CN117932863A - Rapid calculation method for curved surface conformal phased array gain pattern - Google Patents
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Abstract
The rapid development of the phased array radar enables the phased array application scene to be more and more, and the curved surface conformal phased array gain pattern calculation method needs to be optimized urgently, so that the calculated amount is reduced, the calculated time is shortened, and the engineering design requirements are met. The invention provides a gain pattern rapid calculation method applied to an arbitrary curved surface conformal phased array, which is characterized in that radiation fields of all units in the curved surface conformal phased array are inverted to a virtual plane array vertical to beam pointing through fast Fourier transformation, and excitation of the conformal array corresponding to the virtual array under different excitation is obtained through linear superposition synthesis; and performing inverse fast Fourier transform on the synthesized virtual array to obtain a gain pattern of the curved conformal phased array. The method reduces the calculated amount and the calculated time of the gain pattern of the curved surface conformal phased array, and can obtain the gain pattern result in the corresponding polarization direction.
Description
Technical Field
The invention belongs to the field of antennas and microwaves, and particularly relates to a method for rapidly calculating a curved surface conformal phased array gain pattern.
Background
Phased arrays have become the main regime of radar since this century. Compared with the traditional mechanical rotating parabolic antenna, the phased array realizes the functions of rapid beam scanning, space power synthesis, rapid beam shape change, multi-beam formation and the like through modulating the amplitude and the phase of a large number of array antenna units. And the gain achieved by a phased array with a large number of antenna elements also has a stability that is substantially better than that of a conventional antenna. Thus, phased array radar has become the mainstream radar at present.
The rapid development of the phased array radar makes the phased array application scene more and more, and many times, the phased array radar must conform to the carrying platform due to the limitation of the carrying platform, the requirement of the application scene and the like. In this case the phased array surface is no longer planar but curved or more complex. At this time, a Fast Fourier Transform (FFT) method cannot be used to quickly calculate the phased array gain pattern. Currently, the main solution to this problem is to accumulate the radiation fields generated by each cell, which results in a very large calculation effort and a very long calculation time, especially in case of a large number of cells in the array. In the case where pattern synthesis is required for a curved conformal phased array, the computation time and computation effort produced by the accumulation method is often intolerable. Therefore, optimization of the curved surface conformal phased array gain pattern calculation method is urgently needed, so that the calculated amount is reduced, the calculation time is shortened, and the engineering design requirements are met.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a rapid calculation method of a gain pattern applied to an arbitrary curved surface conformal phased array, which overcomes the defects of large calculation amount and low calculation speed of the traditional calculation method, inverts the radiation field of each unit in the curved surface conformal phased array to a virtual plane array perpendicular to the beam direction through Fast Fourier Transform (FFT), and obtains the excitation of the conformal array corresponding to the virtual array under different excitation through linear superposition synthesis; and performing Inverse Fast Fourier Transform (IFFT) on the synthesized virtual array to obtain a gain pattern of the curved conformal phased array. The method reduces the calculated amount and the calculated time of the gain pattern of the curved surface conformal phased array, and can obtain the gain pattern result under the corresponding polarization direction. The method is suitable for pattern calculation and array synthesis and optimization of a large curved surface conformal phased array.
The method specifically comprises the following steps:
1. Establishing a global coordinate system:
The global coordinate system is established according to the requirement, no special requirement exists, as shown in fig. 2, the O g is used as the origin of coordinates to establish the No. 0 coordinate system O g-xgygzg, the corresponding xyz axis base vector is (e xg,eyg,ezg), and the corresponding spherical coordinate system is
2. Establishing a beam local coordinate system:
The beam pointing direction is (x pg,ypg,zpg), and the corresponding spherical coordinates are The virtual array plane normal direction is the same as the beam pointing direction, such as plane 1 or plane 2 in fig. 2. The center O 1 of the plane is taken as the origin of coordinates, the beam direction is taken as the z axis, the x axis and the y axis can be selected according to the needs, no special requirements exist, a beam local coordinate system O 1-x1y1z1 is established, and the corresponding base vector of the xyz axis is (e x1,ey1,ez1). As shown in the coordinate system No. 1 in fig. 2.
In practice, the z-distance between each unit of the curved array and the virtual plane affects the calculation accuracy and the calculation amount. The virtual array plane z-distance should be chosen such that the sum of the vertical distances of the cells in the actual array to the virtual array plane is as small as possible, as plane 2 in fig. 2 is chosen over plane 1.
3. Establishing a unit local coordinate system:
the installation position of the unit under the global coordinate system is O e(xeg,yeg,zeg), and the corresponding spherical coordinate is After the unit is installed, the reference axis of the unit corresponds to the base vector (e xe,eye,eze), and a local coordinate system O e-xeyeze of the unit is established according to the base vector, such as the coordinate system No.2 shown in fig. 2. The x-axis and y-axis directions of each cell local coordinate system should be chosen to be consistent with respect to the physical structure of the cell.
4. Radiation field of the calculation unit:
Calculating a radiation field under a unit coordinate system O e-xeyeze through full-wave simulation software;
According to the coordinate transformation formula, the radiation field in the unit coordinate system is converted into the beam coordinate system O 1-x1y1z1. The spatial sampling is in sinusoidal space equidistant, the distance selection is selected according to the distance between the current unit and the reference plane, and the distance is selected upwards to the nearest 2 N. When the spacing du is selected, du < delta lambda/de, delta is generally not more than 0.1, and the smaller the calculation accuracy is, the higher the calculation amount is.
5. The left-right handed components LHC n1 and RHC n1 of the radiation field of the computing unit in the beam local coordinate system (the conformal array units are installed in different orientations, and generally need to adopt a circular polarization form to form a beam after polarization compensation):
6. Normalizing the left-right handed component:
normalizing the radiation field of each unit in the beam coordinate system by taking the unit (or imaginary unit) of which the unit coordinate system is coincident with the beam coordinate system as a reference;
7. Calculating virtual excitation of each unit:
and calculating excitation coefficients of the units in a virtual array, wherein the unit interval of the virtual array is selected to be half wavelength, and the virtual array is parallel to the xy plane of the beam coordinate system. (the cell pattern reference frame translates to the lower left corner of the virtual array, the cell virtual array size is 2 N×2N, the same as the sine space sampling number, the virtual array lattice points coincide with the fitting plane lattice points, the cell virtual array center is as close as possible to the projection point of the cell on the virtual plane), the phase change of the observation point caused by the translation of the cell coordinate system to the beam coordinate system.
Considering the phase change of each element field component due to the translation of the viewpoint from the element coordinate system to the beam coordinate system, the calculated element normalized left-hand component or right-hand component is transformed to an excitation coefficient of 2 N×2N by a Fast Fourier Transform (FFT), such as region 1 or region 2 in fig. 2.
8. Calculating a virtual excitation plane synthesized by all units:
performing linear synthesis on the virtual excitation distribution and the unit excitation coefficients obtained by fitting each unit to obtain virtual excitation planes of all units:
A m,n is the equivalent excitation at the nth column lattice point of the mth row of the virtual array, a j is the excitation coefficient of the jth cell, For the j-th cell excitation, a fast fourier transform is fitted to the equivalent excitation at the m-th row and n-th column grid points on the virtual plane.
9. Calculating a curved surface conformal phased array gain pattern:
After the step (8), the virtual array to be solved is a conventional land grid array. And obtaining a virtual array factor of the curved surface conformal phased array through Inverse Fast Fourier Transform (IFFT) on the obtained virtual excitation plane. And multiplying the virtual array factor by the zenith unit directional diagram to obtain a directional diagram of the curved surface phased array.
And establishing a beam local coordinate system in the second step, and establishing the local coordinate system according to the beam direction, so that the gain direction diagram of the concerned region can be calculated more accurately, and the polarization mode can be distinguished better. The virtual array plane position is set so that the sum of the vertical distances from each unit in the actual array to the virtual array plane is as small as possible. If the distance of the curved surface conformal phased array surface unit in the beam direction is too far, the curved surface array can be divided into a plurality of sections in the beam direction, each section is fitted by adopting the steps of claim 1, and finally, the sections are overlapped to form a total directional diagram. The normal directions of the several virtual array planes used for fitting are identical. By using the method, the fitting precision of the curved surface conformal array is improved, and the calculated amount of fitting is reduced.
In the fourth step, the radiation field of the unit is calculated, and the radiation field of the unit under the unit coordinate system can be calculated through full-wave simulation software (HFSS, FEKO and the like) or can be directly calculated through theoretical explanatory formula (for example, the unit is a half-wave vibrator, a dipole and the like). The radiation field is converted into a beam coordinate system, the space sampling direction is in sinusoidal space with equal spacing, the spacing selection is selected according to the distance between the current unit and the reference plane, and the distance is selected upwards to the nearest 2 N. When the spacing du is selected, du < delta lambda/de, delta is generally not more than 0.1, and the smaller the calculation accuracy is, the higher the calculation amount is.
And step five, calculating left-right rotation components under a beam local coordinate system, wherein the amplitude normalization process of the left-right rotation components and zenith units can be selected, but the phase normalization is important. The zenith unit is a unit with a unit coordinate system coincident with the beam pointing coordinate system.
And step six, normalizing the left-right rotation component, wherein the coordinate system of the zenith unit is coincident with the beam coordinate system, and if the unit is not arranged in the actual array, setting a virtual zenith unit.
And step seven, calculating virtual excitation of each unit, and considering phase change caused by viewpoint conversion in the conversion process of the unit radiation field from the unit local coordinate system to the beam local coordinate system before fitting the normalized components. The unit virtual excitation is calculated using FFT. The calculated unit radiation field needs to be sampled according to the precision requirement, and the obtained virtual excitation also needs to correspond to the virtual excitation array of the 2 N×2N grid area in the virtual excitation plane according to the precision requirement. The size of the grid region is gradually increased from the nearest to the farthest of the virtual excitation plane. The center of the grid area is located as close as possible to the projection of the cell onto the virtual plane. The size of the virtual excitation array is the same as the number of sinusoidal spatial samples.
And step nine, calculating a gain pattern of the curved surface phased array, obtaining a virtual array factor of the curved surface conformal phased array through IFFT, and multiplying the virtual array factor with the pattern of the zenith unit to obtain the gain pattern after normalization.
The invention has the beneficial effects that
1. The method uses a Fast Fourier Transform (FFT) method to calculate the curved conformal phased array gain pattern, and has high calculation speed and small calculation amount.
2. According to the invention, the FFT is used for inverting the radiation fields of each unit to obtain virtual excitation, the calculation result is comprehensive and accurate, and besides the unit radiation field interval sampling, the calculation process has no theoretical error and no information loss.
3. The method can calculate the left-right rotation component of the radiation according to the requirements, and complete the distinction of the curved surface conformal phased array polarization.
4. The method is suitable for calculating the gain pattern of the conformal phased array with any curved surface.
5. When the conformal array directional diagram is synthesized, inversion from the unit directional diagram to the virtual array is only needed once, and the virtual array of each unit is excitedBy multiplying the excitation coefficient a j of the unit, a lot of time can be saved.
Drawings
FIG. 1 is a flow chart of the method of the present invention.
FIG. 2 is a schematic diagram of a curved conformal phased array and the establishment of coordinate systems according to the present invention.
Fig. 3 is a schematic diagram of an embodiment of the spherical conformal phased array of the present invention.
FIG. 4 shows a unit according to the inventionTo the electric field component amplitude profile.
FIG. 5 shows a unit according to the inventionTo the electric field component phase profile.
Fig. 6 is a graph showing the magnitude distribution of the electric field component in a unit θ according to the present invention.
Fig. 7 is a graph showing the phase distribution of the electric field component of a unit θ according to the present invention.
Fig. 8 is a typical element left-hand amplitude pattern in the beam coordinate system of the present invention.
Fig. 9 is a typical element left-hand phase pattern in the beam coordinate system of the present invention.
FIG. 10 is a graph of the virtual excitation amplitude distribution of a cell according to the present invention.
FIG. 11 is a graph of the virtual excitation phase profile of a cell according to the present invention.
Fig. 12 is a graph of virtual excitation amplitude distribution of all cell combinations of the present invention.
Fig. 13 is a graph of the virtual excitation phase profile of all cell combinations of the present invention.
Fig. 14 is a sinusoidal spatial gain amplitude pattern for a spherical conformal phased array embodiment of the invention.
Fig. 15 is a sinusoidal spatial gain phase pattern for a spherical conformal phased array embodiment of the invention.
Fig. 16 is a gain pattern for a spherical conformal phased array embodiment of the invention.
Fig. 17 is a pitch gain pattern for a spherical conformal phased array embodiment of the invention.
Detailed Description
The following description of the technical solutions in the embodiments of the present invention will be clear and complete, and it is obvious that the described embodiments are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The invention relates to a rapid calculation method applied to a curved surface conformal phased array gain pattern, wherein a flow chart is shown in fig. 1, and comprises the following steps of taking spherical array pattern calculation as an example:
step one: establishing a global coordinate system
The shape of the spherical conformal phased array is shown in fig. 3, the origin (spherical center) O g is selected to establish a global cartesian coordinate system, and the corresponding xyz-axis base vector is (e xg,eyg,ezg).
Step two: establishing a beam local coordinate system
Beam pointing e rp＝(xpg,ypg,zpg), converted to a pointing direction
By establishing a beam local coordinate system, taking beam direction e rp as a z axis, a spherical surface e θp can be selected as an x axis,A cartesian coordinate system is established for the y-axis as shown in fig. 3. The beam plane position is selected according to the minimum vertical distance from all units, and the middle position of all units can be selected, wherein the calculation formula is (R+R cos (theta max)/2. R is spherical radius, and theta max is the maximum included angle of the units deviating from the z axis under the beam local coordinate system.
In the beam local coordinate system, the directional orientation of the antenna unit is selected in the sine space and is an equidistant grid. Grid spacing formula:
du＝δλ/de，δ<0.1；
when the unit direction diagram is interpolated, only the points in the unit circle need to be calculated, and the unit circle is set as follows: u n,vn,wn.
Step three: establishing a unit local coordinate system
Set a unit mounting position asEstablishing a unit local coordinate system, wherein the corresponding relation between the coordinate system and the global coordinate system is as follows:
The conversion of the sinusoidal space (u n,vn,wn) to be solved under the beam local coordinate system to the unit local coordinate system is as follows:
The spherical coordinates in the local coordinate system of the corresponding unit are represented as theta ne and The method comprises the following steps:
step four: radiation field of a computing unit
1. The radiation field of the unit is calculated using full wave simulation software (HFSS, FEKO) or the like, as shown in fig. 4 to 7.
2. According to the coordinates theta ne andInterpolation calculation of the radiation fields E θne and/>, of the cells under the local coordinate system of the cellOr directly calculating a radiation field (such as a half-wave vibrator, a dipole and the like) by using theoretical analysis, and converting the radiation field into a beam local coordinate system:
The far field electric field is perpendicular to the direction of propagation, so both E rn and E rne are 0.
Step five: left-right rotation component of radiation field of calculation unit under beam local coordinate system
The left-right hand component of the radiation field in the beam local coordinate system is:
Step six: normalizing the left-right rotation component
Zenith unit left-right rotation component in reference beam local coordinate systemAnd/>And normalizing:
the zenith unit cell coordinate system coincides with the beam coordinate system and typical normalized left-hand directional diagram calculations are shown in fig. 8 and 9.
Step six: calculating virtual excitation of units
The above normalized pattern phase reference point is a unit position, and the reference point when the virtual array is fitted is a grid point of the left lower corner of the virtual array of the array, and each unit corresponds to a projection point of the virtual array center on the virtual plane as close as possible to the unit, such as the area 1 in fig. 3.
Calculating a phase change of the observation point caused by translation of the unit coordinate system to the beam coordinate system, wherein the origin of the beam coordinate system is selected as O p, and the phase change is as follows:
normalizing the obtained units to left-handed components Or right-hand component/>Fitting to a planar array of 2 N×2N by Fast Fourier Transform (FFT), this example N takes values of 6 to 8, corresponding to the nearest to furthest elements from the virtual excitation plane. The amplitude and phase of the virtual excitation obtained by fitting the set cell positions are shown in fig. 10 and 11, respectively.
Step seven: calculating virtual excitation planes for all cell synthesis
And synthesizing the virtual excitation obtained by fitting each unit to obtain virtual excitation planes of all the units. Typical calculation results are shown in fig. 12 and 13.
Step eight: calculating curved surface conformal phased array gain directional diagram
1. And obtaining a virtual array factor of the curved surface conformal phased array through Inverse Fast Fourier Transform (IFFT) on the calculated virtual excitation plane.
2. And multiplying the virtual array factor by the zenith unit directional diagram to obtain the gain directional diagram of the curved surface phased array.
The final pattern results obtained by calculation are shown in fig. 14 to 17. Fig. 16 and 17 show the comparison of the calculation results of the method of the present invention with the addition method. When the accumulation method is used, the radiation fields of each unit are required to be calculated independently, and finally the total radiation field is obtained by accumulation. The calculation time is only about 0.2% of the summation method, and the final calculation result is almost identical to the summation method. The accuracy and the high efficiency of the invention are fully illustrated.
The present invention is not limited to the above-described specific embodiments, and various modifications and variations are possible. Any modification, equivalent replacement, improvement, etc. of the above embodiments according to the technical substance of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. A method for rapidly calculating a curved surface conformal phased array gain pattern is characterized by comprising the following steps of: the method comprises the following steps:
step one: establishing a global coordinate system
For the form of a curved surface conformal phased array, selecting a coordinate origin, establishing a global Cartesian coordinate system O g-xgygzg, wherein the corresponding xyz axis base vector is (e xg,eyg,ezg), and the corresponding spherical coordinate system is
Step two: establishing a beam local coordinate system;
beam pointing direction e rp(xpg,ypg,zpg), corresponding spherical coordinates of The beam direction e rp is taken as a z axis, an x axis and a y axis are selected according to the need, a beam local coordinate system O 1-x1y1z1 is established, the corresponding xyz axis base vector is (e x1,ey1,ez1), and the sine space to be solved under the beam local coordinate system is (u n,vn,wn);
step three: establishing a unit local coordinate system
The installation position of the unit under the global coordinate system is O e(xeg,yeg,zeg), and the corresponding spherical coordinate isAfter the unit is installed, the reference axis of the unit corresponds to a base vector (e xe,eye,eze), and a unit local coordinate system O e-xeyeze is established according to the base vector;
Converting the sinusoidal space (u n,vn,wn) to be solved under the beam local coordinate system into (u ne,vne,wne) under the unit local coordinate system, corresponding to the spherical coordinates theta ne and theta
Step four: radiation field of a computing unit
According to the spherical coordinates theta ne andCalculating the radiation field E θne and/>, of the cell under the cell local coordinate system O e-xeyeze And converts it into a beam local coordinate system O 1-x1y1z1;
step five: calculating left-right rotation components of a radiation field of the unit under a beam local coordinate system;
Step six: normalizing the left-right rotation component
Normalizing the calculated left-right component of the unit radiation field with respect to the left-right component of the zenith unit under the partial coordinate system of the beam;
Step seven: calculating virtual excitation of units
Fitting the obtained unit normalized left-handed component or right-handed component to a unit excitation coefficient of 2 N×2N through fast Fourier transform;
step eight: calculating virtual excitation planes for all cell synthesis
Performing linear synthesis on the virtual excitation distribution and the unit excitation coefficients obtained by fitting each unit to obtain virtual excitation planes of all units;
step nine: calculating curved surface conformal phased array gain directional diagram
Obtaining a virtual array factor of the curved surface conformal phased array through inverse fast Fourier transform of the calculated virtual excitation plane; and multiplying the virtual array factor by the zenith unit directional diagram to obtain a directional diagram of the curved surface phased array.
2. The method for rapidly calculating the gain pattern of the curved conformal phased array according to claim 1, wherein the method comprises the following steps: when the beam local coordinate system is established, the set virtual array plane position is selected so that the sum of the vertical distances between each unit in the actual array and the virtual array plane is as small as possible.
3. The method for rapidly calculating the gain pattern of the curved conformal phased array according to claim 1, wherein the method comprises the following steps: if the distance of the curved surface conformal phased array surface unit in the beam direction is too far, the curved surface array can be divided into a plurality of sections in the beam direction, then each section is fitted, and finally, the sections are overlapped to form a total directional diagram; the normal directions of the several virtual array planes used for fitting are identical.
4. The method for rapidly calculating the gain pattern of the curved conformal phased array according to claim 1, wherein the method comprises the following steps: the radiation field of the unit under the unit local coordinate system can be calculated through full-wave simulation software, and can also be directly calculated through theoretical interpretation.
5. The method for rapidly calculating the gain pattern of the curved conformal phased array according to claim 1, wherein the method comprises the following steps: the radiation field of the unit is converted into a beam local coordinate system, the space sampling direction is in sinusoidal space equidistant, the distance selection is selected according to the distance between the current unit and the reference surface, and the distance is selected upwards to the nearest 2 N.
6. The method for rapidly calculating the gain pattern of the curved conformal phased array according to claim 1, wherein the method comprises the following steps: calculating virtual excitation of each unit, sampling the calculated unit radiation field according to the precision requirement, and obtaining virtual excitation which corresponds to a virtual excitation array of a 2 N×2N grid area in a virtual excitation plane according to the precision requirement; the size of the grid area is gradually increased from the nearest unit to the farthest unit of the virtual excitation plane, the position center of the grid area is as close to the projection of the unit to the virtual plane as possible, and the size of the virtual excitation array is the same as the sine space sampling number.
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