CN113567766A - Spherical near-field phase measurement method and system based on cubic spline interpolation algorithm - Google Patents
Spherical near-field phase measurement method and system based on cubic spline interpolation algorithm Download PDFInfo
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Abstract
The application particularly relates to a method and a system for measuring a spherical near-field phase based on a cubic spline interpolation algorithm, wherein the method comprises the following steps: acquiring first near-field amplitude data and second near-field amplitude data of a near-field region radiated by a test antenna; obtaining first interpolation amplitude data and second interpolation amplitude data by using a cubic spline interpolation algorithm; calculating iterative field distribution of the first spherical surface based on the first interpolation amplitude data, and calculating initial iterative field distribution of the second spherical surface based on the iterative field distribution of the first spherical surface; based on the initial iterative field distribution, after amplitude substitution, the iterative field distribution of the first spherical surface is obtained through sphere mode expansion, and the iterative field distribution of the first spherical surface contains amplitude data to be verified, which are obtained through calculation; calculating an error value of the first near-field amplitude data and the amplitude data to be verified; if the error value is smaller than the preset value, the electric field phase distribution of the restored first spherical surface is output, and the technical problem that the near field phase is difficult to measure in the spherical surface near field measurement is effectively solved.
Description
Technical Field
The invention relates to the technical field of antennas, in particular to a spherical near-field phase measurement method and system based on a cubic spline interpolation algorithm.
Background
With the development of communication technology and the increase of the size of the antenna, the far-field measurement condition of the antenna cannot be met more and more, and the near-field measurement of the antenna plays a crucial role. The near-field antenna measurement is used for measuring the amplitude and the phase of the near field of the near-field antenna in a small microwave darkroom, and the far-field data of the antenna is indirectly obtained through a strict near-field and far-field conversion algorithm. The measuring method has small occupied area and isolates external interference. However, as the operating frequency of the antenna increases, the measurement of the antenna phase becomes more difficult, requiring more stringent and expensive measurement equipment. In the prior art, a phase-free near-far field conversion algorithm based on a plane occupies the mainstream, and far field data can be obtained through the near-far field conversion algorithm only by measuring amplitude data on two measuring planes without measuring phase data. The spherical near-field measurement is a measurement method which is suitable for various beam antennas and has high measurement precision and good confidentiality. The spherical surface-based phase-free near-field measurement method should be more widely applied.
In the prior art, the spherical phase-free near-field measurement technology adopts two different measurement spherical surfaces for amplitude detection, and uses the spherical wave expansion theory to iterate a spherical electric field, so that the far-field directional diagram of the antenna can be measured by only using the spherical amplitude measurement. Compared with the traditional spherical surface near-field measurement, two or more spherical surfaces are needed for sampling, and the sampling work is complex. As the frequency increases, the wavelength of the antenna decreases as the frequency increases. The half-wavelength sampling interval determined according to the nyquist sampling theorem is very small, which greatly increases the difficulty of testing the antenna near-field data.
Disclosure of Invention
In view of the above problems in the prior art, an object of the present invention is to provide a lightweight network middleware architecture system and a satellite communication method, which can effectively solve the technical problem that the near-field phase is difficult to measure in the spherical near-field measurement, and overcome the technical problem that the near-field phase information is insufficient.
In order to solve the technical problems, the specific technical scheme is as follows:
in one aspect, a method for measuring a spherical near-field phase based on a cubic spline interpolation algorithm is provided, including:
acquiring first near-field amplitude data of a first spherical surface and second near-field amplitude data of a second spherical surface of a near-field region radiated by a test antenna, wherein the first spherical surface and the second spherical surface are separated by a preset distance;
respectively interpolating the first near-field amplitude data and the second near-field amplitude data by using a cubic spline interpolation algorithm to obtain first interpolation amplitude data and second interpolation amplitude data, wherein the number of the first interpolation amplitude data and the second interpolation amplitude data is a target number;
calculating an iterative field distribution of the first spherical surface based on the first interpolated magnitude data, and calculating an initial iterative field distribution of the second spherical surface based on the iterative field distribution of the first spherical surface;
based on the initial iterative field distribution of the second spherical surface, after amplitude substitution, the iterative field distribution of the first spherical surface is obtained through sphere mode expansion, wherein the iterative field distribution of the first spherical surface contains amplitude data to be verified, which are obtained through calculation;
calculating an error value of the first near-field amplitude data and the amplitude data to be verified;
and if the error value is smaller than the preset value, outputting the electric field phase distribution of the restored first spherical surface.
Further, the interpolating the first near-field amplitude data and the second near-field amplitude data by using a cubic spline interpolation algorithm to obtain first interpolated amplitude data and second interpolated amplitude data respectively includes:
inserting a plurality of interpolation nodes in sampling points corresponding to the first near-field amplitude data and the second near-field amplitude data at equal intervals respectively;
respectively substituting the interpolation nodes into a preset cubic spline function, and respectively calculating cubic spline interpolation functions corresponding to the interpolation nodes, wherein the cubic spline interpolation functions are polynomials not more than 3, the second derivative functions of the cubic spline interpolation are continuous, and the second derivative functions of two boundary interpolation nodes in an interpolation interval are both 0;
and sequentially substituting the interpolation nodes into the corresponding cubic spline interpolation functions to obtain corresponding first interpolation amplitude data and second interpolation amplitude data.
Further, the method further comprises:
determining near field data after phase recovery according to the electric field phase of the restored first spherical surface and the first near field amplitude data;
and determining a far-field directional pattern of the antenna according to the near-field data after the phase recovery by using a near-far field transformation theory of mode expansion.
Further, said calculating an iterative field distribution of said first sphere based on said first interpolated magnitude data comprises: the iterative field of the first spherical surface is E'1＝M#1e-j*αWhere j is the imaginary component, M#1Is the first interpolated amplitude data of the first sphere, and α is the initial phase of the first sphere.
Further, said calculating an initial iterative field distribution of said second spherical surface based on said iterative field distribution of said first spherical surface comprises:
determining a mode coefficient according to an initial iteration field of the first spherical surface according to a mode expansion theory of spherical waves;
and determining the initial iterative field distribution of the second spherical surface according to the mode coefficient and the initial iterative field of the first spherical surface.
Further, the calculating an error value of the first near-field amplitude data and the amplitude data to be verified comprises:
substituting the first near-field amplitude data and the amplitude data to be verified into the following formula to obtain the error value epsilon:
wherein: epsilon represents the error value, theta,
respectively two coordinates of a spherical coordinate system,
respectively represent E1In the theta direction and
a field of direction, E1The initial iterative field distribution of the second spherical surface is replaced by amplitude, and then the iterative field distribution of the first spherical surface is obtained by the expansion of the spherical mode,
first interpolation amplitude data M respectively representing first spherical surfaces#1At a ratio of theta and
the magnitude of the direction.
Further, the method further comprises:
if the error value is larger than a preset value, the phase of the iterative field distribution of the first spherical surface is reserved, and the iterative field of the first spherical surface is returned to the step of calculating the initial iterative field distribution of the second spherical surface based on the iterative field distribution of the first spherical surface until the error value is smaller than or equal to the preset value;
or, when the returning times exceed the preset times, outputting the electric field phase distribution of the first spherical surface restored at the last time.
Further, the target number is determined by a sampling period.
In another aspect, provided herein is a spherical near-field phase measurement system based on cubic spline interpolation algorithm, comprising:
a data acquisition module configured to perform acquisition of first near-field amplitude data of a first spherical surface and second near-field amplitude data of a second spherical surface of a near-field region radiated by a test antenna, the first spherical surface and the second spherical surface being spaced by a preset distance;
an interpolation data determination module configured to perform interpolation on the first near-field amplitude data and the second near-field amplitude data using a cubic spline interpolation algorithm to obtain first interpolation amplitude data and second interpolation amplitude data, wherein the first interpolation amplitude data and the second interpolation amplitude data are both in target number;
a first calculation module configured to perform the calculation of the iterative field distribution of the first spherical surface based on the first interpolated magnitude data and the calculation of the initial iterative field distribution of the second spherical surface based on the iterative field distribution of the first spherical surface;
the second calculation module is configured to execute initial iterative field distribution based on the second spherical surface, and after amplitude substitution, the iterative field distribution of the first spherical surface is obtained through sphere mode expansion, wherein the iterative field distribution of the first spherical surface contains the amplitude data to be verified, which is obtained through calculation;
an error calculation module configured to perform calculating an error value of the first near-field amplitude data and the amplitude data to be verified;
and the output module is configured to output the restored electric field phase distribution of the first spherical surface if the error value is smaller than a preset value.
Further, the interpolated data determining module includes:
an interpolation unit configured to perform interpolation of a plurality of interpolation nodes at equal intervals in sampling points corresponding to the first near-field amplitude data and the second near-field amplitude data, respectively;
a function determining unit configured to perform substitution of the plurality of interpolation nodes into preset cubic spline functions respectively, and calculate cubic spline interpolation functions corresponding to the plurality of interpolation nodes respectively, wherein the cubic spline interpolation functions are polynomials not more than 3, the second derivative functions of the cubic spline interpolation are continuous, and the second derivative function values of two boundary interpolation nodes in an interpolation interval are both 0;
an interpolation data determination unit configured to perform sequentially substituting the plurality of interpolation nodes into the corresponding cubic spline interpolation functions to obtain corresponding first interpolation amplitude data and second interpolation amplitude data.
By adopting the technical scheme, the spherical near-field phase measurement method and system based on the cubic spline interpolation algorithm, which are disclosed by the invention, the phase of the near field is restored by combining the phase restoration algorithm of the phase-free spherical near field based on mode expansion and the cubic spline interpolation algorithm, the data of the measured data can be reduced while the restoration precision is ensured, the phase data of the spherical near-field sampling point can be effectively restored, a far-field directional diagram close to a far field is obtained by combining the measured amplitude data, the technical problem that the near-field phase is difficult to measure in the spherical near-field measurement is effectively solved, and the technical problem of insufficient near-field phase information is overcome.
In order to make the aforementioned and other objects, features and advantages of the present invention comprehensible, preferred embodiments accompanied with figures are described in detail below.
Drawings
In order to more clearly illustrate the embodiments or technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic diagram illustrating steps of a spherical near-field phase measurement method based on a cubic spline interpolation algorithm provided in an embodiment of the present disclosure;
FIG. 2 is a schematic diagram illustrating steps of another spherical near-field phase measurement method based on cubic spline interpolation provided in the embodiments herein;
FIG. 3 is a schematic diagram illustrating steps of another spherical near-field phase measurement method based on cubic spline interpolation provided in the embodiments herein;
FIG. 4 is a schematic diagram illustrating steps of another spherical near-field phase measurement method based on cubic spline interpolation provided in the embodiments herein;
FIG. 5 is a schematic structural diagram illustrating a spherical near-field phase measurement system based on a cubic spline interpolation algorithm provided in an embodiment of the present disclosure;
fig. 6 shows a schematic structural diagram of an interpolation data determination module provided in an embodiment herein.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments herein without making any creative effort, shall fall within the scope of protection.
It should be noted that the terms "first," "second," and the like in the description and claims herein and in the above-described drawings are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used is interchangeable under appropriate circumstances such that the embodiments herein described are capable of operation in sequences other than those illustrated or described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, apparatus, article, or device that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed, but may include other steps or elements not expressly listed or inherent to such process, method, article, or device.
In order to solve the above problems, embodiments herein provide a spherical near-field phase measurement method based on a cubic spline interpolation algorithm, which can effectively recover spherical near-field sampling point phase data fig. 1 shows a schematic step diagram of a spherical near-field phase measurement method based on a cubic spline interpolation algorithm provided in embodiments herein, and the present specification provides the method operation steps as described in the embodiments or the flowchart, but may include more or less operation steps based on conventional or non-creative labor. The order of steps recited in the embodiments is merely one manner of performing the steps in a multitude of orders and does not represent the only order of execution. In practice, the method may be executed sequentially or in parallel according to the method shown in the embodiment or the attached drawings when executed in the architecture system of the lightweight network middleware. Specifically, as shown in fig. 1, the method may include:
s102: the method comprises the steps of obtaining first near field amplitude data of a first spherical surface and second near field amplitude data of a second spherical surface of a near field region radiated by a test antenna, wherein the first spherical surface and the second spherical surface are separated by a preset distance.
Specifically, the near field region is shown as being about 4-20 wavelengths from the antenna, and the far field may be considered as infinity.
It should be noted that some antennas are relatively small, and the wavelengths are relatively small, and the certain distance may be tens of wavelengths or tens of wavelengths. Some measured environments are relatively small and may be several wavelengths apart. Therefore, in the present application, the first spherical surface and the second spherical surface are spaced apart by the preset distance, which means that the interval from several wavelengths to several tens of wavelengths is not equal. The two sampling spherical surfaces are concentric spherical surfaces, the antenna is taken as a spherical center, and the value of the interval preset distance is the difference between the radius r1 of the first spherical surface and the radius r2 of the second spherical surface.
In one embodiment, an antenna model is built in the HFSS, and the amplitude data of the first spherical surface and the amplitude data of the second spherical surface of the antenna are obtained through the built model. A pyramidal horn antenna having a frequency of 4.5GHz is used as the device under test in the present embodiment. The near field data is data sampled at certain sampling intervals on a spherical surface near the tested equipment, and first near field amplitude data M of which two sampling spherical surfaces are respectively first spherical surfaces can be obtained through analog simulation#1And second near-field amplitude data M#2。
S104: and respectively interpolating the first near-field amplitude data and the second near-field amplitude data by using a cubic spline interpolation algorithm to obtain first interpolation amplitude data and second interpolation amplitude data, wherein the number of the first interpolation amplitude data and the second interpolation amplitude data is the target number.
In a specific embodiment, fig. 2 shows a schematic step diagram of another spherical near-field phase measurement method based on a cubic spline interpolation algorithm provided in this embodiment, and as shown in fig. 2, the interpolating the first near-field amplitude data and the second near-field amplitude data respectively by using the cubic spline interpolation algorithm to obtain first interpolated amplitude data and second interpolated amplitude data includes:
s202: inserting a plurality of interpolation nodes in sampling points corresponding to the first near-field amplitude data and the second near-field amplitude data at equal intervals respectively;
s204: respectively substituting the interpolation nodes into a preset cubic spline function, and respectively calculating cubic spline interpolation functions corresponding to the interpolation nodes, wherein the cubic spline interpolation functions are polynomials not more than 3, the second derivative functions of the cubic spline interpolation are continuous, and the second derivative functions of two boundary interpolation nodes in an interpolation interval are both 0;
s206: and sequentially substituting the interpolation nodes into the corresponding cubic spline interpolation functions to obtain corresponding first interpolation amplitude data and second interpolation amplitude data.
Illustratively, according to the nyquist theorem:
wherein the content of the first and second substances,
and N is ka +10, and a is the minimum radius surrounding the antenna to be measured. Interval of sampling
Should be less than 7.2 deg., and may be employed in embodiments of this specification
The sampling strategy of (1). In a specific implementation, the pair θ or
Performs interpolation operation in one direction.
Sampling strategy
The original data adopts an interpolation algorithm, and n interpolation nodes X are input at equal intervals in the first near-field amplitude data and the second near-field amplitude data of the sampling points corresponding to the original spherical near-field data0、X1、…Xn-1，Wherein a ═ X0＜X1＜…＜Xn-1＝b，[a，b]Is an interpolation interval. In the examples in the specification, a is 0, b is 180, and n is 20. Respectively substituting the n interpolation nodes into a preset cubic spline function to obtain cubic spline interpolation function values corresponding to the n interpolation nodes, wherein the cubic spline interpolation function is a polynomial not more than 3, the second derivative function of the cubic spline interpolation is continuous, and the boundary interpolation node X of the interpolation interval is located0And Xn-1The second derivative value of (2) is 0. Thereby determining the first interpolated magnitude data as [ a, X ]1、…Xn-2，b]The second interpolation amplitude data is similar to the first interpolation amplitude data and is not described again. It is understood that the number of interpolation nodes provided by the embodiments of the present specification may be 20.
S106: and calculating the iterative field distribution of the first spherical surface based on the first interpolation amplitude data, and calculating the initial iterative field distribution of the second spherical surface based on the iterative field distribution of the first spherical surface.
Specifically, the iteration field of the first spherical surface may be E'1＝M#1e-j*αWhere j is the imaginary component, M#1Is the first interpolated amplitude data of the first sphere, and α is the initial phase of the first sphere. In order to verify the accuracy of the method, in the present embodiment, the initial phase α is selected to be a relatively accurate value, that is, α is 0.
In a specific embodiment, according to the mode expansion theory of spherical waves, determining a mode coefficient according to the initial iteration field of the first spherical surface;
and determining the initial iterative field distribution of the second spherical surface according to the mode coefficient and the initial iterative field of the first spherical surface.
Specifically, the principle can be expanded according to the mode of spherical wavesIn general, the electric field formed by the first spherical surfaceE′1Respectively obtaining the mode coefficients amnAnd bmnCoefficient of mode amnAnd bmnCan be expressed as:
wherein the content of the first and second substances,
is a function of the second class of ball-hank functions, theta,
coordinates in two directions of a spherical coordinate system can be expressed, j is an imaginary part, N is 1, 2, 3, …, N, m is 0, ± 1, ± 2, …, ± N, and represents a mode coefficient, N is ka +10, where a is a size of the antenna, k is a wave number, and m and N represent the mode coefficient.
Representing the near field spherical electric field data of the antenna, in theta and phi directions, respectively, and Smn and S' mn may represent a code number, one with legendre function, and one with differential form of legendre function.
Then, a conversion formula expanded by a ball mode is utilized, and the conversion formula is based on a mode coefficient amnAnd bmnAnd the initial iterative field of the first spherical surface determines an initial iterative field distribution of the second spherical surface, wherein,
wherein, the conversion formula of the ball mode expansion is as follows:
wherein the ratio of gamma, theta,
the coordinates of a spherical coordinate system, N being 1, 2, 3, …, N, m being 0, ± 1, ± 2, …, ± N, m, N represent mode coefficients, amn、bmnThe coefficients of the modes are represented by,
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Is a function of a spherical wave,
the spherical electric field distribution vector is obtained.
Specifically, the mode expansion theory of spherical waves is as follows:
assuming that the smallest sphere of radius a surrounds the antenna, the electric field in the region r < ═ a space can be represented by a linear combination of two vector wave functions as in the above equation (3).
From equation (4), the hankel and legendre functions can be calculated when the values of γ, θ,
when the fixing is carried out, the fixing device,
is a constant matrix of dimension m x n,
and
and the description is omitted.
It should be noted that, the calculation using the multidimensional matrix instead of the circular solution herein can accelerate the solution speed, and if the multidimensional matrix is not used, it is likely that the time for obtaining a result in one time of solution is one minute, and then it may take a long time to finally obtain a reduced phase through multiple iterations, for example, it may take about 2 hours to finally obtain a reduced phase through eight hundred iterations. And this application adopts the multidimensional matrix, and the time that obtains the result once solving is mostly several tenths of a second, can make the solution result faster.
Wherein
And
(i.e., the values of γ, θ,
) Is a unit vector in the spherical coordinate system,
for the second class of spherical-hank-functions,
is a function of legendre. Wherein:
by proximity to an antennaField data measurement, E can be obtainedθ，
From the above equation, it can be seen that only near field data of the antenna needs to be obtained, and far field data of any passive region can be obtained.
Distributing E 'to the initial iterative field of the first spherical surface'1Substituting the initial iterative field distribution E of the second spherical surface into a conversion formula expanded by a spherical mode to calculate2；
It can be seen that theoretical equations (1), (2) are developed from the mode of the spherical wave, and that the iterative field E 'from the first spherical surface'1Respectively obtaining the mode coefficients amnAnd bmn(ii) a An iterative field E 'of a first spherical surface'1Substituting the initial iterative field distribution E of the second spherical surface into conversion formulas (3), (4) and (5) expanded by the spherical mode to calculate2。
S108: and based on the initial iterative field distribution of the second spherical surface, after amplitude substitution, performing spherical mode expansion to obtain the iterative field distribution of the first spherical surface, wherein the iterative field distribution of the first spherical surface contains the amplitude data to be verified obtained through calculation.
In particular, retention E2With an assignment M of phase, amplitude data#2Substitute to obtain
Wherein angel (E)2) Represents the electric field distribution E2The phase data of (1). Unfolding theoretical formulas (1) and (2) according to iterative field E 'of second spherical surface according to mode of spherical wave'2Respectively obtaining the mode coefficients a corresponding to the second spherical surfacemnAnd bmn(ii) a Iterative field E 'of second spherical surface'2Substituting the obtained result into conversion formulas (3), (4) and (5) expanded by the sphere mode to calculate the iterative field distribution E of the first spherical surface1Iterative field distribution of the first sphere E1And the amplitude data to be verified obtained by calculation is contained.
Note that the iterative field E 'of the second spherical surface'2Iterative field E 'from a first spherical surface'1Determining the superposition of the first spherical surfaceE 'substitute'1Is the correct first amplitude data M obtained in the first step1The corresponding phase is in error. Iterative field E 'of second spherical surface obtained by the above-described mode expansion formula'2Has an error in both the second amplitude data and the phase, but because of the substitution of the first amplitude data M1Exact, iterative field E 'of the second sphere'2The phase error of (2) can be reduced to some extent.
S110: and calculating an error value of the first near-field amplitude data and the amplitude data to be verified.
In a specific embodiment, the calculating the error value of the first near-field amplitude data and the amplitude data to be verified includes:
substituting the first near-field amplitude data and the amplitude data to be verified into the following formula to obtain the error value epsilon:
where epsilon represents the error value, theta,
respectively two coordinates of a spherical coordinate system,
respectively represent E1In the theta direction and
a field of direction, E1The initial iterative field distribution of the second spherical surface is replaced by amplitude, and then the iterative field distribution of the first spherical surface is obtained by the expansion of the spherical mode,
first interpolation amplitude data M respectively representing first spherical surfaces#1At a ratio of theta and
the magnitude of the direction.
S112: and if the error value is smaller than the preset value, outputting the electric field phase distribution of the restored first spherical surface.
Specifically, the electric field phase distribution of the reduced first spherical surface is angelE1。
In a preferred embodiment, fig. 3 shows a schematic step diagram of another spherical near-field phase measurement method based on a cubic spline interpolation algorithm provided in the embodiments herein, and as shown in fig. 3, the method further includes:
s702: if the error value is greater than a preset value, the phase distributed by the iterative field of the first spherical surface is reserved, and the iterative field of the first spherical surface is E'1＝M#1e-j*αAnd returning to the step of calculating the initial iterative field distribution of the second spherical surface based on the iterative field distribution of the first spherical surface until the error value is less than or equal to a preset value.
S704: or, when the returning times exceed the preset times, outputting the electric field phase distribution of the first spherical surface restored at the last time. In one particular embodiment, the preset value may be set to-35 db, so that the output recovery phase is relatively accurate. By experimentation, it is also possible to set the first preset value lower, e.g., -50db, -60db, enabling a more accurate reduction phase than-30.
In the iteration step, if the error result epsilon reaches the set precision requirement, namely is smaller than the preset value, the iteration process is stopped, otherwise, only E is reserved1And E 'is prepared'1＝M#1ejaAnd returning to the step of calculating the initial iterative field distribution of the second spherical surface based on the iterative field distribution of the first spherical surface until the error is smaller than the preset value required by the precision or the algorithm iteration reaches the maximum times.
On the basis of the foregoing embodiments, in an embodiment of this specification, fig. 4 shows a schematic step diagram of a spherical near-field phase measurement method based on a cubic spline interpolation algorithm provided in this embodiment, and as shown in fig. 4, the method further includes:
s302: determining near field data after phase recovery according to the electric field phase of the restored first spherical surface and the first near field amplitude data;
s304: and determining a far-field directional pattern of the antenna according to the near-field data after the phase recovery by using a near-far field transformation theory of mode expansion.
Specifically, the electric field phase of the restored first spherical surface may be combined with the measured first near-field amplitude data, so that the near-field data with the recovered phase may be determined, and then, the far-field pattern of the antenna may be obtained from the near-field data by using the near-far field transformation theory of mode deployment. The theory of near-far field transformation belongs to the prior art and is not explained here.
In practical application of the present application, the initial phase α may be set to 0, and the near-field sampling interval is
When the method is adopted for interpolation without adopting an interpolation algorithm, the far-field data can be effectively recovered after 800 iterations. Using sampling intervals
Although the sampling strategy of (2) also meets the Nyquist sampling theorem, far-field data cannot be effectively recovered without adopting an interpolation algorithm. Therefore, the spherical near-field phase measurement method based on the cubic spline interpolation algorithm solves the problem of small application of scenes in the prior art through the cubic spline interpolation algorithm, and the technical scheme provided by the invention can adapt to more measurement scenes and can accurately recover far-field data when the acquired data is less.
In another specific embodiment, use is made of
The sampling strategy of (1) then adopts an interpolation algorithm to carry out interpolation, which is equivalent to that
Sampling points of this sampling strategy. The far field data can be effectively recovered, so that the precision is ensured, the number of sampling points is reduced compared with the original number, and the sampling work difficulty is reduced.
On the other hand, a spherical near-field phase measurement system based on a cubic spline interpolation algorithm is proposed herein, and fig. 5 shows a schematic structural diagram of a spherical near-field phase measurement system based on a cubic spline interpolation algorithm provided in an embodiment herein, as shown in fig. 5, including:
a data obtaining module 901 configured to perform obtaining first near-field amplitude data of a first spherical surface and second near-field amplitude data of a second spherical surface of a near-field region radiated by a test antenna, the first spherical surface and the second spherical surface being separated by a preset distance;
an interpolated data determining module 902 configured to perform interpolation on the first near-field amplitude data and the second near-field amplitude data using a cubic spline interpolation algorithm to obtain first interpolated amplitude data and second interpolated amplitude data, where the number of the first interpolated amplitude data and the number of the second interpolated amplitude data are both target numbers;
a first calculation module 903 configured to perform calculating an iterative field distribution of the first spherical surface based on the first interpolated magnitude data and calculating an initial iterative field distribution of the second spherical surface based on the iterative field distribution of the first spherical surface;
a second calculating module 904, configured to execute initial iterative field distribution based on the second spherical surface, and obtain iterative field distribution of the first spherical surface through sphere mode expansion after amplitude substitution, where the iterative field distribution of the first spherical surface includes calculated amplitude data to be verified;
an error calculation module 905 configured to perform calculating an error value of the first near-field amplitude data and the amplitude data to be verified;
the output module 906 is configured to output the electric field phase distribution of the restored first spherical surface if the error value is smaller than the preset value.
On the basis of the foregoing embodiment, in an embodiment of the present specification, the interpolated data determining module, fig. 6 shows a schematic structural diagram of an interpolated data determining module provided in this embodiment, and as shown in fig. 6, the interpolated data determining module includes:
an inserting unit 9021 configured to perform inserting of a plurality of interpolation nodes at equal intervals in sampling points corresponding to the first near-field amplitude data and the second near-field amplitude data, respectively;
a function determining unit 9022 configured to perform substitution of the plurality of interpolation nodes into preset cubic spline functions respectively, and calculate cubic spline interpolation functions corresponding to the plurality of interpolation nodes respectively, where the cubic spline interpolation functions are polynomials not more than 3, the second derivative functions of the cubic spline interpolation are continuous, and the second derivative function values of two boundary interpolation nodes in an interpolation interval where the second derivative functions are both 0;
an interpolation data determination unit 9023 configured to perform sequentially substituting the plurality of interpolation nodes into the corresponding cubic spline interpolation functions to obtain corresponding first interpolation amplitude data and second interpolation amplitude data.
It should be noted that the principle of the spherical near-field phase measurement system based on the cubic spline interpolation algorithm and the spherical near-field phase measurement method based on the cubic spline interpolation algorithm provided herein are the same, and the technical effect of the spherical near-field phase measurement method based on the cubic spline interpolation algorithm is achieved, and the details are not repeated.
It should be understood that, in various embodiments herein, the sequence numbers of the above-mentioned processes do not mean the execution sequence, and the execution sequence of each process should be determined by its function and inherent logic, and should not constitute any limitation to the implementation process of the embodiments herein.
It should also be understood that, in the embodiments herein, the term "and/or" is only one kind of association relation describing an associated object, meaning that three kinds of relations may exist. For example, a and/or B, may represent: a exists alone, A and B exist simultaneously, and B exists alone. In addition, the character "/" herein generally indicates that the former and latter related objects are in an "or" relationship.
Those of ordinary skill in the art will appreciate that the elements and algorithm steps of the examples described in connection with the embodiments disclosed herein may be embodied in electronic hardware, computer software, or combinations of both, and that the components and steps of the examples have been described in a functional general in the foregoing description for the purpose of illustrating clearly the interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present disclosure.
It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the above-described systems, apparatuses and units may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again.
In the several embodiments provided herein, it should be understood that the disclosed system, apparatus, and method may be implemented in other ways. For example, the above-described apparatus embodiments are merely illustrative, and for example, the division of the units is only one logical division, and other divisions may be realized in practice, for example, a plurality of units or components may be combined or integrated into another system, or some features may be omitted, or not executed. In addition, the shown or discussed mutual coupling or direct coupling or communication connection may be an indirect coupling or communication connection through some interfaces, devices or units, and may also be an electric, mechanical or other form of connection.
The units described as separate parts may or may not be physically separate, and parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units can be selected according to actual needs to achieve the purposes of the embodiments herein.
In addition, functional units in the embodiments herein may be integrated into one processing unit, or each unit may exist alone physically, or two or more units are integrated into one unit. The integrated unit can be realized in a form of hardware, and can also be realized in a form of a software functional unit.
The integrated unit, if implemented in the form of a software functional unit and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solutions of the present invention may be implemented in a form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the methods described in the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The principles and embodiments of this document are explained herein using specific examples, which are presented only to aid in understanding the methods and their core concepts; meanwhile, for the general technical personnel in the field, according to the idea of this document, there may be changes in the concrete implementation and the application scope, in summary, this description should not be understood as the limitation of this document.
Claims (10)
1. A spherical near-field phase measurement method based on a cubic spline interpolation algorithm is characterized by comprising the following steps:
acquiring first near-field amplitude data of a first spherical surface and second near-field amplitude data of a second spherical surface of a near-field region radiated by a test antenna, wherein the first spherical surface and the second spherical surface are separated by a preset distance;
respectively interpolating the first near-field amplitude data and the second near-field amplitude data by using a cubic spline interpolation algorithm to obtain first interpolation amplitude data and second interpolation amplitude data, wherein the number of the first interpolation amplitude data and the second interpolation amplitude data is a target number;
calculating an iterative field distribution of the first spherical surface based on the first interpolated magnitude data, and calculating an initial iterative field distribution of the second spherical surface based on the iterative field distribution of the first spherical surface;
based on the initial iterative field distribution of the second spherical surface, after amplitude substitution, the iterative field distribution of the first spherical surface is obtained through sphere mode expansion, wherein the iterative field distribution of the first spherical surface contains amplitude data to be verified, which are obtained through calculation;
calculating an error value of the first near-field amplitude data and the amplitude data to be verified;
and if the error value is smaller than the preset value, outputting the electric field phase distribution of the restored first spherical surface.
2. The method of claim 1, wherein interpolating the first near-field magnitude data and the second near-field magnitude data using a cubic spline interpolation algorithm to obtain first interpolated magnitude data and second interpolated magnitude data, respectively, comprises:
inserting a plurality of interpolation nodes in sampling points corresponding to the first near-field amplitude data and the second near-field amplitude data at equal intervals respectively;
respectively substituting the interpolation nodes into a preset cubic spline function, and respectively calculating cubic spline interpolation functions corresponding to the interpolation nodes, wherein the cubic spline interpolation functions are polynomials not more than 3, the second derivative functions of the cubic spline interpolation are continuous, and the second derivative functions of two boundary interpolation nodes in an interpolation interval are both 0;
and sequentially substituting the interpolation nodes into the corresponding cubic spline interpolation functions to obtain corresponding first interpolation amplitude data and second interpolation amplitude data.
3. The method of claim 1, further comprising:
determining near field data after phase recovery according to the electric field phase of the restored first spherical surface and the first near field amplitude data;
and determining a far-field directional pattern of the antenna according to the near-field data after the phase recovery by using a near-far field transformation theory of mode expansion.
4. The method of claim 1, wherein said computing an iterative field distribution for the first sphere based on the first interpolated magnitude data comprises: the iterative field of the first spherical surface is E'1＝M#1e-j*αWhere j is the imaginary component, M#1Is the first interpolated amplitude data of the first sphere, and α is the initial phase of the first sphere.
5. The method of claim 1, wherein said calculating an initial iterative field distribution of the second spherical surface based on the iterative field distribution of the first spherical surface comprises:
determining a mode coefficient according to an initial iteration field of the first spherical surface according to a mode expansion theory of spherical waves;
and determining the initial iterative field distribution of the second spherical surface according to the mode coefficient and the initial iterative field of the first spherical surface.
6. The method of claim 1, wherein calculating an error value for the first near-field amplitude data and the amplitude data to be verified comprises:
substituting the first near-field amplitude data and the amplitude data to be verified into the following formula to obtain the error value epsilon:
where epsilon represents the error value, theta,
respectively two coordinates of a spherical coordinate system,
respectively represent E1In the theta direction and
a field of direction, E1The initial iterative field distribution of the second spherical surface is replaced by amplitude, and then the iterative field distribution of the first spherical surface is obtained by the expansion of the spherical mode,
first interpolation amplitude data M respectively representing first spherical surfaces#1At a ratio of theta and
the magnitude of the direction.
7. The method according to any one of claims 1-6, further comprising:
if the error value is larger than a preset value, the phase of the iterative field distribution of the first spherical surface is reserved, and the iterative field of the first spherical surface is returned to the step of calculating the initial iterative field distribution of the second spherical surface based on the iterative field distribution of the first spherical surface until the error value is smaller than or equal to the preset value; alternatively, the first and second electrodes may be,
and when the returning times exceed the preset times, outputting the electric field phase distribution of the first spherical surface restored at the last time.
8. The method of claim 7, wherein the target number is determined by a sampling period.
9. A spherical near-field phase measurement system based on cubic spline interpolation algorithm, the system comprising:
a data acquisition module configured to perform acquisition of first near-field amplitude data of a first spherical surface and second near-field amplitude data of a second spherical surface of a near-field region radiated by a test antenna, the first spherical surface and the second spherical surface being spaced by a preset distance;
an interpolation data determination module configured to perform interpolation on the first near-field amplitude data and the second near-field amplitude data using a cubic spline interpolation algorithm to obtain first interpolation amplitude data and second interpolation amplitude data, wherein the first interpolation amplitude data and the second interpolation amplitude data are both in target number;
a first calculation module configured to perform the calculation of the iterative field distribution of the first spherical surface based on the first interpolated magnitude data and the calculation of the initial iterative field distribution of the second spherical surface based on the iterative field distribution of the first spherical surface;
the second calculation module is configured to execute initial iterative field distribution based on the second spherical surface, and after amplitude substitution, the iterative field distribution of the first spherical surface is obtained through sphere mode expansion, wherein the iterative field distribution of the first spherical surface contains the amplitude data to be verified, which is obtained through calculation;
an error calculation module configured to perform calculating an error value of the first near-field amplitude data and the amplitude data to be verified;
and the output module is configured to output the restored electric field phase distribution of the first spherical surface if the error value is smaller than a preset value.
10. The system of claim 9, wherein the interpolated data determination module comprises:
an interpolation unit configured to perform interpolation of a plurality of interpolation nodes at equal intervals in sampling points corresponding to the first near-field amplitude data and the second near-field amplitude data, respectively;
a function determining unit configured to perform substitution of the plurality of interpolation nodes into preset cubic spline functions respectively, and calculate cubic spline interpolation functions corresponding to the plurality of interpolation nodes respectively, wherein the cubic spline interpolation functions are polynomials not more than 3, the second derivative functions of the cubic spline interpolation are continuous, and the second derivative function values of two boundary interpolation nodes in an interpolation interval are both 0;
an interpolation data determination unit configured to perform sequentially substituting the plurality of interpolation nodes into the corresponding cubic spline interpolation functions to obtain corresponding first interpolation amplitude data and second interpolation amplitude data.
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