Optimization method, device and equipment of sparse concentric ring array and medium

Abstract

The invention provides an optimization method, device, equipment and medium for a sparse concentric annulus array, and the method comprises the steps: obtaining the array antenna parameters of the concentric annulus array, building an array antenna model according to the array antenna parameters, determining the optimal peak side lobe level obtained based on an antenna pattern in the array antenna model as an evaluation target, and carrying out the evaluation of the optimal peak side lobe level. Generating an initial population based on a radius relational expression, performing weight sparseness and disturbance fine tuning on the maximum array element number corresponding to each circular ring radius to obtain an initial array element number group, and performing iterative updating on the circular ring radius of the concentric circular ring array based on an evaluation target, the initial population and all the initial array element number groups to obtain a circular ring number group; iterative updating comprises the steps of performing weight sparseness and disturbance fine tuning on the maximum array element number corresponding to each iterative population; through weight sparseness, disturbance fine tuning and iteration of the circular ring radius, the optimization calculation amount is reduced, the optimization efficiency is improved, the number of array elements is reduced, and the cost is reduced.

Description

Technical Field

[0001] The present application relates to the technical field of array antennas, and in particular to an optimization method, device, equipment and medium for a sparsely distributed concentric circular ring array. Background Art

[0002] Compared with uniform arrays, non-uniform arrays have more freedom in element position and can achieve better radiation performance. Because they have fewer elements, they can achieve advantages such as small system size, low manufacturing cost and low system power consumption. They are widely used in phased arrays, radars and wireless communications. However, due to the complex nonlinear relationship between the position of the array element and the array factor, the optimal design of the array element position has always been a difficult problem in the comprehensive research of sparse arrays. In large-scale array systems, array antennas are required to have fast tracking speed, high reliability, strong anti-interference ability, and at the same time have the characteristics of low cost, easy implementation, and easy conformity with the carrier. It is necessary to design an array antenna with a low sidelobe radiation pattern that can effectively suppress interference signals.

[0003] Concentric ring arrays can be divided into two categories according to the position distribution of array elements: one is a uniform array in which the array elements are distributed on the ring grid according to the rule of half a wavelength apart, and the low sidelobe requirement can be achieved by optimizing the amplitude and phase of the feed; the other is a sparse array in which the array elements are randomly distributed under multiple constraints within a certain array aperture range, and the position distribution of the array elements can be optimized to achieve the low sidelobe requirement. Representative analytical methods for this type of problem include the matrix beam method and the fast Fourier transform method.

[0004] With the development of numerical computing, intelligent optimization algorithms such as genetic algorithm, particle swarm algorithm, differential evolution algorithm and sparrow search algorithm have been applied to the analysis and synthesis of array antennas, improving the calculation efficiency and accuracy. However, with the development and application of large-scale array antennas and the increasing complexity of array antenna structures, traditional optimization algorithms have low solution efficiency and are prone to falling into local optimal solutions when dealing with complex nonlinear problems, which can no longer meet the optimization needs of antenna arrays. Summary of the invention

[0005] The present invention provides an optimization method, device, equipment and medium for a sparsely distributed concentric ring array, so as to solve the technical problems of low solution efficiency and easy falling into a local optimal solution in the above-mentioned array antenna optimization.

[0006] In one embodiment of the present application, the present application provides an optimization method for a sparsely distributed concentric circular ring array, comprising: obtaining array antenna parameters of the concentric circular ring array, the array antenna parameters including the number of circular rings, the minimum array element spacing, and the antenna aperture; establishing an array antenna model according to the array antenna parameters, and determining the optimized peak sidelobe level obtained based on the antenna radiation pattern in the array antenna model as an evaluation target, the array antenna model also including a radius relationship of the circular ring radius; generating an initial population based on the radius relationship, the initial population being used to characterize multiple concentric circular ring arrays A corresponding initial radius group, wherein the initial radius group includes all the ring radii in the concentric ring array; according to the minimum array element spacing and the initial radius group, weighted sparse and perturbation fine-tuning is performed on the maximum number of array elements corresponding to each of the ring radii to obtain an initial array element number group; based on the evaluation target, the initial population, and all the initial array element number groups, the ring radii of the concentric ring array are iteratively updated to obtain a target array element number group and a target radius group, wherein the iterative update includes weighted sparse and perturbation fine-tuning of the maximum number of array elements corresponding to each iterative population.

[0007] In one embodiment of the present application, the weight sparsification and disturbance fine-tuning includes: determining the maximum number of array elements based on the minimum array element spacing and the circular ring radius; determining the first number of array elements according to a preset lower limit weight and the maximum number of array elements; generating an incremental weight based on a preset weight function, and updating the incremental weight according to a preset disturbance variable, wherein the preset disturbance variable is obtained based on a bipolar array and an initial disturbance variable; determining the second number of array elements according to a new incremental weight and the maximum number of array elements; and determining the sum of the first number of array elements and the second number of array elements as the current number of array elements of the circular ring radius.

[0008] In one embodiment of the present application, an initial population is generated based on the radius relationship, including: generating multiple initial degree of freedom allocation vectors according to tent mapping; constraining each of the initial degree of freedom allocation vectors to a degree of freedom solution range to obtain multiple array element degree of freedom allocation vectors, wherein the upper limit of the degree of freedom solution range is obtained based on the array antenna parameters; obtaining an initial population based on the radius relationship and the multiple array element degree of freedom allocation vectors; wherein the radius relationship is used to characterize the relationship between the array element allocatable degrees of freedom, the minimum array element spacing, the ring radius, and the number of the rings.

[0009] In one embodiment of the present application, multiple initial degree of freedom allocation vectors are generated according to tent mapping, including: randomly generating multiple first vectors; taking twice the decimal part corresponding to the first vector respectively to obtain multiple second vectors; generating multiple random numbers based on a preset interval, wherein the preset interval is obtained based on the number of initial populations and the maximum number of iterations; and generating multiple initial degree of freedom allocation vectors according to each of the second vectors and the corresponding random numbers.

[0010] In one embodiment of the present application, the circle radius of the concentric circle array is iteratively updated based on the evaluation target, the initial population, and all the initial array element number groups, including: calculating the initial fitness of multiple initial gray wolf individuals based on the evaluation target and each of the initial array element number groups, and determining multiple leading gray wolf individuals from the top three initial fitnesses, and determining the remaining initial gray wolf individuals as multiple candidate gray wolf individuals, the initial gray wolf individuals are used to characterize the initial radius group in the initial population; calculating the current distance between the candidate gray wolf individuals and each of the leading gray wolf individuals, and determining multiple current gray wolf positions based on the preset nonlinear convergence factor, the candidate gray wolf individuals and each of the current distances; performing The next generation of gray wolf individuals is obtained by weighted summation, and the next generation of gray wolf individuals are corrected for out-of-bounds based on the array antenna parameters to obtain iterative gray wolf individuals, and the iterative gray wolf individuals also include the leading gray wolf individuals; according to the minimum array element spacing and the iterative radius group corresponding to the iterative gray wolf individuals, the maximum number of array elements corresponding to each of the circular ring radii is weighted sparsely adjusted and perturbation fine-tuned to obtain an iterative array element number group; based on the evaluation target, the iterative fitness of multiple iterative gray wolf individuals is calculated respectively, and each of the leading gray wolf individuals is updated according to each of the iterative fitness to obtain multiple new leading gray wolf individuals and multiple new candidate gray wolf individuals, so as to update the gray wolf individuals based on the current distance between the new candidate gray wolf individuals and each of the new leading gray wolf individuals, until the maximum number of iterations is reached.

[0011] In one embodiment of the present application, determination of the preset position weight includes: determining half of the difference between a preset maximum weight factor and a preset minimum weight factor as a first weight factor; determining the product of the first weight factor and an iteration parameter as a second weight factor, wherein the iteration parameter is obtained based on the current number of iterations and the maximum number of iterations; determining the difference between the preset maximum weight factor and the second weight factor as the preset position weight corresponding to the optimal fitness; determining the first weight factor as the preset position weight corresponding to the second optimal fitness; and obtaining the preset position weight corresponding to the third optimal fitness based on the sum of the preset minimum weight factor and the second weight factor.

[0012] In one embodiment of the present application, the method for determining the preset nonlinear convergence factor includes:

[0013]

[0014] Where a is the preset nonlinear convergence factor, t is the current iteration number of iterative update, and t max The maximum number of iterations for iterative updates.

[0015] In one embodiment of the present application, the present application provides an optimization device for a sparsely distributed concentric circular ring array, including: a parameter acquisition module, used to obtain array antenna parameters of the concentric circular ring array, the array antenna parameters including the number of circular rings, the minimum array element spacing and the antenna aperture; a model establishment module, used to establish an array antenna model according to the array antenna parameters, and determine the optimized peak sidelobe level obtained based on the antenna radiation pattern in the array antenna model as an evaluation target, the array antenna model also includes a radius relationship of the circular ring radius; a population generation module, used to generate an initial population based on the radius relationship, the initial population is used to characterize a plurality of concentric circular rings. An initial radius group corresponding to the circular ring array, the initial radius group including all the circular ring radii in the concentric circular ring array; a quantity sparse module, used for performing weight sparse and perturbation fine-tuning on the maximum number of array elements corresponding to each of the circular ring radii according to the minimum array element spacing and the initial radius group, so as to obtain an initial array element quantity group; an iterative update module, used for iteratively updating the circular ring radius of the concentric circular ring array based on the evaluation target, the initial population, and all the initial array element quantity groups, so as to obtain a target array element quantity group and a target radius group, wherein the iterative update includes performing weight sparse and perturbation fine-tuning on the maximum number of array elements corresponding to each iterative population.

[0016] In one embodiment of the present application, the present application provides an electronic device, which includes: one or more processors; a storage device for storing one or more programs, and when the one or more programs are executed by the one or more processors, the electronic device implements the optimization method of the sparsely distributed concentric ring array as described in any of the above embodiments.

[0017] In one embodiment of the present application, the present application provides a computer-readable storage medium having a computer program stored thereon. When the computer program is executed by a processor of a computer, the computer executes the optimization method for the sparsely distributed concentric ring array described in any of the above embodiments.

[0018] Beneficial effects of the embodiments of the present invention: The present invention provides an optimization method, device, equipment and medium for a sparse concentric circular ring array. The embodiments of the present invention optimize the number of array elements by weight sparse and perturbation fine-tuning the maximum number of array elements, and optimize the one-dimensional linear array problem by iteratively updating the radius of the ring. The two-dimensional concentric circular ring array optimization problem is transformed into two one-dimensional optimization problems, which can reduce the complexity of model establishment, reduce the optimization variables of the algorithm, reduce the amount of calculation of the algorithm, and improve the optimization efficiency; and by weight sparse and perturbation fine-tuning the target number of array elements, it is possible to reduce a certain number of array elements while significantly reducing the sidelobe level, thereby reducing the cost of the system.

[0019] It is to be understood that the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] The drawings herein are incorporated into the specification and constitute a part of the specification, showing embodiments consistent with the present application, and together with the specification, are used to explain the principles of the present application. Obviously, the drawings described below are only some embodiments of the present application, and for those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative work. In the drawings:

[0021] Figure 1 A schematic flow chart of an optimization method for a sparsely distributed concentric ring array according to an embodiment of the present application is shown;

[0022] Figure 2 A flowchart of an improved grey wolf optimization algorithm according to an embodiment of the present application is shown;

[0023] Figure 3 The following is a flow chart for optimizing a sparse concentric ring array according to one embodiment of the present application;

[0024] FIG4( a ) shows a distribution diagram of array element positions after numerical simulation optimization according to an embodiment of the present application;

[0025] FIG4( b ) shows a normalized directional diagram after numerical simulation optimization according to an embodiment of the present application;

[0026] Figure 5 shows a normalized directivity diagram of a full-wave simulation result according to an embodiment of the present application;

[0027] FIG6( a ) shows a distribution diagram of array element positions after numerical simulation optimization according to another embodiment of the present application;

[0028] FIG6( b ) shows a normalized directional diagram after numerical simulation optimization according to another embodiment of the present application;

[0029] Figure 7 shows a normalized directivity diagram of a full-wave simulation result according to another embodiment of the present application;

[0030] Figure 8 A block diagram of an optimization device for a sparse concentric ring array according to an embodiment of the present application is shown;

[0031] Fig. 9 A schematic diagram of the structure of a computer system suitable for implementing an electronic device of an embodiment of the present application is shown. DETAILED DESCRIPTION

[0032] The following describes the embodiments of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. The present application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0033] It should be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present application, and thus the drawings only show components related to the present application rather than being drawn according to the number, shape and size of components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed at will, and the component layout may also be more complicated.

[0034] In the following description, a large number of details are discussed to provide a more thorough explanation of the embodiments of the present application. However, it is obvious to those skilled in the art that the embodiments of the present application can be implemented without these specific details. In other embodiments, well-known structures and devices are shown in the form of block diagrams rather than in detail to avoid making the embodiments of the present application difficult to understand.

[0035] In the related art, there are problems in array antenna optimization such as low solution efficiency and easy falling into local optimal solutions.

[0036] In order to solve the above technical problems, the present application provides an optimization method, device, equipment and medium for a sparsely distributed concentric ring array. The implementation details of the technical solution of the embodiment of the present application are elaborated in detail below.

[0037] See also Figure 1 , Figure 1 FIG. 1 is a flow chart showing a method for optimizing a sparsely distributed concentric ring array according to an embodiment of the present application. Figure 1 As shown, in an exemplary embodiment, the optimization method of the sparse concentric ring array includes at least steps S110 to S150, which are described in detail as follows:

[0038] Step S110, obtaining array antenna parameters of the concentric circular array.

[0039] Among them, the array antenna parameters include the number of rings, the minimum array element spacing and the antenna aperture.

[0040] In one embodiment of the present application, the antenna aperture R and the number of rings of the concentric ring array are set according to actual needs. The minimum spacing between array elements d c .

[0041] Step S120: establishing an array antenna model according to the array antenna parameters, and determining the optimized peak sidelobe level obtained based on the antenna pattern in the array antenna model as an evaluation target.

[0042] The array antenna model also includes a radius relationship of the circular ring radius.

[0043] In one embodiment of the present application, the antenna pattern of the concentric ring array is derived, and the antenna pattern is as follows:

[0044]

[0045] Where F is the antenna pattern of the concentric ring array, θ is the antenna elevation angle of the concentric ring array, is the antenna azimuth of the concentric ring array, is the number of rings, N m is the current number of array elements on the mth ring, k = 2π / λ is the wave number, λ is the wavelength, r m is the radius of the mth ring, is the element azimuth corresponding to the nth element of the mth circle.

[0046] In one embodiment of the present application, the array element azimuth angle is as follows:

[0047]

[0048] in, is the element azimuth corresponding to the nth element of the mth circle, N m is the current number of array elements on the mth ring.

[0049] In one embodiment of the present application, the radius relationship is as follows:

[0050]

[0051] In one embodiment of the present application, r m is the radius of the mth ring, d c is the minimum array element spacing, Δr m is the allocatable degree of freedom of the array element, R is the antenna aperture, is the number of rings.

[0052] In one embodiment of the present application, based on the derived antenna pattern, the maximum sidelobe level (peak sidelobe level, PSLL) of the entire plane is selected as the evaluation target. The evaluation targets are as follows:

[0053]

[0054] Among them, PSLL is the evaluation target, F is the antenna radiation pattern of the concentric ring array, θ is the antenna elevation angle of the concentric ring array, is the antenna azimuth of the concentric ring array, F max is the maximum level of the main lobe, θ min is the elevation angle corresponding to the first zero point, r m is the radius of the mth ring, N m is the current number of array elements on the mth ring.

[0055] Step S130, generating an initial population based on the radius relationship.

[0056] The initial population is used to characterize an initial radius group corresponding to a plurality of concentric circular ring arrays, and the initial radius group includes all circular ring radii in the concentric circular ring arrays.

[0057] In one embodiment of the present application, an initial population is generated based on a radius relationship, including: generating multiple initial degree of freedom allocation vectors according to a tent mapping; constraining each initial degree of freedom allocation vector to a degree of freedom solution range to obtain multiple array element degree of freedom allocation vectors, wherein the upper limit of the degree of freedom solution range is obtained based on array antenna parameters; obtaining an initial population based on a radius relationship and multiple array element degree of freedom allocation vectors; wherein the radius relationship is used to characterize the relationship between the array element allocatable degrees of freedom, the minimum array element spacing, the ring radius, and the number of rings.

[0058] In one embodiment of the present application, multiple initial degree of freedom allocation vectors are generated according to tent mapping, including: randomly generating multiple first vectors; taking twice the decimal part corresponding to the first vector respectively to obtain multiple second vectors; generating multiple random numbers based on a preset interval, the preset interval is obtained based on the number of initial populations and the maximum number of iterations; generating multiple initial degree of freedom allocation vectors according to each second vector and the corresponding random number.

[0059] In one embodiment of the present application, the population is initialized by a Tent chaotic map.

[0060] In one embodiment of the present application, the initial degree of freedom allocation vector is generated as follows:

[0061] Z i+1 =(2Z i )mod1+rand(0,1) / N P t max Formula (5)

[0062] Among them, Z i+1 is the chaotic sequence obtained in this iteration, that is, the initial degree of freedom allocation vector; mod is the remainder operation, Z i is the first vector, N Pis the number of individuals in the initial population, t max The maximum number of iterations for iterative updates.

[0063] In one embodiment of the present application, the array element freedom degree allocation vector includes the allocatable freedom degrees of the array elements on each circular ring.

[0064] In one embodiment of the present application, the generated chaotic sequence is constrained to a set degree of freedom solution range according to the constraint conditions, and the array element allocatable degrees of freedom corresponding to the ring in the array element degree of freedom allocation vector are determined as follows:

[0065] Δr m = l m +(U m -l m )Z m Formula (6)

[0066] Among them, Δr m is the allocatable degrees of freedom of the array elements on the mth ring, l m is the lower limit of the degree of freedom solution range, U m is the upper limit of the degree of freedom solution range, Z m is the initial degree of freedom allocation corresponding to the mth ring.

[0067] In one embodiment of the present application, the upper limit of the degree of freedom solution range is l m The value of Where R is the antenna aperture, is the number of rings, d c is the minimum array element spacing. The lower limit of the degree of freedom solution range is 0.

[0068] In one embodiment of the present application, in order to narrow the position search range, the initial radius group may be represented by a radius matrix, and the radius matrix is ​​as follows:

[0069]

[0070] Among them, R is the radius matrix, r1 is the radius of the circle corresponding to the first circle, and r2 is the radius of the circle corresponding to the second circle. For the The radius of the ring corresponding to the ring, d is the vector corresponding to the minimum constraint distance, d c is the minimum array element spacing, ΔR is the array element freedom allocation vector, Δr1 is the array element allocation freedom on the first ring, Δr2 is the array element allocation freedom on the second ring, Δr m The array elements on the mth ring can be allocated degrees of freedom.

[0071] Step S140 , according to the minimum array element spacing and the initial radius group, weighted sparse and perturbation fine-tuning is performed on the maximum number of array elements corresponding to each ring radius to obtain an initial array element number group.

[0072] In one embodiment of the present application, weight sparsification and perturbation fine-tuning include: determining a maximum number of array elements based on a minimum array element spacing and a circular ring radius; determining a first number of array elements based on a preset lower limit weight and a maximum number of array elements; generating an incremental weight based on a preset weight function, and updating the incremental weight based on a preset perturbation variable, wherein the preset perturbation variable is obtained based on a bipolar array and an initial perturbation variable; determining a second number of array elements based on a new incremental weight and the maximum number of array elements; and determining the sum of the first number of array elements and the second number of array elements as the current number of array elements of the circular ring radius.

[0073] In one embodiment of the present application, the maximum number of array elements is determined as follows:

[0074]

[0075] Among them, N max is the maximum number of array elements, r m is the radius of the mth ring, d c is the minimum array element spacing.

[0076] In one embodiment of the present application, the current number of array elements is determined as follows:

[0077] N m =N max ω+N max γ m Formula (9)

[0078] Among them, N m is the current number of array elements on the mth ring, N max is the maximum number of array elements, ω is the preset lower limit weight, γ m is the new incremental weight on the mth ring.

[0079] In one embodiment of the present application, if the number of array elements on each ring is too small, its spatial resolution will be reduced, and the gain and directivity performance of the array will also be affected. Therefore, during the iterative update process, the current number of array elements on each ring is guaranteed to be between one third of the maximum number of array elements and the maximum value, that is, the value of ω is 1 / 3.

[0080] In one embodiment of the present application, the new incremental weight is determined as follows:

[0081] γ m =γ′ m +A + μ m Formula (10)

[0082] Among them, γ m is the new incremental weight on the mth ring, γ′ m is the incremental weight on the mth ring, A + For a bipolar array, μ m is the initial disturbance variable.

[0083] In one embodiment of the present application, A + An array of 1 and -1.

[0084] In one embodiment of the present application, γ′ m Generated by the Kaiser weight function (Kaiser window function) to generate different weight values ​​as needed.

[0085] In one embodiment of the present application, the incremental weight is determined as follows:

[0086]

[0087] Among them, γ′ m is the incremental weight on the mth ring, I0 is the zero-order modified Bessel function, α is the correction parameter, is the number of rings.

[0088] In one embodiment of the present application, different weight values ​​may be generated according to needs using the Kaiser weight function.

[0089] Step S150, iteratively updating the radius of the concentric ring array based on the evaluation target, the initial population, and all the initial array element number groups to obtain a target array element number group and a target radius group. The iterative update includes weighted sparse and perturbation fine-tuning of the maximum number of array elements corresponding to each iterative population.

[0090] In one embodiment of the present application, the radius of the ring is optimized by using an improved grey wolf optimization algorithm, the maximum number of array elements on the ring is thinned using a preset weight function, and the perturbation factor is used for fine-tuning. The obtained array distribution is substituted into the PSLL for calculation to obtain the optimal PSLL.

[0091] In one embodiment of the present application, the optimized array distribution is formed by a target array element quantity group and a target radius group.

[0092] In one embodiment of the present application, the ring radius of the concentric ring array is iteratively updated based on the evaluation target, the initial population, and all the initial array element number groups, including: calculating the initial fitness of multiple initial gray wolf individuals based on the evaluation target and each initial array element number group, and determining multiple leading gray wolf individuals from the top three initial fitnesses, and determining the remaining initial gray wolf individuals as multiple candidate gray wolf individuals, and the initial gray wolf individuals are used to characterize the initial radius group in the initial population; calculating the current distance between the candidate gray wolf individuals and each leading gray wolf individual, and determining multiple current gray wolf positions based on a preset nonlinear convergence factor, the candidate gray wolf individuals and each current distance; The current gray wolf position and the corresponding preset position weights are weighted summed to obtain the next generation gray wolf individual, and the next generation gray wolf individual is corrected for out-of-bounds based on the array antenna parameters to obtain an iterative gray wolf individual, which also includes each leading gray wolf individual; according to the minimum array element spacing and the iterative radius group corresponding to the iterative gray wolf individual, the maximum number of array elements corresponding to each ring radius is weighted sparsely and perturbation fine-tuned to obtain an iterative array element number group; based on the evaluation target, the iterative fitness of multiple iterative gray wolf individuals is calculated respectively, and each leading gray wolf individual is updated according to each iterative fitness, so as to update each iterative gray wolf individual based on the new multiple leading gray wolf individuals until the maximum number of iterations is reached.

[0093] In one embodiment of the present application, the iterative population includes a plurality of iterative gray wolf individuals.

[0094] In one embodiment of the present application, the leading gray wolf individuals are respectively recorded as α wolf, β wolf and δ wolf, and the candidate gray wolf individuals are recorded as ω wolf. The position of α wolf is defined as the historical optimal solution, the position of β wolf is defined as the suboptimal solution, the position of δ wolf is defined as the third optimal solution, and the position of ω wolf is defined as the candidate solution.

[0095] In one embodiment of the present application, the current distance is determined as follows:

[0096]

[0097] Among them, D α is the current distance between each ω wolf and α wolf, C1 is the first first-class random vector, X α (t) is the position of wolf α, D β is the current distance between each ω wolf and β wolf, C2 is the second first-class random vector, X β (t) is the position of β wolf, D δ is the current distance between each ω wolf and δ wolf, C3 is the third first-class random vector, X δ (t) is the position of δ wolf.

[0098] In one embodiment of the present application, the current location is determined as follows:

[0099]

[0100] Among them, X1(t) is the first type of current gray wolf individual obtained based on wolf α, X α (t) is the position of wolf α, A1 is the first random vector of the second type, D α is the current distance between each ω wolf and α wolf, X2(t) is the second type of current gray wolf individual based on β wolf, X β (t) is the position of β wolf, A2 is the second random vector of the second type, D β is the current distance between each ω wolf and β wolf, X3(t) is the third type of current gray wolf individual based on δ wolf, X δ (t) is the position of δ wolf, A3 is the third random vector of the second type, D δ is the current distance between each ω wolf and δ wolf.

[0101] In one embodiment of the present application, the first type of random vector is determined as follows:

[0102] C = 2 rand (0, 1) Formula (14)

[0103] Where C is a first-class random vector and rand(0,1) is a random number in the range [0,1].

[0104] In one embodiment of the present application, the second type of random vector is determined as follows:

[0105] A=2a·rand(0,1)-a Formula (15)

[0106] Where A is a random vector of the second type, a is a preset nonlinear convergence factor, and rand(0,1) is a random number in [0,1].

[0107] In one embodiment of the present application, the preset nonlinear convergence factor is determined as follows:

[0108]

[0109] Among them, a is the preset nonlinear convergence factor, t is the current iteration number, and t max The maximum number of iterations for iterative updates.

[0110] In one embodiment of the present application, determination of the preset position weight includes: determining half of the difference between a preset maximum weight factor and a preset minimum weight factor as a first weight factor; determining the product of the first weight factor and an iteration parameter as a second weight factor, the iteration parameter being obtained based on the current number of iterations and the maximum number of iterations; determining the difference between the preset maximum weight factor and the second weight factor as the preset position weight corresponding to the optimal fitness; determining the first weight factor as the preset position weight corresponding to the second optimal fitness; and obtaining the preset position weight corresponding to the third optimal fitness based on the sum of the preset minimum weight factor and the second weight factor.

[0111] In one embodiment of the present application, the preset position weight is determined as follows:

[0112]

[0113] Among them, η1 is the preset position weight corresponding to the optimal fitness, η max is the preset maximum weight factor, t is, t max is the maximum number of iterations for iterative updating, η min is the preset minimum weight factor, η c is the preset position weight corresponding to the second best fitness, and η3 is the preset position weight corresponding to the third best fitness.

[0114] In one embodiment of the present application, the preset minimum weight factor may be set to 2 / 9, and the preset maximum weight factor may be set to 4 / 9.

[0115] In one embodiment of the present application, the next generation of gray wolf individuals is determined as follows:

[0116] X(t+1)=X1(t)·η1+X2(t)·η2+X3(t)·η3 Formula (18)

[0117] Among them, X(t+1) is the next generation of gray wolf individuals, X1(t) is the first type of current gray wolf individuals obtained based on α wolf, η1 is the preset position weight corresponding to the optimal fitness, X2(t) is the second type of current gray wolf individuals obtained based on β wolf, η2 is the preset position weight corresponding to the second best fitness, X3(t) is the third type of current gray wolf individuals obtained based on δ wolf, η3 is the preset position weight corresponding to the third fitness.

[0118] In one embodiment of the present application, after each position update, it is determined whether the array element position in each next generation gray wolf individual satisfies the constraint conditions, that is, whether it satisfies the constraints of the array antenna parameters. If not, an out-of-bounds correction is performed on the array element position. After the optimized array layout is obtained, the array element position is converted into a real distance interval.

[0119] In one embodiment of the present application, the optimized ring radius rm Substitute it into formula (9), combine the preset weight function to weight the maximum number of array elements on the ring, and use the disturbance factor to make fine adjustments, and calculate the corresponding iterative fitness.

[0120] In one embodiment of the present application, after completing one iteration, the best iterative fitness obtained is compared with the recorded best initial fitness. If the best iterative fitness is better, the best iterative fitness calculated this time and its array element position are retained and recorded, otherwise they remain unchanged.

[0121] In one embodiment of the present application, it is determined whether the maximum number of iterations has been reached. If so, the iteration process is terminated to obtain the best PSLL; if not, the algorithm is returned to the beginning and recalculated.

[0122] In one embodiment of the present application, see Figure 2 , Figure 2 FIG. 4 is a flow chart of an improved gray wolf optimization algorithm according to an embodiment of the present application. Figure 2 As shown, initialize the array antenna parameters (number of array elements, aperture, minimum spacing, etc.), record the initial position of the array: establish the array antenna model; initialize the array population and Tent chaotic mapping: generate the initial population based on the radius relationship; bring in the fitness function to calculate the fitness: calculate the initial fitness of each initial gray wolf individual in the initial population based on the evaluation target; whether the termination condition is met: if the maximum number of iterations is met, the optimal individual is output; if the maximum number of iterations is not met, enter the step of finding α, β, and δ wolves; find α, β, and δ wolves: use the first three fitnesses as α wolf, β wolf, and δ wolf respectively; update parameters a, A, and C: update the preset nonlinear convergence factor a, the second type of random vector A, and the first type of random vector C; update the gray wolf position; boundary constraints and conversion into actual distance intervals: perform out-of-bounds correction on the array element position based on the array antenna parameters and convert it into a real distance interval.

[0123] In one embodiment of the present application, see Figure 3 , Figure 3 FIG. 1 is a flow chart for optimizing a sparsely distributed concentric ring array according to an embodiment of the present application. Figure 3As shown, a mathematical model of a concentric ring array is established, and the array is initialized: an array antenna model is established according to the array antenna parameters; boundary conditions and optimization targets are set: boundary conditions are set based on the array antenna parameters, and the optimal peak sidelobe level obtained based on the antenna pattern in the array antenna model is determined as the evaluation target; the radius of the ring is initialized by using the Tent chaotic mapping, the number of array elements is sparsely distributed by the weight function, and the fitness function value is calculated: the initial population is generated by the Tent chaotic mapping, and the maximum number of array elements on the ring is weighted sparsely distributed by the preset weight function, and the initial fitness of the corresponding initial gray wolf individual is calculated based on the evaluation target; the radius of the ring is optimized by using the improved gray wolf optimization algorithm, the number of array elements is sparsely distributed by the weight function, and the disturbance factor is fine-tuned: the gray wolf individuals are iteratively updated by the improved gray wolf optimization algorithm, and the iterative update includes weighted sparsely distributed and disturbance fine-tuning of the maximum number of array elements corresponding to each iterative population; the fitness function value is calculated, the optimal fitness value is extracted, and the corresponding array element positions are recorded, and the array distribution of the optimal array scheme is output.

[0124] In one embodiment of the present application, a numerical simulation experiment is performed using MATLAB, and the array antenna generated by the numerical simulation is modeled and simulated in the full-wave simulation software HFSS.

[0125] In one embodiment of the present application, the antenna aperture R = 4.98λ, the number of rings The minimum spacing between array elements d c =0.5λ.

[0126] In another embodiment of the present application, the antenna aperture R=4.3λ, the number of rings The minimum spacing between array elements d c =0.5λ.

[0127] In one embodiment of the present application, please refer to FIG. 4(a) and FIG. 4(b), FIG. 4(a) shows an array element position distribution diagram after numerical simulation optimization according to one embodiment of the present application, and FIG. 4(b) shows a normalized directional diagram after numerical simulation optimization according to one embodiment of the present application. As shown in FIG. 4(a) and FIG. 4(b), R = 4.98λ, t max =300, the array distribution after the ring radius is optimized is obtained through numerical simulation experiments, and The optimized target array element number is 194, and the sparsity rate of the uniform array is 43%. Figure 5 , Figure 5 FIG. 2 shows a normalized directivity diagram of a full-wave simulation result according to an embodiment of the present application. Figure 5 As shown, the array distribution corresponding to R=4.98λ is modeled and simulated by HFSS to obtain the normalized directivity pattern.

[0128] In another embodiment of the present application, please refer to FIG. 6(a) and FIG. 6(b), FIG. 6(a) shows an array element position distribution diagram after numerical simulation optimization according to another embodiment of the present application, and FIG. 6(b) shows a normalized directional diagram after numerical simulation optimization according to another embodiment of the present application. As shown in FIG. 6(a) and FIG. 6(b), R = 4.3λ, t max =300, the array distribution after the ring radius is optimized is obtained through numerical simulation experiments, and The optimized target array element number is 147, and the sparsity rate of the uniform array is 35%. Figure 7 , Figure 7 FIG. 2 shows a normalized directivity diagram of a full-wave simulation result according to another embodiment of the present application. Figure 7 As shown, the array distribution corresponding to R=4.3λ is modeled and simulated by HFSS to obtain the normalized directivity pattern.

[0129] In one embodiment of the present application, it can be seen from the above-mentioned optimization results for different antenna apertures that, under the premise of multiple constraints such as fixed antenna aperture, number of circular rings and minimum array element spacing, the hybrid method of the improved grey wolf optimization algorithm and weighted weight function provided by the present application is used to balance local search and global search, and it is not easy to fall into the local optimal result, so that the peak sidelobe level of the array antenna can be well suppressed, and the number of array elements can be greatly reduced, thereby reducing the cost of the antenna system.

[0130] In the embodiments of the present application, the present application converts the two-dimensional concentric circular ring array optimization problem into a one-dimensional linear array problem (circle radius) and a weight function optimization (number of array elements) problem, which can reduce the complexity of model establishment, reduce the optimization variables of the algorithm, reduce the amount of calculation of the algorithm, and improve the optimization efficiency; by optimizing the number of array elements through the weight function, the diversity of the number of array elements can be improved; compared with the uniform array antenna with the same caliber, the sparsely distributed concentric circular ring array antenna of the present application can significantly reduce the sidelobe level while reducing a certain number of array elements, thereby reducing the cost of the system, and providing a solution for the optimization of low sidelobe array antennas.

[0131] See also Figure 8 , Figure 8 A block diagram of an optimization device for a sparse concentric ring array according to an embodiment of the present application is shown. The device may also be applicable to other exemplary implementation environments and specifically configured in other devices, and this embodiment does not limit the implementation environment to which the device is applicable.

[0132] like Figure 8As shown, according to an embodiment of the present application, an optimization device 800 for a sparsely distributed concentric ring array includes: a parameter acquisition module 801, a model building module 802, a population generation module 803, a number sparse module 804 and an iterative update module 805.

[0133] The parameter acquisition module 801 is used to acquire the array antenna parameters of the concentric circular array, and the array antenna parameters include the number of circular rings, the minimum array element spacing and the antenna aperture;

[0134] A model building module 802 is used to build an array antenna model according to the array antenna parameters, and determine the optimized peak sidelobe level obtained based on the antenna pattern in the array antenna model as an evaluation target, wherein the array antenna model also includes a radius relationship of the ring radius;

[0135] A population generation module 803 is used to generate an initial population based on a radius relationship, where the initial population is used to characterize an initial radius group corresponding to a plurality of concentric circular ring arrays, and the initial radius group includes all the circular ring radii in the concentric circular ring arrays;

[0136] The number sparse module 804 is used to perform weight sparse and disturbance fine-tuning on the maximum number of array elements corresponding to each ring radius according to the minimum array element spacing and the initial radius group, so as to obtain an initial array element number group;

[0137] The iterative update module 805 is used to iteratively update the ring radius of the concentric ring array based on the evaluation target, the initial population, and all the initial array element number groups to obtain the target array element number group and the target radius group. The iterative update includes weight sparse and perturbation fine-tuning of the maximum number of array elements corresponding to each iterative population.

[0138] It should be noted that the optimization device for the sparsely distributed concentric circular ring array provided in the above embodiment and the optimization method for the sparsely distributed concentric circular ring array provided in the above embodiment belong to the same concept, wherein the specific manner in which each module and unit performs the operation has been described in detail in the method embodiment and will not be repeated here. In actual applications, the optimization device for the sparsely distributed concentric circular ring array provided in the above embodiment can distribute the above functions to different functional modules as needed, that is, divide the internal structure of the device into different functional modules to complete all or part of the functions described above, and this is not limited here.

[0139] An embodiment of the present application also provides an electronic device, comprising: one or more processors; a storage device for storing one or more programs, wherein when the one or more programs are executed by the one or more processors, the electronic device implements the optimization method of the sparsely distributed concentric ring array provided in the above-mentioned embodiments.

[0140] See also Fig. 9 , Fig. 9 The structure diagram of the computer system suitable for implementing the electronic device of the embodiment of the present application is shown. It should be noted that: Fig. 9 The computer system 900 of the electronic device shown is only an example and should not bring any limitation to the functions and scope of use of the embodiments of the present application.

[0141] like Fig. 9 As shown, the computer system 900 includes a central processing unit (CPU) 901, which can perform various appropriate actions and processes according to the program stored in the read-only memory (ROM) 902 or the program loaded from the storage part 908 to the random access memory (RAM) 903, such as executing the method in the above embodiment. In the RAM 903, various programs and data required for system operation are also stored. The CPU 901, ROM 902 and RAM 903 are connected to each other through a bus 904. An input / output (I / O) interface 905 is also connected to the bus 904.

[0142] The following components are connected to the I / O interface 905: an input section 906 including a keyboard, a mouse, etc.; an output section 907 including a cathode ray tube (CRT), a liquid crystal display (LCD), etc., and a speaker, etc.; a storage section 908 including a hard disk, etc.; and a communication section 909 including a network interface card such as a LAN (Local Area Network) card, a modem, etc. The communication section 909 performs communication processing via a network such as the Internet. A drive 910 is also connected to the I / O interface 905 as needed. A removable medium 911, such as a magnetic disk, an optical disk, a magneto-optical disk, a semiconductor memory, etc., is installed on the drive 910 as needed so that a computer program read therefrom is installed into the storage section 908 as needed.

[0143] In particular, according to an embodiment of the present application, the process described above with reference to the flowchart can be implemented as a computer software program. For example, an embodiment of the present application includes a computer program product, which includes a computer program carried on a computer-readable medium, and the computer program includes a computer program for executing the method shown in the flowchart. In such an embodiment, the computer program can be downloaded and installed from a network through a communication section 909, and / or installed from a removable medium 911. When the computer program is executed by a central processing unit (CPU) 901, various functions defined in the system of the present application are executed.

[0144] It should be noted that the computer-readable medium shown in the embodiment of the present application can be a computer-readable signal medium or a computer-readable storage medium or any combination of the above two. The computer-readable storage medium can be, for example, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media can include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM), a flash memory, an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, wherein a computer-readable computer program is carried. This propagated data signal can take a variety of forms, including but not limited to an electromagnetic signal, an optical signal, or any suitable combination of the above. A computer-readable signal medium may also be any computer-readable medium other than a computer-readable storage medium, which may send, propagate or transmit a program for use by or in conjunction with an instruction execution system, apparatus or device. A computer program contained on a computer-readable medium may be transmitted using any appropriate medium, including but not limited to: wireless, wired, etc., or any suitable combination of the above.

[0145] The flowchart and block diagram in the accompanying drawings illustrate the possible architecture, functions and operations of the system, method and computer program product according to various embodiments of the present application. Wherein, each box in the flowchart or block diagram can represent a module, a program segment, or a part of the code, and the above-mentioned module, program segment, or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram or flowchart, and the combination of boxes in the block diagram or flowchart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.

[0146] The units involved in the embodiments described in the present application can be implemented by software or by hardware, and the units described can also be set in a processor. Among them, the names of these units do not constitute a limitation on the units themselves under certain circumstances. Therefore, the technical solution according to the implementation mode of the present application can be embodied in the form of a software product, which can be stored in a non-volatile storage medium (which can be a CD-ROM, a USB flash drive, a mobile hard disk, etc.) or on a network, including a number of instructions to enable a computing device (which can be a personal computer, a server, a touch terminal, or a network device, etc.) to execute the method according to the implementation mode of the present application.

[0147] Another aspect of the present application also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor of a computer, causes the computer to execute the optimization method of the sparsely distributed concentric ring array provided in the above-mentioned embodiments. The computer-readable storage medium may be included in the electronic device described in the above-mentioned embodiments, or may exist independently without being assembled into the electronic device.

[0148] In the above embodiments, unless otherwise specified, by using serial numbers such as "first" and "second" to describe common objects, it only means that they refer to different instances of the same object, rather than indicating that the objects being described must adopt a given order, whether in time, space, sorting or any other way.

[0149] The above embodiments are merely illustrative of the principles and effects of the present application, and are not intended to limit the present application. Anyone familiar with the technology may modify or change the above embodiments without violating the spirit and scope of the present application. Therefore, all equivalent modifications or changes made by a person of ordinary skill in the art without departing from the spirit and technical ideas disclosed in the present application shall still be covered by the claims of the present application.

Claims

1. A method for optimizing a sparsely distributed concentric ring array, characterized in that: The method comprises: Obtaining array antenna parameters of a concentric circular ring array, wherein the array antenna parameters include the number of circular rings, the minimum array element spacing, and the antenna aperture; An array antenna model is established according to the array antenna parameters, and an optimized peak sidelobe level obtained based on the antenna pattern in the array antenna model is determined as an evaluation target, wherein the array antenna model also includes a radius relationship of a circular ring radius; Generate an initial population based on the radius relationship, the initial population is used to characterize an initial radius group corresponding to a plurality of concentric circular ring arrays, the initial radius group includes all circular ring radii in the concentric circular ring arrays; According to the minimum array element spacing and the initial radius group, weight sparse adjustment and disturbance fine-tuning are performed on the maximum number of array elements corresponding to each of the circular ring radii to obtain an initial array element number group; The circular ring radius of the concentric circular ring array is iteratively updated based on the evaluation target, the initial population, and all initial array element number groups to obtain a target array element number group and a target radius group. The iterative update includes weighted sparse and perturbation fine-tuning of the maximum number of array elements corresponding to each iterative population.

2. The optimization method of the sparse concentric ring array according to claim 1, characterized in that: The weight sparseness and perturbation fine-tuning includes: Determine the maximum number of array elements based on the minimum array element spacing and the radius of the ring; Determine the first number of array elements according to the preset lower limit weight and the maximum number of array elements; Generating an incremental weight based on a preset weight function, and updating the incremental weight according to a preset disturbance variable, wherein the preset disturbance variable is obtained based on a bipolar array and an initial disturbance variable; Determine the second array element number according to the new incremental weight and the maximum array element number; The sum of the first array element quantity and the second array element quantity is determined as the current array element quantity of the circular ring radius.

3. The optimization method of the sparsely distributed concentric ring array according to claim 1, characterized in that: Generating an initial population based on the radius relationship includes: generating a plurality of initial degree of freedom allocation vectors according to the tent mapping; Constraining each of the initial degree of freedom allocation vectors within a degree of freedom solution range to obtain a plurality of array element degree of freedom allocation vectors, wherein the upper limit of the degree of freedom solution range is obtained based on the array antenna parameters; Based on the radius relationship and multiple array element degree of freedom allocation vectors, an initial population is obtained; The radius relationship is used to characterize the relationship between the allocatable degrees of freedom of array elements, the minimum array element spacing, the radius of the ring and the number of the rings.

4. The optimization method of the sparse concentric ring array according to claim 3, characterized in that: Generate multiple initial degree of freedom assignment vectors based on the tent map, including: randomly generating a plurality of first vectors; Take the decimal parts corresponding to twice the first vector respectively to obtain multiple second vectors; Generate multiple random numbers based on a preset interval, where the preset interval is obtained based on the number of the initial population and the maximum number of iterations; A plurality of initial degree of freedom allocation vectors are generated according to each of the second vectors and the corresponding random numbers.

5. The optimization method of the sparse concentric ring array according to any one of claims 1 to 4, characterized in that: Iteratively updating the radius of the concentric circular ring array based on the evaluation target, the initial population, and all initial array element quantity groups, including: Based on the evaluation target and each of the initial array element number groups, the initial fitness of a plurality of initial gray wolf individuals is calculated respectively, and the initial gray wolf individuals with the top three initial fitness are determined as a plurality of leading gray wolf individuals, and the remaining initial gray wolf individuals are determined as a plurality of candidate gray wolf individuals, wherein the initial gray wolf individuals are used to characterize the initial radius group in the initial population; Calculating the current distances between the candidate gray wolf individuals and each of the leading gray wolf individuals respectively, and determining a plurality of current gray wolf positions according to the preset nonlinear convergence factor, the candidate gray wolf individuals and each of the current distances; Based on the weighted sum of each of the current gray wolf positions and the corresponding preset position weights, a next-generation gray wolf individual is obtained, and based on the array antenna parameters, an out-of-bounds correction is performed on the next-generation gray wolf individual to obtain an iterative gray wolf individual, wherein the iterative gray wolf individual also includes each of the leading gray wolf individuals; According to the minimum array element spacing and the iterative radius group corresponding to the iterative gray wolf individual, weight sparse and disturbance fine-tuning are performed on the maximum number of array elements corresponding to each of the ring radii to obtain an iterative array element number group; The iterative fitness of multiple iterative gray wolf individuals is calculated based on the evaluation target, and each of the leading gray wolf individuals is updated according to each of the iterative fitnesses to obtain multiple new leading gray wolf individuals and multiple new candidate gray wolf individuals, so as to update the gray wolf individuals based on the current distance between the new candidate gray wolf individuals and each of the new leading gray wolf individuals until the maximum number of iterations is reached.

6. The optimization method of the sparsely distributed concentric ring array according to claim 5, characterized in that: The determination of the preset position weight includes: Determine half of the difference between the preset maximum weight factor and the preset minimum weight factor as the first weight factor; Determine the product of the first weight factor and an iteration parameter as a second weight factor, wherein the iteration parameter is obtained based on the current number of iterations and the maximum number of iterations; Determine the difference between the preset maximum weight factor and the second weight factor as the preset position weight corresponding to the optimal fitness; Determining the first weight factor as a preset position weight corresponding to a suboptimal fitness; Based on the sum of the preset minimum weight factor and the second weight factor, a preset position weight corresponding to the third fitness is obtained.

7. The optimization method of the sparsely distributed concentric ring array according to claim 5, characterized in that: The method for determining the preset nonlinear convergence factor includes: Where a is the preset nonlinear convergence factor, t is the current iteration number of iterative update, and t max The maximum number of iterations for iterative updates.

8. An optimization device for a sparsely distributed concentric ring array, characterized in that: The device comprises: A parameter acquisition module, used to acquire array antenna parameters of the concentric circular array, wherein the array antenna parameters include the number of circular rings, the minimum array element spacing and the antenna aperture; A model building module, used to build an array antenna model according to the array antenna parameters, and determine the optimized peak sidelobe level obtained based on the antenna pattern in the array antenna model as an evaluation target, wherein the array antenna model also includes a radius relationship of a circular ring radius; A population generation module, used for generating an initial population based on the radius relationship, wherein the initial population is used for characterizing an initial radius group corresponding to a plurality of concentric circular ring arrays, and the initial radius group includes all circular ring radii in the concentric circular ring arrays; A number sparse module, used for performing weight sparse and disturbance fine-tuning on the maximum number of array elements corresponding to each of the circular ring radii according to the minimum array element spacing and the initial radius group, to obtain an initial array element number group; An iterative update module is used to iteratively update the ring radius of the concentric ring array based on the evaluation target, the initial population, and all initial array element number groups to obtain a target array element number group and a target radius group. The iterative update includes weight sparse and perturbation fine-tuning of the maximum number of array elements corresponding to each iterative population.

9. An electronic device, characterized in that: The electronic device comprises: one or more processors; A storage device for storing one or more programs, which, when executed by the one or more processors, enables the electronic device to implement the optimization method for the sparsely distributed concentric ring array as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that: A computer program is stored thereon, and when the computer program is executed by a processor of a computer, the computer is enabled to execute the optimization method for the sparsely distributed concentric circular ring array according to any one of claims 1 to 7.

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