JP2017040573A - Device, method, and program for estimating direction-of-arrival - Google Patents

Abstract

PROBLEM TO BE SOLVED: To enable reduction in the amount of computation for direction-of-arrival estimation.SOLUTION: A direction-of-arrival estimation device according to an embodiment of the present invention includes a matrix computation unit, vector generation unit, matrix generation unit, and evaluation function computation unit. The matrix computation unit computes a correlation matrix using received signals when one or more arrival waves are received by a plurality of antennas. The vector generation unit generates, for every search angle represented by a combination of elevation angle and azimuthal angle, a first mode vector associated with the one or more arrival waves, a second mode vector obtained by partially differentiating the first mode vector with respect to the elevation angle, and a third vector obtained by partially differentiating the first mode vector with respect to the azimuthal angle. When the number of arrival waves is no greater than a threshold, the matrix generation unit generates a matrix for each search angle using an eigenvector, of eigenvectors of the correlation matrix, corresponding to a signal sub-space, the first mode vector, the second mode vector, and the third mode vector. The evaluation function computation unit performs evaluation function computation for direction-of-arrival estimation using a maximum eigenvalue of the matrix.SELECTED DRAWING: Figure 1

Description

  Embodiments described herein relate generally to an arrival direction estimation apparatus, method, and program.

As a technique for estimating the arrival direction of a radio signal, many methods for estimating the arrival direction using the phase difference between antennas using an array antenna have been proposed.
If the polarization of the incoming radio signal does not match the polarization characteristics of each antenna constituting the array antenna, it is affected by polarization loss and fading. As a technique for preventing such deterioration due to the polarization characteristics of radio signals, there is a configuration in which a plurality of antennas having different polarization characteristics are arranged at the same location. For example, by using antennas with three different polarization characteristics whose main polarization directions are linearly independent in a three-dimensional space, the loss due to polarization can be reduced no matter what polarization radio signal arrives. Can receive incoming waves.

  On the other hand, when a radio signal arrives after being reflected, scattered, or diffracted by a scatterer, a large number of highly correlated elementary waves arrive instead of coming from a single direction. At this time, each elementary wave may arrive from a different direction, and the arrival direction estimation performance may be significantly degraded. As a method for estimating such an arrival direction, a method for estimating the arrival direction using a vector obtained by partial differentiation of a mode vector related to a radio signal with an azimuth angle or an elevation angle has been proposed.

A. M. Swindlehurst and M. Viberg, “Subspace Fitting with Diversely Polarized Antenna Arrays,” IEEE Trans. Antennas Propag., Vol. 41, no. 12, pp. 1687-1694, Dec. 1993. D. Asztely, B. Ottersten, and AL Swindlhurst, “Generalized array manifold model for wireless communication channels with local scattering,” IEE Proc. Radar, Sonar Navig., Vol.145, no.1, pp.51-57, Feb 1998.

  However, when using both the method of arranging multiple antennas with different polarization characteristics at the same location and the method of estimating the direction of arrival using a vector obtained by partial differentiation of the signal mode vector by azimuth or elevation, Since the number of vectors is large, a high-order eigenvalue calculation must be performed for each angle to be searched, so that the amount of calculation is problematic.

  The present disclosure has been made to solve the above-described problem, and provides an arrival direction estimation device, method, and program capable of reducing the amount of calculation of arrival direction estimation even when the arrival wave has an angular spread. The purpose is to do.

  The arrival direction estimation apparatus according to the present embodiment includes a matrix calculation unit, an eigenvalue calculation unit, a vector generation unit, an estimation unit, a matrix generation unit, and an evaluation function calculation unit. The matrix calculation unit calculates a correlation matrix using received signals when one or more incoming waves are received by a plurality of antennas. The eigenvalue calculation unit performs eigenvalue decomposition on the correlation matrix and calculates eigenvalues and eigenvectors. The vector generation unit performs partial differentiation of at least one first mode vector related to the one or more incoming waves and at least one first mode vector with respect to an elevation angle for each search angle represented by a combination of an elevation angle and an azimuth angle. And generating at least one second mode vector and at least one third mode vector obtained by partial differentiation of the at least one first mode vector with respect to an azimuth angle. The estimation unit estimates the number of the incoming waves based on the eigenvalue. When the number of arriving waves is equal to or less than a first threshold, the matrix generation unit, for each search angle, a signal eigenvector corresponding to a signal subspace of the eigenvector, the first mode vector, and the second mode A matrix is generated using the mode vector and the third mode vector. The evaluation function calculation unit calculates an evaluation function for direction-of-arrival estimation using the maximum eigenvalue of the matrix when the number of incoming waves is equal to or less than a first threshold value.

The block diagram which shows the arrival direction estimation apparatus which concerns on 1st Embodiment. The block diagram which shows the arrival direction estimation apparatus which concerns on 2nd Embodiment. The block diagram which shows the arrival direction estimation apparatus which concerns on 4th Embodiment.

  Hereinafter, the direction of arrival estimation apparatus, method, and program according to the present embodiment will be described in detail with reference to the drawings. Note that, in the following embodiments, the same reference numerals are assigned to the same operations, and duplicate descriptions are omitted as appropriate.

(First embodiment)
An arrival direction estimation apparatus according to the present embodiment will be described with reference to the block diagram of FIG.
The arrival direction estimation apparatus 100 according to the present embodiment includes first antennas 101-1 to 101-M (also simply referred to as first antenna 101) and second antennas 102-1 to 102-M (also simply referred to as second antenna 102). ), Third antennas 103-1 to 103-M (also simply referred to as third antenna 103), correlation matrix calculation unit 104, eigenvalue calculation unit 105, mode vector generation unit 106, wave number estimation unit 107, matrix generation unit 108, and evaluation A function calculation unit 109 is included.

  The first antenna 101 is a group of M antennas (M is a natural number of 2 or more) having the same polarization characteristics. The same polarization characteristics can be realized by installing antennas having the same shape in the same direction. As the shape of the antenna, any antenna such as a linear antenna, a loop antenna, a patch antenna, or a slot antenna may be used. The second antenna 102 and the third antenna 103 are also antenna groups having the same polarization characteristics. The first antenna 101, the second antenna 102, and the third antenna 103 are antennas having different polarization characteristics. In order to obtain different polarization characteristics, different antennas may be used, or they may be installed in different directions using the same antenna. In the present embodiment, the installation location may be any installation location as long as the first antenna 101, the second antenna 102, and the third antenna 103 have different polarization characteristics.

  Each of the first antenna 101, the second antenna 102, and the third antenna 103 receives one or more incoming waves that are radio signals and obtains a received signal. In the present embodiment, it is assumed that a plurality of antennas having different polarization characteristics are set as one antenna group, and an incoming wave is received by array antennas arranged in a plurality of positions where the antenna groups are different.

  The received signal is then converted to a digital signal. Since the conversion of the received signal into a digital signal may be performed by a general process such as using a radio device (not shown) including a low noise amplifier, a frequency converter, a filter, an AD converter, etc. The description of is omitted.

  Correlation matrix calculation section 104 receives received signals from first antenna 101, second antenna 102, and third antenna 103, and calculates a correlation matrix of a received signal vector expressed using the received signals.

  The eigenvalue calculation unit 105 receives the correlation matrix from the correlation matrix calculation unit 104, performs eigenvalue decomposition on the correlation matrix, and calculates eigenvalues and eigenvectors.

  For each search angle represented by a combination of an elevation angle and an azimuth angle, the mode vector generation unit 106 partially differentiates at least one mode vector related to an incoming wave (first mode vector) and at least one mode vector with respect to the elevation angle. At least one mode vector (second mode vector) and at least one mode vector (third mode vector) obtained by partially differentiating at least one mode vector with respect to an azimuth angle are generated. The mode vector is a vector determined by the antenna arrangement and the signal arrival angle.

  The wave number estimation unit 107 receives the eigenvalue from the eigenvalue calculation unit 105, and estimates the number of incoming waves included in the received signal based on the eigenvalue. The estimation of the number of incoming waves may be performed by using a general method such as the distribution of eigenvalues, the AIC (Akaike Information Criteria) method, the MDL (Minimum Description Length) method, and the description thereof is omitted here.

  The matrix generation unit 108 receives the eigenvector from the eigenvalue calculation unit 105, the first mode vector, the second mode vector, and the third mode vector from the mode vector generation unit 106, and the number of incoming waves from the wave number estimation unit 107, respectively. When the number of arriving waves is equal to or less than the threshold, the matrix generation unit 108, for each search angle, the eigenvector (signal eigenvector) corresponding to the signal subspace of the eigenvector, the first mode vector, the second mode vector, and the second mode vector. A matrix is generated using the three-mode vector. As a generated matrix, a Hermite matrix or a real symmetric matrix is assumed, but in this embodiment, a Hermite matrix will be described as an example.

  The evaluation function calculation unit 109 receives the matrix, the first mode vector, the second mode vector, and the third mode vector from the matrix generation unit 108, and calculates an evaluation function for direction of arrival estimation using the maximum eigenvalue of the matrix. .

Next, the arrival direction estimation processing of the arrival direction estimation apparatus 100 according to the present embodiment will be specifically described.
Consider a case where P independent radio signals arrive as incoming waves and are received by each antenna to obtain a received signal. When the incoming wave arrives after being reflected, scattered and diffracted by the scatterer, the signal does not come from a single direction, but a plurality of highly correlated elementary waves come from different directions.

  At this time, since each elementary wave arrives with a different amplitude difference, phase difference, and polarization characteristic, the signals received by the first antenna 101, the second antenna 102, and the third antenna 103 are (1), (2) and (3) can be expressed respectively.

Here, r ⁽¹⁾ (t) represents an M-dimensional column vector having the reception signals of the first antennas 101-1 to 101-M as elements. r ⁽²⁾ (t) represents an M-dimensional column vector having the reception signals of the second antennas 102-1 to 102-M as elements. r ⁽³⁾ (t) represents an M-dimensional column vector having the reception signals of the third antennas 103-1 to 103-M as elements.

Also, it represents the number of rays of the p-th signal D _p. The complex amplitudes of the d-th elementary waves of the p-th signals received by the first antennas 101-1 to 101-M, the second antennas 102-1 to 102-M, and the third antennas 103-1 to 103-M are expressed as follows. It represents to (4) Formula, (5) Formula, and (6) Formula, respectively.

θ _p represents the center of the arrival direction in the elevation direction for the p-th signal, and φ _p represents the center of the arrival direction in the azimuth direction for the p-th signal. Δθ _{p, d} and Δφ _{p, d} represent the difference from the center direction of the arrival direction of the d-th elementary wave of the p-th signal and the difference from the center direction of the arrival direction of the azimuth angle, respectively. a ⁽¹⁾ (θ, φ), a ⁽²⁾ (θ, φ) and a ⁽³⁾ (θ, φ) are the first antennas 101-1 to 101-101 of signals coming from the elevation angle θ and the azimuth angle φ. -M, M × 1 order mode vectors in the second antennas 102-1 to 102-M and the third antennas 103-1 to 103-M, respectively.

n ⁽¹⁾ (t), n ⁽²⁾ (t), and n ⁽³⁾ (t) are the first antenna 101-1 to 101-M, the second antenna 102-1 to 102-M, and the third antenna. M × 1 order thermal noise vectors in 103-1 to 103-M are respectively shown. s _p (t) represents a complex signal of the p-th incoming wave.

  Correlation matrix calculation section 104 calculates a correlation matrix using the above equations (1) to (3) for received signals received at a plurality of times. Specifically, as shown in equation (7), equations (1) to (3) are combined, and the correlation matrix of equation (8) is calculated for a vector obtained by expanding the dimension of the vector to 3M × 1. To do.

  Δt represents a sampling interval, and k represents a sampling number. Superscript “H” represents complex conjugate transpose. In equation (8), it is assumed that the correlation matrix is calculated for signals sampled at equal intervals, but the sampling intervals need not be equal.

Subsequently, the eigenvalue calculation unit 105 performs eigenvalue decomposition on the correlation matrix R _rr as shown in Equation (9), and calculates eigenvalues and eigenvectors.

E _s represents a 3M × P-order matrix having eigenvectors in the signal subspace as column vectors. Λ _s represents a P × P-order diagonal matrix whose diagonal component is the eigenvalue of the signal subspace, as shown in Equation (10).

E _n represents a 3M × (MP) -order matrix with the eigenvector of the noise subspace as a column vector. Λ _n represents an M × (M−P) _-th order matrix having eigenvalues of the noise subspace as diagonal components, as shown in Equation (11).

  Since the matrix generated by correlation matrix calculation section 104 is a Hermitian matrix, the eigenvalues and eigenvectors of the Hermitian matrix calculated by eigenvalue calculation section 105 satisfy Expressions (12) and (13).

Note that I _3M is a 3M × 3M degree unit matrix.

Here, when Δθ _{p, d} and Δφ _{p, d} are not so large and are negligible, for example, the received signal shown in the equation (7) can be expressed as (14 ).

  As shown in the equation (14), the received signal is represented in a format in which nine mode vectors are weighted and synthesized with nine unknown complex amplitudes for each signal.

  The mode vector generation unit 106 includes an array antenna mode vector composed of the first antennas 101-1 to 101-M, an array antenna mode vector composed of the second antennas 102-1 to 102-M, and a third Each of the mode vectors of the array antenna constituted by the antennas 103-1 to 103-M is generated. In addition, a mode vector obtained by partial differentiation of each of the three mode vectors described above with respect to an elevation angle and a mode vector obtained by partial differentiation with respect to an azimuth angle are output for each combination of the elevation angle θ and the azimuth angle φ. That is, nine mode vectors are generated for one combination of elevation angle θ and azimuth angle φ. At this time, the vectors are normalized so that the Frobenius norm square values of all the mode vectors (the sum of squares of the absolute values of the elements of the vectors) have the same magnitude.

  The matrix generation unit 108 calculates Equation (15) for each elevation angle θ and azimuth angle φ using the eigenvectors of the signal subspace and the mode vector among the eigenvectors calculated by the eigenvalue calculation unit 105.

  Here, the Hermitian matrix of the equation (16) is calculated by multiplying the complex conjugate transpose of the equation (15) from the left by the equation (15).

  The evaluation function calculation unit 109 calculates the maximum eigenvalue ξ of equation (16), and calculates the evaluation function shown in equation (17) using the maximum eigenvalue ξ and the square value of the Frobenius norm of the normalized mode vector. To do.

  The maximum value of ξ is the square value of the Frobenius norm of the mode vector, and when the signal arrival direction matches the elevation angle θ and the azimuth angle φ to be searched, the value of ξ is the square value of the Frobenius norm of the mode vector. Asymptotically. Therefore, the evaluation function takes a maximum value in the direction in which the signal arrives, and it can be estimated that the direction in which the evaluation function becomes the maximum is the arrival direction of the incoming wave.

  Here, the number of dimensions of the matrix shown in the equation (16) is a square matrix having the dimension P of the number of incoming waves. Therefore, when the number of arriving waves is less than or equal to the threshold (for example, when the arriving waves are 2 or 3 waves), the eigenvalues of the low-dimensional matrix may be obtained when obtaining the eigenvalues for calculating the evaluation function. Compared with the case of calculating the eigenvalues of the 9 × 9 Hermitian matrix, the amount of calculation can be greatly reduced.

  According to the first embodiment described above, it is possible to perform highly accurate arrival direction estimation regardless of the polarization characteristics of incoming waves by performing reception using a plurality of antennas having different polarization characteristics. it can. Further, even when the incoming waves have an angular spread, when the number of incoming waves is small, the amount of calculation can be greatly reduced by calculating the eigenvalues of the matrix generated using the eigenvectors of the signal subspace.

(Second Embodiment)
The second embodiment is different in that a plurality of antennas having different polarization characteristics are arranged at the same location.

  An arrival direction estimation apparatus according to the second embodiment will be described with reference to the block diagram of FIG.

  The arrival direction estimation apparatus 200 shown in FIG. 2 includes a first antenna 101, a second antenna 102, a third antenna 103, a correlation matrix calculation unit 104, an eigenvalue calculation unit 105, a wave number estimation unit 107, a matrix generation unit 108, and an evaluation function calculation. Unit 109 and mode vector generation unit 201.

  Except for the mode vector generation unit 201, the same processing as in the first embodiment is performed, and thus the description thereof is omitted here.

The mode vector generation unit 201 generates common mode vectors a ⁽¹⁾ (θ, φ), d _θ ⁽¹⁾ (θ, φ), and d _φ ⁽¹⁾ (θ, φ).

  When an array antenna is configured using antennas having the same polarization characteristics, incoming waves are received with the same power in each antenna of the array antenna. Therefore, with the power as an unknown variable, the mode vector of the array antenna can be defined only by the phase difference between the antennas. When an array antenna is configured using antennas having the same polarization characteristics, the phase difference between the antennas is determined by the arrival direction of the incoming wave, the frequency, and the antenna arrangement.

  Therefore, by installing a plurality of antennas having different polarization characteristics at the same location (referred to as antenna groups) and installing the antenna group at a plurality of different locations, the mode vector of each array antenna is the same as the mode vector. Become.

  In the second embodiment, an array antenna is configured by using a patch antenna, and a horizontally polarized wave and a vertically polarized wave are individually received by changing a feeding method in the patch antenna. Suppose.

  Since the array antenna that receives horizontal polarization and the array antenna that receives vertical polarization are arranged in the same place, the mode vectors for the respective array antennas are the same vector.

As described above, when antennas having different polarization characteristics are installed at the same location, a common mode vector is generated by array antennas having different polarization characteristics. Furthermore, since the mode vector is the same vector, the mode vector obtained by partial differentiation with respect to the elevation angle or the azimuth angle is the same vector between different polarized waves. Therefore, the mode vector generation unit 201 does not need to generate a mode vector for each array antenna having each polarization characteristic, and common mode vectors a ⁽¹⁾ (θ, φ), d _θ ⁽¹⁾ (θ, φ) and d _φ ⁽¹⁾ (θ, φ) may be generated.

  The matrix generation unit 108 may use a common mode vector as a mode vector corresponding to each polarization characteristic.

  In the second embodiment, the case where horizontal and vertical polarizations are handled using a patch antenna as an antenna having different polarization characteristics has been described as an example. However, the second embodiment is limited to a patch antenna. Not what you want. Any antenna may be used as long as it can be installed at the same location. Also, the type of polarization is not limited to two types, but three dipole antennas are arranged along the x-axis, y-axis, and z-axis. You may install in the place.

  According to the second embodiment described above, it is only necessary to generate a common mode vector when a plurality of antennas having different polarization characteristics are arranged at the same location, and the memory amount and the transmission speed between the buses. Can be reduced.

(Third embodiment)
In the above embodiment, the eigenvector of the signal subspace is used among the eigenvectors, and the evaluation function is calculated using the maximum eigenvalue. However, in the third embodiment, the point of using the eigenvector of the noise subspace and the matrix The point which calculates an evaluation function using a minimum eigenvalue differs from the above-mentioned embodiment.

  The correlation matrix generated by the correlation matrix calculation unit 104 generates an LM × LM dimensional matrix, assuming that the number of antennas having different polarization characteristics is L (L is a natural number of 2 or more). At this time, when the number of incoming waves P is large, the dimension of the matrix (Hermitian matrix) generated by the matrix generation unit 108 becomes large, and the amount of calculation is difficult to reduce.

  Therefore, when the number P of incoming waves is greater than the threshold, the eigenvector (noise eigenvector) of the noise subspace among the eigenvectors calculated by the eigenvalue calculation unit 105 is used. The number of incoming waves may be estimated from the distribution of eigenvalues calculated by the eigenvalue calculation unit 105. Thereby, the amount of calculation can be reduced.

  Since the arrival direction estimation apparatus according to the third embodiment is the same as that of FIG. 1 or FIG. 2 except for the processing of the matrix generation unit 108 and the evaluation function calculation unit 109, description thereof is omitted here.

Matrix generating unit 108, when the number P of the incoming wave is larger than the threshold value, using each mode vectors generated eigenvectors of the noise subspace matrix E _n and the mode vector generating unit 106 and column vector (18) Calculate the formula.

  Here, the Hermitian matrix of the equation (19) is calculated by multiplying the equation (18) by the complex conjugate transpose of the equation (18) from the left.

The evaluation function calculation unit 109 calculates the minimum eigenvalue ξ _min of the matrix of the equation (19), and uses the minimum eigenvalue ξ _min and the square value of the Frobenius norm norm of the mode vector to evaluate the evaluation function P _{musical of the} equation (20). Calculate (θ, φ).

The minimum value of ξ _min is zero, and when the direction of arrival of the signal matches the searched elevation angle θ and azimuth angle φ, the value of ξ _min approaches zero. Therefore, it can be estimated that the evaluation function P _music (θ, φ) has a maximum value in the direction in which the incoming wave arrives, and the direction in which the evaluation function becomes the maximum is the arrival direction of the incoming wave.

  Here, the dimension of the matrix of the equation (19) is a (3M-P) -dimensional square matrix. When the number P of incoming waves is larger than the threshold value and the value of 3M-P is about 2 or 3, the eigenvalue obtained for calculating the evaluation function is an eigenvalue of a low-dimensional matrix. Compared with the calculation of eigenvalues of the matrix, the amount of calculation can be greatly reduced.

  Note that when antennas having different polarization characteristics are arranged at the same location as in the second embodiment, the mode vector generated by the mode vector generation unit 106 can be a common mode vector.

  According to the third embodiment described above, when the number of incoming waves is large, by using the eigenvectors of the noise subspace, it is possible to perform highly accurate estimation while reducing the amount of calculation of the arrival direction estimation. it can.

(Fourth embodiment)
The fourth embodiment is different from the above-described embodiment in that the evaluation function is not calculated at all the angles to be searched but is calculated only when it is determined that the evaluation function needs to be calculated. By doing so, the amount of calculation can be further reduced.

  An arrival direction estimation apparatus according to a fourth embodiment will be described with reference to the block diagram of FIG.

  An arrival direction estimation apparatus 300 according to the fourth embodiment includes a first antenna 101, a second antenna 102, a third antenna 103, a correlation matrix calculation unit 104, an eigenvalue calculation unit 105, a mode vector generation unit 106, and a wave number estimation unit 107. The matrix generation unit 108, the determination unit 301, and the evaluation function calculation unit 302 are included.

  Except for the determination unit 301 and the evaluation function calculation unit 302, the same processing as in the first embodiment is performed, and thus description thereof is omitted here.

  The determination unit 301 receives a matrix from the matrix generation unit 108, compares the value of the eigen equation of the matrix with a threshold value, and generates a determination result indicating whether the evaluation function needs to be calculated.

  The evaluation function calculation unit 302 receives the matrix from the matrix generation unit 108 and the determination result from the determination unit 301, and calculates the eigenvalue for the matrix determined to require calculation of the evaluation function, thereby calculating the evaluation function. To do. The evaluation function calculation unit 302 sets a predetermined value as the value of the evaluation function of the matrix that is determined not to require calculation of the evaluation function.

  Next, as shown in the first embodiment and the second embodiment, the determination unit 301 in the case where a matrix is generated using the eigenvector of the signal subspace and the evaluation function is calculated using the maximum eigenvalue of the matrix. The determination process will be described.

  As described above, since the maximum value of the maximum eigenvalue of the matrix generated by the matrix generation unit 108 matches the square value of the Frobenius norm of the mode vector, the searched elevation angle θ and azimuth angle φ are the signal arrival directions. The maximum eigenvalue is asymptotic to the square of the Frobenius norm of the mode vector. On the other hand, when the searched angle and the arrival direction of the signal do not match, the maximum eigenvalue of the equation (16) is smaller than the maximum value.

  Therefore, the determination unit 301 assigns the square value of the Frobenius norm of the mode vector to the eigen equation of the matrix of Equation (16), and when the value obtained as a result of the substitution is less than or equal to the threshold value, for example, a value that is close to zero. In some cases, a determination result indicating that calculation of an evaluation function is necessary is generated.

As a result, since the evaluation function can be calculated only in the vicinity angle of the arrival direction of the incoming wave, the calculation valence of the evaluation function can be reduced, and the amount of calculation can be greatly reduced.
When the highest order coefficient of the eigen equation is positive, if the square value of the Frobenius norm of the mode vector is substituted into the eigen equation, the determination unit 301 sets the threshold value to a positive value because it becomes a real number greater than or equal to zero. That's fine.

  Next, as shown in the third embodiment, a determination process of the determination unit 301 when a matrix is generated using an eigenvector of a noise subspace and an evaluation function is calculated using a minimum eigenvalue of the matrix will be described. .

  As described above, since the minimum value of the minimum eigenvalue of the matrix shown in Equation (19) is zero, the minimum eigenvalue is zero when the searched elevation angle θ and azimuth angle φ match the signal arrival direction. Asymptotically. On the other hand, when the search angle and the arrival direction of the signal do not match, the minimum eigenvalue of equation (19) is a value greater than zero.

  Therefore, the determination unit 301 determines a determination result indicating that the evaluation function needs to be calculated when the value of the intercept of the eigen equation is equal to or less than a threshold value, for example, close to zero, with respect to the matrix shown in Equation (19). Generate. The value of the zeroth-order coefficient of the eigen equation or the value of the determinant may be used instead of the value of the intercept of the eigen equation. Specifically, when the value of the zeroth-order coefficient of the eigen equation is less than or equal to the threshold value, or when the value of the determinant is less than or equal to the threshold value, the determination unit 301 needs to calculate the evaluation function. The determination result shown may be generated.

  According to the fourth embodiment described above, by calculating the evaluation function only for the neighboring angle of the arrival direction of the incoming wave based on the determination result of the determination unit, the arrival direction can be obtained even when the incoming wave has an angular spread. It is possible to perform highly accurate estimation while reducing the amount of calculation for estimation.

  In the above-described embodiment, the case where the arrival direction is estimated using three types of antennas having different polarization characteristics has been described as an example, but the number of antennas is not limited to three types. For example, when four types of antennas are used, a mode vector corresponding to the arrangement of each antenna may be generated by the mode vector generation unit 106 and the matrix generated by the matrix generation unit 108 may be expanded to four dimensions. That is, the number of antennas having different polarization characteristics and the number of matrix dimensions may be the same.

The instructions shown in the processing procedure shown in the above-described embodiment can be executed based on a program that is software. A general-purpose computer system stores this program in advance and reads this program, so that the same effect as that obtained by the arrival direction estimation device described above can be obtained. The instructions described in the above-described embodiments are, as programs that can be executed by a computer, magnetic disks (flexible disks, hard disks, etc.), optical disks (CD-ROM, CD-R, CD-RW, DVD-ROM, DVD). ± R, DVD ± RW, Blu-ray (registered trademark) Disc, etc.), semiconductor memory, or a similar recording medium. As long as the recording medium is readable by the computer or the embedded system, the storage format may be any form. If the computer reads the program from the recording medium and causes the CPU to execute instructions described in the program based on the program, the same operation as the arrival direction estimation device of the above-described embodiment can be realized. . Of course, when the computer acquires or reads the program, it may be acquired or read through a network.
In addition, the OS (operating system), database management software, MW (middleware) such as a network, etc. running on the computer based on the instructions of the program installed in the computer or embedded system from the recording medium implement this embodiment. A part of each process for performing may be executed.
Furthermore, the recording medium in the present embodiment is not limited to a medium independent of a computer or an embedded system, but also includes a recording medium in which a program transmitted via a LAN, the Internet, or the like is downloaded and stored or temporarily stored.
Further, the number of recording media is not limited to one, and when the processing in this embodiment is executed from a plurality of media, it is included in the recording medium in this embodiment, and the configuration of the media may be any configuration.

The computer or the embedded system in the present embodiment is for executing each process in the present embodiment based on a program stored in a recording medium. The computer or the embedded system includes a single device such as a personal computer or a microcomputer. The system may be any configuration such as a system connected to the network.
In addition, the computer in this embodiment is not limited to a personal computer, but includes an arithmetic processing device, a microcomputer, and the like included in an information processing device, and is a generic term for devices and devices that can realize the functions in this embodiment by a program. ing.

  Although several embodiments of the present invention have been described, these embodiments are presented by way of example and are not intended to limit the scope of the invention. These novel embodiments can be implemented in various other forms, and various omissions, replacements, and changes can be made without departing from the spirit of the invention. These embodiments and modifications thereof are included in the scope and gist of the invention, and are included in the invention described in the claims and the equivalents thereof.

100, 200, 300 ... Direction-of-arrival estimation apparatus, 101, 101-1 to 101-M ... first antenna, 102, 102-1 to 102-M ... second antenna, 103, 103-1 , 103-M ... third antenna, 104 ... correlation matrix calculation unit, 105 ... eigenvalue calculation unit, 106 ... mode vector generation unit, 107 ... wave number estimation unit, 108 ... matrix Generation unit, 109, 302... Evaluation function calculation unit, 201... Mode vector generation unit, 301.

Claims (9)

A matrix calculator that calculates a correlation matrix using received signals when one or more incoming waves are received by a plurality of antennas;
An eigenvalue decomposition unit that performs eigenvalue decomposition on the correlation matrix and calculates eigenvalues and eigenvectors;
For each search angle represented by a combination of an elevation angle and an azimuth angle, at least one first mode vector related to the one or more incoming waves and at least one first mode vector obtained by partial differentiation of the at least one first mode vector with respect to an elevation angle. A vector generation unit that generates a two-mode vector and at least one third mode vector obtained by partially differentiating each of the at least one first mode vector with respect to an azimuth angle;
An estimation unit that estimates the number of incoming waves based on the eigenvalue;
When the number of arriving waves is equal to or less than a first threshold, for each search angle, a signal eigenvector corresponding to a signal subspace of the eigenvector, the first mode vector, the second mode vector, and A matrix generation unit that generates a matrix using the third mode vector;
An arrival direction estimation apparatus comprising: an evaluation function calculation unit that calculates an evaluation function for arrival direction estimation using a maximum eigenvalue of the matrix when the number of arrival waves is equal to or less than a first threshold value. The matrix generator, when the number of incoming waves is greater than the first threshold, a noise eigenvector corresponding to a noise subspace of the eigenvector, the first mode vector, and the second mode vector, Generating a matrix using the second mode vector;
The arrival direction estimation apparatus according to claim 1, wherein the evaluation function calculation unit calculates the evaluation function using a minimum eigenvalue of the matrix when the number of incoming waves is greater than the first threshold. A determination unit that compares the value of the eigen equation of the matrix with a second threshold value and generates a determination result indicating whether the calculation of the evaluation function is necessary;
The arrival direction estimation apparatus according to claim 1, wherein the evaluation function calculation unit calculates the evaluation function when the determination result indicates that the calculation of the evaluation function is necessary.   The determination unit is configured to calculate a square value of a norm of each of the first mode vector, the second mode vector, and the third mode vector when the number of incoming waves is equal to or less than a first threshold value. The direction-of-arrival estimation apparatus according to claim 3, wherein when the value assigned to the eigen equation is equal to or less than a third threshold value, it is determined that the evaluation function needs to be calculated. The value of the eigen equation is a zeroth order coefficient of the eigen equation,
The determination unit determines that the evaluation function needs to be calculated when the number of incoming waves is greater than the first threshold and the zeroth order coefficient is equal to or less than a fourth threshold. Item 4. The arrival direction estimation apparatus according to item 3. The value of the eigen equation is the value of the determinant of the matrix;
The determination unit determines that the evaluation function needs to be calculated when the number of incoming waves is greater than the first threshold and the value of the determinant is equal to or less than a fifth threshold. Item 4. The arrival direction estimation apparatus according to item 3.   6. The received signal is a signal received by an array antenna in which a plurality of antennas having different polarization characteristics are used as one antenna group and the antenna groups are arranged at different positions. The arrival direction estimation device according to item 1. Calculate the correlation matrix using the received signal when one or more incoming waves are received by multiple antennas,
Eigenvalue decomposition of the correlation matrix to calculate eigenvalues and eigenvectors;
For each search angle represented by a combination of an elevation angle and an azimuth angle, at least one first mode vector related to the one or more incoming waves and at least one first mode vector obtained by partial differentiation of the at least one first mode vector with respect to an elevation angle. Generating a two-mode vector and at least one third mode vector obtained by partial differentiation of each of the at least one first mode vector with respect to an azimuth angle;
Based on the eigenvalue, estimate the number of incoming waves,
When the number of arriving waves is equal to or less than a first threshold, for each search angle, a signal eigenvector corresponding to a signal subspace of the eigenvector, the first mode vector, the second mode vector, and Generating a matrix using the third mode vector,
A direction-of-arrival estimation method for calculating an evaluation function for direction-of-arrival estimation using a maximum eigenvalue of the matrix when the number of arrival waves is equal to or less than a first threshold value. Computer
Matrix calculation means for calculating a correlation matrix using received signals when one or more incoming waves are received by a plurality of antennas;
Eigenvalue calculating means for eigenvalue-decomposing the correlation matrix and calculating eigenvalues and eigenvectors;
For each search angle represented by a combination of an elevation angle and an azimuth angle, at least one first mode vector related to the one or more incoming waves and at least one first mode vector obtained by partial differentiation of the at least one first mode vector with respect to an elevation angle. Vector generating means for generating a two-mode vector and at least one third mode vector obtained by partial differentiation of the at least one first mode vector with respect to an azimuth angle;
Estimating means for estimating the number of incoming waves based on the eigenvalue;
When the number of arriving waves is equal to or less than a first threshold, for each search angle, a signal eigenvector corresponding to a signal subspace of the eigenvector, the first mode vector, the second mode vector, and Matrix generating means for generating a matrix using the third mode vector;
An arrival direction estimation program for functioning as an evaluation function calculation means for calculating an evaluation function of direction of arrival estimation using the maximum eigenvalue of the matrix when the number of arrival waves is equal to or less than a first threshold.