CN106771672B - The method and device of Far-Field antennas measurement system is carried out based on cubic spline interpolation - Google Patents
The method and device of Far-Field antennas measurement system is carried out based on cubic spline interpolation Download PDFInfo
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Abstract
The embodiment of the invention provides a kind of method and devices that Far-Field antennas measurement system is carried out based on cubic spline interpolation, this method comprises: the first spherical surface Near-field Data of acquisition antenna；Interpolation is carried out to the corresponding sampled point of the first spherical surface Near-field Data using cubic spline interpolation, and determines the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated；Interpolation each corresponding spherical surface Near-field Data of interpolation knot generated and the first spherical surface Near-field Data are combined, the second spherical surface Near-field Data of the antenna is obtained；According to the second spherical surface Near-field Data of the antenna, the far-field pattern of the antenna is acquired.The sampling complexity of antenna damnification can either be reduced by this programme, and can guarantee the far-field pattern of antenna accuracy with higher.
Description
Technical field
The present invention relates to Far-Field antennas measurement system technical fields, in particular to a kind of to carry out antenna based on cubic spline interpolation
The method of far-field measurement and a kind of device that Far-Field antennas measurement system is carried out based on cubic spline interpolation.
Background technique
In recent years, due to the development of the communication technology and Radar Technology, antenna plays vital in wireless communications
Effect, antenna measurement is the important link of Antenna Design, currently, antenna measurement mainly have antenna near field measurement and antenna it is remote
Field measurement is not easy to directly be measured due to influence of the far-field measurement vulnerable to factors such as environment and places of antenna, because
The near field measurement data of antenna are usually obtained the far-field pattern of antenna by stringent Near-far fields transfer by this, the antenna
Far-field pattern is the measurement result of Far-Field antennas measurement system.The near field measurement of antenna mainly has: Planar Near-Field Measurement, cylinder are close
Field measurement and spherical surface near field measurement, wherein spherical surface near field measurement has the antenna, the measuring accuracy that are suitble to various types wave beam because of it
Height, good confidentiality, can all weather operations and be widely used.In the prior art, spherical surface near field measurement data are being utilized
During obtaining the far-field pattern of antenna, in order to reduce the sampling complexity of spherical surface near field measurement data, three are generallyd use
Preserving Interpolation Using method carries out interpolation to the corresponding sampled point of near field measurement data, but since cubic polynomial interpolation method cannot be protected
Card interpolation fitting curve is smooth in entire interpolation section, and the near field measurement data error for the interpolation knot being calculated is larger, from
And the accuracy for resulting in Antenna Far Field directional diagram is not high.
Therefore, the sampling complexity of antenna damnification how had not only been reduced, but also has guaranteed the essence of Antenna Far Field directional diagram
Exactness height becomes urgent problem to be solved.
Summary of the invention
The embodiment of the present invention be designed to provide based on cubic spline interpolation carry out spherical surface far-field measurement method and
Device to solve not only reduce the sampling complexity of antenna damnification in the prior art, but also guarantees Antenna Far Field directional diagram
The high problem of accuracy.Specific technical solution is as follows:
In a first aspect, the embodiment of the invention provides a kind of sides for carrying out Far-Field antennas measurement system based on cubic spline interpolation
Method, comprising:
Acquire the first spherical surface Near-field Data of antenna；
Interpolation is carried out to the corresponding sampled point of the first spherical surface Near-field Data using cubic spline interpolation, and determines and inserts
It is worth the corresponding spherical surface Near-field Data of each interpolation knot generated, wherein all interpolation knots and first spherical surface near field
The total quantity of sampled point corresponding to data is equal to destination number, and the destination number is is marked off according to destination sample interval
Sampled point quantity, the spherical surface near field number according to the antenna determined by predetermined sampling thheorem is divided between the destination sample
According to sampling interval；
By interpolation each corresponding spherical surface Near-field Data of interpolation knot generated and the first spherical surface Near-field Data group
It closes, obtains the second spherical surface Near-field Data of the antenna；
According to the second spherical surface Near-field Data of the antenna, the far-field pattern of the antenna is acquired.
Optionally, it is described the corresponding sampled point of the first spherical surface Near-field Data is carried out using cubic spline interpolation it is slotting
Value, and the step of determining interpolation each interpolation knot generated corresponding spherical surface Near-field Data, comprising:
N interpolation knot X is equally spacedly inputted in the corresponding sampled point of the first spherical surface Near-field Data0、X1、…、
Xn-1, wherein a=X0<X1<…<Xn-1=b, [a, b] are interpolation section；
The n interpolation knot is substituted into respectively in preset cubic spline functions, it is corresponding to acquire n interpolation knot
Cubic spline functions value, wherein the cubic spline functions are multinomial, the sample three times no more than 3 times
The second order derived function of interpolating function is continuous and the interpolating on sides nodes X of the interpolation section0And Xn-1Second order derived function value
It is 0；
It is corresponding that the corresponding cubic spline functions value of the n interpolation knot is determined as the n interpolation knot
Spherical surface Near-field Data.
Optionally, the second spherical surface Near-field Data according to the antenna, acquires the far-field pattern of the antenna
Step, comprising:
Using the second spherical surface Near-field Data of the antenna, ball mode expansion coefficient is calculated；
The ball mode expansion coefficient is substituted into preset far field solution formula, the far field direction number of the antenna is acquired
According to；
According to the far field bearing data of the antenna, the far-field pattern of the antenna is drawn；
Wherein, the formula of the ball mode expansion coefficient is calculated are as follows:
Wherein, amnAnd bmnFor the ball mode expansion coefficient, VθAnd VφFor the second spherical surface Near-field Data of the antenna, fn
And gnFor ball Hankel function, SmnAnd S 'mnFor Legendre function；
The preset far field solution formula are as follows:
Wherein,For the far field bearing data；
Optionally, the step of the first spherical surface Near-field Data of the acquisition antenna, comprising:
The sampling interval of the spherical surface Near-field Data of acquisition antenna is calculated according to the predetermined sampling thheorem；
According to institute's calculated sampling interval, between the first sampling for determining the first spherical surface Near-field Data for acquiring the antenna
Every；Wherein, first sampling interval is greater than institute's calculated sampling interval；
It is acquired according to first spherical surface Near-field Data of first sampling interval to the antenna.
Second aspect carries out Far-Field antennas measurement system based on cubic spline interpolation the embodiment of the invention also provides a kind of
Device, comprising:
Acquisition module, composite module, solves module at interpolating module；
Wherein,
The acquisition module, for acquiring the first spherical surface Near-field Data of antenna；
The interpolating module, for utilizing cubic spline interpolation to the corresponding sampled point of the first spherical surface Near-field Data
Carry out interpolation, and determine the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated, wherein all interpolation knots and
The total quantity of sampled point corresponding to the first spherical surface Near-field Data is equal to destination number, and the destination number is according to target
The quantity for the sampled point that sampling interval is marked off is divided between the destination sample according to described determined by predetermined sampling thheorem
The sampling interval of the spherical surface Near-field Data of antenna；
The composite module, for by the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated and described the
The combination of one spherical surface Near-field Data, obtains the second spherical surface Near-field Data of the antenna；
The solution module acquires the far field side of the antenna for the second spherical surface Near-field Data according to the antenna
Xiang Tu.
Optionally, the interpolating module, comprising:
Interpolation knot submodule is inputted, for equally spacedly defeated in the corresponding sampled point of the first spherical surface Near-field Data
Enter n interpolation knot X0、X1、…、Xn-1, wherein a=X0<X1<…<Xn-1=b, [a, b] are interpolation section；
Interpolating function value submodule is solved, for the n interpolation knot to be substituted into preset cubic spline interpolation respectively
In function, the corresponding cubic spline functions value of n interpolation knot is acquired, wherein the cubic spline functions are not
The second order derived function of multinomial, the cubic spline functions more than 3 times is continuous and the boundary of the interpolation section is inserted
Value node X0And Xn-1Second order derived function value be 0；
It determines spherical surface Near-field Data submodule, is used for the corresponding cubic spline functions value of the n interpolation knot
It is determined as the corresponding spherical surface Near-field Data of the n interpolation knot.
Optionally, the solution module, comprising:
Ball mode expansion coefficient submodule is calculated, for the second spherical surface Near-field Data using the antenna, calculates ball mould
Formula expansion coefficient；
Far field bearing data submodule is solved, for the ball mode expansion coefficient to be substituted into preset far field solution formula
In, acquire the far field bearing data of the antenna；
It draws far-field pattern submodule and draws the remote of the antenna for the far field bearing data according to the antenna
Field pattern；
Wherein, the formula of the ball mode expansion coefficient is calculated are as follows:
Wherein, amnAnd bmnFor the ball mode expansion coefficient, VθAnd VφFor the second spherical surface Near-field Data of the antenna, fn
And gnFor ball Hankel function, SmnAnd S 'mnFor Legendre function；
The preset far field solution formula are as follows:
Wherein,For the far field bearing data；
Optionally, the acquisition module, comprising:
Sampling interval submodule is calculated, for calculating the spherical surface Near-field Data of acquisition antenna according to the predetermined sampling thheorem
Sampling interval；
The first sampling interval submodule is determined, for determining and acquiring the antenna according to institute's calculated sampling interval
First sampling interval of the first spherical surface Near-field Data；Wherein, first sampling interval is greater than between the calculated sampling of institute
Every；
Submodule is acquired, for adopting according to first spherical surface Near-field Data of first sampling interval to the antenna
Collection.
In the method for carrying out Far-Field antennas measurement system provided by the embodiment of the present invention based on cubic spline interpolation, day is acquired
First spherical surface Near-field Data of line；The corresponding sampled point of the first spherical surface Near-field Data is carried out using cubic spline interpolation
Interpolation, and determine the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated；By interpolation each interpolation generated
The corresponding spherical surface Near-field Data of node and the first spherical surface Near-field Data combination, obtain the second spherical surface near field number of the antenna
According to；According to the second spherical surface Near-field Data of the antenna, the far-field pattern of the antenna is acquired.Compared with prior art, originally
Scheme carries out interpolation to the corresponding sampled point of the first spherical surface Near-field Data using cubic spline interpolation, can reduce antenna near-field
The sampling complexity of measurement shortens the antenna damnification time；And cubic spline functions have on entire interpolation section
There are enough slickness, there is excellent mathematical feature, therefore, while reducing the sampling complexity of antenna damnification,
It can also ensure that the Antenna Far Field directional diagram accuracy with higher that antenna near-field data obtain after Near-far fields transfer.
Detailed description of the invention
In order to more clearly explain the embodiment of the invention or the technical proposal in the existing technology, to embodiment or will show below
There is attached drawing needed in technical description to be briefly described, it should be apparent that, the accompanying drawings in the following description is only this
Some embodiments of invention for those of ordinary skill in the art without creative efforts, can be with
It obtains other drawings based on these drawings.
Fig. 1 is a kind of method for carrying out Far-Field antennas measurement system based on cubic spline interpolation provided by the embodiment of the present invention
A kind of flow chart；
Fig. 2 is to adopt provided by the embodiment of the present invention using cubic spline interpolation is corresponding to the first spherical surface Near-field Data
Sampling point carries out interpolation, and determines a kind of specific embodiment party of the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated
Formula flow chart；
Fig. 3 is the second spherical surface Near-field Data provided by the embodiment of the present invention according to antenna, acquires the far field side of antenna
To a kind of specific embodiment flow chart of figure；
Fig. 4 is a kind of device that Far-Field antennas measurement system is carried out based on cubic spline interpolation provided by the embodiment of the present invention
Structural schematic diagram.
Specific embodiment
Following will be combined with the drawings in the embodiments of the present invention, and technical solution in the embodiment of the present invention carries out clear, complete
Site preparation description, it is clear that described embodiments are only a part of the embodiments of the present invention, instead of all the embodiments.It is based on
Embodiment in the present invention, it is obtained by those of ordinary skill in the art without making creative efforts every other
Embodiment shall fall within the protection scope of the present invention.
In order to which the sampling complexity of antenna damnification can either be reduced, and antenna near-field data can be guaranteed through nearly far field
The Antenna Far Field directional diagram accuracy with higher obtained after transformation, the embodiment of the invention provides one kind to be based on cubic spline
The method and device of interpolation method progress Far-Field antennas measurement system.
It is provided for the embodiments of the invention first below a kind of based on cubic spline interpolation progress Far-Field antennas measurement system
Method be introduced.
As described in Figure 1, one kind provided by the embodiment of the present invention is based on cubic spline interpolation and carries out spherical surface far-field measurement
Method, may include steps of:
S110 acquires the first spherical surface Near-field Data of antenna；
Firstly, in the distance for leaving tested 3 λ of antenna to 5 λ (wherein λ is operation wavelength), with a with known characteristic mark
Quasi- antenna or probe are sampled on the spherical surface for surrounding tested antenna, and different sampled points corresponds to different spherical surface near field numbers
According to the spherical surface Near-field Data of all sampled points forms the first spherical surface Near-field Data.
It should be noted that measuring system is using computer as core in the antenna damnification based on spherical surface near field measurement
The heart, by interface output drive signal to controller, controller is used to control standard antenna or the X-direction of probe, the side Y computer
To the movement such as, Z-direction, polarization and orientation, the polarization of antenna, pops one's head in and acquires the spherical surface Near-field Data of tested antenna in real time,
In, the spherical surface Near-field Data of antenna includes the amplitude of antenna near-field, phase etc..
Optionally, in one implementation, the step of the first spherical surface Near-field Data of the acquisition antenna, comprising:
The sampling interval of the spherical surface Near-field Data of acquisition antenna is calculated according to predetermined sampling thheorem；
According to institute's calculated sampling interval, the first sampling interval of the first spherical surface Near-field Data of acquisition antenna is determined；
Wherein, the first sampling interval was greater than institute's calculated sampling interval；
It is acquired according to first spherical surface Near-field Data of first sampling interval to antenna.
It is understood that before the first spherical surface Near-field Data of acquisition antenna, it can be according to predetermined sampling thheorem meter
It calculates the sampling interval of the spherical surface Near-field Data of acquisition antenna, which is the theoretical sampling interval, and acquiring, the first spherical surface is close
It is reference with the theory sampling interval when field data, determines the first sampling interval of the first spherical surface Near-field Data of acquisition antenna,
And then the first spherical surface Near-field Data is acquired according to first sampling interval.
It should be noted that in order to reduce the sampling complexity of the spherical surface near field measurement of antenna, in actual acquisition antenna
When the first spherical surface Near-field Data, it will usually reduce sampled point, i.e. the increase sampling interval, therefore, the first sampling interval was greater than basis
The predetermined sampling thheorem institute calculated sampling interval.For example, when antenna polarization direction be θ polarization andWhen polarization, surround to
On the spherical surface of observation line, respectively in the direction θ andDirection is sampled, at this point, the direction θ andThe predetermined sampling that direction meets is fixed
Reason are as follows: the direction θ andSampling interval on direction is respectively the π of Δ θ≤2/(2N+1),Wherein N=
Ka+10, k are constant, and a is the minimum spherical radius for surrounding antenna, and Δ θ is the sampling interval on the direction θ,ForOn direction
Sampling interval, then in conjunction with the antenna size of tested antenna, working frequency calculate acquisition antenna spherical surface Near-field Data
Sampling interval.It should be noted that those skilled in the art should understand that calculating the sampling interval according to predetermined sampling thheorem
Detailed process, this will not be repeated here.Assuming that being calculated according to predetermined sampling thheoremThe sampling interval in directionIt is 3.6 °, θ
The sampling interval Δ θ in direction is 2 °, but in order to reduce sampling complexity and shorten the sampling time, the first of actual acquisition antenna
During spherical surface Near-field Data,First sampling interval in directionIt is 3.6 °, and the first sampling interval Δ θ in the direction θ is
4 °, therefore, the first sampling interval Δ θ in the direction θ is greater than the sampling interval Δ θ according to the calculated direction θ of predetermined sampling thheorem,
The first spherical surface Near-field Data in the direction θ belongs to the spherical surface Near-field Data of lack sampling, and step S120 is needed to utilize cubic spline interpolation
Method carries out interpolation processing to it.
S120 carries out interpolation to the corresponding sampled point of the first spherical surface Near-field Data using cubic spline interpolation, and really
Determine the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated；
It may belong to the spherical surface Near-field Data of lack sampling by the first spherical surface Near-field Data that step S110 is collected, this
There are biggish errors for the Antenna Far Field data that first spherical surface Near-field Data of sample lack sampling obtains after Near-far fields transfer, can lead
Causing the accuracy of the far field data of antenna reduces.In order to guarantee the accuracy of Antenna Far Field data, need to reduce the of lack sampling
First sampling interval of one spherical surface Near-field Data.In order to not only reduce the sampling complexity of spherical surface near field measurement, but also can protect
The accuracy of Antenna Far Field data is demonstrate,proved, this programme is corresponding using first spherical surface Near-field Data of the cubic spline interpolation to lack sampling
Sampled point carry out interpolation, i.e., be inserted into interpolation knot in the corresponding sampled point of the first spherical surface Near-field Data of lack sampling, thus
Reduce the first sampling interval of the first spherical surface Near-field Data of lack sampling, the first sampling interval after reduction can satisfy predetermined
The sampling interval that sampling thheorem is calculated, so as to play the role of reducing the sampling complexity of spherical surface near field measurement.It needs
It is noted that in Interpolation Process, the total quantity of sampled point corresponding to all interpolation knots and the first spherical surface Near-field Data
Equal to destination number, which is the quantity of the sampled point marked off according to destination sample interval, and the destination sample
Between be divided into sampling interval of spherical surface Near-field Data according to the antenna determined by predetermined sampling thheorem.And cubic spline is inserted
Value method forms the smoothed curve that all interpolation knots are connected by construction cubic spline functions, has excellent
Good mathematical feature, the corresponding cubic spline functions value of each interpolation knot is that the corresponding spherical surface of each interpolation knot is close
Field data, compared with the method in the prior art by cubic polynomial interpolation method to realize Far-Field antennas measurement system, using three times
The corresponding spherical surface Near-field Data of each interpolation knot that spline method is calculated is more in line with reality, can guarantee that antenna is remote
Field data accuracy with higher.Therefore, antenna spherical surface near field measurement sampling complexity is being reduced by cubic spline interpolation
While spending, additionally it is possible to relatively accurately calculate the corresponding spherical surface Near-field Data of interpolation knot.
In order to be laid out it is clear for the sake of, it is subsequent that using cubic spline interpolation, to this, the first spherical surface Near-field Data is corresponding adopts
Sampling point carries out interpolation, and determine the specific implementation of the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated into
Row is discussed in detail.
S130, by interpolation each corresponding spherical surface Near-field Data of interpolation knot generated and the first spherical surface Near-field Data
Combination, obtains the second spherical surface Near-field Data of the antenna；
By by the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated and the first spherical surface Near-field Data
It is combined, it can obtain the second spherical surface Near-field Data of antenna, the sampling of the corresponding sampled point of the second spherical surface Near-field Data
Interval is smaller, can satisfy the sampling interval being calculated according to predetermined sampling thheorem, therefore accuracy with higher, to ask
It obtains the higher spherical surface far field data pad of accuracy and has determined basis.
S140 acquires the far-field pattern of the antenna according to the second spherical surface Near-field Data of the antenna.
Due to the second spherical surface Near-field Data accuracy with higher of antenna, the second spherical surface near field number of antenna
According to can relatively accurately obtain the far field bearing data of antenna after Near-far fields transfer, and then it can draw and show that accuracy is higher
Far-field pattern.
It is subsequent by the second spherical surface Near-field Data according to the antenna for the sake of being laid out and understanding, acquire the remote of the antenna
The specific implementation of field pattern describes in detail.
In the method for carrying out Far-Field antennas measurement system provided by the embodiment of the present invention based on cubic spline interpolation, day is acquired
First spherical surface Near-field Data of line；The corresponding sampled point of the first spherical surface Near-field Data is carried out using cubic spline interpolation
Interpolation, and determine the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated；By interpolation each interpolation generated
The corresponding spherical surface Near-field Data of node and the first spherical surface Near-field Data combination, obtain the second spherical surface near field number of the antenna
According to；According to the second spherical surface Near-field Data of the antenna, the far-field pattern of the antenna is acquired.Compared with prior art, originally
Scheme carries out interpolation to the corresponding sampled point of the first spherical surface Near-field Data using cubic spline interpolation, can reduce antenna near-field
The sampling complexity of measurement shortens the antenna damnification time；And cubic spline functions have on entire interpolation section
There are enough slickness, there is excellent mathematical feature, therefore, while reducing the sampling complexity of antenna damnification,
It can also ensure that the Antenna Far Field directional diagram accuracy with higher that antenna near-field data obtain after Near-far fields transfer.
Optionally, described to utilize cubic spline interpolation to first spherical surface near field in a kind of specific implementation
The corresponding sampled point of data carries out interpolation, and determines the step of the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated
Suddenly, as shown in Fig. 2, may include:
S121 equally spacedly inputs n interpolation knot X in the corresponding sampled point of the first spherical surface Near-field Data0、
X1、…、Xn-1, wherein a=X0<X1<…<Xn-1=b, [a, b] are interpolation section；
It is equally spacedly ascending in the first spherical surface Near-field Data of lack sampling to sequentially input n interpolation knot X0、
X1、…、Xn-1, wherein a=X0<X1<…<Xn-1=b, [a, b] are interpolation section, the numerical values recited of n and the first ball of lack sampling
It the quantity of face Near-field Data, the sampling interval size of the first spherical surface Near-field Data of lack sampling and is calculated according to predetermined sampling thheorem
The factors such as the obtained sampling interval size of spherical surface Near-field Data are related, and therefore, the present invention does not do specific limit to the numerical values recited of n
It is fixed.
The n interpolation knot is substituted into preset cubic spline functions respectively, acquires n interpolation knot by S122
Corresponding cubic spline functions value, wherein the cubic spline functions are multinomial no more than 3 times, the sample three times
The second order derived function of interpolating function is continuous and the interpolating on sides nodes X of the interpolation section0And Xn-1Second order derived function value be
0；
It is equally spacedly ascending in the first spherical surface Near-field Data of lack sampling to sequentially input n interpolation knot X0、
X1、…、Xn-1Afterwards, n interpolation knot is updated to respectively in preset cubic spline functions, it can be in the hope of n interpolation section
The corresponding cubic spline functions value of point.It should be noted that due in default cubic spline functions, three times for this
Spline interpolation function sets interpolation condition and boundary condition, and therefore, preset cubic spline functions are in entire interpolation area
Between there is on [a, b] enough slickness, and there are excellent mathematical feature, the corresponding cubic spline functions of interpolation knot
Value is approximately equal to the corresponding spherical surface Near-field Data of interpolation knot.Wherein, the solution procedure of preset cubic spline functions is such as
Under:
Firstly, defining one by slotting function f (x), wherein interpolation knot is corresponding corresponding for interpolation knot by slotting functional value
Spherical surface Near-field Data.Then close with cubic polynomial area on the section that every two adjacent interpolation knot is endpoint composition
Like f (x), these cubic polynomials are known as cubic spline functions s (x), wherein the cubic spline functions s (x) is not
The second order derived function of multinomial and the cubic spline functions s (x) more than 3 times is continuous, due to cubic spline functions
Second order derived function it is continuous, then its first derivative is necessarily continuous, and former cubic spline functions are also inevitable continuous；And it is described slotting
It is worth the interpolating on sides nodes X in section0And Xn-1Second order derived function value be 0, the expression formula of above-mentioned constraint condition is as follows:
At interior nodes:
At boundary node:
Boundary condition:
Secondly, the second order derived function of construction cubic spline functions.Since cubic spline functions by asking twice
The second order derived function obtained after leading is linear function, therefore, second order derived function the s " (x of cubic spline functionsi)=Mi(i=
0,1,2 ..., n) in section [xi-1,xi] it is linear function, therefore, the second order derived function of cubic spline functions can carry out
It is following to indicate:
In formula, hi=xi-xi-1
Finally, in the second order derived function s " for constructing cubic spline functions after (x), to its second order derived function s " (x)
It is integrated twice, using above-mentioned constraint condition, available one about second order derived functionMatrix equation, thus
Cubic spline functions s (x) can be obtained in the expression formula in each section, and then can be in the hope of any interpolation knot three times
Spline interpolation function value, the cubic spline functions value of the interpolation knot acquired are the corresponding spherical surface near field number of interpolation knot
According to.
It is corresponding to be determined as the n interpolation knot by S123 for the corresponding cubic spline functions value of the n interpolation knot
Spherical surface Near-field Data.
After acquiring the corresponding cubic spline functions value of interpolation knot by step S122, since interpolation knot is corresponding
Cubic spline functions value is the corresponding spherical surface Near-field Data of interpolation knot, by determining the corresponding spherical surface near field of interpolation knot
Data aid in determining whether the second spherical surface Near-field Data of antenna.
Optionally, in a kind of specific implementation, the second spherical surface Near-field Data according to the antenna acquires institute
The step of stating the far-field pattern of antenna, as shown in figure 3, may include:
S131 calculates ball mode expansion coefficient using the second spherical surface Near-field Data of the antenna；
Wherein, the formula of the ball mode expansion coefficient is calculated are as follows:
Wherein, amnAnd bmnFor the ball mode expansion coefficient, VθAnd VφFor the second spherical surface Near-field Data of the antenna, fn
And gnFor ball Hankel function, SmnAnd S 'mnFor Legendre function；
After obtaining the second spherical surface Near-field Data of antenna, need the second spherical surface Near-field Data of antenna carrying out nearly far field
Transformation can just obtain the far field bearing data of antenna, and the method for realizing Near-far fields transfer generallys use ball model-expansion method, because
This, needs to calculate ball mode expansion coefficient amnAnd bmn, by the way that the second spherical surface Near-field Data is updated to above-mentioned calculating ball mode exhibition
In the formula of open system number, the ball mode expansion coefficient of antenna can be precisely calculated.It should be noted that those skilled in the art
Member is it is to be understood that above-mentioned ball mode expansion coefficient, the derivation process of details are not described herein ball mode expansion coefficient.
The ball mode expansion coefficient is substituted into preset far field solution formula, acquires the far field of the antenna by S132
Bearing data；
Wherein, the preset far field solution formula are as follows:
Wherein,For the far field bearing data；
After ball mode expansion coefficient is calculated, ball mode expansion coefficient is updated to above-mentioned preset far field and solves public affairs
In formula, it can acquire the far field bearing data of antennaThe far field bearing data can characterize antenna transmitting radio
The intensity of wave and direction.It should be noted that those skilled in the art are to be understood that above-mentioned preset far field solution formula,
The derivation process of details are not described herein far field solution formula.
S133 draws the far-field pattern of the antenna according to the far field bearing data of the antenna；
After obtaining the far field bearing data of antenna, according to the far field bearing data of antenna, the far field of antenna is drawn out
The far-field pattern of directional diagram, antenna visual in imagely can show the far-field characteristic of antenna, the far field direction of antenna
Figure is the far-field measurement result of antenna.
Compared with prior art, this programme is using cubic spline interpolation to the corresponding sampled point of the first spherical surface Near-field Data
Interpolation is carried out, the sampling complexity of antenna damnification is can reduce, shortens the antenna damnification time；And cubic spline is inserted
Value function has enough slickness on entire interpolation section, has excellent mathematical feature, therefore, is reducing antenna near-field
While the sampling complexity of measurement, additionally it is possible to guarantee the Antenna Far Field direction that antenna near-field data obtain after Near-far fields transfer
Scheme accuracy with higher.
Corresponding to above method embodiment, the embodiment of the invention also provides one kind to carry out day based on cubic spline interpolation
The device of line far-field measurement, as shown in figure 4, may include:
Acquisition module 410, composite module 430, solves module 440 at interpolating module 420；
Wherein,
The acquisition module 410, for acquiring the first spherical surface Near-field Data of antenna；
The interpolating module 420, for being adopted using cubic spline interpolation is corresponding to the first spherical surface Near-field Data
Sampling point carries out interpolation, and determines the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated, wherein all interpolation sections
Point and the first spherical surface Near-field Data corresponding to sampled point total quantity be equal to destination number, the destination number be according to
The quantity for the sampled point that destination sample interval is marked off is divided into according to determined by predetermined sampling thheorem between the destination sample
The sampling interval of the spherical surface Near-field Data of the antenna；
The composite module 430, for by the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated and institute
The combination of the first spherical surface Near-field Data is stated, the second spherical surface Near-field Data of the antenna is obtained；
The solution module 440 acquires the far field of the antenna for the second spherical surface Near-field Data according to the antenna
Directional diagram.
In the method for carrying out Far-Field antennas measurement system provided by the embodiment of the present invention based on cubic spline interpolation, day is acquired
First spherical surface Near-field Data of line；The corresponding sampled point of the first spherical surface Near-field Data is carried out using cubic spline interpolation
Interpolation, and determine the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated；By interpolation each interpolation generated
The corresponding spherical surface Near-field Data of node and the first spherical surface Near-field Data combination, obtain the second spherical surface near field number of the antenna
According to；According to the second spherical surface Near-field Data of the antenna, the far-field pattern of the antenna is acquired.Compared with prior art, originally
Scheme carries out interpolation to the corresponding sampled point of the first spherical surface Near-field Data using cubic spline interpolation, can reduce antenna near-field
The sampling complexity of measurement shortens the antenna damnification time；And cubic spline functions have on entire interpolation section
There are enough slickness, there is excellent mathematical feature, therefore, while reducing the sampling complexity of antenna damnification,
It can also ensure that the Antenna Far Field directional diagram accuracy with higher that antenna near-field data obtain after Near-far fields transfer.
Optionally, the interpolating module 420, comprising:
Interpolation knot submodule 421 is inputted, for equidistant in the corresponding sampled point of the first spherical surface Near-field Data
Ground inputs n interpolation knot X0、X1、…、Xn-1, wherein a=X0<X1<…<Xn-1=b, [a, b] are interpolation section；
Interpolating function value submodule 422 is solved, is inserted for the n interpolation knot to be substituted into preset cubic spline respectively
In value function, the corresponding cubic spline functions value of n interpolation knot is acquired, wherein the cubic spline functions are
The second order derived function of multinomial, the cubic spline functions no more than 3 times is continuous and the boundary of the interpolation section
Interpolation knot X0And Xn-1Second order derived function value be 0；
It determines spherical surface Near-field Data submodule 423, is used for the corresponding cubic spline functions of the n interpolation knot
Value is determined as the corresponding spherical surface Near-field Data of the n interpolation knot.
Optionally, the solution module 440, comprising:
Ball mode expansion coefficient submodule 441 is calculated, for the second spherical surface Near-field Data using the antenna, calculates ball
Mode expansion coefficient；
Far field bearing data submodule 442 is solved, is solved for the ball mode expansion coefficient to be substituted into preset far field
In formula, the far field bearing data of the antenna is acquired；
It draws far-field pattern submodule 443 and draws the antenna for the far field bearing data according to the antenna
Far-field pattern；
Wherein, the formula of the ball mode expansion coefficient is calculated are as follows:
Wherein, amnAnd bmnFor the ball mode expansion coefficient, VθAnd VφFor the second spherical surface Near-field Data of the antenna, fn
And gnFor ball Hankel function, SmnAnd S 'mnFor Legendre function；
The preset far field solution formula are as follows:
Wherein,For the far field bearing data；
Optionally, the acquisition module 410, comprising:
Sampling interval submodule 411 is calculated, for calculating the spherical surface near field of acquisition antenna according to the predetermined sampling thheorem
The sampling interval of data；
The first sampling interval submodule 412 is determined, for determining and acquiring the antenna according to institute's calculated sampling interval
The first spherical surface Near-field Data the first sampling interval；Wherein, first sampling interval is greater than the calculated sampling of institute
Interval；
Acquire submodule 413, for according to first sampling interval to the first spherical surface Near-field Data of the antenna into
Row acquisition.
It should be noted that, in this document, relational terms such as first and second and the like are used merely to a reality
Body or operation are distinguished with another entity or operation, are deposited without necessarily requiring or implying between these entities or operation
In any actual relationship or order or sequence.Moreover, the terms "include", "comprise" or its any other variant are intended to
Non-exclusive inclusion, so that the process, method, article or equipment including a series of elements is not only wanted including those
Element, but also including other elements that are not explicitly listed, or further include for this process, method, article or equipment
Intrinsic element.In the absence of more restrictions, the element limited by sentence "including a ...", it is not excluded that
There is also other identical elements in process, method, article or equipment including the element.
Each embodiment in this specification is all made of relevant mode and describes, same and similar portion between each embodiment
Dividing may refer to each other, and each embodiment focuses on the differences from other embodiments.Especially for system reality
For applying example, since it is substantially similar to the method embodiment, so being described relatively simple, related place is referring to embodiment of the method
Part explanation.
The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the scope of the present invention.It is all
Any modification, equivalent replacement, improvement and so within the spirit and principles in the present invention, are all contained in protection scope of the present invention
It is interior.
Claims (6)
1. a kind of method for carrying out Far-Field antennas measurement system based on cubic spline interpolation characterized by comprising
Acquire the first spherical surface Near-field Data of antenna；
Interpolation is carried out to the corresponding sampled point of the first spherical surface Near-field Data using cubic spline interpolation, and determines interpolation institute
The corresponding spherical surface Near-field Data of each interpolation knot generated, wherein all interpolation knots and the first spherical surface Near-field Data
The total quantity of corresponding sampled point is equal to destination number, and the destination number is adopted for what is marked off according to destination sample interval
The quantity of sampling point is divided into the spherical surface Near-field Data according to the antenna determined by predetermined sampling thheorem between the destination sample
Sampling interval；
Interpolation each corresponding spherical surface Near-field Data of interpolation knot generated and the first spherical surface Near-field Data are combined, is obtained
To the second spherical surface Near-field Data of the antenna；
According to the second spherical surface Near-field Data of the antenna, the far-field pattern of the antenna is acquired；
The second spherical surface Near-field Data according to the antenna, the step of acquiring the far-field pattern of the antenna, comprising:
Using the second spherical surface Near-field Data of the antenna, ball mode expansion coefficient is calculated；
The ball mode expansion coefficient is substituted into preset far field solution formula, the far field bearing data of the antenna is acquired；
According to the far field bearing data of the antenna, the far-field pattern of the antenna is drawn；
Wherein, the formula of the ball mode expansion coefficient is calculated are as follows:
Wherein, amnAnd bmnFor the ball mode expansion coefficient, VθAnd VφFor the second spherical surface Near-field Data of the antenna, fnAnd gn
For ball Hankel function, SmnAnd S 'mnFor Legendre function；
The preset far field solution formula are as follows:
Wherein,For the far field bearing data；
2. the method according to claim 1, wherein described utilize cubic spline interpolation to first spherical surface
The corresponding sampled point of Near-field Data carries out interpolation, and determines the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated
The step of, comprising:
N interpolation knot X is equally spacedly inputted in the corresponding sampled point of the first spherical surface Near-field Data0、X1、…、Xn-1,
In, a=X0<X1<…<Xn-1=b, [a, b] are interpolation section；
The n interpolation knot is substituted into respectively in preset cubic spline functions, n interpolation knot corresponding three is acquired
Secondary spline interpolation function value, wherein the cubic spline functions are inserted for the multinomial no more than 3 times, the cubic spline
The second order derived function of value function is continuous and the interpolating on sides nodes X of the interpolation section0And Xn-1Second order derived function value be 0；
The corresponding cubic spline functions value of the n interpolation knot is determined as the corresponding spherical surface of the n interpolation knot
Near-field Data.
3. method according to claim 1 or 2, which is characterized in that the first spherical surface Near-field Data of the acquisition antenna
Step, comprising:
The sampling interval of the spherical surface Near-field Data of acquisition antenna is calculated according to the predetermined sampling thheorem；
According to institute's calculated sampling interval, the first sampling interval for acquiring the first spherical surface Near-field Data of the antenna is determined；
Wherein, first sampling interval is greater than institute's calculated sampling interval；
It is acquired according to first spherical surface Near-field Data of first sampling interval to the antenna.
4. a kind of device for carrying out Far-Field antennas measurement system based on cubic spline interpolation characterized by comprising
Acquisition module, composite module, solves module at interpolating module；
Wherein,
The acquisition module, for acquiring the first spherical surface Near-field Data of antenna；
The interpolating module, for being carried out using cubic spline interpolation to the corresponding sampled point of the first spherical surface Near-field Data
Interpolation, and determine the corresponding spherical surface Near-field Data of interpolation each interpolation knot generated, wherein all interpolation knots and described
The total quantity of sampled point corresponding to first spherical surface Near-field Data is equal to destination number, and the destination number is according to destination sample
It is spaced the quantity of marked off sampled point, is divided between the destination sample according to the antenna determined by predetermined sampling thheorem
Spherical surface Near-field Data sampling interval；
The composite module is used for interpolation each corresponding spherical surface Near-field Data of interpolation knot generated and first ball
The combination of face Near-field Data, obtains the second spherical surface Near-field Data of the antenna；
The solution module acquires the far-field pattern of the antenna for the second spherical surface Near-field Data according to the antenna；
The solution module, comprising:
Ball mode expansion coefficient submodule is calculated, for the second spherical surface Near-field Data using the antenna, calculates the exhibition of ball mode
Open system number；
Far field bearing data submodule is solved, for the ball mode expansion coefficient to be substituted into preset far field solution formula,
Acquire the far field bearing data of the antenna；
It draws far-field pattern submodule and draws the far field side of the antenna for the far field bearing data according to the antenna
Xiang Tu；
Wherein, the formula of the ball mode expansion coefficient is calculated are as follows:
Wherein, amnAnd bmnFor the ball mode expansion coefficient, VθAnd VφFor the second spherical surface Near-field Data of the antenna, fnAnd gn
For ball Hankel function, SmnAnd S 'mnFor Legendre function；
The preset far field solution formula are as follows:
Wherein,For the far field bearing data；
5. device according to claim 4, which is characterized in that the interpolating module, comprising:
Interpolation knot submodule is inputted, for equally spacedly inputting n in the corresponding sampled point of the first spherical surface Near-field Data
A interpolation knot X0、X1、…、Xn-1, wherein a=X0<X1<…<Xn-1=b, [a, b] are interpolation section；
Interpolating function value submodule is solved, for the n interpolation knot to be substituted into preset cubic spline functions respectively
In, acquire the corresponding cubic spline functions value of n interpolation knot, wherein the cubic spline functions are no more than 3
The second order derived function of secondary multinomial, the cubic spline functions is continuous and the interpolating on sides node of the interpolation section
X0And Xn-1Second order derived function value be 0；
Spherical surface Near-field Data submodule is determined, for determining the corresponding cubic spline functions value of the n interpolation knot
For the corresponding spherical surface Near-field Data of the n interpolation knot.
6. device according to claim 4 or 5, which is characterized in that the acquisition module, comprising:
Sampling interval submodule is calculated, the spherical surface Near-field Data for calculating according to the predetermined sampling thheorem acquisition antenna is adopted
Sample interval；
The first sampling interval submodule is determined, for determining and acquiring the first of the antenna according to institute's calculated sampling interval
First sampling interval of spherical surface Near-field Data；Wherein, first sampling interval is greater than institute's calculated sampling interval；
Submodule is acquired, for being acquired according to first spherical surface Near-field Data of first sampling interval to the antenna.
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| CN107247193B (en) * | 2017-07-07 | 2020-05-08 | 广东曼克维通信科技有限公司 | Antenna near field test method and device |
| CN108595377B (en) * | 2018-04-26 | 2020-07-14 | 西安电子科技大学 | Signal processing method and device |
| CN109241565B (en) * | 2018-08-02 | 2020-09-29 | 北京邮电大学 | Method and device for correcting sampling position error in antenna spherical surface near-field measurement |
| CN109782069B (en) * | 2019-02-27 | 2020-08-11 | 西安电子科技大学 | Method for measuring mutual impedance between antennas |
| CN112798876B (en) * | 2021-03-22 | 2021-06-22 | 上海莱天通信技术有限公司 | Antenna near field measurement method and device by utilizing interpolation algorithm |
| CN113139157B (en) * | 2021-04-22 | 2022-03-08 | 中山香山微波科技有限公司 | Method for calculating main energy direction of DUT (device under test) and computer equipment |
| CN113533867B (en) * | 2021-07-14 | 2022-09-06 | 西安电子科技大学 | Fourier interpolation-based far field pattern rapid measurement method |
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