Method for constructing mathematical model of ultra-wideband heterogeneous array aperture optimization based on frequency band overlapping unit

Abstract

The application discloses a kind of based on the construction method of frequency band overlap unit's ultra-wideband heterogeneous array aperture optimization mathematical model, include the following steps: according to unit type and operating frequency band, heterogeneous array is divided into several subarrays, unit type and operating frequency band are consistent in each subarray;Establish the heterogeneous array directional diagram expression considering the shared aperture when different frequency bands overlap;Further combined with the performance requirements of ultra-wideband, the array radiation performance constraint condition is constructed;According to each operating frequency and scanning angle range, establish the subarray element spacing constraint condition, to avoid producing grating lobe;Establish array aperture constraint condition, for limiting array total aperture size in preset range;Comprehensive above directional diagram expression and various constraint conditions, the ultra-wideband heterogeneous array aperture optimization mathematical model is constructed.The application establishes the construction method of frequency band overlap unit's ultra-wideband heterogeneous array aperture optimization mathematical model, provides theoretical model for subsequent design of ultra-wideband heterogeneous array.

Description

Technical Field

[0001] This invention relates to the field of array antennas, and more specifically to a method for constructing a mathematical model for optimizing the aperture of an ultra-wideband heterogeneous array based on overlapping frequency band units. Background Technology

[0002] With the development of satellite communication and radar detection systems, the requirements for array antennas in terms of operating bandwidth and radiation performance are constantly increasing. However, traditional array antenna designs typically optimize aperture layout and radiation patterns for a single frequency band, making it difficult to meet the comprehensive requirements of ultra-wideband multi-performance indicators under limited aperture and cost constraints.

[0003] In the design of ultra-wideband array antennas, traditional methods mainly include tightly coupled arrays. [1] Multi-aperture arrays and wavelength ratio arrays [2] For a single-channel, single-antenna tightly coupled array, it is usually assembled using a high-frequency half-wavelength spacing, which results in a large number of array channels and high system implementation cost. For a multi-aperture array implemented independently in frequency bands, each frequency band uses an independent array antenna, and the array apertures are independent of each other, failing to achieve antenna resource sharing. Therefore, the overall required aperture is large and the aperture utilization efficiency is low. In addition, the wavelength ratio array in reference [2] can reduce the number of array elements and reduce structural complexity to a certain extent by distributing the array according to the wavelength scale. However, this method usually relies on strict harmonic relationships (such as 2nd harmonic or 3rd harmonic) for design, lacks unified and systematic optimization theory support, and is difficult to apply to the application scenarios of segmented changes in performance indicators such as gain and scanning range under ultra-wideband conditions in multifunctional systems.

[0004] To address the aforementioned issues, a heterogeneous array architecture based on overlapping frequency band elements offers a potential technical approach for achieving ultra-wideband aperture reuse. In this architecture, antenna elements of different subarrays operate in different frequency bands, with some overlap between them. Multiple subarrays operate simultaneously during frequency band overlap, enabling aperture sharing and reuse, potentially improving channel resource utilization and aperture efficiency. However, a unified mathematical modeling and optimization method is currently lacking for this type of heterogeneous array. The aperture optimization problem for this architecture typically involves determining the number of subarrays, dividing the operating frequency bands of each subarray, configuring element spacing and the number of elements, and designing excitation distributions to meet radiation performance requirements. This problem not only involves the mixed optimization of discrete and continuous variables but also performance constraints such as gain and sidelobe levels across multiple frequency bands, while simultaneously considering engineering limitations such as antenna element implementation and aperture size, making modeling and solving quite challenging.

[0005] Therefore, it is necessary to establish a mathematical model for aperture optimization of ultra-wideband heterogeneous arrays based on frequency band overlapping units, so as to provide a theoretical model for subsequent design.

[0006] References:

[0007] [1] D. -M. Sun, Z. -C. Hao, C. -Y. Ding, R. -J. Liu, Z. -J. Guo andH. -Y. Yin, "A low-profile ultra-wideband and wide-scanning phased array for UHF applications," IEEE Trans. Antennas Propag., vol. 71, no. 1, pp. 473-486, Jan. 2023.

[0008] [2] RW Kindt, “Prototype design of a modular ultrawidebandwavelength-scaled array of flared notches,” IEEE Trans. Antennas Propag., vol. 60, no. 3, pp. 1320-1328, Mar. 2012. Summary of the Invention

[0009] To address the aforementioned problems, the present invention aims to establish a method for constructing a mathematical model for optimizing the aperture of an ultra-wideband heterogeneous array based on frequency band overlapping units, so as to achieve unified modeling of the array aperture and its related parameters, thereby providing a theoretical model for the design of heterogeneous arrays.

[0010] The method for constructing a mathematical model for aperture optimization of ultra-wideband heterogeneous arrays based on overlapping frequency band cells includes the following steps:

[0011] Step 1: Divide the heterogeneous array into several sub-arrays according to the cell type and operating frequency band. The cell type and operating frequency band are consistent within each sub-array.

[0012] Step 2: Establish a heterogeneous array pattern representation that considers the shared aperture when different frequency bands overlap.

[0013] Step 3: Further combine the multiple performance requirements of ultra-wideband to construct array radiation performance constraints;

[0014] Step 4: Based on the operating frequency and scanning angle range, establish the subarray element spacing constraints to avoid generating grating lobes;

[0015] Step 5: Establish array aperture constraints to limit the total array aperture size within a preset range;

[0016] Step 6: Based on the above radiation pattern representation and various constraints, construct the mathematical model for aperture optimization of the ultra-wideband heterogeneous array.

[0017] The present invention has the following advantages and beneficial effects:

[0018] (1) A method for constructing a mathematical model for aperture optimization of ultra-wideband heterogeneous arrays based on frequency band overlapping units was developed, providing a general theoretical model for array design;

[0019] (2) Based on the aperture reuse mechanism of frequency band overlap, a unified pattern mathematical model of heterogeneous arrays at different operating frequencies was established, which can represent that multiple subarrays work at the same time when the frequency bands overlap, reflecting the sharing and reuse of array apertures;

[0020] (3) It can simultaneously characterize multiple performance constraints such as gain, sidelobe and scanning range under multi-band conditions, and take into account engineering constraints such as array element spacing, aperture size and hardware implementation, thereby enhancing the model's adaptability and versatility to actual application scenarios. Attached Figure Description

[0021] The accompanying drawings, which are included to further illustrate embodiments of the invention and form part of this application, should not be construed as limiting the embodiments of the invention. In the drawings:

[0022] Figure 1 This is a flowchart illustrating the method for constructing a mathematical model for ultra-wideband heterogeneous array aperture optimization based on frequency band overlapping units according to the present invention.

[0023] Figure 2 This is a schematic diagram of the ultra-wideband heterogeneous array model based on frequency band overlapping units of the present invention. Detailed Implementation

[0024] 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.

[0025] like Figure 1 As shown, the present invention includes the following steps:

[0026] Step 1: Divide the heterogeneous array into several sub-arrays according to the unit type and operating frequency band. The unit type and operating frequency band are the same in each sub-array.

[0027] For ultra-wideband heterogeneous arrays, it is often necessary to use multiple elements operating in different frequency bands, and the operating frequency bands of different elements may overlap. When frequency bands overlap, multiple subarrays can operate simultaneously, enabling the sharing and multiplexing of array apertures, which is expected to improve channel resource utilization and aperture efficiency. Now, let's take... Figure 2 The array shown is an example, consisting of three subarrays operating in different frequency bands. Subarray 1 operates in the low-frequency band, subarray 2 in the mid-frequency band, and subarray 3 in the high-frequency band. Subarrays 1 and 2 have overlapping operating frequency bands, and subarrays 2 and 3 also have overlapping operating frequency bands. The heterogeneous array can be divided into K subarrays based on the unit operating frequency band, with each subarray having the same unit type and operating frequency band. Now, let's take one...

[0028] Let the set be the frequency bands covered by the k-th (k=1,2,…,K) subarray. ,in and Let these represent the lowest and highest frequencies covered by the k-th subarray, respectively. The overall frequency coverage range of the array is denoted as set . .

[0029] Step 2: Establish a heterogeneous array pattern representation that considers the shared aperture when different frequency bands overlap.

[0030] When establishing the mathematical model of the radiation pattern, it is necessary to consider the potential overlap between the frequency bands of the subarrays, where multiple subarrays operate simultaneously when frequency bands overlap. If the frequency point... When multiple subarrays operate simultaneously, frequency reuse occurs, which can be addressed using a set... To describe the numbering of the multiplexed subarray at this frequency. Therefore, the overall array pattern at this frequency is obtained by summing the patterns of the simultaneously operating subarrays, i.e.

[0031]

[0032] in The formula for calculating the radiation pattern of a single array in a multiplexed subarray is as follows:

[0033]

[0034] in This represents the total number of cells in the k-th subarray. This represents the excitation of the nth element in the kth subarray. This represents the wavenumber in free space operating at frequency f. This represents the position vector of the nth element in the kth subarray. Represents the propagation vector. This represents the active element radiation pattern of the nth element in the kth subarray operating at frequency f.

[0035] Step 3: Further combine the multi-performance requirements of ultra-wideband to construct array radiation performance constraints.

[0036] In practical applications, array radiation performance requirements vary widely. This paper presents a modeling process using sidelobe performance and scanning gain constraints as examples. For heterogeneous arrays with overlapping apertures in frequency bands, the sidelobe performance requirement of the array pattern within the scanning range at frequency f can be expressed as:

[0037]

[0038] in Indicates the beam scanning angle. This indicates the scanning range that needs to be considered at frequency f. and These represent the beam scanning at frequency f. The required sidelobe region of the radiation pattern and the corresponding upper limit of the sidelobe level.

[0039] Furthermore, suppose the heterogeneous array operates at frequency point f and scans to... The expected gain of the array pattern at that time is Then the desired gain constraint of the heterogeneous array operating within the scanning range at frequency point f can be expressed as:

[0040]

[0041] in, This represents the maximum gain when the nth unit in the kth subarray is excited individually. The radiation pattern of the active cells after normalization.

[0042] Step 4: Based on the operating frequency and scanning angle range, establish the subarray element spacing constraints to avoid generating grating lobes.

[0043] To avoid the appearance of grating lobes in the radiation pattern, the element spacing of the k-th subarray is constrained. The maximum element spacing is determined by the operating frequency. The maximum scan angle is determined together with the frequency. Since different frequencies may correspond to different maximum scan angles, it is necessary to consider the maximum scan angle for each frequency. Calculate the maximum element spacing, then take the minimum of these spacings to obtain the element spacing constraint for the k-th subarray:

[0044]

[0045] in and This represents the actual minimum physical spacing between two antenna elements in the k-th subarray. and These represent the maximum one-dimensional scan angles of the array along the x and y directions, respectively.

[0046] Step 5: Establish array aperture constraints to limit the total array aperture size within a preset range. Assume the total aperture area of ​​the array is no greater than... Then the aperture constraint of the array can be expressed as

[0047]

[0048] in This represents the aperture area occupied by the k-th subarray.

[0049] Step 6: Based on the above radiation pattern representation and various constraints, construct the mathematical model for aperture optimization of the ultra-wideband heterogeneous array. The optimization variables of this model include:

[0050] (1) The number of subarrays K;

[0051] (2) Number of units in the k-th subarray ;

[0052] (3) The highest frequency of the band covered by the kth subarray and lowest frequency ;

[0053] (4) The position of any cell in the k-th subarray and incentives .

[0054] The constraints of this model include:

[0055] (1) The spacing of the cells in the k-th subarray along the x and y directions and ;

[0056] (2) Sidelobe level, scanning gain or other performance constraints at frequency point f;

[0057] (3) The total aperture area of ​​the array is not greater than .

[0058] Therefore, the method for constructing the mathematical model for ultra-wideband heterogeneous array aperture optimization based on frequency band overlapping units can be described as follows:

[0059]

Claims

1. A method for constructing a mathematical model for optimizing the aperture of an ultra-wideband heterogeneous array based on overlapping frequency band units, characterized in that, Includes the following steps: Step 1: Divide the heterogeneous array into several sub-arrays according to the cell type and operating frequency band. The cell type and operating frequency band are consistent within each sub-array. Step 2: Establish a heterogeneous array pattern representation that considers shared aperture when different frequency bands overlap; Step 3: Further combine the multiple performance requirements of ultra-wideband to construct array radiation performance constraints; Step 4: Based on the operating frequency and scanning angle range, establish the subarray element spacing constraints to avoid generating grating lobes; Step 5: Establish array aperture constraints to limit the total array aperture size within a preset range; Step 6: Based on the above radiation pattern representation and various constraints, construct the mathematical model for aperture optimization of the ultra-wideband heterogeneous array.

2. The method for constructing a mathematical model for ultra-wideband heterogeneous array aperture optimization based on frequency band overlapping units as described in claim 1, characterized in that... In step 1, the heterogeneous array is divided into several subarrays according to cell type and operating frequency band, with each subarray having the same cell type and operating frequency band. First, the heterogeneous array is divided into K subarrays according to cell type and operating frequency band, with each subarray having the same cell type and operating frequency band. The frequency bands covered by the k-th (k=1,2,…,K) subarray are denoted as set, where… and These represent the lowest and highest frequencies covered by the k-th subarray, respectively; the overall frequency coverage of the array is denoted as set. 。 3. The method for constructing a mathematical model for ultra-wideband heterogeneous array aperture optimization based on frequency band overlapping units as described in claim 1, characterized in that... In step 2, a heterogeneous array pattern representation considering shared aperture when different frequency bands overlap is established; when establishing the mathematical model of the pattern, it is necessary to consider the possible overlap between sub-array frequency bands, where multiple sub-arrays operate simultaneously when frequency bands overlap; if the frequency point When multiple subarrays operate simultaneously, i.e., frequency reuse occurs, a combined array is used. ； This indicates the subarray number participating in operation at this frequency point; in this case, the overall array pattern at this frequency point is represented as the sum of the patterns of the participating subarrays, i.e. ； The orientation pattern of the k-th subarray is represented as follows: ； in Let be the total number of cells in the k-th subarray. Let be the excitation weight of the nth cell in the kth subarray. Let f be the wavenumber in free space at frequency f. This represents the position vector of the nth cell in the kth subarray. For propagation vector, This is the active element radiation pattern of the nth element in the kth subarray operating at frequency f.

4. The method for constructing a mathematical model for ultra-wideband heterogeneous array aperture optimization based on frequency band overlapping units as described in claim 1, characterized in that... In step 3, the array radiation performance constraints are further constructed by combining the ultra-wideband multi-performance requirements; among them, the sidelobe level constraint within the array scanning range at frequency point f is expressed as: ； in Indicates the beam scanning angle. This indicates the scanning range that needs to be considered at frequency f. and These represent the beam scanning at frequency f. The required radiation pattern sidelobe region and corresponding upper bound of the sidelobe level; in addition, assume the heterogeneous array operates at frequency f and scans to The expected gain of the array pattern at that time is The desired gain constraint for the heterogeneous array operating within the scanning range at frequency point f is expressed as: ； in, This represents the maximum gain when the nth unit in the kth subarray is excited individually. The radiation pattern of the active cells after normalization.

5. The method for constructing a mathematical model for ultra-wideband heterogeneous array aperture optimization based on frequency band overlapping units as described in claim 1, characterized in that... In step 4, based on the operating frequency and scanning angle range, constraints are established for the element spacing of the subarray to avoid grating lobes. To avoid the appearance of pattern grating lobes, the element spacing of the k-th subarray needs to be constrained. The maximum element spacing is determined by the operating frequency. The maximum scan angle is determined together with the frequency; different frequencies may correspond to different maximum scan angles, and the maximum scan angle varies for each frequency. Calculate the maximum element spacing, then take the minimum of these spacings to obtain the element spacing constraint for the k-th subarray: ； in and This represents the actual minimum physical spacing between two antenna elements in the k-th subarray. and These represent the maximum one-dimensional scan angles of the array along the x and y directions, respectively.

6. The method for constructing a mathematical model for ultra-wideband heterogeneous array aperture optimization based on frequency band overlapping units as described in claim 1, characterized in that... In step 5, array aperture constraints are established to limit the total array aperture size within a preset range; assuming the total aperture area of ​​the array is not greater than... The aperture constraint of the array is then expressed as: ； in This represents the aperture area occupied by the k-th subarray.

7. The method for constructing a mathematical model for ultra-wideband heterogeneous array aperture optimization based on frequency band overlapping units as described in claim 1, characterized in that... In step 6, by combining the above radiation pattern representation and various constraints, a mathematical model for optimizing the aperture of the ultra-wideband heterogeneous array is constructed; the optimization variables of this model include: (1) The number of subarrays K; (2) Number of units in the k-th subarray ; (3) The highest frequency of the band covered by the kth subarray and lowest frequency ; (4) The position of any cell in the k-th subarray and incentives ; The constraints of this model include: (1) The spacing of the cells in the k-th subarray along the x and y directions and ; (2) Sidelobe level and scanning gain at frequency point f; (3) The total aperture area of ​​the array is not greater than ; Therefore, the method for constructing the mathematical model for ultra-wideband heterogeneous array aperture optimization based on frequency band overlapping units is expressed as follows: 。

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