A time-varying modulated opportunity array radar pattern synthesis method

Abstract

The application discloses a time-varying modulation opportunity array radar pattern synthesis method and belongs to the opportunity array radar field. The method comprises the following steps: constructing an opportunity array radar array pattern target function with the minimum side lobe peak level and first-order sideband level as the target, constructing a fuzzy opportunity constraint condition with a subarray position state, a subarray quantity and an array element time sequence in each subarray, obtaining a fuzzy opportunity constraint programming model of the opportunity array radar pattern synthesis, and optimizing and solving the fuzzy opportunity constraint programming model based on an adaptive differential evolution algorithm under the chaos elite and center guide thought to obtain the best array element switch time sequence and position. The trapezoidal pulse modulation is adopted in the application, and compared with the traditional rectangular pulse, the frequency spectrum energy distribution is more efficient; and through the fuzzy opportunity constraint programming model, the direction pattern synthesis can be completed by using 30%-70% of the subarray quantity in the confidence water time, and resource waste is reduced.

Description

Technical Field

[0001] This invention relates to the field of opportunistic array radar, and particularly to a time-varying modulation method for pattern synthesis of opportunistic array radar. Background Technology

[0002] Opportunistic array radar (OAR) takes platform stealth as its core objective. Based on the theory of opportunity, it decomposes and reconstructs radar sub-units, and can flexibly adjust the unit layout and working status according to the mission. It is suitable for stealth (low probability of intercept beam) and anti-stealth (high gain focused beam) requirements, and has key value in complex combat environments.

[0003] To address the problem of radiation pattern synthesis in dynamic OAR scenes, existing research proposes methods including mathematical analysis, intelligent algorithms, and hybrid solutions. These encompass opportunity-constrained programming methods that combine uncertainty in cell position and switching state; schemes that integrate mathematical analysis and intelligent optimization algorithms to address the randomness of cell distribution and the influence of excitation states; and techniques for reconstructing the radiation pattern of non-fixed array elements using improved intelligent optimization algorithms after modeling the dynamic scene. Simultaneously, time-varying modulation technology is used to simplify the feeding network of large-scale arrays. It introduces a time dimension to control electromagnetic radiation, and through high-frequency switching and high-speed digital control, periodically modulates antenna parameters, generating low-sidelobe concealed beams (stealth) or high-gain detection beams (anti-stealth) depending on the mission.

[0004] However, existing technologies have significant shortcomings: First, the optimization of multi-focusing unit parameters does not fully combine the differentiated beam requirements of stealth and anti-stealth, nor does it fully leverage the dynamic shaping advantages of time-varying modulation technology. Second, in time-varying modulation applications, existing optimization strategies do not design differentiated objectives for the two types of tasks, making it difficult to match requirements. Third, modulation methods have limitations; fixed weights cannot dynamically respond to task switching, variable periods or alternative pulses increase overall complexity, and techniques such as subarray partitioning and convex optimization may ignore the impact of timing and sideband levels on stealth, or lead to model distortion and decreased optimality. Fourth, the simplification of the feed network and beam performance are not effectively balanced, making it difficult to meet the stringent requirements of both types of tasks for pattern accuracy.

[0005] In summary, how to combine time-varying modulation with the opportunistic requirements of OAR to design a comprehensive model and algorithm that adapts to the task and takes into account multiple core requirements remains a key bottleneck in the current development of OAR technology. Summary of the Invention

[0006] Purpose of the invention: To address the above problems, the purpose of this invention is to provide a time-varying modulated opportunistic array radar pattern synthesis method.

[0007] Technical Solution: The present invention provides a time-varying modulation method for synthesizing the radiation pattern of an opportunistic array radar, comprising: constructing an objective function for the radiation pattern of the opportunistic array radar with the goal of minimizing the sidelobe peak level and the first-order sideband level; constructing fuzzy opportunistic constraints based on the subarray position state, the number of subarrays, and the timing sequence of the array elements in each subarray; obtaining a fuzzy opportunistic constraint planning model for synthesizing the radiation pattern of the opportunistic array radar; and optimizing the fuzzy opportunistic constraint planning model based on an adaptive differential evolution algorithm under the ideas of chaotic elites and center guidance to obtain the optimal array element switching timing and position.

[0008] Furthermore, the mathematical expression for the fuzzy chance-constrained programming model is:

[0009] ,

[0010] in, Describe the objective function. Indicates the sidelobe peak level. Indicates the first-order sideband level. Represents decision variables, Representing fuzzy variables, Represents fuzzy parameters related to the task scenario; Indicates a measure of chance. Representing mutually independent fuzzy variables, This indicates the operating state of subarray i. A value of 1 indicates that the excitation is on, meaning the subarray participates in pattern synthesis, while a value of 0 indicates that the excitation is off, meaning the subarray does not participate in pattern synthesis. Indicates the confidence level, and N represents the total number of subarrays included in the opportunistic array radar array; This represents the decision variables for the entire opportunistic array radar. This represents the switch sequence of the subarray, where 1 indicates on and 0 indicates off. The nth subarray contains... Each array element, Indicates the first Individual formations, the first The array element in the first Opening and closing of each time slot A value of 1 indicates on, and a value of 0 indicates off; L indicates the modulation period. The number of time slots discretized; Indicates the start time of the array element. Indicates the end time; Subarray The Middle Each array element is paired with the first Time modulation switch status in each target direction This indicates that the modulation period must not exceed the maximum modulation period. ; Subarray The array element space coordinates, Refers to a region;

[0011] In the fuzzy chance-constrained programming model, the first constraint is a fuzzy chance constraint, the second and third constraints represent the working state of the subarray, which are binary decision variable constraints, the fourth constraint is a time constraint, which requires that the start time of the array element be non-negative and the stop time of the array element not exceed the time modulation period, the fifth constraint is a modulation period constraint, and the sixth constraint is a constraint on the spatial layout of the subarray.

[0012] Furthermore, during the modulation period of the opportunistic array radar, trapezoidal pulses are used to modulate the array of the opportunistic array radar.

[0013] The mathematical expression for the trapezoidal pulse is:

[0014] ,

[0015] in, This indicates the start time of a trapezoidal pulse cycle. This indicates the moment when the rising edge is reached within one cycle of a trapezoidal pulse. This indicates the moment when the falling edge is reached within a trapezoidal pulse cycle. This indicates the end time of a trapezoidal pulse cycle. Indicates duration, The weight is determined by the rising or falling edge.

[0016] Furthermore, the steps for optimizing the fuzzy chance-constrained programming model based on the adaptive differential evolution algorithm under the chaotic elite and center-guided ideas to obtain the optimal array element switching timing and position include:

[0017] Step 1: Define the optimization problem and construct the chromosome structure:

[0018] The total array size of the opportunistic array radar is The total array is divided into several arrays of size 1. The subarrays are treated as individual units, and each subarray contains... Each array element has a time modulation period of [number] times. The carrier frequency is ;

[0019] Define the range of variables: subarray position offset , Indicates that the subarray is in Offset in direction Indicates that the subarray is in Offset in direction Indicates the size of the subarray; the activation time of the array elements. Array element activation duration ,in Indicates the shortest duration. Indicates the maximum duration; sets the population size. Variable factors Crossover probability Maximum Algebra Elite ratio and elite center-oriented factors ;

[0020] Step 2: Generate a sequence of chaotic variables to initialize the population;

[0021] Step 3: Calculate the fitness value of the individual with constraints;

[0022] Step 4: Select the top-performing populations based on their fitness. Individuals are evaluated and elite centers are calculated. For each individual, center-oriented mutation is performed. After crossover, fitness calculation, and update calculation, the global optimal solution is updated. The process is iterated until termination and the result is output.

[0023] Further, step 2 includes:

[0024] forward Each individual is initialized using elite-guided initialization, and is initialized near the elite region. For the first individual... The individual in the first The initial position on the dimension is represented as:

[0025] ,

[0026] in, For the first Dimension's elite solution The disturbance radius is... This represents the chaotic value of the (n+1)th subarray, generated by the Tent chaotic map, with a value range of (0,1), which is then transformed to form the offset. ; Defined as:

[0027] ,

[0028] in, The initial chaos value, For control parameters;

[0029] back Each individual is globally initialized using Tent chaotic mapping, and the initial position of each individual is generated using Tent chaotic mapping. The individual in the first Initial position on dimension , represented as:

[0030] ,

[0031] in , They represent the first The lower and upper bounds of the dimensional search space.

[0032] Merging to form a complete initial population .

[0033] Furthermore, step 3 includes:

[0034] Step 31, Decode the individual:

[0035] Each individual corresponds to a set of optimized variable codes, including three core parameters: subarray position offset, array element activation time, and array element activation duration, which map the individual's binary code to the parameter values ​​of the physical implementation.

[0036] Step 32, construct the synthesis pattern of the time-varying modulation function:

[0037] For a single subarray m, the time-varying modulation array factor for the target direction p Represented as:

[0038] ,

[0039] in, , Indicates the angle parameter. This indicates the number of array elements, and k represents the subarray index.

[0040] The overall array pattern is obtained by superimposing the pattern of all subarrays. , represented as:

[0041] ;

[0042] Step 33, Construct the fitness function And perform the calculation, the formula is:

[0043] ,

[0044] in, This represents the weighting coefficient, used to balance the optimization priority of the sidelobe peak level (SLL) and the first-order sideband level (SBL). Indicates a constraint or penalty item. This represents the penalty coefficient, which controls the degree of impact of constraint violations on fitness.

[0045] Furthermore, step 4 includes:

[0046] Step 41, select the previous Individual and computational elite centers:

[0047] Based on the calculated individual fitness values, individuals in the population are ranked from best to worst fitness, and the top... The individual with the best fitness is called the elite individual; the center of the elite individual is calculated, i.e., the th... Population center of the generation Defined as:

[0048] ,

[0049] in, It is the first The middle generation The individual's location;

[0050] Step 42, Center-oriented mutation:

[0051] Mutation is performed on each individual in the population, and an elite center is introduced into the mutation strategy. Mutation strategy after the introduction of this elite center Write it in the following form:

[0052] ,

[0053] in, Scaling factor The guiding individuals selected from the current elite subset. , Individuals selected randomly;

[0054] Step 43, cross operation:

[0055] Binary crossover is used to generate test vectors. The rules are as follows:

[0056] ,

[0057] in, Indicates the first The generation The test vector of each individual, Indicates the first The generation The individual The test vector components of dimension, Indicates the first The generation The mutation vector of each individual, Indicates the first The generation The individual The dimensional mutation vector components, Represents a uniformly random number between 0 and 1. Indicates the first The crossover probability of each individual, ,like Then set it to 1, if Then set it to 0. Indicates a dimension index. This indicates a randomly selected dimension index. Indicates the first The generation The individual The original vector components of dimension;

[0058] Step 44, Fitness Calculation and Update:

[0059] Calculate the fitness of the experimental vector and compare it with the fitness of the original individual. If the experimental individual is better than the current individual, replace it and record the result. and ;in This represents the scaling factor for the i-th individual. Let represent the crossover probability of the i-th individual;

[0060] Add the original instance to an external save file and collect the success parameters for this generation. and The historical mean parameter is updated using a weighted average method. , ;in, Indicates scaling factor A historical memory bank used to store historically successful scaling factor values. Represents the crossover probability A historical memory bank is used to store the probability values ​​of successful crossovers in the past.

[0061] Step 45: Determine the termination condition. If the maximum number of iterations is reached or the set pattern performance index is met, then terminate the optimization and output the optimal chromosome, including the start time of the array element, the end time, and the position of the subarray.

[0062] Beneficial effects: Compared with the prior art, the significant advantages of this invention are:

[0063] 1. This invention can effectively realize pattern synthesis of large-scale opportunistic array radars in dynamic scenarios, taking into account low sidelobes, low sidebands, high dynamic adaptability and efficient optimization performance, and is suitable for electronic warfare applications in complex electromagnetic environments.

[0064] 2. This invention uses trapezoidal pulse modulation, which reduces the sidelobe peak level by at least 8dB and the first-order sideband level by at least 8dB compared to traditional rectangular pulses, resulting in more efficient spectral energy distribution.

[0065] 3. This invention utilizes a fuzzy chance-constrained programming model at a confidence level... At this time, 30%-70% of the number of subarrays can be used to complete the pattern synthesis, reducing resource waste;

[0066] 4. When the method of this invention was verified on the CEC2017 test set, the convergence speed of 10-dimensional and 30-dimensional functions was improved by 20%-30% compared with other existing algorithms, and the pattern synthesis time of a large-scale array of 1600 elements was only 2614.2 seconds, which is more than 50% shorter than existing methods;

[0067] 5. The optimized subarray spacing of this invention can be flexibly adjusted. Within its scope, it adapts to the deployment needs of different platforms, and the complexity of the power supply network is reduced, making it directly applicable to electronic warfare scenarios involving multi-platform collaboration. Attached Figure Description

[0068] Figure 1 A flowchart for optimizing a fuzzy chance-constrained programming model;

[0069] Figure 2 This is a trapezoidal pulse period diagram;

[0070] Figure 3 A comparison of the energy spectral density of trapezoidal pulses and rectangular pulses;

[0071] Figure 4 This is a comparison of the radiation patterns of trapezoidal pulses and rectangular pulses.

[0072] Figure 5 This is a diagram showing a uniform distribution of 4 subarrays.

[0073] Figure 6 Normalized radiation pattern of the center frequency of the 4 subarrays;

[0074] Figure 7 Normalized direction pattern of first-order sidebands of a 4-subarray;

[0075] Figure 8 This is the optimized two-dimensional distributed subarray position distribution diagram of the present invention;

[0076] Figure 9 This is the optimized center frequency normalized radiation pattern of the distributed array according to the present invention;

[0077] Figure 10 This is the optimized first-order sideband normalized direction pattern of the distributed array according to the present invention;

[0078] Figure 11 This is a timing diagram of the array elements in the optimized distributed array of the present invention;

[0079] Figure 12This is a diagram showing the subarray positions in a large planar antenna array with 1600 elements.

[0080] Figure 13 The normalized radiation pattern is the center frequency pattern;

[0081] Figure 14 This is a normalized direction pattern for first-order sidebands.

[0082] Figure 15 This is the normalized sideband level diagram corresponding to the first 20 sidebands;

[0083] Figure 16 This is a membership function curve of a fuzzy variable;

[0084] Figure 17 This represents the correspondence between confidence level and the range of subarray numbers.

[0085] Figure 18 A fuzzy subarray location distribution diagram for fuzzy chance-constrained programming;

[0086] Figure 19 The graph shows the changes in SLL, SBL, and confidence score as a function of the number of algorithm iterations.

[0087] Figure 20 The normalized radiation pattern is the center frequency pattern;

[0088] Figure 21 This is the normalized direction pattern of the first-order sidebands. Detailed Implementation

[0089] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and not intended to limit the scope of the invention. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the embodiments of the present invention, and not all structures.

[0090] In the following description, specific details such as target system architecture and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary detail.

[0091] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0092] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0093] Furthermore, in the description of this application and the appended claims, the terms "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0094] References to "one embodiment" or "some embodiments" in this specification mean that one or more embodiments of this application include the target features, structures, or characteristics described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized.

[0095] This embodiment describes a time-varying modulated opportunistic array radar pattern synthesis method, which includes: constructing an objective function for the opportunistic array radar pattern with the goal of minimizing the sidelobe peak level and the first-order sideband level; constructing fuzzy opportunistic constraints based on the subarray position state, the number of subarrays, and the timing sequence of array elements in each subarray; obtaining a fuzzy opportunistic constraint planning model for opportunistic array radar pattern synthesis; and optimizing the fuzzy opportunistic constraint planning model based on an adaptive differential evolution algorithm under the ideas of chaotic elites and center guidance to obtain the optimal array element switching timing and position.

[0096] As a novel radar system, opportunistic array radars feature numerous antenna elements arranged haphazardly, and the pattern synthesis of large-scale arrays under opportunistic distribution is attracting increasing attention. This invention proposes a time-varying modulation method for opportunistic array radar pattern synthesis. A fuzzy opportunistic constraint programming model is constructed for dynamic scenarios, introducing a time-modulated planar array and optimizing the array's time modulation pulses, element timing, subarray positions, and the number of subarrays. First, to better achieve harmonic beamforming, this example proposes using trapezoidal pulses for time pulse modulation and establishes the corresponding modulation pulse expression. Second, based on the successful history memory adaptive differential evolution (SHADE) algorithm, this example proposes an adaptive differential evolution algorithm under the chaotic elite and center-guided ideas, denoted as SHADE_CG. The SHADE_CG algorithm improves convergence efficiency and accuracy by optimizing the timing of elements and subarray positions within each subarray. Furthermore, considering the opportunism of the array, this example designs subarray fuzzy variables and uses the SHADE_CG algorithm to optimize the number of subarrays and the final global pattern. In addition, the fuzzy opportunistic constraint programming model can optimize relevant variables as needed in dynamic scenarios to address the uncertainty problem during pattern synthesis.

[0097] Furthermore, the mathematical expression for the fuzzy chance-constrained programming model is:

[0098] ,

[0099] in, Describe the objective function. Indicates the sidelobe peak level. Indicates the first-order sideband level. Represents decision variables, Representing fuzzy variables, Represents fuzzy parameters related to the task scenario; Indicates a measure of chance. Representing mutually independent fuzzy variables, This indicates the operating state of subarray i. A value of 1 indicates that the excitation is on, meaning the subarray participates in pattern synthesis, while a value of 0 indicates that the excitation is off, meaning the subarray does not participate in pattern synthesis. Indicates the confidence level, and N represents the total number of subarrays included in the opportunistic array radar array; This represents the decision variables for the entire opportunistic array radar. This represents the switch sequence of the subarray, where 1 indicates on and 0 indicates off. The nth subarray contains... Each array element, Indicates the first Individual formations, the first The array element in the first Opening and closing of each time slot L indicates the period The number of time slots discretized, with each time slot having a length of [missing information]. ; Indicates the start time of the array element, requiring that the start time be non-negative. Indicates the end time, requiring the shutdown time to not exceed the time modulation period. This is used to ensure the rationality of the timing logic of time modulation and to ensure that the working time of array elements, etc., is within one cycle; Subarray The Middle Each array element is paired with the first Time modulation switch status in each target direction This indicates that the modulation period must not exceed the maximum modulation period. ; Subarray The array element space coordinates, Refers to a region;

[0100] In the fuzzy chance-constrained programming model, the first constraint is a fuzzy chance constraint, the second and third constraints represent the working state of the subarray, which are binary decision variable constraints, the fourth constraint is a time constraint, which requires that the start time of the array element be non-negative and the stop time of the array element not exceed the time modulation period, the fifth constraint is a modulation period constraint, and the sixth constraint is a constraint on the spatial layout of the subarray.

[0101] The fuzzy chance-constrained programming model aims to minimize the objective function when the confidence level of the constraints is greater than or equal to the confidence level given in advance by the decision-maker.

[0102] Operating all subarrays simultaneously would be a waste of resources, while too few subarrays participating in pattern synthesis would result in excessively high far-field sidelobe levels. Therefore, a suitable range for the number of subarrays participating in pattern synthesis is defined here as a certain range. This indicates the number of units participating in the synthesis, and These are mutually independent fuzzy variables. Due to the fuzziness, it is assumed that in pattern synthesis, the total number of participating subarrays only needs to satisfy the constraints to a certain extent. Therefore, for a pre-given confidence level... The reliability of the number of subarrays participating in pattern synthesis must be no less than [a certain value]. Then there is , is used to represent fuzzy chance constraints.

[0103] Furthermore, during the modulation period of the opportunistic array radar, trapezoidal pulses are used to modulate the array of the opportunistic array radar.

[0104] The mathematical expression for the trapezoidal pulse is:

[0105] ,

[0106] like Figure 2 The periodicity diagram of the trapezoidal pulse shown is as follows, This indicates the start time of a trapezoidal pulse cycle. This indicates the moment when the rising edge is reached within one cycle of a trapezoidal pulse. This indicates the moment when the falling edge is reached within a trapezoidal pulse cycle. This indicates the end time of a trapezoidal pulse cycle. Indicates duration, The weight is determined by the rising or falling edge.

[0107] In a cycle In a time-modulated signal, if a certain array element from Always on, continuously Seconds, command , , , ,when hour, These represent different moments within a trapezoidal pulse cycle, and these moments are used to define the shape change process of the trapezoidal pulse within one cycle.

[0108] Traditional time-modulated arrays commonly use rectangular pulses, which have simple spectral characteristics and high sidelobes. Trapezoidal pulses have a main lobe width similar to rectangular pulses, but lower sidelobes, making them suitable for scenarios with high requirements for sidelobes and spectral purity. For an 8-element uniform time-modulated linear array, the simulation results of the combined radiation patterns of different pulse modulations are as follows: Figure 3 and Figure 4 As shown, the comparison results of normalized energy spectral density for different pulse forms are obtained, where Figure 3 A comparison of energy spectral densities obtained when modulating trapezoidal pulses and rectangular pulses. Figure 4 As shown in the pattern comparison results, the experiment demonstrates that modulating the array with the trapezoidal pulses used in this example can achieve lower sidelobes.

[0109] Furthermore, an adaptive differential evolution algorithm based on chaotic elites and center-guided ideas is used to optimize and solve the fuzzy chance-constrained programming model, combined with... Figure 1 As shown, the steps to obtain the optimal array element switching timing and position include:

[0110] Step 1: Define the optimization problem and construct the chromosome structure:

[0111] The total array size of the opportunistic array radar is The total array is divided into several arrays of size 1. The subarrays are treated as individual units, and each subarray contains... Each array element has a time modulation period of [number] times. The carrier frequency is ;

[0112] Define the range of variables: subarray position offset , Indicates that the subarray is in Offset in direction Indicates that the subarray is in Offset in direction Indicates the size of the subarray; the activation time of the array elements. Array element activation duration ,in Indicates the shortest duration. Indicates the longest duration; sets the population size. Variable factors Crossover probability Maximum Algebra Elite ratio and elite center-oriented factors ;

[0113] Step 2: Generate a sequence of chaotic variables to initialize the population;

[0114] Step 3: Calculate the fitness value of the individual with constraints;

[0115] Step 4: Select the top-performing populations based on their fitness. Individuals are evaluated and elite centers are calculated. For each individual, center-oriented mutation is performed. After crossover, fitness calculation, and update calculation, the global optimal solution is updated. The process is iterated until termination and the result is output.

[0116] Further, step 2 includes:

[0117] forward Each individual is initialized using elite-guided initialization, and is initialized near the elite region. For the first individual... The individual in the first The initial position on the dimension is represented as:

[0118] ,

[0119] in, For the first Dimension's elite solution The disturbance radius is... The values ​​generated by the Tent chaotic mapping range from (0,1), and are transformed to form the offset. The Tent map is a piecewise linear chaotic map; Defined as:

[0120] ,

[0121] in, The initial chaos value, For control parameters;

[0122] back Each individual is globally initialized using Tent chaos, and its initial position is generated using a Tent chaotic mapping. Simultaneously, the initial positions of some individuals are shifted towards elite regions, which are obtained through heuristic solutions derived from short-term, exploratory optimization. For the ... The individual in the first Initial position on dimension , represented as:

[0123] ,

[0124] in , They represent the first The lower and upper bounds of the dimensional search space.

[0125] Merging to form a complete initial population .

[0126] Furthermore, step 3 includes:

[0127] Step 31, Decode the individual:

[0128] Each individual corresponds to a set of optimized variable codes, including three core parameters: subarray position offset, array element activation time, and array element activation duration, which map the individual's binary code to the parameter values ​​of the physical implementation.

[0129] Step 32, construct the synthesis pattern of the time-varying modulation function:

[0130] The time-varying modulation array factor for a single subarray m with respect to the target direction p is expressed as:

[0131] ,

[0132] in, , Indicates the angle parameter. This indicates the number of array elements, and k represents the subarray index.

[0133] The overall array pattern is obtained by superimposing the pattern patterns of all subarrays, as shown below:

[0134] ;

[0135] Step 33: Construct and calculate the fitness function. The formula is as follows:

[0136] ,

[0137] in, This represents a weighting coefficient used to balance the optimization priority of sidelobe peak levels and first-order sideband levels. In one example, such as... , It focuses more on sidelobe suppression; This represents a constraint penalty term, applied to violations of subarray spacing constraints (such as...). Individuals subject to constraints such as fuzzy chance constraints on the number of subarrays and temporal logic constraints on array elements (such as the range of opening duration) are given penalty values ​​based on the degree of violation, which guides the algorithm to search for feasible solutions. This represents the penalty coefficient, indicating the degree of impact of constraint violation on fitness, such as... This ensures that the fitness of infeasible solutions is significantly higher than that of feasible solutions.

[0138] Furthermore, step 4 includes:

[0139] Step 41, select the previous Individual and computational elite centers:

[0140] Based on the calculated individual fitness values, individuals in the population are ranked from best to worst fitness, and the top... The individual with the best fitness is called the elite individual; the center of the elite individual is calculated, i.e., the th... Population center of the generation Defined as:

[0141] ,

[0142] in, It is the first The middle generation The individual's location;

[0143] Step 42, Center-oriented mutation:

[0144] Mutation is performed on each individual in the population, and an elite center is introduced into the mutation strategy. The purpose is to guide individuals to search towards the global optimum. The mutation strategy after introducing this elite center can be written in the following form:

[0145] ,

[0146] in, Scaling factor The guiding individuals selected from the current elite subset. , Individuals selected randomly;

[0147] Step 43, cross operation:

[0148] Binary crossover is used to generate test vectors. The rules are as follows:

[0149] ,

[0150] in, Indicates the first The generation The test vector of each individual, Indicates the first The generation The individual The test vector components of dimension, Indicates the first The generation The mutation vector of each individual, Indicates the first The generation The individual The dimensional mutation vector components, Represents a uniformly random number between 0 and 1. Indicates the first The crossover probability of each individual, ,like Then set it to 1, if Then set it to 0 to ensure the effectiveness of the crossover operation; Indicates a dimension index. This indicates a randomly selected dimension index, ensuring that at least one dimension of the experimental vector comes from the mutation vector, thus avoiding complete consistency with the original individual. Indicates the first The generation The individual The original vector components of dimension;

[0151] Step 44, Fitness Calculation and Update:

[0152] Calculate the fitness of the experimental vector and compare it with the fitness of the original individual. If the experimental individual is better than the current individual, replace it and record the result. , ;in This represents the scaling factor for the i-th individual, used to control the scaling degree of the difference vector, affecting the magnitude of individual variation. This represents the crossover probability of the i-th individual, which determines the probability that the experimental vector inherits components from the mutated vector during the crossover operation.

[0153] Add the original instance to an external save file and collect the success parameters for this generation. , The historical mean parameter is updated using a weighted average method. , This enhances the parameter adaptive capability; among them, Indicates scaling factor A historical memory bank used to store historically successful scaling factor values. Represents the crossover probability A historical memory bank is used to store the probability values ​​of successful crossovers in the past.

[0154] Step 45: Determine the termination condition. If the maximum number of iterations is reached or the set pattern performance index is met, then terminate the optimization and output the optimal chromosome, including the start time of the array element, the end time, and the position of the subarray.

[0155] To further illustrate the effectiveness and superiority of the time-varying modulation opportunistic array radar pattern synthesis method described in this invention, the following example is provided.

[0156] Assume the distributed array to be optimized has 100 elements distributed on the xoy plane, and each subarray element has a number of elements. The element spacing is half a wavelength. A uniformly dense array, with inter-subarray spacing of 4.2 in both the x and y dimensions. Before optimizing the distributed array, a simulation of the radiation pattern of the distributed array with four subarrays uniformly distributed was first performed for comparison with the optimized results. The results are as follows: Figures 5 to 7 As shown, in this simulation experiment Figure 5 The image shows a uniformly distributed array of four subarrays. Because the spacing between the subarrays is greater than half a wavelength and they are uniformly distributed, as shown... Figure 6 The normalized directional pattern of the center frequency of the four subarrays shown exhibits multiple high sidelobes along the array direction, with the amplitudes of these high sidelobes approaching those of the main lobe. The peak sidelobe amplitude is approximately -7.26 dB. Figure 7 The normalized radiation pattern of the first-order sideband of the four subarrays shown shows that the level of the first-order sideband (i.e., b=1) is approximately -25.17dB.

[0157] This invention optimizes the distributed subarray array and the timing of array elements. The population size is set to 50, the maximum number of iterations to 100, and the minimum x-dimensional and y-dimensional spacing between subarrays to 1.6. The maximum spacing is 4.2. The optimized subarray positions are as follows: Figure 8 As shown, the optimized distributed array center frequency normalized radiation pattern is calculated as follows. Figure 9 As shown, its sidelobe peak value is approximately -16.14 dB, as... Figure 10 The first-order sideband level shown is approximately -33.91 dB. Timing optimization of the array elements is as follows: Figure 11As shown, the activation time and duration of each array element are different within the modulation period, indicating that not all array elements are in working state during the pattern synthesis process.

[0158] In the example, to verify the effectiveness of the time-modulated array and the method described in this invention in the comprehensive optimization of large-scale antenna arrays, a time-modulated surface array with 1600 elements was designed. The distributed array to be optimized has P=64 subarrays distributed on the xoy plane, and each subarray element has a number of elements. The element spacing is half a wavelength. A uniformly dense array with a plane size of The spacing between subarrays in both the x and y dimensions is 4.2. The harmonic order considered , Modulation frequency The side lobe region is restricted to , where the parameters ,parameter The optimized integrated result of a 1600-element large planar antenna array is shown in the figure below. Figures 12 to 15 As shown, where Figure 12 For the optimized subarray positions, Figure 13 The normalized radiation pattern at the center frequency shows that the peak level of the sidelobes in the center band is approximately -30.61 dB. Figure 14 The normalized radiation pattern of the first-order sidebands shows that the maximum first-order sideband level is approximately -36.68 dB. Since large-scale arrays have many elements, the sideband level can rise, leading to problems such as energy leakage and spectral pollution. To demonstrate the effectiveness of the proposed model and algorithm in suppressing sideband levels, Figure 15 The normalized sideband levels corresponding to the first 20 sidebands are given, and the pattern synthesis time is 2614.2 seconds.

[0159] This example considers a dynamic scenario with a single target, taking into account the uncertainties of the task caused by changes in the real environment. The number of subarrays is limited by the operating state and radar resources, requiring a smaller number of subarrays to synthesize the desired radiation pattern of the target. Therefore, it is necessary to solve for the ambiguity regarding the number of subarrays in the model established in this invention. Here, it is assumed... All are trapezoidal fuzzy numbers and are mutually independent. Let... It is a trapezoidal fuzzy variable, for discussion and The size can be obtained as follows Figure 16 and Figure 17 The diagram shows the confidence membership of the trapezoidal fuzzy variables, where... Figure 16 It is a fuzzy variable The membership function curve, Figure 17 Confidence level The correspondence between the range of subarray numbers.

[0160] The scene synthesized from a large planar array of 1600 elements yields 64 subarrays, and the trapezoidal ambiguity numbers are set as follows: , Confidence level After iterative optimization of the algorithm, the distribution of subarrays participating in pattern synthesis becomes sparser, and the number of subarrays is greatly reduced, thus saving a lot of resources. The pattern synthesis result after iterative optimization under fuzzy chance-constrained programming is shown in the figure below. Figures 18 to 21 As shown, where Figure 18 The image shows the location distribution of the fuzzy subarray. Figure 19 The figure shows the changes in SLL, SBL, and confidence score with the number of algorithm iterations. It can be seen that the confidence scores are all above 0.8. Figure 20 The image shows the normalized radiation pattern at the center frequency. It can be seen that the peak sidelobe of the center band is approximately -30.78 dB. Figure 21 The diagram shows the normalized radiation pattern of the first-order sidebands. It can be seen that the maximum first-order sideband level is -39.12 dB, and the radiation pattern synthesis time is 2236.1 seconds. The results indicate that, under relevant opportunity planning, this invention can, at a certain confidence level, synthesize the required radiation pattern using a relatively small number of subarrays.

Claims

1. A time-varying modulated opportunistic array radar pattern synthesis method, characterized in that, include: The objective function of the radar array pattern of the opportunistic array is constructed with the goal of minimizing the sidelobe peak level and the first-order sideband level. Fuzzy opportunistic constraints are constructed with the subarray position state, the number of subarrays, and the timing of the array elements in each subarray. A fuzzy opportunistic constraint planning model for the synthesis of the radar array pattern is obtained. The fuzzy opportunistic constraint planning model is optimized and solved based on the adaptive differential evolution algorithm under the ideas of chaotic elites and center guidance to obtain the optimal array element switching timing and position. The mathematical expression for the fuzzy chance-constrained programming model is: ， in, Describe the objective function. Indicates the sidelobe peak level. Indicates the first-order sideband level. Represents decision variables, Representing fuzzy variables, Represents fuzzy parameters related to the task scenario; Indicates a measure of chance. Representing mutually independent fuzzy variables, This indicates the operating state of subarray i. A value of 1 indicates that the excitation is on, meaning the subarray participates in pattern synthesis, while a value of 0 indicates that the excitation is off, meaning the subarray does not participate in pattern synthesis. Indicates the confidence level, and N represents the total number of subarrays included in the opportunistic array radar array; This represents the decision variables for the entire opportunistic array radar. This represents the switch sequence of the subarray, where 1 indicates on and 0 indicates off. The nth subarray contains... Each array element, Indicates the first Individual formations, the first The array element in the first Opening and closing of each time slot A value of 1 indicates on, and a value of 0 indicates off; L represents the time period. The number of time slots discretized; Indicates the start time of the array element. Indicates the end time; Subarray The Middle Each array element is paired with the first Time modulation switch status in each target direction This indicates that the modulation period must not exceed the maximum modulation period. ; Subarray The array element space coordinates, Refers to a region; In the fuzzy chance-constrained programming model, the first constraint is a fuzzy chance constraint, the second and third constraints represent the working state of the subarray, which is a binary decision variable constraint, the fourth constraint is a time constraint, which requires that the start time of the array element be non-negative and the stop time of the array element not exceed the time modulation period, the fifth constraint is a modulation period constraint, and the sixth constraint is a constraint on the spatial layout of the subarray. During the modulation period of the opportunistic array radar, trapezoidal pulses are used to modulate the radar array. The mathematical expression for the trapezoidal pulse is: ， in, This indicates the start time of a trapezoidal pulse cycle. This indicates the moment when the rising edge is reached within one cycle of a trapezoidal pulse. This indicates the moment when the falling edge is reached within a trapezoidal pulse cycle. This indicates the end time of a trapezoidal pulse cycle. Indicates duration, The weight of the rising or falling edge; The steps for optimizing the fuzzy chance-constrained programming model based on the adaptive differential evolution algorithm under the chaotic elite and center-guided ideas to obtain the optimal array element switching timing and position include: Step 1: Define the optimization problem and construct the chromosome structure: The total array size of the opportunistic array radar is The total array is divided into several arrays of size 1. The subarrays are treated as individual units, and each subarray contains... Each array element has a time modulation period of [number] times. The carrier frequency is ; Define the range of variables: subarray position offset , Indicates that the subarray is in Offset in direction Indicates that the subarray is in Offset in direction Indicates the size of the subarray; the activation time of the array elements. Array element activation duration ,in Indicates the shortest duration. Indicates the maximum duration; sets the population size. Variable factors Crossover probability Maximum Algebra Elite ratio and elite center-oriented factors ; Step 2: Generate a sequence of chaotic variables to initialize the population; Step 3: Calculate the fitness value of the individual with constraints; Step 4: Select the top-performing populations based on their fitness. Each individual is evaluated and its elite center is calculated. For each individual, center-oriented mutation is performed. After crossover, fitness calculation, and update calculation, the global optimal solution is updated. The process is iterated until termination and the result is output.

2. The time-varying modulated opportunistic array radar pattern synthesis method according to claim 1, characterized in that, Step 2 includes: forward Each individual is initialized using elite-guided initialization, and is initialized near the elite region. For the first individual... The individual in the first The initial position on the dimension is represented as: ， in, For the first Dimension's elite solution The disturbance radius is... This represents the chaotic value of the (n+1)th subarray, generated by the Tent chaotic map, with a value range of (0,1), which is then transformed to form the offset. ; Defined as: ， in, The initial chaos value, For control parameters; back Each individual is globally initialized using Tent chaotic mapping, and the initial position of each individual is generated using Tent chaotic mapping. The individual in the first Initial position on dimension , is represented as: ， in , They represent the first The lower and upper bounds of the dimensional search space. Merging to form a complete initial population .

3. The time-varying modulated opportunistic array radar pattern synthesis method according to claim 2, characterized in that, Step 3 includes: Step 31, Decode the individual: Each individual corresponds to a set of optimized variable codes, including three core parameters: subarray position offset, array element activation time, and array element activation duration, which map the individual's binary code to the parameter values ​​of the physical implementation. Step 32, construct the synthesis pattern of the time-varying modulation function: For a single subarray m, the time-varying modulation array factor for the target direction p Represented as: ， in, , Indicates the angle parameter. This indicates the number of array elements, and k represents the subarray index. The overall array pattern is obtained by superimposing the pattern of all subarrays. , is represented as: ； Step 33, Construct the fitness function And perform the calculation, the formula is: ， in, This represents the weighting coefficient, used to balance the optimization priority of the sidelobe peak level (SLL) and the first-order sideband level (SBL). Indicates a constraint or penalty item. This represents the penalty coefficient, which controls the degree of impact of constraint violations on fitness.

4. The time-varying modulated opportunistic array radar pattern synthesis method according to claim 3, characterized in that, Step 4 includes: Step 41, select the previous Individuals and the elite center are calculated: Based on the calculated individual fitness values, individuals in the population are ranked from best to worst fitness, and the top... The individual with the best fitness is called the elite individual; the center of the elite individual is calculated, i.e., the th... The elite center of the era Defined as: ， in, It is the first The middle generation The individual's location; Step 42, Center-oriented mutation: Mutation is performed on each individual in the population, and an elite center is introduced into the mutation strategy. Mutation strategy after the introduction of this elite center Write it in the following form: ， in, Scaling factor The guiding individuals selected from the current elite subset. , Individuals selected randomly; Step 43, cross operation: Binary crossover is used to generate test vectors. The rules are as follows: ， in, Indicates the first The generation The test vector of each individual, Indicates the first The generation The individual The test vector components of dimension, Indicates the first The generation The mutation vector of each individual, Indicates the first The generation The individual The dimensional mutation vector components, Represents a uniformly random number between 0 and 1. Indicates the first The crossover probability of each individual, ,like Then set it to 1, if Then set it to 0. Indicates a dimension index. This indicates a randomly selected dimension index. Indicates the first The generation The individual The original vector components of dimension; Step 44, Fitness Calculation and Update: Calculate the fitness of the experimental vector and compare it with the fitness of the original individual. If the experimental individual is better than the current individual, replace it and record the result. and ;in This represents the scaling factor for the i-th individual. This represents the crossover probability of the i-th individual; Add the original instance to an external save file and collect the success parameters for this generation. and The historical mean parameter is updated using a weighted average method. , ;in, Indicates scaling factor A historical memory bank used to store historically successful scaling factor values. Represents the crossover probability A historical memory bank is used to store the probability values ​​of successful crossovers in the past. Step 45: Determine the termination condition. If the maximum number of iterations is reached or the set pattern performance index is met, then terminate the optimization and output the optimal chromosome, including the start time of the array element, the end time, and the position of the subarray.

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