A method and system for designing low sidelobe patterns of sparse array antennas

Abstract

The present invention discloses a method and system for designing low sidelobe patterns of sparse array antennas. The method comprises: initializing the population using Logistic‑tent chaotic mapping, and optimizing the fitness value of the sparse array antenna pattern through random motion and hard frost puncture crossover. By recalculating the fitness value and updating the position, the system outputs the optimization result when the maximum number of iterations or the accuracy of the solution is reached. The improved RIME algorithm: 1. When initializing the population, a chaotic function is introduced to make the movement and condensation of each rime particle more covering and random. 2. In the hard frost puncture stage, the Levy flight function is introduced to control the puncture distance during the hard frost puncture process, so that the area of ​​information exchange is wider, the information network is larger, and the result is more excellent. The present invention has diversity and randomness, can effectively avoid falling into the local optimum, and obtain the optimized pattern design result within a certain number of iterations, and can also be extended to optimization problems in other engineering fields.

Description

Technical Field

[0001] The invention relates to the technical field of mobile communication antenna design and optimization, and in particular to a method and system for designing low sidelobe patterns of sparse array antennas based on an improved RIME algorithm. Background Art

[0002] The gain provided by a single antenna has defects such as weak directivity, low gain, and wide main lobe when achieving long-distance communication. Array antennas can make up for this shortcoming of single antennas. Compared with single antennas, array antennas increase the coherence of signals and thus obtain higher gain. Therefore, array antennas play an important role in modern wireless communication systems.

[0003] Equidistant array antennas have been widely studied and applied due to their advantages such as ease of mathematical analysis and simple assembly of array structures. However, there are two major shortcomings of equidistant antenna arrays: First, in order to ensure that no grating lobes appear inside the visible area, the spacing between adjacent array elements of equidistant array antennas cannot exceed half the wavelength. In addition, when high gain and high resolution are required, a large array aperture is required, and an equidistant array requires a considerable number of antenna elements, resulting in higher costs. Second, the main lobe width of the array antenna pattern is inversely proportional to the aperture size, so in order to obtain a narrower main lobe width, the designed antenna aperture is often larger, which also leads to higher array design costs.

[0004] If non-uniformly spaced array antennas are used, the above disadvantages can be effectively overcome and the cost can be greatly reduced. The array design can be realized by sparsely distributing antenna elements on a certain aperture. Higher gain and higher resolution can be obtained with fewer antenna elements, which can make the structure simple and the cost low. Therefore, sparsely distributed array antennas have important research significance.

[0005] The sparse array antenna pattern synthesis can meet the required antenna array radiation characteristics as much as possible by determining certain necessary parameters. In the radiation characteristics of the antenna array, the side lobe will cause power waste and affect the adjacent systems. Therefore, generating a directional beam in a specific direction while keeping the sidelobe level (SLL) low can avoid the dispersion of radiation power, which is an important goal of array antenna pattern synthesis.

[0006] The Rime (RIME) optimization algorithm is an evolutionary intelligent swarm optimization algorithm. The inspiration of the Rime optimization algorithm mainly comes from the rime phenomenon in nature in autumn and winter, including the condensation and puncture process of the rime phenomenon, simulating the growth process of rime. The growth process of rime is affected by wind speed. When the wind speed is small and mild, the rime particles will float with the wind and randomly condense with other rime particles to form rime agents, that is, agent populations, and then multiple agent populations form the entire rime population. The condensation of rime has an upper limit and a lower limit, which is used to regularize the initial population so that information can be better transmitted later. When the wind speed is large and strong, the condensed rime agents will grow and puncture with the wind direction, communicate information with other agent populations, and finally compare and select, thereby selecting the best optimization result.

[0007] Some studies have shown that compared with Particle Swarm Optimization (PSO), Differential Evolution (DE), Ant Lion Optimization Algorithm (ALO) and Sparrow Search Algorithm (SSA), RIME has higher accuracy in the optimization process and can effectively converge to the optimal solution of the problem. At the same time, RIME also has strong robustness and adaptability, and it can solve optimization problems in many fields, such as machine learning parameter optimization, image processing, drone path planning, power distribution, etc.

[0008] In the field of mobile communication antenna design, when evolutionary algorithms such as the locust optimization algorithm and the antlion optimization algorithm are used to solve the antenna pattern synthesis problem, if a deep zero point 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 zero point. 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 zero point level. The RIME algorithm has an optimization process of first grouping and condensing and then puncturing and crossing. It explores more search domains and regularizes data in the early stage, and punctures and crosses to communicate information in the middle and late stages to find better values ​​in a more accurate and effective way. Therefore, it can greatly improve the global and local search capabilities and is an algorithm that can better solve the antenna pattern synthesis problem.

[0009] The optimization problem of array element position in the sparse array antenna synthesis problem is a nonlinear optimization problem. At present, a variety of intelligent optimization algorithms have been successfully applied to this problem, such as genetic algorithm, simulated annealing algorithm, particle swarm algorithm, biogeography-based optimization algorithm, gray wolf optimization algorithm, invasive weed optimization algorithm and balanced optimization algorithm. With the deepening of research, the above algorithms generally have defects such as easy to fall into local optimality and slow convergence speed.

[0010] However, similar to other evolutionary algorithms, due to its evolutionary characteristics and randomness, the RIME algorithm also has the problems of long calculation time and slow convergence speed. Summary of the invention

[0011] In view of the defects of the prior art, the present invention provides a method and system for designing low sidelobe patterns of sparse array antennas, initializes the population based on the Logistic chaotic mapping of random variables, improves the mathematical model in the soft frost search behavior, and introduces the Levy flight function into the hard frost puncture process in the algorithm, so that the transmission of information is more random and less likely to fall into the local optimum; and uses the improved RIME algorithm to solve the problem of synthesizing the low sidelobe patterns of sparse array antennas.

[0012] In order to achieve the above invention object, the technical solution adopted by the present invention is as follows:

[0013] A method for designing a low sidelobe pattern of a sparse array antenna comprises the following steps:

[0014] S1. Based on the design model, determine the solution space of the design goal and clarify the directional pattern characteristics that need to be optimized.

[0015] S2. Use the Logistic-tent chaotic mapping method to initialize the positions of individuals in the rime population. Initialize the individual positions of the population through the chaotic mapping method to increase the diversity and randomness of the population.

[0016] S3. Initialize the population matrix, arrange and represent the attributes of individuals according to certain rules to form a population matrix.

[0017] S4. Under low wind speed conditions, proxy rime populations are formed through random movement and condensation.

[0018] S5. Under strong wind conditions, the information among the proxy rime population is communicated through hard frost puncture cross-pollination, and the fitness value of the population is optimized.

[0019] S6. While the hard frost is piercing and crossing, the fitness values ​​of the rime particles are compared and selected.

[0020] S7: After one iteration is completed, the fitness value of each individual is recalculated, and the minimum fitness value, maximum fitness value and corresponding position are updated;

[0021] S8: Determine whether the algorithm has reached the maximum number of iterations or the accuracy of the solution. If so, it outputs the optimized result; otherwise, it returns to S3.

[0022] Furthermore, the design model in S1 specifically includes:

[0023] The model consists of a non-equidistant linear array consisting of 2N ideal point sources.

[0024] The array element positions are symmetrical about the center of the array antenna and the excitation phase is zero.

[0025] The mathematical expression of the directional pattern is:

[0026]

[0027] in is 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.

[0028] Furthermore, Logistic chaotic mapping is used in S2 to initialize the positions of individuals in the rime population. The formula is as follows:

[0029] x(t+1)=μx(t)(1-x(t))

[0030] Where t is the chaotic time step, x(t) is the state of the system or the value of the variable at time point t, and μ is the control parameter.

[0031] Furthermore, the population matrix initialized in S3 is as follows:

[0032]

[0033]

[0034] Among them, R represents the entire two-dimensional matrix, which contains multiple sub-matrices S i , i is the sequence number of the rime agent, j is the sequence number of the rime particle, S i Represents each submatrix in the matrix R, which contains a set of values ​​{x i1 ,x i2 ,...,x ij}, each S i Represents the status or location information of a rime population, x ij is the submatrix S i Every element in .

[0035] Furthermore, the update position formula of random motion and condensation under low wind speed in S4 is as follows:

[0036]

[0037] in, is the new position of the updated particle, i and j represent the jth particle of the i-th time agent. best，j is the jth particle of the best proxy rime in the rime population R. Parameter r1 is a random number in the range (-1, 1), and r1 controls the direction in which the particle moves. ij and Lb ij represents the upper limit in the solution space, r2 is used to control the probability of particle movement, E is a threshold used to control the condition of whether the particle moves, and h is the adhesion, which is a random number in the range of (0, 1) and is used to control the distance between the centers of two frost particles.

[0038] cosθ will change with the number of iterations as shown below:

[0039]

[0040]

[0041] Among them, β is the environmental factor, which follows the number of iterations to simulate the influence of the external environment and is used to ensure the convergence of the algorithm, w represents a constant, and t represents the time step, which is used to control the number of iterations of the algorithm.

[0042] Furthermore, the position update formula of the hard frost puncture intersection under the strong wind condition in S5 is as follows:

[0043]

[0044] Among them, F normr (S i ) represents the normalized value of the current agent fitness value, indicating the chance of the agent being selected at the i-th time. r3 is a random number in the range (-1, 1).

[0045] Furthermore, in S6, the fitness values ​​of the rime particles are compared and selected, and a positive greedy selection mechanism is adopted to replace and record the best fitness value and the best agent generation by generation.

[0046] The present invention also discloses a system for designing low sidelobe patterns of sparse array antennas. The system can be used to implement the above-mentioned method for designing low sidelobe patterns of sparse array antennas, and specifically includes:

[0047] Design target module: responsible for designing the model, determining the solution space of the design target, and clarifying the directional pattern characteristics that need to be optimized.

[0048] Population initialization module: responsible for initializing the positions of individuals in the rime population using the Logistic-tent chaotic mapping method and initializing the population matrix.

[0049] Rime population formation module: responsible for forming proxy rime populations through random movement and condensation under low wind speed conditions.

[0050] Cross optimization module: responsible for communicating information among agent rime populations through frost puncture cross under strong wind conditions and optimizing the fitness value of the population.

[0051] Fitness evaluation module: responsible for comparing and selecting the fitness values ​​of rime particles, and evaluating the quality of rime according to the objective function of the algorithm.

[0052] Iteration control module: responsible for recalculating the fitness value of each individual after an iteration is completed, and updating the minimum fitness value, maximum fitness value and corresponding position.

[0053] Optimization result output module: responsible for determining whether the algorithm has reached the maximum number of iterations or the accuracy of the solution. If so, it outputs the optimized result.

[0054] The present invention also discloses a computer device, including a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned method for designing low sidelobe patterns of sparsely distributed array antennas when executing the program.

[0055] The present invention also discloses a computer-readable storage medium on which a computer program is stored. When the program is executed by a processor, the method for designing a low sidelobe pattern of a sparsely distributed array antenna is realized.

[0056] Compared with the prior art, the advantages of the present invention are:

[0057] 1. The improved RIME algorithm is used for comprehensive design of directional diagrams, which enhances the algorithm's population diversity and local exploration capabilities in the middle and late stages, and effectively avoids falling into local optimality.

[0058] 2. The improved RIME algorithm uses the Logistic sequence in the population initialization stage, which increases the randomness during the search and improves the global search capability of the optimization process.

[0059] 3. The Levy flight function is introduced to improve the hard frost puncture intersection part, which enhances the information search ability of the algorithm and helps to better avoid falling into local optimality.

[0060] 4. While keeping the main lobe width unchanged, the side lobe level is effectively suppressed, forming a side lobe level lower than the index requirement, thereby improving the performance of the radiation pattern.

[0061] 5. For the first time, the optimization algorithm was applied to the problem of synthesizing low sidelobe patterns of sparsely distributed array antennas, and an improved rime optimization algorithm was proposed, providing new ideas and methods for solving this problem.

[0062] 6. The improved rime optimization algorithm used is universal and portable, and can be applied to optimization problems in related fields, expanding the depth and breadth of the application of the rime optimization algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is the directional map obtained by the Grey Wolf Optimization Algorithm in Example 1 of the present invention.

[0064] Figure 2 This is the directional map obtained by the weed optimization algorithm in Example 1 of the present invention.

[0065] Figure 3 This is the directional diagram obtained by the rime optimization algorithm in Example 1 of the present invention.

[0066] Figure 4 This is a convergence curve diagram obtained by the rime optimization algorithm in Example 1 of the present invention.

[0067] Figure 5 This is the directional diagram obtained by improving the rime optimization algorithm in Example 1 of the present invention.

[0068] Figure 6 This is a convergence curve diagram obtained by improving the rime optimization algorithm in Example 1 of the present invention.

[0069] Figure 7 This is a sparse array element position distribution map obtained by improving the rime optimization algorithm in Example 1 of the present invention.

[0070] Figure 8 This is the directional map obtained by the Grey Wolf Optimization Algorithm in Example 2 of the present invention.

[0071] Fig. 9 This is the directional graph obtained by the particle swarm optimization algorithm in Example 2 of the present invention.

[0072] Fig.10 This is the directional diagram obtained by the rime optimization algorithm in Example 2 of the present invention.

[0073] Fig.11 This is a convergence curve diagram obtained by the rime optimization algorithm in Example 2 of the present invention.

[0074] Fig.12 This is the directional diagram obtained by improving the rime optimization algorithm in Example 2 of the present invention.

[0075] Fig.13 This is a convergence curve diagram obtained by improving the rime optimization algorithm in Example 2 of the present invention.

[0076] Fig.14 This is a sparse array element position distribution map obtained by improving the rime optimization algorithm in Example 2 of the present invention. DETAILED DESCRIPTION

[0077] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and examples.

[0078] Example 1

[0079] The present invention provides a method for designing a low sidelobe pattern of a sparse array antenna, comprising:

[0080] Setting up a comprehensive design model for low sidelobe patterns of sparse array antennas with design objectives;

[0081] Obtaining the optimal solution of the design model under the design goal through the improved RIME algorithm;

[0082] The design goal is to form a sidelobe level lower than the expected value in the sidelobe area while ensuring that the main lobe width of the array antenna remains unchanged;

[0083] The improved RIME algorithm adopts a Logistic-tent chaotic mapping based on random variables, a Levy flight function and a mathematical model adjustment strategy;

[0084] The Logistic chaotic map based on random variables is:

[0085] x(t+1)=μx(t)(1-x(t)) (1)

[0086] Where t is the chaotic time step. For any t value x(t)∈[0,1], t is an adjustable parameter to ensure that the mapped x(t) is always in the range [0,1]. x(t) is the proportion of the population size at t to the maximum possible population size. μ is a control parameter with a value range of μ∈[0,4]. Within the range, the larger μ is, the higher the chaos value is. When μ is 4, it is in a completely chaotic state.

[0087] The Levy flight function is:

[0088] When the rime algorithm searches for the optimal solution, the rime particles will gather towards the optimal proxy population. When solving complex problems, the solution obtained in this way is usually not the global optimal solution, which will cause the algorithm to fall into the local optimal solution. Research has found that Levy flight is a random walk motion that combines long and short steps, which increases the search range of particle space and increases particle diversity, thereby jumping out of the local optimal solution and improving the search efficiency of the algorithm.

[0089] Therefore, the Levy flight function is introduced for improvement. The Levy flight random step function is as follows:

[0090]

[0091] In the formula, v and μ are random numbers that obey the normal distribution, and their respective definitions are:

[0092]

[0093] In the above formula, σ v and σ μ The calculation formula is:

[0094]

[0095] In this formula, usually This section Γ is the standard Gamma function.

[0096] The mathematical model is improved as follows:

[0097] Original algorithm formula

[0098]

[0099] in

[0100]

[0101] In the new improvement, Change to And change it into the source formula of MATLAB.

[0102] The following are the specific implementation steps of a method for designing a low sidelobe pattern for a sparse array antenna:

[0103] S0: Set the comprehensive design model of the array antenna pattern. The model is a non-uniformly spaced linear array composed of 2N ideal point sources. The positions of the array elements in the linear array are symmetrical about the center of the array antenna and the excitation phase is zero. The pattern expression is shown in equation (12). The design goal is to form a sidelobe level lower than the expected value in the sidelobe area while ensuring that the array main lobe width remains unchanged:

[0104]

[0105] Where F(θ) represents the array antenna pattern expression, 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.

[0106] The above design model can fully reduce optimization variables, lower calculation costs, and obtain excellent design solutions.

[0107] S1: Based on the design model of S0, the RIME algorithm is initialized for the solution space of its design target. The positions of the individuals in the rime population are initialized using the Logistic chaos mapping formula (1);

[0108] x(t+1)=μx(t)(1-x(t)) (1)

[0109] Where t is the chaotic time step. For any t value x(t)∈[0,1], t is an adjustable parameter to ensure that the mapped x(t) is always in the range [0,1]. x(t) is the proportion of the population size at t to the maximum possible population size. μ is a control parameter with a value range of μ∈[0,4]. Within the range, the larger μ is, the higher the chaos value is. When μ is 4, it is in a completely chaotic state.

[0110]

[0111]

[0112] The representation of the agent population is shown in the formula, and the entire population R can be represented by X ij It is represented by formula (2). In this formula, i is the sequence number of the rime agent, j is the sequence number of the rime particle, and F(S i ) is the fitness value of individual particles in the rime population.

[0113] S2: Under low wind speed conditions, individual rime particles move randomly and condense in a limited space, forming rime agents one after another, i.e., agent populations;

[0114]

[0115] In the formula, is the new position of the updated particle, i and j represent the jth particle of the i-th time agent. best,j is the jth particle of the best proxy rime in the rime population R. Parameter r1 is a random number in the range (-1, 1), and r1 controls the direction in which the particle moves, and cosθ will change with the number of iterations, as shown in the following equation. β is an environmental factor that follows the number of iterations to simulate the influence of the external environment and is used to ensure the convergence of the algorithm, as shown in the following equation. h is the adhesion, which is a random number in the range (0, 1) and is used to control the distance between the centers of two frost particles.

[0116]

[0117]

[0118] S3: After the formation of each rime agent, under the condition of strong wind, each proxy rime population, i.e., rime agent, will harden, thereby piercing and crossing, and exchanging the fitness values ​​in each proxy population, so as to facilitate the selection of the optimal value;

[0119]

[0120] F normr (S i ) represents the normalized value of the current agent fitness value, indicating the chance of the agent being selected at the i-th time. r3 is a random number in the range (-1, 1).

[0121] S4: While the hard frost pierces and crosses, the fitness values ​​of the rime particles will be compared and selected, and the positive greedy selection mechanism is used here.

[0122] Typically, metaheuristic optimization algorithms have a greedy selection mechanism that replaces and records the best fitness value and the best agent after each update. The typical idea is to compare the agent's updated fitness value with the global optimum, and if the updated value is better than the current global optimum, replace the best fitness value and record the agent as the optimal value. The benefit of this operation is that it is simple and fast, but there is nothing outstanding about it, it just serves as a record.

[0123] Therefore, a greedy selection mechanism that actively participates in population updates is proposed to improve the efficiency of global search. The specific idea is to compare the fitness value of the agent after the update with the fitness value of the agent before the update. If the updated fitness value is better than the value before the update, it will be replaced, and the solutions of the two agents will be replaced at the same time. This mechanism improves the quality of the global solution by actively replacing agents, so that there are always good agents in the population. On the other hand, since the positions of agents in the population change significantly with each iteration, it is inevitable that there will be agents that are worse than the population before the update and are not conducive to the next iteration. Therefore, this operation can be used to ensure that the population evolves in a better direction at each iteration.

[0124] S5: After one iteration is completed, the fitness value of each individual is recalculated, and the minimum fitness value, maximum fitness value and corresponding position are updated;

[0125] S6: Determine whether the algorithm has reached the maximum number of iterations or the accuracy of the solution. If so, it outputs the optimization result; otherwise, it returns to S2.

[0126] The present invention is described below in conjunction with simulation experiments.

[0127] 1. Experimental content:

[0128] A pattern synthesis design is performed on a linear array described by equation (10) in which the array element positions are symmetrical about the center of the array antenna. Experimental examples are used to verify the effect of the algorithm proposed in the present invention on the low sidelobe pattern synthesis problem of sparse array antennas.

[0129] Experiment 1: 2N = 20, compared with the 20-element array LAA optimization in the paper "Pattern Synthesis of Uniform and Sparse Linear Antenna Array Using Mayfly Algorithm" published by EUNICE OLUWABUNMIOWOOLA, KEWEN XIA, TING WANG, ABUBAKARUMAR. Among them, the main lobe width 2θ0 = 16° and the side lobe area is θ = [0°, 82°] and θ = [98°, 180°]. The population size is 30 and the number of iterations is 500.

[0130] 2. Experimental results:

[0131] Figure 1 This is the array pattern obtained by optimizing the Grey Wolf optimization algorithm, where the highest level in the sidelobe area is -19.93dB. Figure 2 This is the array pattern obtained by optimizing the weed optimization algorithm, where the maximum level in the sidelobe area is -18.69dB. Figure 3 and Figure 5 The array patterns obtained by optimizing the original rime optimization algorithm and the improved rime optimization algorithm are shown in Figure 2, and the maximum levels of the sidelobe areas are -21.09dB and -22.38dB respectively. It can be seen that the peak sidelobe level of the improved rime optimization algorithm is 1.29dB lower than that of the original rime optimization algorithm, and the main lobe of the original rime optimization algorithm is 2.4° wider than that of the improved rime optimization algorithm; it is 2.45dB lower than the peak sidelobe level of the gray wolf optimization algorithm, and 3.69dB lower than the peak sidelobe level of the weed optimization algorithm, and the main lobe is not widened. Figure 4 and Figure 6 These are the convergence curves obtained by the original rime optimization algorithm and the improved rime optimization algorithm. Figure 7 The array element distribution obtained under the optimal condition of the improved rime algorithm is given. It can be seen that the low sidelobe pattern design method of the sparse array antenna based on the improved RIME algorithm proposed in the present invention can meet the minimum spacing constraint between array elements, and the optimized array element position pattern has a lower peak sidelobe level, and the convergence speed and convergence performance are better, which verifies the effectiveness of the algorithm proposed in the present invention.

[0132] The comparison between the four is shown in Table 1 below (two decimal places are retained):

[0133] Table 1 Comparison of simulation results of different algorithms

[0134] algorithm Peak sidelobe level (dB) Main lobe width Improved rime optimization algorithm -22.38 13.4° Original rime optimization algorithm -21.09 15.8° Gray Wolf Optimization Algorithm -19.93 14.2° Weed Optimization Algorithm -18.69 13.2°

[0135] Example 2

[0136] The present invention is further described below in conjunction with simulation experiments.

[0137] 1. Experimental content:

[0138] A pattern synthesis design is performed on a linear array described by equation (10) in which the array element positions are symmetrical about the center of the array antenna. Experimental examples are used to verify the effect of the algorithm proposed in the present invention on the low sidelobe pattern synthesis problem of sparse array antennas.

[0139] Experiment 1: 2N = 32, compared with the 32-element array LAA in the paper "Pattern Synthesis of Uniform and Sparse Linear Antenna Array Using Mayfly Algorithm" published by EUNICE OLUWABUNMIOWOOLA, KEWEN XIA, TING WANG, ABUBAKARUMAR. The main lobe width 2θ0 = 10° and the side lobe area is θ = [0°, 85°] and θ = [95°, 180°]. The population size is 30 and the number of iterations is 500.

[0140] 2. Experimental results:

[0141] Figure 8 This is the array pattern obtained by optimizing the Grey Wolf optimization algorithm, where the highest level in the sidelobe area is -16.84dB. Fig. 9 This is the array pattern optimized by the particle swarm optimization algorithm, in which the highest level in the sidelobe area is -18.91dB. Fig.10 and Fig.12 The array patterns obtained by the original rime optimization algorithm and the improved rime optimization algorithm are shown in Figure 1, and the maximum levels of the sidelobe areas are -18.98dB and -22.49dB respectively. It can be seen that the peak sidelobe level of the improved rime optimization algorithm is 3.51dB lower than that of the original rime optimization algorithm, 5.65dB lower than that of the gray wolf optimization algorithm, and 3.58dB lower than that of the particle swarm optimization algorithm, and the main lobe is not widened. Fig.11 and Fig.13 These are the convergence curves obtained by the original rime optimization algorithm and the improved rime optimization algorithm. Fig.14The array element distribution obtained under the optimal condition of the improved rime algorithm is given. It can be seen that the low sidelobe pattern design method of the sparse array antenna based on the improved RIME algorithm proposed in the present invention can meet the minimum spacing constraint between array elements, and the optimized array element position pattern has a lower peak sidelobe level, and the convergence speed and convergence performance are better, which verifies the effectiveness of the algorithm proposed in the present invention.

[0142] The comparison between the four is shown in Table 2 below (two decimal places are retained):

[0143] Table 2 Comparison of simulation results of different algorithms

[0144] algorithm Peak sidelobe level (dB) Main lobe width Improved rime optimization algorithm -22.49 8° Original rime optimization algorithm -18.98 8.4° Gray Wolf Optimization Algorithm -16.84 7.4° Particle Swarm Optimization -18.91 7.4°

[0145] Example 3

[0146] A system for designing a low sidelobe pattern of a sparse array antenna is provided. The system can be used to implement the above-mentioned method for designing a low sidelobe pattern of a sparse array antenna, and specifically includes:

[0147] Design target module: responsible for designing the model, determining the solution space of the design target, and clarifying the directional pattern characteristics that need to be optimized.

[0148] Population initialization module: responsible for initializing the positions of individuals in the rime population using the Logistic-tent chaotic mapping method and initializing the population matrix.

[0149] Rime population formation module: responsible for forming proxy rime populations through random movement and condensation under low wind speed conditions.

[0150] Cross optimization module: responsible for communicating information among agent rime populations through frost puncture cross under strong wind conditions and optimizing the fitness value of the population.

[0151] Fitness evaluation module: responsible for comparing and selecting the fitness values ​​of rime particles, and evaluating the quality of rime according to the objective function of the algorithm.

[0152] Iteration control module: responsible for recalculating the fitness value of each individual after an iteration is completed, and updating the minimum fitness value, maximum fitness value and corresponding position.

[0153] Optimization result output module: responsible for determining whether the algorithm has reached the maximum number of iterations or the accuracy of the solution. If so, it outputs the optimized result.

[0154] Example 4

[0155] In another embodiment of the present invention, a terminal device is provided, the terminal device includes a processor and a memory, the memory is used to store a computer program, the computer program includes program instructions, and the processor is used to execute the program instructions stored in the computer storage medium. The processor may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), field-programmable gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc., which are the computing core and control core of the terminal, which are suitable for implementing one or more instructions, and are specifically suitable for loading and executing one or more instructions to implement the corresponding method flow or corresponding functions; the processor described in the embodiment of the present invention can be used for the operation of the above-mentioned sparse array antenna low sidelobe pattern design method.

[0156] Example 5

[0157] In another embodiment of the present invention, a storage medium is also provided, specifically a computer-readable storage medium (Memory), which is a memory device in a terminal device for storing programs and data. It can be understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and the extended storage medium supported by the terminal device. The computer-readable storage medium provides a storage space, which stores the operating system of the terminal. In addition, one or more instructions suitable for being loaded and executed by the processor are also stored in the storage space, and these instructions can be one or more computer programs (including program codes). It should be noted that the computer-readable storage medium here can be a high-speed RAM memory, or a non-volatile memory (non-volatile memory), such as at least one disk storage.

[0158] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the method for designing low sidelobe patterns of sparsely distributed array antennas in the above-mentioned embodiment; one or more instructions in the computer-readable storage medium are loaded and executed by the processor.

[0159] Those skilled in the art will appreciate that embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0160] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0161] These computer program instructions may also be stored in a computer readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0162] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0163] Those skilled in the art will appreciate that the embodiments described herein are intended to help readers understand the implementation methods of the present invention, and should be understood that the protection scope of the present invention is not limited to such special statements and embodiments. Those skilled in the art can make various other specific variations and combinations that do not deviate from the essence of the present invention based on the technical revelations disclosed by the present invention, and these variations and combinations are still within the protection scope of the present invention.

Claims

1. A method for designing a low sidelobe pattern of a sparse array antenna, characterized in that: The following steps are involved: S1. Based on the design model, determine the solution space of the design target and clarify the directional pattern characteristics that need to be optimized; S2. Use the Logistic-tent chaotic mapping method to initialize the positions of the individuals in the rime population, and use the chaotic mapping method to initialize the individual positions of the population to increase the diversity and randomness of the population; S3, initialize the population matrix, arrange and represent the attributes of individuals according to certain rules, and form a population matrix; S4, under low wind speed conditions, the proxy rime population is formed through random movement and condensation; The update position formula of random motion and condensation under low wind speed is as follows: in, is the new position of the updated particle, i and j represent the jth particle of the i-th time agent; R best,j is the jth particle of the best proxy rime in the rime population R; parameter r1 is a random number in the range (-1, 1), and r1 controls the direction in which the particle moves, Ub ij and Lb ij represents the upper limit in the solution space, r2 is used to control the probability of particle movement, E is a threshold used to control the condition of whether the particle moves, and h is the adhesion, which is a random number in the range of (0, 1) and is used to control the distance between the centers of two frost particles; cosθ will change with the number of iterations as shown below: Among them, β is the environmental factor, which follows the number of iterations to simulate the influence of the external environment and is used to ensure the convergence of the algorithm, w represents a constant, and t represents the time step, which is used to control the number of iterations of the algorithm; S5. Under strong wind conditions, the information among the proxy rime population is communicated through hard frost puncture crosses, and the fitness value of the population is optimized; The formula for updating the position of the hard frost puncture intersection under strong wind conditions is as follows: Among them, F normr (S i ) represents the normalized value of the current agent fitness value, indicating the chance of the agent being selected at the i-th time; r3 is a random number in the range (-1, 1); S6. While the hard frost pierces and crosses, the fitness values ​​of the rime particles are compared and selected; S7: After one iteration is completed, the fitness value of each individual is recalculated, and the minimum fitness value, maximum fitness value and corresponding position are updated; S8: Determine whether the algorithm has reached the maximum number of iterations or the accuracy of the solution. If so, it outputs the optimized result; otherwise, it returns to S3.

2. The method for designing a low sidelobe pattern of a sparse array antenna according to claim 1, characterized in that: The design model described in S1 specifically includes: The model consists of a non-equidistant linear array consisting of 2N ideal point sources; The array element positions are symmetrical about the center of the array antenna and the excitation phase is zero; The mathematical expression of the directional pattern is: in is 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 method for designing a low sidelobe pattern of a sparse array antenna according to claim 1, characterized in that: In S2, Logistic chaos mapping is used to initialize the positions of individuals in the rime population. The formula is as follows: x(t+1)=μx(t)(1-x(t)) Where t is the chaotic time step, x(t) is the state of the system or the value of the variable at time point t, and μ is the control parameter.

4. The method for designing a low sidelobe pattern of a sparse array antenna according to claim 1, characterized in that: The population matrix initialized in S3 is as follows: Among them, R represents the entire two-dimensional matrix, which contains multiple sub-matrices S i , i is the sequence number of the rime agent, j is the sequence number of the rime particle, S i Represents each submatrix in the matrix R, which contains a set of values ​​{x i1 ,x i2 ,...,x ij }, each S i Represents the status or location information of a rime population, x ij is the submatrix S i Every element in .

5. The method for designing a low sidelobe pattern of a sparse array antenna according to claim 1, characterized in that: In S6, the fitness values ​​of rime particles are compared and selected, and a positive greedy selection mechanism is adopted to replace and record the best fitness value and the best agent generation by generation.

6. A system for designing low sidelobe patterns of sparse array antennas, characterized in that: The system can be used to implement the method for designing low sidelobe patterns of sparse array antennas according to any one of claims 1 to 5, specifically comprising: Design target module: responsible for designing the model, determining the solution space of the design target, and clarifying the directional pattern characteristics that need to be optimized; Population initialization module: responsible for initializing the positions of individuals in the rime population using the Logistic-tent chaotic mapping method and initializing the population matrix; Rime population formation module: responsible for forming proxy rime populations through random movement and condensation under low wind speed conditions; Cross optimization module: responsible for exchanging information among the proxy rime population through hard frost puncture cross under strong wind conditions and optimizing the fitness value of the population; Fitness evaluation module: responsible for comparing and selecting the fitness values ​​of rime particles, and evaluating the quality of rime according to the objective function of the algorithm; Iteration control module: responsible for recalculating the fitness value of each individual after an iteration is completed, and updating the minimum fitness value, maximum fitness value and corresponding position; Optimization result output module: responsible for determining whether the algorithm has reached the maximum number of iterations or the accuracy of the solution. If so, it outputs the optimized result.

7. A computer device, characterized in that: The invention comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method for designing a low sidelobe pattern of a sparse array antenna as claimed in any one of claims 1 to 5 is implemented.

8. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the program is executed by a processor, the method for designing a low sidelobe pattern of a sparse array antenna as described in one of claims 1 to 5 is implemented.

Images