Antenna array calibration method and antenna array calibration device

Abstract

To provide an antenna array calibration method and an antenna array calibration device with which it is possible to achieve appropriate accuracy of calibration by an appropriate number of calibration data sets.SOLUTION: A characteristic vector of covariance matrix of the signal transmitted from a wave source whose arrival direction is known and received by an array antenna 2 is repeatedly calculated while changing the arrival direction. Real elements constituting the array antenna 2 are arranged symmetrically. A calibration matrix is expressed by the product of an amplitude phase error matrix composed of the amplitude phase error of the real elements and a mutual coupling matrix composed of a mutual coupling between the real elements and a mutual coupling between virtual elements and the real elements. The mutual coupling matrix is such that the degree of freedom of mutual coupling between the real elements is limited on the basis of the arrangement symmetry of the real elements, and the mutual coupling matrix and the amplitude phase error matrix are obtained from the characteristic vectors of covariance matrices by an iterative solution technique.SELECTED DRAWING: Figure 2

Description

Technical Field

[0001] The present invention relates to an antenna array calibration method and an antenna array calibration device for calibrating the mutual coupling between elements of an array antenna and the amplitude-phase error of each element using a wave source with a known arrival direction.

Background Art

[0002] By using an array antenna, it is possible to estimate the arrival direction of radio waves, and the MUSIC method is known as a high-resolution arrival direction estimation method. In the normal MUSIC method, it is assumed that each antenna can receive the incoming wave ideally and independently. However, in an actual array antenna, due to the following error factors, the result as expected by the theory cannot be obtained, which hinders accurate arrival direction estimation.

[0003] The first error factor is the mutual coupling between antenna elements. When an antenna receives an incoming wave, re-radiation occurs due to the current excited on the element, and the mutual coupling between elements occurs when another antenna receives it.

[0004] The second error factor is the amplitude-phase error of each element. Even if antenna elements, feed lines, and receivers of the same specification are arrayed, there are non-uniformities in the actual device, resulting in element-to-element errors in amplitude-phase characteristics.

[0005] Array calibration using a known wave source is performed by changing the arrival direction of the known wave source, receiving it with an array antenna, obtaining a calibration data set, and obtaining unknown variables of the mutual coupling between elements and the amplitude-phase error of each element from the calibration data set.

[0006] Obtaining a calibration data set using the array antenna and receiver used for arrival direction estimation can calibrate including the amplitude-phase error of the receiver, and is considered practically useful because it is easy to obtain high calibration accuracy.

[0007] As shown in FIG. 1, for the array antenna, an antenna arrangement with symmetry, such as an equally spaced linear array in which receiving antennas are arranged linearly at equal intervals or an equally spaced circular array in which receiving antennas are arranged circularly at equal intervals, is often used.

[0008] Non-Patent Document 1 and Non-Patent Document 2 describe an array calibration method that reduces the number of unknown variables based on the symmetry of the arrangement of receiving antennas and enables array calibration with a small number of calibration data sets.

[0009] Let the number of elements of the receiving antenna be N, the number of calibration data sets be M, the complex amplitude of the i-th calibration signal (a signal output from a known wave source) be s i , the arrival angle be θ i , the ideal mode vector be a(θ i ), the mutual coupling matrix representing the mutual coupling between elements be C1, the amplitude-phase error matrix representing the amplitude-phase error of each element be Γ, the received signal vector be r i , and the noise vector be n i . Then, the calibration model is represented by the following equation (1). In the mathematical formula, vectors and matrices are represented by bold characters, but they are regarded as the same as the lowercase characters in the text.

[0010]

Equation

[0011] The amplitude-phase error matrix Γ in Equation (1) is represented by the following equation (2).

[0012]

Equation

[0013] The amplitude-phase error γ of each element in Equation (2) k is represented by the following equation (3).

[0014]

Equation

[0015] In Equation (3), α k represents the amplitude error of each element, and φ k represents the phase error of each element. In the case of a linear array where the antenna elements are arranged on a straight line, if the positions of the elements are x k , (k = 1, ···, N), then the ideal mode vector a(θ i ) is represented by the following Equation (4).

[0016]

Number

[0017] In Equation (4), T represents the transpose, and λ represents the wavelength. The mutual coupling matrix C1 is an N×N square matrix. However, in the case of an antenna arrangement with symmetry such as an equally spaced linear array or an equally spaced circular array, the degree of freedom of mutual coupling between elements can be restricted.

[0018] For example, the mutual coupling matrix C1 of the 4-element equally spaced linear array described in Non-Patent Document 1 is shown in Equation (5). Each element of the mutual coupling matrix (c0 to c5 in Equation (5)) is called the mutual coupling coefficient.

[0019]

Number

[0020] Non-Patent Document 2 describes the mutual coupling matrix of an equally spaced circular array. The mutual coupling matrix C1 between the elements of the 4-element equally spaced circular array is shown in Equation (6).

[0021]

Number

[0022] When the received signal vector r i is received from a signal output from a known arrival angle θ i , it becomes the calibration data set, and the arrival angle θ iBy changing it and repeating the reception M times, M sets of calibration data sets can be obtained, and the mutual coupling matrix C1 and the amplitude-phase error matrix Γ are calculated from the M sets of calibration data sets.

[0023] Received signal r i Let the covariance matrix of be R i and for R i let the j-th eigenvalue be λ j (i) and the j-th eigenvector be e j (i) , λ1 (i) ≥ λ2 (i) ≥ ··· ≥ λ N (i) be so. When the calibration signal is one wave, the calibrated mode vector ΓC1a(θ i ) is proportional to the signal subspace e1 (i) and is orthogonal to the noise subspace {e2 (i) , ···, e N (i)}}.

[0024] Regarding the mutual coupling matrix C1 of the 4-element equally spaced linear array shown in Equation (5), using the property that the calibrated mode vector ΓC1a(θ i ) is orthogonal to the noise subspace, the following Equation (7) holds.

[0025]

Equation

[0026] In Equation (7), * represents the complex conjugate, and H represents the complex conjugate transpose. The unknown variables in Equation (7) are {c0, ···, c5, γ1, ···, γ4}, and when the mutual coupling coefficients and amplitude-phase errors are normalized so that c0 = 1 and γ1 = 1, the number of unknown variables to be solved is 8.

[0027] Since M(N - 1) equations (7) are obtained using the calibration dataset of group M, the number M of calibration datasets required to solve for 8 unknown variables satisfies M(N - 1)≥8, so M≥3. Since equation (7) is difficult to solve directly because it is a product of unknown variables, Non-Patent Document 2 describes obtaining the mutual coupling matrix C1 and the amplitude-phase error matrix Γ by an iterative method.

[0028] In the iterative method described in Non-Patent Document 2, first, the initial value of the mutual coupling matrix C1 is set to the identity matrix. In step 1, by assuming C1 is known, the product of the unknown variables in equation (7) is eliminated, and Γ is obtained from the linearized equation (7). In step 2, by assuming Γ is known, the product of the unknown variables in equation (7) is eliminated, and C1 is obtained from the linearized equation (7). C1 and Γ are obtained by repeating steps 1 and 2.

[0029] Non-Patent Document 3 describes a virtual array calibration method that improves calibration accuracy by adding virtual elements that do not actually exist in addition to the actual elements of the receiving antenna.

[0030] Let the number of actual elements of the receiving antenna be N, the total number of elements including actual and virtual elements be N′, the number of calibration datasets be M, the complex amplitude of the i-th calibration signal (signal output from a known wave source) be s i , the arrival angle be θ i , the ideal mode vector be a(θ i ), the calibration matrix be C0, the received signal vector be r i , and the noise vector be n i . Then, the calibration model is represented by the following equation (8).

[0031]

Equation

[0032] In equation (8), the ideal mode vector a(θ i) is represented by an N'-dimensional vector containing both real elements and virtual elements. In the case of a linear array where real elements and virtual elements are arranged on a straight line, if the positions of the real elements and virtual elements are x k , (k = 1, ···, N'), the ideal mode vector is represented by the following equation (9).

[0033]

Equation

[0034] The calibration matrix C0 is represented by the following equation (10). A column for virtual elements is added to the matrix for N real elements, and it is represented by an N-row N'-column matrix.

[0035]

Equation

[0036] In equation (10), the calibration matrix C0 is a matrix where each element is independent, and it includes the mutual coupling between real elements, the mutual coupling between virtual elements and real elements, and the amplitude-phase error of real elements.

[0037] The received signal vector r i and the noise vector n i are N-dimensional vectors of only real elements. When receiving a signal output from a known arrival angle θ i of a wave source, the received signal vector r i becomes a calibration data set. By changing the arrival angle θ i and repeating the reception M times, M sets of calibration data sets can be obtained, and the calibration matrix C0 is calculated from the M sets of calibration data sets.

[0038] Let the covariance matrix of the received signal r i be R i , and let the j-th eigenvalue of R i be λ j (i) , and the j-th eigenvector be e j (i), λ1 (i) ≥ λ2 (i) ≥ ··· ≥ λ N (i) be set as follows. When the calibration signal is a single wave, the calibrated mode vector C0a(θ i ) is proportional to the signal subspace e1 (i) and is orthogonal to the noise subspace {e2 (i) , ···, e N (i)}}.

[0039] Regarding the calibration matrix C0 shown in Equation (10), using the property that the calibrated mode vector C0a(θ i ) is orthogonal to the noise subspace, the following Equation (11) holds.

[0040]

Number

[0041] Let the vertical vector obtained by arranging the elements c 11 , c 12 , ···, c NN′ of the calibration matrix C0 be the boldface c0. Then the following Equation (12) holds.

[0042]

Number

[0043] Equation (12) can be transformed into the following Equation (13) by setting the matrix formed by arranging the eigenvectors e2 (i) , e3 (i) , ···, e N (i) as E N (i) .

[0044]

Number

[0045] In Equation (13), E N (i)H and a(θ i )T The symbol between them represents the Kronecker product. When using M sets of calibration data sets, the following equation (14) holds.

[0046]

Equation

[0047] In equation (14), when normalizing the calibration matrix C0 and setting any element of boldface c0, for example, c 11 to 1, the remaining elements of boldface c0 can be obtained by the generalized inverse matrix. Since boldface c0 is an NN′-dimensional vector, the number of unknown variables is NN′ - 1.

[0048] E N (i)H Since E is a matrix with N - 1 rows, equation (14) becomes M(N - 1) equations. Therefore, in order to obtain NN′ - 1 unknown variables, a calibration data set with M ≥ (NN′ - 1) / (N - 1) is required. For example, when N = 4 and N′ = 6, the number of unknown variables is 23, and the number of calibration data sets is M ≥ 8.

[0049] Thus, the virtual array calibration method described in Non-Patent Document 3 is a method of increasing the degree of freedom of the calibration matrix to improve the calibration accuracy. It has a large number of unknown variables and requires a large number of calibration data sets.

[0050] When estimating the direction of arrival of a wave source by the MUSIC method using an array antenna, in the case of a calibration method based on the symmetry of the antenna arrangement, â(θ) = ΓC1a(θ), and in the case of the virtual array calibration method, â(θ) = C0a(θ). After calibration, the mode vector â(θ) is calculated, and the matrix E N consisting of the eigenvectors of noise is used to obtain the calibrated MUSIC spectrum P MUSIC (θ) by the following equation (15). â represents a variable with a ~ above a in the mathematical formula.

[0051]

Equation

[0052] In Equation (15), by obtaining the arrival angle θ at which the calibrated MUSIC spectrum P MUSIC (θ) is maximized, calibrated arrival direction estimation can be performed.

Prior Art Documents

Non-Patent Documents

[0053]

Non-Patent Document 1

Non-Patent Document 2

Non-Patent Document 3

Summary of the Invention

Problems to be Solved by the Invention

[0054] Since the array calibration methods described in Non-Patent Document 1 and Non-Patent Document 2 limit the degrees of freedom of mutual coupling based on the symmetry of the antenna arrangement, array calibration can be performed with a small number of unknown variables, that is, a small number of calibration data sets.

[0055] In addition, since the array calibration methods described in Non-Patent Document 1 and Non-Patent Document 2 can obtain mutual coupling and amplitude-phase error separately, it is easy to re-calibrate only the amplitude-phase error or only the mutual coupling.

[0056] However, since the array calibration methods described in Non-Patent Document 1 and Non-Patent Document 2 have low degrees of freedom in mutual coupling, the calibration accuracy is not very high.

[0057] On the other hand, the virtual array calibration method described in Non-Patent Document 3 increases the degrees of freedom of the calibration matrix by adding virtual elements that do not actually exist, enabling high-precision array calibration.

[0058] However, since the virtual array calibration method described in Non-Patent Document 3 has a large number of unknown variables and requires a large number of calibration data sets, and is a method for obtaining a calibration matrix including mutual coupling and amplitude-phase error, it is difficult to re-calibrate only the amplitude-phase error or only the mutual coupling.

[0059] As described above, the conventional calibration methods described above are divided into a low-precision calibration method with a small number of unknown variables and a high-precision calibration method with a large number of unknown variables, and there is a problem that appropriate calibration accuracy cannot be achieved with an appropriate number of calibration data sets.

[0060] The present invention has been made to solve this problem, and an object thereof is to provide an antenna array calibration method and an antenna array calibration apparatus capable of achieving appropriate calibration accuracy with an appropriate number of calibration data sets.

Means for Solving the Problem

[0061] In the antenna array calibration method of the present invention, the eigenvectors of the covariance matrix of the received signals received by the array antenna (2) from a wave source with a known direction of arrival are repeatedly calculated a predetermined number of times while changing the direction of arrival, and a calibration matrix including the mutual coupling between the existing elements constituting the array antenna, the mutual coupling between non-existent virtual elements and the existing elements, and the amplitude-phase error of the existing elements is obtained from the eigenvectors. In the antenna array calibration method, the existing elements are arranged symmetrically, the calibration matrix is represented by the product of an amplitude-phase error matrix having the amplitude-phase error of the existing elements as diagonal elements and a mutual coupling matrix composed of the mutual coupling between the existing elements and the mutual coupling between the virtual elements and the existing elements, the degree of freedom of the mutual coupling between the existing elements is restricted based on the symmetry of the arrangement of the existing elements, and instead of obtaining the calibration matrix, the mutual coupling matrix and the amplitude-phase error matrix are obtained by an iterative solution method.

[0062] Thus, the antenna array calibration method of the present invention restricts the degree of freedom of the mutual coupling between the existing elements based on the symmetry of the arrangement of the existing elements, thereby reducing the number of mutual coupling coefficients that are unknown variables during calibration, and by obtaining the mutual coupling matrix and the amplitude-phase error matrix by an iterative solution method, the number of calibration data sets can be reduced.

[0063] In addition, the antenna array calibration method of the present invention can improve the calibration accuracy by adding virtual elements and adding the mutual coupling between the virtual elements and the existing elements to the mutual coupling matrix. Therefore, the antenna array calibration method of the present invention can achieve an appropriate calibration accuracy with an appropriate number of calibration data sets.

[0064] In the antenna array calibration method of the present invention, the number of existing elements is N, the number of virtual elements is N′ which is the number obtained by adding the number of virtual elements to N, and the predetermined number may be a number less than (NN′ - 1) / (N - 1).

[0065] Thus, the antenna array calibration method of the present invention can reduce the number of calibration data sets compared to the virtual array calibration method described in Non-Patent Document 3.

[0066] Also, in the antenna array calibration method of the present invention, in the mutual coupling matrix, a part of the mutual coupling between the virtual element and the actual element may be zero.

[0067] Thus, the antenna array calibration method of the present invention can change the number of mutual coupling coefficients that are unknown variables during calibration by setting a part of the mutual coupling between the virtual element and the actual element to zero, so that the number of calibration data sets can be changed.

[0068] Also, in the antenna array calibration method of the present invention, in the mutual coupling matrix, among the mutual couplings between the virtual element and the actual element, the mutual couplings other than those with the shortest element-to-element distance between the virtual element and the actual element may be zero.

[0069] Thus, the antenna array calibration method of the present invention can reduce the number of mutual coupling coefficients that are unknown variables during calibration by setting to zero the mutual couplings between the virtual element and the actual element other than those with the shortest distance between the virtual element and the actual element, so that the number of calibration data sets can be reduced.

[0070] Also, in the antenna array calibration method of the present invention, the virtual elements are arranged symmetrically, and in the mutual coupling matrix, based on the symmetry of the arrangement of the virtual elements and the actual elements, the degree of freedom of the mutual coupling between the virtual elements and the actual elements may be restricted.

[0071] Thus, in the antenna array calibration method of the present invention, virtual elements are arranged symmetrically, and based on the symmetry of the arrangement of the virtual elements and the physical elements, by restricting the degree of freedom of mutual coupling between the virtual elements and the physical elements, the number of mutual coupling coefficients that are unknown variables during calibration can be reduced compared to the case where the symmetry of the virtual elements is not assumed, so the number of calibration data sets can be reduced.

[0072] Also, in the antenna array calibration method of the present invention, the virtual elements are arranged symmetrically, and the mutual coupling matrix is based on the symmetry of the arrangement of the virtual elements and the physical elements, the degree of freedom of mutual coupling between the virtual elements and the physical elements is restricted, and a part of the mutual coupling between the virtual elements and the physical elements may be zero.

[0073] Thus, in the antenna array calibration method of the present invention, virtual elements are arranged symmetrically, based on the symmetry of the arrangement of the virtual elements and the physical elements, the degree of freedom of mutual coupling between the virtual elements and the physical elements is restricted, and a part of the mutual coupling between the virtual elements and the physical elements is set to zero. In addition to the characteristics when the virtual elements are arranged symmetrically, since the number of mutual coupling coefficients that are unknown variables during calibration can be changed, the number of calibration data sets can be changed.

[0074] Also, in the antenna array calibration method of the present invention, the virtual elements are arranged symmetrically, the mutual coupling matrix is based on the symmetry of the arrangement of the virtual elements and the physical elements, the degree of freedom of mutual coupling between the virtual elements and the physical elements is restricted, and among the mutual couplings between the virtual elements and the physical elements, the mutual couplings other than those with the shortest element-to-element distance between the virtual elements and the physical elements may be zero.

[0075] Thus, in the antenna array calibration method of the present invention, virtual elements are arranged symmetrically, and based on the symmetry of the arrangement of the virtual elements and the physical elements, the degree of freedom of the mutual coupling between the virtual elements and the physical elements is restricted. Moreover, among the mutual couplings between the virtual elements and the physical elements, by setting to zero the mutual couplings other than those with the shortest distance between the virtual elements and the physical elements, the number of mutual coupling coefficients that are unknown variables during calibration can be reduced, and thus the number of calibration data sets can be reduced.

[0076] In the antenna array calibration apparatus of the present invention, an array antenna (2) that receives a signal transmitted from a wave source with a known direction of arrival, and an eigenvalue analysis unit (31) that repeatedly calculates the eigenvectors of the covariance matrix of the received signal received by the array antenna a predetermined number of times while changing the direction of arrival, and from the eigenvectors calculated by the eigenvalue analysis unit, a calibration matrix including the mutual coupling between the physical elements constituting the array antenna, the mutual coupling between non-existent virtual elements and the physical elements, and the amplitude-phase error of the physical elements, in the antenna array calibration apparatus having a calibration matrix calculation unit, the physical elements are arranged symmetrically, the calibration matrix is represented by the product of an amplitude-phase error matrix having the amplitude-phase error of the physical elements as diagonal elements and a mutual coupling matrix composed of the mutual coupling between the physical elements and the mutual coupling between the virtual elements and the physical elements, the degree of freedom of the mutual coupling between the physical elements is restricted based on the symmetry of the arrangement of the physical elements, and the calibration matrix calculation unit is a mutual coupling / amplitude-phase error calculation unit (32) that obtains the mutual coupling matrix and the amplitude-phase error matrix from the eigenvectors calculated by the eigenvalue analysis unit by an iterative method.

[0077] With this configuration, the antenna array calibration apparatus of the present invention restricts the degree of freedom of the mutual coupling between the physical elements based on the symmetry of the arrangement of the physical elements, thereby reducing the number of mutual coupling coefficients that are unknown variables during calibration, and by obtaining the mutual coupling matrix and the amplitude-phase error matrix by an iterative method, the number of calibration data sets can be reduced.

[0078] In addition, the antenna array calibration device of the present invention can improve the calibration accuracy by adding virtual elements and adding the mutual coupling between the virtual elements and the existing elements to the mutual coupling matrix. Therefore, the antenna array calibration device of the present invention can achieve appropriate calibration accuracy with an appropriate number of calibration data sets.

Effects of the Invention

[0079] The present invention can provide an antenna array calibration method and an antenna array calibration device capable of achieving appropriate calibration accuracy with an appropriate number of calibration data sets.

Brief Description of the Drawings

[0080]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Embodiments for Carrying Out the Invention

[0081] Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[0082] As shown in FIG. 2, the antenna array calibration apparatus 1 includes an array antenna 2, a multi-channel receiver 3, an array calibration processing unit 4, and a memory 5.

[0083] The array antenna 2 is composed of a plurality of receiving antennas 2a to 2d. For example, the receiving antennas 2a to 2d are symmetrically arranged such as in an equally spaced linear array where the receiving antennas 2a to 2d are arranged linearly at equal intervals, or in an equally spaced circular array where the receiving antennas 2a to 2d are arranged circularly at equal intervals. Although four receiving antennas 2a to 2d are shown in FIG. 2, the number of receiving antennas constituting the array antenna 2 is not limited.

[0084] In the antenna array calibration apparatus 1, in the array antenna 2, a signal with a known arrival angle transmitted from a transmitting antenna 11 provided in a transmitter 10 is received. In FIG. 2, the transmitting antenna 11 and the receiving antennas 2a to 2d are shown close to each other, but the transmitting antenna 11 is arranged sufficiently far from the maximum element interval of the receiving antennas 2a to 2d such that plane waves arrive at the receiving antennas 2a to 2d.

[0085] The multi-channel receiver 3 includes frequency converters 20a to 20d and ADCs (A / D converters) 21a to 21d corresponding to the receiving antennas 2a to 2d, respectively. Each of the frequency converters 20a to 20d converts a radio frequency (simply referred to as "RF") signal received by each of the receiving antennas 2a to 2d into an intermediate frequency (simply referred to as "IF") signal, respectively.

[0086] Each of the ADCs 21a to 21d performs AD conversion on the IF signal converted by each of the frequency converters 20a to 20d into a digital signal, respectively.

[0087] Note that each of the frequency converters 20a to 20d may include a quadrature demodulator that converts an IF signal into an in-phase signal (also simply referred to as "I") and a quadrature signal (also simply referred to as "Q"). Alternatively, each of the frequency converters 20a to 20d may be integrally configured to directly convert an RF signal into an I / Q signal. Instead of converting to analog I / Q signals in each of the frequency converters 20a to 20d, each of the ADCs 21a to 21d may include a digital downconverter that converts an AD-converted digital IF signal into a digital I / Q signal.

[0088] When performing AD conversion on analog I / Q signals, two AD converters are required per channel (i.e., one receiving antenna). In order to synchronize the phases between channels, each of the frequency converters 20a to 20d performs frequency conversion using a local signal generator 22 common to each channel, and each of the ADCs 21a to 21d performs AD conversion using a clock signal generator 23 common to each channel.

[0089] In the present embodiment, the array calibration processing unit 4 is configured by a CPU (Central Processing Unit) that executes a program stored in a storage medium such as a ROM (Read Only Memory) or a hard disk device. The array calibration processing unit 4 includes a covariance matrix calculation unit 30, an eigenvalue analysis unit 31, and a mutual coupling / amplitude-phase error calculation unit 32.

[0090] The covariance matrix calculation unit 30 calculates the covariance matrix of the received signals of each channel. The eigenvalue analysis unit 31 calculates the eigenvalues and eigenvectors of the covariance matrix calculated by the covariance matrix calculation unit 30 through eigenvalue analysis.

[0091] The mutual coupling and amplitude-phase error calculation unit 32 calculates a mutual coupling matrix and an amplitude-phase error matrix from the eigenvectors calculated by the eigenvalue analysis unit 31 while changing the arrival angle of the signal transmitted from the transmitter 10 and the transmission antenna 11 which are known wave sources. Instead of changing the arrival angle by changing the position of the transmission antenna 11, the relative arrival angle may be changed by rotating the array antenna 2. The mutual coupling matrix and the amplitude-phase error matrix calculated by the mutual coupling and amplitude-phase error calculation unit 32 are stored in the memory 5. Instead of the mutual coupling matrix, the mutual coupling coefficient may be stored in the memory 5, and instead of the amplitude-phase error matrix, the amplitude-phase error of each element may be stored in the memory 5.

[0092] The arrival direction estimation device 50 in the embodiment of the present invention is shown in FIG. 3. Among the components of the arrival direction estimation device 50, the components having the same configuration as those of the antenna array calibration device 1 are denoted by the same reference numerals and the description thereof is omitted.

[0093] As shown in FIG. 3, the arrival direction estimation device 50 includes an array antenna 2, a multi-channel receiver 3, an arrival direction estimation processing unit 51, and a memory 5. In the arrival direction estimation device 50, in the array antenna 2, a signal with an unknown arrival angle transmitted from the transmission antenna 11a provided in the transmitter 10a is received. The signals transmitted from the transmitter 10a and the transmission antenna 11a may be different signals from the signals transmitted from the transmitter 10 and the transmission antenna 11 in FIG. 2.

[0094] Thus, since the arrival direction estimation device 50 has the same configuration as the antenna array calibration device 1 not only for the array antenna 2 but also for the multi-channel receiver 3, calibration is performed including the amplitude-phase error caused by the hardware constituting the multi-channel receiver 3.

[0095] In the present embodiment, the arrival direction estimation processing unit 51 is configured by a CPU that executes a program stored in a storage medium such as a ROM or a hard disk device. The arrival direction estimation processing unit 51 includes a covariance matrix calculation unit 30, an eigenvalue analysis unit 31, a mode vector calculation unit 52, and a MUSIC calculation unit 53.

[0096] The mode vector calculation unit 52 calculates a calibrated mode vector using the mutual coupling matrix and the amplitude-phase error matrix stored in the memory 5.

[0097] The MUSIC operation unit 53 calculates a MUSIC spectrum from the calibrated mode vector calculated by the mode vector calculation unit 52 and the eigenvectors of the covariance matrix calculated by the eigenvalue analysis unit 31, and calculates the arrival angle at which the MUSIC spectrum peaks as the estimated arrival direction value.

[0098] The estimated arrival direction value calculated by the MUSIC operation unit 53 is displayed on an external display device (not shown). Note that the arrival direction estimation processing unit 51 may also cause the external display device to display a graph of the MUSIC spectrum in addition to the estimated arrival direction value.

[0099] The antenna array calibration method by the antenna array calibration device 1 will be described below.

[0100] In the antenna array calibration method, first, eigenvalue analysis of the covariance matrix calculated by the covariance matrix calculation unit 30 is performed by the eigenvalue analysis unit 31.

[0101] Let the number of elements of the receiving antenna be N, the number of calibration data sets be M, the complex amplitude of the i-th calibration signal (a signal output from a known wave source) be s i , the arrival angle be θ i , the ideal mode vector be a(θ i ), the mutual coupling matrix representing the mutual coupling between each element be C, the diagonal matrix representing the amplitude-phase error of each element be Γ, the received signal vector be r i , and the noise vector be n i .

[0102] Also, similar to the conventional virtual array calibration method described above, virtual elements that do not actually exist are added to the actual elements of the receiving antenna, and the total number of elements, which is the sum of the actual elements and the virtual elements, is set as N'. Assuming that the mutual coupling between each element occurs in the actual elements and virtual elements of the receiving antenna, and the amplitude-phase error of each element is caused by the feeding line and the receiver after the receiving antenna, the calibration model is represented by the following equation (16).

[0103] [Number]

[0104] In equation (16), r i is an N-dimensional vector corresponding to the actual elements, Γ is an N×N square matrix corresponding to the actual elements, C is an N-row N'-column matrix corresponding to the actual elements and the virtual elements, a(θ i ) is an N'-dimensional vector corresponding to the actual elements and the virtual elements, and n i is represented by an N-dimensional vector corresponding to the actual elements.

[0105] Figure 4 shows the dimensions of each variable of the calibration model shown in equation (16). Thus, in equation (16), the calibration matrix C0 in the conventional virtual array calibration method shown in equation (8) is represented by the product of the amplitude-phase error matrix Γ having the amplitude-phase errors of the actual elements as diagonal elements and the mutual coupling matrix C composed of the mutual coupling between the actual elements and the mutual coupling between the virtual elements and the actual elements.

[0106] Note that in Figure 4, the order of the columns of the mutual coupling matrix C and the order of the elements of a(θ i ) arrange the virtual elements on both sides of the actual elements. However, the virtual elements may be arranged together on one side or arranged between the actual elements. Regardless of whether the actual virtual elements are arranged on both sides of the actual elements, they can be arranged arbitrarily.

[0107] In this embodiment, as shown in Figure 5, an example will be described in which one virtual element is added to each side of a 4-element equally spaced linear array.

[0108] In Equation (16), the ideal mode vector a(θ i ) including virtual elements is represented by the following Equation (17).

[0109]

Number

[0110] In Equation (17), T represents transpose, the subscript k = 1, ···, 4 of a i,k corresponds to the physical elements, and the subscript k = 5, 6 of a i,k corresponds to the virtual elements. That is, the second to fifth elements of a(θ i ) represent the ideal mode vectors of the physical elements, and the first and sixth elements represent the ideal mode vectors of the virtual elements. And the second to fifth columns of the mutual coupling matrix C represent the mutual coupling between the physical elements, and the first and sixth columns represent the mutual coupling between the virtual elements and the physical elements. Each element a i of the ideal mode vector a(θ i,k ) is represented by the following Equation (18).

[0111]

Number

[0112] In Equation (18), λ represents the wavelength, and x k represents the position of each element. Note that the ideal mode vectors in Equations (17) to (18) are shown for the case where the transmitting antenna 11 is arranged sufficiently far from the maximum element spacing of the receiving antennas 2a to 2d such that a plane wave arrives at the receiving antennas 2a to 2d. However, if the transmitting antenna 11 is not arranged sufficiently far from the maximum element spacing of the receiving antennas 2a to 2d, it is necessary to change the ideal mode vector according to the distance between the receiving antennas 2a to 2d and the transmitting antenna 11. In Equation (16), Γ is represented by a diagonal matrix consisting of the amplitude-phase errors of the physical elements. The amplitude-phase error matrix Γ of the physical elements is represented by the following Equation (19).

[0113]

Number

[0114] In Equation (19), γ k represents the amplitude-phase error of each element. α k is taken as the amplitude error of each element, and φ k is taken as the phase error of each element. Then, the amplitude-phase error of each element is expressed by the following Equation (20).

[0115]

Number

[0116] In this embodiment, the actual elements of the receiving antenna are arranged symmetrically, and the degree of freedom of the mutual coupling between the actual elements is restricted based on the symmetry of the arrangement of the actual elements. Since the mutual coupling between the actual elements is generally represented by an N×N matrix, when the degree of freedom is not restricted as in the conventional virtual array calibration method described above, there are N 2 variables. However, when the arrangement of the actual elements of the receiving antenna has symmetry, the degree of freedom can be restricted to reduce the number of variables.

[0117] For example, when the degree of freedom is restricted based on the symmetry of the actual elements of the 4-element equally spaced linear array (x2 - x1 = x3 - x2 = x4 - x3) shown in FIG. 5, the mutual coupling matrix C1 between the actual elements is reduced to 6 variables as expressed by the following Equation (21).

[0118]

Number

[0119] Note that even in the case of a 4-element linear array with a left-right symmetric arrangement (x2 - x1 = x4 - x3 ≠ x3 - x2) instead of the 4-element equally spaced linear array shown in FIG. 5, the mutual coupling matrix C1 between the actual elements is expressed by Equation (21).

[0120] When the degrees of freedom are restricted based on the symmetry of the actual elements of the 4-element equally-spaced circular array, the mutual coupling matrix C1 between the actual elements is reduced to 3 variables, as expressed by the following equation (22).

[0121]

Number

[0122] The mutual coupling matrix C applied to the 4-element equally-spaced linear array or the 4-element linear array with left-right symmetry shown in FIG. 5 will be described below. The mutual coupling matrix C is obtained by adding a column representing the mutual coupling between the virtual element and the actual elements to the mutual coupling matrix C1 between the actual elements expressed by equation (21).

[0123] <The first mutual coupling matrix C> The first mutual coupling matrix C is asymmetric with respect to the mutual coupling between the virtual element and the actual elements. That is, the first and sixth columns of the mutual coupling matrix C are the asymmetric coefficients. The virtual element may have a non-symmetric arrangement (x1 - x6 ≠ x5 - x4) or a symmetric arrangement (x1 - x6 = x5 - x4). The first mutual coupling matrix C is expressed by the following equation (23).

[0124]

Number

[0125] <The second mutual coupling matrix C> The second mutual coupling matrix C sets a part of the mutual coupling between the virtual element and the actual elements to zero with respect to the first mutual coupling matrix C. The virtual element may have a non-symmetric arrangement (x1 - x6 ≠ x5 - x4) or a symmetric arrangement (x1 - x6 = x5 - x4), similar to the first mutual coupling matrix C.

[0126] In equation (23), from coefficient c6 to coefficient c 13Although any coefficient among them can be set to zero, coefficients with a long distance between the virtual element and the physical element are sufficiently small. Therefore, it is desirable to set to zero, as much as possible, the coefficients with a long distance between the virtual element and the physical element. That is, in Equation (23), since coefficients with larger subscript numerical values are coefficients with a long distance between the virtual element and the physical element, it is desirable to set the coefficients to zero in descending order of the subscript numerical values.

[0127] For example, since the mutual coupling between a virtual element and a physical element separated by two or more elements is considered to be sufficiently small, the mutual coupling matrix C limited to the mutual coupling between the virtual element and the adjacent physical element (that is, limited to the coefficient with the shortest distance between the virtual element and the physical element) is represented by the following Equation (24).

[0128]

Number

[0129] For Equation (23), in Equation (24), coefficients up to c7 are used, but coefficients up to c9 may be used, or coefficients up to c 11 may be used. That is, in the second mutual coupling matrix C, it is possible to select the number of unknown variables according to the number of calibration data sets.

[0130] <The Third Mutual Coupling Matrix C> The third mutual coupling matrix C assumes symmetry in the arrangement also for the mutual coupling between the virtual element and the physical element, and sets the first column and the sixth column of the mutual coupling matrix C as symmetric coefficients. In the third mutual coupling matrix C, the virtual element needs to have a symmetric arrangement (x1 - x6 = x5 - x4). The distance (x1 - x6) between the virtual element and the physical element may be equal to or different from the distance between the physical elements (x2 - x1, x3 - x2). The third mutual coupling matrix C is represented by the following Equation (25). Thus, the third mutual coupling matrix C has fewer unknown variables than the first mutual coupling matrix C.

[0131]

Number

[0132] <Fourth mutual coupling matrix C> The fourth mutual coupling matrix C sets part of the mutual coupling between the virtual element and the physical element to zero with respect to the third mutual coupling matrix C. In the fourth mutual coupling matrix C, the virtual element needs to have a symmetric arrangement (x1 - x6 = x5 - x4) similar to the third mutual coupling matrix C. The distance (x1 - x6) between the virtual element and the physical element may be equal to or different from the distance (x2 - x1, x3 - x2) between the physical elements.

[0133] In Equation (25), any coefficient among coefficients c6 to c9 can be set to zero. However, since the coefficient with a long distance between the virtual element and the physical element is sufficiently small, it is desirable to set to zero the coefficient with a long distance between the virtual element and the physical element as much as possible. That is, in Equation (25), since the coefficient with a large subscript value is the coefficient with a long distance between the virtual element and the physical element, it is desirable to set the coefficients to zero in descending order of the subscript values.

[0134] For example, since the mutual coupling between the virtual element and the physical element separated by two or more elements is considered to be sufficiently small, the mutual coupling matrix C limited to the mutual coupling between the virtual element and the adjacent physical element (that is, limited to the coefficient with the shortest distance between the virtual element and the physical element) is represented by the following Equation (26). Thus, the fourth mutual coupling matrix C has fewer unknown variables than the second mutual coupling matrix C.

[0135]

Equation

[0136] For Equation (25), Equation (26) uses up to coefficient c6, but it may also use up to coefficient c7 or up to coefficient c8. That is, in the fourth mutual coupling matrix C, it is possible to select the number of unknown variables according to the number of calibration data sets.

[0137] Known arrival angle θ iThe received signal vector r when receiving the signal output from the wave source i serves as the calibration data set, and by changing the arrival angle θ i and repeating the reception M times, M sets of calibration data sets can be obtained, and the mutual coupling matrix C and the amplitude-phase error matrix Γ can be calculated from the M sets of calibration data sets.

[0138] The received signal r i has a covariance matrix R i Let R i have the j-th eigenvalue λ j (i) and the j-th eigenvector e j (i) , λ1 (i) ≥ λ2 (i) ≥ ··· ≥ λ N (i) Let it be so. When the calibration signal is a single wave, the calibrated mode vector ΓCa(θ i ) is proportional to the signal subspace e1 (i) and is orthogonal to the noise subspace {e2 (i) , ···, e N (i)}.

[0139] Regarding the first mutual coupling matrix C shown in Equation (23), using the property that the calibrated mode vector ΓCa(θ i ) is orthogonal to the noise subspace, the following Equation (27) holds.

[0140]

Equation

[0141] In Equation (27), * represents the complex conjugate, and H represents the complex conjugate transpose. The unknown variables in Equation (27) are {c0, ···, c 13, γ1, ···, γ4}, and when the mutual coupling coefficient and the amplitude-phase error are normalized so that c0 = 1 and γ1 = 1, the number of unknown variables to be solved becomes 16. Since M sets of calibration data sets yield M(N - 1) equations of (27), the number of calibration data sets required to solve 16 unknown variables is M ≥ 6.

[0142] Regarding the second mutual coupling matrix C shown in Equation (24), using the property that the calibrated mode vector ΓCa(θ i ) is orthogonal to the noise subspace, the following Equation (28) holds.

[0143]

Equation

[0144] The unknown variables in Equation (28) are {c0, ···, c7, γ1, ···, γ4}, and when the mutual coupling coefficient and the amplitude-phase error are normalized so that c0 = 1 and γ1 = 1, the number of unknown variables to be solved becomes 10. Since M sets of calibration data sets yield M(N - 1) equations of (28), the number of calibration data sets required to solve 10 unknown variables is M ≥ 4.

[0145] Regarding the third mutual coupling matrix C shown in Equation (25), using the property that the calibrated mode vector ΓCa(θ i ) is orthogonal to the noise subspace, the following Equation (29) holds.

[0146]

Equation

[0147] The unknown variables in Equation (29) are {c0, ···, c9, γ1, ···, γ4}, and when the mutual coupling coefficient and the amplitude-phase error are normalized so that c0 = 1 and γ1 = 1, the number of unknown variables to be solved becomes 12. Since M sets of calibration data sets yield M(N - 1) equations of (29), the number of calibration data sets required to solve 12 unknown variables is M ≥ 4.

[0148] Regarding the fourth mutual coupling matrix C shown in Equation (26), using the property that the calibrated mode vector ΓCa(θ i ) is orthogonal to the noise subspace, the following Equation (30) holds.

[0149]

Equation

[0150] The unknown variables in Equation (30) are {c0,···,c6,γ1,···,γ4}. When normalizing the mutual coupling coefficients and amplitude-phase errors such that c0 = 1 and γ1 = 1, the number of unknown variables to be solved becomes 9. Since M(N - 1) equations of Equation (29) are obtained from M sets of calibration data sets, the number of calibration data sets required to solve 9 unknown variables is M ≧ 3.

[0151] As described above, the array calibration method described in Non-Patent Document 1 and Non-Patent Document 2 (hereinafter simply referred to as "calibration method A") and the virtual array calibration method described in Non-Patent Document 3 (hereinafter simply referred to as "calibration method B") have significantly different numbers of unknown variables.

[0152] In contrast, the number of unknown variables of the antenna array calibration method in the present embodiment falls between the number of unknown variables of calibration method A and the number of unknown variables of calibration method B.

[0153] Furthermore, in addition to being able to selectively apply the first to fourth mutual coupling matrices C with different numbers of unknown variables, the antenna array calibration method in the present embodiment can change the number of unknown variables in the second mutual coupling matrix C or the fourth mutual coupling matrix C. Therefore, calibration can be performed with various numbers of unknown variables, and an appropriate number of unknown variables can be selected according to the number of calibration data sets.

[0154] Since equations (27) to (30) are products of unknown variables and thus difficult to solve directly, the mutual coupling matrix C and the amplitude-phase error matrix Γ are obtained by an iterative method. First, as shown in equation (31), a mutual coupling matrix C is formed where the mutual coupling between physical elements constitutes the identity matrix and the mutual coupling between virtual elements and physical elements is zero. init This is used as the initial value of the mutual coupling matrix C.

[0155]

Number

[0156] When re-calibration is performed with substantially the same antenna arrangement, instead of the initial value of the mutual coupling matrix C shown in equation (31), the previous mutual coupling matrix C may be used as the initial value.

[0157] After setting the initial value of the mutual coupling matrix C, the mutual coupling and amplitude-phase error calculation unit 32 obtains C and Γ by an iterative method that repeatedly performs the first step and the second step described below to approximate C and Γ to the solution.

[0158] In the first step, by assuming C is known, the product of the unknown variables in equations (27) to (30) is eliminated, and Γ is obtained from the linearized equations (27) to (30). In the second step, by assuming Γ is known, the product of the unknown variables in equations (27) to (30) is eliminated, and C is obtained from the linearized equations (27) to (30). By this iterative method, C and Γ can be obtained without increasing the number of unknown variables, so the number of calibration data sets can be reduced.

[0159] Since the mutual coupling matrix C mainly depends on the geometric structure of the array antenna, its temperature dependence is relatively small. However, the amplitude-phase error matrix Γ changes according to the temperature characteristics of the feed line and the receiver. Therefore, it is efficient to re-calibrate only the amplitude-phase error matrix Γ when the temperature changes.

[0160] In the antenna array calibration method according to this embodiment, since the mutual coupling matrix C and the amplitude-phase error matrix Γ are independent, the amplitude-phase error matrix Γ can be obtained by fixing the mutual coupling matrix C. In this case, the number of unknown variables is a small number of N - 1, and the amplitude-phase error matrix Γ can be recalibrated with a small number of M ≥ 1 sets of calibration data sets.

[0161] Conversely, in the antenna array calibration method according to this embodiment, the mutual coupling matrix C can be obtained by fixing the amplitude-phase error matrix Γ. As a result, in the antenna array calibration method according to this embodiment, when the antenna arrangement is changed in a state where the temperature change is small, only the mutual coupling matrix C can be recalibrated.

[0162] The direction-of-arrival estimation method by the direction-of-arrival estimation device 50 will be described below.

[0163] In the direction-of-arrival estimation method, first, similar to the antenna array calibration method, eigenvalue analysis of the covariance matrix calculated by the covariance matrix calculation unit 30 is performed by the eigenvalue analysis unit 31.

[0164] Let the covariance matrix of the received signal r be R, and the j-th eigenvalue of R be λ j , and the j-th eigenvector be e j , λ1 ≥ λ2 ≥ ··· ≥ λ N . When there is one incident wave source, the eigenvector of noise is represented as {e2, ···, e N}}. Let the matrix composed of the eigenvectors of noise be E N .

[0165] The mode vector calculation unit 52 calculates the calibrated mode vector a~(θ) = ΓCa(θ) using the amplitude-phase error matrix Γ and the mutual coupling matrix C stored in the memory 5, and the MUSIC calculation unit 53 calculates the calibrated MUSIC spectrum P MUSIC (θ) according to the following mathematical formula (32). a~ indicates a variable with a ~ above a in the mathematical formula.

[0166]

Equation

[0167] The MUSIC calculation unit 53 obtains, as the estimated arrival direction after calibration, the arrival angle θ at which the calibrated MUSIC spectrum P MUSIC (θ) becomes maximum.

[0168] As described above, in the present embodiment, by restricting the degree of freedom of mutual coupling between actual elements based on the symmetry of the arrangement of actual elements, the number of mutual coupling coefficients that are unknown variables during calibration is reduced, and the mutual coupling matrix C and the amplitude-phase error matrix Γ are obtained by an iterative method, so that the number of calibration data sets can be reduced.

[0169] Then, in the present embodiment, by adding virtual elements and adding the mutual coupling between the virtual elements and the actual elements to the mutual coupling matrix C, the calibration accuracy can be improved. Therefore, the present embodiment can realize an appropriate calibration accuracy with an appropriate number of calibration data sets.

[0170] Further, in the present embodiment, by setting a part of the mutual coupling between the virtual elements and the actual elements to zero, the number of mutual coupling coefficients that are unknown variables during calibration can be changed, so that the number of calibration data sets can be changed.

[0171] Also, in the present embodiment, by setting to zero the mutual coupling between the virtual elements and the actual elements other than the one with the shortest distance between the virtual elements and the actual elements, the number of mutual coupling coefficients that are unknown variables during calibration is reduced, so that the number of calibration data sets can be reduced.

[0172] In addition, in the present embodiment, the virtual elements are arranged symmetrically, and based on the symmetry of the arrangement of the virtual elements and the actual elements, by restricting the degree of freedom of the mutual coupling between the virtual elements and the actual elements, the number of mutual coupling coefficients that are unknown variables during calibration can be reduced compared to the case where the symmetry of the virtual elements is not assumed, so that the number of calibration data sets can be reduced.

[0173] In addition, in the present embodiment, the virtual elements are arranged symmetrically, and based on the symmetry of the arrangement of the virtual elements and the actual elements, the degree of freedom of the mutual coupling between the virtual elements and the actual elements is restricted, and by setting a part of the mutual coupling between the virtual elements and the actual elements to zero, the number of mutual coupling coefficients that are unknown variables during calibration can be changed, so that the number of calibration data sets can be changed.

[0174] In addition, in the present embodiment, the virtual elements are arranged symmetrically, and based on the symmetry of the arrangement of the virtual elements and the actual elements, the degree of freedom of the mutual coupling between the virtual elements and the actual elements is restricted, and among the mutual couplings between the virtual elements and the actual elements, by setting the mutual couplings other than those with the shortest distance between the virtual elements and the actual elements to zero, the number of mutual coupling coefficients that are unknown variables during calibration can be reduced, so that the number of calibration data sets can be reduced.

[0175] Hereinafter, the operation and effect of the present embodiment described above will be specifically described with reference to the drawings.

[0176] As shown in FIG. 6, in a graph with the number of unknown variables during calibration on the horizontal axis and the calibration accuracy on the vertical axis, in addition to being able to selectively apply the first to fourth mutual coupling matrices C with different numbers of unknown variables, in the second or fourth mutual coupling matrix C, the number of unknown variables can be changed, so it corresponds to an intermediate region shown as calibration method C between calibration method A and calibration method B.

[0177] More specifically, as shown in FIG. 7, in calibration method A, the coefficients constituting the mutual coupling matrix are up to c5, the number of unknown variables during calibration is 8, and the minimum value of the number M of calibration data sets is 3. Also, in calibration method B, there is no limitation on the coefficients constituting the mutual coupling matrix, the number of unknown variables during calibration is 23, and the minimum value of the number M of calibration data sets is 8.

[0178] In contrast, in the present embodiment shown by calibration method C, when the first mutual coupling matrix C is applied, the coefficients constituting the mutual coupling matrix are up to c 13 and the number of unknown variables during calibration is 16, and the minimum value of the number M of calibration data sets is 6.

[0179] Also, in the present embodiment shown by calibration method C, when the second mutual coupling matrix C is applied and the coefficients constituting the mutual coupling matrix are up to c 11 the number of unknown variables during calibration is 14, and the minimum value of the number M of calibration data sets is 5.

[0180] Also, in the present embodiment shown by calibration method C, when the second mutual coupling matrix C is applied and the coefficients constituting the mutual coupling matrix are up to c9, the number of unknown variables during calibration is 12, and the minimum value of the number M of calibration data sets is 4.

[0181] Also, in the present embodiment shown by calibration method C, when the second mutual coupling matrix C is applied and the coefficients constituting the mutual coupling matrix are up to c7, the number of unknown variables during calibration is 10, and the minimum value of the number M of calibration data sets is 4.

[0182] Also, in the present embodiment shown by calibration method C, when the third mutual coupling matrix C is applied, the coefficients constituting the mutual coupling matrix are up to c9, the number of unknown variables during calibration is 12, and the minimum value of the number M of calibration data sets is 4.

[0183] Further, in the present embodiment represented by calibration method C, when the fourth mutual coupling matrix C is applied and the coefficients constituting the mutual coupling matrix are up to c8, the number of unknown variables during calibration is 11, and the minimum value of the number M of calibration data sets is 4.

[0184] Also, in the present embodiment represented by calibration method C, when the fourth mutual coupling matrix C is applied and the coefficients constituting the mutual coupling matrix are up to c7, the number of unknown variables during calibration is 10, and the minimum value of the number M of calibration data sets is 4.

[0185] Also, in the present embodiment represented by calibration method C, when the fourth mutual coupling matrix C is applied and the coefficients constituting the mutual coupling matrix are up to c6, the number of unknown variables during calibration is 9, and the minimum value of the number M of calibration data sets is 3.

[0186] As described above, the present embodiment can achieve appropriate calibration accuracy with an appropriate number of calibration data sets between calibration method A and calibration method B. Further, the present embodiment can selectively apply the first to fourth mutual coupling matrices C, and by changing the number of unknown variables in the second or fourth mutual coupling matrix C, it can cope with various numbers of calibration data sets and required accuracies.

[0187] Also, in the present embodiment, similar to calibration method A, since the mutual coupling matrix C and the amplitude-phase error matrix Γ can be obtained individually, only the mutual coupling matrix C can be recalibrated, and only the amplitude-phase error matrix Γ can be recalibrated.

[0188] Although the embodiments of the present invention have been disclosed above, it is obvious that those skilled in the art can make changes without departing from the scope of the present invention. It is intended that all such modifications and equivalents be included in the claims described in the claims.

Description of Reference Numerals

[0189] 1 Antenna array calibration device 2 Array antenna 2a - 2d Receiving Antenna 3 Multi - Channel Receiver 4 Array Calibration Processing Unit 5 Memory 10, 10a Transmitter 11, 11a Transmitting Antenna 20a - 20d Frequency Converter 21a - 21d ADC 22 Base Station Signal Generator 23 Clock Signal Generator 30 Covariance Matrix Calculation Unit 31 Eigenvalue Analysis Unit 32 Mutual Coupling and Amplitude - Phase Error Calculation Unit 50 Direction - of - Arrival Estimation Device 51 Direction - of - Arrival Estimation Processing Unit 52 Mode Vector Calculation Unit 53 MUSIC Calculation Unit

Claims

1. Repeatedly calculate the eigenvectors of the covariance matrix of the received signal received by the array antenna (2) from a wave source with a known arrival direction a predetermined number of times while changing the arrival direction, In an antenna array calibration method for obtaining a calibration matrix including mutual coupling between actual elements constituting the array antenna, mutual coupling between virtual elements that do not actually exist and the actual elements, and amplitude-phase errors of the actual elements from the eigenvectors, The actual elements are arranged symmetrically, The calibration matrix is represented by the product of an amplitude-phase error matrix having the amplitude-phase errors of the actual elements as diagonal elements and a mutual coupling matrix composed of mutual coupling between the actual elements and mutual coupling between the virtual elements and the actual elements, The mutual coupling matrix has its degree of freedom of mutual coupling between the actual elements restricted based on the symmetry of the arrangement of the actual elements, Instead of obtaining the calibration matrix, the mutual coupling matrix and the amplitude-phase error matrix are obtained by an iterative method, An antenna array calibration method characterized by this.

2. The number of actual elements is N, the number of virtual elements is N' which is the number of elements obtained by adding the number of virtual elements to N, and the predetermined number of times is less than (NN' - 1) / (N - 1). The antenna array calibration method according to Claim 1.

3. The mutual coupling matrix has a part of the mutual coupling between the virtual elements and the actual elements being zero. The antenna array calibration method according to Claim 1 or Claim 2.

4. Among the mutual couplings between the virtual elements and the actual elements, the mutual coupling matrix has mutual couplings other than those with the shortest element-to-element distance between the virtual elements and the actual elements being zero. The antenna array calibration method according to Claim 1 or Claim 2.

5. The virtual elements are arranged symmetrically, Based on the symmetry of the arrangement of the virtual elements and the actual elements, the mutual coupling matrix has its degree of freedom of mutual coupling between the virtual elements and the actual elements restricted. The antenna array calibration method according to Claim 1 or Claim 2.

6. The virtual elements are arranged symmetrically, Based on the symmetry of the arrangement of the virtual elements and the actual elements, the mutual coupling matrix has its degree of freedom of mutual coupling between the virtual elements and the actual elements restricted, and a part of the mutual coupling between the virtual elements and the actual elements is zero. The antenna array calibration method according to Claim 1 or Claim 2.

7. The virtual elements are arranged symmetrically, Based on the symmetry of the arrangement of the virtual elements and the real elements, the degree of freedom of mutual coupling between the virtual elements and the real elements is restricted in the mutual coupling matrix, and among the mutual couplings between the virtual elements and the real elements, mutual couplings other than those with the shortest element-to-element distance between the virtual elements and the real elements are zero. The antenna array calibration method according to claim 1 or claim 2.

8. An array antenna (2) that receives a signal transmitted from a wave source with a known direction of arrival, An eigenvalue analysis unit (31) that repeatedly calculates the eigenvectors of the covariance matrix of the received signal received by the array antenna a predetermined number of times while changing the direction of arrival, A calibration matrix calculation unit that calculates a calibration matrix including the mutual coupling between the real elements constituting the array antenna, the mutual coupling between the non-existent virtual elements and the real elements, and the amplitude-phase error of the real elements from the eigenvectors calculated by the eigenvalue analysis unit, In an antenna array calibration apparatus having: The real elements are arranged symmetrically, The calibration matrix is represented by the product of an amplitude-phase error matrix having the amplitude-phase error of the real elements as diagonal elements and a mutual coupling matrix composed of the mutual coupling between the real elements and the mutual coupling between the virtual elements and the real elements, Based on the symmetry of the arrangement of the real elements, the degree of freedom of mutual coupling between the real elements is restricted in the mutual coupling matrix, The calibration matrix calculation unit is a mutual coupling / amplitude-phase error calculation unit (32) that obtains the mutual coupling matrix and the amplitude-phase error matrix from the eigenvectors calculated by the eigenvalue analysis unit by an iterative method, Antenna array calibration apparatus.

Images