Taylor Weighting Method for Continuous Surface Sources

Abstract

The present invention discloses a Taylor weighting method for a continuous surface source, which mainly solves the problem that when the existing Taylor weighting method is used for a continuous surface source and a conformal array antenna, the curvature causes the sidelobe level of the radiation pattern to fail to reach the expected value. The present invention equivalentizes the surface source to a three-dimensional virtual source, constructs a Taylor radiation pattern by using the spatial factor of the virtual source; then combines the least squares method to establish a correlation model between the Taylor radiation pattern and the excitation distributions of the surface source and the conformal array antenna, so as to obtain the excitation distributions of the surface source and the conformal array antenna. The present invention can effectively realize the low sidelobe synthesis of the continuous surface source and the conformal array antenna, and improve the radar anti-jamming performance. The simulation results show that the Taylor radiation pattern of the embodiment of the present invention can achieve the expected low sidelobe beam.

Description

Technical Field

[0001] The present invention belongs to the field of antenna design technology, and further relates to a Taylor weighting method for continuous curved surface sources in the field of antenna technology. The present invention can be used for low sidelobe design of conformal array antennas. Background Art

[0002] Low sidelobe antennas are widely used in high-precision, high-confidentiality modern communication systems. They can significantly reduce the interference caused by side lobes, improve system resolution, and improve target detection accuracy. There are two main strategies to achieve low sidelobe beam synthesis of antennas. First, an optimization model is established with low sidelobe beam as the goal, and low sidelobe design is achieved by combining evolutionary algorithms. Since this method is essentially an uncertain strategy, it usually requires a large number of iterations, which is time-consuming and requires high-performance computing resources as a guarantee. Second, a deterministic strategy such as the Taylor weighted method is used to directly establish an association model between low sidelobe beams and antenna excitations, which can easily achieve low sidelobe antennas and save computing resources.

[0003] The 54th Institute of China Electronics Technology Group Corporation disclosed a Taylor weight optimization method based on circular ring conformality in its patent document "A Taylor weight optimization method based on circular ring conformality" (application number CN 202110927133.3, authorization announcement number CN 113708090 B). This method obtains the antenna coordinate distribution in the horizontal direction and the antenna excitation distribution in the vertical direction by projection, and obtains the Taylor weight coefficient of the curved surface conformal antenna by synthesis, thereby achieving a low zero depth in the sidelobe area. However, the method still has the following shortcomings: the essence of this method is to obtain the excitation distribution of the conformal antenna by sampling on the traditional Taylor distribution, and the existence of the curvature of the conformal antenna will still cause the low sidelobe beam synthesized by this method to be far from the expected sidelobe requirements. Therefore, this method cannot directly achieve the expected low sidelobe beam synthesis of continuous curved surface sources or conformal antennas.

[0004] Xiamen University has disclosed a low sidelobe pattern synthesis method for modular array antennas in its patent document "Taylor-Shekunoff Polynomial Design Method for Array Antennas" (application number CN 201510155810.9, authorization announcement number CN 104701639 B). The implementation steps of this method are: the first step is to use the Taylor synthesis method to calculate the array factor pattern of the module; the second step is to use Shekunoff polynomials to obtain the zero-depth pattern; the third step is to combine the pattern product theorem to use zero depth to offset the grating lobe in the array factor to obtain a low sidelobe beam. If the obtained low sidelobe beam cannot meet the expected goal, return to the first step and recalculate. Although this method can achieve low sidelobe beams for continuous curved sources or conformal antennas, the method still has the following shortcomings: from the perspective of the method process, its essence is an organic combination of deterministic strategies and uncertain strategies. On the one hand, it still retains the time-consuming shortcomings of uncertain strategies; on the other hand, it is impossible to directly establish a correlation model between the expected low sidelobe beam and the antenna excitation distribution and obtain an analytical expression for the excitation distribution.

[0005] In summary, although the existing technologies achieve low sidelobe beams by sampling on traditional Taylor distribution through positional relationships or combining optimization models, these methods either have the disadvantage of still failing to meet the expected sidelobe requirements, or are unable to directly give the relationship between the expected low sidelobe and the antenna excitation distribution and the analytical expression of the excitation distribution. Summary of the invention

[0006] The purpose of the present invention is to address the deficiencies of the above-mentioned prior art and propose a Taylor weighted method for continuous curved surface sources, aiming to solve the problems that the existing methods cannot achieve the expected low sidelobe beam, are time-consuming, and cannot obtain an analytical expression for the excitation distribution when applied to continuous curved surface sources or conformal array antennas.

[0007] The idea of ​​achieving the purpose of the present invention is as follows: the design method of the present invention first analyzes the reasons why the spatial factors of the curved source have a "grating lobe effect" and cannot effectively construct a Taylor pattern; on this basis, the curved source is equivalent to a three-dimensional virtual source, and the Taylor pattern is constructed using the spatial factors of the virtual source, thereby solving the problem that the Taylor pattern constructed by the spatial factors of the curved source often does not meet expectations; further, the present invention combines the least squares method to establish an association model between the constructed Taylor pattern and the curved source and the conformal array antenna excitation distribution, and obtains the curved source and conformal array antenna excitation distribution that meet the expected sidelobe level. The present invention solves the problem that the spatial factors of the curved source in the prior art cannot effectively construct the Taylor pattern by making the curved source equivalent to a three-dimensional virtual source and using the virtual source spatial factors to construct the Taylor pattern. The present invention uses the least squares method to obtain the discrete conformal array antenna excitation distribution. In addition to avoiding the design error introduced by the traditional sampling method according to the array element position, the excitation distribution corresponding to the Taylor pattern can still be accurately obtained when considering the mutual coupling effect of the array elements. The design method proposed in this invention can not only ensure that the expected low sidelobe requirements are met, but also directly establish the correlation model between the expected low sidelobe beam and the antenna excitation distribution. It has a clear physical meaning and avoids the serious problem of time-consuming calculation caused by uncertain strategies. The introduction of this design method provides a solution for Taylor weighting of continuous curved sources and conformal array antennas, expands the scope of application of traditional Taylor weighting methods, and is expected to play an important role in modern communication systems.

[0008] To achieve the above object, the technical solution of the present invention is as follows:

[0009] The steps of analyzing the "grating lobe effect" of the curved surface source spatial factor and the reason why the Taylor pattern cannot be effectively constructed are: combining the curved surface source spatial factor formula and case results to vividly demonstrate the "grating lobe effect" of the curved surface source spatial factor.

[0010] Step 1, the curved surface source is equivalent to a three-dimensional virtual source, and based on the spatial factor of the three-dimensional virtual source, the phase of the field component is adjusted to ensure that the side lobes of the directional pattern show an overall downward trend, and the Taylor directional pattern of the curved surface source is constructed;

[0011] Step 2: Using the least squares method, a correlation model between the constructed Taylor pattern and the curved source and conformal array antenna excitation distribution is established to obtain an analytical expression for the excitation distribution.

[0012] Compared with the prior art, the present invention has the following advantages:

[0013] First, the present invention proposes a method for constructing Taylor patterns of equivalent virtual sources for continuous curved surface sources. Compared with the prior art, the present invention can easily obtain Taylor patterns of curved surface sources that meet the expected sidelobe requirements, thereby significantly reducing the interference caused by sidelobe, improving the resolution of radar systems, and improving target detection accuracy.

[0014] Second, because the present invention uses the least square method to obtain the discrete conformal array antenna excitation distribution. On the one hand, it can avoid the design error introduced by the traditional method according to the array element position sampling method; on the other hand, it can still accurately obtain the excitation distribution corresponding to the Taylor pattern when the array element mutual coupling effect is included. This allows the present invention to fully consider the influence of mutual coupling on the antenna pattern, thereby avoiding the pattern distortion problem caused by traditional sampling methods and mutual coupling, and can be directly applied to the low sidelobe beam synthesis of continuous curved surface sources and conformal array antennas in engineering practice. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is a flow chart for implementing the present invention;

[0016] Figure 2 is a schematic diagram of a curved surface source of the present invention;

[0017] Figure 3 is the spatial factor graph of the semi-cylindrical surface source of the present invention;

[0018] Figure 4 It is the -30dB Taylor weighted directivity pattern of the semi-cylindrical source constructed by the present invention;

[0019] Figure 5 It is the field component diagram of the -30dB Taylor weighted directional pattern of the semi-cylindrical source constructed by the present invention; wherein, Figure 5 (a) Figure 5 (b) Figure 5 (c) are the field component diagrams of the -30 dB Taylor weighted directivity diagram of the semi-cylindrical source constructed by the present invention along the x, y, and z coordinate axes;

[0020] Figure 6 It is the -30dB Taylor weighted directivity pattern of the semi-cylindrical source constructed after phase shifting of the present invention;

[0021] Figure 7 It is a relationship diagram of the conformal array element of the present invention in the global rectangular coordinate system, the spherical coordinate system and the local rectangular coordinate system, the spherical coordinate system;

[0022] Figure 8 is the curved surface source Taylor pattern and excitation distribution diagram of the present invention; wherein, Figure 8 (a) Figure 8 (b) Figure 8 (c) Figure 8 (d) are typical sections of the curved source of the present invention. Taylor directivity diagram, excitation amplitude distribution and excitation phase distribution diagram;

[0023] Fig. 9 is a conformal array element and array arrangement diagram of the present invention; wherein, Fig. 9 (a) Fig. 9 (b) are schematic diagrams of conformal array elements and array geometrical arrangement diagrams of the present invention;

[0024] Fig.10 is a typical cut-plane Taylor pattern of the conformal array antenna of the present invention; wherein, Fig.10 (a) Fig.10 (b) are typical cross-sections of the conformal array antenna of the present invention. and Taylor direction diagram. DETAILED DESCRIPTION

[0025] The present invention is a Taylor weighting method for continuous curved surface sources, which is mainly aimed at the problem that the spatial factor of the curved surface source cannot form a Taylor radiation pattern with obvious main-lobe and side-lobe distinction like a plane source, that is, the "grating lobe effect" caused by the curvature, and the expected side-lobe level cannot be achieved. The Taylor weighting of the continuous curved surface source and the conformal array antenna is realized by combining a virtual source and a least squares method.

[0026] Step 1: The curved surface source is equivalent to a three-dimensional virtual source. Based on the spatial factor of the three-dimensional virtual source, the phase of the field component is adjusted to ensure that the side lobes of the directional pattern show an overall downward trend, and the Taylor directional pattern of the curved surface source is constructed.

[0027] The curved surface source refers to a curved surface source that can be discretized into a conformal array antenna.

[0028] The three-dimensional virtual source space factors are as follows:

[0029]

[0030] Among them, F(u,v,w) represents the three-dimensional virtual source space factor along the three viewing directions u,v,w in the global spherical coordinate system, L x , L y and L z denote the length of the surface source along the x, y, and z axes in the global rectangular coordinate system, λ is the wavelength, θ and Respectively represent the angles between the far field direction and the positive directions of the coordinate axes z and x, I vir (x′, y′, z′) represents the excitation of the virtual source at the point (x′, y′, z′) in the global rectangular coordinate system, represents the length of the virtual source along the x-axis in the global rectangular coordinate system, μ represents the oversampling factor, and the value range of μ is 1.2 to 2. (·) It represents the exponential function with the natural constant e as the base, j represents the symbol of the imaginary unit, and π represents the ratio of a circumference to a circumference of ...

[0031] The phase adjustment of the field component refers to adjusting the field component side lobe level of each axis in the global rectangular coordinate system according to the following formula so that it has the same decreasing trend as the field component side lobe level of each axis:

[0032]

[0033] Among them, c z0 It represents the field component along the z-axis after the phase is adjusted by 90°.

[0034] The Taylor pattern expression of the curved surface source is as follows:

[0035]

[0036]

[0037] Among them, E Taylor represents the Taylor pattern of the curved source, C represents the maximum sidelobe level of the Taylor pattern of the curved source, C=cosh(πA), and cosh(·) represents the hyperbolic cosine function. When realizing the Taylor pattern of the curved source, C is a predetermined value, so A can be determined by C=cosh(πA), and further by Sure sin(·) represents the sine function, and Π(·) represents the multiplication symbol.

[0038] The Taylor pattern expression of conformal array antenna is as follows:

[0039]

[0040] in, represents the Taylor pattern of the conformal array antenna, represents the unit pattern of the virtual source in the global spherical coordinate system in the discrete case. The unit pattern is obtained by taking the average value of all conformal array elements in the local spherical coordinate system established with the center of the array element as the origin. M represents the total number of conformal array elements, and f m Represents the unit pattern of a conformal array element in the local spherical coordinate system.

[0041] Step 2: Using the least squares method, a correlation model between the constructed Taylor pattern and the curved source and conformal array antenna excitation distribution is established to obtain an analytical expression for the excitation distribution.

[0042] The association model of the Taylor pattern and the surface source excitation distribution combined with the least squares method is as follows:

[0043] findI surf

[0044] min∫∫ Ω ||G surf Isurf -E Taylor ||2 2 dΩ

[0045] Among them, findI surf It means solving the column vector I consisting of the surface source excitation distribution surf , min∫∫ Ω ||G surf I surf -E Taylor || 2 dΩ is a constraint condition, which means that when G surf I surf -E Taylor When the 2-norm of is minimum, I is obtained surf ,||·|| 2 represents the 2-norm, G surf Indicates that each observation point is The row vector is composed of k, which represents the free space wave constant, r, which represents the position vector of any point on the surface source in the global rectangular coordinate system, and r 0 represents the unit vector of the observation direction in the global spherical coordinate system, and Ω represents the observation space in the global spherical coordinate system.

[0046] The analytical expression of the excitation distribution of the curved surface source is as follows:

[0047] I surf =[∫∫(G surf ) H G surf dΩ] -1 [∫∫(G surf ) H E Taylor dΩ]

[0048] The superscript -1 indicates an inversion operation, and the superscript H indicates a conjugate transpose operation.

[0049] The analytical expression of the excitation distribution of the conformal array antenna is as follows:

[0050]

[0051] Among them, I c represents the excitation distribution of the conformal array antenna, E c Depend on Composition, T m represents the rotation matrix of the mth array element, r m represents the position vector of the mth array element, Represents the Taylor pattern of the conformal array antenna.

[0052] The implementation steps and effects of the embodiments of the present invention are further described below in conjunction with the drawings and embodiments.

[0053] Reference Figure 1 , the steps of the Taylor weighted method for continuous surface source in an embodiment of the present invention are further described.

[0054] Step 1: For large-aperture continuous surfaces, the Huygens source pattern is not very directional and its influence can be ignored. Therefore, the spatial factor of the surface source is used to construct the Taylor pattern. Similar to the spatial factor of the plane source, Figure 2 The spatial factor of the surface source shown can be expressed as:

[0055]

[0056] Among them, F(u,v,w) represents the three-dimensional virtual source space factor along the three viewing directions u,v,w in the global spherical coordinate system, L x , L y and L z denote the length of the surface source along the x, y, and z axes in the global rectangular coordinate system, λ is the wavelength, θ and Respectively represent the angles between the far field direction and the positive directions of the coordinate axes z and x, such as Figure 2 As shown, e () It represents the exponential function with the natural constant e as the base, j represents the symbol of the imaginary unit, and π represents the ratio of a circumference to a circumference of ...

[0057] Step 2: Equivalent the spatial factor of the surface source to the spatial factor of the virtual cuboid source. The spatial factor of the virtual source can be expressed as

[0058]

[0059] Among them, I vir (x′, y′, z′) represents the excitation of the virtual source at the point (x′, y′, z′) in the global rectangular coordinate system, represents the length of the virtual source along the x-axis in the global rectangular coordinate system, μ represents the oversampling coefficient, and the value range of μ is 1.2 to 2.

[0060] Step 3: The key to constructing the Taylor pattern from the continuous source and the ideal spatial factor is to obtain the zero point of the real source, and then reconstruct the zero point of the Taylor pattern by combining the zero point of the ideal spatial factor. Obviously, the zero point of the equivalent virtual source spatial factor is not easy to obtain analytically, so assuming that the virtual source aperture field is uniformly distributed, let I vir (x′, y′, z′) = 1, the rewritten virtual source space factor can be expressed as:

[0061]

[0062] Among them, sin(·) represents the sine function. At this time, the zero point calculation of the surface source is simplified to the zero point calculation of the virtual rectangular source with uniform excitation, which greatly simplifies the difficulty of zero point calculation of any surface source. The zero point of the rewritten virtual source space factor is easy to obtain, and its zero point can be expressed as:

[0063] c x0 = ±n or c y0 = ±n or c z0 =±n,n=0,1,2,….

[0064] Remove the rewritten virtual source space factor in the front Zero points are replaced by the zero points of the ideal space factor, and the other zero points remain unchanged, then a new pattern function can be obtained, that is, the Taylor pattern of the surface source can be expressed as:

[0065]

[0066] Among them, E Taylor represents the Taylor pattern of the curved source, C represents the expected maximum sidelobe level of the Taylor pattern of the curved source, C=cosh(πA), and cosh(·) represents the hyperbolic cosine function. When realizing the Taylor pattern of the curved source, C is a predetermined value, so A can be determined by C=cosh(πA), and further by Sure Π(·) represents a continuous multiplication symbol.

[0067] Step 4: Usually, observe the directional component The change pattern of cosθ in the observation space is inconsistent, and even the change trend is opposite, which leads to the sidelobe level in the far sidelobe area of ​​the constructed curved source Taylor pattern being higher than that in the near sidelobe area, that is, the virtual source has a "grating lobe effect", which can be overcome by mathematical means. Figure 3 The cylindrical surface source shown is used as an example to demonstrate the "grating lobe effect" of the virtual source and a mathematical solution is given.

[0068] Figure 4 Shown Figure 3 (a) shows the semi-cylindrical surface source The -30dB Taylor weighted pattern constructed by the virtual source spatial factor has a maximum sidelobe level of -29.07dB in the near sidelobe area, which basically meets the requirements; the sidelobe level in the far sidelobe area is much greater than -30dB. And the sidelobe level does not decrease in sequence, which shows that the curved source Taylor pattern directly constructed by the virtual source spatial factor produces a "grating lobe effect". The reason is that the zero depth position of the field component of the Taylor pattern constructed by the virtual source spatial factor along the x, y and z directions is offset from the "grating lobe" position. Figure 5 (a) Figure 5 (b) and Figure 5 (c) respectively give Figure 4 The components of the Taylor pattern of the curved source along the x, y and z directions are shown. It is easy to observe that the inconsistent variation patterns of the patterns in the x and z directions lead to the appearance of the "grating lobe effect".

[0069] Therefore, it is necessary to slightly modify the curved source Taylor pattern so that the side lobes of the constructed curved source Taylor pattern show a decreasing trend as a whole. Figure 5 It is easy to think that shifting the phase of the field component along a certain coordinate axis by 90° can ensure that the sidelobe level of the field component along each axis has the same decreasing trend. Figure 3 The Taylor weighting of the semi-cylindrical surface source shown in (a) can shift the field component along the z-axis by 90°, that is, the Taylor directivity diagram of the surface source.

[0070]

[0071] Figure 6 After phase shift The cut-plane -30dB Taylor weighted radiation pattern has a maximum sidelobe level of -33.13dB, which meets the requirements and is comparable to Figure 4 The sidelobe level has shown an overall decreasing trend.

[0072] Step 5, after completing the construction of the curved surface source Taylor pattern, the next step is to obtain the excitation distribution that can form the curved surface source Taylor pattern. The curved surface source spatial factor can also be expressed in the following matrix form:

[0073] F(u,v,w)=G surf I surf

[0074] Among them, I surf It represents the surface source excitation distribution, which is a column vector, G surf Indicates that each observation point is The row vector is composed of k, which represents the free space wave constant, r, which represents the position vector of any point on the surface source in the global rectangular coordinate system, and r 0 A unit vector representing the viewing direction in the global spherical coordinate system.

[0075] The following least squares model is established to obtain the excitation distribution of the surface source:

[0076] find I surf

[0077] min∫∫ Ω ||G surf I surf -E Taylor || 2 dΩ

[0078] Among them, find I surf It means solving the column vector I consisting of the surface source excitation distribution surf , min∫∫ Ω G surf I surf -E Taylor 2 dΩ is a constraint condition, which means that when G surf I surf -E Taylor When the 2-norm of is minimum, I is obtained surf ,||·|| 2 represents the 2-norm, and Ω represents the observation space in the global spherical coordinate system.

[0079] Solving the above least squares model, the analytical expression of the surface source excitation distribution can be obtained as:

[0080] I surf =[∫∫(G surf ) H G surf dΩ] -1 [∫∫(G surf ) H E Taylor dΩ]

[0081] The superscript -1 indicates an inversion operation, and the superscript H indicates a conjugate transpose operation.

[0082] In the traditional method, after obtaining the excitation distribution corresponding to the continuous source Taylor pattern, the excitation distribution of the discrete array antenna is generally obtained according to the array element position. At this time, design errors are often introduced, causing the discrete array pattern to be far different from the continuous source Taylor pattern. Therefore, for conformal array antennas, the least squares method is still used to obtain the Taylor distribution of conformal array antennas.

[0083] For a conformal array antenna containing M array elements, assuming that the radiating elements are well matched, the radiation field can be expressed as:

[0084]

[0085] in, represents the radiation field of the conformal array antenna, T m represents the rotation matrix of the mth array element. m represents the element orientation pattern in the local spherical coordinate system, such as Figure 7 shown. is the complex excitation of the mth array element; r n is the position vector of the nth array element; I c Is The column vector, E c If so, The row vector formed by .

[0086] The Taylor pattern of the conformal array antenna can be expressed as follows based on the Taylor pattern of the curved source:

[0087]

[0088] in, represents the Taylor pattern of the conformal array antenna, It represents the unit radiation pattern of the virtual source in the global spherical coordinate system in the discrete case. The unit radiation pattern is obtained by taking the average value of all conformal array elements in the local spherical coordinate system established with the center of the array element as the origin. In addition, the unit radiation pattern of the array element is usually less than 1 and changes in a single and slow manner. Therefore, for conformal array antennas, The introduction of does not raise the sidelobe level of the array, so Taylor patterns that can be used to construct conformal arrays.

[0089] Similar to the curved source, the analytical expression of the excitation distribution of the conformal array antenna is:

[0090]

[0091] The least squares method is used to obtain the Taylor distribution of conformal array antennas. In addition to avoiding the design error introduced by the traditional array element position sampling method, it can also accurately obtain the excitation distribution corresponding to the Taylor pattern when considering the mutual coupling effect of the array elements.

[0092] The effect of the present invention can be further demonstrated through the following simulation.

[0093] 1. Simulation experimental conditions.

[0094] The software platforms for the simulation experiment of the present invention are: Windows 10 operating system and Matlab R2021b.

[0095] 2. Analysis of simulation content and results.

[0096] There are two simulation experiments of the present invention.

[0097] 2.1 Simulation experiment 1 is the verification of the Taylor pattern of the curved source.

[0098] The surface source used in the simulation experiment 1 of the present invention is as follows Figure 3 As shown, the radius is 4λ, the height is 1570.8mm, and the operating frequency is 2.4GHz.

[0099] The simulation experiment 1 of the present invention adopts the method of the present invention and an existing technology to obtain a -30dB Taylor directional pattern, and then the obtained Taylor directional pattern is plotted as follows: Figure 8(a) and Figure 8 The two curves (b) show that the excitation amplitude and phase distribution corresponding to the -30dB Taylor radiation pattern obtained by the method of the present invention are respectively as follows: Figure 8 (c) and Figure 8 (d) as shown.

[0100] In simulation experiment 1, an existing technology used is:

[0101] Xiamen University proposed a method for synthesizing Taylor patterns of array antennas in its patent application “Taylor-Shekunoff polynomial design method for array antennas” (application number CN 201510155810.9, authorization announcement number CN 104701639 B).

[0102] 2.2 Simulation Experiment 2 is the verification of the Taylor pattern of the conformal array antenna.

[0103] The cylindrical conformal array antenna used in the simulation experiment 2 of the present invention is as follows: Fig. 9 As shown in (b), the geometric model of the array element is as follows Fig. 9 (a) shows the array element dimensions, Table 1 shows the dielectric constant of the dielectric substrate is 2.2. The array operates at 2.4 GHz, the cylinder radius is R = 2.5λ, the array elements are evenly distributed and the spacing is 0.5λ.

[0104] Table 1 Geometric dimensions of conformal front microstrip antenna

[0105]

[0106] Simulation experiment 2 of the present invention adopts the method of the present invention and an existing technology to obtain -30dB Taylor radiation pattern respectively, and then draws the obtained Taylor radiation pattern as shown in the following figure: Fig.10 (a) and Fig.10 (b) The two curves shown.

[0107] In simulation experiment 2, an existing technology used is:

[0108] Xiamen University proposed a method for synthesizing Taylor patterns of array antennas in its patent application “Taylor-Shekunoff polynomial design method for array antennas” (application number CN 201510155810.9, authorization announcement number CN 104701639 B).

[0109] The effects of the present invention are further described below in conjunction with simulation diagrams.

[0110] Based on Example 2, the simulation content and results are as follows:

[0111] Figure 8 (a) and Figure 8 (b) shows the typical cross-sections in and The Taylor pattern of the curved surface source of the cut surface, the horizontal axis represents the observation angle, the unit is °, and the vertical axis represents the normalized pattern, the unit is dB. Among them, the curve marked with a black straight line represents the Taylor pattern of the curved surface source obtained by simulation using the prior art 1, and the curve marked with a gray straight line represents the Taylor pattern of the curved surface source obtained by the method proposed in the present invention. Figure 8 (c) and Figure 8 (d) The excitation replica diagram and phase distribution diagram corresponding to the Taylor radiation pattern of the curved source obtained by the method proposed in the present invention are respectively given.

[0112] Table 2 compares the sidelobe level and mainlobe width of the Taylor pattern of the curved source proposed in the prior art and the present invention at a typical section. Figure 8 It can be seen from (a), (b) and Table 2 that the method proposed in the present invention is easier to achieve the expected sidelobe level when applied to a curved source than the prior art.

[0113] Table 2 Comparison of the main lobe width () and the highest side lobe level (dB) of the typical section of the Taylor radiation pattern of the back curved source

[0114]

[0115] Fig.10 (a) and (b) show typical cross-sections, and The Taylor pattern of the conformal array antenna of the cut surface, the horizontal axis represents the observation angle, the unit is °, and the vertical axis represents the normalized pattern, the unit is dB. Among them, the curve marked with a black straight line represents the Taylor pattern of the conformal array antenna obtained by simulation using the prior art 1, and the curve marked with a gray straight line represents the Taylor pattern of the conformal array antenna obtained by the method proposed in the present invention.

[0116] Table 3 compares the sidelobe level and mainlobe width of the Taylor pattern of the conformal array antenna proposed in the prior art and the present invention at a typical cut plane. Obviously, the Taylor pattern of the conformal array antenna obtained by the method proposed in the present invention is easier to meet the expected sidelobe requirements than the prior art.

[0117] Table 3 Comparison of the main lobe width () and the highest side lobe level (dB) of the typical section of the Taylor pattern of conformal array antenna

[0118]

[0119] The above simulation experiments show that the Taylor weighted method for continuous curved surface sources of the present invention can significantly reduce the sidelobe level compared with the prior art, and perfectly meet the expected low sidelobe level, can significantly reduce the interference caused by the side lobes, and improve the system's anti-interference ability; at the same time, it can directly establish a least squares model of the Taylor radiation pattern and the antenna excitation distribution, give an analytical expression for the excitation distribution, and save computing resources.

[0120] The above description is only an example of the present invention and does not constitute any limitation to the present invention. Any person skilled in the art can think of making possible changes and modifications to the technical solution of the present invention by using the above disclosed methods and technical contents without departing from the content of the technical solution of the present invention. Therefore, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A Taylor weighting method for continuous surface sources, characterized in that: An equivalent virtual source Taylor pattern for a continuous curved surface source is constructed, and a discrete conformal array antenna excitation distribution is obtained using a least squares method. The steps of the Taylor weighted method include the following: Step 1, the curved surface source is equivalent to a three-dimensional virtual source, and based on the spatial factor of the three-dimensional virtual source, the phase of the field component is adjusted to ensure that the side lobes of the directional pattern show an overall downward trend, and the Taylor directional pattern of the curved surface source is constructed; The expression of the Taylor pattern of the surface source is as follows: Among them, E Taylor represents the Taylor pattern of the curved source, C represents the expected maximum sidelobe level of the Taylor pattern of the curved source, C=cosh(πA), cosh(·) represents the hyperbolic cosine function, and C is a predetermined value when realizing the Taylor pattern of the curved source. Therefore, A can be determined by C=cosh(πA), and further by Sure sin(·) represents the sine function, π represents the circumference of a circle, c x0 、c y0 、c z0 They represent the field components along the x-axis, y-axis, and z-axis after the phase is shifted by 90°, Π(·) represents the multiplication symbol, They represent the lengths of the virtual source along the x-axis and y-axis in the global rectangular coordinate system respectively; The Taylor pattern expression of conformal array antenna is as follows: in, represents the Taylor pattern of the conformal array antenna, represents the unit pattern of the virtual source in the global spherical coordinate system in the discrete case. The unit pattern is obtained by taking the average value of all conformal array elements in the local spherical coordinate system established with the center of the array element as the origin. M represents the total number of conformal array elements, and f m Represents the unit pattern of conformal array elements in the local spherical coordinate system; Step 2: Using the least squares method, a correlation model between the constructed Taylor pattern and the curved source excitation distribution and the conformal array antenna excitation distribution is established to obtain an analytical expression for the excitation distribution.

2. The Taylor weighting method for continuous surface sources according to claim 1, characterized in that: The curved surface source described in step 1 refers to a curved surface source that can be discretized into a conformal array antenna.

3. The Taylor weighting method for continuous surface source according to claim 1, characterized in that: The three-dimensional virtual source space factors described in step 1 are as follows: Among them, F(u,v,w) represents the three-dimensional virtual source space factor along the three viewing directions u,v,w in the global spherical coordinate system, L y and L z denote the length of the surface source along the x, y, and z axes in the global rectangular coordinate system, λ is the wavelength, θ and Respectively represent the angles between the far field direction and the positive directions of the coordinate axes z and x, I vir (x′, y′, z′) represents the excitation of the virtual source at the point (x′, y′, z′) in the global rectangular coordinate system, represents the length of the virtual source along the x-axis in the global rectangular coordinate system, μ represents the oversampling factor, and the value range of μ is 1.2 to 2. (·) It represents the exponential function with the natural constant e as the base, j represents the symbol of the imaginary unit, and π represents the ratio of a circumference to a circumference of ...

4. The Taylor weighting method for continuous surface source according to claim 3, characterized in that: Adjusting the phase of the field component described in step 1 means adjusting the field component sidelobe level of each axis in the global rectangular coordinate system according to the following formula so that it has the same decreasing trend as the field component sidelobe level of each axis: Among them, c z0 It represents the field component along the z-axis after the phase is adjusted by 90°.

5. The Taylor weighting method for continuous surface source according to claim 4, characterized in that: The least square method described in step 2 is used to establish the correlation model between the constructed Taylor pattern and the surface source excitation distribution as follows: find surf Among them, find I surf It means solving the column vector I consisting of the surface source excitation distribution surf , min∫∫ Ω ||G surf I surf -E Taylor || 2 dΩ is a constraint condition, which means that when G surf I surf -E Taylor When the 2-norm of is minimum, I is obtained surf ,||·|| 2 represents the 2-norm operation, G surf Indicates that each observation point is The row vector is composed of k, which represents the free space wave constant, r, which represents the position vector of any point on the surface source in the global rectangular coordinate system, r0, which represents the unit vector of the observation direction in the global spherical coordinate system, and Ω, which represents the observation space in the global spherical coordinate system.

6. The Taylor weighting method for continuous surface source according to claim 5, characterized in that: The analytical expression of the surface source excitation distribution described in step 2 is as follows: I surf =[∫∫(G surf ) H G surf dΩ] -1 [∫∫(G surf ) H E Taylor dΩ] The superscript -1 indicates an inversion operation, and the superscript H indicates a conjugate transpose operation.

7. The Taylor weighting method for continuous surface source according to claim 6, characterized in that: The analytical expression of the excitation distribution of the conformal array antenna described in step 2 is as follows: Among them, I c represents the excitation distribution of the conformal array antenna, E c Depend on Composition, T m represents the rotation matrix of the mth array element, r m represents the position vector of the mth array element, Represents the Taylor pattern of the conformal array antenna.

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