CN113806954B - Circular array pattern synthesis method based on forward and backward matrix beam algorithm - Google Patents
Circular array pattern synthesis method based on forward and backward matrix beam algorithm Download PDFInfo
- Publication number
- CN113806954B CN113806954B CN202111120627.7A CN202111120627A CN113806954B CN 113806954 B CN113806954 B CN 113806954B CN 202111120627 A CN202111120627 A CN 202111120627A CN 113806954 B CN113806954 B CN 113806954B
- Authority
- CN
- China
- Prior art keywords
- array
- directional diagram
- circular
- undamped
- complex
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 239000011159 matrix material Substances 0.000 title claims abstract description 36
- 238000001308 synthesis method Methods 0.000 title claims description 7
- 238000000034 method Methods 0.000 claims abstract description 46
- 238000010586 diagram Methods 0.000 claims abstract description 45
- 230000015572 biosynthetic process Effects 0.000 claims abstract description 25
- 238000003786 synthesis reaction Methods 0.000 claims abstract description 24
- 230000002194 synthesizing effect Effects 0.000 claims abstract description 13
- 230000005284 excitation Effects 0.000 claims description 15
- 230000008569 process Effects 0.000 claims description 6
- 238000000354 decomposition reaction Methods 0.000 claims description 4
- 230000009466 transformation Effects 0.000 abstract description 3
- 238000009826 distribution Methods 0.000 description 11
- 238000012876 topography Methods 0.000 description 8
- 239000000470 constituent Substances 0.000 description 7
- 230000010354 integration Effects 0.000 description 7
- 230000014509 gene expression Effects 0.000 description 6
- 230000005855 radiation Effects 0.000 description 6
- 238000005457 optimization Methods 0.000 description 5
- 230000000694 effects Effects 0.000 description 4
- 238000004519 manufacturing process Methods 0.000 description 4
- 239000002245 particle Substances 0.000 description 4
- 238000003491 array Methods 0.000 description 3
- 238000005070 sampling Methods 0.000 description 3
- 230000003044 adaptive effect Effects 0.000 description 2
- 239000013598 vector Substances 0.000 description 2
- 241000370001 Hantavirus Liu Species 0.000 description 1
- 241000255972 Pieris <butterfly> Species 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000004891 communication Methods 0.000 description 1
- 238000013016 damping Methods 0.000 description 1
- 238000013178 mathematical model Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000010606 normalization Methods 0.000 description 1
- 230000000737 periodic effect Effects 0.000 description 1
- 238000001228 spectrum Methods 0.000 description 1
- 230000001131 transforming effect Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
- G06F17/141—Discrete Fourier transforms
- G06F17/142—Fast Fourier transforms, e.g. using a Cooley-Tukey type algorithm
-
- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q21/00—Antenna arrays or systems
Landscapes
- Physics & Mathematics (AREA)
- Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Data Mining & Analysis (AREA)
- Pure & Applied Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Computational Mathematics (AREA)
- Discrete Mathematics (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Algebra (AREA)
- Geometry (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- Variable-Direction Aerials And Aerial Arrays (AREA)
Abstract
The application provides a method for synthesizing a circular arc array directional diagram, which relates to the field of array synthesis and comprises the following steps: determining the radius of an arc array, and giving an arc array pattern to be synthesized and an array element pattern forming the array pattern; respectively carrying out Fourier transformation on the to-be-synthesized circular array directional diagram and the array element directional diagram in the circular array, and converting the to-be-synthesized circular array directional diagram and the array element directional diagram into a form of undamped complex index signal sum; and regarding the problem of the circular array directional diagram synthesis as a parameter estimation problem of the undamped complex exponential signal, estimating the signal parameters by utilizing a forward and backward matrix beam algorithm, and converting the estimated signal parameters into configuration parameters of the circular array to complete the circular array directional diagram synthesis. The method solves the complex circular array directional diagram synthesis problem in a non-iterative mode, and the obtained array element positions are sparsely distributed, so that the comprehensive efficiency is high, and the design cost of a circular array system is reduced.
Description
Technical Field
The application relates to the field of array antenna synthesis, in particular to a circular arc array pattern synthesis method based on a forward and backward matrix beam algorithm.
Background
Conformal array antennas are widely used in modern radar and wireless communication systems because they conform to the surface of a carrier and retain the original structural features and aerodynamic properties of the carrier. Because each antenna element in the conformal array has a different orientation, the array pattern cannot be split into element pattern-by-array factor versions, and thus conformal array pattern synthesis is more complex than linear or planar array pattern synthesis. The current methods for synthesizing conformal array patterns include a random algorithm, a Fourier transform method, an adaptive array method and the like. The random algorithm has universality and can even guarantee the optimal solution in theory, so that the random algorithm is widely applied, but the random algorithm is very time-consuming when used for synthesizing the array pattern, and the random method cannot guarantee that the pattern performance obtained by each synthesis can meet the expected index, so that multiple attempts and multiple iterations are needed. The Fourier transform method can comprehensively obtain continuous line source distribution corresponding to the expected directional diagram, and the array synthesis is completed by uniformly sampling on the obtained continuous line source, but the number of required array elements is very large as the uniform sampling limits the degree of freedom of array element layout, so that the number of sampling points has to be increased to reach the index requirement of the expected directional diagram, and the adaptive array method needs to calculate the inverse of the covariance matrix during synthesis and has higher precision requirement, thus having high calculation cost.
Chinese patent 202110251847.7 discloses a circular arc conformal array pattern synthesis method based on a particle swarm optimization algorithm, which uses a low-complexity fast Fourier transform method to cut the solution space of the particle swarm optimization algorithm, reduces the calculated amount of the algorithm, effectively avoids the problem of local convergence of the particle swarm optimization algorithm, and remarkably improves the algorithm performance of the particle swarm optimization algorithm when the circular arc conformal array pattern multi-target synthesis problem is solved. However, the method does not optimize the position distribution of the array units and still requires iteration to obtain the optimal solution, so that more array elements are needed to achieve a satisfactory effect during synthesis.
Chinese patent 202010852122.9 discloses an array directional diagram synthesis method based on a hybrid differential evolution algorithm and a weighted total least square method, which comprises the steps of firstly calculating to obtain array element currents in an array by using the total least square method, substituting the array element currents into a radiation directional diagram formula to obtain a preliminary radiation directional diagram, and then carrying out further iterative optimization by using the differential evolution algorithm to find an optimal solution. However, the method does not optimize the position of the array element, only considers the excitation weight of the array element, and can obtain the optimal solution only by multiple iterations, so that the total required time is long.
Disclosure of Invention
The technical problems to be solved by the application are as follows: the application provides a circular arc array pattern synthesis method based on a forward and backward matrix beam algorithm, which is long in time consumption and needs more array elements, meets the performance index requirements of patterns to be synthesized, and meets the sparse layout requirements of array units, so that the circular arc array pattern synthesis speed is improved, and an antenna system is simplified.
The application is realized by the following technical scheme, which comprises the following steps:
1) Giving an arc array directional diagram to be synthesized and an array element directional diagram for realizing the array directional diagram, and giving an arc radius;
2) Performing Fourier transform on the circular array directional diagram to be synthesized and the array element directional diagram in the array respectively to obtain corresponding Fourier series, converting the Fourier series into a form of undamped complex index signal sum, and converting the circular array directional diagram comprehensive problem into an undamped complex index signal parameter estimation problem;
3) Estimating parameters of the undamped complex exponential signal by using a forward-backward matrix beam algorithm;
4) And converting the obtained undamped complex index signal parameters into array configuration parameters to complete the direction synthesis of the circular arc array.
Further, performing Fourier transform on the array directional diagram to be synthesized and the array element directional diagram in the array respectively to obtain corresponding Fourier series, converting the corresponding Fourier series into a form of undamped complex index signal sum, and converting the circular arc array directional diagram synthesis problem into an undamped complex index signal parameter estimation problem;
the specific method comprises the following steps: all array element patterns in the array have the same formAnd has rotational symmetry with respect to its position angle, i.e. the array pattern to be integrated +.>Can be expressed as +.>Wherein->R is the radius of the arc where the array is located, phi i Representing the position angle of the ith array element, I i Complex excitation coefficient representing the ith element, < ->The pattern is the i-th array element, M is the total number of array elements contained in the array;
step 2) also includes the step ofAnd->Fourier transforming to obtain F n And f n I.e. +.> In->
Definition of the definitionBy using the time shift property of the Fourier transform +.>Wherein N is a mode number and is an integer, and-N.ltoreq.n.ltoreq.N. Obviously y n In the form of a non-damping complex exponential signal sum and contains information of the position angle of the array elements, the excitation of the array elements and the number of the array elements in the array.
Further, step 3) includes estimating parameters of the undamped complex exponential signal using a forward and backward matrix beam algorithm;
the specific steps are that y is utilized n The matrix of Hanker-Torplitz is composed:wherein y is l ＝[y l-N y l-N+1 y l-N+2 .... y l+N-L ] T L is a matrix parameter, x represents complex conjugate, T represents transpose, and Y is now subjected to singular value decomposition to obtain y=usv H U and V are unitary matrices, H represents a conjugate transpose;
S＝diag{σ 1 ,σ 2 ,σ 3 .....σ M ；σ 1 ≥σ 2 ≥σ 3 ≥.....σ M -wherein for any one sigma m All satisfyGenerally η may be determined based on the accuracy and signal-to-noise ratio of the data, { σ i The singular value of Y, N NFD =2n+1. The choice of values for L, N and M will be determined in the comprehensive examples that follow;
estimating the parameter phi i Equivalent to solving the generalized eigenvalue problem of (1)
(V (M,t) -zV (M,b) )v＝0 (1)
(1) Wherein V is (M,t) And V (M,b) Respectively by V M Deleting the first and last lines, V M Only the first M rows of feature vectors of V are contained, and z is the corresponding M feature values. After the characteristic value of (1) is obtained, the parameter phi i Can be given by the formula (2)
φ i ＝jln(z i ) (2)
(2) Where z=z i . In the process of obtaining the parameter phi i Parameter I after that i The time can be obtained from (3)
In the middle oft＝0,1,2....T-1，T＝7M，I＝I i In->Is the generalized pseudo-inverse of the matrix.
Further, the step 4) further includes determining configuration parameters of the circular arc array by using parameters of the undamped complex exponential signal, and the specific steps are as follows: in obtaining parameter phi of undamped complex index signal i M and I i And then, the method is carried out. Will I i Excitation coefficients (R, phi) corresponding to the array elements i ) And M corresponds to the total number of the array elements. Thus, the combination of the circular array directional diagrams is completed.
Compared with the traditional linear and planar structure array, the circular arc structure array has the advantages that the unit antennas are positioned on the curved surface and have different orientations, so that the circular arc array directional diagram cannot be expressed in the form of the product of the unit directional diagram and the array factor, and the comprehensive circular arc array is more complex. According to the method, the problem of arc array directional diagram synthesis is converted into the problem of parameter estimation of undamped complex exponential signals, the problem of complex arc array synthesis is solved in an analytic mode, rapid synthesis of the arc array directional diagram is realized, and an antenna system is simplified.
The application has high comprehensive efficiency and reduces the design cost of the circular arc array system.
Drawings
The accompanying drawings, which are included to provide a further understanding of embodiments of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the principles of the application. In the drawings:
FIG. 1 is a schematic diagram of a circular array structure;
FIG.2 is a graph of data from corresponding Bessel at different orders for a given variable;
FIG. 3 is a graph calculated from the data of FIG.2 in the literature S.R.Naghesh and T.S.Vedavath, "A procedure for synthesizing a specified sidelobe topography using an arbitrary array," IEEE Trans.antenna s Propagat, vol.43, pp.742-745, july 1995 with reference to the pattern n Is a singular value distribution map of (1);
fig. 4 shows a variation trend chart of the normalized error ζ of the comprehensive example of the present application when different parameters L are selected;
FIG. 5 is a diagram showing a comparison of a pattern integrated with a reference pattern according to an embodiment of the present application;
fig. 6 shows a comparison of the actual integrated array element position distribution obtained by the method of the present application with the array element position distribution of the reference array.
Fig. 7 shows the amplitude distribution diagram of the actual integration of the method of the application into the excitation of the array elements.
Fig. 8 shows the phase distribution diagram of the actual integration of the method of the application into the excitation of the array elements.
Detailed Description
Hereinafter, the terms "comprises" or "comprising" as may be used in various embodiments of the present application indicate the presence of inventive functions, operations or elements, and are not limiting of the addition of one or more functions, operations or elements. Furthermore, as used in various embodiments of the application, the terms "comprises," "comprising," and their cognate terms are intended to refer to a particular feature, number, step, operation, element, component, or combination of the foregoing, and should not be interpreted as first excluding the existence of or increasing likelihood of one or more other features, numbers, steps, operations, elements, components, or combinations of the foregoing.
In various embodiments of the application, the expression "or" at least one of a or/and B "includes any or all combinations of the words listed simultaneously. For example, the expression "a or B" or "at least one of a or/and B" may include a, may include B or may include both a and B.
Expressions (such as "first", "second", etc.) used in the various embodiments of the application may modify various constituent elements in the various embodiments, but the respective constituent elements may not be limited. For example, the above description does not limit the order and/or importance of the elements. The above description is only intended to distinguish one element from another element. For example, the first user device and the second user device indicate different user devices, although both are user devices. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element, without departing from the scope of various embodiments of the present application.
It should be noted that: if it is described to "connect" one component element to another component element, a first component element may be directly connected to a second component element, and a third component element may be "connected" between the first and second component elements. Conversely, when one constituent element is "directly connected" to another constituent element, it is understood that there is no third constituent element between the first constituent element and the second constituent element.
The terminology used in the various embodiments of the application is for the purpose of describing particular embodiments only and is not intended to be limiting of the various embodiments of the application. As used herein, the singular is intended to include the plural as well, unless the context clearly indicates otherwise. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which various embodiments of the application belong. The terms (such as those defined in commonly used dictionaries) will be interpreted as having a meaning that is the same as the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein in connection with the various embodiments of the application.
For the purpose of making apparent the objects, technical solutions and advantages of the present application, the present application will be further described in detail with reference to the following examples and the accompanying drawings, wherein the exemplary embodiments of the present application and the descriptions thereof are for illustrating the present application only and are not to be construed as limiting the present application.
The implementation process of the application is as follows:
1) First determining a reference array pattern to be synthesizedAnd the array element pattern used +.>And determining the radius R of the circular array implementing the reference pattern.
2) We assume that all element patterns in the array have the same formAnd has rotational symmetry about its position angle, i.e. the direction diagram of the circular-arc array to be integrated is set +.>Can be expressed as +.>Fourier series expressions F of the reference array pattern and the array element patterns in the array are now obtained by Fourier transformation, respectively n And f n And get +.>By using the time shift property of the Fourier transform +.>Wherein, i.e.In->φ i Representing the position angle of the ith array element, I i Complex excitation coefficient representing the ith element, < ->The pattern of the ith array element is represented by M, which is the total number of array elements contained in the array. Wherein N is a mode number and is an integer, N is not less than N and not more than N, R is the radius of the circular arc array, < ->
3) By y n The matrix of Hanker-Torplitz is composed:wherein y is l ＝[y l-N y l-N+1 y l-N+2 .... y l+N-L ] T . L is a matrix parameter, which represents complex conjugate, T represents transpose
4) Singular value decomposition of Y yields the equation y=usv H U and V are unitary matrices, H represents a conjugate transpose, s=diag { σ } 1 ,σ 2 ,σ 3 .....σ M ；σ 1 ≥σ 2 ≥σ 3 ≥.....σ M -wherein for any one sigma m All satisfyGenerally η may be determined based on the accuracy and signal-to-noise ratio of the data, { σ n The singular value of Y, N NFD =2n+1. The choice of values for L, N and M will be determined in the comprehensive examples that follow. Estimating the parameter phi i Equivalent to solving the generalized eigenvalue problem of equation (1).
(V (M,t) -zV (M,b) )v＝0 (1)
(1) Wherein V is (M,t) And V (M,b) Respectively by V M Deleting the first and last lines, V M The first M rows of feature vectors containing only V, and z is the corresponding feature value. Obtaining the parameter phi after the characteristic value of (1) i Can be given by the formula (2)
φ i ＝jln(z i ) (2)
5) In (2), z=z i In the process of obtaining the parameter phi i Post parameter I i The time can be obtained from (3)
In the middle oft＝0,1,2....T-1，T＝7M，I＝I i Wherein->Is the generalized pseudo-inverse of the matrix
6) In obtaining parameter phi of undamped complex index signal i M and I i And then, the method is carried out. Will I i Excitation coefficients (R, phi) corresponding to the array elements i ) And M corresponds to the total number of the array elements. Thus, the combination of the circular array directional diagrams is completed.
Comprehensive example one:
any free-standing orientation unit is known from Josefsson, L., persson, P.: 'Conformal array antenna theory and design' (Wiley-IEEE Press, new Jersey,2006,1st edn)The radius of the composition is R circular ring array direction diagram +.>Can be expressed as a pattern expression, i.e. +.>In the middle of Wherein N and p are integers called mode numbers and-N.ltoreq.n.ltoreq.N,/for>For continuous line source corresponding to circular ring array pattern, A n For mode coefficient corresponding to mode n, J n And (beta R) is an n-order Bessel function with an independent variable beta R. Now define N NFD The equation quantity =2n+1 is the magnitude of the modes, and it is known from the properties of the bessel function that for a given variable βr, the higher order bessel function modes will decay rapidly with increasing order. Fig.2 shows the correspondence between the modes and the orders of the bessel function when r=12.5λ, and since the bessel function has symmetry, fig.2 only shows the right half of the order n > 0, as can be seen from the graph when |n| > [ βr]The modes of the Bessel function decay rapidly, ([. Cndot.)]To take the nearest integer value) and for a determined circular array pattern is known C n And D p Is limited, thus for a given radius of the circular array, a limited pattern quantity N is taken NFD The pattern function of the circular array can be accurately represented. Document G.Leone, M.A.Maisto, and R.Pierri, "Application of inverse source reconstruction to conformal antennas synthesis," IEEE Trans. Antennas Propag., vol 66, no.3, pp.1436-1445,2018 have demonstrated an effective pattern weight N that can be radiated by a circular ring radiation source having a radius R NFD ＝2[βR]+1。
The model of example one is the circular arc array pattern shown in fig.2 of literature s.r.naghaeh and t.s.vedavath, "A procedure for synthesizing a specified sidelobe topography using an arbitrary array," IEEE trans.antenna s production, vol.43, pp.742-745, july 1995. The reference pattern is radiated by directional element antennas uniformly distributed over an arc of 12.5 times the wavelength radius. The directional unit directional diagram expression isThis example will integrate the pattern with a smaller total number of elements thereby reducing design costs and simplifying the antenna system. The mathematical model may be expressed as a set of parameters { Q, φ } q ,I q -such that->Wherein ζ is the error limit, q= (1, 2, 3..q.. Q), a->(M,φ m ,I m ) Parameters are configured for the circular arrays in the above documents, where Q < M. In order to evaluate the performance of the actual integrated pattern, we now define a normalized error as: />In->Is the actual integrated pattern. In the present literature->And->Respectively performing Fourier transform to obtain F n And f n I.e.From the time-shift property of the fourier transformation +.>Since "A procedure for synthesizing a specified sidelobe topography using an arbitrary array," IEEE Trans. Antennas Propagat, vol.43, pp.742-745, july 1995, the array element positions in the direction of the circular arc array to be synthesized are known anduniformly distributed on the circular arc, so that y obtained by conversion in this example n A periodic function of n, a period of +.>Wherein R, d is A procedure for synthesizing a specified sidelobe topography using an arbitrary array, vol.43, pp.742-745, july 1995, the radius of the arc of fig.2 and the array element spacing. From the above analysis, it was found that the mode quantity of effective radiation of the ring at the radius was +.>However, the effective radiation range of the pattern to be integrated is +.>I.e., phi = 138 deg. 180 deg., whereas documents G.Leone, F.Munno, and r.pieri, "Radiation of a circular arc source in a limited angle for non-uniform conformal arrays," IEEE trans. Antenna s producing vol.69, no.8, pp.4955-4966, aug 2021 have demonstrated the mode component N 'that it contains when phi 180 deg. i.e., the array pattern radiates in limited space only' NFD ＜N NFD . Thus take ∈>When the method is sufficient to include all the pattern quantities which the circular array pattern can include, the above steps can be known that the method of the application can be used for expressing the coefficient A in the pattern of the general circular array pattern function n Represented by A n ＝y n f n Due to f n Is known, so only y is estimated n The array configuration parameters can complete the array synthesis, and the current relation y n The constituted hank-tueplitz matrix: />Singular value decomposition is performed to obtain y=usv H Wherein y is l ＝[y l-N y l-N+1 y l-N+2 .... y l+N-L ] T . L is a matrix parameter, generally* Representing complex conjugate, T representing transpose, H representing conjugate transpose, U and V being unitary matrices, s=diag { σ } 1 ,σ 2 ,σ 3 .....σ M ；σ 1 ≥σ 2 ≥σ 3 ≥.....σ M In this example, since the number of array elements of the reference pattern is known, the singular value number can be directly determined as the number of array elements, { sigma } m The singular values of Y are, but we find that some of the M singular values that remain are very small compared to others, the singular value spectrum of matrix Y is shown in fig. 3. Although they are also non-zero singular values. This shows that the electromagnetic waves radiated by some array elements contribute very little to the formation of the entire array beam, so that discarding them does not have a substantial effect on the pattern of the entire array. Therefore, some small singular values can be lost to obtain a low rank approximation matrix Y of the matrix Y Q The matrix corresponds to a comprehensive reference pattern with fewer array elements. The smaller singular values can be made directly zero, i.e. Y Q ＝US Q V H Wherein S is Q ＝diag{σ 1 ,σ 2 ,σ 3 .....σ Q ,.. 0,0}, Q.ltoreq.M, from I.T. Jolliffe, principle component anaylsis.2 nd ed.New York Springer-Verlag 2002 knows that the matrix element norm of matrix Y is +.>When p is 2, it is the floro Bei Niwu normal, and it has been demonstrated that matrix Y is Q in all ranks Q The minimum of the mean-French Bei Niwu normal approximation error, i.eIn this comprehensive example we measure matrix Y using the floro Bei Niwu normal Q Approximation error with matrix Y. The Q value can thus be determined from the ζ error limit and the friedel Bei Niwu s norm, i.e. the minimum value of Q in this example can be determined by the following equation.
Zeta is selected depending on actual synthesis to obtain the accuracy of the pattern approaching the original pattern. Where M is A procedure for synthesizing a specified sidelobe topography using an arbitrary array, vol.43, pp.742-745, july 1995 fig.2 refers to the number of array elements comprised in the array, i.e. m=16. Since A procedure for synthesizing a specified sidelobe topography using an arbitrary array, vol.43, pp.742-745, july 1995, fig.2, the side lobe level of the reference pattern is-40 dB, zeta=10 is set in this example based on the design criteria given by Liu Y, nie Z, liu Q H, reducing the number of element in linear of element in a liner antenna array by the matrix pencil method -4 The Q value obtained in (4) was 13. After Q is determined, the radius R is known, so the position angle phi of the new Q array elements q Can be obtained by solving (V) (Q,t) -zV (Q,b) ) Generalized eigenvalue determination of v=0, where V (Q,t) And V (Q,b) Respectively by V Q Deleting the first and last lines, V Q Containing only V M Is the corresponding eigenvalue of the first Q eigenvectors of (a), z. After the feature value z is obtained, the parameter phi q Can be represented by phi q ＝jln(z q ) Given, wherein z=z q . Obtaining the position angle phi of the array element q After that, the array element excites I q Can be formed byFind out +.>Wherein (1)>t＝0,1,2....T-1，T＝7Q，I＝I i Wherein->Is the generalized pseudo-inverse of the matrix. From the literature y.liu, q.h.liu, and z.nie, "Reducing the number of elements in multiple-pattern linear arrays by the extended matrix pencil methods," IEEE trans.antenna s production, vol.62, no.2, pp.652-660, feb.2014, it is known that selecting different L will affect the final pattern combination effect. FIG. 4 shows when->The variation trend of the normalized error ζ when selecting different parameters L when q=13, and after determining Q and N, the best L may be selected according to the variation trend of ζ with L fig. 4, where l= [0.67N ] is selected in this example NFD ]Finally, ζ=3.57×10 is obtained -6 . FIG. 5 compares the actual integrated pattern at Q=13 with the reference pattern of fig.2 in the literature S.R.Naghesh and T.S.Vedavath, "A procedure for synthesizing a specified sidelobe topography using an arbitrary array," IEEE Trans.antenna manufacturing, vol.43, pp.742-745, july 1995. It is apparent that both the defined normalization errors and fig. 5 show that 13 non-equally spaced array elements are sufficient to accurately reconstruct the desired pattern that would be produced by a 16-element equally spaced array element. In addition, it should be noted that the array of fig.2 in s.r. naghaeh and t.s. vedavath, "A procedure for synthesizing a specified sidelobe topography using an arbitrary array," IEEE trans.antenna s production, vol.43, pp.742-745, july 1995 has a symmetrical excitation profile, and the sparse integration of the obtained array element excitation profile based on the method of the present application still maintains this feature, but the method of the present application saves 18.8% of the number of array elements. Finally, it should be pointed out that the whole integration process of the above integration example is carried out on the personal PC terminal of i7-8750H@2.2GHz, and the time period is less than 2 seconds. Fig. 6 shows the actual integrated array element position distribution obtained by the method of the present application and the array element position distribution of the reference array. Finally comprehensively obtaining the maximum distance d between array elements max =0.67 λ, minimum spacing d min =0.55λ, achieving the effect of sparse layout. FIG. 7 shows the actual integration of the process of the applicationAmplitude distribution of the array element excitation. Fig. 8 shows the phase distribution of the excitation of the array elements obtained by the actual integration of the method of the application.
The foregoing description of the embodiments has been provided for the purpose of illustrating the general principles of the application, and is not meant to limit the scope of the application, but to limit the application to the particular embodiments, and any modifications, equivalents, improvements, etc. that fall within the spirit and principles of the application are intended to be included within the scope of the application.
Claims (3)
1. The circular arc array pattern synthesis method based on the forward and backward matrix beam algorithm is characterized by comprising the following steps of:
1) Giving an arc array directional diagram to be synthesized and an array element directional diagram for realizing the array directional diagram, and giving an arc radius;
2) Performing Fourier transform on the circular array directional diagram to be synthesized and the array element directional diagram in the array respectively to obtain corresponding Fourier series, converting the Fourier series into a form of sum of undamped complex index signals, and considering the circular array directional diagram comprehensive problem as a parameter estimation problem of the undamped complex index signals;
3) Estimating parameters of the undamped complex exponential signal by using a forward-backward matrix beam algorithm;
4) Converting the estimated signal parameters into array configuration parameters to complete array synthesis;
performing Fourier transform on the array directional diagram to be synthesized and the array element directional diagram in the array respectively to obtain corresponding Fourier series, converting the Fourier series into a form of a sum of undamped complex index signals, and converting the comprehensive problem of the circular arc array directional diagram into a parameter estimation problem of the undamped complex index signals;
the method comprises the following steps: all array element patterns in the array have the same formAnd has rotational symmetry with respect to its position angle, i.e. the array direction to be integrated +.>Can be expressed as +.>Wherein->R is the radius of the arc where the array is located, phi i Representing the position angle of the ith array element, I i Representing the complex excitation coefficient of the i-th element,the unit pattern of the ith array element is shown, M is the total number of array elements contained in the array;
step 2) also includes the step ofAnd->Respectively performing Fourier transform to obtain F n And f n I.e.In->
Definition of the definitionBy using the time shift property of the Fourier transform +.>Wherein N is a mode number and is an integer, N is not less than N and not more than N, and R is the radius of the circular arc array; y is n In the form of undamped complex exponential signal sums and packetsThe information of the position angle, the excitation and the number of the array elements in the array is contained.
2. The method for synthesizing the circular array pattern based on the forward and backward matrix beam algorithm according to claim 1, wherein the parameters of the undamped complex exponential signal are estimated by using the forward and backward matrix beam algorithm;
the specific steps are that y is utilized n The matrix of Hanker-Torplitz is composed:wherein y is l ＝[y l-N y l-N+1 y l-N+2 .... y l+N-L ] T L is a matrix parameter, x represents complex conjugate, T represents transpose, and Y is now subjected to singular value decomposition to obtain y=usv H U and V are unitary matrices, H represents a conjugate transpose;
S＝diag{σ 1 ,σ 2 ,σ 3 .....σ M ；σ 1 ≥σ 2 ≥σ 3 ≥.....σ M -wherein for any one sigma m All satisfyGenerally η may be determined based on the accuracy and signal-to-noise ratio of the data, { σ i The singular value of Y, N NFD The choice of values for =2n+1, l, n and M will be determined in the following synthesis example;
estimating the parameter phi i Equivalent to solving the generalized eigenvalue problem of (1)
(V (M,t) -zV (M,b) )v＝0 (1)
(1) Wherein V is (M,t) And V (M,b) Respectively by V M Deleting the first and last lines, V M The first M eigenvectors containing only V, z being M eigenvalues corresponding thereto, and obtaining the (1) eigenvalue and then the parameter phi i Can be given by the formula (2)
φ i ＝jln(z i ) (2)
(2) Middle z=z i In the process of obtaining the parameter phi i Parameter I after that i The time can be obtained from (3)
In the middle of Is the generalized pseudo-inverse of the matrix.
3. The method for synthesizing the circular array pattern based on the forward and backward matrix beam algorithm according to claim 2, wherein the method is characterized in that the configuration parameters of the circular array are determined by using the parameters of the undamped complex exponential signal, and comprises the following specific steps: in obtaining parameter phi of undamped complex index signal i M and I i Thereafter, I i Excitation coefficients (R, phi) corresponding to the array elements i ) And (5) corresponding to the positions of the array elements, and M corresponds to the total number of the array elements, so as to complete the synthesis of the circular array directional diagram.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111120627.7A CN113806954B (en) | 2021-09-24 | 2021-09-24 | Circular array pattern synthesis method based on forward and backward matrix beam algorithm |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202111120627.7A CN113806954B (en) | 2021-09-24 | 2021-09-24 | Circular array pattern synthesis method based on forward and backward matrix beam algorithm |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113806954A CN113806954A (en) | 2021-12-17 |
| CN113806954B true CN113806954B (en) | 2023-12-08 |
Family
ID=78940265
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202111120627.7A Active CN113806954B (en) | 2021-09-24 | 2021-09-24 | Circular array pattern synthesis method based on forward and backward matrix beam algorithm |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113806954B (en) |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106650097A (en) * | 2016-12-22 | 2017-05-10 | 厦门大学 | Synthesis method of array antenna shaped beam with controllable excitation amplitude dynamic range |
| WO2019214257A1 (en) * | 2018-05-08 | 2019-11-14 | 深圳光启高等理工研究院 | Method and device for calculating pattern of beam pointing adjustable antenna |
| CN111766455A (en) * | 2020-09-02 | 2020-10-13 | 上海霍莱沃电子系统技术股份有限公司 | Phased array antenna directional pattern prediction method and system based on aperture current method |
| CN112380657A (en) * | 2020-12-01 | 2021-02-19 | 厦门大学 | Directional diagram synthesis method and device of circular ring array antenna |
| CN113033080A (en) * | 2021-03-08 | 2021-06-25 | 浙江大学 | Conformal array directional diagram synthesis method based on solution space cutting particle swarm optimization |
| CN113032989A (en) * | 2021-03-19 | 2021-06-25 | 电子科技大学 | Sparse array optimization algorithm for minimizing array element number by constraining directivity coefficient |
-
2021
- 2021-09-24 CN CN202111120627.7A patent/CN113806954B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106650097A (en) * | 2016-12-22 | 2017-05-10 | 厦门大学 | Synthesis method of array antenna shaped beam with controllable excitation amplitude dynamic range |
| WO2019214257A1 (en) * | 2018-05-08 | 2019-11-14 | 深圳光启高等理工研究院 | Method and device for calculating pattern of beam pointing adjustable antenna |
| CN111766455A (en) * | 2020-09-02 | 2020-10-13 | 上海霍莱沃电子系统技术股份有限公司 | Phased array antenna directional pattern prediction method and system based on aperture current method |
| CN112380657A (en) * | 2020-12-01 | 2021-02-19 | 厦门大学 | Directional diagram synthesis method and device of circular ring array antenna |
| CN113033080A (en) * | 2021-03-08 | 2021-06-25 | 浙江大学 | Conformal array directional diagram synthesis method based on solution space cutting particle swarm optimization |
| CN113032989A (en) * | 2021-03-19 | 2021-06-25 | 电子科技大学 | Sparse array optimization algorithm for minimizing array element number by constraining directivity coefficient |
Non-Patent Citations (5)
| Title |
|---|
| Fast and Accurate Antenna Array Pattern Synthesis Using Iterative FFT via Least-square Active Element Pattern Expansion (LS-AEPE);jingjing Bai;2019 Photonics & Electromagnetics Research Symposium - Fall (PIERS - Fall);全文 * |
| 交叉极化及副瓣约束的任意阵列最优方向性综合;杨晶;刘颜回;白晶晶;柳清伙;聂在平;;电子学报(第03期);全文 * |
| 傅立叶变换与频谱估计的新算法及在电磁工程中的应用;刘颜回;中国博士学位论文全文数据库(第2011年第05期期);全文 * |
| 圆形阵列特征矢量综合法及其在自适应DBF中的应用;朱建良;;现代雷达(第02期);全文 * |
| 稀布阵列天线的压缩感知和入侵杂草优化算法研究;赵晓雯;中国博士学位论文全文数据库(第2016年第08期期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113806954A (en) | 2021-12-17 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN108872946B (en) | Steady beam forming method for joint iteration of steering vector and covariance matrix | |
| CN113032989B (en) | Sparse array optimization method for minimizing array element number by constraining directivity coefficient | |
| CN109490820B (en) | Two-dimensional DOA estimation method based on parallel nested array | |
| CN114745237B (en) | Channel estimation method of intelligent super-surface auxiliary multi-user wireless communication system | |
| CN114124623A (en) | Wireless communication channel estimation method and device | |
| CN113030931B (en) | MIMO radar waveform generation method based on manifold optimization | |
| CN110988816B (en) | Coherent MIMO radar emission waveform design method based on space-time phase coding | |
| CN115084874A (en) | Beam scanning array optimization design method based on heterogeneous subarray non-uniform layout | |
| CN115480206A (en) | Off-grid DOA estimation method | |
| CN113806954B (en) | Circular array pattern synthesis method based on forward and backward matrix beam algorithm | |
| CN113871899A (en) | Method for rapidly generating broadband non-frequency-varying scanning beam of non-uniform spaced linear array | |
| CN113189538B (en) | Ternary array based on mutual mass sparse arrangement and spatial spectrum estimation method thereof | |
| Yang et al. | Robust adaptive beamformer using interpolation technique for conformal antenna array | |
| CN112763972A (en) | Sparse representation-based double parallel linear array two-dimensional DOA estimation method and computing equipment | |
| CN115236589B (en) | Polar region under-ice DOA estimation method based on covariance matrix correction | |
| CN116205143A (en) | Design method for realizing antenna pattern based on physical information neural network | |
| CN112347681B (en) | Robust beam forming method based on mutual coupling characteristic prediction of macro-basis function array | |
| CN114966523A (en) | DOA estimation method based on power iteration algorithm in large-scale MIMO direction finding | |
| CN115575941A (en) | Sparse array-oriented frequency control array MIMO radar target parameter estimation method | |
| CN115421098A (en) | Two-dimensional DOA estimation method for nested area array dimension reduction root finding MUSIC | |
| CN115453450A (en) | Robust DOA estimation method for resisting mutual coupling under nested array | |
| Lugara et al. | Printed antennas analysis by a Gabor frame-based method of moments | |
| CN114609580A (en) | Non-hole co-prime array design method based on non-circular signals | |
| CN113740797B (en) | High-precision single-snapshot target arrival angle estimation method under lens array | |
| CN114994651B (en) | Bistatic mutual MIMO radar target positioning method with channel amplitude-phase error |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |