A quantum heron evolution mechanism wide beam sparse planar array optimization method and system and storage medium

Abstract

The application discloses a quantum heron evolution mechanism wide-beam sparse planar array optimization method and system and a storage medium, relates to the field of array signal processing, and aims at solving the problem that the prior art lacks a method for optimizing a planar antenna array sparsity under high-dimensional multi-constraint conditions based on a quantum evolution operator. The method comprises the following steps: step one, establishing a sparse planar antenna array model and constructing a beam forming target equation; step two, initializing a quantum heron algorithm; step three, calculating the fitness value, the optimal position and the individual local optimal position of each heron; step four, in the hunting stage, each heron updates a quantum rotation angle according to different update strategies according to the number of iterations; step five, in the exploration stage, the heron group is averagely divided, and the individual position of each heron is updated by executing a camouflage strategy and a tracking strategy respectively; step six, the fitness value is calculated, and the global optimal position and the individual local optimal position are updated; and step seven, iterative calculation is performed, and the sparse optimal position of the planar antenna array is output.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and more specifically, to a method, system, and storage medium for optimizing wide-beam sparse planar arrays based on the quantum snake-heron evolution mechanism. Background Technology

[0002] Sparse planar arrays are a special type of antenna array where the spacing between antenna elements is an integer multiple of the minimum element spacing. Compared to uniform planar arrays, sparse planar arrays offer advantages such as lower antenna system failure rate and cost, fewer required elements, and a larger solution space and greater freedom in element placement. Optimizing the element positions in a sparse planar array using swarm intelligence optimization algorithms yields antenna placements closer to the optimal array antenna position and significantly reduces peak sidelobe levels. Furthermore, sparse planar arrays allow for optimized parameter selection based on application requirements, simplify the feed network, and improve the system's adaptive sensing capabilities in complex signal environments, reducing the impact of interference on signal transmission and reception. Therefore, they are widely used in various fields such as communications, radar, sonar, and antenna arrays.

[0003] A search of existing technical literature revealed that Liu Heng et al., in their paper "Constrained Optimization Design of Planar Sparse Array Antennas" published in *Telecommunications Technology* (201, 6, 56(02): 166-170), proposed a differential evolution algorithm based on integer coding, which accelerates the calculation of the array pattern through integer coding and fast Fourier transform. The mathematical analysis and calculation process used in this method are very complex. This not only increases the difficulty of code implementation but may also lead to calculation errors, thus adversely affecting the accuracy of the results. Hrudananda Pradhan et al., in their paper "Designing and optimizing a mutually coupled PlanarArray Antenna using PSO for UHF application" published at the 2013 IEEE Applied Electromagnetics Conference (AEMC), proposed an optimization method for mutually coupled planar array antennas based on particle swarm optimization. This method can significantly improve the antenna's directivity and reduce the half-power beamwidth, but the algorithm is prone to getting trapped in local optima and is sensitive to initial parameters, which has a significant impact on the optimization effect.

[0004] Research on existing technologies has revealed that current methods for optimizing the radiation pattern of sparse planar antenna arrays generally focus on optimizing the excitation amplitude of the antenna elements or the placement of the antennas. No quantum serpentine mechanism has yet been found to optimize the placement of the sparse planar antenna array to achieve the optimal placement for engineering problems such as beam widening and low null depth at the target azimuth. Summary of the Invention

[0005] The technical problem to be solved by this invention is:

[0006] Existing technologies lack methods for solving the sparse optimization problem of planar antenna arrays under high-dimensional multi-constraint conditions based on quantum evolution operators, and for achieving wide-beam low null trap patterns.

[0007] The technical solution adopted by the present invention to solve the above-mentioned technical problems is as follows:

[0008] This invention provides a wide-beam sparse planar array optimization method for the quantum snake-heron evolution mechanism, comprising the following steps:

[0009] Step 1: Establish a sparse planar antenna array model and construct the beamforming target equation;

[0010] Step 2: Set the relevant parameters of the quantum snake-herd evolution mechanism and initialize the quantum position of each snake-herd in the quantum snake-herd flock;

[0011] Step 3: Construct the fitness function of the quantum snake-heron mechanism based on the beamforming objective equation of the sparse array, calculate the fitness value of each snake-heron in the snake-heron flock, and initialize the optimal position in the snake-heron flock and the local optimal position of the individual.

[0012] Step 4: The snake heron flock enters the hunting phase. Each snake heron updates its quantum rotation angle according to different update strategies based on the number of iterations, calculates its fitness value, and updates the global optimal position and the individual local optimal position.

[0013] Step 5: The snake-herd flock enters the exploration phase. The snake-herd flock is divided into two sub-snake-herd flocks, and the positions of each snake-herd individual in the sub-snake-herd flocks are updated by implementing camouflage and tracking strategies respectively.

[0014] Step 6: Calculate the fitness function value and update the global optimum and the individual local optimum.

[0015] Step 7: Determine if the maximum number of iterations has been reached. If not, set the iteration count t = t + 1 and return to step 4. If the maximum number of iterations T has been reached, terminate the loop iteration and output the obtained global optimal position, which is the optimal position for sparse placement of the planar antenna array after optimization.

[0016] Furthermore, the establishment of the sparse planar antenna array model and the construction of the beamforming target equation in step one include the following steps:

[0017] For a rectangular planar array antenna, the number of grid cells in the planar antenna array is set to M×N. The rectangular array is established on the xoy plane of a Cartesian coordinate system, with the edges of the rectangular array parallel to the x-axis and y-axis respectively. There are M array element grids in the direction parallel to the x-axis and N array element grids in the direction parallel to the y-axis. The origin of the coordinate system is set as the starting point of the planar array, and the grid spacing matrices on the x-axis and y-axis are D and D, respectively. x =[d x，1 d x，2 , ..., d x，M-1 ] and D y =[d y，1 d y，2 , ..., d y，N-1 ], using a sparse array, i.e., d x =d x，1 =d x，2 =…=d x，M-1 d y =d y，1 =d y，2 =…=d y，N-1 d x =d y =λ / 2, where d x With d y , where are the grid spacing along the x-axis and y-axis, respectively, and λ is the signal wavelength; the spatial phase difference between the (m, n)th array element and the reference array element located at the origin along the x-axis and y-axis are respectively expressed as:

[0018]

[0019] Where φ is the azimuth angle, θ is the elevation angle, and d m =m·d x d n =n·d y ;

[0020] The spatial phase difference between the (m, n)th array element and the reference array element located at the origin is expressed as:

[0021]

[0022] Let the field intensity radiation pattern function of the (m, n)th antenna be f. m，n (θ, φ), where the complex weighting coefficients of the (m, n)th antenna element are The pattern function of the rectangular area array is then expressed as:

[0023]

[0024] Where j is the imaginary unit, α m，n Let I be the excitation phase of the (m, n)th grid antenna. For a sparse planar array, I mn ∈{0,1} represents the antenna identification mark corresponding to the (m,n)th grid. When the identification mark is "1", it means that an antenna is placed at the (m,n)th grid position. When the identification mark is "0", it means that no antenna is placed at the (m,n)th grid position.

[0025] Assuming the antenna elements in a sparse planar antenna array satisfy omnidirectionality, let f m，n (θ, φ) = 1; when the maximum value of the array's main beam points to (φ0, θ0), The pattern function of a sparse rectangular array is expressed as:

[0026]

[0027] The relative pattern function expression for a sparse planar array is: When each grid of a sparse planar array antenna is occupied by an antenna, and the grid flag bit vector corresponding to the antenna array is I, the beamforming target equation is as follows:

[0028]

[0029] Where M sll (·) To solve for the maximum relative sidelobe level function, S1 represents the sidelobe interval of the azimuth pattern when θ = θ0, and S2 represents... Side lobe intervals of the pitch-hitch pattern.

[0030] Furthermore, step two, which involves setting the relevant parameters of the quantum snake-herd evolution mechanism and initializing the quantum position of each snake-herd in the quantum snake-herd flock, includes the following steps:

[0031] Let the number of snake-herons in the flock be K, the maximum number of iterations be T, and the number of iterations t∈[1,T]. The dimension of the search space for the quantum snake-heron evolution mechanism is equal to the total number of antenna grids in the sparse planar array, both being D. In the t-th iteration, the quantum position of the k-th snake-heron is... The value range of is [0, 1], representing the d-th dimension quantum position of the k-th snake-heron, k = 1, 2, ..., K, d = 1, 2, ..., D; when t = 1, the initial quantum position of the d-th dimension of the k-th snake-heron is set; the measurement rule between the position and quantum position of the k-th snake-heron in the t-th generation is:

[0032]

[0033] in Let the random numbers be uniformly distributed between [0, 1]. Then the position of the k-th snake-heron in the t-th generation is:

[0034] Furthermore, in step three, the fitness function of the quantum snake-heron mechanism is constructed based on the beamforming objective equation of the sparse array, the fitness value of each snake-heron in the flock is calculated, and the optimal position in the flock and the local optimal position of an individual are initialized; this includes the following steps:

[0035] Based on a penalty mechanism and by introducing constraints, the fitness function for the position of the kth snake-heron is designed as follows:

[0036]

[0037] Where p is the penalty factor, and p << 1, The position of the k-th snake-heron is used for the sparse planar array. The maximum relative sidelobe level obtained at the corresponding sparse placement position. S1 represents the sidelobe interval of the azimuth pattern when θ = θ0, and S2 represents... Side lobe intervals of the pitch-hitch pattern. For the desired main lobe half-power width, For sparse identifier bit vectors The corresponding main lobe half-power width, c Rat It is the fill factor of the sparse planar array, e Rat It is the fill factor of the desired sparse planar array, (θ) c φ c ) represents the null direction, s nul (θ c φ c ) represents the actual null depth in the null direction, m nul (θ c φ c ) represents the desired null depth in the null direction;

[0038] The fitness function of each snake-herd in the flock is evaluated to obtain the initial global optimum position of the flock and the local optimum position of each individual snake-herd. This represents the globally optimal position of the entire heron colony up to generation t. Let be the local optimal position of the k-th snake-heron up to the t-th generation.

[0039] Furthermore, step four includes the following steps:

[0040] The heron flock enters the hunting phase, and each heron selects a different update strategy to update its quantum rotation angle based on the iteration number t; when 1≤t<T / 3, the update formula for the d-th dimension of the k-th heron is:

[0041]

[0042] Where γ d Adjust the constant α for the optimal range of the snake-heron flock. d Adjust the constant s for the individual optimization range d Adjust the constant for the hunting range. Let d be the d-th dimension of the locally optimal position of a snake-heron with the label τ in the t-th generation of a snake-heron flock, where τ∈[1,K] and η∈{1,2} is the snake-heron attack coefficient;

[0043] When T / 3 ≤ t < 2T / 3, the quantum rotation angle of the k-th snake-heron in the d-th dimension is:

[0044]

[0045] Where d f =exp((t / T) 4 ) is a nonlinear disturbance factor. To randomly select the d-th dimension of the local optimal position of a snake-heron with the number u in the t-th generation snake-heron flock, where u∈[1,K], These are random numbers between [0, 1] generated according to a normal distribution;

[0046] When 2T / 3 ≤ t ≤ T, the quantum rotation angle of the k-th snake-heron in the d-th dimension is:

[0047]

[0048] in R represents the d-th dimension of the snake-heron's observation of its prey's location. l (d) = C·Levy(D) is the d-th dimension of the Levy flight function, and C is the Levy flight control parameter;

[0049] The quantum position update method for the k-th snake-heron in the d-th dimension during this stage is as follows:

[0050]

[0051] in A random number uniformly distributed between [0, 1]. Let abs(·) be a constant, and abs(·) be the absolute value function.

[0052] Measure the quantum position of the k-th snake-heron in generation t+1 and update the position of the k-th snake-heron during the hunting phase. The updated snake-heron positions are evaluated using a fitness function, and the local optimum position of the k-th snake-heron up to generation t+1 is updated. And the globally optimal position of the snake-herd flock up to generation t+1.

[0053] Furthermore, step five includes the following steps:

[0054] The snake-herd population entered the exploration phase. The population was divided equally, forming Snake-herd Group 1 and Sub-Snake-herd Group 2. Individual snake-herds in Sub-Snake-herd Group 1 were labeled. The camouflage strategy is implemented; the quantum rotation angle of the d-th dimension of the k-th snake-heron in the snake-heron flock 1 is:

[0055]

[0056] Where b f =(1-t / T) 2 These are dynamically changing factors; e1 is the global impact factor, and e2 is the local impact factor.

[0057] Snake heron individual numbers in group 2 Execute the tracking strategy; the quantum rotation angle of the k-th heron in the d-th dimension in the heron flock 2 is:

[0058]

[0059] Where β d For tracking factors, The d-th dimension is used to randomly select the position of the snake-heron with the label i in the t-th generation;

[0060] The quantum position update method for the k-th snake-heron in the d-th dimension during this stage is as follows:

[0061]

[0062] in A random number uniformly distributed between [0, 1]. It is a constant;

[0063] Measure and update the quantum position of the k-th snake-heron.

[0064] This invention provides a wide-beam sparse planar array optimization system based on the quantum serpentine evolution mechanism. The system has a program module corresponding to the steps of the method described in any of the above technical solutions, and executes the steps in the above-described wide-beam sparse planar array optimization method based on the quantum serpentine evolution mechanism when running.

[0065] The present invention also provides a computer-readable storage medium storing a computer program configured to, when invoked by a processor, implement the steps in the wide-beam sparse planar array optimization method for the quantum snake-heron evolution mechanism as described in any one of claims 1 to 6.

[0066] Compared with the prior art, the beneficial effects of the present invention are:

[0067] (1) This invention provides a sparse planar array method for beamwidth and low null depth based on the quantum snake-heron evolution mechanism, which overcomes the obstacle that the convergence accuracy of traditional sparse planar array antenna pattern synthesis method is difficult to improve under multiple constraints.

[0068] (2) This invention integrates the serpentine optimization mechanism with quantum theory. During the optimization of the sparse planar antenna array layout, quantum position, quantum rotation angle, and measurement method are introduced to update the serpentine position, constructing an optimal array placement position that satisfies various constraints. Compared with traditional optimization methods, while maintaining the same half-power beamwidth, the maximum relative sidelobe level of the radiation pattern corresponding to the optimal sparse placement position obtained based on the quantum serpentine optimization mechanism is lower. This allows for more effective suppression of sidelobe interference during signal transmission, significantly improving the overall performance of the antenna array and providing better technical support for applications in communication, radar, and other fields.

[0069] (3) This invention uses the quantum snake-heron evolution mechanism to optimize the placement of the antenna array, so that the array signal forms a null in the interference direction, which enhances the anti-interference ability of the signal during transmission, ensures that the communication system can still operate stably and reliably in a complex and ever-changing interference environment, improves the applicability and reliability of the communication system, and meets the high requirements of actual application scenarios for antenna array performance. Attached Figure Description

[0070] Figure 1 This is a flowchart of the wide-beam sparse planar array optimization method for the quantum snake-heron evolution mechanism in this embodiment of the invention;

[0071] Figure 2 The graph shows the relationship between the number of iterations and fitness of the sparse planar antenna arrays using the three methods when the number of grids is 20×20 in the embodiments of the present invention.

[0072] Figure 3 The sparse planar array radiation pattern of azimuth, elevation and amplitude obtained by optimizing the planar antenna array with 20×20 grids based on the quantum heron evolution mechanism in this embodiment of the invention.

[0073] Figure 4 The diagram shows the radiation pattern in a three-dimensional Cartesian coordinate system of the sparse array result obtained by optimizing the 20×20 planar antenna array in this embodiment of the invention based on the quantum snake-heron evolution mechanism. Detailed Implementation

[0074] To enable those skilled in the art to better understand the present invention, exemplary embodiments or examples of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described embodiments or examples are merely some, not all, of the embodiments or examples of the present invention. All other embodiments or examples obtained by those skilled in the art based on the embodiments or examples of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0075] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0076] Specific Implementation Plan 1: Combining Figure 1 As shown, this invention provides a wide-beam sparse planar array optimization method for the quantum snake-heron evolution mechanism, comprising the following steps:

[0077] Step 1: Establish a sparse planar antenna array model and construct the beamforming target equation;

[0078] Step 2: Set the relevant parameters of the quantum snake-herd evolution mechanism and initialize the quantum position of each snake-herd in the quantum snake-herd flock;

[0079] Step 3: Construct the fitness function of the quantum snake-heron mechanism based on the beamforming objective equation of the sparse array, calculate the fitness value of each snake-heron in the snake-heron flock, and initialize the optimal position in the snake-heron flock and the local optimal position of the individual.

[0080] Step 4: The snake heron flock enters the hunting phase. Each snake heron updates its quantum rotation angle according to different update strategies based on the number of iterations, calculates its fitness value, and updates the global optimal position and the individual local optimal position.

[0081] Step 5: The snake-herd flock enters the exploration phase. The snake-herd flock is divided into two sub-snake-herd flocks, and the positions of each snake-herd individual in the sub-snake-herd flocks are updated by implementing camouflage and tracking strategies respectively.

[0082] Step 6: Calculate the fitness function value and update the global optimum and the individual local optimum.

[0083] Step 7: Determine if the maximum number of iterations has been reached. If not, set the iteration count t = t + 1 and return to step 4. If the maximum number of iterations T has been reached, terminate the loop iteration and output the obtained global optimal position, which is the optimal position for sparse placement of the planar antenna array after optimization.

[0084] Specific Implementation Plan Two: The establishment of the sparse planar antenna array model and the construction of the beamforming target equation, as described in Step One, includes the following steps:

[0085] For a rectangular planar array antenna, the number of grid cells in the planar antenna array is set to M×N. The rectangular array is established on the xoy plane of a Cartesian coordinate system, with the edges of the rectangular array parallel to the x-axis and y-axis respectively. There are M array element grids in the direction parallel to the x-axis and N array element grids in the direction parallel to the y-axis. The origin of the coordinate system is set as the starting point of the planar array, and the grid spacing matrices on the x-axis and y-axis are D and D, respectively. x =[d x,1 ,d x,2 ,...,d x，M-1 ] and D y =[d y,1 ,d y,2 ,...,d y，N-1 ], using a sparse array, i.e., d x =d x，1 =d x，2 =...=d x，M-1 d y =d y，1 =d y，2 =…=d y，N-1 d x =d y =λ / 2, where d x With d y Here, λ represents the grid spacing on the x-axis and y-axis, respectively, and λ is the signal wavelength. Since the distance difference between each antenna element and the target direction determines the phase difference of the signal during transmission, the spatial phase difference between the (m, n)th element and the reference element located at the origin along the x-axis and y-axis are respectively expressed as:

[0086]

[0087] Where φ is the azimuth angle, θ is the elevation angle, and d m =m·d x d n =n·d y ;

[0088] The spatial phase difference between the (m, n)th array element and the reference array element located at the origin is expressed as:

[0089]

[0090] Let the field intensity radiation pattern function of the (m, n)th antenna be f. m，n (θ, φ), where the phase and amplitude weighting coefficients for each antenna element are α. m，n I m，n At this point, the complex weighting coefficients of the (m, n)th antenna element are: The pattern function of the rectangular area array is then expressed as:

[0091]

[0092] Where j is the imaginary unit, α m，n Let I be the excitation phase of the (m, n)th grid antenna. For a sparse planar array, I mn ∈{0,1} represents the antenna identification mark corresponding to the (m,n)th grid. When the identification mark is "1", it means that an antenna is placed at the (m,n)th grid position. When the identification mark is "0", it means that no antenna is placed at the (m,n)th grid position.

[0093] Assuming the antenna elements in a sparse planar antenna array satisfy omnidirectionality, then f can be neglected within the beam scanning range of a rectangular array antenna. m，n The influence of (θ, φ) makes f m，n (θ, φ) = 1; when the maximum value of the array's main beam points to (φ0, θ0), The pattern function of a sparse rectangular array is expressed as:

[0094]

[0095] The relative pattern function expression for a sparse planar array is: When each grid of a sparse planar array antenna is occupied by an antenna, and the grid flag bit vector corresponding to the antenna array is I, the beamforming target equation is as follows:

[0096]

[0097] Where M sll (·) To solve for the maximum relative sidelobe level function, S1 represents the sidelobe interval of the azimuth pattern when θ = θ0, and S2 represents... The side lobe intervals of the pitch-hitch radiation pattern. This implementation scheme is otherwise the same as Specific Implementation Scheme One.

[0098] Specific implementation plan three: Step two involves setting the relevant parameters of the quantum snake-herd evolution mechanism and initializing the quantum position of each snake-herd in the quantum snake-herd flock, including the following steps:

[0099] Let the number of snake-herons in the flock be K, the maximum number of iterations be T, and the number of iterations t∈[1,T]. The dimension of the search space for the quantum snake-heron evolution mechanism is equal to the total number of antenna grids in the sparse planar array, both being D. In the t-th iteration, the quantum position of the k-th snake-heron is... The value range of is [0, 1], representing the d-th dimension quantum position of the k-th snake-heron, k = 1, 2, ..., K, d = 1, 2, ..., D; when t = 1, the initial quantum position of the d-th dimension of the k-th snake-heron is set to . The rule for measuring the position and quantum position of the k-th snake-heron in generation t is as follows:

[0100]

[0101] in Let the random numbers be uniformly distributed between [0, 1]. Then the position of the k-th snake-heron in the t-th generation is: This implementation plan is otherwise the same as Implementation Plan Two.

[0102] Specific Implementation Plan Four: The beamforming target equation described in Step Three constructs the fitness function of the quantum snake-heron mechanism, calculates the fitness value of each snake-heron in the flock, and initializes the optimal position in the flock and the local optimal position of an individual snake-heron; including the following steps:

[0103] The position of each snake-heron can be obtained by measuring its quantum position. The position of the k-th snake-heron then corresponds to a sparse planar array. Based on a penalty mechanism and by introducing constraints, the fitness function for the k-th snake-heron's position is designed using the beamforming objective equation of the sparse array:

[0104]

[0105] Where p is the penalty factor, and p << 1, The position of the k-th snake-heron is used for the sparse planar array. The maximum relative sidelobe level obtained at the corresponding sparse placement position. S1 represents the sidelobe interval of the azimuth pattern when θ = θ0, and S2 represents... Side lobe intervals of the pitch-hitch pattern. For the desired main lobe half-power width, For sparse identifier bit vectors The corresponding main lobe half-power width, c Rat It is the fill factor of the sparse planar array, e Rat It is the fill factor of the desired sparse planar array, (θ) c φ c ) represents the null direction, s nul (θ c φ c ) represents the actual null depth in the null direction, m nul (θ c φ c ) represents the desired null depth in the null direction;

[0106] The fitness function of each snake-herd in the flock is evaluated to obtain the initial global optimum position of the flock and the local optimum position of each individual snake-herd. This represents the globally optimal position of the entire heron colony up to generation t. This represents the local optimal position of the k-th snake-heron up to the t-th generation. This implementation scheme is otherwise identical to specific implementation scheme three.

[0107] Specific implementation plan five: Step four includes the following steps:

[0108] The heron flock enters the hunting phase, and each heron selects a different update strategy to update its quantum rotation angle based on the iteration number t; when 1≤t<T / 3, the update formula for the d-th dimension of the k-th heron is:

[0109]

[0110] Where γ d Adjust the constant α for the optimal range of the snake-heron flock. d Adjust the constant s for the individual optimization range d Adjust the constant for the hunting range. Let d be the d-th dimension of the locally optimal position of a snake-heron with the label τ in the t-th generation of a snake-heron flock, where τ∈[1,K] and η∈{1,2} is the snake-heron attack coefficient;

[0111] When T / 3 ≤ t < 2T / 3, the quantum rotation angle of the k-th snake-heron in the d-th dimension is:

[0112]

[0113] Where d f =exp((t / T) 4 ) is a nonlinear disturbance factor. To randomly select the d-th dimension of the local optimal position of a snake-heron with the number u in the t-th generation snake-heron flock, where u∈[1,K], These are random numbers between [0, 1] generated according to a normal distribution;

[0114] When 2T / 3 ≤ t ≤ T, the quantum rotation angle of the k-th snake-heron in the d-th dimension is:

[0115]

[0116] in R represents the d-th dimension of the snake-heron's observation of its prey's location. l (d) = C·Levy(D) is the d-th dimension of the Levy flight function, and C is the Levy flight control parameter;

[0117] The quantum position update method for the k-th snake-heron in the d-th dimension during this stage is as follows:

[0118]

[0119] in A random number uniformly distributed between [0, 1]. Let abs(·) be a constant, and abs(·) be the absolute value function.

[0120] Measure the quantum position of the k-th snake-heron in generation t+1 and update the position of the k-th snake-heron during the hunting phase. The updated snake-heron positions are evaluated using a fitness function, and the local optimum position of the k-th snake-heron up to generation t+1 is updated. And the globally optimal position of the snake-herd flock up to generation t+1. This implementation plan is otherwise the same as Specific Implementation Plan Four.

[0121] Specific implementation plan six: Step five includes the following steps:

[0122] The snake-herd population entered the exploration phase. The population was divided equally, forming Snake-herd Group 1 and Sub-Snake-herd Group 2. Individual snake-herds in Sub-Snake-herd Group 1 were labeled. The camouflage strategy is implemented; the quantum rotation angle of the d-th dimension of the k-th snake-heron in the snake-heron flock 1 is:

[0123]

[0124] Where b f =(1-t / T) 2 These are dynamically changing factors; e1 is the global impact factor, and e2 is the local impact factor.

[0125] Snake heron individual numbers in group 2 Execute the tracking strategy; the quantum rotation angle of the k-th heron in the d-th dimension in the heron flock 2 is:

[0126]

[0127] Where β d For tracking factors, The d-th dimension is used to randomly select the position of the snake-heron with the label i in the t-th generation;

[0128] The quantum position update method for the k-th snake-heron in the d-th dimension during this stage is as follows:

[0129]

[0130] in A random number uniformly distributed between [0, 1]. It is a constant;

[0131] Measure and update the quantum position of the k-th snake-heron. This implementation plan is otherwise the same as Implementation Plan Five.

[0132] Specific implementation plan seven: Step six includes the following process:

[0133] The fitness function is used to evaluate the snake-herd positions obtained during the hunting and exploration phases of the flock, and the local optimum position of the k-th snake-herd up to generation t+1 is updated. Update the global optimal position of the snake-herd flock up to generation t+1. This implementation plan is otherwise the same as Specific Implementation Plan Six.

[0134] The wide-beam sparse planar array optimization method (algorithm) for the quantum snake-heron evolution mechanism proposed in this invention is the underlying technical core of this invention, and various products can be derived based on the algorithm.

[0135] Based on the method proposed in this invention, a wide-beam sparse planar array optimization system based on the quantum serpentine evolution mechanism is developed using a programming language. This system has program modules corresponding to the steps of the above-mentioned technical solution, and executes the steps in the above-mentioned wide-beam sparse planar array optimization method based on the quantum serpentine evolution mechanism when running.

[0136] The developed system (software) computer program is stored on a computer-readable storage medium. This computer program is configured to implement the steps of the wide-beam sparse planar array optimization method for the quantum heron evolution mechanism described above when called by a processor. In other words, the invention is materialized on a carrier, becoming a computer program product.

[0137] Various implementations of the systems and techniques described herein can be implemented in digital electronic circuit systems, integrated circuit systems, application-specific integrated circuits (ASICs), computer hardware, firmware, software, and / or combinations thereof. These various implementations may include: implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0138] The computational programs (also referred to as programs, software, software applications, or code) of this invention include machine instructions of a programmable processor and can be implemented using high-level procedural and / or object-oriented programming languages, and / or assembly / machine languages. As used herein, the terms "machine-readable medium" and "computer-readable medium" refer to any computer program product, device, and / or apparatus (e.g., disk, optical disk, memory, programmable logic device PLD) for providing machine instructions and / or data to a programmable processor, including machine-readable media that receive machine instructions as machine-readable signals. The term "machine-readable signal" refers to any signal for providing machine instructions and / or data to a programmable processor.

[0139] The beneficial effects of the present invention will be described below with reference to specific embodiments.

[0140] Example 1

[0141] This invention addresses array signal processing, providing a constrained planar antenna array sparse construction method based on the quantum heron evolution mechanism for beam spreading, denoted as QSBOA; and a constrained planar antenna array sparse construction method based on the particle swarm optimization algorithm, denoted as PSO. The specific parameter settings for the particle swarm optimization algorithm are referenced from Yuan Zhihao's article "Two-Dimensional Array Antenna Pattern Synthesis Technology Based on Improved Particle Swarm Optimization Algorithm" published in the *Journal of Electronics and Information Technology*. The constrained planar antenna array sparse construction method based on the heron optimization algorithm is denoted as SBOA. The specific parameter settings for the heron optimization algorithm are referenced from YoufaFu et al.'s article "Secretary bird optimization algorithm: a new metaheuristic for solving global optimization problems" published in *Artificial Intelligence Review*. The QSBOA parameter settings are as follows: where γ... d =0.03, α d =0.09, s d =0.03, β d =0.01, D=400. Maximum number of iterations T=2000, number of snakes and herons K=20, p=0.01, e Rat =0.8, m nul =-33, φ0=0°, θ0=0°, c d =0.03, α d =0.09, s d =0.03, β d =0.01, C = 0.5. The PSO algorithm parameters are set as follows: maximum number of iterations T = 2000, number of sparse planar array grids D = 400, number of particles ξ = 20, acceleration coefficients c1 = 2, c2 = 2, and upper velocity limit v. max =4, lower limit of velocity v min =-4. The SBOA algorithm parameters are set as follows: maximum number of iterations T=2000, number of sparse planar array grids D=400, and Levy flight control parameter ε=0.5.

[0142] like Figure 2 As shown, under high-dimensional multi-constraint conditions, the QSBOA of this invention has higher convergence accuracy than PSO and SBOA.

[0143] like Figure 3 and Figure 4 As shown, the optimized result obtained by QSBOA of the present invention can achieve high-performance pattern synthesis while strictly satisfying multiple constraints such as half-power beamwidth, target azimuth null depth and array sparsity.

[0144] While the present invention has been disclosed above, its scope of protection is not limited thereto. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the present invention, and all such changes and modifications will fall within the scope of protection of the present invention.

Claims

1. A method for optimizing a wide-beam sparse planar array based on the quantum snake-heron evolution mechanism, characterized in that, Includes the following steps: Step 1: Establish a sparse planar antenna array model and construct the beamforming target equation; Step 2: Set the relevant parameters of the quantum snake-herd evolution mechanism and initialize the quantum position of each snake-herd in the quantum snake-herd flock; Step 3: Construct the fitness function of the quantum snake-heron mechanism based on the beamforming objective equation of the sparse array, calculate the fitness value of each snake-heron in the snake-heron flock, and initialize the optimal position in the snake-heron flock and the local optimal position of the individual. Step 4: The snake heron flock enters the hunting phase. Each snake heron updates its quantum rotation angle according to different update strategies based on the number of iterations, calculates its fitness value, and updates the global optimal position and the individual local optimal position. Step 5: The snake-herd flock enters the exploration phase. The snake-herd flock is divided into two sub-snake-herd flocks, and the positions of each snake-herd individual in the sub-snake-herd flocks are updated by implementing camouflage and tracking strategies respectively. Step 6: Calculate the fitness function value and update the global optimum and the individual local optimum. Step 7: Determine if the maximum number of iterations has been reached. If not, set the iteration count to zero. Return to step four; if the maximum number of iterations has been reached. Then the loop iteration terminates, and the optimal position of the sparse placement of the planar antenna array is output; Step four includes the following steps: The heron flock enters the hunting phase, with each heron hunting according to the number of iterations. Choose different update strategies to update its quantum rotation angle; when At that time, the first Only snakes and egrets The formula for updating the quantum rotation angle of a dimension is: in Adjust constants to optimize the range of snake-heron flocks. Adjust constants for the individual optimization range. Adjust the constant for the hunting range. To randomly select the first from the heron flock The code number is The local optimal position of the snake-heron dimension, , This represents the attack coefficient of snakes and herons. For the first The global optimal position of the snake-heron dimension, For the first The generation The local optimal position of the snake-heron. For the first The generation The location of the snake-heron dimension; when At that time, the first Only snakes and egrets The quantum rotation angle of the dimension is: in It is a nonlinear perturbation factor. In the first Randomly select the number from the heron flock. The local optimal position of the snake-heron dimension, , Generated according to a normal distribution Random numbers between; when At that time, the first Only snakes and egrets The quantum rotation angle of the dimension is: in The first time for snake-herons to observe the location of prey dimension; For the first Levy flight function, For Levi's flight control parameters; The first stage Only snakes and egrets The quantum position update method for dimensionality is as follows: in for Random numbers that are uniformly distributed between them. It is a constant. For the absolute value function, Indicates the first The generation The first snake-heron 3D quantum position; For the first The first snake-heron The quantum position is measured and updated in the hunting phase. Location of the snake-heron The updated snake-heron locations are evaluated using a fitness function, and the [number]th [location] is updated. The snake-heron has reached the number of Local optimal position of time And up to the The global optimal position of the heron flock to date ; Step five includes the following steps: The snake-herd population entered the exploration phase. The population was divided equally, forming Snake-herd Group 1 and Sub-Snake-herd Group 2. Individual snake-herds in Sub-Snake-herd Group 1 were labeled. Implement a disguise strategy; Snake and Heron Flock 1 Only snakes and egrets The quantum rotation angle of the dimension is: in For dynamically changing factors, As a global impact factor, Local influencing factors; Snake heron individual numbers in group 2 Execute the tracking strategy; in the second group of snakes and herons Only snakes and egrets The quantum rotation angle of the dimension is: in For tracking factors, To randomly select the first The code number is The location of the snake-heron dimension; The first stage Only snakes and egrets The quantum position update method for dimensionality is as follows: in for Random numbers that are uniformly distributed between them. It is a constant; For the first The quantum position of the snake-heron is measured and its position is updated. .

2. The method for optimizing a wide-beam sparse planar array based on the quantum snake-heron evolution mechanism according to claim 1, characterized in that, Step one, which involves establishing a sparse planar antenna array model and constructing the beamforming objective equation, includes the following steps: For a rectangular planar array antenna, the number of grids in the planar antenna array is set to... Establish the rectangular array in a Cartesian coordinate system On the surface, the edges of the rectangular array are respectively with axis Parallel to the axis, let it be parallel to... In the direction parallel to the axis Array element grid, and In the direction parallel to the axis Array element grid; the origin of the coordinate system is set as the starting point of the planar array. shaft and The grid spacing matrices on the axis are respectively and , using sparse array, i.e. , , ,in and They are respectively shaft and Grid spacing on the axis The signal wavelength; the first Each array element and the reference array element located at the origin are along... shaft and The spatial phase difference between the axes is expressed as follows: in It is the azimuth angle. The pitch angle, , ; No. The spatial phase difference between each array element and the reference array element located at the origin is expressed as: Let the first The field intensity radiation pattern function of each antenna is: At this time, the first The complex weighting coefficients of the antenna array elements are: The pattern function of the rectangular area array is then expressed as: in The imaginary unit, For the first The excitation phase of each grid antenna, for a sparse planar array, Indicates the first The antenna identification tag corresponding to the nth grid cell, when the identification tag value is "1", indicates that the antenna is in the nth grid cell. The antenna is placed at the grid position. When the identification mark is "0", it indicates that the antenna is in the grid position. No antennas are placed in any of the grid positions; Assuming the antenna elements in a sparse planar antenna array satisfy omnidirectionality, let When the maximum value of the array's main beam points to... hour, ; The pattern function of a sparse rectangular array is represented as: The relative pattern function expression for a sparse planar array is: When each grid of a sparse planar array antenna is occupied by an antenna, let the grid flag bit vector corresponding to the antenna array be... The constructed beamforming objective equation is as follows: in To solve for the maximum relative sidelobe level function, express Side lobe intervals of the azimuth pattern. express Side lobe intervals of the pitch-hitch pattern.

3. The method for optimizing a wide-beam sparse planar array based on the quantum snake-heron evolution mechanism according to claim 2, characterized in that, Step two, which involves setting the relevant parameters of the quantum snake-herd evolution mechanism and initializing the quantum position of each snake-herd in the quantum snake-herd flock, includes the following steps: The number of snake-herons in the snake-heron flock is set to The maximum number of iterations is Number of iterations The search space dimension of the quantum snake-heron evolution mechanism is equal to the total number of antenna grids in the sparse planar array. ; in the In the nth iteration, the 1st The quantum position of the snake-heron is , The range of values ​​is , indicating the first The first snake-heron Quantum position, , ;when At that time, set the first The first snake-heron The initial quantum position of the dimension; the first The generation The measurement rule between the position of the snake and the heron and the quantum position is as follows: in for If the random numbers are uniformly distributed between the intervals, then the first... The generation The location of the snake-heron is .

4. The method for optimizing a wide-beam sparse planar array based on the quantum snake-heron evolution mechanism according to claim 3, characterized in that, Step three involves constructing the fitness function of the quantum snake-heron mechanism based on the beamforming objective equation of the sparse array, calculating the fitness value of each snake-heron in the flock, and initializing the optimal position in the flock and the local optimal position of an individual snake-heron; this includes the following steps: Design the first... based on the penalty mechanism and by introducing constraints. The fitness function for the snake-heron position is: in As a penalty factor, and , For sparse planar arrays, the first Location of the snake-heron The maximum relative sidelobe level obtained at the corresponding sparse placement position. , , express Side lobe intervals of the azimuth pattern. express Side lobe intervals of the pitch-hitch radiation pattern. For the desired main lobe half-power width, For sparse identifier bit vectors The corresponding main lobe half-power width, It is the fill factor of a sparse planar array. It is the desired fill factor of the sparse planar array. For the zero-trap direction, The actual zero-depression depth in the zero-depression direction. Let be the desired null depth in the null direction; The fitness function of each snake-herd in the flock is evaluated to obtain the initial global optimum position of the flock and the local optimum position of each individual snake-herd. For the entire heron flock, iterate to the [number]th [number]. The global optimal position at the time of substitution. For the first The snake-heron iteration reached the first The local optimal position when substitution is made.

5. A wide-beam sparse planar array optimization system for a quantum snake-heron evolution mechanism, characterized in that, The system has a program module corresponding to the steps of the method described in any one of claims 1 to 4 above, and executes the steps in the wide-beam sparse planar array optimization method of the quantum snake-heron evolution mechanism described above when running.

6. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program configured to implement, when invoked by a processor, the steps of the wide-beam sparse planar array optimization method for the quantum snake-heron evolution mechanism as described in any one of claims 1 to 4.

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