CN112711852B - Antenna array amplitude-phase distribution design method of plane wave generator - Google Patents

Antenna array amplitude-phase distribution design method of plane wave generator Download PDF

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CN112711852B
CN112711852B CN202011614469.6A CN202011614469A CN112711852B CN 112711852 B CN112711852 B CN 112711852B CN 202011614469 A CN202011614469 A CN 202011614469A CN 112711852 B CN112711852 B CN 112711852B
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杜刘革
呼延思腾
陈伟
于晓旭
何勰
赵佳
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Abstract

The invention discloses an antenna array amplitude and phase distribution design method of a plane wave generator, which comprises the following steps: firstly, establishing a basic model of a plane wave generator: t · X ═ Y; wherein, X represents an excitation signal field, namely an array element field of the antenna array, Y represents a radiation field, and T represents a forward conduction matrix; giving the amplitude and phase distribution of each radiation field point in the radiation field Y; step three, establishing a forward conduction matrix T; and step four, solving the model formula by adopting an inverse scattering problem algorithm to obtain the amplitude and phase distribution of each excitation signal point in the excitation signal field X. The plane wave distribution field obtained by the method disclosed by the invention has small result fluctuation and high precision, can flexibly adjust the array element distribution interval and is convenient for engineering realization.

Description

Antenna array amplitude-phase distribution design method of plane wave generator
Technical Field
The invention relates to the technical field of wireless communication, in particular to an antenna array amplitude and phase distribution design method of a plane wave generator.
Background
In recent years, with the overall progress of 5G communication, a large-scale Multiple Input Multiple Output (MIMO) active array antenna has been widely used as a 5G base station antenna, and unlike a phased array antenna in the radar field, the active array antenna has a larger application scale in the civil market, and also puts more convenience requirements on the measurement of the antenna, and the high-precision machining necessary for the conventional compact field measurement and the cost of manufacturing and construction time are disadvantages for the large-scale application thereof. Therefore, researchers have proposed the concept of a Plane-Wave Converter (PWC) or a Plane-Wave Generator (PWG), that is, an array composed of small-sized array element antennas is used to replace a parabolic reflecting screen to generate Plane waves, and by adjusting the amplitude phase of each array element in the antenna array, electromagnetic fields generated by all the array element antennas are superposed to achieve the Plane Wave effect of equal amplitude and same phase within a certain range at a short distance.
In the design of PWC, the key technology is the determination of the amplitude phase of each array element excitation signal in the antenna array, and the plane wave with the same amplitude and phase can be generated in the near field area of the whole array only by calculating the correct amplitude-phase configuration. At present, most of generation methods of amplitude and phase configuration tables in PWC design adopt a traditional parameter optimization algorithm, such as a genetic optimization algorithm or a particle swarm optimization algorithm, to optimize specific parameters, for example, in a patent with the name of 201810094455.2, which is a quasi-plane wave generator based on an array antenna and a generation method, a continuous tapering function of an antenna array aperture field is designed according to a compact field design principle, amplitude and phase of configuration array element excitation are performed, and distribution functions are as follows, wherein α, β, and γ are 3 parameters to be optimized.
Figure BDA0002874432580000011
The optimization algorithm limits the array amplitude-phase distribution rule, the flexibility of all array elements is difficult to exert, the excitation amplitude-phase of each array element is not taken as the optimization target, and the final effect is difficult to achieve global optimization. The method for optimizing the amplitude and phase of the array elements by using the traditional parameter optimization algorithms such as particle swarm optimization or genetic algorithm is based on the principle of random search, and is easy to fall into local optimization in large unknown quantity (for example, in the design problem of a plane wave converter, the quantity of unknown parameters is twice of the quantity of the array elements), so that the optimal amplitude and phase configuration is difficult to determine.
Disclosure of Invention
In order to solve the technical problems, the invention provides a method for designing the amplitude and phase distribution of an antenna array of a plane wave generator, the obtained plane wave distribution field has small result fluctuation and high precision, the distribution interval of array elements can be flexibly adjusted, and the engineering realization is convenient.
In order to achieve the purpose, the technical scheme of the invention is as follows:
a method for designing the distribution of the antenna array amplitude and phase of a plane wave generator comprises the following steps:
firstly, establishing a basic model of a plane wave generator:
T·X＝Y (1)
wherein, X represents an excitation signal field, namely an array element field of the antenna array, Y represents a radiation field, and T represents a forward conduction matrix;
giving the amplitude and phase distribution of each radiation field point in the radiation field Y;
step three, establishing a forward conduction matrix T;
and step four, solving the formula (1) by adopting an inverse scattering problem algorithm to obtain the amplitude and phase distribution of each excitation signal point in the excitation signal field X.
In the above scheme, the excitation signal field X is composed of M excitation signals, expressed as
X＝[X 1 ,X 2 ,X 3 …X m ] T (2)
Wherein, X m Denotes the M-th excitation signal, M is 1,2, … …, M, X m With amplitude A of the m-th excitation signal m And phase P m Is shown by
Figure BDA0002874432580000021
Or by the real part of the m-th excitation signal
Figure BDA0002874432580000022
And imaginary part
Figure BDA0002874432580000023
Is shown, i.e.
Figure BDA0002874432580000024
The radiation field Y is composed of N radiation field points and is expressed as
Y＝[Y 1 ,Y 2 ,Y 3 …Y n ] T (5)
Wherein Y is n Denotes the nth radiation field point, N is 1,2, … …, N, Y n With amplitude FA of the nth radiation field point n And phase FP n It is shown that,namely, it is
Figure BDA0002874432580000025
Or by the real part of the nth radiation field point
Figure BDA0002874432580000026
And imaginary part
Figure BDA0002874432580000027
Is shown, i.e.
Figure BDA0002874432580000028
The forward conduction matrix T is expressed as
Figure BDA0002874432580000031
Wherein, t nm Expressed as the conductance of the mth excitation signal at the nth radiation field point.
In a further technical scheme, in the step two, each radiation field point Y in the radiation field Y is used n Amplitude of (FA) n And phase FP n Form representation as real part
Figure BDA0002874432580000032
And imaginary part
Figure BDA0002874432580000033
In the form of (1).
In the fourth step, after solving the formula (1), each excitation signal point X in the excitation signal field X is obtained m Real part of
Figure BDA0002874432580000034
And imaginary part
Figure BDA0002874432580000035
Then will beReal part of
Figure BDA0002874432580000036
And imaginary part
Figure BDA0002874432580000037
Form conversion to amplitude A m And phase P m Form (a).
In a further technical scheme, t nm And expressing by using a free space Green function, or expressing by using a radiation field value of an antenna near field region, or calculating an antenna array by adopting an MOM, FDTD and FEM full wave analysis algorithm to obtain a corresponding relation between an excitation signal field and a radiation field.
In a further technical scheme, the algorithm of the inverse scattering problem comprises an OMP algorithm, a BP algorithm, an RMA algorithm, a Gaussian Newton iteration and regularization method thereof and a MUSIC algorithm.
The invention provides an inverse radiation inversion method based on an electromagnetic wave back scattering theory aiming at the problem of array element amplitude phase configuration in PWC design, and utilizes various imaging methods for solving the back scattering problem to carry out imaging analysis on a radiation source so as to obtain the amplitude phase distribution of the radiation array element.
The method provided by the invention is flexible to realize and strong in applicability.
(1) The positive problem model can adopt basic free space Green function calculation, or adopt full wave simulation algorithm to obtain the electromagnetic field amplitude and phase distribution of array elements at a certain distance, or adopt full wave simulation analysis calculation of each array element of the whole array to obtain the electromagnetic field amplitude and phase distribution at a certain distance;
(2) the Inversion algorithm may adopt a Back Propagation (BP) algorithm and a Range Migration (RM) algorithm of microwave imaging, or a PIA (PIA) algorithm and an Orthogonal Matching Pursuit (OMP) algorithm in compressive sensing reconstruction, or gaussian-Newton Inversion (GNI) algorithm, Born Iterative Method (BIM) and regularization methods of various Inverse problems commonly used in microwave tomography;
(3) by adjusting the solving algorithm of the positive problem and the inverse problem, the method is suitable for arrays with various distribution types, such as rectangular uniform distribution, circular distribution, polygonal distribution, random distribution and the like.
The plane wave distribution field obtained by the simulation test method has small fluctuation of results and high precision, can flexibly adjust the array element distribution interval and is convenient for engineering realization.
In addition, the method can be used for designing PWC array element amplitude and phase distribution, and can also be used for designing other special distribution fields, such as Gaussian distribution fields, random distribution fields and the like, and only the final target value needs to be adjusted.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below.
Fig. 1 is a schematic flow chart of a method for designing the amplitude-phase distribution of an antenna array of a plane wave generator according to an embodiment of the present invention;
FIG. 2 is a basic model diagram of a plane wave generator of the present invention;
fig. 3 is a model diagram of a plane wave generator according to embodiments 1 and 2 of the present invention;
FIG. 4 is a quiet zone amplitude distribution diagram based on the OMP algorithm of example 1;
FIG. 5 is a deadband phase distribution diagram based on the OMP algorithm of example 1;
FIG. 6 is a quiet zone amplitude distribution diagram based on Gaussian and Newton iterative algorithm of example 2;
fig. 7 is a quiet zone phase distribution diagram based on the gauss-newton iterative algorithm of example 2.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention.
The invention provides a method for designing the distribution of the antenna array amplitude and phase of a plane wave generator, which comprises the following steps as shown in figure 1:
firstly, a basic model of a plane wave generator is established, as shown in fig. 2:
the array element antennas are positioned in a plane (or not in the same plane) with the z being 0, the array element antennas are arranged in a rectangular, circular or other type with equal spacing or unequal spacing, and the overall calibers of the antenna arrays in the x and y directions are respectively D x And D y The number of array elements is M (4)<M<1024) The M (M is 1,2, … …, M) th array element coordinate is (x) m ,y m ,z m ) The amplitude and phase of the excitation signal are respectively A m And P m Through (x) m ,y m ,z m ) Value and amplitude and phase A of the excitation signal m And P m The value is designed to be w max (D) from the antenna array x ,D y ) Where (typically z ═ z) d In-plane) to form a field distribution (1) of equal amplitude and in phase (or other form)<w<10). If the distance antenna array w max (D) is selected x ,D y ) The coordinates (x) of N (N is 1,2, … …, N) th points of the field point n ,y n ,z n ) Amplitude and phase are each FA n And FP n . This problem is taken as a back-radiation problem, i.e. the distribution FA of the known quantity radiation field n And FP n The unknowns to be solved are the amplitude phase A of the radiation source in a certain area m And P m And (4) distribution situation.
The linear expression of the above model is:
T·X＝Y (1)
wherein, X represents an excitation signal field, namely an array element field of the antenna array, Y represents a radiation field, and T represents a forward conduction matrix;
the excitation signal field X is formed by M excitation signals and is expressed as
X＝[X 1 ,X 2 ,X 3 …X m ] T (2)
Wherein, X m Represents the mth excitation signal, M is 1,2, … …, M, X m With amplitude A of the m-th excitation signal m And phase P m Is shown by
Figure BDA0002874432580000051
The above formula is a complex amplitude expression form, and is generally Z ═ Ae jθ Wherein e represents a natural constant, A represents the amplitude of the complex number Z, and theta represents the angle of the complex number Z;
or by the real part of the m-th excitation signal
Figure BDA0002874432580000052
And imaginary part
Figure BDA0002874432580000053
Is shown, i.e.
Figure BDA0002874432580000054
The radiation field Y is composed of N radiation field points and is expressed as
Y＝[Y 1 ,Y 2 ,Y 3 …Y n ] T (5)
Wherein, Y n Denotes the nth radiation field point, N is 1,2, … …, N, Y n With amplitude FA of the nth radiation field point n And phase FP n Is shown, i.e.
Figure BDA0002874432580000055
The above formula is a complex amplitude-phase expression, and is generally represented by Z ═ Ae jθ Wherein e represents a natural constant, A represents the amplitude of the complex number Z, and theta represents the angle of the complex number Z;
or by the real part of the nth radiation field point
Figure BDA0002874432580000056
And imaginary part
Figure BDA0002874432580000057
Is shown, i.e.
Figure BDA0002874432580000058
The forward conduction matrix T is expressed as
Figure BDA0002874432580000059
Wherein, t nm Expressed as the conductance of the mth excitation signal at the nth radiation field point.
Step two, giving the amplitude and phase distribution of each radiation field point in the radiation field Y, and enabling each radiation field point Y in the radiation field Y to be in a certain range n Amplitude of (FA) n And phase FP n Form representation as real part
Figure BDA0002874432580000061
And imaginary part
Figure BDA0002874432580000062
In the form of (a).
Step three, establishing a forward conduction matrix T, T nm And expressing by using a free space Green function, or expressing by using a radiation field value of an antenna near field region, or calculating an antenna array by using an MOM, FDTD and FEM full-wave analysis algorithm to obtain a corresponding relation between an excitation signal field and a radiation field.
Step four, solving the formula (1) by adopting an inverse scattering problem algorithm to obtain each excitation signal point X in the excitation signal field X m Real part of
Figure BDA0002874432580000063
And imaginary part
Figure BDA0002874432580000064
Then the real part is converted into
Figure BDA0002874432580000065
And imaginary part
Figure BDA0002874432580000066
Form conversion to amplitude A m And phase P m Form (a).
The algorithm of the backscattering problem comprises an OMP algorithm, a BP algorithm, an RMA algorithm, a Gaussian Newton iteration and regularization method thereof and a MUSIC algorithm.
Example 1
In the embodiment, a free space Green function is used as a conduction relation, an OMP algorithm is used as an inverse problem solving algorithm to carry out PWC design, the frequency is selected to be 3GHz, and the antenna aperture D is x ＝D y The antenna array is arranged at equal intervals, and the array element spacing delta x and delta y are both equal to one wavelength lambda. The number of array elements is 20 × 20, that is, M is 400, the generated field is near to the antenna array by a size of 1.5 times the aperture size, that is, w is 1.5, and the schematic diagram is shown in fig. 3:
the method comprises the following concrete steps:
1) setting PWC target quiet area range and array elements as large as the same, wherein the number N of quiet area field points is consistent with the number M of the array elements, and then M is 400. Since plane waves need to be generated, the field value Y is set n (n-1, 2, … …,400) in FA n ＝αY n ＝1，FP n ＝βY n Is equal to 0, i.e
Y＝[1+0i,1+0i…1+0i] T (9)
2) Establishing various items of data of a forward conduction matrix T, T nm Expressed using a free space Green's function, expressed as
Figure BDA0002874432580000067
Where k is 2 pi/λ, expressed as a free space wavenumber, the propagation matrix T is expressed as:
Figure BDA0002874432580000068
wherein r is nm Denoted as the m-th excitation source to the n-th field point Y n Is expressed as
Figure BDA0002874432580000069
3) Using OMP algorithm to solve T.X ═ Y,
inputting:
(1) a forward transmission matrix T of size NxM;
(2) a known parameter Y of size Nx 1;
(3) the sparsity of the signal is epsilon, and the epsilon is also used as a cycle basis of the algorithm;
and (3) outputting:
a target parameter X of size M × 1.
The specific algorithm steps are as follows
a) Recording the residual value gamma 0 Y, sparsity, M, cyclic variable t 0, atomic set ψ 0 Is 0;
b) find the residual value gamma and the column T of the forward conduction matrix m The corner mark m corresponding to the maximum product value of (2);
c) updating the original subset psi i ＝ψ i-1 U { m }, U is the union of mathematical operations, represents to merge with set m, removes the selected column from the forward conduction matrix;
d) calculating residual error
Figure BDA0002874432580000071
t is t +1, and H represents a complex conjugate transpose matrix;
e) judging whether t is larger than epsilon, if so, circularly carrying out b) -d);
thereby obtaining the real part of the array element
Figure BDA0002874432580000072
Imaginary part
Figure BDA0002874432580000073
Is distributed by
Figure BDA0002874432580000074
Figure BDA0002874432580000075
Calculate the amplitude A m And phase P m Obtaining the excitation signal field X ═ X 1 ,X 2 ,X 3 …X m ] T Distribution of the web phase.
Then, the forward transmission equation T.X is substituted into Y, and whether the array can meet the requirement of the plane wave in the quiet area is verified. The amplitude and phase distribution diagrams are shown in fig. 4 and 5. It can be known from the figure that, no matter amplitude or phase diagram, the amplitude fluctuation is less than 1dB and the phase fluctuation is less than +/-1 degree at the central area 20 lambda x 20 lambda in the frame, so that the design initial purpose of the plane wave definition, the dead zone area and the antenna array aperture area approximate to each other is met, and the design expectation is realized.
Example 2
In the embodiment, the PWC design is carried out by taking a free space Green's function as a conduction relation and a Gauss-Newton iteration algorithm as an inverse problem solving algorithm, the basic parameters are the same as the above example, namely, the frequency is selected to be 3GHz, and the antenna aperture D is x ＝D y The antenna array is arranged equidistantly at 20 lambda, and the array element spacing delta x and delta y are both equal to one wavelength lambda. The number of the array elements is 20 × 20, namely M is 400, and the generated field is 1.5 times the aperture size of the antenna array, namely w is 1.5. The method comprises the following concrete steps:
the main steps are the same as in embodiment 1, and for the gauss-newton iterative algorithm in which OMP is replaced, the substantially same inputs as in embodiment 1 are used:
(1) a known parameter Y of size N × 1, determined by equation (9);
(2) a forward conduction matrix T of size NxM calculated by equation (10);
(3) the maximum iteration number n;
(4) given an initial value X of the target parameter of Mx 1 0 ；
The output is:
a target parameter X of size M × 1.
The specific algorithm steps for performing PWC amplitude and phase calculation by using the Gauss-Newton algorithm are as follows:
a) given an input X 0 Solving equation T.X by substituting into the positive problem 0 ＝Y 0 Calculate the corresponding Y 0 。
b) Setting an iteration variable i as 1, and setting an error threshold a;
c) calculating the residual error r i-1 ＝Y i-1 -Y；
d) Judging whether the least square of the residual error r is smaller than an error threshold value a or whether the iteration times is larger than n, if so, ending;
e) updating X i ＝X i-1 -(J H J) -1 J H r i-1 J represents a jacobian matrix, which can be replaced by a forward conduction matrix T, and H represents a complex conjugate transpose matrix;
f) solving equation to calculate Y by substituting positive problem i ；
g) Repeating (c) to (f) to finally obtain the final result.
And then, the forward transmission equation T.X is substituted into Y, and whether the array can meet the requirement of the plane wave in the quiet area is verified. The amplitude/phase distribution diagrams are shown in fig. 6 and 7. It can be known from the figure that, no matter amplitude or phase diagram, the amplitude fluctuation is less than 1dB and the phase fluctuation is less than +/-1 degree at the central area 20 lambda x 20 lambda in the frame, so that the design initial purpose of the plane wave definition, the dead zone area and the antenna array aperture area approximate to each other is met, and the design expectation is realized.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (3)

1. A method for designing the amplitude-phase distribution of an antenna array of a plane wave generator is characterized by comprising the following steps:
firstly, establishing a basic model of a plane wave generator:
T·X＝Y (1)
wherein, X represents an excitation signal field, namely an array element field of the antenna array, Y represents a radiation field, and T represents a forward conduction matrix;
giving the amplitude and phase distribution of each radiation field point in the radiation field Y;
step three, establishing a forward conduction matrix T;
solving the formula (1) by adopting an inverse scattering problem algorithm to obtain the amplitude and phase distribution of each excitation signal point in the excitation signal field X;
the excitation signal field X is formed by M excitation signals and is expressed as
X＝[X 1 ,X 2 ,X 3 …X m ] T (2)
Wherein, X m Denotes the mth excitation signal, M1, 2 m With amplitude A of the m-th excitation signal m And phase P m Is shown, i.e.
Figure FDA0003738596780000011
Or by the real part of the m-th excitation signal
Figure FDA0003738596780000012
And imaginary part
Figure FDA0003738596780000013
Is shown, i.e.
Figure FDA0003738596780000014
The radiation field Y is composed of N radiation field points and is expressed as
Y＝[Y 1 ,Y 2 ,Y 3 …Y n ] T (5)
Wherein, Y n Denotes the nth radiation field point, N being 1,2 n With amplitude FA of the nth radiation field point n And phase FP n Is shown, i.e.
Figure FDA0003738596780000015
Or by the real part of the nth radiation field point
Figure FDA0003738596780000016
And imaginary part
Figure FDA0003738596780000017
Is shown, i.e.
Figure FDA0003738596780000018
The forward conduction matrix T is expressed as
Figure FDA0003738596780000019
Wherein, t nm The conductivity of the mth excitation signal at the nth radiation field point is expressed;
in the second step, each radiation field point Y in the radiation field Y n Amplitude of (FA) n And phase FP n Form expressed as real part
Figure FDA00037385967800000110
And imaginary part
Figure FDA0003738596780000021
In the form of (a);
in the fourth step, after the formula (1) is solved, each excitation signal point X in the excitation signal field X is obtained m Real part of
Figure FDA0003738596780000022
And imaginary part
Figure FDA0003738596780000023
Then the real part is processed
Figure FDA0003738596780000024
And imaginary part
Figure FDA0003738596780000025
Form conversion to amplitude A m And phase P m Forms thereof.
2. The method as claimed in claim 1, wherein t is the number of antenna elements in the plane wave generator nm And expressing by using a free space Green function, or expressing by using a radiation field value of an antenna near field region, or calculating an antenna array by using an MOM, FDTD and FEM full-wave analysis algorithm to obtain a corresponding relation between an excitation signal field and a radiation field.
3. The method as claimed in claim 1, wherein the algorithm of inverse scattering problem includes OMP algorithm, BP algorithm, RMA algorithm, Gaussian Newton iteration and its regularization method, and MUSIC algorithm.
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