A Fast Method for Broadband Non-Frequency Variation Scanning Beam Generation for Non-Uniformly Spacing Linear Arrays

Abstract

This invention discloses a rapid method for generating broadband non-frequency-varying scanning beams for non-uniformly spaced linear arrays, relating to the field of array antennas. It solves the problems of unsatisfactory pattern performance and low synthesis efficiency in broadband non-frequency-varying beam synthesis. The invention includes: correcting the broadband pattern using non-frequency-varying shaping optimization techniques; obtaining filter coefficients based on the corrected broadband pattern; obtaining a feasible broadband pattern using the transformation relationship between the filter coefficients and the broadband pattern; iteratively transforming and correcting the obtained broadband pattern until the broadband patterns obtained before and after the current iteration are the same, stopping the iteration, and outputting the current broadband pattern and the corresponding filter coefficients, thus completing the broadband non-frequency-varying scanning beam generation. This invention has low computational resource requirements and high synthesis efficiency, and can accurately achieve the required non-frequency-varying main lobe characteristics and the desired sidelobe level performance.

Description

Technical Field

[0001] This invention relates to the field of array antennas, and more specifically to a method for rapid generation of broadband non-frequency-varying scanning beams for non-uniformly spaced linear arrays. Background Technology

[0002] When traditional broadband antenna arrays receive broadband signals, the beamwidth changes with frequency, causing the received signal to be low-pass filtered and resulting in linear distortion. However, in some applications, antenna arrays need to have a non-frequency-varying beamwidth characteristic over an ultra-wide bandwidth.

[0003] For example, in some passive radar systems, it is necessary to identify subtle intra-pulse features of signals radiated by enemy systems. This requires the receiving system to achieve ultra-wideband high-fidelity signal reception, a requirement that traditional broadband antenna arrays cannot meet. Typically, a filter-summing array is used to achieve broadband non-frequency-varying beamforming. Each element channel of this array is connected to an analog-to-digital converter and a digital filter, and each filter contains a set of filter coefficients, resulting in a large number of filter coefficients that need to be optimized. Furthermore, broadband non-frequency-varying beamforming requires imposing constraints on frequency points within the ultra-wideband and angles within the visible space. When considering beam scanning, the visible space will be further expanded. Therefore, broadband non-frequency-varying beamforming faces enormous computational complexity.

[0004] In recent years, numerous methods have been proposed for broadband non-frequency-varying beamforming, such as analytical methods, convex optimization methods, least squares methods, and Fourier transform methods. While these techniques have achieved considerable success, most are only applicable to uniformly spaced antenna arrays, and to avoid grating lobes at high frequencies, the element spacing is typically set to half the wavelength corresponding to the highest frequency. To meet the directivity requirements in ultra-wideband frequencies, the filtering and summing arrays designed using these techniques generally require a large number of antenna elements, leading to significant complexity and high implementation costs. To reduce the required number of elements, the degrees of freedom in the array structure can be increased by adjusting the element positions, and non-uniformly spaced arrays can be used for synthesis. Therefore, beamforming techniques for non-uniformly spaced arrays have significant engineering application value.

[0005] Most existing synthesis techniques for non-uniformly spaced arrays only consider single-frequency or narrowband cases, such as the traditional alternating projection method. They do not consider the requirement of non-frequency-varying beamwidth and synthesize element excitations rather than digital filter coefficients. In the field of broadband non-frequency-varying beamforming, only a few synthesis techniques are applicable to non-uniformly spaced arrays. For example, the relationship between beam pattern characteristics and array position is constructed using asymptotic theory, and then a broadband non-frequency-varying beam pattern is designed based on this relationship. However, the asymptotic theory method cannot precisely control the sidelobes of the broadband beam pattern. Another example is using matrix beamforming to reconstruct the element excitation and position information of a non-uniformly spaced linear array. However, the matrix beamforming method requires knowledge of the amplitude and phase of the target broadband beam pattern at each spatial angle, while in practice, only the performance indicators of the target broadband beam pattern are generally known.

[0006] Chinese Patent 202011092350.7 discloses a broadband beamforming method based on SOCP. This method transforms the array synthesis problem into establishing and solving a convex optimization problem, thereby estimating the weight vector of the beamformer. This method can be applied to arbitrary array layouts and exhibits good robustness to system errors and angular deviations. However, because this method requires optimizing the weights of all beamformers and applying convex constraints to all pattern sampling points, it consumes a significant amount of synthesis time and computational memory. If computational resources are limited, this method cannot handle large-scale array synthesis.

[0007] Chinese Patent 201310236613.0 discloses a multi-octave constant beamwidth beamforming method based on nested arrays. This method uses a non-uniformly spaced linear array composed of multiple nested sub-arrays with different apertures to receive broadband signals, and performs non-frequency-varying beamwidth processing on the sub-band corresponding to each sub-array, thereby achieving non-frequency-varying characteristics across the entire frequency band. This method features low computational complexity and good broadband pattern control accuracy. However, this method is only applicable to specific nested array layouts, thus imposing strict limitations on the array aperture size, number of array elements, and bandwidth ratio, and cannot meet the array synthesis requirements of general cases.

[0008] Chinese Patent 201310236613.0 discloses a broadband adaptive beamforming method based on interference suppression model optimization. This method employs orthogonal subspace projection to insert nulls and combines it with a broadband non-frequency-varying beamforming method to achieve broadband non-frequency-varying beamforming effects with flexible control over sidelobes and nulls. If a non-uniform Fourier transform is used, this method has the potential to be extended to non-uniformly spaced linear array synthesis. However, this method requires pre-designing a single-frequency reference desired radiation pattern based on known radiation pattern performance indicators. Selecting a suitable reference radiation pattern is relatively difficult; if an inappropriate one is chosen, the performance of the generated broadband non-frequency-varying radiation pattern will be less than ideal. Summary of the Invention

[0009] To address the technical problems mentioned above—namely, the unsatisfactory radiation pattern performance and low integration efficiency in broadband non-frequency variable beamforming—this invention proposes a novel broadband non-frequency variable beamforming method that considers beam scanning.

[0010] This invention is applicable to non-uniformly spaced linear arrays with arbitrary layouts. It can accurately achieve the required main lobe non-frequency variation and sidelobe suppression performance while maintaining high overall efficiency, and can also meet the beam scanning requirements commonly used in practical applications.

[0011] This invention is achieved through the following technical solution:

[0012] The method steps of the present invention are as follows:

[0013] Step 1: Select the initial broadband pattern based on the non-uniformly spaced linear array of the given target;

[0014] Step 2: Correct the broadband radiation pattern using non-frequency-varying shaping optimization techniques;

[0015] Step 3: Obtain the filter coefficients based on the corrected broadband pattern, and use the transformation relationship between the filter coefficients and the broadband pattern to obtain the realizable broadband pattern.

[0016] Step 4: Iterate through Step 2 and Step 3 on the broadband pattern obtained in Step 3 until the broadband pattern obtained before and after the current iteration is the same. Stop the iteration and output the broadband pattern and the corresponding filter coefficients at this time to complete the broadband non-frequency variable scanning beam generation.

[0017] Furthermore, the detailed steps are as follows:

[0018] Step 1) Given a target non-uniformly spaced linear array to be broadband synthesized, assuming the array contains N array elements and each array element is connected to a digital filter of length L. Set initial filter coefficients, making all filter coefficients of the array 1, and select the broadband pattern corresponding to this set of initial filter coefficients as the initial broadband pattern.

[0019] Step 2) Preset the broadband integrated radiation pattern performance indicators. Based on the preset requirements, use non-frequency-varying shaping optimization techniques to correct any non-compliant parts of the initial broadband radiation pattern, resulting in a corrected broadband radiation pattern whose performance meets the specified indicators. The non-frequency-varying shaping optimization technique includes two parts: main lobe frequency-varying correction and side lobe level correction. Main lobe frequency-varying correction reduces the frequency variation characteristics of the main beam in the target frequency band, while side lobe level correction controls the distribution and level of the side lobes in the broadband visible space.

[0020] Step 3) By utilizing the transformation relationship between the broadband pattern and the filter coefficients, a set of filter coefficients of size N×L can be obtained from the modified broadband pattern. Due to the limited size of the given array structure, the obtained filter coefficients usually cannot accurately realize the modified broadband pattern, but can only realize a broadband pattern with approximate performance. This realized broadband pattern may not still meet the specified pattern performance indicators.

[0021] Step 4) Return the result of the realizable broadband pattern to Step 2), and repeat Steps 2) and 3) one by one to obtain the next generation of realizable broadband patterns. Iterate through the above operations until the updated realizable broadband pattern is the same as the previous generation result, and output the filter coefficients corresponding to the next generation of realizable broadband patterns.

[0022] In step 1), no specific requirements are made for the number of array elements, the position of array elements, the length of the digital filter, and the operating bandwidth of the non-uniformly spaced linear array.

[0023] In step 2), to quantify the non-frequency-varying characteristics of the main lobe of the target broadband pattern, a frequency variation factor σ is introduced, which is defined as follows:

[0024]

[0025]

[0026] Where P(·,·) is the broadband pattern, f k It is the operating frequency. The spatial location within the main lobe range. The smaller σ is, the better the non-frequency-varying characteristics of the target's broadband pattern.

[0027] In step 2), the main lobe frequency variation correction is to adjust the frequency variation of the main lobe within the range U. ML The value at each spatial location is replaced with the average value of that spatial angle along the frequency. Let σ D Given the expected threshold of the frequency variation factor, the main lobe frequency variation correction can be expressed as:

[0028]

[0029] Where u m ∈U ML , P′ ML (·,·) represents the main lobe portion of the corrected broadband pattern. To ensure that the maximum value of the broadband pattern remains unchanged before and after correction, the obtained P′ ML (·,·) needs to be multiplied by a scaling factor for fine-tuning, which is defined as follows:

[0030]

[0031] In step 2), the sidelobe level correction is to adjust the level within the sidelobe range U.SL Values ​​that do not meet the requirements are suppressed to below the desired threshold. Let Γ SL The desired threshold for sidelobe level requirements can be expressed as:

[0032]

[0033] Where u m ∈U SL , P′ SL (·,·) represents the sidelobe portion of the corrected broadband pattern. Furthermore, ξ∈[0,1] is an overvoltage factor used to accelerate the reduction of the achieved sidelobe level.

[0034] In step 3), the transformation relation used includes two expressions. One is the matrix product expression for calculating the broadband radiation pattern of the filter coefficients, and the other is the matrix product expression for calculating the filter coefficients of the broadband radiation pattern obtained by matrix inversion using the least squares method.

[0035] In step 4), a maximum number of iterations can be preset, typically no less than 1000. Synthesis is complete when the updated realizable broadband pattern is the same as the previous generation result or when the maximum number of iterations is reached.

[0036] The present invention has the following advantages and beneficial effects:

[0037] a) This invention establishes the transformation relationship between broadband radiation patterns and filter coefficients, making it possible to extend the traditional alternating projection framework to broadband synthesis.

[0038] b) The array factor mathematical model used in this invention does not specify the position of the array elements, so it can be applied to non-uniformly spaced linear arrays with various layouts.

[0039] c) This invention employs an alternating projection framework with very low computational complexity, thus achieving high overall efficiency and requiring very low computational resources.

[0040] d) The iterative process of this invention employs non-frequency-varying shaping optimization technology, enabling the obtained broadband pattern considering beam scanning to accurately achieve the required non-frequency-varying main lobe characteristics and the desired sidelobe level performance. Attached Figure Description

[0041] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0042] Figure 1 This is a flowchart of the method of the present invention;

[0043] Figure 2 This is a schematic diagram of the filtering and summing array model of the present invention;

[0044] Figure 3 This is a schematic diagram of the element layout of a 42-element non-uniformly spaced linear array in an embodiment of the present invention;

[0045] Figure 4 This is a comprehensive broadband non-frequency-varying scanning pattern in an embodiment of the present invention;

[0046] Figure 5 As described in the embodiments of the present invention Figure 4 Cross-sectional view at f = 0.4 GHz.

[0047] Figure 6 As described in the embodiments of the present invention Figure 4 The corresponding filter coefficient distribution diagram. Detailed Implementation

[0048] Before providing a detailed description of any embodiment of the present invention, it should be understood that the application of the present invention is not limited to the details of the structures shown in the following description or drawings. The present invention may employ other embodiments and may be implemented or performed in various ways. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive improvement are within the scope of protection of the present invention.

[0049] like Figure 1 As shown, the present invention includes the following steps:

[0050] 1) Select the initial broadband pattern based on the non-uniformly spaced linear array of the given target;

[0051] Given a target non-uniformly spaced linear array to be broadband synthesized, the array contains N array elements, and each array element is connected to a digital filter of length L. Initial filter coefficients are set so that all filter coefficients of the array are 1, and the broadband pattern corresponding to this set of initial filter coefficients is selected as the initial broadband pattern.

[0052] 2) Broadband radiation pattern corrected using non-frequency-varying shaping optimization technology;

[0053] The preset broadband integrated beam pattern performance indicators are established. Based on these preset requirements, non-frequency-varying shaping optimization techniques are used to correct any non-compliant portions of the initial broadband beam pattern, resulting in a corrected broadband beam pattern whose performance meets the specified indicators. The non-frequency-varying shaping optimization technique comprises two parts: main lobe frequency-varying correction and side lobe level correction. Main lobe frequency-varying correction reduces the frequency variation characteristics of the main beam in the target frequency band, while side lobe level correction controls the distribution and magnitude of the side lobes within the broadband visible space.

[0054] 3) Obtain the filter coefficients based on the corrected broadband pattern, and use the transformation relationship between the filter coefficients and the broadband pattern to obtain the realizable broadband pattern;

[0055] By utilizing the transformation relationship between the broadband radiation pattern and the filter coefficients, a set of filter coefficients of size N×L can be obtained from the modified broadband radiation pattern. Due to the finite size of the given array structure, the obtained filter coefficients typically cannot accurately realize the modified broadband radiation pattern; they can only achieve a broadband radiation pattern with approximate performance. This realized broadband radiation pattern may not necessarily still meet the specified radiation pattern performance specifications.

[0056] 4) Iterate through steps 2 and 3 on the broadband pattern obtained in step 3 until the broadband pattern obtained before and after the current iteration is the same. Stop the iteration and output the broadband pattern and the corresponding filter coefficients at this time to complete the broadband non-frequency variable scanning beam generation.

[0057] Return the result of the realizable broadband pattern to step 2), and repeat steps 2) and 3) one by one to obtain the next generation of realizable broadband patterns. Iterate through the above operations until the updated realizable broadband pattern is the same as the previous generation result, and output the filter coefficients corresponding to the next generation of realizable broadband patterns.

[0058] Example:

[0059] like Figure 2 The filter summation array shown consists of N array elements non-uniformly distributed along the x-axis, with the element positions denoted as x. n =[x0,x1,…,x N-1 ] T Each element of the array is connected to an analog-to-digital converter and an FIR digital filter to provide the frequency-dependent excitation required to generate the non-frequency-varying beam. Each FIR digital filter contains L filter coefficients, and the l-th coefficient of the n-th filter is denoted as h. l,n When a bandwidth is f∈[f L ,f U When a broadband signal is incident on this non-uniformly spaced array, the resulting far-field broadband radiation pattern considering beam scanning can be expressed as follows:

[0060]

[0061] Where, Δ t Let θ be the time sampling interval, θ be the wave propagation direction measured along the wide side of the linear array, and φ ∈ [-φ]. max ,φ max ] represents the direction of the scanning beam, and c represents the wave propagation speed in the medium. Since equation (1) does not limit the position of the array elements, it can be applied to non-uniformly spaced linear arrays with arbitrary layouts.

[0062] Let u = sinθ - sinφ, then the broadband pattern will be transformed into a function of f and u, i.e., P(f,u). For numerical computation, f and u are respectively treated with f... k =f L +kΔ f (where Δ) f =(f U -f L ) / (K-1), And 0≤k≤K-1) and u m =-u max +mΔ u (where Δ) u =2u max / (M-1), u max =1+sinφ max , And uniform sampling is performed for (0≤m≤M-1). Then, the discretized broadband pattern {P(f)} is... k ,u m )} can be represented as a matrix product in the following form:

[0063]

[0064] in

[0065]

[0066] P k =[P(f k ,u0),P(f k ,u1),…,P(f k ,u M-1 )] T (4)

[0067]

[0068] h n =[h 0,n ,h 1,n ,…,h L-1,n ] T (6)

[0069]

[0070] S k =[s k,0 ,s k,1 ,…,s k,M-1 ] T (8)

[0071] In equation (8), in Represented as the Kronecker product, and

[0072]

[0073]

[0074] matrix It stores the feature information of a given non-uniformly spaced linear array, and its matrix size is MK×NL. Generally, MK >> NL, therefore the following equation can be obtained using the least squares method:

[0075]

[0076]

[0077] in, yes The left inverse matrix has a size of NL×MK, (·) + This represents the pseudo-inverse operator, where I is the identity matrix and δ > 0 is the regularization coefficient used to improve numerical stability.

[0078] For a given non-uniformly spaced linear array, the array synthesis problem of broadband non-frequency-varying scanning beams can be transformed into a problem of searching for solutions to the intersection of two sets, which are respectively feasible sets. and expected set feasible set It contains all broadband radiation patterns that can be generated by a given array, i.e.

[0079]

[0080] in It is the set of complex numbers. Furthermore, the expected set... It consists of all broadband patterns that satisfy the desired pattern performance, and these broadband patterns are not required to be generated by an actual array. Clearly, the intersection of the two sets... This represents the solution space of the target array synthesis problem, where any element within the intersection is a solution that meets the requirements. The traditional alternating projection method provides a strategy for quickly obtaining solutions from the intersection, which involves alternately projecting a candidate solution onto... and This gradually narrows the gap between the candidate solution and the intersection solution. This classic method is only used for single-frequency or narrowband synthesis, but by combining equations (2)-(12), the traditional alternating projection framework can be extended to broadband non-frequency-varying scanning beam synthesis. The following are the specific steps included in the extended alternating projection framework.

[0081] Step 1): Given a target non-uniformly spaced linear array, select an initial broadband pattern.

[0082] For a non-uniformly spaced linear array, the generalized alternating projection framework proceeds in the following iterative form:

[0083]

[0084] Where the superscript 'q' indicates the iteration order, and To the feasible set respectively and expected set Projection operator. The iterative process begins with an initial broadband pattern. It consists of a set of preset initial filter coefficients. The broadband pattern is generated. Since the broadband pattern is continuously projected and updated during the iteration process, the final synthesis result is not sensitive to the initial choice; therefore, theoretically... It can be any value. For simplicity, we can let...

[0085] Step 2): Use non-frequency-varying shaping optimization technology to obtain the corrected broadband radiation pattern.

[0086] Based on the preset radiation pattern performance indicators, in the desired projection In the process, non-frequency-variable shaping optimization techniques are used to optimize the broadband radiation pattern. The non-compliant parts are corrected. Non-frequency-varying shaping optimization techniques include main lobe frequency variation correction and side lobe level correction, which are used to reduce the frequency variation characteristics of the main beam in the target frequency band and to control the distribution and level of the side lobes in the broadband visible space, respectively. These two correction methods will be described in detail below.

[0087] a) Main lobe frequency variation correction

[0088] Assuming the required broadband pattern needs to be within the entire main lobe range U ML To maintain the non-frequency-varying characteristics of the main lobe of the target broadband pattern, a frequency variation factor σ is introduced, which is defined as follows:

[0089]

[0090]

[0091] in For U ML Inner spatial location ( and ), Discrete spatial location variables The total number of points. The smaller σ is, the better the non-frequency-varying characteristics of the target broadband radiation pattern. Let σ D If σ is the expected threshold of the frequency variation factor, then σ ≤ σ DThis refers to the requirements that the non-frequency-varying characteristics must meet. If the σ of the obtained broadband radiation pattern exceeds σ... D Then, main lobe frequency variation correction is required, which will be applied to the main lobe range U. ML The value at each spatial location within the spectrum is replaced with the average value along the frequency. The main lobe portion of the corrected broadband pattern (u... m ∈U ML This can be expressed as

[0092]

[0093] To ensure that the maximum value of the broadband pattern remains unchanged before and after the correction, the obtained P′ ML (·,·) needs to be multiplied by a scaling factor for fine-tuning, which is defined as follows:

[0094]

[0095] This coefficient is the ratio of the maximum values ​​of the broadband radiation pattern before and after the correction. Specifically, when σ ≤ σ D At that time, ρ = 1.

[0096] b) Sidelobe level correction

[0097] Assume the upper boundary of the sidelobe of the desired broadband pattern is Γ. SL It is defined across the entire frequency band [f L ,f U The range of the sidelobe U SL Within this range, it can be used to describe the desired sidelobes and the performance requirements of the null. If the sidelobes of the obtained broadband pattern exceed Γ... SL Then, sidelobe level correction is required to reduce the excess to Γ. SL The following is the sidelobe portion of the corrected broadband pattern (u). m ∈U SL This can be expressed as

[0098]

[0099] Where ξ∈[0,1] is the overvoltage factor, which is used to accelerate the reduction of the achieved sidelobe level, thereby reducing the number of iterations required to complete the synthesis.

[0100] Using non-frequency-varying shaping optimization techniques, the required corrected broadband pattern can be derived from the following desired projection. produce

[0101]

[0102] After the desired projection, the resulting corrected broadband radiation pattern can be expressed as:

[0103] Step 3): Use the transformation relationship between the broadband radiation pattern and the filter coefficients to obtain the realizable broadband radiation pattern.

[0104] After the desired projection, the resulting corrected broadband radiation pattern can be expressed as: Limited by the actual number of array elements and the length of the filter, It may not be possible to generate it from a given non-uniformly spaced linear array. Therefore, the feasible set can be... Inner distance Recent realizable broadband patterns are used as an alternative. By combining equations (2) and (11), the transformation relationship between the broadband pattern and the filter coefficients can be obtained. Using this transformation relationship, the desired realizable broadband pattern can be obtained from the following feasible projection. produce

[0105]

[0106] Step 4): Iteratively perform "correction + transformation" on the obtained broadband pattern until the results before and after the iteration are equal.

[0107] After feasible projection, the resulting realizable broadband pattern may not meet the desired pattern performance indicators. Therefore, the desired projection and feasible projection in steps 2) and 3) will be performed again to obtain a new generation of realizable broadband patterns to improve the performance of the realized pattern. The alternating projection process of equation (14) will continue until the updated realizable broadband pattern is the same as the previous generation result. (At this point, the intersection solution required for the search problem has been found), or the number of iterations reaches the preset maximum number of iterations q = Q. The final synthesized broadband pattern can be represented as

[0108]

[0109] Its amplitude and phase will be significantly different from the initial broadband pattern, which also indicates the initial filter coefficients. The choice of has little impact on the choice of the overall result.

[0110] Unlike other optimization methods, the array synthesis method proposed in this invention leverages the low computational complexity of the alternating projection method, thus achieving high synthesis efficiency. Furthermore, since the array structure remains unchanged during the synthesis process, large-scale matrices are minimized in the proposed method flow. and It also remains unchanged. To avoid double counting, and The calculations should be performed in advance, and the results should be called in each iteration to further improve overall efficiency. Besides... and Since no other large-scale matrices are involved in the synthesis process, the method of this invention also has good storage efficiency. Compared with the method of this invention, convex optimization methods (such as the SOCP method) not only require storage... and Multiple large-scale matrices for configuring the direction pattern constraints also need to be stored.

[0111] The specific implementation of the broadband non-frequency-variable scanning beamforming method for a non-uniformly spaced linear array proposed in this invention can be further given through the following simulation examples and results:

[0112] In this simulation example, the desired broadband pattern has a scanning range of φ∈[-45°,45°], and maintains σ in the target frequency band f∈[0.4,1]GHz. D =0.28dB non-frequency-varying characteristic. Meanwhile, within the sidelobe region, the upper boundary of the sidelobe is set to Γ. SL = -18dB. To verify the applicability of the method of the present invention, four beamwidth cases are considered: 40°, 20°, 10°, and 5°. For these four cases, four non-uniformly spaced linear arrays designed by asymptotic theory are used, with the parameter configuration of the asymptotic theory being β = 2 / u. max and in This refers to the main lobe width in radians. The number of elements in these four arrays are 12, 22, 42, and 83, respectively. For example, Figure 3 The element layout of a 42-element non-uniform array is shown. It is assumed that each element of these four linear arrays is connected to an FIR digital filter of length 27, and the time sampling interval is Δ. t = 1 / (2GHz).

[0113] The method of this invention uses Δ f =0.046GHz and Δ u =0.01 Uniform sampling is performed on f and u, i.e., K=14 and M=341. In the non-frequency-varying shaping optimization technique, the overvoltage factor is set to ξ=0.56, which is equivalent to the sidelobe exceeding Γ. SL The portion will be compressed to less than Γ SL At 5dB. Additionally, set The initial filter coefficients are given, and Q = 1000 represents the maximum number of iterations. The synthesis results for these four cases are shown in Table 1, including the frequency variation factor σ achieved, the maximum sidelobe level achieved, the required number of iterations, and the computation time (simulated using a laptop equipped with an i7-10510U@1.80GHz). It can be seen that for all four cases, the broadband radiation pattern synthesized by the method of this invention accurately satisfies Γ. SLThe sidelobe upper boundary requirement is -18dB. Furthermore, the achieved frequency variation factors are all below the specified threshold σ. D = 0.28dB. As an example, Figure 4 The broadband non-frequency-variable scanning pattern of a 42-element linear array synthesis is shown, and Figure 5 Showing Figure 4 The cross-sectional view at f = 0.4 GHz shows the defined upper boundary of the sidelobes, indicated by the red dashed line. It can be seen that the synthesized radiation pattern exhibits excellent non-frequency-varying performance and sidelobe control. Figure 6 Showing Figure 4 The amplitude distribution of the normalized filter coefficients corresponding to the broadband radiation pattern. Regarding overall efficiency, as the array element size increases from 12 elements to 83 elements, the computation time of the method in this invention only increases from 1.32 seconds to 18.55 seconds. This reflects the high efficiency of the method in this invention, and that increasing the number of array elements does not significantly increase the required computational cost.

[0114] Table 1 is as follows:

[0115] Number of array elements Main lobe width Maximum sidelobe level Frequency variation factor Number of iterations computation time 12 40° -18.02dB 0.25dB 65 1.32 seconds 22 20° -18.02dB 0.28dB 28 3.30 seconds 42 10° -18.09dB 0.27dB 31 8.43 seconds 83 5° -18.13dB 0.28dB 18 18.55 seconds

[0116] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for rapid generation of broadband non-frequency-varying scanning beams for non-uniformly spaced linear arrays, characterized in that, Includes the following steps: Step 1: Select the initial broadband radiation pattern based on the non-uniformly spaced linear array of the given target, specifically as follows: N array elements are non-uniformly distributed along the x-axis, and their positions are represented as x. n =[x0,x1,…,x N-1 ] T Each element of the array is connected to an analog-to-digital converter and an FIR digital filter to provide the frequency-dependent excitation required to generate non-frequency-varying beams; each FIR digital filter contains L filter coefficients, and the l-th coefficient of the n-th filter is denoted as h. l,n When a bandwidth is f∈[f L ,f U When a broadband signal is incident on this non-uniformly spaced array, the resulting far-field broadband radiation pattern considering beam scanning can be expressed as follows: Where, Δ t Let θ be the time sampling interval, θ be the wave propagation direction measured along the wide side of the linear array, and φ ∈ [-φ]. max ,φ max ] represents the direction of the scanning beam, and c represents the wave propagation speed in the medium; Let u = sinθ - sinφ, then the broadband pattern will be transformed into a function of f and u, i.e., P(f,u); To use numerical calculations, f is used for both f and u. k =f L +kΔ f and u m =-u max +mΔ u Perform uniform sampling. Where, Δ f =(f U -f L ) / (K-1), And 0≤k≤K-1, Δ u =2u max / (M-1), u max =1+sinφ max , And 0≤m≤M-1, then, the discretized broadband pattern {P(f k ,u m )} can be represented as a matrix product in the following form: in P k =[P(f k ,u0),P(f k ,u1),…,P(f k ,u M-1 )] T (4) h n =[h 0,n ,h 1,n ,…,h L-1,n ] T (6) S k =[s k,0 ,s k,1 ,…,s k,M-1 ] T (8) In equation (8), in Represented as the Kronecker product, and matrix Given a non-uniformly spaced linear array containing feature information, and with matrix size MK×NL, where MK >> NL, the following formula can be obtained using the least squares method: in, yes The left inverse matrix has a size of NL×MK, (·) + This represents the pseudo-inverse operator, where I is the identity matrix and δ > 0 is the regularization coefficient used to improve numerical stability. For a given non-uniformly spaced linear array, the array synthesis problem of broadband non-frequency-varying scanning beams can be transformed into a problem of searching for solutions to the intersection of two sets, which are respectively feasible sets. and expected set feasible set It contains all broadband radiation patterns that can be generated by a given array, i.e. in For the set of complex numbers, the expected set The intersection of two sets consists of all broadband radiation patterns that satisfy the desired radiation pattern performance. This is the solution space of the target array synthesis problem, where any element within the intersection is a solution that meets the requirements; For a non-uniformly spaced linear array, the generalized alternating projection framework proceeds in the following iterative form: Where the superscript 'q' indicates the iteration order, and To the feasible set respectively and expected set The projection operator's iterative process begins with an initial broadband pattern. It consists of a set of preset initial filter coefficients. Generate, cause Step 2: Correct the broadband radiation pattern using non-frequency-varying shaping optimization techniques; Step 3: Obtain the filter coefficients based on the corrected broadband pattern, and use the transformation relationship between the filter coefficients and the broadband pattern to obtain the realizable broadband pattern. Step 4: Iterate through Step 2 and Step 3 on the broadband pattern obtained in Step 3 until the broadband pattern obtained before and after the current iteration is the same. Stop the iteration and output the broadband pattern and the corresponding filter coefficients at this time to complete the broadband non-frequency variable scanning beam generation.

2. The method for rapid generation of broadband non-frequency-varying scanning beams for non-uniformly spaced linear arrays according to claim 1, characterized in that, In step 1, for a given target containing an array of N array elements, each array element is connected to a digital filter of length L. The initial filter coefficients of the array are set to all 1, and the broadband pattern corresponding to the initial filter coefficients is selected as the initial broadband pattern.

3. The method for rapid generation of broadband non-frequency-varying scanning beams for non-uniformly spaced linear arrays according to claim 2, characterized in that, The broadband integrated pattern performance index of a given target is corrected to a preset broadband integrated pattern performance index using non-frequency-varying shaping optimization technology, thereby correcting the broadband pattern of the given target. This includes main lobe frequency variation correction and side lobe level correction. The main lobe frequency variation correction will be located within the main lobe range U. ML The value at each spatial location is replaced with the average value along the frequency at the corresponding spatial angle, and the sidelobe level correction will be located within the sidelobe range U. SL Values ​​that do not meet the requirements are suppressed to below the expected threshold.

4. The method for rapid generation of broadband non-frequency-varying scanning beams for non-uniformly spaced linear arrays according to claim 3, characterized in that, During the iteration process, the broadband radiation pattern of a given target is continuously projected and updated under an alternating projection framework. A desired broadband radiation pattern set is constructed based on the specified radiation pattern performance indicators, and a feasible broadband radiation pattern set is constructed based on the constraints of the actual number of array elements and filter length. The initial broadband radiation pattern is iteratively projected under the desired and feasible sets.

5. The method for rapid generation of broadband non-frequency-varying scanning beams for non-uniformly spaced linear arrays according to claim 4, characterized in that, For main lobe frequency-varying correction, a frequency variation factor σ is introduced, which is defined as follows: Where P(·,·) is the broadband radiation pattern, f k It is the operating frequency ( And 0≤k≤K-1), where K is the discrete frequency f k Total points Main lobe range U ML Inner spatial location ( and ), Discrete spatial location variables Total points; σ D Given the expected threshold of the frequency variation factor, the main lobe frequency variation correction can be expressed as: Where u m ∈U ML , P′ ML (·,·) represents the main lobe portion of the corrected broadband pattern; This includes adding a scaling factor for fine-tuning to the main lobe portion of the corrected broadband pattern: The scaling factor is as shown in the formula above.

6. The method for rapid generation of broadband non-frequency-varying scanning beams for non-uniformly spaced linear arrays according to claim 4, characterized in that, It also includes the introduction of Γ in sidelobe level correction. SL , Γ SL To determine the desired threshold for sidelobe level, the sidelobe level is corrected as follows: Where u m ∈U SL , P′ SL (·,·) represents the sidelobe portion of the corrected broadband pattern, and ξ∈[0,1] is the overvoltage factor, which is used to accelerate the reduction of the sidelobe level.

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