A method for synthesizing a co-excitation amplitude sparse reconfigurable array

Abstract

The application provides a common excitation amplitude sparse reconfigurable array synthesis method and relates to information transmission and processing technology.The application comprises the following steps: 1) constructing a mathematical optimization model by using the radiation characteristic requirements and the nulling requirements of a beam to be synthesized, and solving the model by using the particularity of conjugate symmetric excitation and a continuous convex approximation algorithm; and 2) introducing a slack variable to help solve the feasible point by using a feasible point tracking algorithm, and overcoming the infeasible solution caused by the non-convex constraint.The application has the advantages that a sparse array can form multiple radiation direction patterns, and meet multiple different application scenarios; the number of array elements is reduced by designing the sparse array, so that the system cost is further reduced; the characteristic of conjugate symmetric excitation weight reduces the optimization variables, so that the application has the advantage on a large array; and 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] The present application relates to information transmission and processing technology, in particular to a method for synthesizing a co-excitation amplitude sparse reconfigurable array. BACKGROUND

[0002] Reconfigurable arrays can generate different radiation patterns according to task requirements, and have important application value in modern wireless systems such as airborne radars, satellite communications and mobile communications. Literature [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 literature [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 with common excitation amplitude based on the consistency calculation concept of sensor network and semi-definite relaxation technology, however these methods failed to effectively solve the synthesis problem of reconfigurable array beam in sparse array environment and with DRR constraints; with the deepening of research, effective technologies for the synthesis problem of sparse reconfigurable array have been gradually proposed. Literature [3] Li L, Guo R, You P, et al. Pattern-Reconfigurable Sparse Linear Array Synthesis Under Minimum Element Spacing Control by Alternating Sequential Quadratic Programming[J]. IEEE Antennas and Wireless Propagation Letters, 2023, 22(6): 1271-1275. proposed a new alternating sequential quadratic programming method to synthesize reconfigurable sparse linear array with DRR constraints, but the excitation amplitudes are not the same, which increases the complexity of the feed network; literature [4] Cui Z, Zhang Q, An J, et al. Multibeam Synthesis for a Reconfigurable Sparse Array 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] In order to achieve the above object, the technical scheme adopted by the present application is as follows:

[0005] A common excitation amplitude sparse reconfigurable array synthesis method applied to a symmetric array, characterized in that it comprises the following steps:

[0006] Step 1: constructing an array structure by using a configuration mode of a set of attenuators and a set of phase shifters; wherein, the number of synthesized beam patterns is ;

[0007] Step 2: constructing a corresponding mathematical optimization model based on the radiation characteristic requirements of the beams to be synthesized, the anti-interference requirements, the dynamic range required by the attenuators, and the requirement of reducing the number of array elements;

[0008] By using the characteristics of conjugate symmetric excitation of the symmetric array and the continuous convex approximation method, and by introducing relaxation variables, the mathematical optimization model is solved by using the feasible point tracking method, and the common excitation amplitude sparse reconfigurable array synthesis is completed.

[0009] Further, the specific mode of step 2 is:

[0010] Constructing a corresponding mathematical optimization model:

[0011]

[0012] Wherein, N is the number of array elements, t represents the iteration number, the initial value of , , ; and the initial value of ; the relaxation variables and the initial value of ;

[0013] ;

[0014] Indicates the unit pattern of each array element, ; is the array element spacing; is the wave number corresponding to the operating wavelength; is the wavelength corresponding to the operating frequency of the array antenna; ; the superscript indicates the transposition operation;

[0015] and indicate the main lobe region of the th beam M is the number of sampling points in the main lobe region; represents the upper limit of the amplitude response of the first beam side lobe region ;represents the upper limit of the amplitude response of the first beam null region ;represents the upper limit of the amplitude response of the first beam null region ; represents the corresponding angle of the synthesized beam in the main lobe region ; represents the corresponding angle of the synthesized beam in the side lobe region ; represents the corresponding angle of the synthesized beam in the null region ; represents the corresponding angle of the synthesized beam in the null region ; represents the corresponding angle of the synthesized beam in the null region ; represents the corresponding angle of the synthesized beam in the null region

[0016] is the excitation of the first array element of the synthesized first beam, the initial value of which is 1; , , is the DRR upper limit constraint; is the conjugate transpose operator. The iterative process is repeated until the maximum number of iterations is reached or all constraints meet the preset requirements.

[0017] Compared with the prior art, the beneficial effects of the present application are as follows:

[0018] The present application effectively reduces the number of attenuators by using the method of multiple beams sharing a set of excitation amplitudes based on the strict conjugate symmetry of each set of excitation vectors, and the special nature of excitation conjugate symmetry reduces the optimization variables by half, highlighting the advantages of the present application in large arrays; at the same time, combined with the design of sparse array, the number of array elements is further reduced, thereby significantly saving system cost, and by adjusting the excitation phase, expanding the solution space and improving the radiation performance of the antenna, the diversified needs in practical applications are met. In addition, the DRR constraint is added, so that the dynamic range and quantization accuracy required by the attenuator are reduced, thereby simplifying the hardware complexity and improving the realizability. BRIEF DESCRIPTION OF DRAWINGS

[0019]

[0020] Figure 1 is a top view of the coaxial feed rectangular microstrip patch antenna structure in the embodiment of the present application.

[0021] Figure 2 is a side view of the coaxial feed rectangular microstrip patch antenna structure in the embodiment of the present application.

[0022] Figure 3Sparse reconfigurable beam pattern for 16 beams in the embodiment of the present application.

[0023] Figure 4 Antenna selection pattern in the embodiment of the present application.

[0024] Figure 5 Normalized excitation amplitude pattern in the embodiment of the present application. DETAILED DESCRIPTION

[0025] The present application is further described below in conjunction with the accompanying drawings and specific embodiments.

[0026] A sparse reconfigurable array synthesis method of common excitation amplitude, applied to a symmetric array, characterized in that it comprises the following steps:

[0027] Step 1: using a set of attenuators and a set of phase shifters to construct the array structure; wherein, the number of synthesized beam patterns is determined;

[0028] Step 2: based on the radiation characteristics requirements of the beams to be synthesized, the anti-interference requirements, the dynamic range required by the attenuators, and the requirement of reducing the number of array elements, a corresponding mathematical optimization model is constructed;

[0029] The conjugate symmetric excitation characteristics of the symmetric array and the continuous convex approximation method are used, and relaxation variables are introduced, and the mathematical optimization model is solved by using the feasible point tracking method, to complete the sparse reconfigurable array synthesis of common excitation amplitude.

[0030] Further, the specific method of step 2 is:

[0031] A corresponding mathematical optimization model is constructed:

[0032]

[0033] Wherein, N is the number of array elements, t represents the number of iterations, the initial value of , , ; and the initial value of ; the relaxation variables and the initial value of

[0034] ;

[0035] represents the element pattern of each array element, ; is the array element spacing; is the wave number corresponding to the operating wavelength; is the wave number corresponding to the operating wavelength; is the wave number corresponding to the operating wavelength; denotes the transpose operation;

[0036] and denotes the response lower bound and upper bound at the th beam main lobe region , M is the number of sampling points in the main lobe region; denotes the response lower bound and upper bound at the th beam side lobe region ; denotes the response lower bound and upper bound at the th beam null region ; denotes the corresponding angle of the synthesized beam in the main lobe region ; denotes the corresponding angle of the synthesized beam in the side lobe region ; denotes the corresponding angle of the synthesized beam in the null region ;

[0037] is the excitation of the th array element of the synthesized th beam, the initial value of is 1; , is the DRR upper bound constraint; is the conjugate transpose operator.

[0038] The iterative solution is obtained through the CVX tool kit, and the iterative process is repeatedly repeated until the maximum number of iterations is reached or all constraints meet the preset requirements.

[0039] Specifically, considering a uniform linear array composed of antennas, a synthesized beam pattern is to be synthesized, and the pattern at the target direction can be expressed as:

[0040]

[0041]

[0042] wherein, ; is the array element spacing; is the wave number corresponding to the operating wavelength; is the wavelength corresponding to the operating frequency of the array antenna; ; is the element pattern of the th element; is the steering vector; is the element excitation of the th beam; is the excitation of the th element of the th beam; the superscript denotes the transpose operation.

[0043] The application adopts a configuration scheme of one set of attenuators and sixteen sets of phase shifters, aiming to realize the reduction of system cost by minimizing the number of attenuators. For the radiation characteristics of the focused beam, the array synthesis pattern needs to realize the maximization of the main lobe gain and the minimization of the beam width, to ensure that the radiation energy is highly focused in the specified area, so as to achieve the optimal far field detection performance; for the synthesis of the flat top beam, the array needs to form a uniform radiation area with extremely small gain fluctuation in the specified wide angle domain, and the core constraint is the flatness of the main lobe area, to ensure the consistency of the performance in the area and avoid the occurrence of detection or communication blind spots; for the cosecant beam, the array generated pattern needs to make its radiation characteristics highly consistent with the ideal cosecant function in the specified angle range, to realize the uniform coverage of the space target and the effective compensation of the distance loss; for the beam scanning, the array needs to have the ability to realize the fast, continuous and accurate electric control scanning of the main lobe pointing while maintaining any of the above beam shapes. In addition, all the radiation characteristics need to meet the low sidelobe level to suppress interference, and have the ability to form deep nulls in a specific area to resist strong interference, and these multi-functional and high-performance beams must be realized on a unified and limited complexity hardware platform. In addition, in order to simplify the hardware complexity and improve the realizability, the DRR constraint is added to control the fluctuation range of the excitation amplitude. In order to realize the sparsity of the array antenna and ensure the convexity of the objective function, the -norm is adopted as the objective function. Based on the above analysis, under the condition that the excitation amplitudes are the same, the mathematical optimization problem of the sparse reconfigurable array synthesis can be expressed as:

[0044]

[0045] wherein, and denote the lower and upper bounds of the response of the th beam main lobe area ; denotes the upper bound of the th beam sidelobe area level; denotes the excitation of the 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 synthesized 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] where is the real part operator, extracting the real part of a complex number. The absolute value of is obviously 1, and the latter part is the sum of the product of any two complex numbers and its conjugate product, which is twice the real part of the product of the two complex numbers, thus the imaginary part of the equation cancels out, so is a real number, whose 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, which represents the steering vector . The remaining part after extracting part. The beam pattern amplitude response can be re-expressed as , where

[0059]

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

[0061]

[0062] Next, the co-excitation amplitude constraint contained in the formula is also non-convex, so the constraint can be equivalently written as the following two inequality constraints:

[0063]

[0064] It is obvious that the non-convexity in the formula is because of . Assuming is the estimate of , according to the Cauchy-Schwarz inequality, the lower bound of can be obtained as:

[0065]

[0066] When ​The equality holds. Using the formula The non-convex constraint can be relaxed as

[0067]

[0068] In addition, for the DRR constraint is non-convex. Therefore, introduce an auxiliary variable and let then , and The DRR constraint can be transformed into the following constraint:

[0069]

[0070] Therefore, combined with the formula , , the non-convex optimization problem can be transformed into a convex optimization problem :

[0071]

[0072] To solve the infeasible solution problem caused by the non-convex constraint in step 2, this scheme realizes the feasible solution of the optimization problem by introducing a relaxation variable. The specific implementation steps are as follows:

[0073] To solve the infeasible solution problem caused by the non-convex constraint in step 2, this scheme realizes the feasible solution of the optimization problem by introducing a relaxation variable. The specific implementation steps are as follows: To solve the infeasible solution problem caused by the non-convex constraint in step 2, this scheme realizes the feasible solution of the optimization problem by introducing a relaxation variable. The specific implementation steps are as follows: To solve the infeasible solution problem caused by the non-convex constraint in step 2, this scheme realizes the feasible solution of the optimization problem by introducing a relaxation variable. The specific implementation steps are as follows: To solve the infeasible solution problem caused by the non-convex constraint in step 2, this scheme realizes the feasible solution of the optimization problem by introducing a relaxation variable. The specific implementation steps are as follows: To solve the infeasible solution problem caused by the non-convex constraint in step 2, this scheme realizes the feasible solution of the optimization problem by introducing a relaxation variable. The specific implementation steps are as follows: To solve the infeasible solution problem caused by the non-convex constraint in step 2, this scheme realizes the feasible solution of the optimization problem by introducing a relaxation variable. The specific implementation steps are as follows: To solve the infeasible solution problem caused by the non-convex constraint in step 2, this scheme realizes the feasible solution of the optimization problem by introducing a relaxation variable. The specific implementation steps are as follows:

[0074]

[0075] where and are penalty parameters, , ; 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-oriented 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 multiple beam scanning results of the present application all meet preset requirements, and are on key performance indicators such as Sidelobe Level (SLL), NULL, Dynamic Range Ratio (DRR), etc. Specifically, while reaching the indicators, the present application can still effectively control the excitation amplitude dynamic range. According to specific requirements, the minimum excitation amplitude dynamic range is obtained, and since the smaller excitation amplitude dynamic range helps to reduce the coupling phenomenon between the array elements and the complexity of the feed network, the smaller the DRR value is, the better. In addition, the present application optimizes the number of array elements to 19 through sparse array design, reduces 2 antennas, i.e. , which indicates that the nth antenna is not selected; it shows that the present application significantly reduces the complexity of the array while maintaining excellent radiation performance.

[0080] Those skilled in the art will realize that the embodiments described are for the purpose of aiding the reader in understanding the principles of the present application, and should be understood as not limiting the scope of protection of the present application to the embodiments described. The present application can have various modifications and changes for those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the present application shall be included in the scope of protection of the claims of the present application.

Claims

1. A method for synthesizing a co-excitation amplitude sparse reconfigurable array, applied to a symmetrical array, characterized in that, The method comprises the following steps: Step 1, adopt a set of attenuators and The array structure is constructed in a configuration mode of a set of phase shifters; wherein, is the number of synthesized beam patterns; Step 2, based on the radiation characteristic requirements of the beams to be synthesized, the anti-interference requirements, the dynamic range required by the attenuator and the requirement of reducing the number of array elements, a corresponding mathematical optimization model is constructed; The mathematical optimization model is solved by using the conjugate symmetric excitation characteristics of the symmetric array and the continuous convex approximation method, introducing a relaxation variable and using the feasible point tracking method, and the sparse reconfigurable array synthesis of the common excitation amplitude is completed; Specifically, the corresponding mathematical optimization model is constructed as follows: ； where N is the number of array elements, t represents the iteration number, the initial value of 1, , , ; and the initial value of 1, ; relaxation variable and the initial value of 0; ； unit pattern of each array element, ; is an array element spacing; is a wave number corresponding to the operating wavelength; is a wavelength corresponding to the operating frequency of the array antenna; ; superscript denotes a transpose operation; and denote the lower and upper bounds of the response at the th beam main lobe region , M is the number of sampling points within the main lobe region; denote the lower and upper bounds of the response at the th beam side lobe region ; denote the lower and upper bounds of the response at the th beam null region ; denote the corresponding angle of the synthesized beam within the main lobe region ; denote the corresponding angle of the synthesized beam within the side lobe region ; denote the corresponding angle of the synthesized beam within the null region ; is the initial value of the excitation of the m-th array element of the n-th beam; is the initial value of the excitation of the m-th array element of the n-th beam; is the initial value of the excitation of the m-th array element of the n-th beam; is the initial value of the excitation of the m-th array element of the n-th beam; , , is the upper bound constraint of the DRR; is the conjugate transpose operator; The iterative solution is performed through the CVX tool kit, and the iteration process is repeatedly performed until the maximum iteration number is reached or all constraints meet the preset requirements.

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