Near-field sparse antenna array layout optimization method and device, equipment and medium

Abstract

The embodiment of the invention provides a near-field sparse antenna array layout optimization method and device, equipment and a medium. The method comprises the following steps: firstly, determining the minimum aperture of a sparse antenna array according to resolution; then determining a transmitting array aperture and a receiving array aperture according to the minimum aperture of the sparse antenna array, the number of transmitting array elements and the number of receiving array elements; further, according to the transmitting array aperture and the receiving array aperture, constructing an optimization problem including a target function and a constraint condition; converting the optimization problem by adopting a mathematical approximation method to obtain a solvable convex optimization problem; and finally, solving the convex optimization problem through a convex optimization solver to obtain an array element position vector of the sparse antenna array. Through the method, the calculation efficiency and accuracy of the array element position of the sparse antenna array are improved.

Description

Technical Field

[0001] This application relates to the field of radar sensing technology, and in particular to a method, apparatus, device and medium for optimizing the layout of a near-field sparse antenna array. Background Technology

[0002] Sparse antenna arrays have been widely used in wireless communication, radar detection, and imaging. In these applications, the radiation pattern performance (main lobe width and side lobe level) of the antenna array directly affects the system's anti-jamming capability, target resolution accuracy, and energy consumption. While traditional uniform linear arrays (ULAs) can achieve controllable main lobe pointing, they require a large number of elements to meet high-resolution requirements, leading to a significant increase in hardware cost, power consumption, and complexity. Sparse antenna arrays reduce the number of elements through non-uniform arrangement, but sparsification can easily lead to increased side lobe or grating lobe levels, resulting in performance degradation in complex electromagnetic environments. Therefore, there is an urgent need for an efficient, low-side-lobe sparse array layout method.

[0003] In existing technologies, sparse antenna array layout optimization methods are generally based on swarm intelligence optimization algorithms. The basic idea is to update the position or switching state of antenna elements in continuous iteration by simulating the collaborative search and evolution mechanism of individuals in the group, so as to simultaneously satisfy objectives such as sidelobe suppression, beamforming and array sparsity.

[0004] However, existing sparse antenna array layout optimization methods are computationally complex, prone to getting trapped in local optima, and have low computational efficiency. Summary of the Invention

[0005] This application provides a method, apparatus, device, and medium for optimizing the layout of a near-field sparse antenna array, in order to solve the problems of high computational complexity, easy getting trapped in local optima, and low computational efficiency in the prior art.

[0006] In a first aspect, embodiments of this application provide a method for optimizing the layout of a near-field sparse antenna array, including:

[0007] Determine the minimum aperture of the sparse antenna array based on the resolution;

[0008] The aperture of the transmitting array and the aperture of the receiving array are determined based on the minimum aperture of the sparse antenna array, the number of transmitting elements, and the number of receiving elements.

[0009] Based on the transmit array aperture and the receive array aperture, an optimization problem is constructed that includes an objective function and constraints. The objective function is used to characterize the sidelobe level of the antenna array.

[0010] The optimization problem is transformed using mathematical approximation methods to obtain a solvable convex optimization problem;

[0011] The convex optimization problem is solved by a convex optimization solver to obtain the element position vectors of the sparse antenna array.

[0012] In one possible implementation, determining the transmit array aperture and the receive array aperture based on the minimum aperture of the sparse antenna array, the number of transmit elements, and the number of receive elements includes:

[0013] Based on the minimum aperture of the sparse antenna array, the number of transmitting elements, and the number of receiving elements, the initial transmitting array aperture and the initial receiving array aperture are calculated.

[0014] The initial transmit array aperture and the initial receive array aperture are rounded down to determine the transmit array aperture and the receive array aperture.

[0015] In one possible implementation, constructing an optimization problem containing an objective function and constraints based on the transmit array aperture and the receive array aperture includes:

[0016] Based on the aperture of the transmitting array and the aperture of the receiving array, the position vector method for the transmitting antenna element and the position vector of the receiving antenna element are determined.

[0017] Based on the position vectors of the transmitting antenna array elements and the receiving antenna array elements, the point target response function of the antenna array is determined;

[0018] The objective function is established with minimizing the maximum sidelobe level of the point target response function as the optimization objective.

[0019] The constraints are constructed based on the spacing between adjacent transmitting antenna elements, the spacing between adjacent receiving antenna elements, the number of transmitting and receiving antenna elements, and the arrangement area of ​​the transmitting and receiving antenna elements.

[0020] In one possible implementation, the transformation of the optimization problem using mathematical approximation methods to obtain a solvable convex optimization problem includes:

[0021] By using slack variables, the optimization problem is transformed into a non-convex optimization problem with sidelobe level constraints;

[0022] The sidelobe level constraint is approximated by using second-order Taylor expansion and continuous convex approximation techniques, so that the sidelobe level constraint is transformed into a convex constraint based on the position vectors of the transmit antenna array elements and the receive antenna array elements.

[0023] Based on the convex constraints and the constraint conditions, a solvable convex optimization problem is obtained.

[0024] In one possible implementation, solving the convex optimization problem using a convex optimization solver to obtain the element position vectors of the sparse antenna array includes:

[0025] Step a: Set the initial receiving antenna element position vector to a fixed value, and construct the first convex optimization subproblem using the transmitting antenna element position vector as the optimization variable;

[0026] Step b: Solve the first convex optimization subproblem using a convex optimization solver to obtain the updated transmit antenna array element position vector;

[0027] Step c: Set the updated transmit antenna element position vector to a fixed value, and construct a second convex optimization subproblem using the receive antenna element position vector as the optimization variable;

[0028] Step d: Solve the second convex optimization subproblem using a convex optimization solver to obtain the updated receiving antenna array element position vector;

[0029] Iteratively execute steps a to d until a preset convergence condition is met, and then determine the updated transmit antenna element position vector and the updated receive antenna element position vector as the element position vectors of the sparse antenna array.

[0030] In one possible implementation, the preset convergence condition is: in two adjacent iterations, the norm of the difference between the updated transmit antenna element position vector and the transmit antenna element position vector of the previous iteration, and the norm of the difference between the updated receive antenna element position vector and the receive antenna element position vector of the previous iteration are both less than a preset threshold, or the number of iterations reaches the maximum number of iterations.

[0031] In one possible implementation, before determining the updated transmit antenna element position vector and the updated receive antenna element position vector as the element position vectors of the sparse antenna array, the method further includes:

[0032] Step e: Determine whether the first spacing between any adjacent transmit antenna element positions in the updated transmit antenna element position vector is an integer multiple of half a wavelength, and determine whether the second spacing between any adjacent receive antenna element positions in the updated receive antenna element position vector is an integer multiple of half a wavelength.

[0033] Step f: For spacings that do not meet the half-wavelength integer multiple constraint, adjust the positions of the transmitting antenna elements and / or receiving antenna elements corresponding to the spacing to the nearest half-wavelength integer multiple position.

[0034] Step g: Determine whether the minimum spacing between adjacent antenna array elements satisfies the constraint conditions;

[0035] Step h: If the conditions are met, accept the position adjustment; otherwise, reject the position adjustment.

[0036] Repeat steps e to h until the position vectors in the updated transmit antenna element position vector and the updated receive antenna element position vector no longer undergo new position adjustments.

[0037] Secondly, embodiments of this application provide a near-field sparse antenna array layout optimization device, comprising:

[0038] The first determining module is used to determine the minimum aperture of the sparse antenna array based on the resolution.

[0039] The second determining module is used to determine the aperture of the transmitting array and the aperture of the receiving array based on the minimum aperture of the sparse antenna array, the number of transmitting elements, and the number of receiving elements.

[0040] The construction module is used to construct an optimization problem containing an objective function and constraints based on the transmit array aperture and the receive array aperture, wherein the objective function is used to characterize the sidelobe level of the antenna array;

[0041] The processing module is used to transform the optimization problem using mathematical approximation methods to obtain a solvable convex optimization problem;

[0042] The solution module is used to solve the convex optimization problem through a convex optimization solver to obtain the element position vectors of the sparse antenna array.

[0043] In one possible implementation, the second determining module is specifically used for:

[0044] Based on the minimum aperture of the sparse antenna array, the number of transmitting elements, and the number of receiving elements, the initial transmitting array aperture and the initial receiving array aperture are calculated.

[0045] The initial transmit array aperture and the initial receive array aperture are rounded down to determine the transmit array aperture and the receive array aperture.

[0046] In one possible implementation, the building module is specifically used for:

[0047] Based on the aperture of the transmitting array and the aperture of the receiving array, the position vector method for the transmitting antenna element and the position vector of the receiving antenna element are determined.

[0048] Based on the position vectors of the transmitting antenna array elements and the receiving antenna array elements, the point target response function of the antenna array is determined;

[0049] The objective function is established with minimizing the maximum sidelobe level of the point target response function as the optimization objective.

[0050] The constraints are constructed based on the spacing between adjacent transmitting antenna elements, the spacing between adjacent receiving antenna elements, the number of transmitting and receiving antenna elements, and the arrangement area of ​​the transmitting and receiving antenna elements.

[0051] In one possible implementation, the processing module is specifically used for:

[0052] By using slack variables, the optimization problem is transformed into a non-convex optimization problem with sidelobe level constraints;

[0053] The sidelobe level constraint is approximated by using second-order Taylor expansion and continuous convex approximation techniques, so that the sidelobe level constraint is transformed into a convex constraint based on the position vectors of the transmit antenna array elements and the receive antenna array elements.

[0054] Based on the convex constraints and the constraint conditions, a solvable convex optimization problem is obtained.

[0055] In one possible implementation, the solving module is specifically used for:

[0056] Step a: Set the initial receiving antenna element position vector to a fixed value, and construct the first convex optimization subproblem using the transmitting antenna element position vector as the optimization variable;

[0057] Step b: Solve the first convex optimization subproblem using a convex optimization solver to obtain the updated transmit antenna array element position vector;

[0058] Step c: Set the updated transmit antenna element position vector to a fixed value, and construct a second convex optimization subproblem using the receive antenna element position vector as the optimization variable;

[0059] Step d: Solve the second convex optimization subproblem using a convex optimization solver to obtain the updated receiving antenna array element position vector;

[0060] Iteratively execute steps a to d until a preset convergence condition is met, and then determine the updated transmit antenna element position vector and the updated receive antenna element position vector as the element position vectors of the sparse antenna array.

[0061] In one possible implementation, the preset convergence condition is: in two adjacent iterations, the norm of the difference between the updated transmit antenna element position vector and the transmit antenna element position vector of the previous iteration, and the norm of the difference between the updated receive antenna element position vector and the receive antenna element position vector of the previous iteration are both less than a preset threshold, or the number of iterations reaches the maximum number of iterations.

[0062] In one possible implementation, the near-field sparse antenna array layout optimization device further includes an adjustment module, which, before determining the updated transmit antenna element position vector and the updated receive antenna element position vector as the element position vectors of the sparse antenna array, is configured to:

[0063] Step e: Determine whether the first spacing between any adjacent transmit antenna element positions in the updated transmit antenna element position vector is an integer multiple of half a wavelength, and determine whether the second spacing between any adjacent receive antenna element positions in the updated receive antenna element position vector is an integer multiple of half a wavelength.

[0064] Step f: For spacings that do not meet the half-wavelength integer multiple constraint, adjust the positions of the transmitting antenna elements and / or receiving antenna elements corresponding to the spacing to the nearest half-wavelength integer multiple position.

[0065] Step g: Determine whether the minimum spacing between adjacent antenna array elements satisfies the constraint conditions;

[0066] Step h: If the conditions are met, accept the position adjustment; otherwise, reject the position adjustment.

[0067] Repeat steps e to h until the position vectors in the updated transmit antenna element position vector and the updated receive antenna element position vector no longer undergo new position adjustments.

[0068] Thirdly, embodiments of this application provide an electronic device, including: a memory and a processor;

[0069] The memory stores computer-executed instructions;

[0070] The processor executes computer execution instructions stored in the memory, causing the processor to perform the first aspect and / or various possible implementations of the first aspect as described above.

[0071] Fourthly, embodiments of this application provide a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the first aspect and / or various possible implementations of the first aspect.

[0072] The near-field sparse antenna array layout optimization method, apparatus, device, and medium provided in this application first determine the minimum aperture of the sparse antenna array based on resolution to ensure that the array's range resolution meets requirements, providing basic physical parameters for subsequent determination of array element positions. Then, combining the minimum aperture, the number of transmitting elements, and the number of receiving elements, the transmitting array aperture and receiving array aperture are determined, achieving a reasonable allocation of the overall array size, satisfying both resolution requirements and considering array sparsity and practical manufacturing feasibility. Further, an optimization problem containing objective functions and constraints is constructed based on the transmitting and receiving array apertures, providing a clear mathematical model for optimization. Subsequently, a mathematical approximation method is used to transform the optimization problem. By introducing relaxation variables, second-order Taylor expansion, and continuous convex approximation techniques, the originally highly non-convex sidelobe level constraints are transformed into convex constraints regarding the positions of transmitting and receiving elements, allowing the problem to be solved using existing convex optimization methods, reducing computational complexity and improving solution stability. Finally, a convex optimization solver is used to solve the transformed convex optimization problem, obtaining the sparse antenna array element position vector that meets performance indicators. Attached Figure Description

[0073] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0074] Figure 1 A flowchart illustrating the near-field sparse antenna array layout optimization method provided in this application embodiment. Figure 1 ;

[0075] Figure 2 A flowchart illustrating the near-field sparse antenna array layout optimization method provided in this application embodiment. Figure 2 ;

[0076] Figure 3 A schematic diagram of the near-field sparse antenna array layout optimization device provided in the embodiments of this application;

[0077] Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application.

[0078] The accompanying drawings illustrate specific embodiments of this application, which will be described in more detail below. These drawings and descriptions are not intended to limit the scope of the concept in any way, but rather to illustrate the concept of this application to those skilled in the art through reference to particular embodiments. Detailed Implementation

[0079] Exemplary embodiments will now be described in detail, examples of which are illustrated in the accompanying drawings. When the following description relates to the drawings, unless otherwise indicated, the same numbers in different drawings denote the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this application. Rather, they are merely examples of apparatuses and methods consistent with some aspects of this application as detailed in the appended claims.

[0080] Sparse antenna arrays have been widely used in wireless communication, radar detection, and imaging. In these applications, the radiation pattern performance of the antenna array directly determines the system's anti-jamming capability and target resolution accuracy. Traditional uniform linear arrays, by arranging antenna elements at equal intervals, can achieve controllable main lobe pointing. However, to achieve a narrow main lobe and improve resolution, a large number of antenna elements are required, which significantly increases the number of RF channels and system power consumption. Sparse antenna array technology can achieve a narrow main lobe and reduce the number of required antenna elements through non-uniformly distributed antenna elements, thereby reducing hardware complexity. However, as the sparsity of the antenna array increases, the sidelobe or grating lobe levels of the antenna array increase, leading to a severe degradation in system performance under complex electromagnetic interference environments. Therefore, there is an urgent need for an efficient, low-sidelobe sparse array layout method.

[0081] In existing technologies, sparse antenna array layout optimization methods are generally based on swarm intelligence optimization algorithms, such as genetic algorithms and simulated annealing algorithms. The basic idea of ​​these algorithms is to update the position or on / off state of antenna elements in continuous iterations by simulating the cooperative search and evolution mechanism of individuals in a swarm, so as to simultaneously satisfy objectives such as sidelobe suppression, beamforming, and array sparsity.

[0082] However, existing sparse antenna array layout optimization methods have a huge search space in high-dimensional sparse array optimization problems. Swarm intelligence algorithms often require a large number of iterations and individual evaluations, resulting in high computational overhead and slow convergence speed. Furthermore, premature convergence may occur during the swarm search process, causing the optimization results to remain at a suboptimal solution and making it difficult to further improve.

[0083] Based on this, this application proposes a near-field sparse antenna array layout optimization method. Addressing the issues of high computational complexity and low iterative efficiency in solving sparse antenna array layout optimization problems using swarm intelligence algorithms, the inventors conceived of transforming the originally highly non-convex, globally search-required maximum sidelobe level optimization problem into a convex optimization problem that can be approximated. This would avoid the large-scale random search and complex iterations of swarm intelligence algorithms. Specifically: First, relaxation variables are introduced to explicitly define the maximum sidelobe level constraint; then, second-order Taylor expansion and continuous convex approximation techniques are used to transform the non-convex constraint into a convex constraint. Through this mathematical approximation, the problem is transformed into a form that can be efficiently processed by a convex optimization solver, thereby significantly reducing the computational load and improving the solution efficiency while maintaining array resolution and sidelobe performance. This method achieves the optimization goal of sparse antenna array element layout and solves the problems of high computational cost and slow convergence speed of traditional swarm intelligence algorithms in large-scale array layouts.

[0084] The technical solution of this application and how the technical solution of this application solves the above-mentioned technical problems are described in detail below with specific embodiments. These specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of this application will now be described with reference to the accompanying drawings.

[0085] Figure 1 A flowchart illustrating the near-field sparse antenna array layout optimization method provided in this application embodiment. Figure 1 ;like Figure 1 As shown, the method includes:

[0086] S101. Determine the minimum aperture of the sparse antenna array based on the resolution.

[0087] It should be noted that, based on the physical relationship between resolution and equivalent aperture, this application converts the resolution specification into a lower limit for the minimum aperture of a sparse antenna array, assuming that the range resolution must reach a certain level. Therefore, according to the resolution calculation formula, the minimum aperture of the sparse antenna array that meets the resolution requirements is:

[0088]

[0089] in, It is the carrier wavelength. For the direction where resolution is required.

[0090] Understandably, this approach provides a physical lower limit for the entire layout design, ensuring that the distance / angle resolution requirements are met even in the worst-case scenario. At the same time, it reduces the design space from unbounded to a controllable range with a clear physical scale, laying the foundation for subsequent aperture allocation and optimization and reducing the ineffective search space.

[0091] S102. Determine the aperture of the transmitting array and the aperture of the receiving array based on the minimum aperture of the sparse antenna array, the number of transmitting elements, and the number of receiving elements.

[0092] In one possible approach, the initial transmit array aperture and the initial receive array aperture are first calculated based on the minimum aperture of the sparse antenna array, the number of transmit array elements, and the number of receive array elements; then, the initial transmit array aperture and the initial receive array aperture are rounded down to determine the transmit array aperture and the receive array aperture.

[0093] It should be understood that, based on the proportion of the number of transmitting array elements M and the number of receiving array elements N, the minimum aperture of the sparse antenna array is allocated to the initial transmitting array aperture and the initial receiving array aperture. Furthermore, to facilitate actual antenna array fabrication and production, the initial transmitting array aperture and the initial receiving array aperture need to be rounded to ensure they are integer multiples of half the wavelength, thus ultimately determining the transmitting array aperture and the receiving array aperture. Specifically:

[0094] Given the number of transmitting array elements M and the number of receiving array elements N, then the transmitting array aperture and the receiving array aperture are:

[0095] ;

[0096] Where M is the number of transmitting array elements; N is the number of receiving array elements; The aperture of the transmitting array; For the receiver array aperture; This indicates rounding up to the nearest integer.

[0097] Understandably, this approach ensures that the sum of the transmit and receive array apertures of the sparse antenna array is close to the minimum required aperture, thereby achieving the predetermined range resolution target. On the other hand, by rounding the aperture to an integer multiple of half the wavelength, it ensures that the array is feasible in physical manufacturing and installation, while reducing the cumulative effect of phase error, thus guaranteeing the beamforming accuracy and sidelobe suppression performance of the array in actual operation.

[0098] S103. Based on the aperture of the transmitting array and the aperture of the receiving array, construct an optimization problem that includes the objective function and constraints.

[0099] The objective function is used to characterize the sidelobe level of the antenna array.

[0100] In one feasible approach, firstly, the position vectors of the transmitting and receiving antenna elements are determined based on the apertures of the transmitting and receiving arrays. Then, based on these position vectors, the point target response function of the antenna array is determined. Next, an objective function is established with the goal of minimizing the maximum sidelobe level of the point target response function. Finally, constraints are constructed based on the spacing between adjacent transmitting and receiving antenna elements, the number of transmitting and receiving antenna elements, and the arrangement area of ​​the transmitting and receiving antenna elements.

[0101] It should be understood that, firstly, based on the apertures of the transmitting and receiving arrays, the positions of the transmitting and receiving antenna elements are represented in vector form. This clearly describes the specific location of each antenna element within the array. Then, these position vectors are used to calculate the point target response function of the entire array, which can be understood as the array's imaging capability of a target in different directions, reflecting the array's beamforming and sidelobe characteristics. Next, the maximum sidelobe level in the point target response function is used as the optimization target. That is, by adjusting the positions of the array elements, the array is made to minimize sidelobes while maintaining imaging resolution, thereby reducing the impact of interference and false targets.

[0102] Furthermore, when constructing constraints, it is necessary to consider the minimum spacing between array elements, the number of antennas in the array, and the range within which transmitting and receiving array elements can be arranged. This ensures that the elements are not too close together, which could lead to coupling effects or manufacturing difficulties, while also ensuring that the array size and distribution meet the requirements of actual processing and installation. Through this objective function and constraint, both the imaging accuracy and anti-interference performance of the antenna array can be guaranteed, and the final arrangement result can be made feasible.

[0103] Specifically, the position of the transmitting antenna array element can be represented as... The position of the receiving antenna array element can be represented as To satisfy the minimum aperture condition for a sparse antenna array, the position of the first transmitting antenna element is set at the origin, i.e. Position the terminal transmitting antenna array elements The position of the first receiving antenna element is set at the origin, that is... Position the antenna of the end receiving array element Therefore, the next step only requires setting the middle of the transmitting antenna array. Individual elements and receiving antenna array The positions of each array element are designed to meet the requirements for low sidelobe levels.

[0104] Based on the positions of the transmitting and receiving antenna elements, the point target response function of the antenna array can be determined as follows:

[0105]

[0106] In the formula, These are position coordinate variables. Therefore, the maximum sidelobe level of the antenna array can be expressed as:

[0107]

[0108] in, This refers to the sidelobe region of the antenna array.

[0109] To minimize the maximum sidelobe level of the antenna array by arranging the antenna elements, an optimization problem with constraints and an objective function is constructed based on the spacing between adjacent transmit antenna elements, the spacing between adjacent receive antenna elements, the number of transmit and receive antenna elements, and the arrangement area of ​​the transmit and receive antenna elements.

[0110]

[0111] In the formula, constraints C1 and C2 represent the constraints on the size of the arrangement area of ​​the transmitting antenna array elements and the receiving antenna array elements, respectively. Constraints C3 and C4 represent the constraints on the distance between adjacent antennas to avoid inter-antenna coupling characteristics, which must not be less than the minimum allowable distance. .

[0112] S104. The optimization problem is transformed using mathematical approximation methods to obtain a solvable convex optimization problem.

[0113] In one feasible approach, firstly, by using slack variables, the optimization problem is transformed into a non-convex optimization problem containing sidelobe level constraints; then, the sidelobe level constraints are approximated using second-order Taylor expansion and continuous convex approximation techniques, so that the sidelobe level constraints are transformed into convex constraints based on the position vectors of the transmit antenna elements and the receive antenna elements; finally, based on the convex constraints and constraint conditions, a solvable convex optimization problem is obtained.

[0114] It should be understood that since the optimization problem established in S103 is a highly non-convex optimization problem, it is difficult to solve directly using existing methods. Therefore, it is necessary to transform the optimization problem into a solvable convex optimization problem. Specifically, firstly, a relaxation variable is introduced to transform the complex optimization objective into a non-convex problem with sidelobe level constraints, which can more clearly characterize the constraints on array performance. Next, using second-order Taylor expansion and continuous convex approximation, the originally very complex, non-convex sidelobe constraints are approximated as convex constraints, that is, the difficult-to-solve surface problem is replaced by an easily handled convex surface. Finally, the obtained convex constraints are combined with the previous basic conditions to form a problem that can be directly solved using convex optimization methods.

[0115] Specifically, introduce slack variables The optimization problem in S103 can be equivalently transformed into the following optimization problem:

[0116]

[0117] In the formula, C1 and C2 constraints represent the constraints on the size of the arrangement area of ​​the transmitting antenna array elements and the receiving antenna array elements, respectively; C3 and C4 constraints represent that in order to avoid the coupling characteristics between antennas, the distance between adjacent antennas must not be less than the minimum allowable distance; C5 is the introduced sidelobe level constraint.

[0118] However, since the C5 constraint in the above problem is a highly non-convex constraint, the optimization problem remains a non-convex optimization problem, which is difficult to solve directly using existing methods. Therefore, this application's embodiment uses second-order Taylor expansion and continuous convex approximation techniques to approximate the sidelobe level constraint, transforming it into a convex constraint based on the position vectors of the transmit and receive antenna elements. Specifically:

[0119] Firstly, further expanding the left side of constraint C5, we have:

[0120]

[0121] Because the above formula contains The function term is a highly nonconvex function, therefore at the point... and to , Using the second-order Taylor approximation, we have the following formula:

[0122]

[0123] Because for any The function has And any The function has ,so , The upper bound functions can be expressed as follows:

[0124]

[0125]

[0126] Therefore, constraint C5 can be restated as follows:

[0127] Based on the new C5 constraint formula, the corresponding convex optimization problem is:

[0128]

[0129] Understandably, this method transforms a non-convex problem that originally required extensive iterations and random searches using swarm intelligence algorithms to find an approximate solution into a convex problem that can be solved efficiently, greatly reducing computational complexity. On the other hand, the approximation process in the embodiment ensures solution efficiency while also preserving key performance indicators in the array design, making the final solution both reasonable and close to optimal, thus improving the accuracy of the solution.

[0130] S105. Solve the convex optimization problem using a convex optimization solver to obtain the element position vectors of the sparse antenna array.

[0131] The near-field sparse antenna array layout optimization method provided in this application first determines the minimum aperture of the sparse antenna array based on the resolution, ensuring that the array's range resolution meets the requirements and providing basic physical parameters for subsequent determination of array element positions. Then, combining the minimum aperture, the number of transmitting array elements, and the number of receiving array elements, the transmitting array aperture and the receiving array aperture are determined, achieving a reasonable allocation of the overall array size, satisfying both resolution requirements and considering array sparsity and practical manufacturing feasibility. Further, an optimization problem containing objective functions and constraints is constructed based on the transmitting array aperture and the receiving array aperture, providing a clear mathematical model for optimization solution. Subsequently, a mathematical approximation method is used to transform the optimization problem. By introducing relaxation variables, second-order Taylor expansion, and continuous convex approximation techniques, the originally highly non-convex sidelobe level constraints are transformed into convex constraints regarding the positions of transmitting and receiving array elements, making the problem solvable by existing convex optimization methods, reducing computational complexity and improving solution stability. Finally, a convex optimization solver is used to solve the transformed convex optimization problem to obtain the sparse antenna array element position vector that meets the performance indicators.

[0132] Figure 2A flowchart illustrating the near-field sparse antenna array layout optimization method provided in this application embodiment. Figure 2 ,like Figure 2 As shown, in this embodiment... Figure 2 Based on the examples, the process of solving convex optimization problems using a convex optimization solver is described in detail. The method includes:

[0133] S201. Set the initial position vector of the receiving antenna array element to a fixed value, and construct the first convex optimization subproblem using the position vector of the transmitting antenna array element as the optimization variable.

[0134] It should be understood that by breaking down the complex problem that originally involved both transmitting and receiving elements, each optimization only processes a subset of variables, thus simplifying the solution process. That is, the initial position vector of the receiving antenna elements is set to a fixed value, while only the position of the transmitting antenna elements can be adjusted, and then a convex optimization problem is established for the transmitting elements.

[0135] Specifically, in the (i+1)th iteration, given the position vector of the transmit antenna array elements obtained in the ith iteration... and the position vector of the receiving antenna array element (i.e., the initial position vector of the receiving antenna elements), and then using the position vector of the transmitting antenna elements as the optimization variable, the first convex optimization subproblem is defined as:

[0136]

[0137] In the formula, C1 represents the constraint on the size of the area where the transmitting antenna elements are arranged, and C3 represents the minimum allowable distance between adjacent transmitting antennas to avoid inter-antenna coupling. ; The objective function is for convex optimization.

[0138] S202. Solve the first convex optimization subproblem using a convex optimization solver to obtain the updated transmit antenna array element position vector.

[0139] It is understandable that an optimized set of transmit element positions is obtained by solving a convex optimization solver, so that the sidelobe level is as low as possible when the receive element is fixed.

[0140] S203. Set the updated transmit antenna element position vector to a fixed value, and construct the second convex optimization subproblem using the receive antenna element position vector as the optimization variable.

[0141] It should be understood that in this embodiment, the updated transmit antenna element position vector is set to a fixed value, and only the position of the receive antenna element can be adjusted. Then, a convex optimization problem is established for the receive element.

[0142] Specifically, the updated positions of the transmit antenna elements obtained in the (i+1)th iteration Given the positions of the receiving antenna elements obtained in the i-th iteration Using the position vectors of the receiving antenna array elements as optimization variables, a second convex optimization subproblem is constructed:

[0143]

[0144] S204. Solve the second convex optimization subproblem using a convex optimization solver to obtain the updated receiving antenna array element position vector.

[0145] Understandably, the updated receiver element positions are obtained by solving the second convex optimization subproblem using a convex optimization solver. In this way, both the transmitter and receiver element positions undergo an iterative optimization round, with each round progressively reducing the array's maximum sidelobe level.

[0146] S205. Iterate through S201 to S204 until the preset convergence condition is met, and determine the updated transmit antenna element position vector and the updated receive antenna element position vector as the element position vector of the sparse antenna array.

[0147] In one possible implementation, the preset convergence condition is: in two adjacent iterations, the norm of the difference between the updated transmit antenna element position vector and the transmit antenna element position vector of the previous iteration, and the norm of the difference between the updated receive antenna element position vector and the receive antenna element position vector of the previous iteration are both less than a preset threshold, or the number of iterations reaches the maximum number of iterations.

[0148] It should be understood that by continuously and alternately optimizing the positions of the transmit and receive antenna elements, the sidelobe performance of the entire array is gradually improved until the optimization result stabilizes. Specifically, each iteration updates the positions of the transmit and receive elements and compares the new position vectors with those of the previous iteration. If the changes in the transmit and receive element position vectors are very small in two consecutive iterations (i.e., the norm of the difference is below a set threshold), it indicates that the optimization has basically stabilized and no longer produces significant improvements. In addition, the number of iterations reaches a set maximum value to prevent the algorithm from running for an extended period. Once either condition is met, the current transmit and receive element position vectors are determined as the final sparse antenna array element position vectors.

[0149] Understandably, this approach ensures that the iterative optimization process has ample opportunity to improve array performance while avoiding unnecessary redundant calculations, resulting in an array layout that is close to optimal in terms of sidelobe control and resolution.

[0150] It should also be noted that, to facilitate the actual production and manufacturing of sparse antenna linear arrays, before determining the updated transmit antenna element position vectors and receive antenna element position vectors as the element position vectors of the sparse antenna array, it is necessary to adjust the obtained transmit antenna element positions and receive antenna element positions to ensure that as many transmit antenna element positions and receive antenna element positions as possible satisfy the half-wavelength integer multiple constraint. Specifically:

[0151] First, determine whether the first spacing between any adjacent transmit antenna element positions in the updated transmit antenna element position vector is an integer multiple of half the wavelength, and determine whether the second spacing between any adjacent receive antenna element positions in the updated receive antenna element position vector is an integer multiple of half the wavelength. Then, for spacings that do not meet the half-wavelength integer multiple constraint, adjust the transmit antenna element position and / or receive antenna element position corresponding to the spacing to the nearest half-wavelength integer multiple position. Further, determine whether the minimum spacing between adjacent antenna elements meets the constraint condition. Then, if it meets the constraint condition, accept the position adjustment; if it does not meet the constraint condition, reject the position adjustment. Finally, repeat the above method until the position vectors in the updated transmit antenna element position vector and the updated receive antenna element position vector no longer undergo new position adjustments.

[0152] It should be understood that the main purpose of this embodiment is to make the final array element positions easier to achieve in actual production and manufacturing, while maintaining array performance. Specifically, it first checks whether the spacing between any adjacent elements in the updated transmitting and receiving arrays is an integer multiple of half a wavelength. This ensures the phase relationship and manufacturing accuracy between the elements. For element spacing that does not meet this constraint, the corresponding element positions are adjusted to the nearest integer multiple of half a wavelength.

[0153] In addition, after adjustment, it is necessary to check again whether the minimum spacing requirement is met between adjacent array elements to prevent array elements from being too close, which could lead to coupling or installation difficulties. If the constraint is met, the position adjustment is accepted; otherwise, the adjustment is rejected. This process is repeated until the positions of all array elements no longer require adjustment.

[0154] Understandably, this approach ensures the feasibility of the array in engineering processing and installation, improving manufacturing precision and stability. On the other hand, it maintains the array's design performance as much as possible, including sidelobe suppression and resolution, so that the final array element positions meet both physical manufacturing requirements and are close to the optimized design goals.

[0155] Figure 3 This is a schematic diagram of the near-field sparse antenna array layout optimization device provided in the embodiments of this application; as shown below. Figure 3 As shown, the device includes:

[0156] The first determining module 301 is used to determine the minimum aperture of the sparse antenna array based on the resolution.

[0157] The second determining module 302 is used to determine the aperture of the transmitting array and the aperture of the receiving array based on the minimum aperture of the sparse antenna array, the number of transmitting elements, and the number of receiving elements.

[0158] The construction module 303 is used to construct an optimization problem containing an objective function and constraints based on the aperture of the transmitting array and the aperture of the receiving array. The objective function is used to characterize the sidelobe level of the antenna array.

[0159] Processing module 304 is used to transform the optimization problem using mathematical approximation methods to obtain a solvable convex optimization problem;

[0160] The solver module 305 is used to solve convex optimization problems through a convex optimization solver to obtain the element position vectors of the sparse antenna array.

[0161] In one possible implementation, the second determining module 302 is specifically used for:

[0162] The initial transmit array aperture and the initial receive array aperture are calculated based on the minimum aperture of the sparse antenna array, the number of transmit elements, and the number of receive elements.

[0163] The initial transmit array aperture and the initial receive array aperture are rounded down to determine the transmit array aperture and the receive array aperture.

[0164] In one possible implementation, the construction module 303 is specifically used for:

[0165] The position vector method for the transmitting antenna elements and the position vector of the receiving antenna elements are determined based on the aperture of the transmitting array and the aperture of the receiving array.

[0166] The point target response function of the antenna array is determined based on the position vectors of the transmitting antenna array elements and the receiving antenna array elements.

[0167] The objective function is established with minimizing the maximum sidelobe level of the point target response function as the optimization objective.

[0168] Constraints are constructed based on the spacing between adjacent transmitting antenna elements, the spacing between adjacent receiving antenna elements, the number of transmitting and receiving antenna elements, and the arrangement area of ​​the transmitting and receiving antenna elements.

[0169] In one possible implementation, the processing module 304 is specifically used for:

[0170] By using slack variables, the optimization problem is transformed into a non-convex optimization problem with sidelobe level constraints;

[0171] The sidelobe level constraint is approximated by using second-order Taylor expansion and continuous convex approximation techniques, so that the sidelobe level constraint is transformed into a convex constraint based on the position vectors of the transmit antenna array elements and the position vectors of the receive antenna array elements.

[0172] Based on the convex constraints and constraints, a solvable convex optimization problem is obtained.

[0173] In one possible implementation, the solver module 305 is specifically used for:

[0174] Step a: Set the initial receiving antenna element position vector to a fixed value, and construct the first convex optimization subproblem using the transmitting antenna element position vector as the optimization variable;

[0175] Step b: Solve the first convex optimization subproblem using a convex optimization solver to obtain the updated transmit antenna array element position vector;

[0176] Step c: Set the updated transmit antenna element position vector to a fixed value, and construct the second convex optimization subproblem using the receive antenna element position vector as the optimization variable;

[0177] Step d: Solve the second convex optimization subproblem using a convex optimization solver to obtain the updated receiving antenna array element position vector;

[0178] Iteratively execute steps a to d until the preset convergence condition is met, and determine the updated transmit antenna element position vector and the updated receive antenna element position vector as the element position vector of the sparse antenna array.

[0179] In one possible implementation, the preset convergence condition is: in two adjacent iterations, the norm of the difference between the updated transmit antenna element position vector and the transmit antenna element position vector of the previous iteration, and the norm of the difference between the updated receive antenna element position vector and the receive antenna element position vector of the previous iteration are both less than a preset threshold, or the number of iterations reaches the maximum number of iterations.

[0180] In one possible implementation, the near-field sparse antenna array layout optimization device further includes an adjustment module, which, before determining the updated transmit antenna element position vectors and the updated receive antenna element position vectors as the element position vectors of the sparse antenna array, is configured to:

[0181] Step e: Determine whether the first spacing between any adjacent transmit antenna element positions in the updated transmit antenna element position vector is an integer multiple of half a wavelength, and determine whether the second spacing between any adjacent receive antenna element positions in the updated receive antenna element position vector is an integer multiple of half a wavelength.

[0182] Step f: For spacing that does not meet the half-wavelength integer multiple constraint, adjust the position of the transmitting antenna element and / or the receiving antenna element corresponding to the spacing to the nearest half-wavelength integer multiple position.

[0183] Step g: Determine whether the minimum spacing between adjacent antenna array elements satisfies the constraint conditions;

[0184] Step h: If the conditions are met, accept the position adjustment; otherwise, reject the position adjustment.

[0185] Repeat steps e to h until the position vectors in the updated transmit antenna element position vector and the updated receive antenna element position vector no longer undergo new position adjustments.

[0186] The near-field sparse antenna array layout optimization device provided in this application embodiment can execute the method provided in the above method embodiment. Its implementation principle and technical effect are similar, and will not be described in detail here.

[0187] Figure 4 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Figure 4 As shown, the electronic device 40 provided in this embodiment includes at least one processor 401 and a memory 402. Optionally, the device 40 further includes a communication component 403. The processor 401, memory 402, and communication component 403 are connected via a bus 404.

[0188] In a specific implementation, at least one processor 401 executes computer execution instructions stored in memory 402, causing at least one processor 401 to perform the above-described method.

[0189] The specific implementation process of processor 401 can be found in the above method embodiments, and its implementation principle and technical effect are similar. It will not be repeated here.

[0190] In the above embodiments, it should be understood that the processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), etc. The general-purpose processor can be a microprocessor or any conventional processor. The steps of the method disclosed in this invention can be directly implemented by a hardware processor, or implemented by a combination of hardware and software modules within the processor.

[0191] The memory may include random access memory (RAM) and may also include non-volatile memory (NVM), such as at least one disk storage device.

[0192] The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, the buses shown in the accompanying drawings are not limited to a single bus or a single type of bus.

[0193] This application also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, implement the above-described method.

[0194] The aforementioned readable storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as static random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The readable storage medium can be any available medium accessible to a general-purpose or special-purpose computer.

[0195] An exemplary readable storage medium is coupled to a processor, enabling the processor to read information from and write information to the readable storage medium. Of course, the readable storage medium can also be a component of the processor. The processor and the readable storage medium can reside in an Application Specific Integrated Circuit (ASIC). Alternatively, the processor and the readable storage medium can exist as discrete components in the device.

[0196] The division of units is merely a logical functional division; in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be indirect coupling or communication connection through some interfaces, devices, or units, and may be electrical, mechanical, or other forms.

[0197] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0198] In addition, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit.

[0199] If a function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0200] Those skilled in the art will understand that all or part of the steps of the above-described method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When executed, the program performs the steps of the above-described method embodiments; and the aforementioned storage medium includes various media capable of storing program code, such as ROM, RAM, magnetic disks, or optical disks.

[0201] Finally, it should be noted that other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein, and is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope. The scope of the invention is limited only by the appended claims.

Claims

1. A method for optimizing the layout of a near-field sparse antenna array, characterized in that, include: Determine the minimum aperture of the sparse antenna array based on the resolution; The aperture of the transmitting array and the aperture of the receiving array are determined based on the minimum aperture of the sparse antenna array, the number of transmitting elements, and the number of receiving elements. Based on the transmit array aperture and the receive array aperture, an optimization problem is constructed that includes an objective function and constraints. The objective function is used to characterize the sidelobe level of the antenna array. The optimization problem is transformed using mathematical approximation methods to obtain a solvable convex optimization problem; The convex optimization problem is solved by a convex optimization solver to obtain the element position vectors of the sparse antenna array.

2. The method according to claim 1, characterized in that, The step of determining the transmit array aperture and the receive array aperture based on the minimum aperture of the sparse antenna array, the number of transmit elements, and the number of receive elements includes: Based on the minimum aperture of the sparse antenna array, the number of transmitting elements, and the number of receiving elements, the initial transmitting array aperture and the initial receiving array aperture are calculated. The initial transmit array aperture and the initial receive array aperture are rounded down to determine the transmit array aperture and the receive array aperture.

3. The method according to claim 1, characterized in that, The step of constructing an optimization problem containing an objective function and constraints based on the transmit array aperture and the receive array aperture includes: Based on the aperture of the transmitting array and the aperture of the receiving array, the position vector method for the transmitting antenna element and the position vector of the receiving antenna element are determined. Based on the position vectors of the transmitting antenna array elements and the receiving antenna array elements, the point target response function of the antenna array is determined; The objective function is established with minimizing the maximum sidelobe level of the point target response function as the optimization objective. The constraints are constructed based on the spacing between adjacent transmitting antenna elements, the spacing between adjacent receiving antenna elements, the number of transmitting and receiving antenna elements, and the arrangement area of ​​the transmitting and receiving antenna elements.

4. The method according to claim 1, characterized in that, The process of transforming the optimization problem using mathematical approximation methods to obtain a solvable convex optimization problem includes: By using slack variables, the optimization problem is transformed into a non-convex optimization problem with sidelobe level constraints; The sidelobe level constraint is approximated by using second-order Taylor expansion and continuous convex approximation techniques, so that the sidelobe level constraint is transformed into a convex constraint based on the position vectors of the transmit antenna array elements and the receive antenna array elements. Based on the convex constraints and the constraint conditions, a solvable convex optimization problem is obtained.

5. The method according to claim 1 or 3, characterized in that, The step of solving the convex optimization problem using a convex optimization solver to obtain the element position vectors of the sparse antenna array includes: Step a: Set the initial receiving antenna element position vector to a fixed value, and construct the first convex optimization subproblem using the transmitting antenna element position vector as the optimization variable; Step b: Solve the first convex optimization subproblem using a convex optimization solver to obtain the updated transmit antenna array element position vector; Step c: Set the updated transmit antenna element position vector to a fixed value, and construct a second convex optimization subproblem using the receive antenna element position vector as the optimization variable; Step d: Solve the second convex optimization subproblem using a convex optimization solver to obtain the updated receiving antenna array element position vector; Iteratively execute steps a to d until a preset convergence condition is met, and then determine the updated transmit antenna element position vector and the updated receive antenna element position vector as the element position vectors of the sparse antenna array.

6. The method according to claim 5, characterized in that, The preset convergence condition is as follows: in two adjacent iterations, the norm of the difference between the updated transmit antenna element position vector and the transmit antenna element position vector of the previous iteration, and the norm of the difference between the updated receive antenna element position vector and the receive antenna element position vector of the previous iteration are both less than a preset threshold, or the number of iterations reaches the maximum number of iterations.

7. The method according to claim 5, characterized in that, Before determining the updated transmit antenna element position vector and the updated receive antenna element position vector as the element position vectors of the sparse antenna array, the method further includes: Step e: Determine whether the first spacing between any adjacent transmit antenna element positions in the updated transmit antenna element position vector is an integer multiple of half a wavelength, and determine whether the second spacing between any adjacent receive antenna element positions in the updated receive antenna element position vector is an integer multiple of half a wavelength. Step f: For spacings that do not meet the half-wavelength integer multiple constraint, adjust the positions of the transmitting antenna elements and / or receiving antenna elements corresponding to the spacing to the nearest half-wavelength integer multiple position. Step g: Determine whether the minimum spacing between adjacent antenna array elements satisfies the constraint conditions; Step h: If the conditions are met, accept the position adjustment; otherwise, reject the position adjustment. Repeat steps e to h until the position vectors in the updated transmit antenna element position vector and the updated receive antenna element position vector no longer undergo new position adjustments.

8. A near-field sparse antenna array layout optimization device, characterized in that, include: The first determining module is used to determine the minimum aperture of the sparse antenna array based on the resolution. The second determining module is used to determine the aperture of the transmitting array and the aperture of the receiving array based on the minimum aperture of the sparse antenna array, the number of transmitting elements, and the number of receiving elements. The construction module is used to construct an optimization problem containing an objective function and constraints based on the transmit array aperture and the receive array aperture, wherein the objective function is used to characterize the sidelobe level of the antenna array; The processing module is used to transform the optimization problem using mathematical approximation methods to obtain a solvable convex optimization problem; The solution module is used to solve the convex optimization problem through a convex optimization solver to obtain the element position vectors of the sparse antenna array.

9. An electronic device, characterized in that, include: Memory, processor; The memory stores computer-executed instructions; The processor executes computer execution instructions stored in the memory, causing the processor to perform the method as described in any one of claims 1-7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions, which, when executed by a processor, are used to implement the method as described in any one of claims 1-7.

Images