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 and virtual 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 element 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 virtual elements and real elements is limited on the basis of the arrangement symmetry of the virtual elements and real elements. 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 apparatus for calibrating mutual coupling between elements of an array antenna and amplitude and phase errors of each element using a wave source with a known direction of arrival. [Background technology]

[0002] Using an array antenna makes it possible to estimate the direction of arrival of radio waves, and the MUSIC method is known as a high-resolution method for estimating direction of arrival. The conventional MUSIC method assumes that each antenna can ideally and independently receive the incoming waves, but in actual array antennas, the following error factors exist, which prevent the theoretical results from being obtained and hinder accurate direction of arrival estimation.

[0003] The first error source is mutual coupling between antenna elements. When an antenna receives an incoming wave, a current is excited in the element, causing re-radiation, which is then received by another antenna, resulting in mutual coupling between the elements.

[0004] The second error factor is the amplitude and phase error of each element. Even if antenna elements, feed lines, and receivers with identical specifications are arrayed, there will be nonuniformity in the actual device, which will result in errors between elements in the amplitude and phase characteristics.

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

[0006] Obtaining a calibration data set using the array antenna and receiver used for direction-of-arrival estimation is considered to be practically beneficial because it allows calibration including the receiver's amplitude and phase errors and makes it easier to achieve high calibration accuracy.

[0007] As shown in Figure 1, array antennas often use symmetrical antenna arrangements, such as a uniform linear array in which receiving antennas are arranged at equal intervals in a straight line, or a uniform circular array in which receiving antennas are arranged at equal intervals in a circle.

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

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

[0010]

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

[0012]

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

[0014]

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[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 antenna elements are arranged in a straight line, the position of each element is expressed as x k ,(k=1,...,N), the ideal mode vector a(θ i ) is expressed by the following equation (4).

[0016]

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[0017] In equation (4), T represents the transpose, and λ represents the wavelength. The mutual coupling matrix C1 is an N × N square matrix, but if the antenna arrangement is symmetric, such as in a uniformly spaced linear array or a uniformly spaced circular array, the degrees of freedom for mutual coupling between elements can be limited.

[0018] For example, the mutual coupling matrix C1 of a four-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 a mutual coupling coefficient.

[0019]

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[0020] Non-Patent Document 2 describes the mutual coupling matrix of a uniformly spaced circular array, and the mutual coupling matrix C1 between elements of a four-element uniformly spaced circular array is shown in equation (6).

[0021]

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[0022] Known angle of arrival θ i The received signal vector r when receiving the signal output from the wave source i is the calibration data set, and the arrival angle θ iBy repeating reception M times while changing the parameter, M sets of calibration data sets can be acquired, 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 The covariance matrix of i Let R i Let the j-th eigenvalue of λ j (i) , the jth eigenvector is e j (i) ,λ1 (i) ≧λ2 (i) ≧ ≧ λ N (i) When the calibration signal is one wave, the calibrated mode vector ΓC1a(θ i ) is the signal subspace e1 (i) is proportional to the noise subspace {e2 (i) ,···,e N (i)} is orthogonal to

[0024] For the mutual coupling matrix C1 of the four-element equally spaced linear array shown in equation (5), the calibrated mode vector ΓC1a(θ i ) is orthogonal to the noise subspace, the following equation (7) holds:

[0025]

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[0026] In equation (7), * represents the complex conjugate, H represents complex conjugate transpose. The unknown variables in equation (7) are {c0, ,c5,γ1, ,γ4}, and if the mutual coupling coefficient and amplitude / phase error are normalized to c0 = 1 and γ1 = 1, the number of unknown variables to be solved becomes eight.

[0027] Since M(N-1) equations (7) are obtained from M sets of calibration data sets, the number M of calibration data sets required to solve for eight unknown variables is M≧3, since M(N-1)≧8. Since equation (7) is a product of unknown variables and is therefore difficult to solve directly, Non-Patent Document 2 describes a method of finding the mutual coupling matrix C1 and the amplitude-phase error matrix Γ by an iterative solution method.

[0028] In the iterative solution method described in Non-Patent Document 2, first, the initial value of the mutual coupling matrix C1 is set to an identity matrix. In Step 1, by assuming that C1 is known, the product of unknown variables in Equation (7) is resolved, and Γ is found using the linearized Equation (7). In Step 2, by assuming that Γ is known, the product of unknown variables in Equation (7) is resolved, and C1 is found using the linearized Equation (7). Steps 1 and 2 are repeated to find C1 and Γ.

[0029] Non-Patent Document 3 describes a virtual array calibration method that improves calibration accuracy by adding non-existent virtual elements in addition to the real elements of the receiving antenna.

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

[0031]

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[0032] In equation (8), the ideal mode vector a(θ i) is expressed as an N'-dimensional vector that includes both real and virtual elements. In the case of a linear array in which real and virtual elements are arranged on a line, the positions of the real and virtual elements are expressed as x k , (k=1,···,N′), the ideal mode vector is expressed by the following equation (9).

[0033]

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[0034] The calibration matrix C0 is expressed as a matrix of N rows and N' columns, in which columns for virtual elements are added to a matrix for NxN real elements, as expressed by the following equation (10).

[0035]

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[0036] In equation (10), the calibration matrix C0 is a matrix in which all elements are independent, and includes mutual coupling between real elements, mutual coupling between virtual elements and real elements, and amplitude and phase errors of real elements.

[0037] The received signal vector r in Eq. (8) i and noise vector n i is an N-dimensional vector of only real elements. Known angle of arrival θ i The received signal vector r when receiving the signal output from the wave source i is the calibration data set, and the arrival angle θ i By repeating reception M times while changing the matrix C0, M sets of calibration data sets can be acquired, and the calibration matrix C0 is calculated from the M sets of calibration data sets.

[0038] Received signal r i The covariance matrix of i Let R i Let the j-th eigenvalue of λ j (i) , the jth eigenvector is e j (i),λ1 (i) ≧λ2 (i) ≧ ≧ λ N (i) When the calibration signal is one wave, the calibrated mode vector C0a(θ i ) is the signal subspace e1 (i) is proportional to the noise subspace {e2 (i) ,···,e N (i)} is orthogonal to

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

[0040]

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[0041] Each element c of the calibration matrix C0 11 ,c 12 ,···,c NN′ If the vertical vector of these is c0 in bold, the following equation (12) holds.

[0042]

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[0043] Equation (12) is the eigenvector e2 (i) ,e3 (i) ,···,e N (i) The matrix of these is E N (i) This can be transformed into the following equation (13).

[0044]

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

[0046]

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[0047] In equation (14), the calibration matrix C0 is normalized to any element of c0 in bold, for example, c 11 If we set is 1, the remaining elements of c0 in bold can be found using the generalized inverse matrix. Since c0 in bold is an N-dimensional vector, there are N-1 unknown variables.

[0048] E N (i)H Since is a matrix with N-1 rows, equation (14) becomes M(N-1) equations. Therefore, to find N'-1 unknown variables, M≧(N'-1) / (N-1) calibration data sets are required. For example, when N=4 and N'=6, there are 23 unknown variables, and the number of calibration data sets is M≧8.

[0049] As described above, the virtual array calibration method described in Non-Patent Document 3 is a method for increasing the degrees of freedom of the calibration matrix to improve calibration accuracy, but 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 using the MUSIC method with an array antenna, the calibrated mode vector a~(θ) is calculated using a~(θ) = ΓC1a(θ) in the case of a calibration method based on the symmetry of the antenna arrangement, or a~(θ) = C0a(θ) in the case of a virtual array calibration method, and the matrix E consisting of the eigenvectors of the noise is calculated. N Using the calibrated MUSIC spectrum P MUSIC (θ) can be calculated using the following formula (15): a~ indicates a variable with ~ above it in the formula.

[0051]

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[0052] In equation (15), the calibrated MUSIC spectrum P MUSIC By finding the arrival angle θ at which (θ) is maximized, a calibrated direction of arrival estimation can be performed. [Prior art documents] [Non-patent literature]

[0053] [Non-Patent Document 1] Kenjiro Chiba, Hiroyoshi Yamada, Yoshio Yamaguchi, "Experimental Verification of Antenna Array Calibration Using Known Wave Sources", IEICE Technical Report, AP2002-41, pp.7-12, July 2002 [Non-patent document 2] Rokuzo Hara, Hiroyoshi Yamada, Yoshio Yamaguchi, "An Iterative Array Calibration Method Reducing the Number of Calibration Datasets", Transactions of the Institute of Electronics, Information and Communications Technology (B), vol. J86-B, no. 9, pp. 1906-1913, September 2003 [Non-patent document 3] Takashi Naito, Hiroyoshi Yamada, Yoshio Yamaguchi, "Array Calibration Method Using Virtual Elements for DOA Estimation", Transactions of the Institute of Electrical and Electronics Engineers (B), vol. J92-B, no. 1, pp. 216-223, Jan. 2009 Summary of the Invention [Problem to be solved by the invention]

[0054] 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, making it possible to perform array calibration with fewer unknown variables, i.e., a smaller calibration data set.

[0055] Furthermore, the array calibration methods described in Non-Patent Documents 1 and 2 can determine the mutual coupling and the amplitude and phase errors separately, making it easy to recalibrate only the amplitude and phase errors or only the mutual coupling.

[0056] However, the array calibration methods described in Non-Patent Document 1 and Non-Patent Document 2 do not have very high calibration accuracy due to the limited degree of freedom in mutual coupling.

[0057] On the other hand, the virtual array calibration method described in Non-Patent Document 3 increases the degree of freedom of the calibration matrix by adding non-existent virtual elements, thereby enabling highly accurate array calibration.

[0058] However, the virtual array calibration method described in Non-Patent Document 3 has a large number of unknown variables, requires a large number of calibration data sets, and is a method for determining a calibration matrix that includes mutual coupling and amplitude / phase errors, making it difficult to recalibrate only the amplitude / phase errors or only the mutual coupling.

[0059] As described above, the conventional calibration methods described above are divided into two types: low-accuracy calibration methods using a small number of unknown variables, and high-accuracy calibration methods using a large number of unknown variables, and have the problem that they are unable to achieve adequate calibration accuracy with an adequate number of calibration data sets.

[0060] The present invention has been made to solve this problem, and an object of the present invention is to provide an antenna array calibration method and an antenna array calibration device that can achieve appropriate calibration accuracy with an appropriate number of calibration data sets. [Means for solving the problem]

[0061] The antenna array calibration method of the present invention includes repeatedly calculating eigenvectors of a covariance matrix of a received signal, the received signal having been transmitted from a wave source with a known direction of arrival, by an array antenna (2) while changing the direction of arrival a predetermined number of times, and determining, from the eigenvectors, a calibration matrix including mutual couplings between real elements constituting the array antenna, mutual couplings between non-existent virtual elements and the real elements, and amplitude and phase errors of the real elements, wherein the real elements and the virtual elements are arranged symmetrically, and the calibration matrix is ​​expressed by the product of an amplitude and phase error matrix having the amplitude and phase errors of the real elements as diagonal elements and a mutual coupling matrix including the mutual couplings between the real elements and the mutual couplings between the virtual elements and the real elements, and the degree of freedom of the mutual coupling matrix is ​​not restricted for the mutual couplings between the real elements, but the degree of freedom of the mutual couplings between the virtual elements and the real elements is restricted based on the symmetry of the arrangement of the virtual elements and the real elements, From the eigenvectors, The mutual coupling matrix and the amplitude-phase error matrix are determined by an iterative solution method.

[0062] As described above, the antenna array calibration method of the present invention limits the degree of freedom of mutual coupling between virtual elements and real elements based on the symmetry of the arrangement of the virtual elements and real elements, thereby reducing the number of mutual coupling coefficients that serve as unknown variables during calibration, and also reduces the number of calibration data sets by determining the mutual coupling matrix and the amplitude-phase error matrix by an iterative method.

[0063] Furthermore, the antenna array calibration method of the present invention can improve calibration accuracy by adding virtual elements and adding the mutual coupling between the virtual elements and real elements to the mutual coupling matrix. Therefore, the antenna array calibration method of the present invention can achieve 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 real elements may be N, the number of virtual elements added to N may be N', and the predetermined number of times may be smaller than (NN'-1) / (N-1).

[0065] In this way, 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] In the antenna array calibration method of the present invention, the mutual coupling matrix may be such that some of the mutual couplings between the virtual elements and the real elements are zero.

[0067] In this way, the antenna array calibration method of the present invention can change the number of mutual coupling coefficients, which are unknown variables during calibration, by setting some of the mutual couplings between virtual elements and real elements to zero, and therefore can change the number of calibration data sets.

[0068] In the antenna array calibration method of the present invention, the mutual coupling matrix may set mutual couplings between the virtual elements and the real elements to zero except for the mutual coupling between the virtual element and the real element with the shortest inter-element distance.

[0069] In this way, the antenna array calibration method of the present invention sets to zero all mutual couplings between virtual elements and real elements except for those between virtual elements and real elements with the shortest inter-element distance, thereby reducing the number of mutual coupling coefficients that become unknown variables during calibration and making it possible to reduce the number of calibration data sets.

[0070] In the antenna array calibration method of the present invention, the real elements may be arranged without symmetry, and the mutual coupling matrix may be such that, among the mutual couplings between the virtual elements and the real elements, mutual couplings between the virtual elements and the real elements other than the one with the shortest inter-element distance are zero.

[0071] In this way, the antenna array calibration method of the present invention sets to zero the mutual couplings between virtual elements and real elements other than those between virtual elements and real elements with the shortest inter-element distance, even when the real elements are arranged asymmetrically. This reduces the number of mutual coupling coefficients that become unknown variables during calibration, and therefore makes it possible to reduce the number of calibration data sets.

[0072] The antenna array calibration device of the present invention includes an array antenna (2) that receives signals transmitted from a wave source whose arrival direction is known, an eigenvalue analysis unit (31) that repeatedly calculates eigenvectors of a covariance matrix of received signals received by the array antenna a predetermined number of times while changing the arrival direction, and a calibration matrix calculation unit that calculates a calibration matrix including mutual couplings between real elements that constitute the array antenna, mutual couplings between non-existent virtual elements and the real elements, and amplitude and phase errors of the real elements, from the eigenvectors calculated by the eigenvalue analysis unit, in which the real elements and the virtual elements are arranged symmetrically. The calibration matrix is ​​expressed by the product of an amplitude / phase error matrix having the amplitude / phase errors of the real elements as diagonal elements and a mutual coupling matrix consisting of mutual couplings between the real elements and mutual couplings between the virtual elements and the real elements, and the mutual coupling matrix does not restrict the degree of freedom of mutual coupling between the real elements, but restricts the degree of freedom of mutual coupling between the virtual elements and the real elements based on the symmetry of the arrangement of the virtual elements and the real elements, and the calibration matrix calculation unit is configured to be a mutual coupling / amplitude / phase error calculation unit (32) that finds the mutual coupling matrix and the amplitude / phase error matrix by an iterative solution from the eigenvectors calculated by the eigenvalue analysis unit.

[0073] With this configuration, the antenna array calibration apparatus of the present invention limits the degrees of freedom of mutual coupling between virtual elements and real elements based on the symmetry of the arrangement of the virtual elements and real elements, thereby reducing the number of mutual coupling coefficients that serve as unknown variables during calibration, and also reduces the number of calibration data sets by determining the mutual coupling matrix and the amplitude-phase error matrix by an iterative method.

[0074] Furthermore, the antenna array calibration apparatus of the present invention can improve calibration accuracy by adding virtual elements and adding the mutual coupling between the virtual elements and real elements to the mutual coupling matrix. Therefore, the antenna array calibration apparatus of the present invention can achieve appropriate calibration accuracy with an appropriate number of calibration data sets. [Effects of the Invention]

[0075] The present invention can provide an antenna array calibration method and an antenna array calibration device that can achieve appropriate calibration accuracy with an appropriate number of calibration data sets. [Brief explanation of the drawings]

[0076] [Figure 1] FIG. 1 is a conceptual diagram for explaining the antenna arrangement of an array antenna, where (a) shows the antenna arrangement of an equally spaced linear array, and (b) shows the antenna arrangement of an equally spaced circular array. [Figure 2] FIG. 2 is a block diagram of an antenna array calibration apparatus according to an embodiment of the present invention. [Figure 3] FIG. 3 is a block diagram of an arrival direction estimation device according to an embodiment of the present invention. [Figure 4] FIG. 4 is a conceptual diagram showing the dimensions of each variable of a calibration model according to an embodiment of the present invention. [Figure 5] FIG. 5 is a conceptual diagram showing an example of an antenna arrangement in which one virtual element is added to each side of a four-element linear array. [Figure 6] FIG. 6 is a conceptual diagram showing the effects of the embodiment of the present invention in the form of a graph. [Figure 7] FIG. 7 is a conceptual diagram showing, in a table format, the effects of the embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0077] Hereinafter, embodiments of the present invention will be described with reference to the drawings.

[0078] As shown in FIG. 2, the antenna array calibration device 1 includes an array antenna 2, a multi-channel receiver 3, an array calibration processing unit 4, and a memory 5.

[0079] The array antenna 2 is made up of multiple receiving antennas 2a to 2d. The receiving antennas 2a to 2d may be arranged symmetrically or asymmetrically. Examples of array antennas in which receiving antennas are arranged symmetrically include an equally spaced linear array in which receiving antennas are arranged at equal intervals in a line, and an equally spaced circular array in which receiving antennas are arranged at equal intervals in a circle. Note that while four receiving antennas 2a to 2d are shown in FIG. 2, this does not limit the number of receiving antennas that make up the array antenna 2.

[0080] In the antenna array calibration device 1, the array antenna 2 receives a signal with a known angle of arrival transmitted from a transmitting antenna 11 provided in a transmitter 10. Note that although the transmitting antenna 11 and the receiving antennas 2a to 2d are shown close to each other in Fig. 2, the transmitting antenna 11 is actually placed farther away than the maximum element spacing of the receiving antennas 2a to 2d so that a plane wave arrives at the receiving antennas 2a to 2d.

[0081] 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 (also simply referred to as "RF") signal received by the receiving antennas 2a to 2d into an intermediate frequency (also simply referred to as "IF") signal.

[0082] Each of the ADCs 21a to 21d performs AD conversion on the IF signals converted by each of the frequency converters 20a to 20d to convert them into digital signals.

[0083] Each of the frequency converters 20a to 20d may include a quadrature demodulator that converts an IF signal into an in-phase (also simply referred to as "I") signal and a quadrature (also simply referred to as "Q") signal. Alternatively, each of the frequency converters 20a to 20d may be integrally configured to convert an RF signal directly into an I / Q signal. Instead of converting into an analog I / Q signal in each of the frequency converters 20a to 20d, each of the ADCs 21a to 21d may include a digital down-converter that converts the AD-converted digital IF signal into a digital I / Q signal.

[0084] When analog I / Q signals are AD converted, two AD converters are required per channel (i.e., per receiving antenna). To synchronize the phases between channels, each of the frequency converters 20a to 20d performs frequency conversion using a local oscillator 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.

[0085] In this embodiment, the array calibration processor 4 is configured by a CPU (Central Processing Unit) that executes programs stored in a storage medium such as a ROM (Read Only Memory), a hard disk drive, etc. The array calibration processor 4 has a covariance matrix calculation unit 30, an eigenvalue analysis unit 31, and a mutual coupling and amplitude / phase error calculation unit 32.

[0086] The covariance matrix calculation unit 30 calculates the covariance matrix of the received signal 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 by eigenvalue analysis.

[0087] 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 angle of arrival of the signal transmitted from the transmitter 10 and transmitting antenna 11, which are known wave sources. Instead of changing the angle of arrival by changing the position of the transmitting antenna 11, the relative angle of arrival may be changed by rotating the array antenna 2. The mutual coupling matrix and amplitude / phase error matrix calculated by the mutual coupling and amplitude / phase error calculation unit 32 are stored in memory 5. The mutual coupling coefficient may be stored in memory 5 instead of the mutual coupling matrix, and the amplitude / phase error of each element may be stored in memory 5 instead of the amplitude / phase error matrix.

[0088] An arrival direction estimation apparatus 50 according to an embodiment of the present invention is shown in Fig. 3. Note that, among the components of arrival direction estimation apparatus 50, the same components as those in antenna array calibration apparatus 1 are given the same reference numerals and descriptions thereof will be omitted.

[0089] 3, an 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, the array antenna 2 receives a signal with an unknown arrival angle transmitted from a transmitting antenna 11a provided in a transmitter 10a. The signal transmitted from the transmitter 10a and the transmitting antenna 11a may be a signal different from the signal transmitted from the transmitter 10 and the transmitting antenna 11 in FIG.

[0090] In this way, since the direction of arrival estimation device 50 has the same configuration as the antenna array calibration device 1, not only the array antenna 2 but also the multi-channel receiver 3, calibration is performed including amplitude and phase errors caused by the hardware that makes up the multi-channel receiver 3.

[0091] In this embodiment, the direction-of-arrival estimation processing unit 51 is configured by a CPU that executes a program stored in a storage medium such as a ROM, a hard disk drive, etc. The direction-of-arrival estimation processing unit 51 has a covariance matrix calculation unit 30, an eigenvalue analysis unit 31, a mode vector calculation unit 52, and a MUSIC operation unit 53.

[0092] 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 .

[0093] The MUSIC calculation 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 an estimated arrival direction value.

[0094] The arrival direction estimation value calculated by the MUSIC calculation unit 53 is displayed on an external display device (not shown). Note that the arrival direction estimation processing unit 51 may also display a graph of the MUSIC spectrum on an external display device in addition to the arrival direction estimation value.

[0095] The antenna array calibration method using the antenna array calibration device 1 will be described below.

[0096] In the antenna array calibration method, first, an eigenvalue analysis unit 31 performs an eigenvalue analysis of the covariance matrix calculated by the covariance matrix calculation unit 30 .

[0097] Let N be the number of elements of the receiving antenna, M be the number of calibration data sets, and s be the complex amplitude of the i-th calibration signal (the signal output from a known wave source). i , the angle of arrival is θ i , the ideal mode vector is a(θ i ), the mutual coupling matrix representing the mutual coupling between each element is C, the diagonal matrix representing the amplitude and phase error of each element is Γ, and the received signal vector is r i , the noise vector is n i , let's say.

[0098] As in the conventional virtual array calibration method described above, the total number of elements, which is the sum of the real and virtual elements, is N', and the real elements of the receiving antenna are added to the virtual elements. Assuming that mutual coupling between elements occurs in the real and virtual elements of the receiving antenna, and that amplitude and phase errors of each element occur due to the feed line and receiver downstream of the receiving antenna, the calibration model is expressed by the following equation (16).

[0099]

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[0100] In equation (16), r i is an N-dimensional vector corresponding to the real elements, Γ is an N × N square matrix corresponding to the real elements, C is an N-row N' matrix corresponding to the real elements and virtual elements, a(θ i ) is an N'-dimensional vector corresponding to real and virtual elements, n i is expressed as an N-dimensional vector corresponding to the real elements.

[0101] Figure 4 shows the dimensions of each variable in the calibration model shown in equation (16). In this way, in equation (16), the calibration matrix C0 in the conventional virtual array calibration method shown in equation (8) is expressed as the product of the amplitude and phase error matrix Γ, whose diagonal elements represent the amplitude and phase errors of the real elements, and the mutual coupling matrix C, which consists of the mutual coupling between the real elements and the mutual coupling between the virtual elements and the real elements.

[0102] In FIG. 4, the order of the columns of the mutual coupling matrix C and a(θ i ) the order of elements is such that virtual elements are placed on both sides of real elements, but virtual elements may be placed together on one side, or virtual elements may be placed between real elements, and any arrangement is possible regardless of whether actual virtual elements are placed on both sides of real elements.

[0103] In this embodiment, as shown in FIG. 5, an example will be described in which one virtual element is added to each side of a four-element linear array at an equal distance (x1-x6=x5-x4).

[0104] In equation (16), the ideal mode vector a(θ i ) is expressed by the following equation (17).

[0105]

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[0106] In equation (17), T represents the transposition, and a i,k The subscript k=1,...,4 corresponds to the real elements, and a i,k The subscript k=5,6 corresponds to the virtual element. i The second to fifth elements of the mutual coupling matrix C represent the mutual coupling between real elements, and the first and sixth columns represent the mutual coupling between virtual and real elements. The ideal mode vector a(θ i ) each element a i,k is expressed by the following equation (18).

[0107]

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[0108] In equation (18), λ represents the wavelength, and x k represents the position of each element. Note that, equations (17) and (18) show the ideal mode vector when the transmitting antenna 11 is placed far enough away than the maximum element spacing of the receiving antennas 2a to 2d so that a plane wave arrives at the receiving antennas 2a to 2d. However, if the transmitting antenna 11 is not placed far enough away than the maximum element spacing of the receiving antennas 2a to 2d, the ideal mode vector must be changed according to the distance between the receiving antennas 2a to 2d and the transmitting antenna 11. In equation (16), Γ is expressed as a diagonal matrix consisting of amplitude and phase errors of the actual elements. The amplitude and phase error matrix Γ of the actual elements is expressed by the following equation (19).

[0109]

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[0110] In equation (19), γ k represents the amplitude and phase error of each element. k is the amplitude error of each element, and φ k If is the phase error of each element, the amplitude and phase error of each element is expressed by the following equation (20).

[0111]

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[0112] In this embodiment, the arrangement of the real elements of the receiving antenna is either asymmetric or symmetric, so the mutual coupling matrix C1 between the real elements is expressed as an arbitrary N × N matrix with no restrictions on the degrees of freedom of the coefficients, as expressed by the following equation (21).

[0113]

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[0114] The mutual coupling matrix C applied to this embodiment will be described below. The mutual coupling matrix C is obtained by adding a column representing the mutual coupling between virtual elements and real elements to the mutual coupling matrix C1 between real elements expressed by equation (21). In this embodiment, the virtual elements are arranged symmetrically. Therefore, in the mutual coupling matrix C, the degree of freedom of the mutual coupling between the virtual elements and real elements is limited based on the symmetry of the arrangement of the virtual elements.

[0115] <First mutual coupling matrix C> In the first mutual coupling matrix C, the positional relationship between the virtual elements and the real elements must be symmetrical in order to limit the degree of freedom of mutual coupling between the virtual elements and the real elements, and to satisfy the relationships x2-x6=x5-x3, x3-x6=x5-x2, the real elements must also be arranged symmetrically (x2-x1=x4-x3). In the first mutual coupling matrix C, the coefficients of the first and sixth columns are set symmetrically, as expressed in the following equation (22).

[0116]

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[0117] <Second mutual coupling matrix C> The second mutual coupling matrix C sets a part of the mutual coupling between the virtual elements and the real elements to zero, in contrast to the first mutual coupling matrix C.

[0118] In equation (22), the coefficient c 16 to coefficient c 19 It is possible to set any coefficient to zero, but since the coefficients with long distances between virtual elements and real elements are sufficiently small, it is preferable to set the coefficients with long distances between virtual elements and real elements to zero. That is, in equation (22), the coefficients with larger subscripts are the coefficients with long distances between virtual elements and real elements, so it is preferable to set the coefficients with larger subscripts to zero in descending order.

[0119] For example, since the mutual coupling between a virtual element and a real element that is two elements or more away is considered to be sufficiently small, the mutual coupling matrix C limited to the mutual coupling between the virtual element and the adjacent real element (i.e., limited to the coefficients that provide the shortest distance between the virtual element and the real element) is expressed by the following equation (23).

[0120]

number

[0121] When limited to the mutual coupling between a virtual element and an adjacent real element as in equation (23), the positional relationship between the virtual element and the adjacent real element needs to be symmetrical (x1-x6=x5-x4), so the real elements may be arranged asymmetrically (x2-x1≠x4-x3).

[0122] In equation (23) compared to equation (22), the coefficient c 16 Although it was used up to the coefficient c 17 may be used up to the coefficient c 18 That is, in the second mutual coupling matrix C, the number of unknown variables can be selected according to the number of calibration data sets.

[0123] Coefficient c for equation (22) 17 up to, or coefficient c 18 When using the above, as with the first mutual coupling matrix C, the positional relationship between the virtual elements and the real elements must be symmetrical in order to limit the degree of freedom of the mutual coupling between the virtual elements and the real elements, and in order to satisfy the relationships x2-x6=x5-x3 and x3-x6=x5-x2, the real elements must also be arranged symmetrically (x2-x1=x4-x3).

[0124] When the array antenna 2 is configured as a four-element equally spaced linear array (x2-x1=x3-x2=x4-x3), the real elements are arranged symmetrically, so either the first mutual coupling matrix C or the second mutual coupling matrix C can be applied.

[0125] Known angle of arrival θ i The received signal vector r when receiving the signal output from the wave source i is the calibration data set, and the arrival angle θ i By repeating reception M times while changing the parameter, M sets of calibration data sets can be acquired, and the mutual coupling matrix C and the amplitude-phase error matrix Γ are calculated from the M sets of calibration data sets.

[0126] Received signal r i The covariance matrix of i Let Ri Let the j-th eigenvalue of λ j (i) , the jth eigenvector is e j (i) ,λ1 (i) ≧λ2 (i) ≧ ≧ λ N (i) When the calibration signal is one wave, the calibrated mode vector ΓCa(θ i ) is the signal subspace e1 (i) is proportional to the noise subspace {e2 (i) ,···,e N (i)} is orthogonal to

[0127] For the first mutual coupling matrix C shown in equation (22), the calibrated mode vector ΓCa(θ i ) is orthogonal to the noise subspace, the following equation (24) holds.

[0128]

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[0129] In equation (24), * represents the complex conjugate, H represents the complex conjugate transpose. The unknown variables in equation (24) are {c0, ,c 19 ,γ1,···,γ4}, and if the mutual coupling coefficient and amplitude / phase error are normalized to c0=1 and γ1=1, the number of unknown variables to be solved becomes 22. Since M(N-1) equations (24) are obtained from M calibration data sets, the number of calibration data sets required to solve the 22 unknown variables is M≧8.

[0130] For the second mutual coupling matrix C shown in equation (23), the calibrated mode vector ΓCa(θ i ) is orthogonal to the noise subspace, the following equation (25) holds.

[0131]

number

[0132] The unknown variables in equation (25) are {c0, ,c 16 ,γ1,···,γ4}, and if the mutual coupling coefficient and amplitude / phase error are normalized to c0=1 and γ1=1, the number of unknown variables to be solved becomes 19. Since M(N-1) equations (25) are obtained from M calibration data sets, the number of calibration data sets required to solve the 19 unknown variables is M≧7.

[0133] As mentioned above, the array calibration methods described in Non-Patent Documents 1 and 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") differ greatly in the number of unknown variables.

[0134] In contrast, the number of unknown variables in the antenna array calibration method of this embodiment falls between the number of unknown variables in calibration method A and the number of unknown variables in calibration method B.

[0135] Furthermore, the antenna array calibration method according to this embodiment can selectively apply the first and second mutual coupling matrices C having different numbers of unknown variables. In addition, the number of unknown variables in the second mutual coupling matrix C can be changed. Therefore, calibration can be performed with various numbers of unknown variables, and an appropriate number of unknown variables can be selected depending on the number of calibration data sets.

[0136] Since each of the equations (24) to (25) is a product of unknown variables and is therefore difficult to solve directly, the mutual coupling matrix C and the amplitude-phase error matrix Γ are calculated by an iterative solution. First, as shown in equation (26), the mutual coupling matrix C is calculated so that the mutual coupling between real elements forms a unit matrix and the mutual coupling between virtual elements and real elements becomes zero. init is the initial value of the mutual coupling matrix C.

[0137]

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[0138] When recalibration is performed with approximately the same antenna arrangement, the previous mutual coupling matrix C may be used as the initial value instead of the initial value of the mutual coupling matrix C shown in equation (26).

[0139] The mutual coupling and amplitude / phase error calculation unit 32 sets an initial value of the mutual coupling matrix C, and then calculates C and Γ by an iterative solution method in which C and Γ approach solutions by repeating the first and second steps described below.

[0140] In the first step, by assuming that C is known, the products of unknown variables in each of equations (24) to (25) are resolved, and Γ is found using the linearized equations (24) to (25). In the second step, by assuming that Γ is known, the products of unknown variables in each of equations (24) to (25) are resolved, and C is found using the linearized equations (24) to (25). This iterative solution method makes it possible to find C and Γ without increasing the number of unknown variables, thereby reducing the number of calibration data sets.

[0141] The mutual coupling matrix C mainly depends on the geometric structure of the array antenna, and therefore its temperature dependence is relatively small. However, the amplitude and phase error matrix Γ changes depending on the temperature characteristics of the feed line and receiver. Therefore, it is efficient to recalibrate only the amplitude and phase error matrix Γ when the temperature changes.

[0142] In the antenna array calibration method of this embodiment, the mutual coupling matrix C and the amplitude / phase error matrix Γ are independent, and therefore the amplitude / phase error matrix Γ can be found by fixing the mutual coupling matrix C. In this case, the number of unknown variables is a small number (N-1), and it is possible to recalibrate the amplitude / phase error matrix Γ with a small number of calibration data sets (M≧1 sets).

[0143] Conversely, the antenna array calibration method of this embodiment can find the mutual coupling matrix C by fixing the amplitude-phase error matrix Γ. As a result, the antenna array calibration method of this embodiment can recalibrate only the mutual coupling matrix C when the antenna arrangement is changed with little temperature change.

[0144] The method of estimating the direction of arrival by the direction of arrival estimation device 50 will be described below.

[0145] In the direction of arrival estimation method, first, as in the antenna array calibration method, the eigenvalue analysis unit 31 performs eigenvalue analysis of the covariance matrix calculated by the covariance matrix calculation unit 30 .

[0146] Let R be the covariance matrix of the received signal r, and let λ be the j-th eigenvalue of R. j , the jth eigenvector is e j ,λ1≧λ2≧···≧λ N When there is one unknown wave source, the eigenvector of the noise is {e2, ,e N} The matrix consisting of noise eigenvectors is expressed as E N Let's say.

[0147] 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 Calculate (θ). a~ indicates a variable in the formula with ~ above it.

[0148]

number

[0149] The MUSIC calculation unit 53 calculates the calibrated MUSIC spectrum P MUSIC The arrival angle θ at which (θ) is maximized is determined as the estimated arrival direction after calibration.

[0150] As described above, in this embodiment, the degree of freedom of the mutual coupling between the virtual elements and the real elements is limited based on the symmetry of the arrangement of the virtual elements and the real elements, thereby reducing the number of mutual coupling coefficients that become unknown variables during calibration, and by determining the mutual coupling matrix C and the amplitude-phase error matrix Γ by an iterative solution method, the number of calibration data sets can be reduced.

[0151] In this embodiment, the calibration accuracy can be increased by adding virtual elements and adding the mutual coupling between the virtual elements and real elements to the mutual coupling matrix C. Therefore, in this embodiment, a moderate calibration accuracy can be achieved with a moderate number of calibration data sets.

[0152] Furthermore, in this embodiment, by setting some of the mutual couplings between virtual elements and real elements to zero, the number of mutual coupling coefficients that become unknown variables during calibration can be changed, and therefore the number of calibration data sets can be changed.

[0153] Furthermore, in this embodiment, among the mutual couplings between virtual elements and real elements, all mutual couplings except those between virtual elements and real elements with the shortest inter-element distance are set to zero, thereby reducing the number of mutual coupling coefficients that become unknown variables during calibration, and therefore the number of calibration data sets can be reduced.

[0154] Furthermore, in this embodiment, the real elements are arranged without symmetry, and among the mutual couplings between the virtual elements and the real elements, mutual couplings other than those between the virtual elements and the real elements with the shortest inter-element distance are set to zero. This reduces the number of mutual coupling coefficients that become unknown variables during calibration, even in the case where the real elements are arranged without symmetry, and therefore makes it possible to reduce the number of calibration data sets.

[0155] The effects of the above-described embodiment will now be described in detail with reference to the drawings.

[0156] As shown in FIG. 6, in a graph in which the horizontal axis represents the number of unknown variables at the time of calibration and the vertical axis represents the calibration accuracy, this embodiment can selectively apply first and second mutual coupling matrices C each having a different number of unknown variables. In addition, the number of unknown variables in the second mutual coupling matrix C can be changed, so this embodiment corresponds to an intermediate region indicated as calibration method C between calibration method A and calibration method B.

[0157] More specifically, as shown in Fig. 7, in calibration method A, the coefficients constituting the mutual coupling matrix are limited to c5, the number of unknown variables at the time of calibration is 8, and the minimum value of the number M of calibration data sets is 3. In addition, in calibration method B, there is no limit to the coefficients constituting the mutual coupling matrix, the number of unknown variables at the time of calibration is 23, and the minimum value of the number M of calibration data sets is 8.

[0158] In contrast, in the present embodiment shown in the calibration method C, when the first mutual coupling matrix C is applied, the coefficients constituting the mutual coupling matrix are c 19 The number of unknown variables at the time of calibration is 22, and the minimum value of the number M of calibration data sets is 8.

[0159] In addition, in this embodiment shown as calibration method C, a second mutual coupling matrix C is applied, and the coefficients constituting the mutual coupling matrix are set to c 18 In this case, the number of unknown variables at the time of calibration is 21, and the minimum value of the number M of calibration data sets is 7.

[0160] In addition, in this embodiment shown as calibration method C, a second mutual coupling matrix C is applied, and the coefficients constituting the mutual coupling matrix are set to c 17 In this case, the number of unknown variables at the time of calibration is 20, and the minimum value of the number M of calibration data sets is 7.

[0161] In addition, in this embodiment shown as calibration method C, a second mutual coupling matrix C is applied, and the coefficients constituting the mutual coupling matrix are set to c 16 In this case, the number of unknown variables at the time of calibration is 19, and the minimum value of the number M of calibration data sets is 7.

[0162] As described above, this embodiment can achieve appropriate calibration accuracy with an appropriate number of calibration data sets between calibration method A and calibration method B. Furthermore, this embodiment can accommodate various numbers of calibration data sets and required accuracy by selectively applying the first and second mutual coupling matrices C and changing the number of unknown variables in the second mutual coupling matrix C.

[0163] Furthermore, in this embodiment, similar to calibration method A, the mutual coupling matrix C and the amplitude-phase error matrix Γ can be calculated separately, so that it is possible to recalibrate only the mutual coupling matrix C, or only the amplitude-phase error matrix Γ.

[0164] While the present invention has been described with reference to exemplary embodiments, it will be apparent to those skilled in the art that modifications may be made without departing from the scope of the present invention, and it is intended that all such modifications and equivalents be included within the scope of the appended claims. [Explanation of symbols]

[0165] 1. Antenna array calibration equipment 2 Array antenna 2a~2d Receiving antennas 3 Multi-channel receiver 4. Array calibration processing section 5. Memory 10, 10a transmitter 11, 11a Transmitting antenna 20a~20d Frequency converter 21a~21d ADC 22 Local oscillator signal generator 23 Clock signal generator 30 Covariance matrix calculation section 31 Eigenvalue analysis section 32 Mutual coupling / amplitude phase error calculation section 50 Direction of arrival estimation device 51 Direction of arrival estimation processing unit 52 Mode vector calculation section 53 MUSIC calculation section

Claims

1. a signal transmitted from a wave source having a known direction of arrival and received by an array antenna (2); and a calculation of an eigenvector of a covariance matrix of a received signal, the eigenvector being calculated a predetermined number of times while changing the direction of arrival; In an antenna array calibration method, a calibration matrix including mutual couplings between real elements constituting the array antenna, mutual couplings between non-existent virtual elements and the real elements, and amplitude and phase errors of the real elements is obtained from the eigenvectors, the real elements and the virtual elements are arranged symmetrically; the calibration matrix is ​​expressed by the product of an amplitude / phase error matrix having the amplitude / phase errors of the real elements as diagonal elements and a mutual coupling matrix consisting of mutual couplings between the real elements and mutual couplings between the virtual elements and the real elements; the mutual coupling matrix does not restrict the degree of freedom of mutual coupling between the real elements, but restricts the degree of freedom of mutual coupling between the virtual elements and the real elements based on the symmetry of the arrangement of the virtual elements and the real elements; the mutual coupling matrix and the amplitude-phase error matrix are determined from the eigenvectors by an iterative solution method; The antenna array calibration method according to the present invention is characterized in that:

2. 2. The antenna array calibration method according to claim 1, wherein the number of real elements is N, the number of virtual elements added to N is N', and the predetermined number of times is smaller than (NN'-1) / (N-1).

3. 3. The antenna array calibration method according to claim 1, wherein the mutual coupling matrix has a part of mutual couplings between the virtual elements and the real elements that are zero.

4. 3. The antenna array calibration method according to claim 1, wherein the mutual coupling matrix has zero mutual couplings between the virtual elements and the real elements, except for those between the virtual elements and the real elements with the shortest inter-element distance.

5. the real elements are arranged without symmetry; 3. The antenna array calibration method according to claim 1, wherein the mutual coupling matrix has zero mutual couplings between the virtual elements and the real elements, except for those between the virtual elements and the real elements with the shortest inter-element distance.

6. an array antenna (2) for receiving a signal transmitted from a wave source having a known direction of arrival; an eigenvalue analysis unit (31) that repeatedly calculates eigenvectors of a covariance matrix of a received signal received by the array antenna a predetermined number of times while changing the arrival direction; a calibration matrix calculation unit that calculates, from the eigenvectors calculated by the eigenvalue analysis unit, a calibration matrix that includes mutual couplings between real elements that configure the array antenna, mutual couplings between non-existent virtual elements and the real elements, and amplitude and phase errors of the real elements; In an antenna array calibration apparatus having the real elements and the virtual 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 real elements as diagonal elements and a mutual coupling matrix consisting of mutual couplings between the real elements and mutual couplings between the virtual elements and the real elements; the mutual coupling matrix does not restrict the degree of freedom of mutual coupling between the real elements, but restricts the degree of freedom of mutual coupling between the virtual elements and the real elements based on the symmetry of the arrangement of the virtual elements and the real elements; the calibration matrix calculation unit is a mutual coupling / amplitude / phase error calculation unit (32) that determines the mutual coupling matrix and the amplitude / phase error matrix by an iterative solution method from the eigenvectors calculated by the eigenvalue analysis unit; Antenna array calibration equipment.

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