other directions. Moreover, in many application scenarios, there are certain restrictions on the cost and complexity of the equipment. If traditional arrays are to achieve performance requirements such as high resolution, they often require more array elements, which increases the cost, size and weight of the equipment.

[0003] The sparse linear array can effectively reduce the sidelobe level by non-uniformly distributing the array element positions. Under the same antenna aperture requirements, the sparse linear array can reduce the number of array elements, which is very beneficial for reducing costs, equipment size and complexity. At the same time, it can optimize the antenna's directional pattern without increasing the number of array elements. In the fields of radar detection and signal coverage in communications, it can better focus the signal in the target direction and reduce interference from other directions, thus adapting to the development needs of modern high-precision, cost-effective and miniaturized equipment.

[0004] The Pelican Optimization Algorithm (POA) is a new type of swarm intelligence optimization algorithm. The inspiration of the Pelican Optimization Algorithm is mainly based on a series of natural behaviors of pelicans living and hunting in nature. Pelicans are large, long-billed, gregarious birds with particularly large throats, similar to bags, and usually feed on fish. They often cooperate with each other to hunt. Once they identify their prey, they will fly down from high altitudes, rush towards the prey, and then spread their wings on the water surface, forcing the fish to swim to shallow waters, which helps them capture the prey. The mathematical model describing the Pelican Optimization Algorithm has three stages: initialization, moving towards the prey, and spreading wings on the water. In the moving towards the prey stage, the pelican will first identify and lock the prey, and then force the prey to shallow waters. In the spreading wings on the water stage, the pelican will rush towards the prey, then push the prey onto the water surface, and finally store the prey in the bag at the throat, and then continue to capture the next prey.

[0005] Some studies have shown that compared with Particle Swarm Optimization (PSO), Ant Lion Optimization Algorithm (ALO) and Sparrow Search Algorithm (SSA), POA has higher accuracy in the optimization process and can effectively converge to the optimal solution of the problem. At the same time, POA also has strong robustness and adaptability, and it can solve optimization problems in many fields, such as heterogeneous wireless sensor networks, microgrid energy management and automatic facial emotion recognition.

[0006] In the field of mobile communication antenna design, when evolutionary algorithms such as the Runner-root Algorithm (RRA) and the Multi-Verse Optimization Algorithm (MVO) are used to solve the antenna pattern synthesis problem, if a deep null is placed in the target direction, the sidelobe level will increase accordingly or the main lobe width will be widened, which cannot meet the ideal requirements of both the sidelobe level and the deep null. Moreover, they lack exploration in the middle and late stages of optimization and are prone to fall into local optimality, resulting in an increase in the sidelobe level of the target pattern or an increase in the deep null level. POA has an optimization process of identifying and locking prey, so in the early exploration, it can obtain a more accurate position, and in the middle and late stages, it conducts local neighborhood searches to find a better position in a more accurate way. Therefore, it can greatly improve the global and local search capabilities and is a better algorithm for solving the antenna pattern synthesis problem.

[0007] But similar to other intelligent swarm optimization algorithms, POA also suffers from problems such as premature convergence, imbalance between exploration and exploitation, and lack of population diversity. Summary of the invention

[0008] In view of the defects of the prior art, the purpose of the present invention is to propose a method for obtaining the optimal solution to the array antenna pattern synthesis problem through an improved Pelican optimization algorithm, and thereby obtaining the best design scheme. This method adds a triangle walk strategy to the POA to improve the convergence accuracy and convergence speed of the algorithm. By optimizing the position of the array antenna elements, under the premise that the main lobe width is not widened, a sidelobe level lower than the index requirement and a deep null point in a specific direction are formed, thereby optimizing and solving the complex array antenna pattern synthesis problem.

[0009] The technical solution of the present invention is as follows:

[0010] A sparse array antenna design method based on an improved Pelican optimization algorithm includes:

[0011] Setting up a comprehensive design model of sparse array antenna patterns with design objectives;

[0012] Obtaining the optimal solution of the design model under the design goal through the improved POA;

[0013] The design goal is to optimize the array element spacing of the array antenna, so as to form a sidelobe level lower than the expected value in the sidelobe area while ensuring that the main lobe width of the antenna array remains unchanged, and to form a deep null point at a specified position;

[0014] The improved POA includes the following two stages of moving towards prey and flapping wings on water, as well as the position update model of the pelican after adding the triangular swimming strategy:

[0015]

[0016]

[0017] in, They represent the new states of the pelican in the phase of moving towards prey, the phase of spreading wings on the water, and the phase of triangular swimming. i represents the new position of the pelican at the tth iteration of each stage. rand in all the above formulas represents a random number between 0 and 1. i Represents the objective function value.

[0018] In formula (1), x i,j represents the state of the i-th pelican in the j-dimensional space, p j represents the position of the prey in the j-dimensional space, and I is a random number from 1 to 2.

[0019] In formula (3), R is a constant equal to 0.2, t represents the current number of iterations, and T represents the maximum number of iterations; the coefficient Represents the radius of the neighborhood of a group member, where a local search is performed near each member to converge to a better solution. This coefficient is effective for POA to develop capabilities and get closer to the optimal global solution. In the initial iterations, the value of this coefficient is large, so a larger area around each member is considered. As the number of algorithm iterations increases, decreases, resulting in a smaller neighborhood radius for each member. This allows us to scan the area around each member in the population with smaller and more precise steps so that POA can converge to a solution closer to the global optimum based on the usage concept.

[0020] In formulas (5) and (6), C represents the center of mass, X z and X k Indicates that in X i The value generated around, W represents the number of walks, R mRepresents a random number from 1 to m, where m represents the number of problem variables.

[0021] According to some specific embodiments of the present invention, the design model is set as follows:

[0022] The model is an unequally spaced linear array composed of 2N ideal point sources, and the excitation current amplitude in the linear array is centrally symmetric and the excitation phase is zero. The array antenna pattern expression is as follows:

[0023]

[0024] Wherein, F(θ) represents the expression of the array antenna pattern, k=2π / λ represents the wave number, d is the spacing between array elements, λ is the free space wavelength, and θ is the angle between the ray direction and the array axis.

[0025] According to some specific embodiments of the present invention, in the improved POA, the fitness of each individual is obtained by the following fitness function value:

[0026]

[0027] Where, fit is the fitness function value, PSL is the peak sidelobe level (Peak Sidelobe Level, PSL for short), TPSL is the target peak sidelobe level (TargetPeakSidelobeLevel, TPSL for short), NSLL is the null sidelobe level (Null SidelobeLevel, NSLL for short), α and β are weight coefficients, and satisfy α+β=1, F(θ i ) represents the array antenna pattern distribution function, i represents the current i-th deep zero point, and N0 is the number of deep zero points.

[0028] According to some specific embodiments of the present invention, the design method includes:

[0029] S1: Based on the design model, the solution space of the design target is initialized by POA according to the following model;

[0030] x i,j = l j +rand·(u j -l j ),i=1,2,...,N,j=1,2,...,m (10)

[0031] Each pelican is randomly generated between the upper and lower bounds of the given problem. i,j is the value of the jth variable specified by the ith candidate solution, N is the number of population members, m is the number of problem variables, rand is a random number in the interval [0,1], and uj and l j They represent the upper and lower position boundaries of the pelican respectively.

[0032] S2: After initialization, in the current iteration, the fitness function value of each pelican in the population is calculated, and the pelican individual with the smallest fitness function value in the population is selected as the current best individual X through the following model: best , and it is considered that this is the most suitable position for the pelican to hunt, that is, the optimal solution. Its fitness function value is f best ; At the same time, the fitness function value of the prey is set to prepare for the next hunting.

[0033] f best =min(f(X i )) (11)

[0034]

[0035] S3: Enter the stage of moving towards the prey. By comparing the fitness function values ​​of the pelican and the prey, the new state of the pelican is updated using formula (1), and the position of the pelican is updated using formula (2);

[0036] S4: Entering the stage of spreading wings on the water, based on the prey position information obtained in the stage of moving towards the prey, the pelican will fly to the water surface, flap its wings, and force the prey into the shallow water area. At this time, the new state of the pelican in the stage of spreading wings on the water is updated using formula (3), and then compared with the objective function value, and formula (4) is used to determine whether the new position of the pelican needs to be updated.

[0037] S5: Entering the triangular walking stage, based on the last updated position of the pelican in the water wing-spreading stage, the pelican position update model of the triangular walking stage described in formulas (5) and (6) is used to update the pelican position in the triangular walking stage;

[0038] S6: After the above three stages of iterative updates are completed, the fitness function values ​​of all pelicans in the population are calculated, and then they are sorted from small to large according to the fitness function values, and the pelican with the smallest fitness function value is selected, the best individual pelican is updated, and the position of the next pelican is determined;

[0039] S7: After each iteration, determine whether the algorithm has reached the maximum number of iterations. If so, the algorithm ends and outputs the optimal solution X best Otherwise, after increasing the number of iterations, return to S2 and continue iterating.

[0040] According to some specific embodiments of the present invention, the individual fitness is obtained by the following calculation model:

[0041]

[0042] Where, fit is the fitness function value, PSL is the peak sidelobe level (Peak Sidelobe Level, PSL for short), TPSL is the target peak sidelobe level (Target Peak Sidelobe Level, TPSL for short), NSLL is the null sidelobe level (Null Sidelobe Level, NSLL for short), α and β are weight coefficients, and satisfy α+β=1, F(θ i ) represents the array antenna pattern distribution function, i represents the current i-th deep zero point, and N0 is the number of deep zero points.

[0043] According to some specific embodiments of the present invention, the weight coefficients α and β are selected as follows: according to the degree to which the directional diagram of the design area is close to the design target, the weight coefficient of the area with slow search is increased, and the values ​​of α and β are obtained through experiments.

[0044] The present invention has the following beneficial effects:

[0045] In the design method of the present invention, an improved POA is used to perform a comprehensive design of the array antenna pattern. By adding a triangular wandering strategy, the relative position relationship between multiple pelicans is effectively utilized to optimize the individual positions of the pelicans, thereby enhancing the POA's fine search capability in the local search area. This helps prevent the algorithm from falling into the local optimum, and is conducive to the algorithm's rapid convergence to the global optimal solution. At the same time, it also enhances the algorithm's local exploration capability in the middle and late stages, thereby being able to obtain better target sidelobe levels and deep zero point levels.

[0046] The present invention adopts a triangle walking strategy in POA. In the original POA, the entire exploration and development process only has two stages: moving towards the prey and spreading wings on the water, and there are fewer development stages, which may lead to an imbalance between exploration and development, and the algorithm cannot find a better solution. By adding triangle walking after the two update stages of the algorithm, the balance between exploration and development of the algorithm can be effectively balanced, allowing the algorithm to jump out of the local optimum and find a better solution.

[0047] The present invention uses an improved Pelican optimization algorithm to synthesize the array antenna pattern. By optimizing the array element spacing of the array antenna, the side lobe level is effectively suppressed without widening the main lobe width, forming a side lobe level lower than the index requirement and a deep zero point in a specific direction.

[0048] This paper uses the Pelican optimization algorithm for the design of array antenna pattern synthesis problems for the first time, and proposes an improved Pelican optimization algorithm to address the problems of slow convergence and easy local optimality when solving the array antenna pattern synthesis problem. Based on the imbalance problem of the exploration and development stages of the Pelican optimization algorithm, we add a triangular walk strategy to the development stage of the Pelican optimization algorithm to balance the relationship between the two, jump out of the local optimality, and find the best solution.

[0049] The improved Pelican optimization algorithm used in the present invention has strong versatility and portability, can be applied to optimization problems in related fields, and can also be combined with other algorithms. It not only proposes new ideas and methods for the problem of array antenna radiation pattern synthesis, but also effectively expands the application depth and breadth of the Pelican optimization algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 This is the directional graph obtained by the multi-version optimization algorithm in Example 1.

[0051] Figure 2 This is the directional diagram obtained by the original Pelican optimization algorithm in Example 1.

[0052] Figure 3 This is a convergence curve diagram obtained by the original Pelican optimization algorithm in Example 1.

[0053] Figure 4 This is the directional diagram obtained by improving the Pelican optimization algorithm in Example 1.

[0054] Figure 5 This is a convergence curve diagram obtained by improving the Pelican optimization algorithm in Example 1.

[0055] Figure 6 This is the directional diagram obtained by the rotating root algorithm in Example 2.

[0056] Figure 7 This is the directional diagram obtained by the original Pelican optimization algorithm in Example 2.

[0057] Figure 8 This is a convergence curve diagram obtained by the original Pelican optimization algorithm in Example 2.

[0058] Fig. 9 This is the directional diagram obtained by improving the Pelican optimization algorithm in Example 2.

[0059] Fig.10 This is a convergence curve diagram obtained by improving the Pelican optimization algorithm in Example 2. DETAILED DESCRIPTION

[0060] The present invention is described in detail below in conjunction with the embodiments and drawings, but it should be understood that the embodiments and drawings are only used to exemplify the present invention and do not constitute any limitation on the protection scope of the present invention. All reasonable changes and combinations within the scope of the inventive concept of the present invention fall within the protection scope of the present invention.

[0061] According to the technical method of the present invention, some specific implementation methods of the sparse array antenna design method based on the improved Pelican optimization algorithm include the following steps:

[0062] S0 sets the comprehensive design model of the array antenna pattern. The model is an unequally spaced linear array composed of 2N ideal point sources, and the excitation current amplitude in the linear array is centrally symmetric and the excitation phase is zero. The pattern expression is shown in equation (14). The design goal is to optimize the element spacing of the array antenna, form a sidelobe level lower than the expected value in the sidelobe area while ensuring that the main lobe width of the array remains unchanged, and form a deep zero point at the specified position:

[0063]

[0064] Wherein, F(θ) represents the expression of the array antenna pattern, k=2πfλ represents the wave number, d is the spacing between array elements, λ is the free space wavelength, and θ is the angle between the ray direction and the array axis.

[0065] The above design model can fully reduce optimization variables, lower calculation costs, and obtain excellent design solutions.

[0066] S1: Based on the design model of S0, POA is initialized for the solution space of its design target.

[0067] According to some specific embodiments of the present invention, the initialization includes: setting the initial evolutionary generation t=1, setting the population size N, the maximum number of iterations of the algorithm T, the dimension m of the problem, and the feasible solution space of the problem, and randomly generating a set of initial solutions:

[0068]

[0069] Where N is the population size, X is the population matrix of pelicans, and X i It is the i-th pelican.

[0070] S2: After initialization, in the current iteration, the fitness function value of each pelican in the population is calculated, and the pelican individual with the smallest fitness function value in the population is selected as the current best individual X through the following model: best , and it is considered that this is the most suitable position for the pelican to hunt, that is, the optimal solution. Its fitness function value is f best ; At the same time, the fitness function value of the prey is set to prepare for the next hunting.

[0071] f best =min(f(X i )) (16)

[0072]

[0073] S3: Further, in the process of iterative calculation, the fitness function values ​​of all individuals are calculated. The fitness function value of each individual can be calculated by formula (16);

[0074]

[0075] Where, fit is the fitness function value, PSL is the peak sidelobe level (Peak Sidelobe Level, PSL for short), TPSL is the target peak sidelobe level (Target Peak Sidelobe Level, TPSL for short), NSLL is the null sidelobe level (Null Sidelobe Level, NSLL for short), α and β are weight coefficients, and satisfy α+β=1, F(θ i ) represents the array antenna pattern distribution function, i represents the current i-th deep zero point, and N0 is the number of deep zero points. The weight coefficient is selected as follows: according to the degree to which the pattern of each design area is close to the design target, the weight coefficient of the slowly evolving area can be appropriately increased. After repeated experiments, the values ​​of α and β are determined.

[0076] S4: Enter the stage of moving towards the prey. By comparing the fitness function values ​​of the pelican and the prey, the new state of the pelican is updated using formula (1), and the position of the pelican is updated using formula (2);

[0077] S5: Entering the stage of spreading wings on the water, based on the prey position information obtained in the stage of moving towards the prey, the pelican will fly to the water surface, flap its wings, and force the prey into the shallow water area. At this time, the new state of the pelican in the stage of spreading wings on the water is updated using formula (3), and then compared with the objective function value, and formula (4) is used to determine whether the new position of the pelican needs to be updated.

[0078] S6: Entering the triangular walking stage, based on the last updated position of the pelican in the water wing-spreading stage, the pelican position update model of the triangular walking stage described in formulas (5) and (6) is used to update the pelican position in the triangular walking stage;

[0079] S7: After the iterative update of the above three stages is completed, the fitness function values ​​of all pelicans in the population are calculated, and then they are sorted from small to large according to the fitness function values, and the pelican with the smallest fitness function value is selected, the best individual pelican is updated, and the position of the next pelican is determined;

[0080] S8: After each iteration, determine whether the algorithm has reached the maximum number of iterations. If so, the algorithm ends and outputs the optimal solution X best Otherwise, after increasing the number of iterations, return to S2 and continue iterating.

[0081] Example 1

[0082] The present invention is described below in conjunction with simulation experiments.

[0083] 1. Experimental content:

[0084] The directional pattern synthesis design is carried out for the sparse linear array with centrosymmetric current amplitude and zero phase described by equation (8), and an experimental example is used to verify the effect of the algorithm proposed in the present invention on the directional pattern synthesis problem of sparse array antenna.

[0085] Experiment 1: 2N=20, excitation current I n =1, and compared with the 20-element array in the paper "Linear Antenna Array Pattern Synthesis Using Multi-Verse Optimization Algorithm" published by Raghuvanshi, Anoop. Among them, the main lobe width 2θ0 = 16° and the side lobe area is θ = [0°, 82°] and θ = [98°, 180°], and the deep zero points are placed at θ equal to 64°, 76°, 104° and 116°. The population size is 30 and the number of iterations is 1000.

[0086] 2. Experimental results:

[0087] Figure 1 It is the array radiation pattern obtained by optimizing the multi-version optimization algorithm, in which the highest level in the sidelobe area is -22.06dB. At the position where θ is equal to 64° and 76°, the deep zero point values ​​are -70.00dB and -78.11dB respectively, and the main lobe width is 18.2°. Figure 2 and Figure 3 It is the sparse array antenna pattern and the convergence curve of the optimization results obtained by optimizing the original Pelican algorithm. The highest level in the sidelobe area is -23.35dB. At the positions where θ is equal to 64° and 76°, the deep zero point values ​​are -86.33dB and -82.62dB respectively, and the main lobe width is 18.2°. Figure 4 and Figure 5It is the sparse array antenna pattern and the convergence curve of the optimization result obtained by the improved Pelican algorithm optimization. The highest level in the sidelobe area is -23.54dB. At the position where θ is equal to 64° and 76°, the deep zero point values ​​are -88.85dB and -83.77dB respectively, and the main lobe width is 17.6°. It can be seen that the peak sidelobe level of the improved Pelican optimization algorithm is 0.19dB lower than the peak sidelobe level of the original Pelican optimization algorithm, and 1.48dB lower than the peak sidelobe level of the multi-version optimization algorithm. Moreover, at a specific deep zero point position, the deep zero point value is lower and the main lobe width is narrower. This verifies the effectiveness of the algorithm proposed in the present invention.

[0088] The comparison between the three is shown in Table 1 below (two decimal places are retained):

[0089] Table 1 Comparison of simulation results of different algorithms

[0090]

[0091] Example 2

[0092] The present invention is further described below in conjunction with simulation experiments.

[0093] 1. Experimental content:

[0094] The directional pattern synthesis design is carried out for the sparse linear array with centrosymmetric current amplitude and zero phase described by equation (8), and an experimental example is used to verify the effect of the algorithm proposed in the present invention on the directional pattern synthesis problem of sparse array antenna.

[0095] Experiment 1: 2N = 32, array element spacing I n =1, and compared with the 32-element array in the paper "Runner-root algorithm to control side lobe level and null depths in linear antenna arrays" published by Subhashini, KR. Among them, the main lobe width 2θ0=6°, the side lobe area is θ=[0°,87°] and θ=[93°,180°], and the deep zeros are placed at θ=81° and 99°. The population size is 30 and the number of iterations is 1000.

[0096] 2. Experimental results:

[0097] Figure 6 This is the array pattern optimized by the wheel root algorithm, where the highest level in the sidelobe area is -18.60dB, and the deep zero points corresponding to θ at 81° and 99° are -85.39dB. Figure 7 and Figure 8It is the sparse array antenna radiation pattern and the convergence curve of the optimization result obtained by optimizing the original Pelican optimization algorithm in Example 2, wherein the highest level in the sidelobe area is -19.74dB, and the deep zero point corresponding to θ at 81° and 99° is -106.92dB. Fig. 9 and Fig.10 The sparse array antenna pattern and the convergence curve of the optimization results obtained by the improved Pelican optimization algorithm in Example 2, the highest level in the sidelobe area is -19.94dB, and the deep zero points corresponding to θ at 81° and 99° are -117.00dB. It can be seen that the peak sidelobe level of the improved Pelican optimization algorithm is 0.2dB lower than the peak sidelobe level of the original Pelican optimization algorithm, and 1.34dB lower than the peak sidelobe level of the runner root algorithm. In the comparison of the deep zero points of θ at 81° and 99°, the value obtained by the improved Pelican optimization algorithm is 10.08dB lower than the value obtained by the original Pelican optimization algorithm, and 31.61dB lower than the value obtained by the runner root algorithm. The effectiveness of the algorithm proposed in the present invention is further verified.

[0098] The comparison between the three is shown in Table 2 below (two decimal places are retained):

[0099] Table 2 Comparison of simulation results of different algorithms

[0100]

[0101] The above embodiments are only preferred implementations of the present invention, and the protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, improvements and modifications without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A sparse array antenna design method based on an improved Pelican optimization algorithm, characterized by: The position update formulas for the two stages of moving towards prey and spreading wings on the water are improved by adding a triangular walking strategy after these two stages, and the improved Pelican Optimization Algorithm (POA) is used to solve the problem of array antenna pattern synthesis; including: Setting up a comprehensive design model of sparse array antenna patterns with design objectives; Obtaining the optimal solution of the design model under the design goal through the improved POA; The design goal is to optimize the array element spacing of the sparse array antenna, so as to form a side lobe level lower than the expected value in the side lobe area while ensuring that the main lobe width of the array antenna remains unchanged, and to form a deep null point in the specified position direction; The improved POA includes the following two stages of moving towards prey and flapping wings on water, as well as the position update model of the pelican after adding the triangular swimming strategy: in, They represent the new states of the pelican in the phase of moving towards prey, the phase of spreading wings on water, and the phase of triangular swimming; X i represents the new position of the pelican at the tth iteration of each stage; rand in all the above formulas represents a random number between 0 and 1, and all F i represents the objective function value; In formula (1), x i,j represents the state of the i-th pelican in the j-dimensional space, p j represents the position of the prey in the j-dimensional space, and I is a random number from 1 to 2; In formula (3), R is a constant equal to 0.2, t represents the current number of iterations, and T represents the maximum number of iterations; In formulas (5) and (6), C represents the center of mass, X z and X k Indicates that in X i The value generated around, W represents the number of walks, R m Represents a random number from 1 to m, where m represents the number of problem variables.

2. The design method of sparse array antenna based on improved Pelican optimization algorithm according to claim 1 is characterized in that: The design model is set up as follows: The model is an unequally spaced linear array composed of 2N ideal point sources, and the excitation current amplitude in the linear array is centrally symmetric and the excitation phase is zero. The array antenna pattern expression is: Wherein, F(θ) represents the expression of the array antenna pattern, k=2π / λ represents the wave number, d is the array element spacing, λ is the free space wavelength, and θ is the angle between the ray direction and the array axis.

3. The design method of sparse array antenna based on improved Pelican optimization algorithm according to claim 1, characterized in that: In the improved POA, the fitness of each individual is obtained by the following fitness function value expression: Where fit is the fitness function value, PSL is the peak sidelobe level, TPSL is the target peak sidelobe level, NSLL is the deep zero level, α and β are weight coefficients, and α+β=1, F(θ i ) represents the array antenna pattern distribution function, i represents the current i-th deep zero point, and N0 is the number of deep zero points.

4. The design method of sparse array antenna based on improved Pelican optimization algorithm according to claim 1, characterized in that: The following steps are involved: S1: Based on the design model, the solution space of the design target is initialized by POA according to the following model; x i,j =l j +rand·(u j -l j ),i=1,2,…,N,j=1,2,…,m (10) Each pelican is randomly generated between the upper and lower bounds of the given problem; where x i,j is the value of the jth variable specified by the ith candidate solution, N is the number of population members, m is the number of problem variables, rand is a random number in the interval [0,1], and u j and l j They represent the upper and lower position boundaries of the pelican respectively; S2: After initialization, in the current iteration, the fitness function value of each pelican in the population is calculated, and the pelican individual with the smallest fitness function value in the population is selected as the current best individual X through the following model: best , which is considered to be the most suitable hunting position for pelicans, i.e. the optimal solution; its fitness function value is f best ; At the same time, the fitness function value of the prey is set to prepare for the next hunt; f best =min(f(X i )) (11) S3: Enter the stage of moving towards the prey. By comparing the fitness function values ​​of the pelican and the prey, the new state of the pelican is updated using formula (1), and the position of the pelican is updated using formula (2); S4: Entering the stage of spreading wings on the water, based on the prey position information obtained in the stage of moving towards the prey, the pelican will fly to the water surface, flap its wings, and force the prey into the shallow water area. At this time, the new state of the pelican in the stage of spreading wings on the water is updated using formula (3), and then compared with the objective function value, and formula (4) is used to determine whether the new position of the pelican needs to be updated; S5: Entering the triangular walking stage, based on the last updated position of the pelican in the water wing-spreading stage, the pelican position update model of the triangular walking stage described in formulas (5) and (6) is used to update the pelican position in the triangular walking stage; S6: After the above three stages of iterative updates are completed, the fitness function values ​​of all pelicans in the population are calculated, and then they are sorted from small to large according to the fitness function values, and the pelican with the smallest fitness function value is selected, the best individual pelican is updated, and the position of the next pelican is determined; S7: After each iteration, determine whether the algorithm has reached the maximum number of iterations. If so, the algorithm ends and outputs the optimal solution X best ; Otherwise, after increasing the number of iterations, return to S2 and continue iterating.

5. The design method of sparse array antenna based on improved Pelican optimization algorithm according to claim 4 is characterized in that: The initialization includes: setting the initial evolutionary generation t=1, setting the population size N, the maximum number of iterations of the algorithm T, the dimension m of the problem, and the feasible solution space of the problem, and randomly generating a set of initial solutions: Where N is the population size, X is the population matrix of pelicans, and X i It is the i-th pelican.

6. The design method of sparse array antenna based on improved Pelican optimization algorithm according to claim 4, characterized in that: The individual fitness is obtained through the following calculation model: Where fit is the fitness function value, PSL is the peak sidelobe level, TPSL is the target peak sidelobe level, NSLL is the deep zero level, α and β are weight coefficients, and α+β=1, F(θ i ) represents the array antenna pattern distribution function, i represents the current i-th deep zero point, and N0 is the number of deep zero points.

7. The sparse array antenna design method based on the improved Pelican optimization algorithm according to claim 3 or 6, characterized in that: The weight coefficients α and β are selected in the following manner: according to the degree to which the directional diagram of the design area is close to the design target, the weight coefficient of the area with slow evolution is increased, and the values ​​of α and β are obtained through experiments.

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