A non-uniform subarray partitioning method based on dynamic genetic algorithm

Abstract

The application discloses a non-uniform subarray partitioning method based on a dynamic genetic algorithm, and relates to the technical field of airspace anti-interference of unmanned aerial vehicles. The method uses dynamic multi-point crossover and multi-point mutation strategies to improve individual diversity, expand a search range, uses dynamic crossover and mutation probabilities to accelerate convergence speed, finally selects a highest sidelobe level absolute value of subarray weighted adaptive beam forming as a fitness function to be optimized, and obtains an optimal subarray partitioning scheme. The method uses the dynamic multi-point crossover and multi-point mutation strategies to improve the individual diversity, expand the search range, and uses the dynamic crossover and mutation probabilities to accelerate the convergence speed.

Description

Technical Field

[0001] This invention relates to the field of anti-interference technology in the airspace of unmanned aerial vehicles (UAVs), and in particular to a non-uniform subarray partitioning method based on a dynamic genetic algorithm. Background Technology

[0002] Traditional uniform non-overlapping subarrays divide each element evenly into subarrays, resulting in identical subarray structures and an equal number of elements. However, the resulting grating lobes and nulls degrade beamforming performance. Uniform overlapping subarrays have the same structure and number of elements, but partial element reuse leads to overly complex feed networks, hindering engineering implementation. In contrast, non-uniform non-overlapping subarrays have different structures and numbers of elements, and no element reuse, effectively suppressing grating lobes and nulls. Therefore, researching non-uniform non-overlapping subarray partitioning methods has significant theoretical research value and engineering practical value.

[0003] In recent years, genetic algorithms have been widely used in low sidelobe, sparse array design, beamforming, and subarray partitioning. Traditional genetic algorithms often employ simple genetic operations, such as single-point crossover or mutation, and the crossover and mutation probabilities are fixed, resulting in a small search range and slow convergence speed. Summary of the Invention

[0004] In view of this, this invention proposes a non-uniform subarray partitioning method based on a dynamic genetic algorithm. This method achieves better convergence performance and faster convergence speed compared to traditional genetic algorithms.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A non-uniform subarray partitioning method based on a dynamic genetic algorithm includes the following steps;

[0007] Step 1: Initialize the parameters of the dynamic genetic algorithm, including the number of array elements M, the number of subarrays L, and the initial crossover probability P. c 1(0), Initial number of intersections P c 2(0), minimum crossover probability P c 1 min Minimum number of intersections P c 2 min Initial mutation probability P m 1(0), Initial mutation rate P m 2(0), Maximum mutation probability P m 1 max Maximum variation rate P m 2 max Maximum number of iterations α max And the range of constraints on the number of array elements in each subarray;

[0008] Step 2: Randomly generate an initial population. Each individual in the population is considered as a chromosome. Set a variable α to indicate the number of iterations of the genetic algorithm, and let α = 1.

[0009] Step 3: Decode each chromosome in the current population to obtain the subarray partitioning scheme corresponding to the chromosome, and then calculate the fitness value of the subarray partitioning scheme, which is recorded as the fitness value of the chromosome.

[0010] Step 4: Perform selection, crossover, and mutation operations on the chromosomes in the current population; then determine whether each chromosome in the latest population meets the constraints. If it does, proceed to step 5; otherwise, correct the chromosomes and proceed to step 5.

[0011] Step 5: Update the crossover and mutation-related parameters;

[0012] Step 6, determine α = α max Does this hold true if α = α? max If the condition is met, then according to step 3, calculate the fitness value of each subarray partitioning scheme in the latest population, select the subarray partitioning scheme with the largest fitness value in the latest population as the final subarray partitioning scheme, and complete the non-uniform subarray partitioning based on the dynamic genetic algorithm; if α = α max If this is not true, then let α = α + 1, and continue with step 3.

[0013] Furthermore, the specific method for randomly generating the initial population in step 2 is as follows:

[0014] Based on the requirements of the number of array elements, the number of subarrays, and the constraints on the number of array elements, calculate all the splitting schemes that meet the requirements;

[0015] Randomly select some partitioning schemes. For each selected partitioning scheme: use n-bit binary encoding to represent the subarray number corresponding to one array element, 2 n-1 <L≤2 n Sort M n-bit binary codes in ascending order to form an individual in the initial population; in each individual, the same n-bit binary code indicates that they belong to the same subarray, and the number of the same n-bit binary code indicates the number of array elements contained in the subarray corresponding to that n-bit binary code.

[0016] Furthermore, the specific method for step 3 is as follows:

[0017] For each chromosome, its M n-bit binary codes are converted into M decimal codes to obtain a subarray partitioning scheme. The adaptive beamforming pattern under this subarray partitioning scheme is then obtained according to the following formula:

[0018]

[0019] Where G(θ) is the adaptive beamforming diagram under this subarray partitioning scheme, θ is the signal incident angle, and w sub Let T be the weighted vector of each subarray calculated according to the MVDR method, T be the subarray forming matrix corresponding to the subarray partitioning scheme, α(θ) be the steering vector of the desired signal, the superscript H indicates the conjugate transpose, and |·| indicates the modulus value;

[0020] Determine the main lobe peak in the adaptive beamforming diagram, then search for the first null point on the left and right sides of the main lobe peak. Search for the maximum level outside the first null point on the left and right sides, and record the absolute value of the maximum level as the fitness value corresponding to the subarray partitioning scheme, which is the fitness value of the chromosome.

[0021] Furthermore, step 4 is specifically implemented as follows:

[0022] Step 401: Normalize the fitness values ​​of all chromosomes in the current population, and use the roulette wheel method to repeatedly select one chromosome from the current population as the chromosome for the next generation population until the number of chromosomes in the next generation population is the same as the number of chromosomes in the initial population.

[0023] Step 402: Divide the chromosomes in the latest population into groups of two. For each group of chromosomes, generate a crossover random number between 0 and 1. If the generated crossover random number is less than the crossover probability P... c If 1(α), then a crossover operation is performed on this set of chromosomes. Specifically, the n-bit binary codes at corresponding positions of the two chromosomes are matched sequentially. One or more consecutive n-bit binary codes that do not match are recorded as a crossover position. If the number of crossover positions is greater than P, then... c 2(α), then P is randomly selected from all positions to be crossed. c Perform a crossover operation on 2(α) crossover positions. If the number of crossover positions is less than or equal to P... c If 2(α), then this set of chromosomes will not undergo crossover; if the generated random crossover number is not less than the crossover probability P c If 1(α), then this set of chromosomes will not undergo crossover; where P c 1(α) is the crossover probability at the α-th iteration, P c 2(α) represents the number of intersections in the α-th iteration, P c 1(α)∈[0,1];

[0024] Step 403: For each chromosome, generate a random mutation number between 0 and 1. If the generated random mutation number is less than the mutation probability P... mIf 1(α), then for each n-bit binary code in the chromosome, a random mutation number between 0 and 1 is generated. If the generated random mutation number is less than the mutation rate P, m 2(α), then all the current n-bit binary codes are inverted bit by bit. If the generated random number of mutation points is not less than the mutation rate P m If 2(α), then the current n-bit binary code will not be mutated; if the generated mutated random number is not less than the mutation probability P m If 1(α), then the chromosome will not undergo mutation; P m 1(α) is the mutation probability at the α-th iteration, P m 2(α) represents the mutation rate at the α-th iteration, P m 1(α), P m 2(α)∈[0,1];

[0025] Step 404: For each chromosome in the latest population, determine whether there is a subarray number that does not meet the subarray number requirement or the subarray number constraint range. If so, replace the chromosome corresponding to the chromosome before the crossover or mutation and then execute step 5. If not, sort the M n-bit binary codes in the chromosome in ascending order and then execute step 5.

[0026] Furthermore, step 5 is specifically implemented as follows:

[0027]

[0028] Among them, P c 2(0) = L-2, QZ(·) indicates rounding.

[0029] Due to the adoption of the above technical solution, the beneficial effects of this invention compared with the prior art are as follows:

[0030] 1. This invention employs dynamic multi-point crossover and multi-point mutation strategies to enhance individual diversity and expand the search range. It utilizes dynamic crossover and mutation probabilities to accelerate convergence and selects the absolute value of the highest sidelobe level as the fitness function for optimization, thereby achieving non-uniform subarray partitioning of the array.

[0031] 2. This invention can effectively reduce the hardware cost and computational complexity of UAV airspace anti-jamming system, while obtaining a higher highest sidelobe level than the adaptive beamforming of the full array element, which has certain reference value for engineering practice. Attached Figure Description

[0032] Figure 1 This is an overall flowchart of a non-uniform subarray partitioning method based on a dynamic genetic algorithm in an embodiment of the present invention.

[0033] Figure 2 This is a schematic diagram of a splitting scheme selected in an embodiment of the present invention.

[0034] Figure 3 To Figure 2 A diagram illustrating the encoding of the splitting scheme.

[0035] Figure 4 This is a diagram of the subarray weighted adaptive beamforming model in an embodiment of the present invention.

[0036] Figure 5 This is a schematic diagram of the cross operation in an embodiment of the present invention. Detailed Implementation

[0037] The invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0038] A non-uniform subarray partitioning method based on dynamic genetic algorithm, such as Figure 1 As shown, it includes the following steps;

[0039] Step 1: Initialize the parameters of the dynamic genetic algorithm, including the number of array elements M, the number of subarrays L, and the initial crossover probability P. c 1(0), Initial number of intersections P c 2(0), minimum crossover probability P c 1 min Minimum number of intersections P c 2 min Initial mutation probability P m 1(0), Initial mutation rate P m 2(0), Maximum mutation probability P m 1 max Maximum variation rate P m 2 max Maximum number of iterations α max And the range of constraints on the number of array elements in each subarray;

[0040] Specifically, in the first embodiment, M = 64 array elements are divided into L = 8 subarrays, with initial crossover probability and crossover point number P. c 1(0) = 0.9, P c 2(0) = L-2, the minimum crossover probability and the number of crossover points P in the later stages of evolution. c 1 min =0.6, P c 2 min =1, initial mutation probability and mutation rate P m 1(0) = 0.1, P m 2(0) = 0.15, the maximum mutation rate and mutation point rate P in the later stage of evolution. m 1 max =0.3, Pm 2 max =0.35, iteration number α max =200, and the number of array elements in the subarray is constrained to [4,12].

[0041] Step 2: Randomly generate an initial population. Each individual in the population is considered as a chromosome. Set a variable α to indicate the number of iterations of the genetic algorithm, and let α = 1.

[0042] Step 3: Decode each chromosome in the current population to obtain the subarray partitioning scheme corresponding to the chromosome, and then calculate the fitness value of the subarray partitioning scheme, which is recorded as the fitness value of the chromosome.

[0043] Step 4: Perform selection, crossover, and mutation operations on the chromosomes in the current population; then determine whether each chromosome in the latest population meets the constraints. If it does, proceed to step 5; otherwise, correct the chromosomes and proceed to step 5.

[0044] Step 5: Update the crossover and mutation related parameters;

[0045] Step 6, determine α = α max Does this hold true if α = α? max If the condition is met, then according to step 3, calculate the fitness value of each subarray partitioning scheme in the latest population, select the subarray partitioning scheme with the largest fitness value in the latest population as the final subarray partitioning scheme, and complete the non-uniform subarray partitioning based on the dynamic genetic algorithm; if α = α max If this is not true, then let α = α + 1, and continue with step 3.

[0046] Specifically, the maximum fitness value in the population obtained in each iteration is recorded, and the maximum fitness values ​​of all iterations are used to form the output iteration curve.

[0047] Furthermore, the specific method for randomly generating the initial population in step 2 is as follows:

[0048] Based on the requirements of the number of array elements, the number of subarrays, and the constraints on the number of array elements, calculate all the splitting schemes that meet the requirements;

[0049] Randomly select 40% of the partitioning schemes. For each selected partitioning scheme: use n-bit binary encoding to represent the subarray number corresponding to one array element, 2 n-1 <L≤2 n Sort M n-bit binary codes in ascending order to form an individual in the initial population; in each individual, the same n-bit binary code indicates that they belong to the same subarray, and the number of the same n-bit binary code indicates the number of array elements contained in the subarray corresponding to that n-bit binary code.

[0050] Furthermore, the specific method for step 3 is as follows:

[0051] For each chromosome, its M n-bit binary codes are converted into M decimal codes to obtain a subarray partitioning scheme. The adaptive beamforming pattern under this subarray partitioning scheme is then obtained according to the following formula:

[0052]

[0053] Where G(θ) is the adaptive beamforming diagram under this subarray partitioning scheme, θ is the signal incident angle, and w sub The weighted vector of each subarray is calculated according to the Minimum Variance Distortionless Response (MVDR) algorithm. T is the subarray forming matrix corresponding to the subarray partitioning scheme. α(θ) is the steering vector of the desired signal. The superscript H indicates the conjugate transpose. |·| indicates the modulus value. max indicates the maximum value.

[0054] Specifically, Figure 4 This is a diagram of the subarray weighted adaptive beamforming model in an embodiment of the present invention, where d represents the element spacing and θ represents the subarray weighted adaptive beamforming model. i Let w1, w2, w3, ... w be the incident angles of each signal. M The amplitude weights are calculated for M array elements, g1, g2, ..., g L The digital weighting of the L subarrays is given by y(t), which is the array output signal after beamforming.

[0055] Determine the main lobe peak in the adaptive beamforming pattern, then search for the first null point on the left and right sides of the main lobe peak. Search for the maximum level outside the first null point on the left and right sides, which is the highest sidelobe level of the entire pattern. Record the absolute value of the maximum level as the fitness value corresponding to the subarray partitioning scheme, which is the fitness value of the chromosome.

[0056] Furthermore, step 4 is specifically implemented as follows:

[0057] Step 401: Normalize the fitness values ​​of all chromosomes in the current population, and use the roulette wheel method to repeatedly select one chromosome from the current population as the chromosome for the next generation population until the number of chromosomes in the next generation population is the same as the number of chromosomes in the initial population.

[0058] Specifically, the fitness value of each individual is first calculated, then normalized, and finally, a roulette wheel-like process is simulated, starting from 0 and sequentially accumulating the normalized fitness value until the accumulated value exceeds a random number (usually between 0 and 1). When the accumulated value exceeds the random number, the current individual is selected as the chosen individual. This process is repeated until a sufficient number of individuals are selected to form the next generation population.

[0059] Step 402: Divide the chromosomes in the latest population into groups of two. For each group of chromosomes, generate a crossover random number between 0 and 1. If the generated crossover random number is less than the crossover probability P... c If 1(α), then a crossover operation is performed on this set of chromosomes. Specifically, the n-bit binary codes at corresponding positions of the two chromosomes are matched sequentially. One or more consecutive n-bit binary codes that do not match are recorded as a crossover position. If the number of crossover positions is greater than P, then... c 2(α), then P is randomly selected from all positions to be crossed. c Perform a crossover operation on 2(α) crossover positions. If the number of crossover positions is less than or equal to P... c If 2(α), then this set of chromosomes will not undergo crossover; if the generated random crossover number is not less than the crossover probability P c If 1(α), then this set of chromosomes will not undergo crossover; where P c 1(α) is the crossover probability at the α-th iteration, P c 2(α) represents the number of intersections in the α-th iteration, P c 1(α)∈[0,1];

[0060] Specifically, in the initial stage of a genetic algorithm, the differences between individuals are significant. At this stage, choosing a higher crossover probability and a larger number of crossover points to perform more crossover operations helps promote population diversity, thereby accelerating the search for the optimal solution. However, in the middle and later stages of the optimization iteration process, continuing to use a high crossover probability and a large number of crossover points may cause the algorithm to diverge. Therefore, to prevent this, we need to gradually reduce the crossover probability and the number of crossover points, prompting the algorithm to focus more on a refined search within the current search space, rather than blindly continuing to search for solutions in a larger space. This approach can effectively improve the quality of optimization results while maintaining the algorithm's convergence speed.

[0061] Step 403: For each chromosome, generate a random mutation number between 0 and 1. If the generated random mutation number is less than the mutation probability P... m If 1(α), then for each n-bit binary code in the chromosome, a random mutation number between 0 and 1 is generated. If the generated random mutation number is less than the mutation rate P, m2(α), then all the current n-bit binary codes are inverted bit by bit. If the generated random number of mutation points is not less than the mutation rate P m If 2(α), then the current n-bit binary code will not be mutated; if the generated mutated random number is not less than the mutation probability P m If 1(α), then the chromosome will not undergo mutation; P m 1(α) is the mutation probability at the α-th iteration, P m 2(α) represents the mutation rate at the α-th iteration, P m 1(α), P m 2(α)∈[0,1];

[0062] Specifically, in the initial stage of a genetic algorithm, the differences between individuals are significant. At this stage, choosing a lower mutation probability and fewer mutation points helps individuals evolve into better ones, because a lower mutation probability and fewer mutation points mean that the chromosomes change less between generations, thus accelerating convergence to the optimal solution. However, in the middle and later stages of evolution, it is necessary to choose a higher mutation probability and more mutation points. This is because a higher mutation probability and more mutation points can increase chromosome diversity, helping to escape local optima and explore a wider solution space.

[0063] Step 404: For each chromosome in the latest population, determine whether there is a subarray number that does not meet the subarray number requirement or the subarray number constraint range. If so, replace the chromosome corresponding to the chromosome before the crossover or mutation and then execute step 5. If not, sort the M n-bit binary codes in the chromosome in ascending order and then execute step 5.

[0064] Furthermore, step 5 is specifically implemented as follows:

[0065]

[0066] Among them, P c 2(0) = L-2, QZ(·) indicates rounding; P c 1(0)>P c 1 min P c 2(0)>P c 2 min P m 1(0)<P m 1 max P m 2(0)<P m 2 max And P c 1(0), P c 2(0), P c 1min P c 2 min P m 1(0), P m 2(0), P m 1 max P m 2 max ∈[0,1].

[0067] The following is the second embodiment:

[0068] In the second embodiment, there are 16 array elements, divided into 4 subarrays. Figure 2 As one of the splitting schemes, Figure 3 for Figure 2 A diagram illustrating the encoding of the splitting scheme. Figure 5 A diagram illustrating the crossing of two chromosomes;

[0069] In summary, this invention, based on a dynamic genetic algorithm, employs dynamic multi-point crossover and multi-point mutation strategies to enhance individual diversity and expand the search range. It utilizes dynamic crossover and mutation probabilities to accelerate convergence and selects the absolute value of the highest sidelobe level as the fitness function for optimization, thereby achieving non-uniform subarray partitioning of the array. This invention also effectively reduces the hardware cost and computational complexity of UAV airspace anti-jamming systems, while achieving a lower highest sidelobe level than adaptive beamforming with all array elements.

[0070] Those skilled in the art will recognize that the described embodiments are intended to help readers understand the principles of the invention and should be understood as not limiting the scope of protection of the invention to the described embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A non-uniform subarray partitioning method based on a dynamic genetic algorithm, characterized in that, Includes the following steps; Step 1: Initialize the parameters of the dynamic genetic algorithm, including the number of array elements M, the number of subarrays L, and the initial crossover probability. Initial number of intersections Minimum crossover probability Minimum number of intersections Initial mutation probability Initial mutation rate Maximum mutation probability Maximum mutation rate Maximum number of iterations And the range of constraints on the number of array elements in each subarray; Step 2, randomly generate the initial population: Based on the requirements of the number of array elements, the number of subarrays, and the constraints on the number of array elements, calculate all the splitting schemes that meet the requirements; Randomly select some partitioning schemes. For each selected partitioning scheme, use n-bit binary encoding to represent the subarray number corresponding to one array element. Sort M n-bit binary codes in ascending order to form an individual in the initial population; in each individual, the same n-bit binary code indicates that they belong to the same subarray, and the number of the same n-bit binary code indicates the number of array elements contained in the subarray corresponding to that n-bit binary code. Each individual in the population is considered as a chromosome, and a variable is set to indicate the number of iterations of the genetic algorithm. ,make =1; Step 3: Decode each chromosome in the current population to obtain the subarray partitioning scheme corresponding to that chromosome, then calculate the fitness value of that subarray partitioning scheme and record it as the fitness value of that chromosome; specifically: For each chromosome, its M n-bit binary codes are converted into M decimal codes to obtain a subarray partitioning scheme. The adaptive beamforming pattern under this subarray partitioning scheme is then obtained according to the following formula: ； in, This is an adaptive beamforming diagram under this subarray partitioning scheme. The angle of signal incidence. Let T be the weighted vector of each subarray calculated using the MVDR method, and let T be the subarray forming matrix corresponding to this subarray partitioning scheme. Let H be the steering vector of the desired signal, and let H denote the conjugate transpose. Indicates the modulo value; Determine the main lobe peak in the adaptive beamforming diagram, then search for the first null point on the left and right sides of the main lobe peak. Search for the maximum level outside the first null point on the left and right sides, and record the absolute value of the maximum level as the fitness value corresponding to the subarray partitioning scheme, which is the fitness value of the chromosome. Step 4: Perform selection, crossover, and mutation operations on the chromosomes in the current population; then determine whether each chromosome in the latest population meets the constraints. If it does, proceed to step 5; otherwise, correct the chromosomes and proceed to step 5. Step 5: Update the crossover and mutation-related parameters; Step 6, Determine = Whether it is true or not, if = If the condition is met, then according to step 3, calculate the fitness value of each subarray partitioning scheme in the latest population, select the subarray partitioning scheme with the largest fitness value in the latest population as the final subarray partitioning scheme, and complete the non-uniform subarray partitioning based on the dynamic genetic algorithm; if = If it is not valid, then let = +1, and continue with step 3.

2. The non-uniform subarray partitioning method based on dynamic genetic algorithm according to claim 1, characterized in that, The specific method for step 4 is as follows: Step 401: Normalize the fitness values ​​of all chromosomes in the current population, and use the roulette wheel method to repeatedly select one chromosome from the current population as the chromosome for the next generation population until the number of chromosomes in the next generation population is the same as the number of chromosomes in the initial population. Step 402: Divide the chromosomes in the latest population into groups of two. For each group of chromosomes, generate a crossover random number between 0 and 1. If the generated crossover random number is less than the crossover probability... Then, a crossover operation is performed on the set of chromosomes. Specifically, the n-bit binary codes at corresponding positions of the two chromosomes are matched sequentially. One or more consecutive n-bit binary codes that do not match are marked as a crossover position. If the number of crossover positions is greater than 1, the crossover operation is performed. Then, randomly select from all the positions to be crossed. Perform a crossover operation on each of the following crossover positions. If the number of crossover positions is less than or equal to... If the number of chromosomes generated is not less than the crossover probability, then no crossover operation will be performed on that group of chromosomes; If the chromosomes in this group do not undergo crossover, then no crossover operation will be performed. Let be the crossover probability at the α-th iteration. The number of intersections at the α-th iteration. ∈[0,1]; Step 403: For each chromosome, generate a random mutation number between 0 and 1. If the generated random mutation number is less than the mutation probability... Then, for each n-bit binary code in the chromosome, a random mutation number between 0 and 1 is generated. If the generated random mutation number is less than the mutation rate... If the current n-bit binary code is inverted bit by bit, and the generated random mutation point number is not less than the mutation point rate... If the current n-bit binary code is not mutated, then no mutation will be performed; if the generated mutated random number is not less than the mutation probability... If the chromosome does not mutate, then the chromosome will not undergo mutation. Let be the mutation probability at the α-th iteration. Let be the mutation rate at the α-th iteration. , ∈[0,1]; Step 404: For each chromosome in the latest population, determine whether there is a subarray number that does not meet the requirement of the number of subarrays or the requirement of the number of array elements. If so, replace the chromosome corresponding to the chromosome before the crossover or mutation, and then proceed to step 5. If not, sort the M n-bit binary codes in the chromosome in ascending order and then proceed to step 5.

3. The non-uniform subarray partitioning method based on dynamic genetic algorithm according to claim 2, characterized in that, The specific method for step 5 is as follows: ； ； ； ； in, -2, This indicates rounding.

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