Subarray Distributed Array Optimization Method Based on Improved Genetic Algorithm

Abstract

This invention proposes a subarray distributed array design method based on an improved genetic algorithm. The steps are as follows: establishing a mathematical model of the peak sidelobe level of the subarray distributed array; establishing an optimization model with the peak sidelobe level PSLL and the number of subarrays N as optimization objectives; improving the genetic algorithm; and solving the optimization model using the improved genetic algorithm to obtain the design result of the subarray distributed array. This invention effectively improves the optimization efficiency of the subarray distributed array, reduces the number of subarrays in the subarray distributed array while reducing the peak sidelobe level, and lowers the cost of digital channels.

Description

Technical Field

[0001] This invention belongs to the field of array antenna signal processing technology, and relates to a subarray distributed array optimization method, specifically a subarray distributed array optimization method based on an improved genetic algorithm, which can be applied to target detection in radar systems. Background Technology

[0002] The subarray distributed array is composed of multiple subarrays with unequal spacing. The radar signal is simulated by the subarrays and then connected to a digital receiver for digital beamforming, which can reduce the number of digital channels and reduce costs. The unequal spacing of the array elements breaks the periodicity of the array energy, thereby eliminating grating lobes. In addition, the subarray distributed array can increase the array aperture to improve the main lobe resolution and reduce the peak sidelobe level without weighting.

[0003] With the continuous advancement of modern radar systems, they are required to achieve higher angle measurement accuracy, stronger anti-jamming capabilities, and lower costs. Modern radar systems place higher demands on subarray distributed arrays, such as higher gain, narrower beamwidth, lower cost, and lower peak sidelobe levels. Increasing array gain necessitates increasing the number of array elements; achieving a narrower beamwidth requires increasing the array aperture, which in turn means increasing the number of array elements. Increasing the number of array elements means increasing the number of digital channels required by the radar system. In array radar systems based on digital beamforming, the design of digital channels is extremely complex and expensive. Furthermore, subarray distributed arrays also suffer from the drawback of excessively high peak sidelobe levels.

[0004] To eliminate the above-mentioned defects, it is necessary to optimize the subarray distributed array. While the array has high gain and narrow beam, the number of its subarrays should be optimized to reduce the cost of digital channels. On the other hand, it is necessary to optimize the peak sidelobe level while reducing the number of subarrays to improve the anti-interference capability of the radar system.

[0005] To reduce the digital channel cost and peak sidelobe level of subarray distributed arrays, existing optimization methods are generally based on optimization algorithms such as genetic algorithms. However, when applying genetic algorithms to subarray distributed array design, problems such as premature convergence, getting trapped in local optima, and poor convergence inevitably arise due to the large computational load and difficulty in finding the optimal solution. Researchers have improved genetic algorithms when optimizing subarray distributed arrays. For example, the patent application CN114371447A, published in 2022 and entitled "Sidelobe Suppression Method for Subarray-Level Distributed Frequency Control Array Based on Improved Genetic Algorithm", discloses an optimized array layout method for subarray distributed arrays based on an improved genetic algorithm to suppress peak sidelobe level. This method first improves the genetic algorithm to a niche genetic algorithm based on a pre-selection mechanism. Then, the improved genetic algorithm is used to suppress the grating lobes and sidelobes of the subarray-level distributed frequency control array to obtain the optimized array layout result of the subarray distributed array. The advantage of this method is that by incorporating a competition mechanism between parents and offspring into the genetic algorithm, it makes the algorithm more likely to escape local optima, and it better suppresses the sidelobes of the subarray distributed array compared to traditional genetic algorithms. However, its shortcomings are: the improved genetic algorithm, by adopting a competition mechanism between parents and offspring, increases the complexity of the genetic algorithm, resulting in a slower convergence speed; and the lack of optimization of the number of subarrays during the subarray distributed array optimization process leads to higher digital channel costs. Summary of the Invention

[0006] The purpose of this invention is to overcome the defects of the prior art and propose a subarray distributed array optimization method based on an improved genetic algorithm to solve the technical problems of high peak sidelobe level and high digital channel cost in the prior art.

[0007] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0008] (1) Establish a mathematical model for the peak sidelobe level of the subarray distributed array:

[0009] Establish a mathematical model for the peak sidelobe level (PSLL) of a subarray distributed array consisting of K array elements, including N sparsely arranged subarrays, and each subarray includes M array elements uniformly arranged, where N≥1, M≥1, and K=M·N;

[0010] (2) Establish an optimization model:

[0011] The optimization objectives are the peak sidelobe level (PSLL) of the pattern of the subarray distributed array and the number of subarrays (N), with the spacing d between elements within the subarray and the minimum spacing D between subarrays as the optimization targets. min The optimization model with constraints on the aperture L of the distributed array and subarrays:

[0012]

[0013] Where W1 and W2 are the optimized weights for the peak sidelobe level PSLL and the number of subarrays N, respectively, and Y = [y1, y2, ..., y n ,…,y N ] represents the position vector of the submatrix, y n Let n be the position of the nth subarray, where 1 ≤ n ≤ N;

[0014] (3) Improve the genetic algorithm:

[0015] By using y n -y n-1 ≥D min The initial population randomly generated in the genetic algorithm is replaced by an initial population randomly generated for the constraints, and the remaining individuals except those with the largest fitness value are selected for a roulette wheel test, thus improving the genetic algorithm.

[0016] (4) Solving the optimization model based on an improved genetic algorithm:

[0017] (4a) Initialize the improved genetic algorithm with iteration number t, maximum iteration number T, T≥200, individual is the position vector Y of the subarray, population G includes X individuals, and the current population is G. t X≥2, and let t=1;

[0018] (4b) via y n -y n-1 ≥D min The minimum spacing D between pairs of subarrays min Apply constraints and randomly generate an initial population G1 = [Y1, Y2, ..., Y] containing X individuals that meets the constraints. x ,...,Y X ], where Y x For the x-th individual, 2 ≤ x ≤ X;

[0019] (4c) Calculate the population G t Each individual Y x fitness value F(Y) x ), and select the individual with the highest fitness value among the X individuals into population G. t Then, the remaining individuals are selected into population G using a roulette wheel selection method based on their fitness. t The population after the selection operation is obtained;

[0020] (4d) Encode each individual in the population after the selection operation into binary form, and then perform a crossover operation and a mutation operation on all individuals in the binary-encoded population to obtain the population G after the t-th mutation. t ”;

[0021] (4e) Determine whether t≥T holds true. If so, obtain the optimized population G. * And execute step (5); otherwise, let t = t + 1, G t =G t ", and proceed to step (4c);

[0022] (5) Obtain the optimization results of the subarray distributed array:

[0023] For population G * Decode the individual with the highest fitness value to obtain the optimal number of subarrays N. best and position Y best And according to N best and Y best Calculate the number of array elements within the subarray. The number of subarrays obtained is N best The subarray position is Y best The number of array elements in the subarray is M best The optimized subarray distributed array.

[0024] Compared with the prior art, the present invention has the following advantages:

[0025] (1) In the process of solving the optimization model by using an improved genetic algorithm, the initial population randomly generated by the genetic algorithm is replaced by an initial population randomly generated by the genetic algorithm through preset constraints, so that all the generated individuals are feasible solutions. Furthermore, the individuals with the largest fitness values ​​are selected for roulette wheel selection, which avoids the defect that the population stops evolving in the later stages of the iteration due to the small difference in fitness values ​​of the individuals. This accelerates the convergence speed and effectively improves the optimization efficiency of the subarray distributed array compared with the prior art.

[0026] (2) The present invention establishes an optimization model with the peak sidelobe level of the radiation pattern of the subarray distributed array and the number of subarrays as optimization objectives. By solving this optimization model, the number of subarrays in the subarray distributed array can be effectively reduced while reducing the peak sidelobe level. Compared with the prior art, this reduces the cost of digital channels. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating the implementation of the present invention.

[0028] Figure 2 This is a schematic diagram of the subarray positions in the optimized subarray distributed array of the present invention.

[0029] Figure 3 This is a comparison chart of the fitness value iteration curves of the present invention and the prior art.

[0030] Figure 4 This is the distribution pattern of the subarray of the present invention and the prior art. Detailed Implementation

[0031] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0032] Reference Figure 1 The present invention includes the following steps:

[0033] Step 1) Establish a mathematical model for the peak sidelobe level of the subarray distributed array:

[0034] To calculate the peak sidelobe level (PSLL) of a subarray distributed array with different element structures, a mathematical model for the PSLL of a subarray distributed array is established, consisting of N sparsely arranged subarrays with K elements, and each subarray includes M uniformly arranged elements, where N≥1, M≥1, and K=M·N. The expression for its patterned peak sidelobe level (PSLL) is:

[0035] PSLL = maxF(θ)

[0036] F(θ)=S1(θ,θ0)S2(θ,θ0)

[0037]

[0038]

[0039] Where F(θ) = S1(θ,θ0)S2(θ,θ0) is the pattern function of the distributed array of subarrays, and S1(θ,θ0)S2(θ,θ0) is the pattern function of the distributed array of subarrays.

[0040] , respectively, are the array factors of the distributed array and the subarray. Let λ be the wave number, θ0 be the wavelength and angle of the incident signal, respectively, and d be the spacing between the elements in the subarray. Y = [y1, y2, ..., y n ,...,y N ] represents the position vector of the submatrix, y n Let be the position of the nth subarray, where 1 ≤ n ≤ N. In this embodiment, d = 2.6 mm, the incident signal wavelength λ = 6.18 mm, and the incident signal angle θ0 = 0°.

[0041] Step 2) Establish an optimization model:

[0042] To effectively reduce the number of subarrays in a distributed subarray array while lowering the peak sidelobe level (PSLL), an optimization objective is established using the PSLL and the number of subarrays (N) as the optimization targets, along with the spacing d between elements within a subarray and the minimum spacing D between subarrays. min The optimization model with constraints on the aperture L of the distributed array and subarrays:

[0043]

[0044] Wherein, W1 and W2 are the optimization weights for the peak sidelobe level (PSLL) and the number of subarrays (N), respectively. In this embodiment, the aperture of the constrained distributed subarray is L = 500 mm, and the optimization weights are W1 = W2 = 0.5.

[0045] Step 3) Improve the genetic algorithm:

[0046] By using y n -y n-1 ≥D min The initial population generated randomly under the constraints is replaced by the initial population generated randomly in the genetic algorithm. This ensures that all individuals in the generated initial population are feasible solutions. Furthermore, the individuals with the highest fitness values ​​are selected for a roulette wheel test. This avoids the defect that the population stops evolving in the later stages of the iteration due to the small difference in fitness values ​​between individuals, thereby accelerating the convergence speed and improving the genetic algorithm.

[0047] Step 4) Solve the optimization model based on the improved genetic algorithm:

[0048] (4a) Initialize the improved genetic algorithm with iteration number t, maximum iteration number T, T≥200, individual is the position vector Y of the subarray, population G includes X individuals, and the current population is G. t X≥2, and let t=1. In this embodiment, the maximum number of iterations T=200, and the number of individuals in the population X=500.

[0049] (4b) via y n -y n-1 ≥D min The minimum spacing D between pairs of subarrays min Apply constraints and randomly generate an initial population G1 = [Y1, Y2, ..., Y] containing X individuals that meets the constraints. x ,...,Y X ], where Y x Let x be the x-th individual, and 2 ≤ x ≤ X.

[0050] (4c) Calculate the population G t Each individual Y x fitness value F(Y) x ), and select the individual with the highest fitness value among the X individuals into population G. t Then, the remaining individuals are selected into population G using a roulette wheel selection method based on their fitness. t The population after the selection operation is obtained. F(Y) x The formula for calculating ) is:

[0051]

[0052] in, Individual Y x The corresponding peak sidelobe level and number of subarrays in the distributed array.

[0053] The process of implementing roulette is as follows: calculate the value of each individual Y. x The ratio of the fitness value to the total fitness value S(Y) x ), S(Y x That is, individual Y. x The probability of being selected is determined by dividing each individual into several segments distributed in an interval of [0, 1]. The length of each individual segment is the probability of being selected. Then, a number is randomly generated in the interval of [0, 1]. If the number falls on a certain segment, the individual corresponding to that segment is selected.

[0054] S(Y x The formula for calculating ) is:

[0055]

[0056] (4d) Encode each individual in the population after the selection operation into binary form, and then perform a crossover operation and a mutation operation on all individuals in the binary-encoded population to obtain the population G after the t-th mutation. t The specific steps for implementing crossover and mutation operations are as follows:

[0057] (4d1) Randomly select population G t Two individuals are selected, and then a natural number no greater than the length of the selected individual is randomly generated as the starting position for crossover, according to the crossover probability P. c By swapping the binary codes of two individuals at the end of the crossover starting position, we obtain the resulting population G. t ', where P c This represents the crossover probability. In this embodiment, the crossover probability P... c =2%.

[0058] (4d2) For the population G after crossover t The binary codes of each individual are traversed, and a random number u in the range of 0 to 1 is generated. If u < P m Then, by changing "0" to "1" or "1" to "0" in the binary code, we obtain the population G after the t-th mutation. t ", where P m This represents the mutation probability. In this embodiment, the mutation probability P is... m =0.1%.

[0059] (4e) Determine whether t≥T holds true. If so, obtain the optimized population G. * And execute step (5); otherwise, let t = t + 1, G t =G t Then proceed to step (4c).

[0060] Step 5) Obtain the design results of the subarray distributed array:

[0061] For population G * Decode the individual with the highest fitness value to obtain the optimal number of subarrays N. best and position Y best And according to N best and Y best Calculate the number of array elements within the subarray. The number of subarrays obtained is N best The subarray position is Y best The number of array elements in the subarray is M best The optimized subarray distributed array. The number of subarrays is 7, and the element positions of the subarrays are referenced... Figure 2 Taking the first subarray on the left as the reference subarray, the spacing of the other 6 subarrays relative to the reference subarray is 72.1mm, 143.1mm, 215.6mm, 287.2mm, 357.9mm, and 429.8mm, and the number of array elements in the subarray is 27.

[0062] The technical effects of this invention will be further explained below with reference to simulation experiments:

[0063] 1. Simulation conditions and content:

[0064] Hardware environment: Intel(R) Xeon(R) CPU E3-1231 v3, clock speed 3.40GHz, 32.0GB memory, 64-bit operating system. Software environment: Microsoft Windows 10 Professional Edition, MATLAB 2019 simulation software.

[0065] Simulation 1: The optimization efficiency of this invention and the existing patent for a subarray-level distributed frequency-controlled array sidelobe suppression method based on an improved genetic algorithm is simulated, and the results are as follows: Figure 3 As shown.

[0066] Simulation 2: The peak sidelobe levels of this invention and existing patents for subarray-level distributed frequency-controlled array sidelobe suppression methods based on improved genetic algorithms are simulated, and the results are as follows: Figure 4 As shown.

[0067] 2. Simulation Result Analysis:

[0068] refer to Figure 3The fitness iteration curve of the existing patent reaches its maximum value at generation 124, while the fitness iteration curve of the present invention reaches its maximum value at generation 67. The results show that the convergence speed of the present invention is faster and effectively improves the optimization efficiency of the subarray distributed array.

[0069] refer to Figure 4 (a), Figure 4 (a) shows the radiation pattern of the subarray distributed array of the present invention. It can be seen that the normalized gain of the second highest peak in the radiation pattern of the present invention, excluding the highest peak, is -16.1 dB; Reference Figure 4 (b), Figure 4 (b) shows the direction of the subarray distributed array in the prior art. It can be seen that the normalized gain of the second highest peak (excluding the highest peak) in the prior art pattern is -15.8dB. The results show that the peak sidelobe level of the subarray distributed array optimized by the present invention is 16.1dB, while the peak sidelobe level of the prior art is -15.8dB. Furthermore, the present invention has 7 subarrays, while the prior art has 189 subarrays. This indicates that the present invention effectively reduces the number of subarrays in the subarray distributed array while reducing the peak sidelobe level, thereby reducing the cost of the digital channel compared to the prior art.

Claims

1. A method for optimizing a subarray distributed array based on an improved genetic algorithm, characterized in that, Comprise the following steps: (1) Establishing a subarray distributed array peak sidelobe level mathematical model: A subarray distributed array peak sidelobe level PSLL mathematical model is established, which comprises N subarrays arranged sparsely and each subarray comprises M array elements arranged uniformly, wherein N≥1, M≥1, and K=M*N; (2) Establishing an optimization model: An optimization model is established, in which the peak side lobe level (PSLL) of the directional diagram of the subarray distributed array and the number of subarrays (N) are optimization objectives, the interval (d) of the array elements in the subarray, the minimum interval (D) between the subarrays, and the aperture (L) of the subarray distributed array are constraint conditions min An optimization model is established, in which the peak side lobe level (PSLL) of the directional diagram of the subarray distributed array and the number of subarrays (N) are optimization objectives, the interval (d) of the array elements in the subarray, the minimum interval (D) between the subarrays Wherein, W1 and W2 are optimization weights of peak sidelobe level PSLL and subarray number N respectively, Y = [y1, y2, …, yN] is a position vector of subarray, yn is the position of the nth subarray, 1≤n≤N. n ,...,y N ] for the position vector of the subarray, y n n is the position of the nth subarray, 1≤n≤N. (3) Improving the genetic algorithm: By taking y n -y n-1 ≥D min The initial population randomly generated is replaced by the initial population randomly generated as a constraint condition, and the roulette operation is performed on the rest of the individuals except the individual with the maximum fitness value, so as to improve the genetic algorithm. (4) Solving the optimization model based on the improved genetic algorithm: (4a) initialize the iteration number of the improved genetic algorithm as t, the maximum iteration number as T, T≥200, the individual as the position vector Y of the subarray, the population G including X individuals, the current population as G t , X≥2, and let t=1; (4b) via y n -y n-1 ≥D min The minimum spacing D between pairs of subarrays min Apply constraints and randomly generate an initial population G1 = [Y1, Y2, ..., Y] containing X individuals that meets the constraints. x ,...,Y X ], where Y x For the x-th individual, 2 ≤ x ≤ X; (4c) Calculate the fitness value F(Y t of each individual Y x in the population G x , and select the individual with the highest fitness value from the X individuals into the population G t , and select the remaining individuals into the population G t according to the size of the fitness value using the roulette wheel method, to obtain the population after the selection operation. (4d) binary-encoding each individual in the population after the selection operation, and performing a mutation operation on all individuals in the binary-encoded population after a crossover operation to obtain the population G after the tthmutation t "; (4e) determine if t > T is true, if yes, get the optimized population G * and perform step (5); otherwise, let t = t + 1, G t = G t and perform step (4c); (5) Obtaining the optimization result of the subarray distributed array: The population G * The individual with the maximum fitness value in the population G is decoded to obtain the optimal subarray number N best And the position Y best According to N best And Y best , the number of array elements in the subarray is calculated The optimal subarray distribution array with the subarray number N best , the subarray position Y best , and the number of array elements M best in the subarray is obtained.

2. The method of claim 1, wherein, In the step (2), the expression of the peak sidelobe F(θ) of the directivity pattern of the subarray distributed array mathematical model is: PSLL = max F(θ) F(θ) = S1(θ, θ0) S2(θ, θ0) Wherein, F(θ) is the subarray distributed array directivity function, S1(θ, θ0), S2(θ, θ0) are the array factors of the subarray distributed array and the subarray respectively, is the wave number, λ, θ0 are the wavelength and angle of the incident signal respectively.

3. The method of claim 1, wherein, The population G is calculated in step (4b) t The fitness value F(Y x ) of each individual Y x is calculated as follows: wherein, respectively, for individual Y x Corresponding subarray distribution peak sidelobe level, subarray quantity.

4. The method of claim 1, wherein, The step (4d) is implemented by performing a mutation operation after performing a crossover operation on the individuals in the population G t The step (4d) is implemented by performing a mutation operation after performing a crossover operation on the individuals in the population G (4d1) randomly selecting two individuals from the population G t , then randomly generating a natural number not greater than the length of the individual as a crossover start position, and exchanging the binary codes of the two individuals from the next segment of the crossover start position according to a crossover probability P c to obtain the population G t after crossover, wherein P c represents the crossover probability; (4d2) the population G after crossover t traversing the binary code of each individual, while generating a random number u in the range of 0 to 1, if u < P m then changing "0" to "1" or "1" to "0" in the binary code, to obtain the population G after the tth mutation t , where P m represents the mutation probability.

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