An antenna array sparse synthesis method based on improved white shark algorithm

Abstract

The application provides a sparse antenna pattern synthesis method based on an improved white shark algorithm, and belongs to the technical field of radio frequency antennas. The method is mainly used for solving the problem that an intelligent optimization algorithm is prone to falling into local optimization and slow convergence in a sparse antenna sidelobe suppression process, thereby reducing the sidelobe suppression capability of the sparse antenna. The application is based on the white shark algorithm, and a population partition strategy and an adaptive parameter are added in the algorithm. The white shark position is brought into the fitness function value for calculation, the white shark is divided into subpopulations according to the size of the fitness function value of the white shark individual and the size of the fitness value change between two times of iteration, and different search modes are used in different subpopulations. An adaptive function is added in the search, and the search radius changes with the change of the iteration number. The method has the global search capability and fast convergence, and improves the sidelobe and main lobe suppression capability of the sparse antenna.

Description

Technical Field

[0001] This invention belongs to the field of radio frequency antenna technology and is mainly applied in the field of antenna array pattern synthesis. Background Technology

[0002] With the widespread application of array antennas in wireless communication systems, the optimization of array antennas has attracted much attention. To ensure that the antenna array radiation pattern does not exhibit grating lobes, the spacing between adjacent elements in a uniform antenna array cannot exceed half a wavelength. Therefore, when high gain and high resolution are required for the antenna array, the array aperture length must be very large. Uniformly spaced arrays require a considerable number of antenna elements, making them very expensive. Using sparsely spaced array antennas with non-uniform spacing can significantly reduce costs. Optimizing the array layout involves studying the relationship between antenna array performance and array geometry, and then optimizing the array structure to obtain superior performance indicators.

[0003] Antenna array synthesis is the inverse problem of array analysis. Given radiation characteristics, it synthesizes the total number of antenna elements, their spatial distribution, the excitation amplitude distribution of each element, and the excitation phase distribution of each element to ensure that certain radiation characteristics of the array meet given requirements or that the radiation pattern approximates a predetermined pattern as closely as possible. Currently, there are two main optimization methods in array optimization: one is a sparse array where elements are randomly placed in a uniform grid, and the other is a sparse array with a certain aperture and element spacing. Although sparse arrays cannot compare with sparse arrays in terms of optimization degrees of freedom, they are easier to encode, have a simpler structure, and their element arrangement follows a predictable pattern, making them widely used in array optimization.

[0004] Many problems in engineering can be transformed into function evaluation problems, and array antenna optimization is no exception. Traditional mathematical optimization methods, such as linear programming and gradient descent, have limitations in solving complex optimization problems. Each computation can only provide a feasible solution based on given weights, but cannot provide solutions tailored to the preferences of different decision-makers. Therefore, intelligent algorithms offer new approaches to providing universal solutions. Examples include Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Differential Evolutionary Algorithms (DE), and Artificial Bee Colony Algorithms (ABC). These swarm intelligence algorithms are conceptually simple, easy to implement, and possess strong search capabilities. For the application of intelligent algorithms in array optimization, the main concerns are the algorithms' tendency to get trapped in local optima and their slow convergence speed. Summary of the Invention

[0005] This invention is mainly used to solve the problem that intelligent optimization algorithms are prone to getting stuck in local optima and have slow convergence speed in the process of sparse antenna sidelobe suppression, thereby reducing the sidelobe suppression capability of sparse antennas.

[0006] The technical solution adopted in this invention is as follows:

[0007] A sparse synthesis method for antenna arrays based on an improved White Shark algorithm includes the following steps:

[0008] Step 1: Establish a sparse antenna array model, and place the array elements sequentially according to the number of array elements in the sparse antenna and the spacing between array elements in the full array;

[0009] Step 2: Generate an initial population. The initial population consists of randomly generated amplitude weights of antenna array elements, corresponding to the positions of the white shark. Sort the amplitude weights and select a portion of the antenna array elements from largest to smallest according to a set percentage, setting their amplitude weights to 1, and the rest to 0.

[0010] Step 3: Construct the fitness function, input the initial population into the calculation, and divide the population into potential subpopulation and normal subpopulation based on the change in fitness value of each individual in two consecutive iterations and the current fitness value.

[0011] Step 4: Keep the potential subgroup moving in its own direction of travel, and move towards the direction of individual optimality. The ordinary subgroup moves towards the global optimal direction and the optimal direction of other white shark individuals with a set probability.

[0012] Step 5: Move in the same direction as in Step 4 and update the position of the white shark;

[0013] Step 6: Simulate the schooling behavior of great white sharks and move to the optimal position;

[0014] Step 7: Return to Step 3 to recalculate the fitness value after the move, update the global optimum and individual optimum, until the maximum number of iterations is reached, and obtain the final global optimum result, that is, the sparsity of the antenna array elements; where the global optimum is the one with the largest fitness value among all individuals, and the individual optimum is the one with the largest fitness value in the iteration.

[0015] Furthermore, in step 1, the sparse array model of the antenna is established using the following method, with the formula as follows:

[0016]

[0017] In the formula, f mn Indicates the working state of the corresponding array element: f mn =1 indicates that there is an array element at the corresponding position, f mn =0 indicates that there is no array element at the corresponding position, and M array elements along the y direction are spaced at a set interval d. m N array elements are evenly arranged along the z-direction at a set spacing d. z Uniform arrangement, θ and For azimuth and elevation angles, This represents the maximum beam direction.

[0018] Furthermore, in step 2, the antenna population size and the amplitude weight of each antenna element correspond to the number of white sharks and their positions. The white shark positions are a matrix composed of random numbers ranging from 0 to 1. The matrix is ​​converted into a 1-dimensional matrix, the amplitude values ​​are sorted, and a portion of the antenna elements are selected from largest to smallest according to a set percentage to set their amplitude weights to 1, while the rest are set to 0.

[0019] Furthermore, step 3 specifically involves:

[0020] Calculate the sidelobe level of the antenna pattern:

[0021]

[0022] In the formula, s1 and s2 represent θ = θ0 and θ0 respectively. The sidelobe intervals in the azimuth and pitch directions are calculated based on the radiation pattern, and the maximum sidelobe level is determined by optimizing f. mn Minimize the sum of the maximum sidelobe levels in the azimuth and elevation directions of the planar array (MSLL); divide the population based on the calculated fitness values, using the following parameters:

[0023]

[0024] In the formula, Fb(i) and F(i) are the fitness values ​​of an individual in the two iterations, i represents the i-th individual, W is the number of individuals, λ1 is 1, λ2 is 2, α represents the magnitude of the change in fitness value between the two iterations, and β represents the normalized fitness value of the individual; the calculated R values ​​are sorted, and the population is divided into potential subpopulation and ordinary subpopulation according to the sorting.

[0025] Furthermore, step 4 specifically involves:

[0026] Different search methods are used for different subgroups, and the speed formula is as follows:

[0027] v_new1=μ(v+r*(wbest-WSO_Positions))

[0028] v_new2=μ(v+r*(wbest(rand)-WSO_Positions))

[0029] v_new3=μ(v+r*(gbest-WSO_Positions))

[0030]

[0031] In the formula, p max Take 0.9, p minTake 0.4, r is a random number between 0 and 1, k is the current iteration number, G is the total number of iterations, wbest(rand) represents a random best value among other individuals, v represents the speed of the white shark before the update, v_new1, v_new2 and v_new3 represent the speed of the white shark after the update, wbest represents the individual best value, gbest represents the global best value, and WSO_Positions represents the position of the white shark before the update;

[0032] The potential subgroup continues to move towards its own optimal direction using the velocity formula v_new1. Individuals in the ordinary subgroup are compared with a generated random number using the parameter η. Those with a value greater than or equal to η move towards the globally optimal direction using the velocity formula v_new3, while those with a value less than η move towards the optimal direction of other white shark individuals using the velocity formula v_new2. η is:

[0033]

[0034] Where i represents the i-th individual, W is the number of individuals, and k is the current iteration number.

[0035] Furthermore, in step 5, the position of the great white shark is updated using the velocity formula obtained in step 4. A parameter is used to simulate the intensity of the great white shark's hearing and smell to determine whether the great white shark should maintain its current position or continue exploring using the velocity formula, as follows:

[0036] WSO_Positions_new=WSO_Positions×(~wo)+(ub×a+lb×b)rand<mv

[0037] WSO_Positions_new=WSO_Positions+v / f rand>mv

[0038] wo = xor(a, b)

[0039] In the formula, a = sgn(WSO_Positions-ub) > 0 and b = sgn(WSO_Positions-lb) < 0 are binary vectors used to indicate whether the elements in the great white shark's position exceed the upper and lower limits ub and lb. If they exceed the upper and lower limits, they are placed at the boundary. f is the wave frequency, WSO_Positions_new represents the updated great white shark position, rand is a random number, ~wo means inversion, and mv represents the great white shark's auditory and olfactory intensity. The great white shark's action is determined by comparing the random number rand and mv.

[0040] Furthermore, in step 6, the behavior of a school of great white sharks is simulated to converge towards the optimal position, as shown in the following formula:

[0041] WSO_Positions_new=gbest+rand×D×sgn(rand-0.5)

[0042] In the formula, D is the distance between the white shark's current position and the optimal position, and 1 and -1 are given by the sgn function to change the direction of the search.

[0043] This invention treats sparse antenna construction as a constrained optimization problem, and then combines an improved white shark algorithm with multiple swarm strategies for this problem. This improves upon the shortcomings of intelligent algorithms in solving discrete optimization problems, such as low convergence speed and accuracy, while overcoming the tendency of traditional intelligent algorithms like genetic algorithms to get trapped in local optima. It also effectively suppresses the maximum relative sidelobe level when dealing with sparse problems. Simulation results demonstrate that the proposed synthesis method achieves both high convergence accuracy and speed when handling array problems. Attached Figure Description

[0044] Figure 1 This is a flowchart of the antenna sparse synthesis method based on the improved white shark algorithm of the present invention;

[0045] Figure 2 This is the convergence curve of the simulation example algorithm of this invention;

[0046] Figure 3 This is a simulation example of the sparse antenna element distribution diagram of the present invention;

[0047] Figure 4 This is a simulation example of the elevation pattern of a sparse antenna in this invention.

[0048] Figure 5 This is the azimuth pattern of a sparse antenna, a simulation example of the present invention. Detailed Implementation

[0049] like Figure 1 As shown, the antenna array sparse synthesis method based on the improved white shark algorithm of this invention includes the following steps:

[0050] Step 1: Establish a sparse antenna array model, and place the array elements sequentially according to the number of array elements in the sparse antenna and the spacing between array elements in the full array;

[0051] The sparse array model of the antenna is established using the following method, with the formula as follows:

[0052]

[0053] In the formula, f mn Indicates the working state of the corresponding array element: f mn =1 indicates that there is an array element at the corresponding position, f mn =0 indicates that there is no array element at the corresponding position, and M array elements along the y direction are spaced at a set interval d. mN array elements are evenly arranged along the z-direction at a set spacing d. z Uniform arrangement, θ and For azimuth and elevation angles, This represents the maximum beam direction.

[0054] Step 2: Generate an initial population. The initial population consists of randomly generated amplitude weights of antenna array elements, corresponding to the positions of the white shark. Sort the amplitude weights and select a portion of the antenna array elements from largest to smallest according to a set percentage, setting their amplitude weights to 1, and the rest to 0.

[0055] Specifically, the antenna population size and the amplitude weight of each antenna element correspond to the number of white sharks and their positions. The white shark positions are a matrix composed of random numbers ranging from 0 to 1. The matrix is ​​converted into a 1D matrix, the amplitude values ​​are sorted, and a portion of the antenna elements are selected from largest to smallest according to a set percentage, with their amplitude weights set to 1, and the rest set to 0.

[0056] Step 3: Construct the fitness function, input the initial population into the calculation, and divide the population into potential subpopulation and normal subpopulation based on the change in fitness value of each individual in two consecutive iterations and the current fitness value.

[0057] Specifically:

[0058] Calculate the sidelobe level of the antenna pattern:

[0059]

[0060] In the formula, s1 and s2 represent θ = θ0 and θ0 respectively. The sidelobe intervals in the azimuth and pitch directions are calculated based on the radiation pattern, and the maximum sidelobe level is determined by optimizing f. mn Minimize the sum of the maximum sidelobe levels in the azimuth and elevation directions of the planar array (MSLL); divide the population based on the calculated fitness values, using the following parameters:

[0061]

[0062] In the formula, Fb(i) and F(i) are the fitness values ​​of an individual in the two iterations, i represents the i-th individual, W is the number of individuals, λ1 is 1, λ2 is 2, α represents the magnitude of the change in fitness value between the two iterations, and β represents the normalized fitness value of the individual; the calculated R values ​​are sorted, and the population is divided into potential subpopulation and ordinary subpopulation according to the sorting.

[0063] Step 4: Keep the potential subgroup moving in its own direction of travel, and move towards the direction of individual optimality. The ordinary subgroup moves towards the global optimal direction and the optimal direction of other white shark individuals with a set probability.

[0064] Specifically:

[0065] Different search methods are used for different subgroups, and the speed formula is as follows:

[0066] v_new1=μ(v+r*(wbest-WSO_Positions))

[0067] v_new2=μ(v+r*(wbest(rand)-WSO_Positions))

[0068] v_new3=μ(v+r*(gbest-WSO_Positions))

[0069]

[0070] In the formula, p max Take 0.9, p min Take 0.4, r is a random number between 0 and 1, k is the current iteration number, G is the total number of iterations, wbest(rand) represents a random best value among other individuals, v represents the speed of the white shark before the update, v_new1, v_new2 and v_new3 represent the speed of the white shark after the update, wbest represents the individual best value, gbest represents the global best value, and WSO_Positions represents the position of the white shark before the update;

[0071] The potential subgroup continues to move towards its own optimal direction using the velocity formula v_new1. Individuals in the ordinary subgroup are compared with a generated random number using the parameter η. Those with a value greater than or equal to η move towards the globally optimal direction using the velocity formula v_new3, while those with a value less than η move towards the optimal direction of other white shark individuals using the velocity formula v_new2. η is:

[0072]

[0073] Where i represents the i-th individual, W is the number of individuals, and k is the current iteration number.

[0074] Step 5: Update the great white shark's position using the velocity formula obtained in Step 4. Use a parameter to simulate the intensity of the great white shark's hearing and smell to determine whether it should maintain its current position or continue exploring using the velocity formula, as follows:

[0075] WSO_Positions_new=WSO_Positions×(~wo)+(ub×a+lb×b)rand<mv

[0076] WSO_Positions_new=WSO_Positions+v / f rand>mv

[0077] wo = xor(a, b)

[0078] In the formula, a = sgn(WSO_Positions-ub) > 0 and b = sgn(WSO_Positions-lb) < 0 are binary vectors used to indicate whether the elements in the great white shark's position exceed the upper and lower limits ub and lb. If they exceed the upper and lower limits, they are placed at the boundary. f is the wave frequency, WSO_Positions_new represents the updated great white shark position, rand is a random number, ~wo means inversion, and mv represents the great white shark's auditory and olfactory intensity. The great white shark's action is determined by comparing the random number rand and mv.

[0079] Step 6: Simulate the schooling behavior of great white sharks and move to the optimal position; the formula is as follows:

[0080] WSO_Positions_new=gbest+rand×D×sgn(rand-0.5)

[0081] In the formula, D is the distance between the white shark's current position and the optimal position, and 1 and -1 are given by the sgn function to change the direction of the search.

[0082] Step 7: Return to Step 3 to recalculate the fitness value after the move, update the global optimum and individual optimum, until the maximum number of iterations is reached, and obtain the final global optimum result, that is, the sparsity of the antenna array elements; where the global optimum is the one with the largest fitness value among all individuals, and the individual optimum is the one with the largest fitness value in the iteration.

[0083] Simulation content: Sidelobe level optimization is performed on an array with 200 elements and a scale of 10×20 for both azimuth and elevation angles, with a sparsity of 54%. Figure 2 , 3 4 and 5 are the optimization results.

Claims

1. A sparse synthesis method for antenna arrays based on an improved white shark algorithm, characterized in that, Includes the following processes: Step 1: Establish a sparse antenna array model, and place the array elements sequentially according to the number of array elements in the sparse antenna and the spacing between array elements in the full array; Step 2: Generate an initial population. The initial population consists of randomly generated amplitude weights for antenna elements, corresponding to the positions of the white shark. Sort the amplitude weights and select a portion of the antenna elements from largest to smallest according to a set percentage, setting their amplitude weights to 1, while setting the rest to 0. Step 3: Construct the fitness function, input the initial population into the calculation, and divide the population into potential subpopulation and normal subpopulation based on the change in fitness value of each individual in two consecutive iterations and the current fitness value. Step 4: Keep the potential subgroup moving in its own direction of travel, and move towards the direction of individual optimality. The ordinary subgroup moves towards the global optimal direction and the optimal direction of other white shark individuals with a set probability. Step 5: Move in the same direction as in Step 4 and update the position of the white shark; Step 6: Simulate the schooling behavior of great white sharks and move to the optimal position; Step 7: Return to Step 3 to recalculate the fitness value after the move, update the global optimum and individual optimum, until the maximum number of iterations is reached, and obtain the final global optimum result, which is the sparse situation of the antenna array elements; where the global optimum is the one with the largest fitness value among all individuals, and the individual optimum is the one with the largest fitness value in the iteration. Step 4 specifically involves: Different search methods are used for different subgroups, and the speed formula is as follows: In the formula, Take 0.9, Take 0.4, A random number between 0 and 1 This represents the current iteration number. This represents the total number of iterations. This represents the optimal value of a random other individual. This indicates the speed of the White Shark before the update. , and This indicates the updated speed of the White Shark. Represents the individual's optimal value. This represents the global optimum. This indicates the location of the white shark before the update; Potential subgroups use velocity formula Continuing to move in the direction that is optimal for each individual, individuals in the ordinary subgroup generate random numbers and parameters. Compare, greater than or equal to Use the speed formula Move towards the globally optimal direction, less than Use the speed formula It tends to move in the direction that is optimal for other individual white sharks; for: in Indicates the first Individual, For the number of individuals, This represents the current iteration number.

2. The sparse synthesis method for antenna arrays based on the improved white shark algorithm according to claim 1, characterized in that, In step 1, the sparse array model of the antenna is established using the following method: The formula is: In the formula, Indicates the working status of the corresponding array element: =1 indicates that there is an array element at the corresponding position. =0 indicates that there is no array element at the corresponding position, and M array elements along the y direction are spaced at a set interval. N array elements are evenly arranged along the z-direction at a set spacing. Evenly arranged, and For azimuth and elevation angles, ( , () indicates the maximum beam direction.

3. The sparse synthesis method for antenna arrays based on the improved white shark algorithm according to claim 1, characterized in that, In step 2, the antenna population size and the amplitude weight of each antenna element correspond to the number of white sharks and their positions. The white shark positions are a matrix composed of random numbers ranging from 0 to 1. The matrix is ​​converted into a 1-dimensional matrix, the amplitude values ​​are sorted, and a portion of the antenna elements are selected from largest to smallest according to a set percentage to set their amplitude weights to 1, while the rest are set to 0.

4. The sparse synthesis method for antenna arrays based on the improved white shark algorithm according to claim 2, characterized in that, Step 3 specifically involves: Calculate the sidelobe level of the antenna pattern: In the formula, and express = and = The sidelobe intervals in the azimuth and pitch directions are calculated based on the radiation pattern, and the maximum sidelobe level is then optimized. Minimize the sum of the maximum sidelobe levels in the azimuth and elevation directions of the planar array (MSLL); divide the population based on the calculated fitness values, using the following parameters: 、 、 In the formula, and These are the fitness values ​​of an individual in the previous and next iterations, respectively. Indicates the first Individual, For the number of individuals, Take 1, Take 2, This indicates the magnitude of the change in an individual's fitness value between two consecutive tests. This represents the normalized individual fitness value; the calculated R values ​​are sorted, and the population is divided into potential subpopulations and ordinary subpopulations according to the sorting.

5. The sparse synthesis method for antenna arrays based on the improved white shark algorithm according to claim 1, characterized in that, In step 5, the position of the great white shark is updated using the velocity formula obtained in step 4. A parameter is used to simulate the intensity of the great white shark's hearing and smell to determine whether the great white shark should maintain its current position or continue exploring using the velocity formula, as follows: In the formula, and It is a binary vector used to indicate whether the elements at the great white shark's position exceed the upper and lower boundaries. and If it exceeds the upper and lower limits, place it at the boundary. For wave frequency, This indicates the updated location of the Great White Shark. It is a random number. middle Indicates negation, The intensity of a great white shark's hearing and smell is represented by random numbers. and Comparison determines the great white shark's actions.

6. The sparse synthesis method for antenna arrays based on the improved white shark algorithm according to claim 5, characterized in that, In step 6, the schooling behavior of great white sharks is simulated to converge towards the optimal position, as shown in the following formula: In the formula, The distance between the white shark's current position and its optimal position is determined by... The function takes 1 and -1 as inputs to change the direction of the search.

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