Sparse reconfigurable array synthesis method of co-excitation amplitude

Abstract

The invention provides a common excitation amplitude sparse reconfigurable array synthesis method, and relates to an information transmission and processing technology. The method comprises the following steps: 1) constructing a mathematical optimization model through a radiation characteristic requirement and a null requirement of a to-be-synthesized wave beam, and solving the mathematical optimization model by using particularity of conjugate symmetric excitation and a continuous convex approximation algorithm; 2) utilizing a feasible point tracking algorithm, introducing a slack variable to help to solve a feasible point, and overcoming a non-feasible solution caused by non-convex constraint; the method has the advantages that a plurality of radiation directional diagrams can be formed by one sparse array, so that a plurality of different application scenes can be met; the number of array elements is reduced through the design of a sparse array, so that the system cost is further reduced; due to the characteristic of excitation weight conjugate symmetry, optimization variables are remarkably reduced, and the advantages of the method on a large-scale array are highlighted; the DRR constraint is added, so that the dynamic range and the quantization precision required by the attenuator are reduced, and the hardware complexity is simplified.

Description

Technical Field

[0001] This invention relates to information transmission and processing technology, and in particular to a method for synthesizing sparse reconfigurable arrays with co-excitation amplitude. Background Technology

[0002] Reconfigurable arrays can generate different radiation patterns according to mission requirements, and have important application value in modern wireless systems such as airborne radar, satellite communication and mobile communication. References [1] Zhang X, Liang J, Fan X, et al. Reconfigurable array beampattern synthesis via conceptual sensor network modeling and computation[J]. IEEE Transactions on Antennas and Propagation,2020, 68(6): 4512-4525. and [2] Fuchs B. Application of convex relaxation to array synthesis problems[J]. IEEE Transactions on Antennas and Propagation,2013, 62(2): 634-640. respectively proposed reconfigurable arrays based on the sensor network consensus calculation concept and semi-definite relaxation technology to realize the common excitation amplitude. However, these methods failed to effectively solve the synthesis problem of reconfigurable array beams in sparse array environment and under DRR constraints. With the deepening of research, effective technologies for the synthesis problem of sparse reconfigurable arrays have been gradually proposed. Reference [3] Li L, Guo R, You P, et al. Pattern-Reconfigurable SparseLinear Array Synthesis Under Minimum Element Spacing Control by AlternatingSequential Quadratic Programming[J]. IEEE Antennas and Wireless Propagation Letters, 2023, 22(6): 1271-1275. A new alternating sequence quadratic programming method is proposed to synthesize reconfigurable sparse linear arrays with DRR constraints, but the excitation amplitudes are different, which increases the complexity of the feed network; Reference [4] Cui Z, Zhang Q, An J, et al. Multibeam Synthesis for a Reconfigurable SparseArray via a New Consensus PDD Framework[J].IEEE Transactions on Antennas and Propagation, 2023, 72(2): 1541-1555. A new consistency penalty dual decomposition method is proposed, which can achieve satisfactory radiation patterns with fewer antennas in different application scenarios. However, the method does not achieve DRR constraint, nor does it share the excitation amplitude. Reference [5] Nai SE, Ser W, Yu ZL, et al. Beampattern synthesis for linear and planar arrays with antenna selection by convex optimization[J]. IEEE Transactions on Antennas and Propagation, 2010, 58(12): 3923-3930. It studies the special property of the excitation of the conjugate symmetric antenna of the symmetric array, which makes the upper and lower bound constraints of the beam convex. Then, by iteratively minimizing the weighted objective function, the beam index is accurately satisfied, and a sparse array with fewer antennas is generated. However, this method is only applied in single beam synthesis. Reference [6] Mehanna O, Huang K, Gopalakrishnan B, Konar A, &Sidiropoulos N D. Feasible Point Pursuit and Successive Approximation of Non-Convex QCQPs[J].IEEE Signal Processing Letters, 2014, 22(7):804-808. This paper proposes a joint optimization method for non-convex problems based on feasible point pursuit and continuous convex approximation. By linearizing the non-convex part and iteratively solving, a relatively optimal feasible solution is successfully obtained, demonstrating the algorithm's potential in solving non-convex problems. Based on this, this invention combines the characteristics of conjugate symmetric excitation weights, convex optimization algorithms, and feasible point pursuit algorithms to study beam synthesis problems with co-excitation amplitudes and DRR constraints in sparse reconfigurable arrays. This is a relatively unstudied but significant area. Summary of the Invention

[0003] In view of this, this invention proposes a sparse reconfigurable array synthesis method with co-excitation amplitude. This method combines the characteristics of the conjugate symmetric antenna excitation of a symmetric array, a convex optimization algorithm, and a feasible point tracking algorithm to systematically solve the beam synthesis problem of sparse reconfigurable arrays under co-excitation amplitude and DRR constraints. The specific implementation steps are as follows:

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A sparse reconfigurable array synthesis method with co-excitation amplitude, applied to symmetric arrays, is characterized by comprising the following steps:

[0006] Step 1, using a set of attenuators and The array structure is constructed using a configuration of phase shifters; among which... This represents the number of integrated beam patterns.

[0007] Step 2: Based on the radiation characteristics requirements of the beam that needs to be integrated, the anti-interference requirements, the dynamic range required by the attenuator, and the requirement to reduce the number of array elements, construct the corresponding mathematical optimization model.

[0008] By utilizing the characteristics of conjugate symmetric excitation of symmetric arrays and the continuous convex approximation method, and by introducing slack variables, the mathematical optimization model is solved using the feasible point pursuit method, thus completing the synthesis of sparse reconfigurable arrays with co-excitation amplitude.

[0009] Furthermore, the specific method for step 2 is as follows:

[0010] Construct the corresponding mathematical optimization model:

[0011]

[0012] Where N is the number of array elements, and t represents the number of iterations. The initial value is 1. , , ; and The initial value is 1. ; slack variables and The initial value is 0;

[0013] ;

[0014] This represents the element radiation pattern of each array element. ; It is the spacing between array elements; It is the wavenumber corresponding to the operating wavelength; It is the wavelength corresponding to the operating frequency of the array antenna; ; superscript Indicates the transpose operation;

[0015] and Indicates the first Each beam main lobe region The lower and upper bounds of the response at the point, M is the number of sampling points in the main lobe region; Indicates the first Beamside lobe region The upper bound of the level; Indicates the first Beam null region The upper bound of the amplitude response; This indicates the synthesized beam in the main lobe region. The corresponding angle inside; The integrated beam is located in the sidelobe region. The corresponding angle inside; This indicates the integrated beam in the null region. The corresponding angle inside;

[0016] To comprehensively The first beam The incentive of each array element The initial value is 1; , , For DDR upper bound constraints; It is the conjugate transpose operator.

[0017] The solution is obtained through an iterative process using the CVX toolkit. This process is repeated until the maximum number of iterations is reached or all constraints meet the preset requirements.

[0018] Due to the adoption of the above technical solution, the beneficial effects of this invention compared with the prior art are as follows:

[0019] This invention, based on the strict conjugate symmetry of each set of excitation vectors, effectively reduces the number of attenuators by employing a method where multiple beams share a single set of excitation amplitudes. Furthermore, the unique characteristic of excitation conjugate symmetry halves the optimization variables, highlighting the advantages of this invention in large arrays. Simultaneously, combined with sparse array design, it further reduces the number of array elements, thereby significantly saving system costs. Moreover, by adjusting the excitation phase, the solution space is expanded, improving the antenna's radiation performance to meet diverse needs in practical applications. In addition, the inclusion of DRR constraints reduces the required dynamic range and quantization accuracy of the attenuators, thus simplifying hardware complexity and improving feasibility. Attached Figure Description

[0020] Figure 1 This is a top view of the coaxial-fed rectangular microstrip patch antenna structure in an embodiment of the present invention.

[0021] Figure 2 This is a side view of the coaxial-fed rectangular microstrip patch antenna structure in an embodiment of the present invention.

[0022] Figure 3This is a sparse reconfigurable beammap of 16 beams in an embodiment of the present invention.

[0023] Figure 4 This is an antenna selection diagram in an embodiment of the present invention.

[0024] Figure 5 This is a normalized excitation amplitude diagram in an embodiment of the present invention. Detailed Implementation

[0025] The invention will be further described below with reference to the accompanying drawings and specific embodiments.

[0026] A sparse reconfigurable array synthesis method with co-excitation amplitude, applied to symmetric arrays, is characterized by comprising the following steps:

[0027] Step 1, using a set of attenuators and The array structure is constructed using a configuration of phase shifters; among which... This represents the number of integrated beam patterns.

[0028] Step 2: Based on the radiation characteristics requirements of the beam that needs to be integrated, the anti-interference requirements, the dynamic range required by the attenuator, and the requirement to reduce the number of array elements, construct the corresponding mathematical optimization model.

[0029] By utilizing the characteristics of conjugate symmetric excitation of symmetric arrays and the continuous convex approximation method, and by introducing slack variables, the mathematical optimization model is solved using the feasible point pursuit method, thus completing the synthesis of sparse reconfigurable arrays with co-excitation amplitude.

[0030] Furthermore, the specific method for step 2 is as follows:

[0031] Construct the corresponding mathematical optimization model:

[0032]

[0033] Where N is the number of array elements, and t represents the number of iterations. The initial value is 1. , , ; and The initial value is 1. ; slack variables and The initial value is 0;

[0034] ;

[0035] This represents the element radiation pattern of each array element. ; It is the spacing between array elements; It is the wavenumber corresponding to the operating wavelength; It is the wavelength corresponding to the operating frequency of the array antenna; ; superscript Indicates the transpose operation;

[0036] and Indicates the first Each beam main lobe region The lower and upper bounds of the response at the point, M is the number of sampling points in the main lobe region; Indicates the first Beamside lobe region The upper bound of the level; Indicates the first Beam null region The upper bound of the amplitude response; This indicates the synthesized beam in the main lobe region. The corresponding angle inside; The integrated beam is located in the sidelobe region. The corresponding angle inside; This indicates the integrated beam in the null region. The corresponding angle inside;

[0037] To comprehensively The first beam The incentive of each array element The initial value is 1; , , For DDR upper bound constraints; It is the conjugate transpose operator.

[0038] The solution is obtained through an iterative process using the CVX toolkit. This process is repeated until the maximum number of iterations is reached or all constraints meet the preset requirements.

[0039] Specifically, consider by A uniform linear array composed of several antennas needs to be integrated. Beam pattern, target direction The orientation pattern at a location can be represented as:

[0040]

[0041]

[0042] in, ; It is the spacing between array elements; It is the wavenumber corresponding to the operating wavelength; It is the wavelength corresponding to the operating frequency of the array antenna; ; For the first The unit radiation pattern of each array element; For guiding vector; To comprehensively Each beam's array element is excited; To comprehensively The first beam The incentive of each array element; superscript This indicates the transpose operation.

[0043] This invention employs a configuration of one attenuator and sixteen phase shifters, aiming to reduce system cost by minimizing the number of attenuators. Regarding the radiation characteristics of the focused beam, the array-synthesized pattern must maximize the main lobe gain and minimize the beamwidth to ensure highly focused radiated energy within a specified area, thereby achieving optimal far-field detection performance. For the synthesis of flat-top beams, the array must form a uniform radiation region with minimal gain fluctuations within a specified wide-angle domain. The core constraint is the flatness of the main lobe region to ensure consistent performance within this area and avoid detection or communication blind spots. For cosecant beams, the array-generated pattern must ensure that its radiation characteristics closely match the ideal cosecant function within a specified angular range to achieve uniform coverage of spatial targets and effective compensation for range loss. For beam scanning, the array must possess the capability to achieve rapid, continuous, and precise electronically controlled scanning of the main lobe while maintaining any of the aforementioned beam shapes. Furthermore, all radiation characteristics must satisfy low sidelobe levels to suppress interference and possess the ability to form deep nulls in specific regions to counteract strong interference. These multifunctional, high-performance beams must be implemented on a unified hardware platform with limited complexity. Additionally, to simplify hardware complexity and improve feasibility, DRR constraints are incorporated to control the fluctuation range of the excitation amplitude. To achieve sparsity of the array antenna and ensure the convexity of the objective function, this scheme adopts... - Norm as the objective function. Based on the above analysis, under the condition of the same excitation amplitude, the comprehensive mathematical optimization problem of sparse reconfigurable arrays can be expressed as:

[0044]

[0045] in, and Indicates the first Each beam main lobe region The lower and upper bounds of the response at the location; Indicates the first Beamside lobe region The upper bound of the level; Indicates the first Beam null region The upper bound of the amplitude response; This indicates the synthesized beam in the main lobe region. The corresponding angle inside; The integrated beam is located in the sidelobe region. The corresponding angle inside; This indicates the integrated beam in the null region. The corresponding angle inside.

[0046] At this point, an auxiliary variable is introduced. The goal is to separate the excitation amplitude of each beam. Based on the above derivation, the optimization problem... It can be rewritten as:

[0047]

[0048] A mathematical optimization model was constructed based on the beam's radiation characteristics, anti-interference requirements, and the need to reduce system costs. Next, the characteristics of conjugate symmetric antenna excitation configuration and the continuous convex approximation algorithm are used to solve the target optimization problem. Solve the problem.

[0049] Specifically, the process includes the following steps:

[0050] First, the non-convex constraint in the main lobe constraint of the mathematical optimization model of the above sparse reconfigurable array. The characteristics of the conjugate symmetric antenna excitation configuration can be transformed into convex constraints. The specific steps are as follows:

[0051] Applying conjugate symmetric weights, its formal expression is: For example ,in It is the conjugate transpose operator. Therefore... The formula can be written as:

[0052]

[0053] Element radiation patterns of all antennas They are all equal and are real numbers, that is Next, extract This embodiment takes an odd-numbered array as an example, which can be... The formula can be further rewritten as:

[0054]

[0055] right Taking the absolute value of both sides of the equation yields the beam pattern amplitude response in the optimized model, which is:

[0056]

[0057] in It is the real part operator, which extracts the real part. The absolute value of is clearly 1. The latter part is the sum of the product of any two complex numbers and their conjugate product, which is twice the real part of the product of these two complex numbers. Therefore, the imaginary part of the expression cancels out entirely. It is a real number, and any of its lower and upper bounds are convex, thus solving the problem caused by the non-convex lower bound constraint of the main lobe.

[0058] To facilitate the explanation of the following steps, a new vector is introduced here. Indicates the guide vector extract The remaining portion after partial representation. The beam pattern amplitude response can then be re-expressed as... ,in The specific form is as follows:

[0059]

[0060] Based on the above reasoning, the main lobe constraint in the mathematical optimization model of sparse reconfigurable arrays This can be transformed into a fully convex constraint, expressed as:

[0061]

[0062] Next, the formula Includes co-excitation amplitude constraints It is also non-convex, therefore, it can be... The constraints are equivalent to the following two inequality constraints:

[0063]

[0064] Obviously, the formula The non-convexity in is due to the existence of Assuming yes The This estimate, according to the Cauchy-Schwarz inequality, yields... The lower bound is:

[0065]

[0066] when The equation holds true when the time is right. Using the formula... Non-convex constraints can be Relaxation is:

[0067]

[0068] Furthermore, regarding DRR constraints It is non-convex. Therefore, an auxiliary variable is introduced. and order ,but ,and The DRR constraint can then be transformed into the following constraint:

[0069]

[0070] Therefore, combining the formula , , This can solve non-convex optimization problems. Transform into a convex optimization problem :

[0071]

[0072] To address the infeasibility issue caused by non-convex constraints in step 2, this solution introduces slack variables to obtain a feasible solution to the optimization problem. The specific implementation steps are as follows:

[0073] For the relaxed non-convex constraints and main lobe constraint For infeasible solutions caused by overly strict requirements, appropriate slack variables are introduced. and The optimization problem after transformation A feasible solution is obtained; simultaneously, to further enhance the sparsity of the activation vector, a reweighted approach is adopted. The norm minimization method optimizes the objective function by introducing a number. To avoid denominator The result is zero. Ultimately, the mathematical optimization problem of achieving multiple beam synthesis with a sparse array under the condition of the same excitation amplitude can be expressed as:

[0074]

[0075] in, and It is a penalty parameter. , ; and The initial value is 1. To adjust the penalty parameters, where... These values ​​are set based on actual experimental results, ensuring that the multi-beam sparse reconfigurable beam pattern meets the expected radiation requirements. The solution is obtained iteratively using the CVX toolkit, with the iteration process repeating continuously until the maximum number of iterations is reached or all constraints meet the preset requirements.

[0076] Simulation example:

[0077] Simulation results were used to verify the performance of the proposed method in multi-beam radiation under a sparse array design when multiple beams have the same excitation amplitude. Considering the mutual coupling problem between array elements, a uniform linear array model consisting of 21 coaxially fed rectangular microstrip patch antennas was designed using HFSS high-frequency electromagnetic simulation software, further verifying the application effect of the proposed method in a practical array antenna. Specific parameters are as follows: scanning... The interval is [interval], and the range is [range]. The 16 beams have a transition zone on both sides of the target direction. The zero-depression area is The zero depth is -50dB; the upper limit of the sidelobe horizontal range is -25dB; and the DRR is set to 2.9.

[0078] To verify this invention, specific experiments were conducted. Figure 1 , Figure 2 These are top and side views of the coaxial-fed rectangular microstrip patch antenna structure in this invention. The main parameters of the coaxial-fed rectangular microstrip patch antenna element are as follows: the dielectric substrate is Rogers RT5880 material with a relative permittivity of 2.2; the substrate thickness H = 1.575 mm; and the substrate length W... S =60mm, width L S =50mm; the length of the radiating patch is W=48.4mm and the width is L=39.1mm; the antenna adopts a coaxial feeding method, and the feeding point is located at the center line of the patch length direction (i.e., W / 2=24.2mm), and the distance from the patch edge on one side in the width direction is L1=22.85mm; Figure 3 The sparse reconfigurable beam diagram of the 16 beams of the present invention is shown in the figure. The expected radiation requirements in this embodiment are: sidelobe level -25dB, null limit -50dB, and multiple target-directing beams can be realized at the same time. Figure 4 This is an antenna selection diagram for the present invention. The "×" at both ends indicate that the antenna is not selected, and the circle in the middle indicates that the antenna is selected. Figure 5 The normalized excitation amplitude diagram of the present invention is shown in the figure. The normalized excitation amplitudes of the 16 beams completely overlap, which means that the 16 beams can be implemented using a single attenuator.

[0079] The beam scanning results of this invention all meet the preset requirements and are satisfactory in key performance indicators such as sidelobe level (SLL), null depth (NULL), and dynamic range ratio (DRR). Specifically, this invention achieves all indicators while effectively controlling the excitation amplitude dynamic range. The minimum excitation amplitude dynamic range is obtained according to specific requirements. Since a smaller excitation amplitude dynamic range helps reduce coupling between array elements and reduce the complexity of the feed network, a smaller DRR value is better. Furthermore, this invention optimizes the number of array elements to 19 through a sparse array design, reducing the number of antennas by two. If the result is 0, it means that the nth antenna was not selected; this shows that the present invention significantly reduces the complexity of the array while maintaining excellent radiation performance.

[0080] Those skilled in the art will recognize that the described embodiments are intended to help readers understand the principles of the invention and should be understood as not limiting the scope of protection of the invention to the described embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A sparse reconfigurable array synthesis method with shared excitation amplitude, applied to symmetric arrays, characterized in that, Includes the following steps: Step 1, using a set of attenuators and The array structure is constructed using a configuration of phase shifters; among which... This represents the number of integrated beam patterns. Step 2: Based on the radiation characteristics requirements of the beam that needs to be integrated, the anti-interference requirements, the dynamic range required by the attenuator, and the requirement to reduce the number of array elements, construct the corresponding mathematical optimization model. By utilizing the characteristics of conjugate symmetric excitation of symmetric arrays and the continuous convex approximation method, and by introducing slack variables, the mathematical optimization model is solved using the feasible point pursuit method, thus completing the synthesis of sparse reconfigurable arrays with co-excitation amplitude.

2. The sparse reconfigurable array synthesis method with shared excitation amplitude according to claim 1, characterized in that, The specific method for step 2 is as follows: Construct the corresponding mathematical optimization model: ； Where N is the number of array elements, and t represents the number of iterations. The initial value is 1. , , ; and The initial value is 1. ; slack variables and The initial value is 0; ； This represents the element radiation pattern of each array element. ; It is the spacing between array elements; It is the wavenumber corresponding to the operating wavelength; It is the wavelength corresponding to the operating frequency of the array antenna; ; superscript Indicates the transpose operation; and Indicates the first Each beam main lobe region The lower and upper bounds of the response at the point, M is the number of sampling points in the main lobe region; Indicates the first Beamside lobe region The upper bound of the level; Indicates the first Beam null region The upper bound of the amplitude response; This indicates the synthesized beam in the main lobe region. The corresponding angle inside; The integrated beam is located in the sidelobe region. The corresponding angle inside; This indicates the integrated beam in the null region. The corresponding angle inside; To comprehensively The first beam The incentive of each array element The initial value is 1; , , For DDR upper bound constraints; It is the conjugate transpose operator; The solution is obtained through an iterative process using the CVX toolkit. This process is repeated until the maximum number of iterations is reached or all constraints meet the preset requirements.

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