Near-field Measurement Method of Linear Array Antenna Based on Multipole and Amplitude Term Compensation

Abstract

The present invention proposes a near-field measurement method for a linear array antenna based on multipole and amplitude term compensation. The implementation steps are as follows: obtaining the near-field electric field signals at three operating frequency points of the linear array antenna; constructing a near-field multipole model and a far-field point model; obtaining the near-field multipole expansion coefficient vector; obtaining the far-field electric field signal vector; compensating the amplitude term of the far-field electric field signal vector at the central operating frequency; and obtaining the near-field measurement results of a single cross-section of the linear array antenna. In the process of obtaining the near-field measurement results of the linear array antenna, the present invention compensates the amplitude term of the far-field electric field signal vector at the central operating frequency with the obtained differential far-field electric field signal vector to obtain the compensated far-field electric field signal of a single cross-section, avoiding the defect of large amplitude term errors in extrapolating the far-field electric field signal caused by directly applying the multipole expansion in a two-dimensional problem to the measurement of a two-dimensional simplified three-dimensional problem in the prior art, and effectively improving the measurement accuracy.

Description

Technical Field

[0001] The present invention belongs to the technical field of antenna measurement, and relates to a near-field measurement method for a linear array antenna, specifically to a near-field measurement method for a linear array antenna based on multi-pole and amplitude term compensation, which can be used for the design, research and development, and maintenance of linear array antennas. Background Art

[0002] One-dimensional linear antenna arrays have extensive applications in technical design fields such as base station antenna design and phased array design. The research, design, and maintenance of one-dimensional linear array antennas are inseparable from near-field measurement technology. Usually, when performing near-field measurement on an array antenna, a three-dimensional sampling and scanning near-field measurement method is required. Since a one-dimensional linear antenna array mainly focuses on the radiation pattern and electric field signal characteristics of the array dimension section plane, a two-dimensional simplified near-field measurement method of a single section plane can be used for a one-dimensional linear antenna array. The near-field measurement methods can be divided into spectral expansion method, equivalent source method, multi-pole method, etc. in the far-field extrapolation method. For the traditional multi-pole method, usually, a discrete near-field electric field signal vector at the center operating frequency of the antenna array to be measured is obtained through sampling, then a two-dimensional multi-pole model is constructed and the transfer operator matrix is calculated, and the multi-pole expansion coefficients are calculated through the electric field signal vector and the transfer operator matrix. Finally, the far-field extrapolation is performed on the multi-pole expansion coefficient vector to obtain the far-field single-section plane electric field signal. The measurement efficiency and result accuracy of near-field measurement have a crucial impact on antenna design work, so the research on high-efficiency and high-precision near-field measurement is very important.

[0003] However, in the near-field measurement methods based on multipoles proposed in the current academic community, the calculation of the multipole expansion coefficients is based on a two-dimensional field, while the data obtained from actual sampling is in a three-dimensional field. If the far-field extrapolation of the multipole expansion coefficients is directly performed, it will lead to an amplitude term error in the measurement, and the accuracy of the far-field extrapolation is affected by the size of the multipole model. For example, in the article "Equivalence between Kim Method and Omi Method in Single-Cut Near-to-Far-Field Transformations for Antenna Near-Field Measurements" on pages 0771 - 0772 of the conference proceedings of the 2019 International Conference on Electromagnetics in Advanced Applications (ICEAA) by M. Hirose and S. Kurokawa in 2019, a new method for near-field measurement of a two-dimensional single cut plane of a linear antenna array using the multipole method is disclosed. This method first obtains the near-field electric field signal vector at the operating frequency point of the linear array antenna, then constructs a two-dimensional multipole model and calculates the transfer operator matrix, calculates the multipole expansion coefficient vector through the electric field signal matrix and the transfer operator matrix, and finally performs far-field extrapolation on the multipole expansion coefficient vector and uses weighted Fourier transform to obtain the continuous far-field single cut plane electric field signal. Compared with the traditional measurement method, this method uses weighted Fourier transform, which compensates the measurement results to a certain extent and improves the measurement accuracy. However, its deficiencies are as follows: The real two-dimensional problem extends infinitely and uniformly in the vertical dimension, while the two-dimensional simplified three-dimensional problem satisfies the far-field condition in the vertical dimension. These two correspond to different Green's function attenuation terms, which are reflected as a difference in the first derivative in mathematical expressions. Therefore, if the multipole expansion in the two-dimensional problem is directly used in the measurement of the two-dimensional simplified three-dimensional problem, it will lead to a certain error in the amplitude term of the extrapolated far field, affecting the accuracy of the measurement; Secondly, due to the small number of multipoles in the two-dimensional multipole model, the number of elements in the corresponding multipole expansion vector is small, which will affect the accuracy of the final far field. Summary of the Invention

[0004] The object of the present invention is to propose a near-field measurement method for a linear array antenna based on multipoles and amplitude term compensation in view of the above-mentioned deficiencies of the existing technology, so as to solve the technical problems existing in the prior art, such as the low measurement accuracy caused by the error of the extrapolated far-field amplitude term and the small number of multipoles in the two-dimensional multipole model.

[0005] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0006] (1) Obtain the near-field electric field signals at three operating frequency points of the linear array antenna:

[0007] (1a) Initialize the operating frequency points of the linear array antenna centered at the origin of the plane polar coordinate system to f0. The corresponding wavelength and wave number of f0 are λ0 and k = 2π / λ0 respectively. The length of the linear array antenna is d;

[0008] (1b) Calculate two differential operating frequency points f1 = f0 + Δf and f2 = f0 - Δf of the linear array antenna through the differential bandwidth Δf, and perform C samplings on the near-field region of the linear array antenna at the frequency points f0, f1, and f2 respectively, to obtain the discrete near-field electric field signal vectors U0 = {U 01 , U 02 ,..., U 0c ,..., U 0C}, U1 = {U 11 , U 12 ,..., U 1c ,..., U 1C}, and U2 = {U 21 , U 22 ,..., U 2c ,..., U 2C} of f0, f1, and f2 respectively. Among them, Δf ∈ [0.001 MHz, 100 MHz], and U 0c , U 1c , U 2c respectively represent the discrete near-field electric field signals of the c-th sampling point corresponding to f0, f1, and f2 with coordinates . r c , respectively represent the polar axis coordinate and polar angle coordinate of the c-th sampling point, and c ∈ {1, 2,..., C};

[0009] (2) Construct a near-field multipole model and a far-field point model:

[0010] Construct a near-field multipole model centered at the origin of the polar coordinate system, which includes L multipole points evenly distributed on a circle with a radius of d, and a far-field point model with N field points evenly distributed on a circle with a radius of D. Among them, represents rounding up. The polar coordinate of the l-th near-field multipole in the near-field multipole model is (d, β l ), and β l represents the polar angle coordinate of the l-th near-field multipole, l ∈ {1, 2,..., L}, N > 2L. The polar coordinate of the n-th far-field point in the far-field point model is (D, α n ), and α nDenote the polar angle coordinates of the n-th far-field point, where n ∈ {1, 2,..., N};

[0011] (3) Obtain the near-field multipole expansion coefficient vector:

[0012] (3a) Calculate the near-field transfer operator T c , θ c ) and the coordinates (d, β l ) of each near-field multipole point, and combine all the near-field transfer operators into a near-field transfer operator matrix T c,l of dimension C × L, where the calculation formula of the near-field transfer operator T C×L is: c,l The calculation formula is:

[0013]

[0014] where is the Hankel function of the second kind of order l, e represents the natural logarithm, and j represents the imaginary number;

[0015] (3b) Calculate the differential near-field electric field signal vector U3 = U1 - U2 through the discrete near-field electric field signal vectors U1 and U2 of f1 and f2, and use the method of moments to calculate the near-field multipole expansion coefficient vector J0 and the differential near-field multipole expansion coefficient vector J3 of the center operating frequency through the discrete near-field electric field signal vector U0 of f0 and the differential near-field electric field signal vector U3 and the near-field transfer operator matrix T C×L respectively;

[0016] (4) Obtain the far-field electric field signal vector:

[0017] (4a) Calculate the far-field transfer operator A n ) and the coordinates (d, β l ) of each near-field multipole point, and combine all the far-field transfer operators into a far-field transfer operator matrix A n,l of dimension N × L, where the calculation formula of the far-field transfer operator A N×L is: n,l The calculation formula is:

[0018]

[0019] (4b) Use the method of moments and calculate the center operating frequency far-field electric field signal vector V0 and the differential far-field electric field signal vector V3 through the near-field multipole expansion coefficient vector J0 and the differential near-field multipole expansion coefficient vector J3 of the center operating frequency and the far-field transfer operator matrix A C×L respectively;

[0020] (5) Perform amplitude term compensation on the center operating frequency far-field electric field signal vector:

[0021] Compensate the amplitude term of the far-field electric field signal vector V0 at the center operating frequency through the differential far-field electric field signal vector V3 to obtain the single-plane electric field signal vector V:

[0022] V = [V3 - V0]q + V0

[0023] where q is the compensation coefficient and q ∈ [0, 1];

[0024] (6) Obtain the near-field measurement result of the single plane of the linear array antenna:

[0025] Restore and transform the discrete single-plane electric field signal vector V through the Nyquist sampling theorem to obtain the continuous single-plane far-field electric field signal

[0026] Compared with the prior art, the present invention has the following advantages:

[0027] 1. In the process of obtaining the near-field measurement result of the single plane of the linear array antenna, the present invention first constructs a near-field multipole model and a far-field point model, then obtains the near-field multipole expansion coefficient vectors of the two near-field electric field signals of the linear array antenna, and then calculates the two near-field multipole expansion coefficient vectors using the far-field transfer operator matrix. Then, the obtained differential far-field electric field signal vector is used to compensate the amplitude term of the far-field electric field signal vector at the center operating frequency to obtain the compensated single-plane far-field electric field signal, avoiding the defect of large error in the extrapolated far-field electric field signal amplitude term caused by directly applying the multipole expansion in a two-dimensional problem to the measurement of a two-dimensional simplified three-dimensional problem in the prior art, and effectively improving the measurement accuracy;

[0028] 2. The present invention constructs a near-field multipole model and a far-field point model, where the number of far-field points in the far-field point model is much larger than the number of multipole points in the near-field multipole model. Finally, the far-field calculation is performed on the far-field point model with a larger model. Compared with directly performing the far-field calculation on the near-field multipole model in the prior art, it avoids the problem that the number of multipoles in the two-dimensional multipole model is small and the number of elements in the corresponding multipole expansion vector is small, which affects the final far-field accuracy, and further improves the measurement accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] Figure 1 is the implementation flowchart of the present invention;

[0030] Figure 2 is a schematic diagram of the linear antenna array structure, near-field multipole model and far-field point model of the present invention;

[0031] Figure 3 is the simulation result diagram of the single-plane far-field electric field signal obtained by the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0032] In order to make the objectives, technical solutions and advantages of the present invention more clear and understandable, the following further describes the present invention in detail with reference to the accompanying drawings and specific embodiments:

[0033] Step 1) Obtain the near-field electric field signals at three operating frequency points of the linear array antenna:

[0034] (1a) Refer to Figure 2 , the center of the linear array antenna is located at the origin of the plane polar coordinate system, the antenna is arranged along the direction perpendicular to the polar axis. Initialize the operating frequency points of the linear array antenna as f0, the corresponding wavelength and wave number of f0 are λ0 and k = 2π / λ0 respectively, and the length of the linear array antenna is d. In this embodiment, f0 = 10 GHz, λ0 = 0.03 m, and d = 1.2 m;

[0035] (1b) Calculate two differential operating frequency points f1 = f0 + Δf and f2 = f0 - Δf of the linear array antenna through the differential bandwidth Δf, and perform C samplings on the near-field region of the linear array antenna at the frequency points f0, f1, and f2 respectively. The sampling method can be linear sampling, circular sampling or other plane sampling methods, and obtain the discrete near-field electric field signal vectors U0 = {U 01 , U 02 ,..., U 0c ,..., U 0C}, U1 = {U 11 , U 12 ,..., U 1c ,..., U 1C}, and U2 = {U 21 , U 22 ,..., U 2c ,..., U 2C} of f0, f1, and f2. Among them, Δf ∈ [0.001 MHz, 100 MHz], U 0c , U 1c , and U 2c respectively represent the discrete near-field electric field signals of the c-th sampling point corresponding to f0, f1, and f2 with coordinates , r c , respectively represent the polar axis coordinate and polar angle coordinate of the c-th sampling point, c ∈ {1, 2,..., C}, and in this embodiment, C = 51;

[0036] Step 2) Construct a near-field multipole model and a far-field point model:

[0037] Refer to Figure 2, a near-field multipole model with its center at the origin of the polar coordinate system, including L multipole points evenly distributed on a circle with a radius of d, and a far-field point model with N field points evenly distributed on a circle with a radius of D is constructed. Among them, denotes rounding up. The polar coordinates of the l-th near-field multipole in the near-field multipole model are (d, β l ), β l represents the polar angle coordinate of the l-th near-field multipole, l ∈ {1, 2,..., L}. D, as the radius of the far-field point model, needs to satisfy the far-field condition of the antenna. Therefore, the number of far-field points in the far-field point model needs to be much larger than the number of multipole points in the near-field multipole model. Only by performing far-field calculations on the far-field point model with a larger model at the end can the problem of affecting the final far-field accuracy due to the small number of multipoles in the two-dimensional multipole model be avoided. Therefore, N > 2L. The polar coordinates of the n-th far-field point in the far-field point model are (D, α n ), α n represents the polar angle coordinate of the n-th far-field point, n ∈ {1, 2,..., N}. In this embodiment, L = 251, N = 502, and D = 96;

[0038] Step 3) Obtain the near-field multipole expansion coefficient vector:

[0039] (3a) Calculate the near-field transfer operator T c through the coordinates (r c ) of each sampling point and the coordinates (d, β l ) of each near-field multipole point, and combine all near-field transfer operators into a near-field transfer operator matrix T c,l with a dimension of C × L. Among them, the calculation formula of the near-field transfer operator T C×L is: c,l

[0040]

[0041] where is the l-th order Hankel function of the second kind, e represents the natural logarithm, and j represents the imaginary number;

[0042] ​(3b) By establishing the correspondence between the established multipole model and the radiation characteristics at any near-field position, the near-field measurement problem can be described as the following matrix equation system. Using the near-field measurement position coordinates, the measured electric field signals, and the multipole model, a linear equation system with the unknowns to be solved being the multipole expansion coefficients can be obtained. Solving this equation system can obtain the discrete multipole expansion coefficients characterizing the radiation characteristics of the array antenna to be measured. Therefore, through the discrete near-field electric field signal vectors U1 and U2 of f1 and f2, calculate the differential near-field electric field signal vector U3 = U1 - U2, and use the method of moments. Through the discrete near-field electric field signal vector U0 of f0 and the differential near-field electric field signal vector U3 respectively and the near-field transfer operator matrix T C×L , calculate the near-field multipole expansion coefficient vector J0 and the differential near-field multipole expansion coefficient vector J3 at the center operating frequency. The calculation formulas are:

[0043] U p = T C×L J p

[0044] where p ∈ {0, 3};

[0045] Step 4) Obtain the far-field electric field signal vector:

[0046] (4a) Calculate the far-field transfer operator A n through the coordinates (D, α l ) of each far-field point and the coordinates (d, β n,l ) of each near-field multipole point, and combine all the far-field transfer operators into a far-field transfer operator matrix A N×L with dimensions N × L. The calculation formula for the far-field transfer operator A n,l is:

[0047]

[0048] (4b) By establishing the correspondence between the established multipole model and the far-field radiation characteristics at any position, the far-field conversion problem can be described as the following matrix equation system. Using the far-field point model and the multipole expansion coefficients, a linear equation system with the unknowns to be solved being the far-field electric field signals can be obtained. Solving this equation system can obtain the discrete multipole expansion coefficients characterizing the radiation characteristics of the array antenna to be measured. Therefore, use the method of moments, and through the near-field multipole expansion coefficient vector J0 and the differential near-field multipole expansion coefficient vector J3 at the center operating frequency respectively and the far-field transfer operator matrix A C×L calculate the far-field electric field signal vector V0 and the differential far-field electric field signal vector V3 at the center operating frequency. The calculation formulas are:

[0049] V p = A N×L J p ;

[0050] Step 5) Perform amplitude term compensation on the far-field electric field signal vector at the center operating frequency:

[0051] The real two-dimensional problem extends infinitely and uniformly in the vertical dimension, while the two-dimensional simplified three-dimensional problem satisfies the far-field condition in the vertical dimension. There are different Green's function attenuation terms corresponding to these two situations, which are reflected as a difference in the first derivative in mathematical expressions. For the first derivative data of the electric field signal at a frequency point, it can be approximated as the difference far-field electric field signal transformed from the difference near-field electric field signals at two frequency points near this frequency point. Therefore, the amplitude term of the far-field electric field signal vector V0 at the center operating frequency is compensated by the difference far-field electric field signal vector V3 to obtain the single-plane electric field signal vector V:

[0052] V = [V3 - V0]q + V0

[0053] where q is the compensation coefficient, q ∈ [0, 1], and in this embodiment, q = 0.7;

[0054] Step 6) Obtain the near-field measurement result of the single plane of the linear array antenna:

[0055] The near-field measurement result of the single plane of the linear array antenna usually needs to be expressed in the form of a continuous signal. Therefore, the discrete single-plane electric field signal vector V is restored and transformed through the Nyquist sampling theorem to obtain the continuous single-plane far-field electric field signal Its expression is:

[0056]

[0057] where V n represents the nth element of the vector V, π is the pi, is the polar axis angle coordinate.

[0058] The technical effects of the present invention will be described below in combination with simulation experiments.

[0059] 1. Simulation conditions and content:

[0060] The simulation is completed using the commercial electromagnetic simulation software FEKO.

[0061] The single-plane far-field electric field signal obtained by the present invention is simulated, and the results are as Figure 3 shown.

[0062] 2. Analysis of simulation results:

[0063] Refer to Figure 3, the horizontal axis represents the angle of the single-plane electric field signal, and the vertical axis represents the normalized gain value of the continuous single-plane far-field electric field signal. The solid line in the figure represents the true far-field single-plane electric field signal, the dotted line represents the single-plane far-field electric field signal obtained by this method, and the thin dotted line below represents the relative error between the single-plane far-field electric field signal obtained by this method and the true far-field single-plane electric field signal. It can be seen that the maximum relative error is below -55 dB.

[0064] The above description is only a specific example of the present invention, which is only used to illustrate the technical solution of the present invention, rather than constituting any limitation to the present invention. Obviously, those of ordinary skill in the art can still modify the technical solutions recorded in the foregoing embodiments, or equivalently replace some or all of the technical features therein; and these modifications or replacements under the idea of the present invention all belong to the protection scope of the present invention.

Claims

1. A near-field measurement method for a linear array antenna based on multi-pole and amplitude term compensation, characterized in that, It includes the following steps: (1) Obtain the near-field electric field signals at three operating frequency points of the linear array antenna: (1a) Initialize the operating frequency points of the linear array antenna centered at the origin of the plane polar coordinate system as f0. The corresponding wavelength and wavenumber of f0 are λ0 and k = 2π / λ0 respectively. The length of the linear array antenna is d; (1b) Calculate two differential operating frequency points f1 = f0 + Δf and f2 = f0 - Δf of the linear array antenna through the differential bandwidth Δf, and perform C samplings on the near-field region of the linear array antenna at the frequency points f0, f1, and f2 respectively, to obtain the discrete near-field electric field signal vectors U0 = {U 01 , U 02 ,..., U 0c ,..., U 0C}, U1 = {U 11 , U 12 ,..., U 1c ,..., U 1C} and U2 = {U 21 , U 22 ,..., U 2c ,..., U 2C} of f1 and f2, where Δf ∈ [0.001 MHz, 100 MHz], and U 0c , U 1c , U 2c respectively represent the discrete near-field electric field signals of the c-th sampling point corresponding to f0, f1, and f2 with the coordinates , and r c , respectively represent the polar axis coordinate and polar angle coordinate of the c-th sampling point, and c ∈ {1, 2,..., C}; (2) Construct a near-field multipole model and a far-field point model: Construct a near-field multipole model with the center of construction located at the origin of the polar coordinate system, including L multipole points evenly distributed on a circle with a radius of d, and a far-field point model with N field points evenly distributed on a circle with a radius of D. Among them, denotes rounding up. The polar coordinates of the l-th near-field multipole in the near-field multipole model are (d, β l ), where β l represents the polar angle coordinate of the l-th near-field multipole, and l ∈ {1, 2,..., L}. The polar coordinates of the n-th far-field point in the far-field point model are (D, α n ), where α n represents the polar angle coordinate of the n-th far-field point, and n ∈ {1, 2,..., N}. (3) Obtain the near-field multipole expansion coefficient vector: (3a) Calculate the near-field transfer operator T c through the coordinates (r c , θ l ) of each sampling point and the coordinates (d, β c,l ) of each near-field multipole point, and combine all the near-field transfer operators into a near-field transfer operator matrix T C×L with dimensions C×L, where the calculation formula of the near-field transfer operator T c,l is: Among them, is the l-th order Hankel function of the second kind, e represents the natural logarithm, and j represents the imaginary number; (3b) Calculate the differential near-field electric field signal vector U3 = U1 - U2 from the discrete near-field electric field signal vectors U1 and U2 of f1 and f2, and use the method of moments to calculate the near-field multipole expansion coefficient vector J0 and the differential near-field multipole expansion coefficient vector J3 of the center operating frequency through the discrete near-field electric field signal vector U0 of f0 and the differential near-field electric field signal vector U3 respectively, and the near-field transfer operator matrix T C×L , respectively; (4) Obtain the far-field electric field signal vector: (4a) By the coordinates of each far-field point (D, α n ) and the coordinates of each near-field multipole point (d,β l ) Calculate the far-field transfer operator A n,l , and combine all far-field transfer operators into a far-field transfer operator matrix A with dimension N×L N×L , where the far-field transfer operator A n,l The calculation formula is: (4b) The method of moments is adopted, and the far-field electric field signal vector V0 and the differential far-field electric field signal vector V3 at the central operating frequency are calculated by using the near-field multipole expansion coefficient vector J0 and the differential near-field multipole expansion coefficient vector J3 at the central operating frequency and the far-field transfer operator matrix A respectively C×L Calculate the far-field electric field signal vector V0 and the differential far-field electric field signal vector V3 at the central operating frequency; (5) Perform amplitude-term compensation on the far-field electric field signal vector at the center operating frequency: Perform amplitude-term compensation on the far-field electric field signal vector V0 at the center operating frequency through the differential far-field electric field signal vector V3 to obtain the single-plane electric field signal vector V: V = [V3 - V0]q + V0 where q is the compensation coefficient and q ∈ [0, 1]; (6) Obtain the near-field measurement results of a single plane of the linear array antenna: The discrete single-plane electric field signal vector V is restored and transformed by the Nyquist sampling theorem to obtain a continuous single-plane far-field electric field signal 2. The near-field measurement method of the linear array antenna based on multipole and amplitude term compensation according to claim 1, characterized in that In step (3b), the calculation of the near-field multipole expansion coefficient vector J0 and the differential near-field multipole expansion coefficient vector J3 at the center operating frequency, the calculation formula is: U p = T C×L J p where p ∈ {0, 3}.

3. The near-field measurement method of a linear array antenna based on multipole and amplitude term compensation according to claim 2, wherein In step (4b), the calculation of the far-field electric field signal vector V0 and the differential far-field electric field signal vector V3 at the center operating frequency, the calculation formula is: V p = A N×L J p 。 4. The near-field measurement method of a linear array antenna based on multipole expansion and amplitude term compensation according to claim 1, wherein The continuous single-plane far-field electric field signal described in step (6) Its expression is: where V n represents the n-th element of vector V, π is the circumference ratio, is the angular coordinate of the polar axis.

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