A method and system for optimizing the position of auxiliary array elements for sidelobe cancellation

Abstract

This invention discloses a method and system for optimizing the position of auxiliary array elements for sidelobe cancellation. The method includes: initializing a population, where the chromosomes of individual populations are composed of the possible position indices of auxiliary array elements; constructing a fitness function, calculating the fitness of the initial population, and recording the optimal auxiliary array element position; generating a mutant population using a differential evolution (DE) strategy; performing a crossover operation on the mutant population using a binary crossover method to form a test population; selecting a new generation population from the previous generation population and the test population using a greedy strategy; updating the historical records of the scaling factor and crossover probability factor; reducing the population size using the LPSR algorithm; iteratively evolving the population; and outputting the iterative optimization process and the optimal auxiliary array element position. This invention achieves efficient optimization of auxiliary array element positions by adaptively adjusting the key parameters of the differential evolution algorithm, with low computational complexity and fast convergence speed. It can be used in radar sidelobe interference suppression technology and can improve the radar's adaptability to different interference environments.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, specifically to an auxiliary array element position optimization method and system for sidelobe cancellation, and more specifically to an improved differential evolution-based auxiliary array element position optimization method and system for sidelobe cancellation. Background Technology

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

[0003] Generally, common sidelobe cancellers achieve interference cancellation by optimizing the weights of specified main and auxiliary channels. However, in practical applications, the positions of different auxiliary channels significantly affect the performance of the sidelobe canceller. To improve the performance of the sidelobe canceller, the positions of the array elements in the auxiliary array need to be optimized. The Differential Evolution (DE) algorithm, with its advantages of fast convergence speed and strong global search capability, is widely used in such optimization problems. By optimizing the selection, the optimal combination of array element positions is found, thereby better suppressing sidelobe interference and improving signal quality.

[0004] In 2013, to study the impact of auxiliary antenna configuration methods on the performance of adaptive sidelobe cancellation systems, Su Baowei et al. designed auxiliary antenna configuration schemes such as independent array elements, subarrays, and array element combinations. Simulation comparisons showed that when auxiliary antennas were in the same row or column, the cancellation performance would significantly decrease. In 2022, Zhang ZM et al., focusing on the application of sidelobe cancellation technology in practical engineering, proposed that the distance between auxiliary antennas has a significant impact on sidelobe cancellation performance, especially when auxiliary antennas are densely arranged, where the sidelobe cancellation performance may decrease.

[0005] Compared to other evolutionary algorithms, the differential evolution algorithm has advantages such as fewer control parameters, stronger robustness, and stronger global search capability. However, it also has some shortcomings, mainly including the tendency to get trapped in local optima and premature convergence. Therefore, many scholars at home and abroad have made various improvements to the differential evolution algorithm.

[0006] In 2013, Tanabe et al. proposed a Success-History based Adaptive Differential Evolution (SHADE) algorithm. In 2014, Tanabe et al. proposed LSHADE, an improved version of SHADE that incorporates 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, leveraging the advantages of multiple differential mutation operators and emphasizing the best-performing operator. In 2022, Yi et al. proposed an adaptive differential algorithm integrating operators. This algorithm uses two sets of mutation and crossover operators to generate offspring, better balancing the algorithm's development and exploration capabilities. Furthermore, an integrated adaptive parameter control strategy dynamically adjusts the algorithm's parameter settings, further improving search performance.

[0007] Currently, traditional sidelobe cancellation techniques typically rely on complex hardware designs and fixed algorithms. These methods suffer from problems such as fixity, high computational complexity, and optimization limitations. Fixed algorithms struggle to find a globally optimal solution and are prone to getting trapped in local optima, affecting cancellation performance. Furthermore, traditional methods are usually designed based on specific system configurations and interference environments, lacking adaptability to different interference environments. Summary of the Invention

[0008] In view of this, the present invention provides an auxiliary element position optimization method and system for sidelobe cancellation, which can at least partially solve the problems mentioned above, such as the complexity of calculation, the tendency to get trapped in local optima, the impact on cancellation effect, and the lack of adaptability to changing interference environments during the sidelobe cancellation process.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] In a first aspect, the present invention provides an auxiliary element position optimization method for sidelobe cancellation, comprising the following steps:

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

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

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

[0014] S4: The new population is crossovered using the binary crossover method to form an experimental population;

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

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

[0017] S7: Reduce the population size using the LPSR algorithm, calculate the size of the next generation population, compare it with the size of the current generation population, and discard the worst individual in the current generation population or maintain the size of the current generation population based on fitness to obtain the next generation population.

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

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

[0020] Secondly, the present invention also provides an auxiliary element position optimization system for sidelobe cancellation, comprising:

[0021] The signal processing module is used to read the position coordinates of the array elements, complete the array element position encoding, population initialization, and historical record and elimination archive initialization. The chromosome of the population is composed of the possible position indices 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 position of the auxiliary element with the best fitness and its fitness value.

[0023] The mutation module is used to perform mutation operations on the positions of auxiliary array elements using the DE / current-to-pbest / 1 mutation strategy to generate a mutation population.

[0024] The crossover module is used to perform crossover operations on a new population using the binary crossover method to form an experimental population.

[0025] The selection module is used to apply a greedy strategy to select a new generation of population from the current population and the experimental population, and update the positions of auxiliary array elements in the population.

[0026] The parameter update module is used to update 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 values ​​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 using the LPSR algorithm, calculate the size of the next generation population, compare it with the size of the current generation population, and discard the worst individual in the current generation population or maintain the size of the current generation population based on fitness to obtain the next generation population.

[0028] The iteration module is used to iteratively evolve the 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 positions.

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

[0031] This invention employs an improved differential evolution algorithm to optimize the selection of adaptive sidelobe cancellation auxiliary element positions. By adaptively adjusting key parameters of the differential evolution algorithm and combining it with array signal processing techniques, it achieves efficient optimization of the adaptive sidelobe cancellation auxiliary element positions. This method not only improves adaptability to different interference environments but also reduces computational complexity and accelerates convergence speed. It can be used in radar sidelobe interference suppression technology to enhance the radar's adaptability to various interference environments. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0033] Figure 1 The flowchart shows the improved differential evolution auxiliary element position optimization method for sidelobe cancellation provided by this invention.

[0034] Figure 2 The array configuration diagram provided by this invention.

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

[0036] Figure 4 This is a comparison of the fitness iteration curves of the proposed method and the traditional algorithm after 20 Monte Carlo experiments.

[0037] Figure 5 An adaptive radiation pattern is used to suppress individual interference by employing the optimized selection of auxiliary array element positions.

[0038] Figure 6An adaptive radiation pattern is used to suppress multiple interferences by employing the optimized selection of auxiliary array element positions.

[0039] Figure 7 This is a block diagram of the improved differential evolution auxiliary array element position optimization system for sidelobe cancellation provided by the present invention. Detailed Implementation

[0040] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] like Figure 1 As shown, this invention provides a method for optimizing the position of auxiliary array elements based on improved differential evolution for sidelobe cancellation, comprising the following steps:

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

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

[0044] S3: Employ the Differential Evolution (DE) mutation strategy to mutate the positions of auxiliary array elements, generating a mutant population;

[0045] S4: The new population is crossovered using the binary crossover method to form an experimental population;

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

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

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

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

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

[0051] In this embodiment of the invention, combined with Figure 2 As shown, for example, the array in step S1 is a 48×6 uniform surface array with a total of 288 array elements. The array elements are numbered sequentially from 1 to 288, and four array elements are selected as auxiliary array elements, with the remaining array elements forming the main array. Assuming the target signal is incident at 45°, an interference signal is selected and traversed 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 this embodiment of the invention, the four auxiliary element positions are used to form a chromosome in the differential evolution algorithm, i.e., an auxiliary element combination, and each auxiliary element position is called a gene. The initial population P of the auxiliary element positions 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] Where, x j For the j-th auxiliary element position (gene), X i Let NP be the combination of positions of the i-th auxiliary element (chromosome), D be the population size, and U be the number of auxiliary elements. b and L b This represents the upper and lower bounds of the search space.

[0057] In this embodiment of the invention, the improved differential evolution algorithm requires initializing historical records and external archives, where the historical record M... F and M CR This stores control parameters (scaling factor F and crossover probability factor CR), for example, initialized to 0.5:

[0058]

[0059] M F,i and M CR,iLet F and CR represent the scaling factor F and crossover probability factor recorded in the i-th iteration, respectively, which are the same in each iteration. H is a custom capacity for the historical record, defined as 60 in this embodiment.

[0060] Elimination archive A is used to store elimination solutions, and it is initialized to an empty set:

[0061]

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

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

[0064]

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

[0066] In step S2, to ensure that the auxiliary array elements maintain effective anti-interference performance within the spatial coverage area, their null depths at different interference incident angles and their ability to cancel interference within the spatial coverage area are comprehensively considered. Therefore, the fitness function in step S2 is constructed as the sum of the absolute values ​​of the null depths of the interference signal at each traversal angle after sidelobe cancellation, based on the angles at which the interference signal traverses all coverage areas. This function is then used to evaluate the quality of each individual in the initial population.

[0067] Construction of the fitness function:

[0068] The impact of auxiliary element position combinations on sidelobe cancellation performance is evaluated, and the optimal element position combination is selected. All possible interference incident angles are traversed, and the null depth of the interference signal after sidelobe cancellation is calculated for each angle. The sum of the absolute values ​​of the null depths at all interference incident angles is calculated as a comprehensive evaluation criterion.

[0069] Step S2 constructs a fitness function to convert the quality of the auxiliary element position combination into a numerical value, providing a basis for subsequent evolutionary operations.

[0070] In this embodiment of the invention, the DE / current-to-pbest / 1 mutation strategy in step S3 not only uses information about the best individual, but also uses information about other better individuals, using the differences between these individuals as the direction guiding population evolution. 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 To randomly select from the top p fitness combinations of auxiliary array elements in the current population, X i,G For the i-th auxiliary array element combination in the G-th iteration, X r1,G X is a combination of auxiliary array elements randomly selected from the population P in the Gth iteration. r2,G F is a combination of auxiliary array elements randomly selected from P∪A. i The scaling factor is generated by the following formula:

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

[0074] Among them, randc i Denotes the Cauchy distribution, M F,i To extract from historical records M F A scaling factor randomly selected from the data. Using historical data M. F The scaling factor F can be adaptively adjusted to better suit the current search process.

[0075] The purpose of step S3 is to mutate the positions of the auxiliary array elements, generating a mutated population to provide a basis for subsequent crossover and selection operations. This step employs a DE / current-to-pbest / 1 mutation strategy.

[0076] 1. Components of a 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 as X. i,G .

[0079] pbest: represents a randomly selected auxiliary element from the top p fitness combinations in the current population, denoted as X. pbest,G .

[0080] r1, r2: Represent two distinct combinations of auxiliary array elements randomly selected from the population P in the G-th iteration, denoted as X. r1,G and X r2,G .

[0081] 2. Mutation operation:

[0082] The core of mutation operations is generating mutated individuals V. i,G , of which F i This is a scaling factor used to control the degree of variation.

[0083] 3. The mutation process:

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

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

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

[0087] 4. Characteristics of mutation strategies:

[0088] The pbest individual is introduced: By introducing the pbest individual, the mutation operation can better utilize historical information and improve search efficiency. Through the difference operation, the mutation operation can generate more diverse individuals and avoid getting trapped in local optima.

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

[0090] In this embodiment of the invention, step S4 uses a binary crossover to perform a crossover operation on the pair position combination.

[0091] S4.1: Randomly select the intersection point j of chromosomes (auxiliary element position combinations). rand ;

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

[0093]

[0094] In formula (9) U i,j,G j represents the position of the new auxiliary array element generated after the crossover. rand For randomly selected intersection points, V i,j,G V is the combination of positions of the variant auxiliary array elements. i,G The position of the j-th auxiliary element; X i,j,G The original auxiliary array element position combination X i,G The position of the j-th auxiliary element; the crossover probability CR i It is generated by the following formula:

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

[0096] randn in formula (10) i It follows a Gaussian distribution, M CR,i To extract from historical records M CR The crossover probability is randomly selected from the data. Using historical data M... CR The crossover probability (CR) can be adaptively adjusted to better suit the current search process.

[0097] The purpose of step S4 is to combine the mutated individuals with the original individuals through a crossover operation to generate an experimental population. This step uses a binary crossover method, as detailed below:

[0098] 1. Components of a crossover operation:

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

[0100] Selecting the intersection point: Randomly select the intersection point j of the chromosome (the combination of auxiliary element positions). rand .

[0101] Crossover operation: based on crossover probability CR or gene location j rand The positions of the new auxiliary array elements are combined into U.i,G The position of the j-th auxiliary element is inherited from the combination of mutated auxiliary element positions V. i,G Or the original auxiliary array element position combination X i,G .

[0102] 2. Crossover process:

[0103] Step 1: Randomly select the intersection point j of chromosomes (auxiliary element position combinations). rand .

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

[0105] 3. Crossover Strategy: Crossover operations are simple and easy to implement. The frequency of crossover operations can be controlled by the crossover probability (CR). Crossover operations can generate more diverse individuals and avoid getting trapped in local optima.

[0106] Step S4 uses a binary crossover method to combine the mutated individuals with the original individuals to generate the experimental population. This step, through the selection of crossover points and the crossover operation, effectively improves the search efficiency and solution quality of the algorithm.

[0107] In this embodiment of the invention, step S5 selects a better individual as the array element position combination for the new population based on a 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 experimental individual evolves than the original individual, then the original array element position combination X is changed. i,G Store in the obsolescence archive A. If the obsolescence archive exceeds its capacity, delete the excess data.

[0108] In this process, the population update uses a greedy criterion to select the better individuals:

[0109]

[0110] In the formula, f(U) i,G f(X) represents the fitness function value of the position combination of the i-th auxiliary element in the experimental population. i,G X is the fitness function value of the i-th auxiliary element position combination in the current population. i,G+1 To select the new combination of auxiliary array element positions, X i,G This represents the original combination of auxiliary element positions, i.e., the combination of the i-th auxiliary element positions in the current population; U i,GThe combination of positions of the i-th auxiliary array element in the experimental population generated in the G-th iteration.

[0111] Step S5 is a crucial step in the technical solution of this invention. It selects a new generation of population from the current population and the experimental population using a greedy strategy, thereby achieving population evolution. That is, in each iteration, the auxiliary array element positions with higher fitness values ​​from the current population and the experimental population are selected to enter the new generation of population.

[0112] In formula (11), if the fitness value of the i-th auxiliary element position combination in the test population is greater than or equal to the fitness value of the i-th auxiliary 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 index used to evaluate the quality of the combination of auxiliary array element positions. In this invention, the fitness function is the sum of the absolute values ​​of the null depths of the interference signal at each traversal angle after the sidelobe cancellation is calculated, based on the angles at which the interference signal traverses all coverage areas.

[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 includes several combinations of auxiliary element positions.

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

[0117] In this embodiment of the 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 successfully evolved individuals in each iteration in S. F and S CR In the middle, the k-th unit of the historical record is set 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 historical record cell k is incremented by 1;

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

[0122] in:

[0123]

[0124] In the formula, M CR,k,G+1 It represents the crossover probability factor of the k-th historical record unit in the (G+1)-th iteration; S represents the crossover probability factor-weighted average of successfully evolved individuals; CR M represents the set of crossover probability factors for successfully evolving individuals; CR,k,G W represents the crossover probability factor of the k-th historical record unit in the G-th iteration; a This is a weighted average, used to control the degree of influence of successfully evolved individuals on the current F and CR.

[0125] M F,k,G+1 This represents the scaling factor of the k-th historical record unit in the (G+1)-th iteration; S represents the scaling factor-weighted Lehmer average of successfully evolved individuals; F M represents the set of scaling factors for successfully evolving individuals. F,k,G This represents the scaling factor of the k-th historical record unit in the G-th iteration.

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

[0127]

[0128] Wherein, mean(): calculates the average of the set; the Lehmer mean gives greater influence to parameters that contribute significantly. Compared to the arithmetic mean, the Lehmer mean is larger, which can prevent premature convergence caused by excessively small control parameters. S CR,k S represents the crossover probability factor for the k-th successfully evolved individual; F,k This represents the scaling factor for the k-th successfully evolved individual. Additionally, the weight vector w... k It can improve parameter fitness, which is calculated based on the absolute value of the difference between the fitness function values ​​between the experimental element position combination and the original element position combination:

[0129]

[0130] Δf k =|f(U k,G )-f(X k,G (17)

[0131] Δf kf(U) is the absolute value of the difference between the fitness function values ​​of the current element position combination and the previous generation element position combination. k,G f(X) represents the fitness function value of the position combination of the k-th auxiliary element in the experimental population. k,G ) represents the fitness function value of the position combination of the k-th auxiliary element in the current population.

[0132] Step S6 is a crucial step in the technical solution of this invention. It is responsible for updating two key parameters of the differential evolution algorithm: the scaling factor F and the crossover probability factor CR, thereby ensuring the algorithm's search capability and convergence speed. Step S6 updates the historical records and calculates new F and CR based on the scaling factor F and crossover probability factor CR of successfully evolved individuals, as well as the absolute value of the difference between the fitness function values ​​of the current element position combination and the previous generation element position combination.

[0133] Step S6 adaptively adjusts F and CR to enable the algorithm to better balance exploration and development capabilities during the search process, thereby improving the algorithm's search ability and convergence speed, and ultimately finding the optimal combination of auxiliary array element positions.

[0134] In this embodiment of the invention, step S7 reduces the population size using the LPSR algorithm, including:

[0135] 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 ;

[0136] S7.2: If the next generation population size is NP G+1 Smaller than the current generation population size NP G Then, the current generation of the population is sorted according to the fitness function value, and the worst NP is discarded. G -NP G+1 The combination of array element positions yields a population size of NP. G+1 The next generation of the population will have its elimination archive A reduced as the population size decreases; otherwise, the current population size NP will be maintained. G ;

[0137]

[0138] NP in formula (18) init The initial population size is 60 in this example, NP. min The minimum population size is 4 in this example, FES is the number of times the current fitness function is evaluated, and MAXFES is the number of times the maximum fitness function is evaluated, which is 500 in this example.

[0139] Step S7 describes how to dynamically adjust the population size using the Linear Population Reduction (LPSR) algorithm to adapt to the needs of the evolutionary process. Its main purpose is to maintain the algorithm's search capability while avoiding the computational complexity and resource consumption caused by an excessively large population size. Steps S7.1 and S7.2 above maintain an appropriate population size at different stages of evolution by dynamically adjusting the population size. In the early stages of evolution, a larger population size ensures the algorithm's search capability and avoids getting trapped in local optima. As evolution progresses, the population size gradually decreases, reducing computational complexity and resource consumption, and improving the algorithm's efficiency. This allows the algorithm to maintain optimal performance at different stages of evolution.

[0140] In embodiments of the present invention, such as Figure 3 As shown, the table mainly presents the optimal fitness iteration curves and average fitness iteration curves of the proposed method and the traditional algorithm, illustrating the changes in fitness values ​​during the iteration process and reflecting the optimization capability and convergence speed of the algorithms. The x-axis represents the number of iterations for both algorithms, and the y-axis represents the fitness function values ​​for both algorithms. Figure 3 As can be seen, in the fitness iteration curve, the curve of the algorithm proposed in this invention rises faster than that of the traditional algorithm, indicating that it can find a better solution more quickly in the initial stage. Ultimately, the fitness value of the algorithm proposed in this invention is significantly higher than that of the traditional algorithm, which shows that the algorithm proposed in this invention achieves better results in optimization problems.

[0141] In embodiments of the present invention, such as Figure 4 As shown, to avoid random occurrences, the Monte Carlo experiment was repeated 20 times with the same parameters. Simulation analysis of the proposed method and traditional algorithms yielded the optimal fitness iteration curve and the average fitness iteration curve. The x-axis represents the number of iterations for both algorithms, and the y-axis represents the fitness function values ​​for both algorithms. Figure 4 As can be seen, under the same number of iterations, the algorithm proposed in this invention converges faster than the traditional algorithm, reflecting its ability to quickly obtain a better solution. Furthermore, as iterations proceed, the fitness curve of the algorithm proposed in this invention typically shows smaller fluctuations, indicating better stability during the search process and its ability to effectively remain near a better solution. Ultimately, the fitness value of the algorithm proposed in this invention is significantly higher than that of the traditional algorithm, demonstrating that the algorithm proposed in this invention achieves superior results in optimization problems.

[0142] In this embodiment of the invention, the optimized array element positions are [12, 265, 43, 156], which are used as auxiliary array elements. Three interferences are selected and incident from 22°, 40°, and 52° respectively, and adaptive sidelobe cancellation is performed to obtain an adaptive radiation pattern, as shown below. Figure 5 and Figure 6As shown in the figure. This demonstrates that, after optimization by the method of this invention, it is possible to select auxiliary array element position combinations with better anti-interference performance more efficiently, verifying that the algorithm proposed in this invention can effectively optimize the selection of auxiliary array element positions.

[0143] Based on the same inventive concept, this invention also provides an improved differential evolution auxiliary array element position optimization system for sidelobe cancellation. Since the principle of the problem solved by this system is similar to the aforementioned improved differential evolution auxiliary 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 described again.

[0144] This invention also provides an auxiliary element position optimization system for sidelobe cancellation, referring to... Figure 7 As shown, it includes:

[0145] The signal processing module is used to read the position coordinates of the array elements, complete the array element position encoding, population initialization, and historical record and elimination archive initialization. The chromosome of the population is composed of the possible position indices of the auxiliary array elements.

[0146] The fitness function module is used to construct the fitness function, substitute the population into the fitness function, and record the position of the auxiliary element with the best fitness and its fitness value.

[0147] The mutation module is used to perform mutation operations on the positions of auxiliary array elements using the DE / current-to-pbest / 1 mutation strategy to generate a mutation population.

[0148] The crossover module is used to perform crossover operations on a new population using the binary crossover method to form an experimental population.

[0149] The selection module is used to apply a greedy strategy to select a new generation of population from the current population and the experimental population, and update the positions of auxiliary array elements in the population.

[0150] The parameter update module is used to update 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 values ​​between the current array element position combination and the previous generation array element position combination.

[0151] The population size reduction module is used to reduce the population size using the LPSR algorithm, calculate the size of the next generation population, compare it with the size of the current generation population, and discard the worst individual in the current generation population or maintain the size of the current generation population based on fitness to obtain the next generation population.

[0152] The iteration module is used to iteratively evolve the population until the maximum number of iterations is reached;

[0153] The output module is used to output the iterative optimization process and the optimal auxiliary array element positions.

[0154] In this embodiment, the system achieves efficient optimization 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 cost, and improving flexibility.

[0155] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0156] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those 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 invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded 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, Includes the following steps: S1: Read the coordinates of the array element positions, complete the array element position encoding, population initialization, and historical record and elimination archive initialization. The chromosome of the population is composed of the possible position indices of the auxiliary array elements. S2: Construct a fitness function, and substitute the initial population obtained in step S1 into the fitness function, and record the position of the auxiliary element with the best fitness and its fitness value; S3: Use the differential evolution DE / current-to-pbest / 1 mutation strategy to mutate the positions of auxiliary array elements to generate a mutant population; S4: The new population is crossovered using the binary crossover method to form an experimental population; S5: Apply a greedy strategy to select a new generation of population from the current population and the experimental population, and update the positions of auxiliary elements in the population; S6: Based on the absolute value of the difference between the fitness function values ​​between the current element position combination and the previous generation element position combination, update the historical records of the scaling factor F and the crossover probability factor CR. S7: Reduce the population size using the LPSR algorithm, calculate the size of the next generation population, compare it with the size of the current generation population, and discard the worst individual in the current generation population or maintain the size of the current generation population based on fitness to obtain the next generation population. S8: Iterate and evolve the population until the maximum number of iterations is reached; S9: Output the iterative optimization process and the optimal auxiliary element position; In step S2, the fitness function is the sum of the absolute values ​​of the null depths of the interference signal at each traversal angle after sidelobe cancellation, based on the angles at which the interference signal traverses all coverage areas. Where, N θ θ represents the total number of traversal angles, and H represents the conjugate transpose of the weight vector; w represents the beam weight vector, used to balance the importance of null depth at different angles; a represents the signal steering vector. 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 To randomly select from the top p fitness combinations of auxiliary array elements in the current population, X i,G For the i-th auxiliary array element combination in the G-th iteration, X r1,G X is a combination of auxiliary array elements randomly selected from the population P in the Gth iteration. r2,G F is a combination of auxiliary array elements randomly selected from P∪A. i The scaling factor is generated by the following formula: F i =randc i (M F,i ,0.1) (8) Among them, randc i Denotes the Cauchy distribution, M F,i To extract from historical records M F Randomly selected from; Step S4 includes: 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 the number is less than or equal to the crossover probability CR, i Or gene location j=j rand When the new auxiliary element position combination U is used, the j-th auxiliary element position will inherit the j-th auxiliary element position of the mutated auxiliary element position combination V; otherwise, it will inherit the j-th auxiliary element position of the original auxiliary element position combination X. The formula is as follows: In formula (9) U i,j,G j represents the position of the new auxiliary array element generated after the crossover. rand For randomly selected intersection points, V i,j,G V is the combination of positions of the variant auxiliary array elements. i,G The position of the j-th auxiliary element; X i,j,G The original auxiliary array element position combination X i,G The position of the j-th auxiliary element; the crossover probability CR i It is generated by the following formula: CR i =randn i (M CR,i ,0.1) (10) randn in formula (10) i It follows a Gaussian distribution, M CR,i To extract from historical records M CR Randomly selected from; The population update in step S5 uses a greedy criterion to select the better individuals: In the formula, f(U) i,G f(X) represents the fitness function value of the position combination of the i-th auxiliary element in the experimental population. i,G X is the fitness function value of the i-th auxiliary element position combination in the current population. i,G+1 To select the new combination of auxiliary array element positions, X i,G This represents the original combination of auxiliary element positions, i.e., the combination of the i-th auxiliary element positions in the current population; U i,G The combination of positions of the i-th auxiliary array element in the experimental population generated in the G-th iteration.

2. The method for optimizing the position of auxiliary array elements for sidelobe cancellation according to claim 1, characterized in that, In step S1, the initial population P of the possible positions of the auxiliary array elements is determined by 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) Where, x j Let X be the position of the j-th auxiliary element. i Let NP be the combination of positions of the i-th auxiliary array element, D be the population size, and U be the number of auxiliary array elements. b and L b This serves as the upper and lower bounds of the search space; The initialization of the historical record and obsolescence archive includes: Historical Records M CR and M F The control parameters are stored in the middle, namely the crossover probability factor CR and the scaling factor F; Where H is the capacity of the custom history record; The elimination archive A is used to store elimination solutions, and it is initialized to an empty set.

3. An auxiliary element position optimization system for sidelobe cancellation, characterized in that, The system, employing the auxiliary element position optimization method for sidelobe cancellation as described in any one of claims 1-2, comprises: The signal processing module is used to read the position coordinates of the array elements, complete the array element position encoding, population initialization, and historical record and elimination archive initialization. The chromosome of the population is composed of the possible position indices 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 position of the auxiliary element with the best fitness and its fitness value. The mutation module is used to perform mutation operations on the positions of auxiliary array elements using the DE / current-to-pbest / 1 mutation strategy to generate a mutation population. The crossover module is used to perform crossover operations on a new population using the binary crossover method to form an experimental population. The selection module is used to apply a greedy strategy to select a new generation of population from the current population and the experimental population, and update the positions of auxiliary array elements in the population. The parameter update module is used to update 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 values ​​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 using the LPSR algorithm, calculate the size of the next generation population, compare it with the size of the current generation population, and discard the worst individual in the current generation population or maintain the size of the current generation population based on fitness to obtain the next generation population. The iteration module is used to iteratively evolve the 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 positions.

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