A comprehensive method for dual-band hybrid sparse array beamforming

Abstract

The present invention discloses a dual-band hybrid sparse array beam synthesis method, which belongs to the field of array antenna beam synthesis technology. The method comprises the following steps: (1) parameter setting; (2) iterative optimization of an improved genetic algorithm for an A-band sparse array; (3) algorithm post-processing to obtain array mapping and array performance index parameters; (4) B-band sparse array optimization pre-processing to obtain a B-band dual-array index matrix based on the A-band array sparse matrix and the B-band dual-array array area allocation; (5) the same process as (2); (6) the same process as (3); (7) obtaining the array arrangement of the dual-band hybrid sparse array based on the array mapping of the A-band array and the B-band dual-array. The method adopts the method of interleaved placement of subarrays and dual-band serial optimization to effectively solve the problem of dual-band hybrid sparse array and has high engineering application value.

Description

Technical Field

[0001] The present invention relates to a dual-band hybrid sparse array beam arrangement method, belonging to the technical field of array antenna beam synthesis. Background Art

[0002] In recent years, as weapon platforms have become increasingly equipped with electronic equipment and space has become increasingly limited, the demand for integrated antenna RF front-ends has become increasingly urgent. Antennas must achieve multi-band, multi-functional integration to support various functions such as radar, communications, and measurement and control. After the antenna RF front-end is integrated, in order to reduce the system's hardware and software complexity and cost, practical engineering often requires planar arrays to achieve a large aperture with as few antenna elements as possible to achieve narrow beams or high spatial resolution while maintaining low sidelobe levels. Using a non-uniform sparse planar array is an effective solution, but it increases the array layout space. To save layout space, a dual-band hybrid sparse array can be used to achieve spatial multiplexing. However, the sparse arrangement of elements often leads to increased sidelobe levels in the directional pattern, and the comprehensive optimization of dual-band hybrid sparse arrays is even more complex.

[0003] The purpose of antenna array synthesis is to optimize the array element positions and their excitation methods while maintaining a low sidelobe level so that the antenna can meet the desired radiation characteristics with the least number of elements. Beam synthesis of non-uniform planar arrays is a highly nonlinear optimization problem involving multiple unknowns. In recent years, modern intelligent optimization algorithms such as simulated annealing algorithms, genetic algorithms, particle swarm algorithms, and differential evolution algorithms have been widely used in array synthesis and have achieved many research results. These traditional optimization algorithms are essentially natural algorithms based on randomness and have strong versatility. However, when applied to certain complex models such as the dual-band hybrid sparse array mentioned in this invention, problems such as premature convergence or long convergence time may occur, making it difficult to find a global optimal solution. Summary of the Invention

[0004] To solve the above problems, the present invention proposes a dual-band hybrid sparse array beam synthesis method, which improves the selection operator, crossover operator and mutation operator of the genetic algorithm to improve the algorithm efficiency.

[0005] A dual-band hybrid sparse array beam synthesis method includes the following steps:

[0006] Step 1: Set parameters, including array parameters such as frequency, subarray size, number of subarrays, and sparsity rate, and parameters of the improved genetic algorithm including population size, number of iterations, crossover probability, and mutation probability;

[0007] Step 2: pre-processing the improved genetic algorithm for the A-band array, including setting optimization parameters and creating an initial population;

[0008] Step 3: Iteratively optimize the improved genetic algorithm of the A-band array to obtain the best individual in each generation;

[0009] Step 4: Post-process the improved genetic algorithm of the A-band array to obtain the array mapping of the A-band array and the array performance index parameters of the array pattern, gain, sidelobe level, and beamwidth based on the best individual;

[0010] Step 5: Pre-process the optimization of the two arrays in the B-band, and obtain the index matrix of the B-band dual array based on the array area allocation of the A-band array and the B-band dual array;

[0011] Step 6: Pre-process the improved genetic algorithm of the two arrays in the B-band column, convert the index matrix obtained in step 5 into the B-band dual-array optimization parameters, and create an initial population;

[0012] Step 7, iterative optimization of the improved genetic algorithm for the two arrays of the B-band column. The iterative optimization of the improved genetic algorithm for the two arrays of the B-band column is performed synchronously to obtain the best individuals of each generation;

[0013] Step 8: Post-processing is performed on the two arrays in the B-band column using the improved genetic algorithm. The array mappings of the two arrays in the B-band column and array performance parameters such as array pattern, gain, sidelobe level, and beamwidth are obtained based on the best individual.

[0014] Step 9: Obtain the array arrangement of the dual-band hybrid sparse array based on the array mapping of the A-band array and the B-band dual array.

[0015] Furthermore, the spacing between the dual-band sub-arrays is in a multiple relationship, and the dual-band sub-arrays are interspersed and arranged in a mixed manner.

[0016] Furthermore, the number of subarrays and array sparsity remain unchanged during the algorithm operation.

[0017] Furthermore, the optimization parameters in step 2 and step 6 are sparse matrices of the array, including binary coding and real number coding, and the two forms can be converted into each other;

[0018] Binary encoding:

[0019] P_B=(b1,b2,......,b N_sa-1 ,b N_sa )

[0020] Among them, N_sa is the maximum number of sub-arrays that can be arranged when the array area is densely packed, b m Indicates whether the mth sub-array is retained, the value is 1 if it is retained, and 0 if it is not retained;

[0021] Real number encoding method:

[0022] P_R=(a1,a2,......,a N_p-1 ,a N_p )

[0023] Among them, N_p is the number of sub-arrays in the array after the array area is sparsely distributed according to the set sparse rate, a m is the real number code of the mth sub-matrix, and its value range is [0, N_sa-N_p].

[0024] The conversion relationship between binary coding and real number coding:

[0025] P_R=find(P_B=1)-linspace(1,N_p,N_p)

[0026] Among them, find(P_B=1) corresponds to b m = 1, all the values ​​of m are arranged from small to large, and linspace(1,N_p,N_p) is the integer arrangement vector from 1 to N_p;

[0027] P_B=zeros(1,N_sa)

[0028] P_B(P_R+linspace(1,N_p,N_p))=1

[0029] Among them, zeros(1,N_sa) defines a zero-value vector with 1 row and N_sa columns.

[0030] Furthermore, the fitness functions in steps 3 and 7 are:

[0031]

[0032] The above formula represents the fitness value of the mth individual in a population with M individuals, where It represents the absolute value of the maximum sidelobe level of the mth unit, and its fitness is 0≤fm≤1. The lower the sidelobe level obtained by the individual, the greater its fitness value.

[0033] Furthermore, the selection operators in steps 3 and 7 adopt random competition and best-retained selection strategies.

[0034] Furthermore, the crossover operators in steps 3 and 7 adopt a two-point crossover strategy and a real number encoding method, and set a dynamic crossover probability during the algorithm operation. In the early stage of genetic evolution, the crossover probability is relatively large, and the probability gradually decreases in the middle and late stages.

[0035] Furthermore, the mutation operators in steps 3 and 7 use uniform mutation and inversion operations. First, the entire population is divided into two sub-populations on average. One sub-population undergoes uniform mutation using real number coding; the other sub-population undergoes inversion operation. After the operation of each sub-population is completed, it is combined into a new group using binary coding. At the same time, a dynamic mutation probability is set during the operation of the algorithm. In the early stage of genetic evolution, the mutation probability is relatively high, and the probability gradually decreases in the middle and late stages.

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] In view of the characteristics of dual-band hybrid sparse array, the idea of ​​sub-array-level interleaving placement and dual-band serial optimization is adopted to reduce the optimization complexity. Through the above means, the problem of dual-band hybrid sparse array is well solved, which has high engineering application value. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 It is a flow chart of the dual-band hybrid sparse array beam synthesis method of the present invention.

[0039] Figure 2 This is the A-band sparse array optimization convergence performance curve of the present invention.

[0040] Figure 3 This is the B-band sparse array optimization convergence performance curve of the present invention.

[0041] Figure 4 This is the B-band dual-surface array area allocation of the present invention.

[0042] Figure 5 This is the sub-array distribution diagram of the dual-band hybrid sparse array optimized by the present invention.

[0043] Figure 6 This is the normalized array pattern of the A-band sparse array optimized by the present invention.

[0044] Figure 7 This is the normalized array pattern of the B-band sparse array 1 after optimization by the present invention.

[0045] Figure 8 This is the normalized array pattern of the B-band sparse array 2 after optimization by the present invention. DETAILED DESCRIPTION

[0046] The present invention will be further described below with reference to the accompanying drawings and examples.

[0047] like Figure 1 As shown, a dual-band hybrid sparse array beam synthesis method includes the following steps:

[0048] (1) Parameter setting, including array parameters such as frequency, subarray size, number of subarrays, and sparsity rate, and algorithm parameters such as population size, number of iterations, crossover probability, and mutation probability. The spacing between dual-band units is in a multiple relationship, and the number of subarrays and array sparsity rate remain unchanged during the algorithm operation.

[0049] (2) Pre-processing of the improved genetic algorithm for the A-band sparse array, including setting optimization parameters and creating the initial population;

[0050] The optimization parameter is a sparse matrix of an array, including two forms of binary coding and real number coding, and the two forms can be converted into each other.

[0051] ①Binary encoding method:

[0052] P_B=(b1,b2,......,b N_sa-1 ,b N_sa )

[0053] Among them, N_sa is the maximum number of sub-arrays that can be arranged when the array area is densely packed, b m Indicates whether the mth sub-matrix is ​​retained, the value is 1 if retained, and 0 if not.

[0054] ② Real number encoding method:

[0055] P_R=(a1,a2,......,a N_p-1 ,a N_p )

[0056] Among them, N_p is the number of sub-arrays in the array after the array area is sparsely distributed according to the set sparse rate, a m is the real number code of the mth sub-matrix, and its value range is [0, N_sa-N_p].

[0057] ③The conversion relationship between binary coding and real number coding:

[0058] P_R=find(P_B=1)-linspace(1,N_p,N_p)

[0059] Among them, find(P_B=1) corresponds to b m = 1, arrange the vectors from small to large, and linspace(1,N_p,N_p) is the integer arrangement vector from 1 to N_p.

[0060] P_B=zeros(1,N_sa)

[0061] P_B(P_R+linspace(1,N_p,N_p))=1

[0062] Among them, zeros(1,N_sa) defines a zero-value vector with 1 row and N_sa columns.

[0063] (3) Iterative optimization of the algorithm, including determination of fitness function, selection, crossover, mutation, population update, termination judgment, etc.;

[0064] Among them, the fitness function is set as:

[0065]

[0066] The above formula represents the fitness value of the mth individual in a population with M individuals, where Represents the absolute value of the maximum sidelobe level of the mth unit. It can be seen that its fitness 0≤f m ≤1, the lower the sidelobe level obtained by the individual, the greater its fitness value.

[0067] The selection operator adopts a random competition + best retention selection strategy. Each time a selection is made, two individuals compete with each other and the better individuals are selected to enter the next generation. This can reduce the selection error to a certain extent and retain the best individuals of each generation.

[0068] The crossover operator adopts a two-point crossover strategy and uses real number coding. At the same time, a dynamic crossover probability is set during the algorithm operation. In the early stage of genetic evolution, the crossover probability is relatively large, and the probability gradually decreases in the middle and late stages.

[0069] The mutation operator uses a uniform mutation plus a reverse operation. First, the entire population is divided equally into two subpopulations. One subpopulation undergoes uniform mutation using real number encoding; the other subpopulation undergoes a reverse operation. After these operations, the subpopulations are combined into a new population using binary encoding. A dynamic mutation probability is also set during the algorithm's execution. In the early stages of genetic evolution, the probability is higher, but it gradually decreases in the middle and later stages.

[0070] (4) Post-processing of the A-band array algorithm, obtaining array mapping and array performance parameters such as array pattern, gain, sidelobe level, and beamwidth based on the best individual;

[0071] Substitute the sparse matrix of the best individual into the following formula for total field synthesis:

[0072]

[0073] in,

[0074]

[0075] T x and T y are all used as intermediate quantities, w(n,m) is a sparse matrix, is the beam pointing angle.

[0076] (5) Pre-processing of the B-band sparse array optimization: Based on the A-band array sparse matrix and the array area allocation of the B-band dual array, the index matrix of the B-band dual array is obtained;

[0077] The empty spaces after the A-band array is sparsely arranged in the array area are used as the locations for the B-band dual-array sparse arrangement:

[0078] P_s=kron[not(P_end),ones(2,3)]

[0079] Among them, P_end is the sparse matrix obtained by optimizing the A-band array surface. One A-band sub-array position can be placed with 2 rows and 3 columns of B-band sub-arrays. P_end is inverted and then expanded to 2 rows and 3 columns to obtain the saturated matrix P_s of the full-area B-band array.

[0080] Define a symbol matrix ind, store the element numbers of the P_s matrix with a value of 1 into the symbol matrix ind, and obtain the index matrix of the positions that can be deployed in the B frequency band (excluding the positions occupied by the A frequency band sub-array).

[0081] According to the B-band dual-array array area allocation, the internal order of the ind index matrix elements is adjusted to update the dual-array array index matrix.

[0082] (6) Pre-processing of the improved genetic algorithm for two sparse arrays in the B band: the index matrix obtained in step (5) is converted into the optimized parameters of the dual arrays in the B band to create the initial population;

[0083] ①Binary encoding method:

[0084] P_B=(b1,......,b n_ind1 ,b n_ind1+1 ,......,b n_ind1+n_ind2 )

[0085] Among them, n_ind1 is the maximum number of sub-arrays that can be arranged when the B-band array surface 1 is densely arranged in the array area, n_ind2 is the maximum number of sub-arrays that can be arranged when the B-band array surface 2 is densely arranged in the array area, b m Indicates whether the mth sub-matrix is ​​retained, the value is 1 if retained, and 0 if not.

[0086] ② Real number encoding method:

[0087] P_R=(a1,......,a N_p1 / 2 ,a N_p1 / 2+1 ,......,a N_p1 )

[0088] Among them, N_p1 is the number of sub-arrays in the B-band 2 array after the array area is sparsely distributed according to the set sparse rate, a m is the real number code of the mth submatrix. When m≤N_p1 / 2, the value range is [0,n_ind1-N_p1 / 2]; when m>N_p1 / 2, the value range is [0,n_ind2-N_p1 / 2].

[0089] (7) Algorithm iterative optimization, B-band dual-array synchronously, including determination of fitness function, selection, crossover, mutation, population update, termination judgment, etc. The specific operations are the same as step (3);

[0090] (8) Post-processing of the B-band dual-array algorithm: obtain the array mapping of each dual-array and array performance index parameters such as array pattern, gain, sidelobe level, and beamwidth based on the best individual. The specific operation is the same as step (4);

[0091] (9) Based on the array mapping of the A-band array and the B-band dual array, the array arrangement of the dual-band mixed sparse array is obtained.

[0092] The following is a specific structure:

[0093] First, determine the maximum allowable array spacing using the following formula:

[0094] d<λ max / (1+sin(θ max ))

[0095] where λ max is the maximum wavelength of electromagnetic waves in the working frequency band, θ max The maximum scanning angle of the phased array antenna is 45°. Taking the array spacing of the two frequency bands into comprehensive consideration and satisfying the above formula, the array spacing of the antenna unit in band A is 11.2mm×11.2mm, and the array spacing of the antenna unit in band B is 5.6mm×5.6mm, which are multiples of each other.

[0096] The dual-band antenna features three sparse arrays, one operating in Band A and the other two in Band B. The array area is approximately 600mm long and 450mm wide. Taking into account the array area, system EIRP, and antenna single-channel output power, the A-band array utilizes a subarray-level sparse array across the entire array area, comprising 44 subarrays with a sparsity ratio of 0.489. The two B-band arrays each have an equal number of 54 subarrays, occupying half the array area. The vacancies left by the A-band array are then replaced with a subarray-level sparse array with a sparsity ratio of 0.391. The A-band subarrays utilize a 4×6 array element layout, while the B-band subarrays utilize a 4×4 array element layout.

[0097] After the parameters are set, iterative optimization is performed according to steps (2) to (8). The convergence performance curves of the sparse array optimization of the A band and the B band are shown in Figure 2. Figure 2 、 Figure 3 As shown in Figure 2, both converge in the late stage of the iteration.

[0098] Among them, in step (5), the array area allocation of the dual array surface in the B band is as follows: Figure 4 As shown, the internal order of the ind index matrix elements is adjusted to obtain the B-band dual-array index matrix.

[0099] The subarray distribution diagram of the dual-band hybrid sparse array is obtained through step (9), as shown in Figure 5 As shown, it includes 3 sparse array planes, including 1 in the A frequency band in the array area, the first array plane in the B frequency band in the left half of the array area, and the second array plane in the B frequency band in the right half of the array area. The three array planes are placed in the gaps of the sub-arrays in a mixed arrangement.

[0100] The normalized directional pattern of the sparse array in two frequency bands can be obtained, such as Figures 6 to 8 As shown, the normal sidelobe level of the array in band A is ≤-18.5dB, and ≤-17.5dB after scanning 45°; the normal sidelobe level of both arrays in band B is ≤-14.0dB, and ≤-13.5dB after scanning 45°. Compared with the uniformly arranged array, the sidelobe level is significantly reduced, meeting the design specifications.

[0101] The above are only preferred embodiments of the present invention and are not intended to limit the patent scope of the present invention. Any equivalent process transformation or parameter change made using the contents of the present invention specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present invention.

Claims

1. A synthesis method for dual-band hybrid sparse array beams, characterized in that: The following steps are involved: Step 1: Set parameters, including array parameters such as frequency, subarray size, number of subarrays, and sparsity rate, and parameters of the improved genetic algorithm including population size, number of iterations, crossover probability, and mutation probability; Step 2: pre-processing the improved genetic algorithm for the A-band array, including setting optimization parameters and creating an initial population; Step 3: Iteratively optimize the improved genetic algorithm of the A-band array to obtain the best individual in each generation; Step 4: Post-process the improved genetic algorithm of the A-band array to obtain the array mapping of the A-band array and the array performance index parameters of the array pattern, gain, sidelobe level, and beamwidth based on the best individual; Step 5: Pre-process the optimization of the two arrays in the B-band, and obtain the index matrix of the B-band dual array based on the array area allocation of the A-band array and the B-band dual array; Step 6: Pre-process the improved genetic algorithm of the two arrays in the B-band column, convert the index matrix obtained in step 5 into the B-band dual-array optimization parameters, and create an initial population; Step 7, iterative optimization of the improved genetic algorithm for the two arrays of the B-band column. The iterative optimization of the improved genetic algorithm for the two arrays of the B-band column is performed synchronously to obtain the best individuals of each generation; Step 8: Post-processing is performed on the two arrays in the B-band column using the improved genetic algorithm. The array mappings of the two arrays in the B-band column and array performance parameters such as array pattern, gain, sidelobe level, and beamwidth are obtained based on the best individual. Step 9: Obtain the array arrangement of the dual-band hybrid sparse array based on the array mapping of the A-band array and the B-band dual array.

2. The method for synthesizing a dual-band hybrid sparse array beam according to claim 1, characterized in that: The distance between the dual-band sub-arrays is in multiples, and the dual-band sub-arrays are interspersed and mixed.

3. The method for synthesizing dual-band hybrid sparse array beams according to claim 1, characterized in that: The number of subarrays and array sparsity remain unchanged during the algorithm operation.

4. The method for synthesizing dual-band hybrid sparse array beams according to claim 1, characterized in that: The optimization parameters in step 2 and step 6 are sparse matrices of the array, including binary coding and real number coding, and the two forms can be converted into each other; Binary encoding: P_B=(b1,b2,......,b N_sa-1 ,b N_sa ) Among them, N_sa is the maximum number of sub-arrays that can be arranged when the array area is densely packed, b m Indicates whether the mth sub-array is retained, the value is 1 if it is retained, and 0 if it is not retained; Real number encoding method: P_R=(a1,a2,......,a N_p-1 ,a N_p ) Among them, N_p is the number of sub-arrays in the array after the array area is sparsely distributed according to the set sparse rate, a m is the real number code of the mth sub-matrix, and its value range is [0, N_sa-N_p]; The conversion relationship between binary coding and real number coding: P_R=find(P_B=1)-linspace(1,N_p,N_p) Among them, find(P_B=1) corresponds to b m = 1, all the values ​​of m are arranged from small to large, and linspace(1,N_p,N_p) is the integer arrangement vector from 1 to N_p; P_B=zeros(1,N_sa) P_B(P_R+linspace(1,N_p,N_p))=1 Among them, zeros(1,N_sa) defines a zero-value vector with 1 row and N_sa columns.

5. The method for synthesizing dual-band hybrid sparse array beams according to claim 1, characterized in that: The fitness function in step 3 and step 7 is: The above formula represents the fitness value of the mth individual in a population with M individuals, where It represents the absolute value of the maximum sidelobe level of the mth unit, and its fitness is 0≤fm≤1. The lower the sidelobe level obtained by the individual, the greater its fitness value.

6. The method for synthesizing dual-band hybrid sparse array beams according to claim 1, characterized in that: The selection operators in steps 3 and 7 adopt random competition and best-retain selection strategies.

7. The method for synthesizing dual-band hybrid sparse array beams according to claim 1, characterized in that: The crossover operator in steps 3 and 7 adopts a two-point crossover strategy and uses real number coding. At the same time, a dynamic crossover probability is set during the algorithm operation. In the early stage of genetic evolution, the crossover probability is relatively large, and the probability gradually decreases in the middle and late stages.

8. The method for synthesizing dual-band hybrid sparse array beams according to claim 1, characterized in that: The mutation operators in steps 3 and 7 use uniform mutation and inversion operations. First, the entire population is divided into two sub-populations. One sub-population undergoes uniform mutation using real number coding; the other sub-population undergoes inversion operation. After the operations on each sub-population are completed, they are combined into a new group using binary coding. At the same time, a dynamic mutation probability is set during the algorithm operation. In the early stage of genetic evolution, the mutation probability is relatively high, and the probability gradually decreases in the middle and late stages.

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