Non-uniform sparse sampling single-section near-field test system and method

Abstract

The invention discloses a non-uniform sparse sampling single-section near-field test system and method, and belongs to the technical field of test. According to the method, the single-section radiation field is expressed in a matrix form, the unknown transmission coefficient is solved from the system of linear equations through an inverse matrix method, and the defect that a traditional single-section near-field test method based on fast Fourier transform depends on the distribution uniformity of near-field samples is overcome; under the assumption that antenna transmission coefficients have sparsity, a compressed sensing technology is introduced, L1 norm minimization constraint is applied to a transmission coefficient vector q to ensure the sparsity, and under the condition that the number M of single-section near-field samples is smaller than the number J of unknown coefficients, the transmission coefficients can be solved from an underdetermined linear equation set; according to the invention, a non-uniform sampling-based single-section near-field test method is realized, and the flexibility of a sampling mode is improved; the number of sampling points and the scanning time are reduced, and the testing efficiency is improved; and the far-field reconstruction precision is higher.

Description

Technical Field

[0001] The present invention belongs to the technical field of testing, and particularly relates to a non-uniform sparse sampling single-plane near-field testing system and method. Background Art

[0002] The single-plane near-field antenna testing technology is an important means in modern antenna performance evaluation. Its basic principle is to scan and sample the interested plane (such as the E-plane or H-plane) in the near field range through a probe, and through strict mathematical transformation, reconstruct the near-field data into the far-field radiation characteristics of this plane. In order to ensure the reconstruction accuracy, the traditional method usually needs to satisfy the Nyquist sampling law and appropriately perform oversampling to avoid aliasing and data loss.

[0003] Existing technical solutions:

[0004] The traditional single-plane near-field antenna testing method needs to discretely and uniformly sample the interested plane in the near field range through a probe, as Figure 1 shown.

[0005] 1. First, calculate the maximum sampling interval:

[0006]

[0007] where N is the truncation order:

[0008]

[0009] where r is the minimum radius enclosing the antenna under test, and k is the wave number:

[0010]

[0011] where λ is the operating wavelength:

[0012]

[0013] where f is the operating frequency and c is the speed of light in vacuum.

[0014] 2. On the plane of the antenna under test that is of interest, measure the near field w m (r0, θ) of the antenna under test with a radius of r0 at the sampling interval required in step 1. The subscript m represents the generalized near-field component, which can be the θ or φ component.

[0015] 3. Since the near field w m (r0, θ) can be expressed as:

[0016]

[0017] According to the properties of the inverse Fourier transform, calculate the transmission coefficient of the antenna under test:

[0018]

[0019] wherein is the second kind of Hankel function.

[0020] 4. Using the distance-invariance of the transmission coefficient, calculate the far field of this section as follows:

[0021]

[0022] Disadvantages of the prior art:

[0023] In actual tests, oversampling is usually appropriately performed to avoid aliasing and data loss. This strategy improves the reconstruction accuracy to a certain extent, but also brings significant problems in terms of efficiency, including an increase in the complexity of data acquisition and processing due to the excessive number of sampling points, the need for the probe to stop and start frequently during the scanning process, which reduces the test efficiency, and the extension of the test time as the number of sampling points increases. Summary of the Invention

[0024] In view of the above technical problems existing in the prior art, the present invention proposes a non-uniform sparse sampling single-section near-field test system and method, which is reasonably designed, overcomes the deficiencies of the prior art, and has good effects.

[0025] To achieve the above object, the present invention adopts the following technical solutions:

[0026] A non-uniform sparse sampling single-section near-field test system includes a sampling module, a reconstruction module, a calculation module, and a control module; wherein,

[0027] The sampling module is configured to sample an interested section according to non-uniform sparse sampling coordinates within the near-field range to obtain near-field data;

[0028] The reconstruction module is configured to solve an underdetermined linear equation system based on the compressed sensing theory with the minimization of the L1 norm as the optimization objective to reconstruct the transmission coefficient of the antenna;

[0029] The calculation module is configured to calculate the far-field radiation pattern of the section according to the reconstructed transmission coefficient;

[0030] The control module is configured to control the scanning process of the sampling module and optimize the non-uniform sparse sampling coordinates according to the antenna characteristics.

[0031] In addition, the present invention also mentions a non-uniform sparse sampling single-section near-field test method, which uses the above-mentioned non-uniform sparse sampling single-section near-field test system and includes the following steps:

[0032] Step 1: Determine the truncation order N according to the operating frequency and size of the antenna under test;

[0033] Step 2: Construct a non-uniform sparse sampling coordinate θ that satisfies finite equidistribution, and determine the sensing matrix Ψ composed of its corresponding basis functions according to the non-uniform sparse sampling coordinate;

[0034] Step 3: In the near-field range, sample the cross-section of interest of the antenna under test according to the non-uniform sparse sampling coordinate to obtain the near-field data w m (r0, θ), where the subscript m represents the generalized near-field component; r0 is the radius;

[0035] Step 4: Based on the compressed sensing theory, with the minimization of the L1 norm as the optimization goal, solve the following underdetermined linear equation system to reconstruct the transmission coefficient vector q of the antenna:

[0036]

[0037] where ε represents the allowable error level; w represents the measurement vector composed of the near-field complex signals received by the probe;

[0038] Step 5: Calculate the far-field radiation pattern of the cross-section according to the reconstructed transmission coefficient vector q.

[0039] Preferably, in Step 2, constructing a non-uniform sparse sampling coordinate that satisfies finite equidistribution includes the following steps:

[0040] Step 2.1: Determine the number of sampling points M, where M < J, and J = 2N + 1 is the dimension of the transmission coefficient vector q;

[0041] Step 2.2: Optimize the sampling positions according to the characteristics of the antenna under test so that the sensing matrix Ψ satisfies the finite equidistribution condition.

[0042] Preferably, the sensing matrix Ψ satisfies the finite equidistribution condition, which means that for any transmission coefficient vector q and constant δ ∈ (0, 1), the following inequality is satisfied:

[0043]

[0044] Preferably, in Step 4, to solve the L1 norm minimization problem, the basis pursuit algorithm or the basis pursuit denoising algorithm is used.

[0045] Preferably, in Step 3, scanning sampling is performed through a near-field probe.

[0046] The beneficial technical effects brought by the present invention:

[0047] 1. Realize a single-cross-section near-field test method based on non-uniform sampling, increasing the flexibility of the sampling method;

[0048] 2. The single-plane near-field testing method based on sparse sampling is realized, reducing the number of sampling points and the scanning time, and improving the testing efficiency.

[0049] 3. Under the same sampling conditions, compared with the traditional single-plane near-field testing method based on fast Fourier transform, the method proposed by the present invention has higher far-field reconstruction accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] Figure 1 It is a schematic diagram of an existing single-plane uniform sampling scheme (taking the xoz-plane scanning sampling as an example);

[0051] Figure 2 It is a schematic diagram of the single-plane non-uniform sparse sampling scheme proposed by the present invention (taking the xoz-plane scanning sampling as an example);

[0052] Figure 3 It is the basic flow chart of the method of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0053] The following further describes the present invention in detail with reference to the drawings and specific embodiments:

[0054] The principle of the non-uniform sparse sampling single-plane near-field testing method based on compressive sensing proposed by the present invention is to utilize the sparsity of the transmission coefficient of the antenna under test, and perform non-uniform and sparse discrete sampling at the sampling coordinates that meet the conditions (as Figure 2 shown), and use the L1 norm minimization as the optimization problem model to solve the underdetermined linear equations and reconstruct the unknown coefficients, and then calculate the far-field radiation characteristics of this plane.

[0055] First, the principle and premise of the present invention are described.

[0056] Consider the matrix form representation of the single-plane radiation field of the antenna:

[0057] w = ψq

[0058] where the vector represents the measured near field w m (r0, θ), the matrix Ψ is composed of basis functions and can be expressed as:

[0059]

[0060] where, is the second kind of Hankel function. The vector represents the transmission coefficient Q n , and J = 2N + 1. r0 represents the test distance, and θ represents the elevation angle in the spherical coordinate system.

[0061] In the case of sparse sampling, the inverse problem is ill-posed, and the upper bound of the rank of matrix Ψ is M < J. Therefore, this underdetermined linear equation system has no unique solution.

[0062] Now, adding the assumption that there are at most s non-zero terms, where s < J or s << J at this time, it can also be said that vector q is s-sparse. Under this assumption, mathematically, the transmission coefficient can be reconstructed using s + 1 near-field samples That is, according to the measured near-field signal solve the optimization problem:

[0063]

[0064] This optimization problem provides the vector q with the fewest non-zero terms in the solution space. However, this problem is NP-hard and computationally difficult to solve. Therefore, the above formula is simplified to an L1 norm minimization problem:

[0065]

[0066] There is an effective solution to the above convex problem, and the restricted isometry property defines a sufficient condition for successful reconstruction. For any and constant δ ∈ (0, 1), if

[0067]

[0068] then matrix Ψ satisfies the restricted isometry property.

[0069] Secondly, the basic implementation process of the present invention is given, as Figure 3 shown:

[0070] 1. First, according to the operating frequency and size of the antenna to be measured, calculate the truncation order N:

[0071]

[0072] where r is the minimum radius enclosing the antenna to be measured, and k is the wave number:

[0073]

[0074] where λ is the operating wavelength:

[0075]

[0076] where f is the operating frequency and c is the speed of light in vacuum.

[0077] 2. Give the distribution of the sampling coordinates θ that satisfies the restricted isometry property and the corresponding ψ composed of basis functions;

[0078] 3. On the cross-section of interest of the antenna under test, measure the near-field \(w_m(r_0,\theta)\) of the antenna under test at the sampling coordinates required in step 2, where the subscript \(m\) represents the generalized near-field component, which can be the \(\theta\) or \(\varphi\) component; \(\varphi\) is the azimuth angle in the spherical coordinate system. m (r0,θ), where the subscript m represents the generalized near-field component, which can be the θ or φ component; φ is the azimuth angle in the spherical coordinate system.

[0079] 4. Establish a matrix equation through the measured near-field signal vector \(w\) in step 3 and the matrix \(\varPsi\), establish an L1-norm minimization optimization problem based on the assumption of the sparsity of the transmission coefficient, and solve it by methods such as basis pursuit or basis pursuit denoising:

[0080]

[0081] where \(\varepsilon\) represents the allowed error level.

[0082] 5. Calculate the far-field radiation pattern of this cross-section using the obtained transmission coefficient.

[0083] Key points and protected points of the present invention

[0084] 1. The present invention expresses the single-cross-section radiation field in matrix form and solves the unknown transmission coefficient from this linear equation set through the inverse matrix method, overcoming the dependence of the traditional single-cross-section near-field test method based on the fast Fourier transform on the uniformity of the near-field sample distribution.

[0085] 2. Under the assumption of the sparsity of the antenna transmission coefficient, the compressed sensing technology is introduced, and the L1-norm minimization constraint is imposed on the transmission coefficient vector \(q\) to ensure its sparsity. When the number \(M\) of single-cross-section near-field samples is less than the number \(J\) of unknown coefficients, the transmission coefficient can be solved from the underdetermined linear equation set.

[0086] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by those skilled in the art within the essence of the present invention should also fall within the protection scope of the present invention.

Claims

1. A non-uniform sparse sampling single-section near-field test system, characterized in that, It includes a sampling module, a reconstruction module, a calculation module, and a control module; among them, The sampling module is configured to sample the cross-section of interest within the near field range according to non-uniform sparse sampling coordinates to obtain near-field data; The reconstruction module is configured to solve the underdetermined linear equations based on the compressed sensing theory with the minimization of the L1 norm as the optimization goal to reconstruct the transmission coefficient of the antenna; The calculation module is configured to calculate the far-field radiation pattern of the cross-section according to the reconstructed transmission coefficient; The control module is configured to control the scanning process of the sampling module and optimize the non-uniform sparse sampling coordinates according to the antenna characteristics.

2. A non-uniform sparse sampling single-plane near-field testing method, characterized in that, Using a non-uniform sparse sampling single-cross-section near-field test system as described in claim 1, it includes the following steps: Step 1: Determine the truncation order N according to the operating frequency and size of the antenna under test; Step 2: Construct non-uniform sparse sampling coordinates θ that satisfy finite equidistance, and determine the sensing matrix Ψ composed of its corresponding basis functions according to the non-uniform sparse sampling coordinates; Step 3: In the near-field range, sample the cross-section of interest of the antenna under test according to the non-uniform sparse sampling coordinates to obtain the near-field data w m (r0,θ), where the subscript m represents the generalized near-field component; r0 is the radius; m (r0,θ), the subscript m represents the generalized near-field component; r0 is the radius; Step 4: Based on the compressed sensing theory, with the minimization of the L1 norm as the optimization goal, solve the following underdetermined linear equations to reconstruct the transmission coefficient vector q of the antenna: Where, ε represents the allowable error level; w represents the measurement vector composed of the near-field complex signals received by the probe; Step 5: Calculate the far-field radiation pattern of the cross-section according to the reconstructed transmission coefficient vector q.

3. The non-uniform sparse sampling single-plane near-field testing method according to claim 2, wherein In step 2, constructing non-uniform sparse sampling coordinates that satisfy finite equidistance includes the following steps: Step 2.1: Determine the number of sampling points M, where M < J, and J = 2N + 1 is the dimension of the transmission coefficient vector q; Step 2.2: Optimize the sampling positions according to the characteristics of the antenna under test so that the sensing matrix Ψ satisfies the finite equidistance condition.

4. The non-uniform sparse sampling single-section near-field testing method according to claim 2, characterized in that The sensing matrix Ψ satisfies the finite equidistance condition, which means that for any transmission coefficient vector q and constant δ ∈ (0, 1), the following inequality is satisfied:

5. The non-uniform sparse sampling single-plane near-field testing method according to claim 2, wherein In step 4, to solve the L1 norm minimization problem, the basis pursuit algorithm or the basis pursuit denoising algorithm is used.

6. The non-uniform sparse sampling single-plane near-field testing method according to claim 2, wherein, In step 3, scanning sampling is performed through a near-field probe.

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