A phase recovery method for a spherical dipole array based on phase iteration

Abstract

The application relates to a phase recovery method based on a phase iteration spherical dipole array, belonging to the field of communication, and comprising the following steps: constructing the relationship between the spherical dipole array and the electric field generated thereby, inputting the non-phase near-field measurement data, and assuming a phase to change the non-phase near-field into the near-field measurement data with the assumed phase; bringing the near-field measurement data with the assumed phase into a cost function; taking the assumed phase as an iteration individual, utilizing the cost function to perform iteration, finding the individual in the current iteration through an iteration algorithm, and calculating the value of the cost function; when the iteration times reach the upper limit or the cost function meets the expected result, taking the phase at the time as the phase data of the non-phase measurement near-field. The application iterates the phase of the measurement field instead of the size of the dipole, avoids the defect that the upper limit of the size of the dipole is unknown, and can reduce the error caused by the computer storage to a certain extent, and greatly improves the convergence.

Description

Technical Field

[0001] This invention relates to the field of communication technology, and in particular to a phase recovery method based on a spherical dipole array with phase iteration. Background Technology

[0002] Antenna measurements can generally be categorized into three types based on the test site: compact field measurement, far-field measurement, and near-field measurement. Compact field measurement uses mirrors and arrays to generate plane waves to simulate an infinite far-field environment; however, the high precision required for the equipment makes the entire system very expensive. Far-field measurement is susceptible to interference from external environments, such as varying electromagnetic conditions and weather conditions, leading to inaccurate results and difficulties in ensuring confidentiality. In near-field testing, the relatively short distance between the antenna and the measuring equipment reduces the propagation path and the influence of the external environment, thus improving measurement accuracy and precision. It also offers good confidentiality and the advantage of all-weather operation. Furthermore, it eliminates the need for large far-field test sites or complex measuring equipment, resulting in the lowest overall system setup cost.

[0003] Near-field measurement has wide applications in the antenna field. Based on the shape of the scanning surface, it can be divided into planar measurement, cylindrical measurement, and spherical measurement. Planar measurement is mainly used for testing pencil-beam antennas. These antennas typically have strong radiation capability in one direction, such as directional antennas in radar. Cylindrical measurement is for fan-beam antennas. These antennas typically radiate signals within a cylindrical area, such as satellite communication antennas. However, the drawback of these two scanning methods is that when scanning at the edge of the scanning area, the scanning surface is truncated, resulting in a lack of information within the truncated area when performing near-field and far-field changes. This makes it impossible to accurately calculate the far-field radiation characteristics. Only when partial information about the radiation direction, such as the beam pointing, is known can the scanning surface be manually defined to reduce errors. Spherical measurement is a more universal method, applicable to various types of antennas with various beams. By scanning the antenna within a spherical area, spherical measurement can obtain the antenna's radiation characteristics in all directions. This is of great significance for comprehensive antenna performance evaluation and analysis of radiation characteristics in different directions. Combining antenna spherical measurement with near-field and far-field transformation techniques, such as converting near-field spherical measurement data into the antenna's radiation pattern in the far field, has significant practical application value in fields such as communications, radar, and remote sensing.

[0004] The mainstream spherical near-field to far-field conversion algorithms mainly include the mode expansion method and the equivalent dipole source reconstruction method. The mode expansion method is a widely used numerical method for solving electromagnetic field distribution problems. It represents the field distribution established by the antenna under test (AUT) in space as a linear combination of a set of spherical wave functions, calculates weighting coefficients using near-field measurement data, and thus achieves accurate calculation of the electromagnetic field distribution. Its advantages lie in its wide applicability, its flexibility in applying it to various problems, and its high efficiency and accuracy. However, the mode expansion method requires accurate sampling data, continuous and regular sampling surfaces, and cannot perform near-field to far-field conversion without phase. The equivalent dipole source reconstruction method uses an equivalent source to replace the AUT, and calculates the radiation characteristics of the equivalent source to use as the radiation characteristics of the AUT. The greatest advantage of the equivalent dipole source reconstruction method is its high versatility; it can use any available electromagnetic field information, such as electric field values, magnetic field values, phase information, amplitude information, and can even solve for the equivalent dipole array under phase-free near-field measurement conditions, finally obtaining the far-field radiation characteristics of the AUT.

[0005] Among existing phase retrieval algorithms, the most common approach is to use iterative sampling with dual-plane data. However, this requires near-field data to be acquired on two planes. While machine learning can also be used for phase retrieval, these methods share the common limitation of only being able to perform phase retrieval on a single plane, thus requiring prior knowledge of the main lobe's orientation. When the shape of the radiation source and the main lobe's orientation are unknown, and only data from a single sampling plane is available, a satisfactory result cannot be obtained. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art and provide a phase recovery method for spherical dipole arrays based on phase iteration, thereby solving the deficiencies of the prior art.

[0007] The objective of this invention is achieved through the following technical solution: a phase recovery method based on a spherical dipole array using phase iteration, the phase recovery method comprising:

[0008] Step 1: Construct the relationship between the spherical dipole array and its generated electric field, and input phase-free near-field measurement data. And assume a phase Transforming phaseless near-field data into near-field measurement data with an assumed phase, i.e. E r E θ and Let θ represent the electric field in spherical coordinates. r is the position of the dipole in spherical coordinates;

[0009] Step 2: Substitute the near-field measurement data with the assumed phase into the cost function. In this context, m is the number of near-field measurements, and n is the number of equivalent dipoles;

[0010] Step 3: Using the assumed phase Φ(t) as the iterative individual, apply the cost function. The process involves iteration, using an iterative algorithm to find the individual in the current iteration, and calculating the cost function. The value;

[0011] Step 4: When the number of iterations reaches the upper limit or the cost function... If the expected result is met, the phase at this time is taken as the phase data of the near field without phase measurement; otherwise, repeat step two.

[0012] The relationship between the constructed spherical dipole array and the electric field it generates includes:

[0013] Let matrix A m×n x n =b m The inverse problem is the problem of finding the parameters of a radiation source from discrete near-field measurement data, where A m×n ∈C m×n The near-field measurement b is described m ∈C m With the parameter x representing the equivalent source n ∈C n The relationship between them;

[0014] The electric field equation generated by an electric dipole at the center of the coordinate system can be transformed into the electric field equation generated by an electric dipole at any position using the coordinate transformation formula:

[0015]

[0016]

[0017]

[0018] Among them, E x E y E z Let P be the magnitude component of the electric field generated by the dipole in a Cartesian coordinate system, η be the magnitude of the wave impedance in free space, and P be the magnitude component of the electric field generated by the dipole in a Cartesian coordinate system. x ,P y ,P z Let g1(r), g2(r), and f(r) be the components of the electric dipole moment in Cartesian coordinates, k be the wave number in free space, and g1(r), g2(r), and f(r) all represent functions.

[0019] Again, using the coordinate transformation formula, perform two coordinate transformations on the three electric field equations to transform the electric field E...x E y E z and dipole P x ,P y ,P z Transform E into spherical coordinates respectively r E θ , and P r ,P θ , get Among them, T ErPr T ErPθ and E r and P r ,P θ , Relationship parameters, T EθPr T EθPθ and E θ and P r ,P θ , Relationship parameters and They represent and P r ,P θ , Relationship parameters between them;

[0020] Choosing a set of uniform electric dipoles along the tangential direction of the sphere as the equivalent source of the antenna under test to replace the original radiation source, the equation relating the electric dipoles and the electric field is rewritten as follows:

[0021] The input is phase-free near-field measurement data. And assume a phase Transforming phaseless near-field measurements into near-field measurements with an assumed phase includes:

[0022] The relation matrix A is decomposed using singular value decomposition. m×n The decomposition into three multiplicative matrices is as follows Among them, U m×m and V n×n Let diag(s) be a Hermitian matrix. n ) is a diagonal matrix;

[0023] Using the least squares method Estimate the parameters x of a feasible equivalent source. n And set a phase vector for the measured phaseless near field. At this time, the near-field measurement value b m Represented as Furthermore Convert to

[0024] Will Substitute From

[0025] at this time but The least squares solution is y n =diag(s n -1 )d n ,Right now Among them, (U) m×n ) H Indicates (U) m×m ) H The first n columns;

[0026] at this time The lower bound is ||-d m-n || 2 , let the lower bound‖-d m-n || 2 Approaching 0, we obtain a new least squares problem as follows: The cost function of the iterative algorithm is used to find the solution to this least squares problem, which is a set of vectors. That is, phase data of the near field without phase measurement.

[0027] This invention offers the following advantages: a phase recovery method for a spherical dipole array based on phase iteration avoids the drawback of an unknown upper limit for dipole size by iteratively measuring the phase of the field instead of the size of the dipoles. Furthermore, it can reduce errors caused by computer storage to some extent, significantly improving convergence. Good phase recovery results are achieved even under single-spherical sampling conditions and when the specific radiation source is unknown. Attached Figure Description

[0028] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0029] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of the embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the detailed description of the embodiments of this application provided below with reference to the accompanying drawings is not intended to limit the scope of protection of the claimed application, but merely represents selected embodiments of this application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application. The present invention will be further described below with reference to the accompanying drawings.

[0030] like Figure 1 As shown, this invention specifically relates to a phase recovery method for a spherical dipole array based on phase iteration, which includes two parts: establishing the relationship between the spherical dipole array and the electric field, and recovering the phase without phase sampling. Specifically, it includes the following:

[0031] 1. The relationship between a spherical dipole array and the electric field it generates;

[0032] The problem of finding the parameters of a radiation source from discrete near-field measurement data can be viewed as the inverse problem of the following matrix equation:

[0033] A m×n x n =b m (1.1)

[0034] Where m is the number of near-field measurements, n is the number of equivalent dipoles, and matrix A m×n ∈C m×n This describes the measurement vector, which is the near-field measurement value b. m ∈C m With the parameter x representing the equivalent source n ∈C n The relationship between them (in the spherical dipole equivalence method, this parameter represents the size of the dipole).

[0035] To find the relationship matrix A between an electric dipole in spherical coordinates and the electric field it produces at any point in space. m×n ∈C m×n First, the electric field equation generated by the electric dipole at the center of the coordinate system is transformed into the electric field equation generated by the electric dipole at any position using the coordinate transformation formula, as shown in equation (1.2):

[0036]

[0037]

[0038]

[0039] E x E y E z Let P be the magnitude component of the electric field generated by the dipole in a Cartesian coordinate system, η be the magnitude of the wave impedance in free space, and P be the magnitude component of the electric field generated by the dipole in a Cartesian coordinate system. x ,P y ,P z Let θ be the components of the electric dipole moment in a rectangular coordinate system. r is the position of the dipole in spherical coordinates, k is the wave number in free space, and other functions are shown in equation (1.3):

[0040]

[0041]

[0042]

[0043] We then perform two coordinate transformations on equation (1.2) using the coordinate transformation formula again, to transform the electric field E... x E y E z and dipole P x ,P y ,P z Transform E into spherical coordinates respectively r E θ , and P r ,P θ , The following relationship is obtained: (1.4)

[0044]

[0045]

[0046]

[0047] T ErPr T ErPθ , T EθPr T EθPθ , and E r E θ , and P r ,P θ , The relationship parameters between them.

[0048] When constructing the equivalent dipole model, we treat the spherical electric dipoles as currents. When the density of electric dipoles is sufficiently high, these electric dipoles are equivalent to the equivalent surface current. According to the equivalence principle, the equivalent electric dipoles can be used to replace the AUT (Anti-Under-Tec System) in calculating the far field. Theoretically, electric dipoles, magnetic dipoles, or a combination of both can be used as equivalent sources, and there are many combinations to construct the model. According to Love's equivalence principle, the original radiation source can be replaced by the equivalent surface current. Therefore, this algorithm selects a set of uniform electric dipoles in the tangential direction of the spherical surface as the equivalent source of the antenna under test.

[0049] At this point, the equation relating the dipole and the field can be written in matrix form similar to equation (1.1):

[0050]

[0051] 2. Phase recovery algorithm based on phase iteration;

[0052] Under the condition of having only phase-free near-field measurement data, vector b m Since it is phase-free, equation (1.1), which is also equation (1.6), can be rewritten as:

[0053] |A m×n x n |=|b m |(2.1)

[0054] In order to solve equation (2.1), we can consider (1.6) as A. m×n x n =b m Rewrite it in the form of:

[0055]

[0056] When m > n, the number of equations exceeds the number of independent variables, meaning the number of near-field measurements exceeds the number of dipole arrays. In this case, the system of equations may have no solution from a purely mathematical perspective. However, if the rank of the entire system of equations is n, then the system has a unique solution. More simply, the dipole array, calculated from the n linearly uncorrelated equations in the system, is the vector x. n The remaining equations should be satisfied.

[0057] That is, the condition that a dipole array needs to satisfy is: for the formula Solving the inverse problem corresponding to the first n equations yields (x1, x2, ..., x...). n ), and satisfy The remaining equations.

[0058] The phased near-field electric field of the antenna under test should satisfy the above set of equations. Based on this condition, when only the phaseless near-field electric field is available, if an assumed phase is randomly assigned to the phaseless sample value, it is not possible to ensure that the rank of the set of equations (2.2) is n. As long as a phase data that satisfies equation (2.2) is found for the phaseless data, phase recovery of the phaseless near-field can be achieved.

[0059] Furthermore, the relation matrix A is further analyzed through singular value decomposition. m×n Decomposed into three multiplicative matrices:

[0060]

[0061] U m×m V n×n It is a Hermitian matrix, diag(s) n ) is a diagonal matrix.

[0062] Due to systematic or measurement errors, it is difficult to find an exact solution to the phase-free problem in equation (2.1). A feasible x can be estimated using the least squares method. n As shown below:

[0063]

[0064] At this point, it is assumed that the measured phaseless field is given an assumed phase vector. At this time, the near-field measurement value b m It can be represented as The problem in (2.4) can be rewritten as follows:

[0065]

[0066] Substituting formula (2.3) into formula (2.5), we obtain formula (2.6) as shown below:

[0067]

[0068] Among them, (U) m×m ) H Indicates (U) m×m Perform the conjugate transpose, at this time,

[0069] The least squares solution to the entire system of equations (2.5) is: y n =diag(s n -1 )d n ,Right now:

[0070] Among them (U) m×n )H Indicates (U) m×m ) H The first n columns.

[0071] At this point, (2.5) has a lower bound ||-d m-n || 2 As we explained before, when the phase and amplitude meet the actual conditions, the entire system of equations (2.2) should have a solution. Considering that the dipole cannot be completely equivalent to the AUT and other errors generated during the calculation or measurement process, the lower bound of equation (2.5) is ||-d||. m-n || 2 It should be close to 0 rather than equal to 0, that is, ||-d m-n || 2 The smaller the value, the more randomly |b is assigned. m | phase vector The more realistic it is.

[0072] At this point, the entire phase retrieval algorithm becomes a new least squares problem, which is solved by finding a suitable... Make ||d m-n || 2 Minimum:

[0073]

[0074] Equation (2.7) is used as the cost function of the iterative algorithm to find the solution to this least squares problem. The solution is a set of vectors. That is, phase data of the near field without phase measurement.

[0075] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and improvements, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A phase recovery method for a spherical dipole array based on phase iteration, characterized in that: The phase recovery method includes: Step 1: Construct the relationship between the spherical dipole array and its generated electric field, and input phase-free near-field measurement data. And assume a phase Transforming phaseless near-field data into near-field measurements with an assumed phase, i.e. , , , and Represents the electric field in spherical coordinates. , It is the position of the dipole in spherical coordinates; Step 2: Substitute the near-field measurement data with the assumed phase into the cost function. middle, It is the number of near-field measurements. It is the number of equivalent dipoles. Represents the Hermitian matrix Perform conjugate transpose; Step 3: Assume the phase As an iterative individual, utilizing the cost function The process involves iteration, using an iterative algorithm to find the individual in the current iteration, and calculating the cost function. The value; Step 4: When the number of iterations reaches the upper limit or the cost function... If the expected result is met, the phase at this time is taken as the phase data of the near field without phase measurement; otherwise, repeat step two.

2. The phase recovery method for a spherical dipole array based on phase iteration according to claim 1, characterized in that: The relationship between the construction of the spherical dipole array and the electric field it generates includes: matrix The inverse problem is the problem of finding the parameters of a radiation source from discrete near-field measurement data, where... Describes near-field measurements With the parameter representing the equivalent source The relationship between them; The electric field equation generated by an electric dipole at the center of the coordinate system can be transformed into the electric field equation generated by an electric dipole at any position using the coordinate transformation formula: ； ； ； in, Let represent the magnitude components of the electric field generated by the dipole in a Cartesian coordinate system. The magnitude of the wave impedance in free space. The components of the electric dipole moment in a rectangular coordinate system. It is the wavenumber in free space. , and Both represent functions; Again, using the coordinate transformation formula, perform two coordinate transformations on the three electric field equations to transform the electric field... and dipole Transformed into spherical coordinates respectively and ,get , , ,in, , and They represent and Relationship parameters , and They represent and Relationship parameters , and They represent and Relationship parameters between them; A set of uniform electric dipoles along the tangential direction of the sphere is chosen as the equivalent source of the antenna under test to replace the original radiation source. The equation relating the electric dipoles and the electric field is then rewritten as follows: .

3. The phase recovery method for a spherical dipole array based on phase iteration according to claim 2, characterized in that: The input is phase-free near-field measurement data. And assume a phase Transforming phaseless near-field measurements into near-field measurements with an assumed phase includes: The relation matrix is ​​decomposed using singular value decomposition. The decomposition into three multiplicative matrices is as follows ,in, and It is a Hermitian matrix. It is a diagonal matrix; Using the least squares method Estimate the parameters of a feasible equivalent source. And set a phase vector for the measured phaseless near field. At this time, the near-field measurement value Represented as , and thus Convert to ; Will Substitute From ; at this time , ,but The least squares solution is ,Right now ,in, express The former List; at this time The lower bound is Let the lower realm Approaching 0, we obtain a new least squares problem as follows: The cost function of the iterative algorithm is used to find the solution to this least squares problem, which is a set of vectors. That is, phase data of the near field without phase measurement.

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