Auxiliary array element position optimization method and system for sidelobe cancellation

Abstract

The invention discloses an auxiliary array element position optimization method and system for sidelobe cancellation, and the method comprises the steps: initializing a population, and enabling chromosomes of individuals of the population to be composed of possible position indexes of auxiliary array elements; constructing a fitness function, calculating the fitness of the initial population, and recording the position of an optimal auxiliary array element; a differential evolution (DE) strategy is adopted to generate a variation population; performing crossover operation on the variation population through a binomial crossover method to form a test population; selecting a new-generation population from the previous-generation population and the test population by applying a greedy strategy; updating historical records of the scaling factor and the crossover probability factor; the population scale is reduced through an LPSR algorithm; iteratively evolving the population; and outputting an iterative optimization process and an optimal auxiliary array element position. According to the method, the key parameters of the differential evolution algorithm are adaptively adjusted, the positions of the auxiliary array elements are efficiently optimized, the calculation complexity is low, the convergence speed is high, the method can be used for the radar sidelobe interference suppression technology, and the adaptability of the radar to different interference environments can be improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of array signal processing, and specifically relates to a method and system for optimizing auxiliary array element positions for sidelobe cancellation, and more specifically to a method and system for optimizing auxiliary array element positions for sidelobe cancellation based on improved differential evolution. Background Art

[0002] In modern communication and radar systems, interfering signals can seriously affect system performance, especially interfering signals coming from the sidelobe region of the antenna pattern.

[0003] In general, common sidelobe cancellers achieve the purpose of interference cancellation by optimizing the weights of the specified main channel and auxiliary channel. However, in practical applications, different auxiliary channel positions also have a significant impact on the performance of the sidelobe canceller. In order to improve the performance of the sidelobe canceller, it is necessary to optimize the position of the array elements in the auxiliary array. Differential Evolution (DE) is widely used in such optimization problems due to its advantages such as fast convergence speed and strong global search capability. The best combination of array element positions is found through optimization selection, so as to better suppress sidelobe interference and improve signal quality.

[0004] In 2013, in order to study the impact of auxiliary antenna configuration methods on the performance of the adaptive sidelobe cancellation system, Su Baowei and others designed auxiliary antenna configuration schemes such as independent array elements, sub-array planes, and array element combinations. Through simulation comparison, it was found that when the auxiliary antennas are in the same row or column, the cancellation performance will be severely reduced. In 2022, Zhang ZM and others proposed that the distance between auxiliary antennas has a significant impact on the sidelobe cancellation performance in actual engineering applications, especially when the auxiliary antennas are densely arranged, the sidelobe cancellation performance may be reduced.

[0005] Compared with other evolutionary algorithms, the differential evolution algorithm has the advantages of fewer control parameters, strong robustness, and strong global search capabilities. However, it also has some shortcomings, mainly the disadvantages of being easy to fall into local optimality and premature maturity. Therefore, many scholars at home and abroad have made many improvements to the differential evolution algorithm.

[0006] In 2013, Tanabe et al. proposed a Success-Historybased Adaptive Differential Evolutionz (SHADE) algorithm. In 2014, Tanabe et al. proposed an improved version of the SHADE algorithm, LSHADE, which introduced linear population size reduction (LPSR). L-SHADE adaptively adjusts the three control parameters of the differential evolution algorithm (scaling factor F, crossover rate CR, and population size NP). In 2020, Sallam KM et al. proposed an improved DE optimization algorithm that utilizes the advantages of multiple differential mutation operators and emphasizes the operator with the best performance. In 2022, Yi et al. proposed an adaptive differential algorithm with integrated operators, which uses two sets of mutation operators and crossover operators to generate offspring to better balance the development and exploration capabilities of the algorithm. In addition, an adaptive parameter control strategy is integrated to dynamically adjust the parameter settings of the algorithm to further improve the search effect.

[0007] At present, traditional sidelobe cancellation technology usually relies on complex hardware design and fixed algorithms. These methods have problems such as fixedness, high computational complexity and optimization limitations. It is difficult for fixed algorithms to find the global optimal solution and they are prone to fall into the local optimal solution, which affects the cancellation effect. In addition, traditional methods are usually designed based on specific system configurations and interference environments, and lack adaptability to different interference environments. Summary of the invention

[0008] In view of this, the present invention provides a method and system for optimizing the position of auxiliary array elements for sidelobe cancellation, which can at least partially solve the above-mentioned problems in the sidelobe cancellation process, such as complex calculations, easy falling into local optimality, affecting the cancellation effect, and lack of adaptability to changing interference environments.

[0009] In order to achieve the above object, the present invention adopts the following technical solution:

[0010] In a first aspect, the present invention provides a method for optimizing auxiliary array element positions for sidelobe cancellation, comprising the following steps:

[0011] S1: Read the coordinates of the array element position, complete the array element position coding, population initialization, and historical record and elimination archive initialization. The chromosome of the population is composed of the possible position index of the auxiliary array element;

[0012] S2: construct a fitness function, substitute the initial population obtained in step S1 into the fitness function, and record the auxiliary array element position with the best fitness and its fitness value;

[0013] S3: Use differential evolution DE / current-to-pbest / 1 mutation strategy to mutate the auxiliary array element position to generate a mutant population;

[0014] S4: Perform crossover operation on the new population through binomial crossover method to form a test population;

[0015] S5: Apply the greedy strategy to select a new generation of population from the current population and the test population, and update the position of the auxiliary array elements in the population;

[0016] S6: based on the absolute value of the difference between the fitness function value of the current array element position combination and the previous generation array element position combination, update the historical records of the scaling factor F and the crossover probability factor CR;

[0017] S7: Reduce the population size through the LPSR algorithm, calculate the next generation population size, and compare it with the current generation population size. Discard the worst individual in the current generation population or maintain the current generation population size according to the fitness to obtain the next generation population;

[0018] S8: Iterate the evolution population until the maximum number of iterations is reached;

[0019] S9: Output the iterative optimization process and the optimal auxiliary array element position.

[0020] In a second aspect, the present invention further provides an auxiliary array element position optimization system for sidelobe cancellation, comprising:

[0021] The signal processing module is used to read the coordinates of the array element position, complete the array element position coding, population initialization, and historical record and elimination archive initialization. The chromosome of the population is composed of the possible position indexes of the auxiliary array elements;

[0022] The fitness function module is used to construct the fitness function, substitute the population into the fitness function, and record the auxiliary array element position with the best fitness and its fitness value;

[0023] A mutation module is used to perform mutation operations on the auxiliary array element positions using the DE / current-to-pbest / 1 mutation strategy to generate a mutant population;

[0024] The crossover module is used to perform a crossover operation on the new population through the binomial crossover method to form a test population;

[0025] A selection module is used to select a new generation of population from the current population and the test population using a greedy strategy, and to update the positions of the auxiliary array elements in the population;

[0026] A parameter updating module, used for updating the historical records of the scaling factor F and the crossover probability factor CR based on the absolute value of the difference between the fitness function value between the current array element position combination and the previous generation array element position combination;

[0027] The population size reduction module is used to reduce the population size through the LPSR algorithm, calculate the next generation population size, and compare it with the current generation population size. According to the fitness, the worst individual in the current generation population is discarded or the current generation population size is maintained to obtain the next generation population;

[0028] An iteration module, used to iterate the evolutionary population until the maximum number of iterations is reached;

[0029] The output module is used to output the iterative optimization process and the optimal auxiliary array element position.

[0030] It can be seen from the above technical solution that compared with the prior art, the present invention has the following advantages:

[0031] The present invention uses an improved differential evolution algorithm to optimize the position of the auxiliary array element for adaptive sidelobe cancellation, and realizes efficient optimization of the position of the auxiliary array element for adaptive sidelobe cancellation by adaptively adjusting the key parameters of the differential evolution algorithm and combining array signal processing technology. This method not only improves the adaptability to different interference environments, but also reduces the computational complexity and accelerates the convergence speed; it can be used for radar sidelobe interference suppression technology and can improve the adaptability of radar to different interference environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0033] Figure 1 A flow chart of a method for optimizing array element positions based on improved differential evolution for sidelobe cancellation provided by the present invention.

[0034] Figure 2 This is an array formation diagram provided by the present invention.

[0035] Figure 3 It is a comparison chart of the fitness iteration curves of the method proposed in the present invention and the traditional algorithm.

[0036] Figure 4 The figure is a comparison chart of the fitness iteration curves of 20 Monte Carlo experiments between the method proposed in the present invention and the traditional algorithm.

[0037] Figure 5 An adaptive pattern for suppressing a single interferer by using an optimized selection of auxiliary array element positions.

[0038] Figure 6An adaptive pattern for suppressing multiple interferences using optimized selected auxiliary array element positions.

[0039] Figure 7 A block diagram of a system for optimizing array element positions based on improved differential evolution for sidelobe cancellation provided by the present invention. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] like Figure 1 As shown, the present invention provides an improved differential evolution-assisted array element position optimization method for sidelobe cancellation, comprising the following steps:

[0042] S1: Read the coordinates of the array element position, complete the array element position coding, population initialization, and historical record and elimination archive initialization. The chromosome of the population is composed of the possible position index of the auxiliary array element;

[0043] S2: construct a fitness function, substitute the initial population obtained in step S1 into the fitness function, and record the auxiliary array element position with the best fitness and its fitness value;

[0044] S3: Use the differential evolution DE / current-to-pbest / 1 (Differential Evolution, DE) mutation strategy to mutate the auxiliary array element position and generate a mutant population;

[0045] S4: Perform crossover operation on the new population through binomial crossover method to form a test population;

[0046] S5: Apply the greedy strategy to select a new generation of population from the current population and the test population, and update the position of the auxiliary array elements in the population;

[0047] S6: based on the absolute value of the difference between the fitness function value of the current array element position combination and the previous generation array element position combination, update the historical records of the scaling factor F and the crossover probability factor CR;

[0048] S7: Reduce the population size through the Linear Population Size Reduction (LPSR) algorithm, calculate the next generation population size, and compare it with the current generation population size. Discard the worst individual in the current generation population or maintain the current generation population size according to the fitness to obtain the next generation population.

[0049] S8: Iterate the evolution population until the maximum number of iterations is reached;

[0050] S9: Output the iterative optimization process and the optimal auxiliary array element position.

[0051] In the embodiment of the present invention, combined with Figure 2 As shown, for example, the array in step S1 is a 48×6 uniform array with a total of 288 array elements. The array elements are numbered from 1 to 288 in sequence, and 4 of them are selected as auxiliary array elements, and the remaining array elements constitute the main array. Assume that the target signal is incident at 45°, and select an interference to traverse from 0° to 90°. The initial population size is 60, the number of iterations is 500, the upper and lower bounds of the search space are 1 and 288 respectively, and the number of auxiliary array elements is 4.

[0052] In the embodiment of the present invention, the four auxiliary array element positions are composed of chromosomes in the differential evolution algorithm, that is, auxiliary array element combinations, and each auxiliary array element position is called a gene. The initial population P of the auxiliary array element position is composed of random vectors:

[0053] P=[X1,…,X i ] T i=1,…,NP (1)

[0054] X i =[x1,x2,…,x j ] j=1,…,D (2)

[0055] x j = rand[L b ,U b ] (3)

[0056] Among them, x j is the jth auxiliary array element position (gene), X i is the i-th auxiliary array element position combination (chromosome), NP is the population size, D is the number of auxiliary array elements, U b and L b are the upper and lower bounds of the search space.

[0057] In the embodiment of the present invention, the improved differential evolution algorithm needs to initialize the historical records and external archives, and the historical records M F and M CR The control parameters (scaling factor F and crossover probability factor CR) are stored in, for example, initialized to 0.5:

[0058]

[0059] M F,i and M CR,iThey represent the scaling factor F and the crossover probability factor CR recorded in the ith iteration, which are the same in each iteration. Wherein, H is the capacity of the user-defined historical record, which is defined as 60 in this embodiment.

[0060] The elimination archive A is used to store the elimination solutions, which is initialized to an empty set:

[0061]

[0062] The purpose of step S1 is to initialize the differential evolution algorithm and prepare for the subsequent iterative evolution process, which lays the foundation for the iterative evolution process of the differential evolution algorithm and ensures that the algorithm can effectively search and optimize.

[0063] In the embodiment of the present invention, the auxiliary array element position range constraint is manually given, and the auxiliary array element position constraint condition is greater than the lower limit L of the search space. b , which is smaller than the upper bound U of the search space b Therefore, in step S2, the population fitness function is constructed as follows:

[0064]

[0065] Among them, N θ is the total number of test angles, which is 91 in this embodiment, and θ is the degree of the traversal angle; where H represents the conjugate transpose of the weight vector. w represents the beam weight vector, which is used to balance the importance of the null depth at different angles. a represents the signal steering vector. The larger F is, the greater the null depth of the interference signal is, and the better the sidelobe cancellation performance is.

[0066] In step S2, in order to ensure that the auxiliary array element can maintain effective anti-interference performance within the spatial coverage range, its null depth at different interference incident angles and its ability to cancel interference within the spatial coverage range are comprehensively considered. Therefore, the fitness function in step S2 is constructed as the angle of the interference signal traversing all coverage areas and calculating the sum of the absolute values ​​of the null depth of the interference signal at each traversal angle after sidelobe cancellation. And use this function to evaluate the quality of each individual in the initial population.

[0067] Construction of fitness function:

[0068] Evaluate the impact of auxiliary array element position combinations on sidelobe cancellation performance and select the optimal array element position combination. Traverse all possible interference incident angles and calculate the null depth of the interference signal after sidelobe cancellation at each angle. Calculate the sum of the absolute values ​​of the null depths at all interference incident angles as a comprehensive evaluation criterion.

[0069] Step S2 converts the quality of the auxiliary array element position combination into a numerical value by constructing a fitness function, which provides a basis for subsequent evolution operations.

[0070] In the embodiment of the present invention, the DE / current-to-pbest / 1 mutation strategy in step S3 not only uses the information of the best individual, but also uses the information of other better individuals, and uses the difference between these individuals as the direction to guide the evolution of the population. The DE / current-to-pbest / 1 mutation strategy can be expressed by formula (7):

[0071] V i,G =X i,G +F i ·(X pbest,G -X i,G )+F i ·(X r1,G -X r2,G ) (7)

[0072] Among them, X pbest,G is to randomly select from the top p auxiliary array element combinations in the current population in terms of fitness, X i,G is the i-th auxiliary array element combination of the G-th iteration, X r1,G is the auxiliary array element combination randomly selected from the population P of the Gth iteration, X r2,G is a combination of auxiliary array elements randomly selected from P∪A, F i is the scaling factor, generated by:

[0073] F i =randc i (M F,i ,0.1) (8)

[0074] Among them, randc i represents the Cauchy distribution, M F,i From the historical record M F A randomly selected scaling factor in . Using the history M F The scaling factor F can be adaptively adjusted to make it more suitable for the current search process.

[0075] The purpose of step S3 is to perform mutation operations on the auxiliary array element positions to generate a mutant population, which provides a basis for subsequent crossover and selection operations. This step adopts the DE / current-to-pbest / 1 mutation strategy:

[0076] 1. Composition of mutation strategy:

[0077] The DE / current-to-pbest / 1 mutation strategy consists of the following three parts:

[0078] Current population: represents the i-th auxiliary array element combination in the population P of the G-th iteration, denoted by X i,G .

[0079] pbest: represents a random selection from the top p auxiliary array element combinations in the current population, denoted by X pbest,G .

[0080] r1, r2: represent two different auxiliary array element combinations randomly selected from the population P of the Gth iteration, denoted by X r1,G and X r2,G .

[0081] 2. Mutation operation:

[0082] The core of the mutation operation is to generate the mutant individual V i,G , where F i is a scaling factor used to control the degree of variation.

[0083] 3. Mutation process:

[0084] Step 1: Calculate X pbest,G With X i,G The difference between the two and multiplied by the scaling factor F i , and get the first difference vector.

[0085] Step 2: Calculate X r1,G With X r2,G The difference between the two and multiplied by the scaling factor F i , and obtain the second difference vector.

[0086] Step 3: Add the two difference vectors and add them to X i,G Add them together to get the variant individual V i,G .

[0087] 4. Characteristics of mutation strategy:

[0088] Introducing pbest individuals: By introducing pbest individuals, mutation operations can better utilize historical information and improve search efficiency. Through differential operations, mutation operations can generate more diverse individuals and avoid falling into local optimality.

[0089] Step S3 uses the DE / current-to-pbest / 1 mutation strategy to mutate the auxiliary array element positions and generate a mutant population, which provides a basis for subsequent crossover and selection operations. This step effectively improves the algorithm's search efficiency and solution quality by introducing pbest individuals and differential operations, as well as adaptively adjusting the scaling factor F.

[0090] In the embodiment of the present invention, in step S4, a binomial crossover is used to perform a crossover operation on the pixel position combination.

[0091] S4.1: Randomly select the crossover point j of the chromosome (auxiliary array element position combination) rand ;

[0092] S4.2: According to formula (9), randomly select a number between 0 and 1, if it is less than or equal to the crossover probability CR i Or gene position j = j rand When , the jth auxiliary array element position of the new auxiliary array element position combination U will inherit the jth auxiliary array element position of the variant auxiliary array element position combination V, otherwise it will inherit the jth auxiliary array element position of the original auxiliary array element position combination X. The formula is as follows:

[0093]

[0094] In formula (9), U i,j,G is the position of the new auxiliary array element generated after the crossover, j rand is a randomly selected intersection point, V i,j,G is the variable auxiliary array element position combination V i,G The jth auxiliary array element position; X i,j,G is the original auxiliary array element position combination X i,G The jth auxiliary array element position; the crossover probability CR i Generated by:

[0095] CR i =randn i (M CR,i ,0.1) (10)

[0096] randn in formula (10) i is a Gaussian distribution, M CR,i From the historical record M CR The crossover probability of random selection in . Using the history M CR The crossover probability CR can be adaptively adjusted to make it more suitable for the current search process.

[0097] The purpose of step S4 is to combine the mutant individuals with the original individuals through a crossover operation to generate a test population. This step uses the binomial crossover method, which is as follows:

[0098] 1. Composition of crossover operation:

[0099] The binomial crossover method consists of the following two steps:

[0100] Select crossover point: Randomly select the crossover point j of the chromosome (auxiliary array element position combination) rand .

[0101] Crossover operation: According to the crossover probability CR or gene position j rand , the new auxiliary array element position combination Ui,G The jth auxiliary array element position is inherited from the variant auxiliary array element position combination V i,G Or the original auxiliary array element position combination X i,G .

[0102] 2. Crossover process:

[0103] Step 1: Randomly select the crossover point j of the chromosome (auxiliary array element position combination) rand .

[0104] Step 2: Randomly pick a number between 0 and 1, if it is less than or equal to the crossover probability CR or gene position j rand = j, then the new auxiliary array element position combination U i,G The jth auxiliary array element position will be inherited from the variant auxiliary array element position combination V i,G The jth auxiliary array element position is inherited from the original auxiliary array element position combination X i,G The j-th auxiliary array element position.

[0105] 3. Crossover strategy: The crossover operation is simple and easy to implement. The frequency of the crossover operation can be controlled by the crossover probability CR. The crossover operation can generate more diverse individuals and avoid falling into the local optimum.

[0106] Step S4 combines the mutant individuals with the original individuals through the binomial crossover method to generate a test population. This step effectively improves the algorithm's search efficiency and solution quality by selecting crossover points and crossover operations.

[0107] In the embodiment of the present invention, step S5 selects a better individual as the array element position combination of the new population based on the greedy criterion. In addition to updating the population, the improved differential evolution algorithm L-SHADE also needs to update the elimination archive. If a better test individual than the original individual is evolved, the original array element position combination X is replaced. i,G Store in the elimination archive A. If the elimination archive exceeds the capacity, delete the corresponding excess.

[0108] Among them, the population update adopts the greedy criterion to select better individuals:

[0109]

[0110] In the formula, f(U i,G ) is the fitness function value of the ith auxiliary array element position combination in the test population, f(X i,G ) is the fitness function value of the i-th auxiliary array element position combination in the current population, X i,G+1 is the new auxiliary array element position combination after selection, X i,G is the original auxiliary array element position combination, that is, the i-th auxiliary array element position combination in the current population; U i,GThe i-th auxiliary array element position combination in the test population generated for the G-th iteration.

[0111] Step S5 is a crucial step in the technical solution of the present invention, which selects a new generation of population from the current population and the test population through a greedy strategy, thereby realizing population evolution. That is, each iteration selects the auxiliary array element position combination with a higher fitness value in the current population and the test population to enter the new generation of population.

[0112] In formula (11), if the fitness value of the i-th auxiliary array element position combination in the test population is greater than or equal to the fitness value of the i-th auxiliary array element position combination in the current population, then the combination in the test population is selected to enter the new generation population; otherwise, the combination in the current population is selected to enter the new generation population.

[0113] The fitness function is an indicator for evaluating the quality of the auxiliary array element position combination. In the present invention, the angles at which the interference signal traverses all coverage areas and the sum of the absolute values ​​of the null depths of the interference signal at each traversal angle after sidelobe cancellation is calculated as the fitness function.

[0114] Current population: The population formed after multiple iterations, containing several combinations of auxiliary array element positions.

[0115] Experimental population: The population generated through mutation and crossover operations, which also contains several auxiliary array element position combinations.

[0116] In step S5, a greedy strategy is used to select auxiliary array element position combinations with higher fitness values ​​to enter the new generation population, thereby achieving population evolution and ultimately finding the optimal auxiliary array element position combination.

[0117] In the embodiment of the present invention, step S6 updates the historical records of the scaling factor F and the crossover probability factor CR, including:

[0118] S6.1: Store the scaling factor F and crossover probability factor CR of the successfully evolved individuals in each iteration in S F and S CR And set the kth unit of the historical record to 1;

[0119] S6.2: Update the kth unit of the history record according to formulas (12) and (13);

[0120] S6.3: After each iteration, the history record unit k is incremented by 1;

[0121] S6.4: When the history record unit k exceeds the capacity H, it is reset to 1;

[0122] in:

[0123]

[0124] Where M CR,k,G+1 represents the crossover probability factor of the kth historical record unit in the G+1th iteration; represents the weighted average of the crossover probability factors of the successfully evolved individuals; S CR represents the crossover probability factor set of the successfully evolved individuals; M CR,k,G represents the crossover probability factor of the kth historical record unit in the Gth iteration; W a It is a weighted average value, which is used to control the influence of the successfully evolved individuals on the current F and CR.

[0125] M F,k,G+1 represents the scaling factor of the kth historical record unit in the G+1th iteration; represents the scaling factor weighted Lehmer mean of the successfully evolved individuals; S F Represents the set of scaling factors of successfully evolved individuals. F,k,G Represents the scaling factor of the k-th history unit in the G-th iteration.

[0126] W l is the weighted Lehmer average, which is used to control the influence of the successfully evolved individuals on the current F and CR. If the Gth iteration does not evolve a better experimental array element position combination than the previous generation array element position combination, the historical record will not be updated. The weighted average W a and the weighted Lehmer mean W l Update via:

[0127]

[0128] Among them, mean(): calculates the average value of the set; Lehmer mean makes the parameters with large contribution have greater influence. Compared with the arithmetic mean, the value of Lehmer mean is large, which can avoid premature phenomenon caused by too small control parameters. CR,k represents the crossover probability factor of the kth successfully evolved individual; S F,k represents the scaling factor of the kth successfully evolved individual. In addition, the weight vector w k The parameter adaptability can be improved, which is calculated based on the absolute value of the difference between the fitness function value between the test array element position combination and the original array element position combination:

[0129]

[0130] Δf k is the absolute value of the difference between the fitness function value of the current array element position combination and the previous generation array element position combination. k,G ) represents the fitness function value of the kth auxiliary array element position combination in the test population. f(X k,G) represents the fitness function value of the kth auxiliary array element position combination in the current population.

[0131] Step S6 is a key step in the technical solution of the present invention, which is responsible for updating two key parameters of the differential evolution algorithm: scaling factor F and crossover probability factor CR, so as to ensure the search capability and convergence speed of the algorithm. Step S6 updates the historical records and calculates new F and CR based on the scaling factor F and crossover probability factor CR of the successfully evolved individuals, and the absolute value of the difference in fitness function value between the current array element position combination and the previous generation array element position combination.

[0132] Step S6 adaptively adjusts F and CR so that the algorithm can better balance the exploration and development capabilities during the search process, thereby improving the algorithm's search capability and convergence speed, and ultimately finding the optimal auxiliary array element position combination.

[0133] In the embodiment of the present invention, step S7 reduces the population size by using the LPSR algorithm, including:

[0134] S7.1: Calculate the next generation population size NP according to formula (18) G+1 , determine the next generation population size NP G+1 Is it smaller than the current generation population size NP? G ;

[0135] S7.2: If the next generation population size is NP G+1 Smaller than the current generation population size NP G , then sort the current generation population according to the fitness function value and discard the worst NP G -NP G+1 The array element position combination, the population size is NP G+1 The next generation population, the elimination archive A will also decrease as the population size decreases; otherwise, maintain the current population size NP G ;

[0136]

[0137] NP in formula (18) init is the initial population size, which is 60 in this example, NP min is the minimum population size, which is 4 in this example, FES is the number of current fitness function evaluations, and MAXFES is the maximum number of fitness function evaluations, which is 500 in this example.

[0138] Step S7 describes how to dynamically adjust the population size through the linear population size reduction (LPSR) algorithm to adapt to the needs of the evolutionary process. Its main purpose is to avoid the computational complexity and resource consumption caused by an excessively large population size while maintaining the algorithm's search capability. The role of the above steps S7.1 and S7.2 is to maintain an appropriate population size at different stages of evolution by dynamically adjusting the population size. In the early stages of evolution, the population size is large, which can ensure the algorithm's search capability and avoid falling into a local optimum. As evolution proceeds, the population size gradually decreases, which can reduce computational complexity and resource consumption and improve the efficiency of the algorithm. Enable the algorithm to maintain optimal performance at different stages of evolution.

[0139] In the embodiment of the present invention, Figure 3 As shown in the figure, the method proposed in the present invention and the traditional algorithm, namely the optimal fitness iteration curve and the average fitness iteration curve of the two algorithms, are mainly statistically analyzed, showing the fitness value change of the algorithm during the iteration process, reflecting the optimization ability and convergence speed of the algorithm. The x-axis represents the number of iterations of the two algorithms, and the y-axis represents the fitness function value of the two algorithms. Figure 3 It can be seen that in the fitness iteration curve, the curve of the algorithm proposed in the present invention rises faster than that of the traditional algorithm, indicating that it can find a better solution more quickly in the initial stage. Finally, the fitness value of the algorithm proposed in the present invention is significantly higher than that of the traditional algorithm, which shows that the algorithm proposed in the present invention has achieved better results in the optimization problem.

[0140] In the embodiment of the present invention, Figure 4 As shown in the figure, in order to avoid accidental phenomena, the Monte Carlo experiment was repeated 20 times with the same parameters, and the method proposed by the present invention and the traditional algorithm were simulated and analyzed to obtain the optimal fitness iteration curve and the average fitness iteration curve. The x-axis represents the number of iterations of the two algorithms, and the y-axis represents the fitness function value of the two algorithms. Figure 4 It can be seen that under the same number of iterations, the proposed algorithm converges faster than the traditional algorithm, which reflects the ability of the method to quickly obtain a better solution. In addition, as the iteration proceeds, the fitness curve of the proposed algorithm usually shows smaller fluctuations, indicating that it has better stability during the search process and can effectively stay near the better solution. Finally, the fitness value of the proposed algorithm is significantly higher than that of the traditional algorithm, which shows that the proposed algorithm has achieved better results in the optimization problem.

[0141] In the embodiment of the present invention, the optimized array element position is [12, 265, 43, 156], which is used as the auxiliary array element. Three interferences are selected to be incident from 22°, 40° and 52° respectively, and adaptive sidelobe cancellation is performed to obtain an adaptive directional pattern, such as Figure 5 and Figure 6This shows that after the optimization by the method of the present invention, the auxiliary array element position combination with better anti-interference performance can be selected more efficiently, which verifies that the algorithm proposed by the present invention can effectively optimize the selection of the auxiliary array element position.

[0142] Based on the same inventive concept, an embodiment of the present invention further provides an improved differential evolution-assisted array element position optimization system for sidelobe cancellation. Since the principle of solving the problem by this system is similar to the aforementioned improved differential evolution-assisted array element position optimization method for sidelobe cancellation, the implementation of this system can refer to the implementation of the aforementioned method, and the repeated parts will not be repeated.

[0143] The present invention also provides an auxiliary array element position optimization system for sidelobe cancellation, referring to Figure 7 As shown, including:

[0144] The signal processing module is used to read the coordinates of the array element position, complete the array element position coding, population initialization, and historical record and elimination archive initialization. The chromosome of the population is composed of the possible position indexes of the auxiliary array elements;

[0145] The fitness function module is used to construct the fitness function, substitute the population into the fitness function, and record the auxiliary array element position with the best fitness and its fitness value;

[0146] A mutation module is used to perform mutation operations on the auxiliary array element positions using the DE / current-to-pbest / 1 mutation strategy to generate a mutant population;

[0147] The crossover module is used to perform a crossover operation on the new population through the binomial crossover method to form a test population;

[0148] A selection module is used to select a new generation of population from the current population and the test population using a greedy strategy, and to update the positions of the auxiliary array elements in the population;

[0149] A parameter updating module, used for updating the historical records of the scaling factor F and the crossover probability factor CR based on the absolute value of the difference between the fitness function value between the current array element position combination and the previous generation array element position combination;

[0150] The population size reduction module is used to reduce the population size through the LPSR algorithm, calculate the next generation population size, and compare it with the current generation population size. According to the fitness, the worst individual in the current generation population is discarded or the current generation population size is maintained to obtain the next generation population;

[0151] An iteration module, used to iterate the evolutionary population until the maximum number of iterations is reached;

[0152] The output module is used to output the iterative optimization process and the optimal auxiliary array element position.

[0153] In this embodiment, the system achieves efficient optimization selection of auxiliary array element positions through an improved differential evolution algorithm, thereby improving sidelobe cancellation performance, reducing computational complexity, increasing convergence speed, improving adaptability, reducing costs, and improving flexibility.

[0154] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0155] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for optimizing the position of auxiliary array elements for sidelobe cancellation, characterized in that: The following steps are involved: S1: Read the coordinates of the array element position, complete the array element position coding, population initialization, and historical record and elimination archive initialization. The chromosome of the population is composed of the possible position index of the auxiliary array element; S2: construct a fitness function, substitute the initial population obtained in step S1 into the fitness function, and record the auxiliary array element position with the best fitness and its fitness value; S3: Use differential evolution DE / current-to-pbest / 1 mutation strategy to mutate the auxiliary array element position to generate a mutant population; S4: Perform crossover operation on the new population through binomial crossover method to form a test population; S5: Apply the greedy strategy to select a new generation of population from the current population and the test population, and update the position of the auxiliary array elements in the population; S6: based on the absolute value of the difference between the fitness function value of the current array element position combination and the previous generation array element position combination, update the historical records of the scaling factor F and the crossover probability factor CR; S7: Reduce the population size through the LPSR algorithm, calculate the next generation population size, and compare it with the current generation population size. Discard the worst individual in the current generation population or maintain the current generation population size according to the fitness to obtain the next generation population; S8: Iterate the evolving population until the maximum number of iterations is reached; S9: Output the iterative optimization process and the optimal auxiliary array element position.

2. The auxiliary array element position optimization method for sidelobe cancellation according to claim 1, characterized in that: In step S1, the initial population P of possible positions of the auxiliary array elements is composed of a random vector composition: P=[X1,…,X i ] T i=1,…,NP (1) X i =[x1,x2,…,x j ] j=1,…,D (2) x j =rand[L b ,U b ] (3) Among them, x j is the position of the jth auxiliary array element, X i is the position combination of the ith auxiliary array element, NP is the population size, D is the number of auxiliary array elements, U b and L b are the upper and lower bounds of the search space; The history record and the elimination archive initialization include: History M CR and M F The control parameters are stored in , that is, the cross probability factor CR and the scaling factor F; Where H is the capacity of the custom historical records; The elimination archive A is used to store the elimination solutions, which is initialized to an empty set.

3. The auxiliary array element position optimization method for sidelobe cancellation according to claim 2, characterized in that: In step S2, the fitness function is the angle of the interference signal traversing all coverage areas and calculating the sum of the absolute values ​​of the null depth of the interference signal at each traversal angle after sidelobe cancellation: Among them, N θ is the total number of traversed angles, and θ is the degree of the traversed angles.

4. The auxiliary array element position optimization method for sidelobe cancellation according to claim 3, characterized in that: In step S3, the differential evolution DE / current-to-pbest / 1 mutation strategy includes: V i,G =X i,G +F i ·(X pbest,G -X i,G )+F i ·(X r1,G -X r2,G ) (7) Among them, X pbest,G is to randomly select from the top p auxiliary array element combinations in the current population in terms of fitness, X i,G is the i-th auxiliary array element combination of the G-th iteration, X r1,G is the auxiliary array element combination randomly selected from the population P of the Gth iteration, X r2,G is a combination of auxiliary array elements randomly selected from P∪A, F i is the scaling factor, generated by: F i =randc i (M F,i ,0.1) (8) Among them, randc i represents the Cauchy distribution, M F,i From the historical record M F Randomly selected from .

5. The auxiliary array element position optimization method for sidelobe cancellation according to claim 4, characterized in that: The step S4 comprises: S4.1: Randomly select the intersection point j of the auxiliary array element position combination rand ; S4.2: According to formula (9), randomly select a number between 0 and 1, if it is less than or equal to the crossover probability CR i Or gene position j = j rand When , the j-th auxiliary array element position of the new auxiliary array element position combination U will inherit the j-th auxiliary array element position of the mutated auxiliary array element position combination V, otherwise it will inherit the j-th auxiliary array element position of the original auxiliary array element position combination X, and the formula is as follows: In formula (9), U i,j,G is the position of the new auxiliary array element generated after the crossover, j rand is a randomly selected intersection point, V i,j,G is the variable auxiliary array element position combination V i,G The jth auxiliary array element position; X i,j,G is the original auxiliary array element position combination X i,G The jth auxiliary array element position; the crossover probability CR i Generated by: CR i =randn i (M CR,i ,0.1) (10) randn in formula (10) i is a Gaussian distribution, M CR,i From the historical record M CR Randomly selected from .

6. The auxiliary array element position optimization method for sidelobe cancellation according to claim 5, characterized in that: The population update in step S5 adopts the greedy criterion to select the better individuals: In the formula, f(U i,g ) is the fitness function value of the ith auxiliary array element position combination in the test population, f(X i,G ) is the fitness function value of the i-th auxiliary array element position combination in the current population, X i,G+1 is the new auxiliary array element position combination after selection, X i,G is the original auxiliary array element position combination, that is, the i-th auxiliary array element position combination in the current population; U i,G The i-th auxiliary array element position combination in the test population generated for the G-th iteration.

7. An auxiliary array element position optimization system for sidelobe cancellation, characterized in that: include: The signal processing module is used to read the coordinates of the array element position, complete the array element position coding, population initialization, and historical record and elimination archive initialization. The chromosome of the population is composed of the possible position indexes of the auxiliary array elements; The fitness function module is used to construct the fitness function, substitute the population into the fitness function, and record the auxiliary array element position with the best fitness and its fitness value; A mutation module is used to perform mutation operations on the auxiliary array element positions using the DE / current-to-pbest / 1 mutation strategy to generate a mutant population; The crossover module is used to perform a crossover operation on the new population through the binomial crossover method to form a test population; A selection module is used to select a new generation of population from the current population and the test population using a greedy strategy, and to update the positions of the auxiliary array elements in the population; A parameter updating module, used for updating the historical records of the scaling factor F and the crossover probability factor CR based on the absolute value of the difference between the fitness function value between the current array element position combination and the previous generation array element position combination; The population size reduction module is used to reduce the population size through the LPSR algorithm, calculate the next generation population size, and compare it with the current generation population size. According to the fitness, the worst individual in the current generation population is discarded or the current generation population size is maintained to obtain the next generation population; An iteration module, used to iterate the evolutionary population until the maximum number of iterations is reached; The output module is used to output the iterative optimization process and the optimal auxiliary array element position.

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