Antenna array plane directional diagram forming method for analyzing and solving phase weighted value

Abstract

The invention relates to an antenna array plane directional diagram forming method for analyzing and solving a phase weighted value, which comprises the following steps of: analyzing and solving the phase weighted value: obtaining target electric field distribution at an antenna array plane through Fourier transform according to a target directional diagram; electric field distribution is decomposed into a weighted sum of two pure phase fields, and an antenna array plane is divided into two groups of array element subsets which are distributed alternately according to the weighted sum; phase distribution corresponding to the pure phase field is loaded to the two array element subsets, a radiation field with a target forming directional diagram is obtained through array synthesis, and the directional diagram comprises a main lobe corresponding to the target directional diagram and a side lobe caused by a periodic grating lobe; and side lobe optimization: by adjusting the phase distribution of the target directional diagram and traversing the side lobe intensity of the actual directional diagram under different phase parameters, selecting the phase distribution enabling the side lobe to be the lowest as an optimized target phase so as to suppress the side lobe caused by the grating lobe. According to the method, the phase weighted value is solved through rapid analysis, and accurate control over the antenna directional diagram is achieved.

Description

Technical Field

[0001] This invention relates to the field of transmission system design technology, and in particular to an analytical method for determining the antenna array radiation pattern by solving the phase weighting value. Background Technology

[0002] The rapid development of wireless communication, radar, and satellite communication has placed higher demands on the performance of antenna systems. These systems require antenna arrays to be able to flexibly adjust their radiation patterns to adapt to different operating environments and mission requirements. For example, in multi-user communication systems, antennas need to be able to track multiple users simultaneously while suppressing interference signals; in radar systems, antennas need to be able to achieve high-resolution target detection and tracking.

[0003] Phase-weighted methods adjust the phase of the excitation signals for each element using phase shifters, enabling more precise control over the shape and orientation of the antenna pattern. The advantage of this method is that adjusting the phase weights can significantly affect the antenna's pattern characteristics, including main lobe width, sidelobe level, and beam pointing.

[0004] However, traditional methods for calculating phase weights to achieve specific antenna pattern shaping have limitations. First, existing algorithms all use iterative optimization. Due to the high degree of computational freedom, the results are prone to getting trapped in local optima, leading to deviations in the optimized pattern. Second, in dynamically changing environments, the phase weights need to be adjusted in real time to adapt to these changes. However, existing phase weight calculation methods are slow and computationally burdensome, requiring minutes to obtain results. Therefore, existing methods still face challenges in achieving high-precision pattern generation and fast response. Summary of the Invention

[0005] To address the existing technical problems, this invention provides a method for analytically solving the phase weighting value for antenna array pattern shaping.

[0006] The specific content of this invention is as follows: A method for analytically solving the phase weighting value of an antenna array pattern, comprising the following steps:

[0007] Analytical solution of phase weighting: Based on the target radiation pattern, the target electric field distribution at the antenna array is obtained through Fourier transform; the electric field distribution is decomposed into a weighted sum of two pure phase fields, and the antenna array is divided into two sets of alternating array element subsets accordingly; the phase distribution corresponding to the pure phase field is loaded onto the two sets of array element subsets respectively, and the radiation field with the target shaped radiation pattern is obtained by array synthesis, wherein the radiation pattern includes the main lobe corresponding to the target radiation pattern and the side lobes caused by the periodic grating lobe;

[0008] Sidelobe optimization: By adjusting the phase distribution of the target radiation pattern and iterating through the actual sidelobe intensity of the radiation pattern under different phase parameters, the phase distribution that minimizes the sidelobes is selected as the optimized target phase to suppress the sidelobes caused by the grating lobe.

[0009] Furthermore, the analytical solution for the phase weighting includes:

[0010] First, consider the target's orientation map. Its form can be expressed as:

[0011] ,

[0012] in and These represent the amplitude and phase of the radiation pattern, respectively. For azimuth angle With pitch angle The direction vector is denoted as , According to the Fourier transform, the target electric field distribution at the antenna array is... Represented as:

[0013] ,

[0014] in and These represent the amplitude and phase of the target electric field, respectively. Let be the coordinates of the plane where the antenna is located. This is the wavelength of the electromagnetic wave emitted by the antenna array at this time. The corresponding wave vector, since any complex field can always be decomposed into the sum of two pure phase fields, can be... Split into ,and ,in:

[0015] ,

[0016] in Amplitude distribution The maximum value, considering the case of a rectangular array, is the th The coordinates of an antenna can be represented as:

[0017] ,

[0018] in and The spacing between the antenna elements in the x and y directions represents the distance between the antenna elements. The antenna elements are then divided into... and Two parts, each loaded with a phase distribution. and ,in and Represented as:

[0019] Therefore, the electric field distribution of the antenna array can be written as:

[0020] ,

[0021] At this point, the radiation pattern of the antenna array can be obtained by Fourier transform, written as:

[0022] ,

[0023] According to the convolution theorem:

[0024] ,

[0025] in

[0026]

[0027]

[0028] symbol Represents convolution.

[0029] The results show that the array pattern is a periodic function with grating lobes, and its th... The position of the grating lobe of the level is located at Considering the zeroth order of the array pattern, it is written as:

[0030] ,

[0031] Other higher-level terms are treated as distractors; unified writing is required. Therefore, the overall array pattern can be written as:

[0032] ,

[0033] Within a certain angular domain The array pattern is mainly composed of zero-order lobes, so it can approximate the pattern of the target, and its interference terms are high-order grating lobes.

[0034] Furthermore, sidelobe optimization includes: adjusting the phase weighting value obtained after complex field encoding by changing the phase distribution of the target radiation pattern, thereby optimizing the final generated radiation pattern distribution. The method involves setting the phase distribution of the target radiation pattern as follows:

[0035] ,

[0036] in The phase coefficient is related to the antenna aperture that generates the target pattern, and is obtained through ergodic iteration. The method involves adjusting the sidelobe intensity based on the actual radiation pattern. The values ​​are assigned to optimize the sidelobes of the actual obtained radiation pattern.

[0037] This invention achieves precise control of the antenna pattern by rapidly and analytically solving the phase weighting value. This not only improves the performance of the antenna system but also enhances its adaptability and flexibility in complex environments, providing a more efficient technical solution for fields such as wireless communication, radar, and satellite communication. Attached Figure Description

[0038] The invention will be further explained below with reference to the accompanying drawings.

[0039] Figure 1 The antenna array pattern is shown in the example when a uniform phase is loaded.

[0040] Figure 2 The example shows an alternating arrangement of two pure phase field distributions.

[0041] Figure 3 The orientation pattern needs to be assigned for the implementation example.

[0042] Figure 4 The phase weighting value of the antenna array is calculated for the example.

[0043] Figure 5 The image shows the actual weighted antenna array radiation pattern of the embodiment. Detailed Implementation

[0044] This invention provides a method for analytically solving phase weighting values ​​for antenna array pattern shaping, comprising the following steps:

[0045] The analytical solution steps for the phase weighting value are as follows: Based on the target radiation pattern, the target electric field distribution at the antenna array is obtained through Fourier transform; the electric field distribution is decomposed into a weighted sum of two pure phase fields, and the antenna array is divided into two sets of alternating array element subsets accordingly; the phase distribution corresponding to the pure phase field is applied to the two sets of array element subsets respectively, and the radiation field with the target shaped radiation pattern is obtained by array synthesis, wherein the radiation pattern includes the main lobe corresponding to the target radiation pattern and the side lobes caused by the periodic grating lobes;

[0046] Sidelobe optimization steps: By adjusting the phase distribution of the target radiation pattern and iterating through the actual radiation pattern sidelobe intensities under different phase parameters, the phase distribution that minimizes the sidelobes is selected as the optimized target phase to suppress the sidelobes caused by the grating lobe.

[0047] The specific methods for each step are as follows:

[0048] 1. Analytical solution of phase weighting

[0049] First, consider the target's orientation map. Its form can be expressed as:

[0050] ,

[0051] in and These represent the amplitude and phase of the radiation pattern, respectively. For azimuth angle With pitch angle The direction vector is denoted as , According to the Fourier transform, the target electric field distribution at the antenna array is... Represented as:

[0052] ,

[0053] in and These represent the amplitude and phase of the target electric field, respectively. Let be the coordinates of the plane where the antenna is located. This is the wavelength of the electromagnetic wave emitted by the antenna array at this time. The corresponding wave vector. Since any complex field can always be decomposed into the sum of two pure phase fields, it can be... Split into ,and ,in:

[0054] ,

[0055] in Amplitude distribution The maximum value of . Considering the case of a rectangular array, the first The coordinates of an antenna can be represented as:

[0056] ,

[0057] in and These represent the spacing between the antenna elements in the x and y directions, respectively. The antenna elements are divided into... and Two parts, each loaded with a phase distribution. and ,in and Represented as:

[0058] Therefore, the electric field distribution of the antenna array can be written as:

[0059] .

[0060] At this point, the radiation pattern of the antenna array can be obtained by Fourier transform, written as:

[0061] ,

[0062] According to the convolution theorem:

[0063] ,

[0064] in

[0065]

[0066]

[0067] symbol Represents convolution.

[0068] The results show that the array pattern is a periodic function with grating lobes, and its th... The position of the grating lobe of the level is located at Considering the zeroth order of the array pattern, it is written as:

[0069] ,

[0070] Other higher-level terms are treated as distractors; unified writing is required. Therefore, the overall array pattern can be written as:

[0071] .

[0072] Within a certain angular domain The array pattern is mainly composed of zero-order lobes, so it can approximate the pattern of the target, and its interference terms are high-order grating lobes.

[0073] 2. Sidelobe optimization

[0074] Since the phase distribution of a radiation pattern typically has a certain degree of freedom, the phase weighting value obtained after complex field encoding can be adjusted by changing the phase distribution of the target radiation pattern, thereby optimizing the final generated radiation pattern distribution. The method involves setting the phase distribution of the target radiation pattern as follows:

[0075] ,

[0076] in The phase coefficient is related to the antenna aperture that generates the target pattern, and is obtained through ergodic iteration. The method involves using the sidelobe intensity of the actual radiation pattern calculated in step 1 to... The values ​​are assigned to optimize the sidelobes of the actual obtained radiation pattern.

[0077] The method of this application will be further explained below with reference to a specific example.

[0078] Taking a rectangular array with 41×41 elements as an example, considering a point source with a transmission wavelength of λ, and the elements spaced 0.4λ apart in the x and y directions, the unweighted antenna array pattern is as follows. Figure 1 As shown.

[0079] like Figure 2 As shown, this embodiment shows the arrangement of alternating loading of two pure phase fields.

[0080] like Figure 3 The diagram shown is the radiation pattern to be shaped in this embodiment. After performing a Fourier transform on the radiation pattern, it is decomposed into the sum of two pure phase fields using a complex field coding algorithm, according to... Figure 2 The arrangement of (a,b) is loaded into two pure phase fields respectively, and the above steps are repeated to traverse using the sidelobe optimization algorithm. The optimal value was found to be 0.93. The computation time on a typical consumer computer (i7-9700 3.0GHz) was 300 milliseconds.

[0081] like Figure 4 As shown, this is the phase weighting value of the antenna array calculated in the embodiment.

[0082] like Figure 5 As shown, the antenna array pattern after actual weighting in the embodiment is as follows: within the falling edge range of the main lobe flat-top beam, its intensity fluctuation is ±0.81dB, and outside the main lobe range, the maximum sidelobe is -17dB.

[0083] This invention enables precise control of the antenna pattern, thereby reducing interference, improving communication and detection quality and system performance, and enhancing its adaptability and flexibility in complex environments. Furthermore, the optimized phase weight calculation process reduces computational resource consumption, improves system operating efficiency, lowers hardware costs, and enhances economic efficiency. This invention provides a more efficient technical solution for fields such as wireless communication, radar, and satellite communication, promotes the development of related technologies, and lays the foundation for achieving higher-performance antenna systems.

[0084] Many specific details have been set forth in the foregoing description to provide a thorough understanding of the present invention. However, the above description is merely a preferred embodiment of the present invention, and the present invention can be implemented in many other ways different from those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed above. Furthermore, any person skilled in the art can make many possible variations and modifications to the technical solutions of the present invention, or modify them into equivalent embodiments, using the methods and techniques disclosed above, without departing from the scope of the present invention. Any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention, without departing from the content of the present invention, shall still fall within the protection scope of the present invention.

Claims

1. A method for analytically solving phase weighting values ​​for antenna array pattern shaping, characterized in that: Includes the following steps: Analytical solution of phase weighting: Based on the target radiation pattern, the target electric field distribution at the antenna array is obtained through Fourier transform; the electric field distribution is decomposed into a weighted sum of two pure phase fields, and the antenna array is divided into two sets of alternating array element subsets accordingly; the phase distribution corresponding to the pure phase field is loaded onto the two sets of array element subsets respectively, and the radiation field with the target shaped radiation pattern is obtained by array synthesis, wherein the radiation pattern includes the main lobe corresponding to the target radiation pattern and the side lobes caused by the periodic grating lobe; Sidelobe optimization: By adjusting the phase distribution of the target pattern and iterating through the sidelobe intensities of the actual pattern under different phase parameters, the phase distribution that minimizes the sidelobes is selected as the optimized target phase to suppress the sidelobes caused by the grating lobe.

2. The method for analytically solving the phase weighting value of an antenna array pattern according to claim 1, characterized in that: The analytical solution for phase weighting includes: First, consider the target's orientation map. Its form can be expressed as: ， in and These represent the amplitude and phase of the radiation pattern, respectively. For azimuth angle With pitch angle The direction vector is denoted as , According to the Fourier transform, the target electric field distribution at the antenna array is... Represented as: ， in and These represent the amplitude and phase of the target electric field, respectively. Let be the coordinates of the plane where the antenna is located. This is the wavelength of the electromagnetic wave emitted by the antenna array at this time. The corresponding wave vector, since any complex field can always be decomposed into the sum of two pure phase fields, can be... Split into ,and ,in: ， in Amplitude distribution The maximum value, considering the case of a rectangular array, is the th The coordinates of an antenna can be represented as: ， in and The spacing between the antenna elements in the x and y directions represents the distance between the antenna elements. The antenna elements are then divided into... and Two parts, each loaded with a phase distribution. and ,in and Represented as: Therefore, the electric field distribution of the antenna array can be written as: ， At this point, the radiation pattern of the antenna array can be obtained by Fourier transform, written as: ， According to the convolution theorem: ， in ， ， symbol Represents convolution. The results show that the array pattern is a periodic function with grating lobes, and its th... The position of the grating lobe of the level is located at Considering the zeroth order of the array pattern, it is written as: ， Other higher-level terms are treated as distractors; unified writing is required. Therefore, the overall array pattern can be written as: ， Within a certain angular domain The array pattern is mainly composed of zero-order lobes, so it can approximate the pattern of the target, and its interference terms are high-order grating lobes.

3. The method for analytically solving the phase weighting value of an antenna array pattern according to claim 2, characterized in that: Sidelobe optimization includes adjusting the phase weighting value obtained after complex field encoding by changing the phase distribution of the target radiation pattern, thereby optimizing the final generated radiation pattern distribution. The method involves setting the phase distribution of the target radiation pattern as follows: ， in The phase coefficient is related to the antenna aperture that generates the target radiation pattern, and is obtained through ergodic iteration. The method involves adjusting the sidelobe intensity based on the actual radiation pattern. The values ​​are assigned to optimize the sidelobes of the actual obtained radiation pattern.

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