Beam broadening constrained antenna array sparse method

Abstract

The invention provides a beam broadening constrained antenna array sparse method, and belongs to the field of array signal processing. Quantum coding is carried out on lion group individuals, evolution is carried out by simulating a quantum revolving door, the position of a lion is updated by designing a quantum revolving angle to evolve a quantum position, a new algorithm for solving a discrete optimization problem is designed, and the application limitation that an original lion group algorithm cannot solve a continuous optimization problem is broken through. According to the method, the optimal sparse array structure meeting the beam broadening and bestrewing rate constraint conditions is obtained in antenna position construction, compared with a traditional directional diagram synthesis method, the method has large antenna gain under the condition of the same half-power beam width, convergence speed and convergence precision are improved, and meanwhile, the convergence efficiency is improved. The constraint condition is met when the lower maximum relative sidelobe level is obtained, and finally, the effectiveness and superiority of the directional diagram comprehensive method for constructing the sparse array based on the quantum lion group mechanism are explained by the simulation result.

Description

Technical Field

[0001] The invention belongs to the field of array signal processing, and in particular relates to a constrained antenna array sparse method for beam broadening. Background Art

[0002] Sparse array is an important branch in the field of array antennas. Compared with uniform arrays, the spacing between array elements in sparse arrays can be freely changed within a certain range of constraints. Under the same array aperture, sparse arrays only need a smaller number of array elements to obtain the same radiation performance as uniform array antennas. In addition, the directional patterns of transmission and reception can be automatically adjusted according to the combination of multiple antennas through intelligent antenna technology, which can effectively improve the directional pattern performance of array antennas. At the same time, according to different application requirements, the optimization of parameter selection can be achieved, which not only simplifies the array's feed network, but also reduces the weight and manufacturing cost of the antenna system, playing an important role in radar, wireless communication, electronic countermeasures and other systems.

[0003] Through the search of existing technical literature, it is found that Ramonika Sengupta et al. published "Spare Linear Array Synthesis Using Exponential Analysys" at the 2023 IEEE Conference on Antenna Measurements and Applications (CAMA) and proposed a sparse non-uniform linear array synthesis method based on exponential analysis to optimize the antenna position of the sparse array. However, this method involves relatively complex mathematical analysis and calculation processes, including exponential analysis, Hankel matrix construction, and Cadzow iteration. These steps not only increase the difficulty of implementation, but may also introduce calculation errors and affect the accuracy of the results. Zeng Hao, Cai Wanhan, Ren Zhigang, et al. published "Sparse Array Constrained Optimization Based on Dynamic Search Strategy Discrete Particle Swarm Algorithm" in "Journal of Electronics" (2023, 51(04): 783-791.) and proposed an algorithm based on a comprehensive particle learning strategy of multiple fusions. The global and local search capabilities of the algorithm are well balanced, but the algorithm converges slowly and is prone to fall into local extremes.

[0004] The search results of existing literature show that the existing sparse antenna array pattern synthesis methods generally optimize the excitation amplitude or sparse position of the sparse array, and no quantum lion group mechanism has been designed to obtain the optimal sparse antenna array pattern for the beam broadening constraint problem. Summary of the invention

[0005] The object of the present invention is to provide a constrained antenna array sparse method for beam broadening.

[0006] The purpose of the present invention is achieved through the following technical solutions:

[0007] A constrained antenna array sparse method for beam broadening, the specific steps are as follows:

[0008] Step 1: Establish a sparse array antenna model and establish the constrained beamforming objective equation for beam expansion;

[0009] Step 2: Initialize the position of the quantum lion and set related parameters, and get the position of the mth lion in the tth generation

[0010] Step 3: Construct a fitness function based on steps 1 and 2, calculate the fitness value of each lion, and penalize it according to the constraints, and set the position with the best fitness value in the lion group as the lion king position;

[0011] Step 4: The lion king, hunting lions and cubs in the lion group update their quantum positions according to their own learning strategies. After obtaining the quantum position corresponding to each lion, the quantum position of the lion is measured and updated through the measurement formula to obtain the position of the mth lion.

[0012] Step 5: Calculate the updated fitness value of each lion position, set the position with the best fitness value as the lion king position, and update the lion king position;

[0013] Step 6: Determine whether the maximum number of iterations T has been reached. If not, set t=t+1 and return to step 4. If the maximum number of iterations T has been reached, terminate the loop iteration and obtain the global optimal position, that is, the optimal placement position of the sparse array antenna after optimization. Output the fitness value, that is, the maximum relative sidelobe level of the sparse array reaches the minimum value when the half-power beam width is limited.

[0014] Furthermore, the directional pattern of the array antenna in step 1 is a graph of the amplitude characteristic of the antenna system and the spatial scanning angle, and the directional pattern of the sparse antenna array is calculated as follows:

[0015] For a sparse array of N grids with equal spacing to be optimized, the mathematical expression for determining the excitation w is: in{·} T represents the matrix transpose operator, is the phase weight vector of the excitation, j is the imaginary unit, and the antenna marker vector of the grid is I = [I1, I2, ..., I N ] T , n=1,2,...,N,I n ∈{0,1} is the antenna flag corresponding to the nth grid. When its value is "1", it means that the antenna is placed at the nth grid position. When its value is "0", it means that the antenna is not placed at the nth grid position.

[0016] When the incident angle of a unit plane wave on the linear array is θ, the input operation vector a(θ) of the sparse linear array is composed of two parts: (1) ψ is generated by the change in the relative position between adjacent array elements, ψ = [ψ1, ψ2, ..., ψ N ]; l is an adjustable constant vector, representing the array element spacing vector, l = [l1, l2, ..., l N ] T , l n represents the distance between the n grid antenna placement points and the first grid antenna placement point, then ψ is represented by l, k = 2π / λ is the wave constant, λ represents the wavelength of the wave used when the array antenna is working; (2) a(θ) is generated by the change of the excited phase weight vector, and the expression of a(θ) is as follows: Therefore, the expression of the directional pattern function is Then the expression of the relative pattern function P(θ) is where F max =max{|F(θ)|}, lg{·} represents the logarithmic operation with base 10; the grid flag vector I is obtained according to the calculation formula of the directional diagram Among them, M SLL (·) is the function for calculating the maximum relative sidelobe level of the antenna array, max{|F(θ)|} is the main lobe peak of the pattern, and S represents the sidelobe area in the pattern.

[0017] Furthermore, in step 2, the number of lions is set to M, the maximum number of iterations is T, the number of sparse array antenna grids, i.e. the dimension of the search space, is D, and the proportion factor of the hunting lions is β; in the tth iteration, the quantum position of the mth lion in the search space is The value range of is between [0,1], which represents the d-dimensional quantum position of the m-th lion, m = 1, 2, ..., M, d = 1, 2, ..., D; the measurement method of the d-dimensional position of the m-th lion is in is a random number uniformly distributed between [0,1], then the position of the mth lion in the tth generation is Initially, t=1, and the initial quantum position is randomly initialized within the defined interval.

[0018] Furthermore, in step 3, the position of each lion is obtained by measuring the quantum position of each lion. At this time, there is a one-to-one correspondence between the antenna flag and the position of each quantum lion; the position of the mth quantum lion corresponds to a sparse array, and the mth lion position is calculated according to the maximum relative sidelobe level of the corresponding directional pattern. Bring in the fitness function based on the penalty mechanism, and calculate the position of the mth quantum lion in the population Evaluate the fitness function, m = 1, 2, ..., M, and design the fitness function as in For the sparse flag bit vector The maximum relative sidelobe level calculated when is the expected main lobe half-power width, Sparse flag bit vector The main lobe half-power width obtained by calculation is c Rat is the fill rate obtained by calculation, e Rat is the expected population rate, p is the penalty factor, and p<<1. If the constraint condition is not met, the penalty function is used to penalize the model function value. The fitness value is calculated for each lion position, and the fitness of each lion is obtained. The lion position with the best fitness in the lion group is selected as the optimal position of the lion group, that is, the lion king position. is the local optimal position of the mth lion when it iterates to the tth generation, where k∈[1,M], The global optimal position of the entire lion group when it iterates to the tth generation; the initial global optimal lion position is set as the lion king position, and its corresponding fitness value is stored.

[0019] Furthermore, the step 4 defines that the lion king with the label m=1 uses the simulated quantum rotating gate to update its d-th dimension quantum position as Where m = 1 represents the lion king number. and When , the Lion King's d-dimensional quantum rotation angle update equation is In other cases, the update equation of the lion's d-dimensional quantum rotation angle is is a random number uniformly distributed between [0,1]. is a constant, e1 and e2 are constants that determine the influence of the local optimal position and the global optimal position on the quantum rotation angle, respectively. represents the dth dimension of the local optimal position of the hunting lion labeled k in the tth generation, abs(·) represents the absolute value of each position element in the vector, and sgn(·) is the sign function with the value {-1, 0, 1};

[0020] Define the disturbance factor of the hunting lion's movement range as in It represents the maximum step length of a hunting lion moving within its activity range. and are respectively represented as the maximum and minimum values ​​of each dimension in the activity range space of the t-th generation lion; when and When , the quantum rotation angle of the mth hunting lion in the dth dimension is In other cases, the quantum rotation angle of the mth hunting lion in the dth dimension is Where m∈[2,Mβ] represents the hunting lion number, is a random number uniformly distributed between [0,1]. is a random number generated according to a standard normal distribution, is a constant, where is the position of the i-th hunting lion in the t-th generation randomly selected, i∈[2,Mβ], β is the proportion factor of hunting lions, s d is the constant for adjusting the activity range of the hunting lion. Under this strategy, the quantum position of the mth hunting lion in the dth dimension is updated as

[0021] Define the disturbance factor of the lion cub's movement range as The mth lion cub chooses different learning strategies to update its d-dimensional quantum rotation angle according to probability, where m∈[Mβ+1,M]; when the strategy selection factor of the mth lion cub in the tth generation When , the quantum rotation angle of the mth lion cub in the dth dimension is when hour, b∈[2,Mβ]; when hour where s m is a random number uniformly distributed between [0,1]. is a random number generated according to the standard normal distribution; when and hour, is a random number uniformly distributed between [0,1]. is a constant, represents the dth dimension of the local optimal position of the hunting lion labeled b in the tth generation, is the reference position of the lion cub away from the hunting range of the lion group, c d is the constant for adjusting the activity range of the lion cub, and the quantum position of the mth lion cub in the dth dimension is updated to

[0022] After obtaining the quantum position corresponding to each lion, the measurement formula Measure the quantum position of the lion and update the position of the mth lion in is a random number uniformly distributed between [0,1].

[0023] Furthermore, the step 5 calculates the fitness function value of each lion after the update, and judges the pros and cons of the position of each lion in the lion group according to the fitness function value, and sets the position with the best fitness value as the lion king position. The position of the lion king of the t+1 generation is Where m = 1; for the mth lion in the t+1th generation lion group, according to its updated position m∈[2,M], evaluate the fitness function of each lion in the lion group, and update the historical optimal position of the mth lion up to the t+1th generation to And update the global optimal position of the lion group until the t+1th generation to

[0024] The beneficial effects of the present invention are:

[0025] (1) The present invention improves the contradiction between the convergence speed and convergence accuracy of the traditional antenna pattern synthesis method, and at the same time improves the convergence speed and convergence accuracy.

[0026] (2) Compared with the traditional antenna pattern synthesis method, the present invention aims at the actual engineering needs of the research direction of beam broadening antenna pattern synthesis. The present invention quantum encodes the lion group individuals and simulates the quantum rotating gate to evolve. By designing the quantum rotation angle evolution quantum position to update the lion position, a new algorithm for solving discrete optimization problems is designed, breaking through the application limitation of the original lion group algorithm that cannot solve continuous optimization problems. In the antenna position construction, the optimal sparse array structure that meets the beam broadening and filling rate constraints is obtained. Compared with the traditional pattern synthesis method, the present invention has a larger antenna gain under the same half-power beam width, better optimization effect, and wider applicability.

[0027] (3) In the sparse construction of the constrained antenna array with beam broadening based on the quantum lion group mechanism proposed in the present invention, while improving the convergence speed and convergence accuracy, a lower maximum relative sidelobe level is obtained and the constraint conditions are satisfied. The simulation results illustrate the effectiveness and superiority of the directional pattern synthesis method for constructing a sparse array based on the quantum lion group mechanism. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 : Block diagram of the sparse construction method of constrained antenna array based on beam broadening of quantum lion group mechanism of the present invention;

[0029] Figure 2 : The relationship between the number of iterations and fitness of the three methods when the number of grids is 300;

[0030] Figure 3 : Sparse array patterns of azimuth and amplitude of three methods when the number of grids is 300. DETAILED DESCRIPTION

[0031] The present invention is further described below in conjunction with the accompanying drawings.

[0032] The present invention discloses a sparse method for constrained antenna array with beam broadening. A sparse construction method for constrained antenna array with beam broadening based on quantum lion group mechanism is designed, which is denoted as QLSO; a sparse construction method for constrained antenna array with beam broadening based on particle swarm algorithm is denoted as PSO, and the parameter setting of particle swarm algorithm is specifically referred to "Application of particle swarm algorithm in array antenna pattern synthesis" published by Wang Weibo in "Journal of Xidian University". The sparse construction method for constrained antenna array with beam broadening based on lion group algorithm is denoted as LSO, and the parameter setting of lion group algorithm is specifically referred to "A swarm intelligence algorithm-lion group algorithm" published by Liu Shengjian in "Pattern Recognition and Artificial Intelligence". The QLSO parameter settings for this simulation experiment are as follows. Set the number of sparse array grids D=300, the maximum number of iterations T=1000, and the number of lions M=20. The hunting lion proportional factor β=0.5. p=0.01, β2=30,e Rat =0.8, e1=0.06,e2=0.02,s d =0.05, c d =0.03. The PSO experimental parameters are set as follows: maximum number of iterations T = 1000, number of particles ξ = 20, acceleration coefficients c1 = 2, c2 = 2, speed limit v max =4, speed lower limit v min = -4. The LSO parameters are set as follows: maximum number of iterations T = 1000, number of lions The hunting lion scale factor μ=0.5. The optimization results of the quantum lion group mechanism are compared with those of the traditional lion group algorithm and the particle swarm algorithm, and the maximum relative sidelobe levels of the directional patterns of the sparse array under different optimization algorithms are compared, which reflects the advantages of the method designed by the present invention over the traditional method.

[0033] The present invention provides a constrained antenna array sparse method for beam broadening, which mainly includes the following steps:

[0034] Step 1: Establish a sparse array antenna model and establish the constrained beamforming objective equation for beam expansion.

[0035] The directional pattern of an array antenna refers to the graph of the amplitude characteristics of the antenna system and the spatial scanning angle. Taking a linear array as an example, the calculation method of the directional pattern of a sparse antenna array is explained. For a sparse array with N grids of equal spacing to be optimized, the mathematical expression for determining the excitation w is: in{·} T represents the matrix transpose operator, is the phase weight vector of the excitation, j is the imaginary unit, and the antenna marker vector of the grid is I = [I1, I2, ..., I N ] T , n=1,2,...,N,I n∈{0,1} is the antenna flag corresponding to the nth grid. When its value is "1", it means that the antenna is placed at the nth grid position. When its value is "0", it means that the antenna is not placed at the nth grid position. is the phase weight vector, is the excitation phase of the nth grid antenna. Assume that when the incident angle of the unit plane wave to the linear array is θ, the input operation vector a(θ) of the sparse linear array is formed by combining two parts: (1) ψ is generated by the change in the relative position between adjacent array elements, ψ = [ψ1, ψ2, ..., ψ N ]. l is an adjustable constant vector, representing the array element spacing vector, l = [l1, l2, ..., l N ] T , l n represents the distance between the n grid antenna placement points and the first grid antenna placement point. Then ψ can be represented by l, k = 2π / λ is the wave constant, λ represents the wavelength of the wave used when the array antenna is working; (2) a(θ) is generated by the change of the excited phase weight vector, and the expression of a(θ) is as follows: Therefore, the expression of the directional pattern function is Then the expression of the relative pattern function P(θ) is where F max =max{|F(θ)|}, lg{·} represents the logarithmic operation with base 10; the grid flag vector I is obtained according to the calculation formula of the directional diagram Among them, M SLL (·) is the function for calculating the maximum relative sidelobe level of the antenna array, max{|F(θ)|} is the main lobe peak of the pattern, and S represents the sidelobe area in the pattern.

[0036] Step 2: Initialize the quantum lion position and set related parameters.

[0037] Assume the number of lions is M, the maximum number of iterations is T, the number of sparse array antenna grids (i.e. the dimension of the search space) is D, and the proportion factor of the hunting lions is β. In the tth iteration, the quantum position of the mth lion in the search space is The value range of is between [0,1], which represents the d-dimensional quantum position of the m-th lion, m = 1, 2, ..., M, d = 1, 2, ..., D. The measurement method of the d-dimensional position of the m-th lion is in is a random number uniformly distributed between [0,1], then the position of the mth lion in the tth generation is Initially, t=1, and the initial quantum position is randomly initialized within the defined interval.

[0038] Step three, construct a fitness function, calculate the fitness value of each lion, and penalize it according to the constraints, and set the position with the best fitness value in the lion group as the lion king position.

[0039] By measuring the quantum position of each lion, the position of each lion can be obtained. At this time, there is a one-to-one correspondence between the antenna flag and the position of each quantum lion. The position of the mth quantum lion corresponds to a sparse array. According to the maximum relative sidelobe level of the corresponding directional pattern, the position of the mth lion is calculated. Bring in the fitness function based on the penalty mechanism, and calculate the position of the mth quantum lion in the population Evaluate the fitness function, m = 1, 2, ..., M, and design the fitness function as in For the sparse flag bit vector The maximum relative sidelobe level calculated when is the expected main lobe half-power width, Sparse flag bit vector The main lobe half-power width obtained by calculation is c Rat is the fill rate obtained by calculation, e Rat is the expected population rate, p is the penalty factor, and p<<1. If the constraint condition is not met, the penalty function is used to penalize the model function value. The fitness value is calculated for each lion position, and the fitness of each lion is obtained. The lion position with the best fitness in the lion group is selected as the optimal position of the lion group, that is, the lion king position. is the local optimal position of the mth lion when it iterates to the tth generation, where k∈[1,M], The global optimal position of the entire lion group when it iterates to the tth generation. The initial global optimal lion position is set as the lion king position, and its corresponding fitness value is stored.

[0040] Step 4: The lion king, hunting lions and cubs in the lion group update their quantum positions according to their own learning strategies.

[0041] Define the lion king with label m=1 to use the simulated quantum rotating gate to update its d-th dimension quantum position as Where m = 1 represents the lion king number. and When , the Lion King's d-dimensional quantum rotation angle update equation is In other cases, the update equation of the lion's d-dimensional quantum rotation angle is is a random number uniformly distributed between [0,1]. is a constant, e1 and e2 are constants that determine the influence of the local optimal position and the global optimal position on the quantum rotation angle, respectively. represents the d-th dimension of the local optimal position of the hunting lion labeled k in the t-th generation, abs(·) represents the absolute value of each position element in the vector, and sgn(·) is the sign function with values ​​{-1, 0, 1}.

[0042] Define the disturbance factor of the hunting lion's movement range as in It represents the maximum step length of a hunting lion moving within its activity range. and are respectively represented as the maximum and minimum values ​​of each dimension in the activity range space of the t-th generation lion. and When , the quantum rotation angle of the mth hunting lion in the dth dimension is In other cases, the quantum rotation angle of the mth hunting lion in the dth dimension is Where m∈[2,Mβ] represents the hunting lion number, is a random number uniformly distributed between [0,1]. is a random number generated according to a standard normal distribution, is a constant, where is the position of the i-th hunting lion in the t-th generation randomly selected, i∈[2,Mβ], β is the proportion factor of hunting lions, s d is the constant for adjusting the activity range of the hunting lion. Under this strategy, the quantum position of the mth hunting lion in the dth dimension is updated as

[0043] Define the disturbance factor of the lion cub's movement range as The mth lion cub chooses different learning strategies to update its d-dimensional quantum rotation angle according to probability, where m∈[Mβ+1,M]. When , the quantum rotation angle of the mth lion cub in the dth dimension is when hour, b∈[2,Mβ]. hour where s m is a random number uniformly distributed between [0,1]. is a random number generated according to the standard normal distribution. and hour, is a random number uniformly distributed between [0,1]. is a constant, represents the dth dimension of the local optimal position of the hunting lion labeled b in the tth generation, is the reference position of the lion cub away from the hunting range of the lion group, c d is the constant for adjusting the activity range of the lion cub, and the quantum position of the mth lion cub in the dth dimension is updated to

[0044] After obtaining the quantum position corresponding to each lion, the measurement formula Measure the quantum position of the lion and update the position of the mth lion in is a random number uniformly distributed between [0,1].

[0045] Step 5: Calculate the fitness value of each lion after the position is updated, and update the position of the lion king.

[0046] Calculate the fitness function value of each lion after the update, judge the pros and cons of the position of each lion in the lion group according to the fitness function value, set the position with the best fitness value as the lion king position, and the position of the lion king of the t+1 generation is Where m = 1. For the mth lion in the t+1th generation lion group, according to its updated position m∈[2,M], evaluate the fitness function of each lion in the lion group, and update the historical optimal position of the mth lion up to the t+1th generation to And update the global optimal position of the lion group until the t+1th generation to

[0047] Step six, determine whether the maximum number of iterations T is reached. If not, set t=t+1 and return to step four. If the maximum number of iterations T is reached, terminate the loop iteration, obtain the global optimal position, that is, the optimal placement position of the sparse array antenna after optimization, and output the fitness value, that is, the maximum relative sidelobe level of the sparse array reaches the minimum value when the half-power beam width is limited.

[0048] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A constrained antenna array sparse method for beam broadening, characterized by: Step 1: Establish a sparse array antenna model and establish the constrained beamforming objective equation for beam expansion; Step 2: Initialize the position of the quantum lion and set related parameters, and get the position of the mth lion in the tth generation Step 3: Construct a fitness function based on steps 1 and 2, calculate the fitness value of each lion, and penalize it according to the constraints, and set the position with the best fitness value in the lion group as the lion king position; Step 4: The lion king, hunting lions and cubs in the lion group update their quantum positions according to their own learning strategies. After obtaining the quantum position corresponding to each lion, the quantum position of the lion is measured and updated through the measurement formula to obtain the position of the mth lion. Step 5: Calculate the updated fitness value of each lion position, set the position with the best fitness value as the lion king position, and update the lion king position; Step 6: Determine whether the maximum number of iterations T is reached. If not, set t=t+1 and return to step 4. If the maximum number of iterations T is reached, the loop iteration is terminated, and the global optimal position, that is, the optimal placement position of the sparse array antenna obtained after optimization, is obtained, and the fitness value is output, that is, the maximum relative sidelobe level of the sparse array reaches the minimum value when the half-power beam width is limited.

2. The constrained antenna array sparse method for beam broadening according to claim 1, characterized in that: The directional pattern of the array antenna in step 1 is a graph of the amplitude characteristics of the antenna system and the spatial scanning angle. The directional pattern of the sparse antenna array is calculated as follows: For a sparse array of N grids with equal spacing to be optimized, the mathematical expression for determining the excitation w is: in{·} T represents the matrix transpose operator, is the phase weight vector of the excitation, j is the imaginary unit, and the antenna marker vector of the grid is I = [I1, I2, ..., I N ] T , n=1,2,...,N,I n ∈{0,1} is the antenna flag corresponding to the nth grid. When its value is "1", it means that the antenna is placed at the nth grid position. When its value is "0", it means that the antenna is not placed at the nth grid position. When the incident angle of a unit plane wave on the linear array is θ, the input operation vector a(θ) of the sparse linear array is composed of two parts: (1) ψ is generated by the change in the relative position between adjacent array elements, ψ = [ψ1, ψ2, ..., ψ N ]; l is an adjustable constant vector, representing the array element spacing vector, l = [l1, l2, ..., l N ] T , l n represents the distance between the n grid antenna placement points and the first grid antenna placement point, then ψ is represented by l, k = 2π / λ is a wave constant, λ represents the wavelength of the wave used when the array antenna is working; (2) a(θ) is generated by the change of the excited phase weight vector, and the expression of a(θ) is as follows: Therefore, the expression of the directional pattern function is Then the expression of the relative pattern function P(θ) is Among them, F max =max{|F(θ)|}lg{·} represents the logarithmic operation with base 10; the grid flag vector I is obtained according to the calculation formula of the directional diagram Among them, M SLL (·) is the function for calculating the maximum relative sidelobe level of the antenna array, max{|F(θ)|} is the main lobe peak of the pattern, and S represents the sidelobe area in the pattern.

3. The constrained antenna array sparse method for beam broadening according to claim 1, characterized in that: In step 2, the number of lions is set to M, the maximum number of iterations is set to T, the number of sparse array antenna grids, i.e. the dimension of the search space, is set to D, and the proportion factor of the hunting lions is set to β; in the tth iteration, the quantum position of the mth lion in the search space is The value range of is between [0,1], which represents the d-dimensional quantum position of the m-th lion, m = 1, 2, ..., M, d = 1, 2, ..., D; the measurement method of the d-dimensional position of the m-th lion is in is a random number uniformly distributed between [0,1], then the position of the mth lion in the tth generation is Initially, t=1, and the initial quantum position is randomly initialized within the defined interval.

4. The constrained antenna array sparse method for beam broadening according to claim 1, characterized in that: In step 3, the position of each lion is obtained by measuring the quantum position of each lion. At this time, there is a one-to-one correspondence between the antenna flag and the position of each quantum lion. The position of the mth quantum lion corresponds to a sparse array. According to the maximum relative sidelobe level of the corresponding directional pattern, the position of the mth lion is Bring in the fitness function based on the penalty mechanism, and calculate the position of the mth quantum lion in the population Evaluate the fitness function, m = 1, 2, ..., M, and design the fitness function as in For the sparse flag bit vector The maximum relative sidelobe level calculated when is the desired main lobe half-power width, Sparse flag bit vector The main lobe half-power width obtained by calculation is c Rat is the fill rate obtained by calculation, e Rat is the expected population rate, p is the penalty factor, and p<<1. If the constraint condition is not met, the penalty function is used to penalize the model function value. The fitness value is calculated for each lion position, and the fitness of each lion is obtained. The lion position with the best fitness in the lion group is selected as the optimal position of the lion group, that is, the lion king position. is the local optimal position of the mth lion when it iterates to the tth generation, where k∈[1,M], The global optimal position of the entire lion group when it iterates to the tth generation; the initial global optimal lion position is set as the lion king position, and its corresponding fitness value is stored.

5. The constrained antenna array sparse method for beam broadening according to claim 1, characterized in that: The step 4 defines that the lion king with the label m=1 uses the simulated quantum rotating gate to update its d-th dimension quantum position as Where m = 1 represents the lion king number. and When , the Lion King's d-dimensional quantum rotation angle update equation is In other cases, the update equation of the lion's d-dimensional quantum rotation angle is is a random number uniformly distributed between [0,1]. is a constant, e1 and e2 are constants that determine the influence of the local optimal position and the global optimal position on the quantum rotation angle, respectively. represents the dth dimension of the local optimal position of the hunting lion labeled k in the tth generation, abs(·) represents the absolute value of each position element in the vector, and sgn(·) is the sign function with the value {-1, 0, 1}; Define the disturbance factor of the hunting lion's movement range as in It represents the maximum step length of a hunting lion moving within its activity range. and are respectively represented as the maximum and minimum values ​​of each dimension in the activity range space of the t-th generation lion; when and When , the quantum rotation angle of the mth hunting lion in the dth dimension is In other cases, the quantum rotation angle of the mth hunting lion in the dth dimension is Where m∈[2,Mβ] represents the hunting lion number, is a random number uniformly distributed between [0,1]. is a random number generated according to a standard normal distribution, is a constant, where is the position of the i-th hunting lion in the t-th generation randomly selected, i∈[2,Mβ], β is the proportion factor of hunting lions, s d is the hunting lion activity range adjustment constant. Under this strategy, the quantum position of the mth hunting lion in the dth dimension is updated to Define the disturbance factor of the lion cub's movement range as The mth lion cub chooses different learning strategies to update its d-dimensional quantum rotation angle according to probability, where m∈[Mβ+1,M]; when the strategy selection factor of the mth lion cub in the tth generation When , the quantum rotation angle of the mth lion cub in the dth dimension is when hour, b∈[2,Mβ]; when hour where s m is a random number uniformly distributed between [0,1]. is a random number generated according to the standard normal distribution; when and hour, is a random number uniformly distributed between [0,1]. is a constant, represents the dth dimension of the local optimal position of the hunting lion labeled b in the tth generation, is the reference position of the lion cub away from the hunting range of the lion group, c d is the constant for adjusting the activity range of the lion cub, and the quantum position of the mth lion cub in the dth dimension is updated to After obtaining the quantum position corresponding to each lion, the measurement formula Measure the quantum position of the lion and update the position of the mth lion in is a random number uniformly distributed between [0,1].

6. The constrained antenna array sparse method for beam broadening according to claim 1, characterized in that: The step 5 calculates the fitness function value of each lion after the update, and judges the pros and cons of the position of each lion in the lion group according to the fitness function value, and sets the position with the best fitness value as the lion king position. The position of the lion king of the t+1 generation is Where m = 1; for the mth lion in the t+1th generation lion group, according to its updated position m∈[2,M], evaluate the fitness function of each lion in the lion group, and update the historical optimal position of the mth lion up to the t+1th generation to And update the global optimal position of the lion group until the t+1th generation to

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