JP3836095B2 - Radio wave arrival direction detection method and apparatus - Google Patents

Description

  The present invention relates to a radio wave arrival direction detection method using an array antenna that includes a plurality of antenna elements and can change directivity characteristics, and more particularly to an electronically controlled waveguide array that can adaptively change directivity characteristics. The present invention relates to a radio wave arrival direction detection method and apparatus using an antenna device (Electronically Steerable Passive Array Radiator Antenna).

  Estimating the angle of arrival (DOA) of signals incident on an array antenna is an interesting and important issue in digital array processing. Several methods have been proposed to solve this problem. In particular, the MUSIC (MUltiple SIgnal Classification) algorithm described in Non-Patent Document 6 is widely known as providing a result asymptotically approaching an unbiased estimator.

  By the way, an electronically controlled waveguide array antenna device proposed in Patent Document 1 and the like is provided with an excitation element to which a radio signal is fed and a predetermined distance from the excitation element, and at least a radio signal is not fed. An array antenna including one non-excitation element and a variable reactance element connected to the non-excitation element is provided, and the directivity characteristic of the array antenna is changed by changing the reactance value of the variable reactance element. Can do. This electronically controlled waveguide array antenna device is an attractive antenna because it has a simpler hardware configuration than conventional phased array antennas. In recent years, it has been actively applied to wireless communication and high-resolution azimuth estimation. Has been studied. The electronically controlled waveguide array antenna device has a single power feed and can receive only one data at each time. This point is fundamentally different from the conventional phased array in which the reception data of all the elements can be observed at each time.

  As is obvious from the principle of the electronically controlled waveguide array antenna device, a simple beam former can be realized by obtaining reactance value sets for forming directional beams in different directions and switching the beams according to them. However, due to the principle of the electronically controlled waveguide array antenna apparatus that forms a beam using electromagnetic coupling, the element spacing cannot be increased and the antenna aperture becomes relatively small. Therefore, it has been difficult to form a sharp pencil beam and improve the resolution.

  As methods for realizing high resolution with a small antenna aperture, the MUSIC method (see Non-Patent Document 2), the ESPRIT (Estimation of Signal Parameters via Rotational Invariance Techniques) method (see Non-Patent Document 3), and MODE (Method of). Application of a super-resolution method such as a “Direction Estimation” method (see Non-Patent Document 4) (also referred to as WSF (Weighted Subspace Fitting) method (see Non-Patent Document 5)) is conceivable. Plapous et al. Showed that the MUSIC method can be applied to an electronically controlled waveguide array antenna device assuming that the transmission signal is not time-dependent (see Non-Patent Document 6). Although the assumption of a transmission signal having no time dependency is very limited, this concept is extended to a transmission waveform signal having a preamble signal that repeats periodically (see Non-Patent Document 7). In reality, it is difficult to control the reactance value with high accuracy, but the problem can be solved by calibrating the equivalent weight matrix, and the high resolution azimuth angle can be estimated by the MUSIC method. It has been demonstrated by experiments (see Non-Patent Document 8). Although the MUSIC method itself cannot separate and detect coherent waves, Hirata et al. Perform SSP (Spatial Smoothing Processing) (non-patented) by performing inverse transformation (equivalent element space transformation) using the obtained equivalent weight matrix. (Ref. 9), so that coherent waves can be separated and detected (see Non-Patent Document 10).

JP 2001-24431A. T. Ohira et al., “Electrically steerable passive array radiator antennas for low-cost analog adaptive beamforming”, IEEE International Conference Phased Array System Technology, pp. 101-104, Dana Point, California, U.S.A., May 2000. R. O. Schmidt, "Multiple emitter location and signal parameter estimation", IEEE Transactions on Antennas and Propagation, Vol.AP-34, No.3, pp.276-280, Mar.1986 R. Roy et al., “ESPRIT-Estimation of signal parameters via rotational invariance techniques”, IEEE Transactions on Acoustic Speech and Signal Processing, Vol. ASSP-37, No. 7, pp. 984-995, July 1989. P. Stoica et al., "Novel eigenanalysis method for direction estimation", IEE Proceeding, Vol.137, Pt.F, No.1, pp.19-26, February 1990. H. Krim et al., "Two decades of array signal processing research", IEEE Signal Processing Magazine, Vol.13, No.4, pp.67-94, July 1996. C. Plapous et al., “Reactance domain MUSIC method using an electronically controlled waveguide array antenna device”, IEICE Technical Report, IEICE, Vol. RCS2002-147, pp. 1-8, August 2002. E. Taillefer et al., “Reactance-domain MUSIC for ESPAR antennas (Experiment)”, Proceedings of Wireless Communication Network Conference, WCNC2003, pp.98-102, New Orleans, U.S.A., March 2003. Akifumi Hirata et al., “High-resolution direction-of-arrival estimation of electronically controlled waveguide array antenna device calibrated with equivalent weight matrix”, IEICE Technical Report, IEICE, Vol. A. P2002-226, pp. 1-8, March 2003. T. J. Shan et al., “On spatial smoothing for direction-of-arrival estimation of coherent waves”, IEEE Transactions on Acoustic Speech and Signal Processing, Vol.ASSP-33, No.4, pp.806-811, August1985. Akifumi Hirata et al., “` Coherent 2 direction-of-arrival estimation experiment by reactance domain MUSIC method using electronically controlled waveguide array antenna device ", IEICE Technical Report, IEICE, Vol. A. P2003-24, pp. 59-64, March 2003. Tatsuya Nakazawa et al., “Multipath parameter estimation using 3D MODE method”, IEICE Technical Report, IEICE, Vol. A. P 2001-88, pp. 101-107, October 2001. M. P. Clark et al., “Two-dimensional model analysis based on maximum likelihood”, IEEE Transactions on Signal Processing, Vol.42, No.6, pp.1443-1451, June 1994. Hiroki Yamada et al., “Comparison study on mutual calibration of array antenna elements and their accuracy”, IEICE technical report, IEICE, Vol. A. P2002-218, pp. 179-186, March 2003. C. M. S. See, "Sensor array calibration in the presence of mutual coupling and unknown sensor gains and phases", Electronics Letters, Vol. 30, No. 3, pp.373-375, March 1994.

  The above studies have been made in a circular 7-element monopole electronically controlled waveguide array antenna apparatus having an excitation element at the center, and DOA estimation is also one-dimensional only in the azimuth direction. In addition, the conventional technique has a problem that the accuracy is still low when the arrival direction is estimated by identifying two incoherent waves.

  The object of the present invention is to solve the above problems, to estimate the direction of arrival of radio waves in two dimensions, and to estimate the direction of arrival of radio waves with higher accuracy compared to the prior art without distinguishing between coherent and incoherent. An object of the present invention is to provide a radio wave arrival direction detection method and apparatus.

The radio wave arrival direction detecting method according to the first aspect of the present invention includes an excitation element for receiving a radio signal and at least three non-excitation elements arranged in a lattice shape, and a variable element connected to each of the non-excitation elements. A radio wave using a square array antenna that includes a reactance element and changes a directivity by operating each of the non-excitation elements as a director or a reflector by changing a reactance value of each of the variable reactance elements. A direction of arrival detection method,
Receiving each radio signal by the array antenna using a plurality of different radiation patterns respectively set by a plurality of sets of reactance values of each variable reactance element, detecting each received signal received, and detecting the received A correlation matrix R _y indicating a correlation between the plurality of received signals is calculated, and eigenvalues and eigenvectors for the received signals for each azimuth are calculated using the eigenvalue decomposition method based on the calculated correlation matrix R _y. , Using an eigenvector corresponding to the eigenvalue of the maximum value for each direction of each azimuth angle, an equivalent weight matrix consisting of equivalent vectors representing weights for each direction vector of the radiation pattern by each variable reactance element of the array antenna Calibrating, and
When a plurality of sets of reactance values of the different variable reactance elements are set, the received signals received by the array antenna are detected, and a correlation matrix R _y representing the correlation between the received signals is calculated. , each correlation matrix R _y, which is calculated above to calculate the eigenvalues and eigenvectors of the above correlation matrix R _y with respect to eigenvalue decomposition to the received signal, the estimated value sigma ² of the calculated correlation matrix R _y and noise power Calculating a correlation matrix R _s converted into a predetermined element space in which inter-element coupling is canceled, and calculating eigenvalues and eigenvectors of the calculated correlation matrix R _s using an eigenvalue decomposition method;
Based on the eigenvalues and eigenvectors of the calculated correlation matrix R _s , the angle of the radio wave arrival direction is estimated by solving a polynomial rooted in a parameter corresponding to the one-dimensional or two-dimensional radio wave arrival direction using the MODE method. And calculating.

In the radio wave arrival direction detection method, the step of estimating and calculating the angle of the radio wave arrival direction may include a matrix B (B ^H) extending a noise subspace which is a space orthogonal to the signal subspace Es composed of eigenvalues of the signal. B) It is characterized in that the angle of the radio wave arrival direction is estimated and calculated by solving a one-way polynomial having a relationship between the matrix B in ⁻¹ B ^H and the arrival direction.

Further, in the radio wave arrival direction detection method, the step of estimating and calculating the angle of the radio wave arrival direction includes a matrix B (B ^H) that forms a noise subspace which is a space orthogonal to the signal subspace Es composed of eigenvalues of the signal. B) Matrix Wn obtained by performing Cholesky decomposition on the normalization matrix Wn for eliminating the bias of the parameter matrix B that is a function of each coefficient vector in the binary polynomial having a relationship with the arrival direction and the matrix B in ⁻¹ B ^{H When 1/2} is defined and Wn = (B ^H B) ⁻¹ , a matrix B (B ^H B) ⁻¹ that spans a noise subspace that is orthogonal to the signal subspace Es composed of eigenvalues of the signal as the likelihood function including B ^H is substantially minimized, calculated by iterative calculation of the coefficient vector of the two polynomials, two angles of a radio wave arrival direction by solving a binary polynomial And calculating estimates.

According to a second aspect of the present invention, there is provided a radio wave direction-of-arrival detection device, wherein an excitation element for receiving a radio signal and at least three non-excitation elements are arranged in a lattice shape, and each variable element is connected to each of the non-excitation elements. A radio wave using a square array antenna that includes a reactance element and changes a directivity by operating each of the non-excitation elements as a director or a reflector by changing a reactance value of each of the variable reactance elements. A direction-of-arrival detection device,
Receiving each radio signal by the array antenna using a plurality of different radiation patterns respectively set by a plurality of sets of reactance values of each variable reactance element, detecting each received signal received, and detecting the received A correlation matrix R _y indicating a correlation between the plurality of received signals is calculated, and eigenvalues and eigenvectors for the received signals for each azimuth are calculated using the eigenvalue decomposition method based on the calculated correlation matrix R _y. , Using an eigenvector corresponding to the eigenvalue of the maximum value for each direction of each azimuth angle, an equivalent weight matrix consisting of equivalent vectors representing weights for each direction vector of the radiation pattern by each variable reactance element of the array antenna Means to calibrate;
When a plurality of sets of reactance values of the different variable reactance elements are set, the received signals received by the array antenna are detected, and a correlation matrix R _y representing the correlation between the received signals is calculated. Eigenvalue decomposition of each calculated correlation matrix R _y to calculate eigenvalues and eigenvectors of each correlation matrix R _y with respect to the received signal, and the calculated correlation matrix R _y and noise power estimate σ ² are obtained. means for calculating and used to calculate the correlation matrix R _s, which is converted to a predetermined element space cancels the inter element coupling, the eigenvalue decomposition method eigenvalues and eigenvectors of the calculated correlation matrix R _s based,
Based on the eigenvalues and eigenvectors of the calculated correlation matrix R _s , the angle of the radio wave arrival direction is estimated by solving a polynomial rooted in a parameter corresponding to the one-dimensional or two-dimensional radio wave arrival direction using the MODE method. And calculating means.

Further, in the radio wave arrival direction detecting device, the means for estimating and calculating the angle of the radio wave arrival direction is a matrix B (B ^H) that forms a noise subspace that is a space orthogonal to the signal subspace Es composed of the eigenvalues of the signal. B) It is characterized in that the angle of the radio wave arrival direction is estimated and calculated by solving a one-way polynomial having a relationship between the matrix B in ⁻¹ B ^H and the arrival direction.

Further, in the radio wave arrival direction detecting device, the means for estimating and calculating the angle of the radio wave arrival direction is a matrix B (B ^H) that forms a noise subspace that is orthogonal to the signal subspace Es composed of eigenvalues of the signal. B) Matrix Wn obtained by performing Cholesky decomposition on the normalization matrix Wn for eliminating the bias of the parameter matrix B that is a function of each coefficient vector in the binary polynomial having a relationship with the arrival direction and the matrix B in ⁻¹ B ^{H When 1/2} is defined and Wn = (B ^H B) ⁻¹ , a matrix B (B ^H B) ⁻¹ that spans a noise subspace that is orthogonal to the signal subspace Es composed of eigenvalues of the signal as the likelihood function including B ^H is substantially minimized, calculated by iterative calculation of the coefficient vector of the two polynomials, estimated two angles DOA by solving a binary polynomial And calculating by.

  Therefore, according to the radio wave arrival direction detection method and apparatus according to the present invention, the radio wave arrival direction can be estimated in two dimensions, and the radio wave arrival direction can be estimated with higher accuracy compared to the prior art without distinguishing between coherent and incoherent. It can be carried out.

  Hereinafter, embodiments according to the present invention will be described with reference to the drawings. In addition, the same code | symbol is attached | subjected about the same component.

  The inventors of the present invention pay attention to the fact that the circular electronically controlled waveguide array antenna device disclosed in Patent Document 1 or the like is a planar array antenna, so that in principle two-dimensional estimation is also possible. For the purpose of estimating the direction of arrival of two-dimensional coherent waves, we have found that various algorithms can be applied by adopting a square array of electronically controlled waveguide array antenna devices. In the present embodiment, a MODE method, which is a maximum likelihood estimation method capable of directly separating coherent waves, is employed. As an example, a nine-element (3 × 3) monopole rectangular electronically controlled waveguide using a central antenna element as an excitation element A two-dimensional DOA estimation method using an array antenna apparatus will be described. Since the antenna element is a monopole, estimation of the zenith (elevation angle = 90 degrees) direction is essentially unsuitable, but multipath wave separation estimation is possible without using SSP. Here, analysis by the moment method is performed, and the basic characteristics of the two-dimensional MODE method using the electronically controlled waveguide array antenna device are clarified.

  FIG. 1 is a block diagram showing a configuration of a radio wave arrival direction detecting apparatus according to an embodiment of the present invention using an array antenna apparatus 100 which is a nine-element rectangular electronically controlled waveguide array antenna apparatus. It is sectional drawing which shows the detailed structure of the array antenna apparatus 100 of FIG.

  In FIG. 1, an array antenna apparatus 100 is composed of nine antenna elements provided in a grid pattern on a ground conductor 11 at positions parallel to an xy coordinate system orthogonal in 3 rows and 3 columns. The nine antenna elements are preferably provided with respect to the x-axis and the y-axis at a distance Δx in the x-axis direction and a distance Δy in the y-axis direction. Of these nine antenna elements, the central antenna element arranged at the origin O of the xy coordinate system is used as an excitation element A5, and the surrounding antenna elements are used as non-excitation elements A1 to A9 (excluding A5). The lengths of the excitation element A5 and the non-excitation elements A1 to A9 (excluding A5) are configured to be, for example, about λ / 4 (where λ is the wavelength of the desired wave). The ground conductor 11 has a rectangular shape having a length in the x-axis direction of 4Δx or more and a length in the y-axis direction of 4Δy or more, and a substantially electrically infinite size. The feeding point of the excitation element A5 is connected to the low noise amplifier (LNA) 1 of the radio receiver 4 via the coaxial cable 9, and the non-excitation elements A1 to A9 (except A5) are respectively variable reactance elements 12-. 1 to 12-9 (excluding 12-5), the reactance values of these variable reactance elements 12-1 to 12-9 (excluding 12-5) are determined by reactance value signals from the reactance value controller 10. Is set.

  In the longitudinal cross-sectional view of the array antenna device 100 of FIG. 2, the excitation element A5 is electrically insulated from the ground conductor 11, and the non-excitation elements A1 to A9 (except A5) are variable reactance elements 12-1 to 12-9 (excluding 12-5) is grounded to the ground conductor 11 at a high frequency. The variable reactance elements 12-1 to 12-9 (excluding 12-5) are, for example, variable capacitance diodes whose reactance values change when a control voltage (or a bias voltage) is applied. Is applied via a reactance value signal from the reactance value controller 10. The reactance value controller 10 is a controller based on a digital signal processor, and refers to digital voltage values set in advance in the reactance value table memory 13, and includes eight built-in D / A converters (not shown). .) Is used to convert the digital voltage value into an analog control voltage value, and this control voltage value is used as a reactance value signal to each of the variable reactance elements 12-1 to 12-9 (excluding 12-5) of the array antenna apparatus 100. )), Corresponding directional beam patterns are formed on the array antenna apparatus 100.

  The operation of the variable reactance elements 12-1 to 12-9 (excluding 12-5) will be described. For example, the longitudinal lengths of the excitation element A5 and the non-excitation elements A1 to A9 (excluding A5) are substantially equal. For example, when the variable reactance element 12-1 has inductance (L property), the variable reactance element 12-1 becomes an extension coil, and the electrical length of the non-excitation element A1 is compared with the excitation element A5. It becomes long and works as a reflector. On the other hand, for example, when the variable reactance element 12-1 has capacitance (C), the variable reactance element 12-1 becomes a shortening capacitor, and the electrical length of the non-excitation element A1 becomes shorter than that of the excitation element A5. Acts as a director. Further, the non-excitation elements A2 to A9 (excluding A5) connected to the other variable reactance elements 12-2 to 12-9 (excluding 12-5) operate similarly. Accordingly, in the array antenna apparatus 100 of FIG. 1, the reactance values of the variable reactance elements 12-1 to 12-9 (excluding 12-5) connected to the non-excitation elements A1 to A9 (excluding A5) are set. By changing, the plane directivity characteristic of the array antenna apparatus 100 can be changed.

In the array antenna control apparatus of FIG. 1, the array antenna apparatus 100 includes an azimuth angle φ defined by a clockwise angle from the x axis on the xy plane and a z-axis direction, as shown in the upper left of FIG. The radio signal is received in the direction of elevation θ from the zenith direction (hereinafter referred to as the zenith elevation angle) θ, and the received signal, which is the received radio signal, is output from the coaxial cable 9 connected to the excitation element A5. Is done. The output received signal is input to the down converter 2 via the low noise amplifier 1 of the wireless receiver 4, and the down converter 2 frequency-converts the input received signal into an intermediate frequency signal of a predetermined intermediate frequency, Output to the A / D converter 3. The A / D converter 3 converts the input analog intermediate frequency signal into a digital intermediate frequency signal, and then outputs the digital intermediate frequency signal to the radio wave arrival direction detection computer 20. Furthermore, the radio wave arrival direction detection computer 20 calculates a correlation matrix R _y (see Equation 4 described later) of the intermediate frequency signal based on the input intermediate frequency signal, and performs the two-dimensional MODE method according to the present invention. The arrival angle of the received radio signal is calculated, and the result is output to the CRT display 21 and displayed. Here, in the present embodiment, the radio wave arrival direction detection computer 20 performs the eigenvalue decomposition process (step S2) after executing the process of calibrating and calculating the equivalent weight matrix (step S1) as shown in FIG. Then, the arrival angle estimation process (step S3) is executed to estimate and calculate the arrival directions of the zenith elevation angle θ and the azimuth angle φ, and display them on the CRT display 21.

  When executing the processing of step S1, a rotation mechanism 30 is provided that mechanically rotates the array antenna apparatus 100 about the excitation element A5 based on a control signal from the radio wave arrival direction detection computer 20. ing.

Next, the formulation of the problem in this embodiment will be described below. In the array antenna apparatus 100 of FIG. 1, consider a case where d incident waves are respectively coming from (θ _k , φ _k ) directions (k = 1, 2,..., D). The complex amplitude of each incident wave is s _k (t). If the received signals at the antenna elements A1 to A9 can be observed, the received signal r (x _i , y _j , t) of the element located at the coordinates (x _i , y _j ) in the xy coordinate system is It is expressed as In this specification, the number number of the black brackets in which the mathematical formula is imaged and the formula number of the square brackets in which the mathematical formula is input are used in combination. The formula number is assigned to the last part of the formula using the format of “formula (1)” as the formula number (note that there are formulas that are not given for simplification).

Here, f _c is the carrier frequency of the radio signal, c is the speed of light. In the array antenna apparatus 100 according to the present embodiment, as shown in FIG. 1, the received signal r (x ₂ , y ₂ ) output from the excitation element A5 that is one antenna element located at the center is observed, and the others The variable reactance elements 12-1 to 12-9 (excluding 12-5) are connected to the non-excitation elements A1 to A9 (excluding A5). At this time, the received signal y _m (t) by the array antenna apparatus 100 is expressed by the following equation.

[Formula 1]
y _m (t) = w _m ^T r (t) + n _m (t) (2)

  However, r (t) is a vector represented by the following equation.

[Formula 2]
r (t)
= [R (x ₁ , y ₁ , t), r (x ₁ , y ₂ , t),
r (x ₁ , y ₃ , t), ...,
r (x ₃ , y ₁ , t), r (x ₃ , y ₂ , t),
r (x ₃ , y ₃ , t)] ^T
(3)

Here, T is a symbol representing transposition of a matrix. w _m is an equivalent weight vector determined by the reactance value set of the non-excited element, and is expressed by the following equation.

[Formula 3]
w _m
= 2Re [Z ₀ ]
(Z + diag [jx _m1 ,..., Jx _m4 , Z ₀ , jx _m6 ,..., Jx _m9 ]) ⁻¹ u ₀
(4)

Here, Re [Z ₀ ] is a real part of the internal impedance Z ₀ of the wireless receiver 4, and Z is an impedance matrix relating to mutual coupling between elements of the array antenna apparatus 100. U ₀ is a unit vector defined by the following equation. Furthermore, diag [•] means a diagonal matrix. N _m (t) is white Gaussian noise generated in the receiver.

[Formula 4]
u ₀ = [0, ..., 0,1,0, ..., 0] ^T

  Next, the equivalent element space conversion used in this embodiment will be described in detail below. The two-dimensional MODE method applied in the present embodiment is also one of the super-resolution methods, and is originally a high-resolution arrival direction estimation method using amplitude and phase information of received signals of each element. Therefore, the array antenna device 100 in which the reception data of each element cannot be obtained cannot be applied directly. The present inventors add a preamble signal that repeatedly transmits the same waveform for each reactance value set to the transmission signal, and convert it into element space data in which inter-element coupling is canceled as shown in Expression (1). . Note that equivalent element space conversion is disclosed in Non-Patent Document 10. When the reactance value set switching interval (frame interval) is T and the sampling interval is Δt, the transmission preamble signal is expressed by the following equation.

[Formula 5]
s _k (kT + iΔt) = s _k (lT + iΔt),
k = 1, 2,..., M,
l = 1, 2,..., M,
i = 1, 2,..., n _max
(5)

here,
[Formula 6]
n _max Δt ≦ T
It is.

  M is the number of reactance value sets used. When a received signal obtained by M independent reactance value sets using such a transmission signal is displayed as a vector, the following equation is obtained from equations (1) and (2).

[Formula 7]
y (iΔt)
= [Y ₁ (iΔt), y ₂ (iΔt),..., Y _M (iΔt)] ^T
= WAs (iΔt) + n (6)

  Here, the equivalent weight matrix W and the steering matrix A are expressed by the following equations.

[Formula 8]
A = [a (θ ₁ , φ ₁ ), a (θ ₂ , φ ₂ ),..., A (θ _d , φ _d )]
(7b)

[Formula 9]
a (θ _k , φ _k )
= [Exp (j2πf _c ((x ₁ / c) sin θ _k cos φ _k
+ (Y ₁ / c) sinθ _k sinφ _k )),
exp (j2πf _c ((x ₁ / c) sin θ _k cos φ _k
+ (Y ₂ / c) sinθ _k sinφ _k )), ..., ...,
exp (j2πf _c ((x ₃ / c) sin θ _k cos φ _k
+ (Y ₃ / c) sinθ _k sinφ _k ))] ^T
(7c)

[Formula 10]
s (iΔt)
= [S ₁ (iΔt),..., S _d (iΔt)] ^T
(7d)

From equation (6), if the equivalent weight matrix W is accurately known even in the electronically controlled waveguide array antenna device, a signal in an equivalent element space used in a normal super-resolution array antenna is obtained by the following conversion. A correlation matrix R _S is obtained.

[Formula 11]
R _{S
^{= W -1 (R y -σ 2}} I) (W -1) H
= ASA ^H (8a)

[Formula 12]
R _y = E [yy ^H ] (8b)

[Formula 13]
S = E [ss ^H ] (8c)

The above equations (8a), (8b), and (8c) are equations representing equivalent element space conversion. Here, E [•] is a time average value (or ensemble average value) in a predetermined time period assuming an ergodic property, and a superscript ^H represents Hermitian transpose of the matrix. Σ ² is noise power. If the above-mentioned data is obtained within a time period in which fluctuations in the radio wave environment can be ignored, various signal processing adaptively used in the super-resolution array antenna can be applied by this conversion.

  The reactance value of the reactance value set corresponding to the equivalent weight matrix W is determined by the voltage applied to the variable reactance elements 12-1 to 12-9 (excluding 12-5). Further, the mutual coupling between the antenna elements can be derived by a known moment method or the like. However, if there are variations in the elements such as the variable reactance elements 12-1 to 12-9 (excluding 12-5), the set values are different. Since the super resolution method has a large characteristic deterioration due to an error factor, in such a case, it is necessary to estimate (calibrate) the equivalent weight matrix itself (see Non-Patent Document 10), which will be described in detail later. To do.

  As described above, array antenna device 100 that is an electronically controlled waveguide array antenna device is an array antenna that changes the directivity of an antenna by controlling the reactance of a non-excitation element. That is, the reactance domain reception data obtained by changing the reactance value corresponds to the reception data obtained by the shaped beam, that is, the reception data in the beam space region, from the viewpoint of antenna directivity. That is, Expression (6) is the same shape as the beam space conversion expression of a normal super resolution array.

Next, the relationship between the received signal y (t) and the correlation matrix R _y will be described below. The equivalent weight matrix W is an equivalent matrix that represents the weighting of each direction vector of the radiation pattern by the variable reactance element in the array antenna apparatus 100, and using this, the received signal sequence in vector notation is expressed by the following equation. The

At this time, from the relationship between the correlation matrix and the eigenvector, the correlation matrix R _y between the plurality of sequence signals detected from the plurality of received signals is expressed by the following equation.

Here, λ _i is an eigenvalue, and e _l is the l-th eigenvector (l = 1, 2,..., L) extending the signal subspace. That is, nine eigenvalues and nine eigenvectors can be obtained by eigenvalue decomposition of the correlation matrix _Ry . For example, the MUSIC spectrum of the array antenna apparatus 100 is expressed by the following equation using the equivalent weight matrix W (see Non-Patent Document 10).

である。 here,

It is.

That is, in the MUSIC method, a MUSIC spectrum can be calculated from a matrix E _N made up of noise eigenvectors, and an arrival angle can be calculated based on the MUSIC spectrum. In this embodiment, a modified two-dimensional MODE method is used.

  Next, the calibration process (step S1 in FIG. 3) of the “equivalent weight matrix” of the array antenna apparatus 100 from the signal subspace using the nine directivity patterns including the omni pattern will be described below.

  Each element of the impedance matrix Z is unknown. In order to obtain a sharp MUSIC spectrum and improve the angular resolution, it is necessary to calibrate the equivalent weight matrix W including the impedance matrix Z. In this embodiment, a method for estimating an equivalent weight matrix using a signal eigenvector corresponding to an eigenvalue of a signal using a received signal sequence received with nine directivity patterns as a calibration method is proposed. In the calibration, only one wave is arriving (L = 1), and plane waves arrive sequentially from 24 directions.

Although the specific details of the calibration procedure will be described later, the outline thereof will be described. As shown in FIG. 4, first, the radio wave arrival direction viewed from the array antenna device 100 as the receiving antenna is fixed at 0 ° (step In S12, θ = 0 °). Next, the reactance values of the variable reactance elements 12-1 to 12-9 (excluding 12-5) are set to 9 types (m = 0, 1,..., 8) as shown in Table 1, and directivity is set. The pattern is rotated to obtain a received signal sequence y _m (t) (steps S13 to S16). t represents a sampling time, and sampling is performed once per symbol. A signal of P samples (= P symbols) is received for each directivity pattern. The received signal sequence is expressed as a vector as in Equation 3 (step S18), and after eigenvalue decomposition is performed on the correlation matrix _Ry in Equation 4 (step S19), a signal eigenvector corresponding to the eigenvalue (maximum eigenvalue) of the signal is obtained. e ₁ ⁽¹⁾ is acquired (step S20).

  A reactance value set used in the present embodiment is shown in Table 1. In Table 1, −90Ω is the minimum reactance value of the variable reactance element 12, and −4.77Ω is the maximum reactance value of the variable reactance element 12. Since the radiation pattern of m = 0 is a square array, it is a pattern having periodicity every 90 degrees of azimuth, and m = 1 to 8 are sector patterns having main beams at azimuth angles of 45 degrees. is there.

Next, the radio wave arrival direction is fixed at 15 ° (step S12), and the signal eigenvector e ₁ ⁽²⁾ is acquired by the same procedure (steps S13 to S20). Thereafter, when the direction of arrival of radio waves is set in 24 directions at intervals of 0 ° to 15 ° and the same procedure is repeated, 24 signal eigenvectors are obtained (repetitive flow of S12-S22). Since the radio wave arrival direction is known and the direction vector of the direction is also known, the following equation is established.

Here, the eigenvector [e ₁ ⁽¹⁾ e ₁ ⁽²⁾ ... E ₁ ⁽²⁴⁾ ] corresponding to the eigenvalue of the maximum value at each azimuth calculated in the above calibration procedure is replaced with the matrix E _s. When the steering matrix [a (φ ₁ ) a (φ ₂ )... A (φ ₂₄ )] composed of steering vectors for each azimuth is replaced with the matrix A, the equivalent weight matrix W is expressed by the following equation (Non-Patent Document) 14).

  As is apparent from the above equation 8, the equivalent weight matrix W is obtained by converting the eigenvector matrix Es consisting of the maximum eigenvalue at each azimuth calculated in the above calibration procedure and the steering consisting of the steering vector for each azimuth. Calibration is performed using the matrix A.

Next, conversion to an element space using an array set will be described below. The equivalent weight matrix W in Equation 3 can be obtained with high accuracy by calibration processing using a signal subspace. Subsequent W represents an equivalent weight matrix after the calibration process. The equivalent weight matrix W includes inter-element coupling between antenna elements, and the MODE method cannot be applied with the correlation matrix R _{y as} it is. Therefore, conversion to an element space (element space) in which the coupling between elements is canceled by an inverse matrix of the equivalent weight matrix W is performed using the following expression.

[Formula 14]
R _s = W ⁻¹ (R _y −σ ² ) (W ⁻¹ ) ^H (8a)

Here, eigenvalues and eigenvectors can be calculated by eigenvalue decomposition of the correlation matrix _Ry, and the eigenvalues of the L signals thus obtained are represented by λ _i (i = 1, 2,..., L). Since the eigenvalues of other noises can be expressed by λ _i (i = L + 1, L + 2,..., 9), the noise power estimation value obtained by averaging the (9−L) noise eigenvalues The square value σ ² is obtained by the following equation.

  Next, the two-dimensional MODE method according to this embodiment will be described below. Various super resolution methods can be applied by equivalent element space conversion. In particular, the square array shown in FIG. 1 does not depend on the array shape, such as the SAGE (Space Alternating Generalized Expectation Maximization Algorithm) method or the EM (Expectation Maximization Algorithm) method. Numerous algorithms such as law can be applied.

  Unlike the MUSIC method and ESPRIT method, the MODE method is a method capable of separating and detecting coherent waves without applying a correlation suppression method such as SSP. When SSP is applied, the effective array aperture is reduced due to sub-arraying, which results in degradation of estimation accuracy. Such deterioration does not exist in the MODE method that does not require subarraying (see Non-Patent Document 11). The extension of the MODE method to two dimensions uses the formulation of the IQML (Interactive Quadratic Maximum Likelihood) method reported by Non-Patent Document 12. The outline of the two-dimensional MODE method is shown below. When the equivalent element spatial correlation matrix obtained by Expression (8a) is expanded by eigenvalue, the following expression is obtained.

[Formula 15]
_{R S = E S A S E} S H (9a)
[Formula 16]
E _S = [e ₁ ,..., E _{d ′} ] (9b)
[Formula 17]
Λ _S = diag [λ ₁ ,..., Λ _{d ′} ] (9c)

Here, λ _{d ′} is the main eigenvalue of the matrix R _S , d ′ = d if all incident waves are incoherent, and d ′ <d if coherent waves exist. Note that the noise component has already been removed from the matrix _RS . Orthogonal space signal subspace E _S obtained in MODE method, i.e. by estimating the noise subspace, to determine the direction of arrival of the incident wave. This likelihood function is given by the following equation, and in the present embodiment, a matrix B that minimizes the likelihood function is calculated.

[Formula 18]
F _w
= Tr [B (B ^H B) ^-1 B ^H R _S ]
= Tr [B (B ^H B) ⁻¹ B ^H E _S Λ _S E _S ^H ] (10)

Here, Tr [•] is a trace or diagonal sum of a matrix of arguments. Also,
[Formula 19]
B (B ^H B) ^-1 B ^H
Is a matrix that creates a noise subspace. In one-dimensional DOA estimation with a linear array antenna in which antenna elements are arranged on a straight line on the x axis in FIG. 1, the following relationship is established between this matrix B and the azimuth angle φ _k. .

[Property] Relationship between matrix B and azimuth angle φ _k (linear array one-dimensional estimation):

[Formula 20]
z _k = exp (j2π (fΔx / c) cosφ _k ),
(K = 1, 2,..., D)

  Consider a polynomial of the following formula rooted at the above formula.

  Based on the coefficients of the polynomial at this time, a coefficient vector b and a coefficient matrix B are defined as follows:

[Formula 21]
b = [b ₀ , b ₁ ,..., b _d ] ^T (12a)

  At this time, the relationship of the following equation is established between the matrix B and the mode vector A.

[Formula 22]
B ^H A = 0 (13)

From this relationship, it is understood that the direction of arrival can be estimated by adopting the form of equation (12a) as the form of the noise subspace and estimating the coefficient vector b. In order to extend this property to two dimensions, two polynomials relating to the incoming zenith elevation angle θ _k and the incoming azimuth angle φ _k of the incident wave are required. It is known that there exists a polynomial having the following relationship.

[Property 2] Relationship between coefficients of polynomial and (θ _k , φ _k ) (square array two-dimensional estimation):
Define the following two polynomials:

[Formula 23]
U (z) = u ₀ z ^d + u ₁ z ^d−1 +... + U _d−1 z + u _d (14a)
[Formula 24]
^{_{V (z) = v 0 z}} d-1 + v 1 z d-2 + ... + v d-2 z + v d-1 (14b)

  Here, the reason why the number of terms differs between the polynomial U (z) and the polynomial V (z) is that the MODE method uses the property, and the polynomial U (z) and the polynomial V (Z) is not a vector or matrix but a scalar quantity. Here, the definition is as follows.

[Formula 25]
u = [u ₀ ,..., u _d ] ^T
[Formula 26]
v = [v ₀ ,..., v _d−1 ] ^T
[Formula 27]
μ _k ⁽¹⁾ = sin θ _k cos φ _k
[Formula 28]
μ _k ⁽²⁾ = sin θ _k sin φ _k

When defined as described above, there exists a mapping ψ that associates a coefficient vector set (u, v) and an azimuth coefficient set (μ _k ⁽²⁾ , μ _k ⁽¹⁾ ) as in the following equation.

[Formula 29]
(U, v)
= Ψ ((exp (j2π (fΔy / c) μ _k ⁽²⁾ ),
exp (j2π (fΔx / c) μ _k ⁽¹⁾ )))
(15)

  At this time, Expression (14a) and Expression (14b) satisfy the relationship of the following expression.

[Formula 30]
U (exp (j2π (fΔy / c) μ _k ⁽²⁾ )) = 0,
k = 1, 2,..., d (16a)

[Formula 31]
V (exp (j2π (fΔy / c) μ _k ⁽²⁾ ))
= Exp (j2π (fΔx / c) μ _k ⁽¹⁾ ),
k = 1, 2,..., d (16b)

  Here, the matrix U is a (Ly−d) × Ly matrix. Due to this property, the two-dimensional MODE method makes it possible to estimate a set of θ and φ parameters. Finding coefficient vectors u and v of such a polynomial is the next problem. First, equation (10) can be modified as the following equation.

[Formula 32]
_{F w (u, v) =} ‖Wn 1/2 B H E S Λ 1/2 ‖ ² (17a)

[Formula 33]
Wn = (B ^H B) ⁻¹ (17b)

Here, the matrix Wn ^1/2 is a matrix after the Cholesky decomposition of the normalization matrix W, and is a normalization matrix for eliminating the bias of the matrix B. The matrix B is a parameter matrix that is a function of the coefficient vectors u and v. The matrix Λ ^1/2 is represented by the diagonal matrix diag [√ (λ ₁ ), √ (λ ₂ ),..., √ (λ _d )] (when d ′ = d) using the equation (9c). Is done. Now, when the Kronecker operator is introduced, the mode vector is expressed by the following equation.

[Formula 34]
a (θ _k , φ _k ) = a (μ _k ⁽¹⁾ , μ _k ⁽²⁾ )

  Here, when the matrix U is constructed based on the above [Property 1] by paying attention to the coefficient vector u, the following equation is established.

[Formula 35]
Ua (μ _k ⁽²⁾ ) = 0 (18)

  Therefore, the relationship of the following equation is required.

Here, I _i represents an i × i unit matrix. Similarly, if attention is paid to the coefficient vector v and the matrix V is defined in the same manner as [Property 1], the following equation is obtained from [Property 2].

[Formula 36]
Va (μ _k ⁽²⁾ )
= Exp (j2π (fΔx / c) μ _k ⁽¹⁾ ) Iha (μ _k ⁽²⁾ )
(20a)

[Formula 37]
Ih = [I _{Ly-d + 1} | 0,... 0]
(20b)

Here, Ih is (L _y −d + 1) × L _y matrix. [Formula 38] on both sides of the above formula
exp (j2π (ifΔx / c) μ _k ⁽¹⁾ )
i = 1, 2,..., L _x −2
The following formula is obtained by multiplying and arranging.

は（Ｌ_ｘ×Ｌ_ｙ）×１のベクトルである。また、Ｖは（Ｌ_ｙ−ｄ＋１）×Ｌ_ｙの行列である。式（１９）及び式（２１）の各右辺は信号部分空間に対応し、この両式を積み重ねても、その直交関係は成立する。それを次式のごとく２次元ＭＯＤＥ法の行列Ｂとする。 Here, a (μ _k ⁽²⁾ ) is a vector of L _y × 1, and a (μ _k ⁽¹⁾ ) is a vector of L _x × 1. Therefore,

Is a vector of (L _x × L _y ) × 1. V is a matrix of (L _y −d + 1) × L _y . Each right side of the equations (19) and (21) corresponds to the signal subspace, and even if these equations are stacked, the orthogonal relationship is established. Let it be a matrix B of the two-dimensional MODE method as shown in the following equation.

  The denominator on the right side of the above equation is a matrix of {(Lx−1) × (Ly−d + 1)} × (Lx × Ly), and d is the number d of incident waves. The coefficient vectors u and v may be determined so that the likelihood function of Expression (17a) is minimized with respect to this matrix B. If such coefficient vectors u and v are obtained, it is possible to estimate a two-dimensional DOA as a root of a polynomial from the above [Property 2]. Now, in the equation (22), the coefficient vectors u and v are incorporated in a complicated form, but with a slight modification, it can be reduced to simultaneous equations relating to the coefficient vectors u and v as in the following equations.

Here, the above equation can be derived as follows. B ^H E _S Λ ^{1/2 on} the right side of the equation (17a) is given by the following equation.

  When the above equation 17 is used, it can be transformed as the following equation, and equation (23) can be derived.

For the structure of the matrix G _i , refer to the appendix attached at the end of the specification. The two-dimensional direction of arrival can be estimated from the relationship between the roots of the polynomial by the vector f obtained by this equation, that is, the coefficient vectors u and v. However, the above equation includes a normalization matrix Wn ^1/2 for normalizing the noise subspace by the matrix B. Actually, since the normalization matrix Wn ^1/2 is unknown, it is usually necessary to perform iterative estimation in which the initial value is a unit matrix, the normalization matrix Wn ^1/2 is constructed from the obtained estimation result, and the estimation is repeated. Become. However, the matrix W ^1/2 is a normalization matrix for eliminating the bias of the matrix B. In general,
[Formula 39]
Wn ^1/2 = I
Good estimation results are obtained even in the first estimation result, and convergence is achieved by several iterations.

Here, the azimuth angle coefficients μ _k ⁽²⁾ and μ _k ⁽¹⁾ are formulated to be estimated in this order, but the azimuth coefficient μ _k ⁽¹⁾ and μ _k ⁽²⁾ are changed by changing the order of the data vectors. It is also possible to define the coefficients of the polynomial so that they are estimated in this order. In reality, there may be cases where the same zenith elevation angle θ _k or azimuth angle φ _k is present, and therefore, a device for merging two estimation results having different estimation orders is required.

  FIG. 3 is a flowchart showing a radio wave arrival direction estimation process which is a main routine executed by the radio wave arrival direction detection computer 20 of the radio wave arrival direction detection apparatus of FIG. In step S1 in FIG. 3, the process of calibrating and calculating the equivalent weight matrix in FIG. 4 is executed, in step S2, the eigenvalue decomposition process in FIG. 5 is executed, and in step S3, the arrival angle estimation process in FIG. And the radio wave arrival direction estimation process ends.

  FIG. 4 is a flowchart showing processing (step S1) for calibrating and calculating the equivalent weight matrix which is a subroutine of FIG. The reactance value table memory 13 stores, for example, nine reactance value sets (m = 0, 1, 2,..., 8) shown in Table 1 in order to sequentially set the radiation patterns. . However, this is an example, and may be a plurality of different reactance value sets including at least one set of omni patterns and a plurality of sets of sector pattern reactance values. Alternatively, it may be a plurality of different reactance value sets including a reactance value set of a plurality of sets of sector patterns that do not include an omni pattern.

In step S11 of FIG. 4, the radio wave arrival direction setting parameter n is initialized to 1, and in step S12, the array antenna apparatus 100 is mechanically rotated using the rotation mechanism 30 and transmitted radio signal. Is set so that the incoming azimuth angle φ = 15 × (n−1) [degrees]. Next, in step S13, the radiation pattern parameter m is initialized to 0. In step S14, the reactance value controller 10 is controlled to read out the mth reactance value set from the reactance value table memory 13, and each variable of the array antenna apparatus 100 is changed. The reactance elements 12-1 to 12-9 (except 12-5) are set. In step S15, the received signal y _m (t) is received and stored in the temporary storage memory in the radio wave arrival direction detection computer 20. In step S16, it is determined whether or not the radiation pattern parameter m ≧ 8. If NO, the radiation pattern parameter m is incremented by 1 in step S17, and the process returns to step S14. On the other hand, if YES in step S16, the process proceeds to step S18.

Next, the nine received signals y _m (t) stored in the temporary storage memory in step S18 are stored in the temporary storage memory in the radio wave arrival direction detection computer 20 as received signal vectors as shown in Equation 3, and in step S19. The correlation matrix R _y is calculated using Equation 4 based on the received signal vector, and a plurality of eigenvalues and a plurality of eigenvectors for the received signal are calculated using the eigenvalue decomposition method. Further, in step S20, an eigenvector corresponding to the eigenvalue (maximum eigenvalue) of the signal among a plurality of calculated eigenvectors is set to e ₁ ^(n), and whether or not the radio wave arrival direction setting parameter n ≧ 24 is determined in step S21. When NO is determined, the process proceeds to step S22, the radio wave arrival direction setting parameter n is incremented by 1, and the process returns to step S12. On the other hand, if “YES” in the step S21, the process proceeds to a step S23, where the matrix E _S composed of the obtained signal eigenvectors and the steering matrix A composed of the steering vectors of the respective radiation patterns are used. Is used to estimate and calculate the calibrated equivalent weight matrix W and return to the original main routine.

  FIG. 5 is a flowchart showing eigenvalue decomposition processing (step S2) which is a subroutine of FIG.

In step S31 of FIG. 5, the radiation pattern parameter m is initialized to 0. In step S32, the mth reactance value set is read from the reactance value table memory 13, and each variable reactance element 12-1 to 12-9 of the array antenna apparatus 100 is read. (Except 12-5) Set to 8. At this time, the reception signal y _m (t) is received in step S33 and stored in the temporary storage memory in the radio wave arrival direction computer 20, and in step S34, it is determined whether m ≧ 8, and if NO After incrementing the radiation pattern parameter m by 1 in step S35, the process returns to step S32. On the other hand, when YES is determined in the step S34, the nine received signals y _m (t) stored in the temporary storage memory in the step S36 are stored in the temporary storage memory as received signal vectors as shown in Equation 3. Next, in step S37, a correlation matrix R _y is calculated using the equation (8b) based on the received signal vector, and 9 eigenvalues and 9 eigenvectors for the received signal are calculated using the eigenvalue decomposition method, and step S38 is performed. Based on the eigenvalue of noise calculated in step (1), an average value σ ² of noise power averaged using Equation 9 is calculated. Further, in step S39, the correlation matrix R _s converted to the element space is calculated using the equation (8a) based on the correlation matrix R _y and the estimated noise power σ ² , and the eigenvalue decomposition method (equation ( After calculating 9 eigenvalues and 9 eigenvectors for R _s using 9a) to (9c)), the process returns to the original main routine.

  FIG. 6 is a flowchart showing an arrival direction estimation process (step S3) which is a subroutine of FIG.

In step S41 in FIG. 6, the incoming signal number parameter k is initialized to 1, and in step S42, the matrix G _k is calculated using the equations (24), (25a), (25b), and (25c), and in step S43, the parameter Gk is calculated. It is determined whether or not k ≧ signal arrival signal number d. If NO, the parameter k is incremented by 1 in step S44, and the process returns to step S42. On the other hand, if YES in step S43, unit matrix I which is an initial value is set in normalized matrix Wn ^1/2 in step S45, and iteration number parameter loop is initialized to 1 in step S46. Next, in step S47, a vector f (f = [u ₀ ... U _d | v ₀ ... V _d−1 ] ^T ) that minimizes the expression (23) is calculated by a known QR decomposition method, and the expression ( 22), a two-dimensional MODE method matrix B ^H is obtained, and a normalization matrix Wn is calculated by equation (17b). In step S49, it is determined whether the iteration number parameter loop ≧ the preset iteration number parameter loop _th. If the determination is NO, the iteration number parameter loop is incremented by 1 in step S50, and the process returns to step S47. On the other hand, if “YES” in the step S49, the roots of U (z) and V (z) are calculated by using the vector f in the step S51 by using the expression (15) by the expressions (14a) and (14b). Next, in step S52, the following formula [Formula 40] described above is used.
μ _k ⁽¹⁾ = sin θ _k cos φ _k ,
[Formula 41]
μ _k ⁽²⁾ = sin θ _k sin φ _k
From the relationship, the elevation angle from the zenith (zenith elevation angle) θ _k and the azimuth angle φ _k (k = 1, 2,..., D) are estimated and calculated, and displayed on the CRT display 21 to return to the original main routine.

  The inventors of the present invention made a prototype of the radio wave arrival direction detection device according to the present embodiment and performed a simulation thereof, and obtained the following simulation results.

In the following, basic characteristics of the MODE method using the 9-element square array antenna apparatus 100 composed of monopoles are shown by numerical analysis using the moment method. In the simulation, the antenna element length was 3 cm, the element wire radius was 0.5 mm, and the element spacing Δx = Δy = 3 cm. Further, the carrier frequency f _c is 2.45 GHz, the monopole antenna element length approximately lambda / 4 corresponds to a rectangular monopole array antenna in which at lambda / 4 intervals. In the analysis by the moment method, the ground conductor 11 of an infinite ground plane is assumed. In the following analysis, in order to accurately grasp the characteristics of the electronically controlled waveguide array antenna device, a plane wave arrives at the array antenna device 100 of FIG. 1 together with the estimation (that is, calibration) of the equivalent weight matrix W and each simulation data. The received value at the time is obtained by the moment method and used. When a plurality of waves are incident, the transmission power is constant (s _{i in} equation (7d) is not necessarily constant). For simplicity, the number of incoming waves is known and no noise is added.

  Since it is a 9-element electronically controlled waveguide array antenna apparatus, the rank of the reactance matrix W for performing equivalent element space conversion is 9. Therefore, at least nine independent reactance value sets are required. Here, nine reactance value sets shown in Table 1 above were used.

[Numerical calculation results: Estimating arrival direction of one wave in various directions]
FIGS. 7 and 8 are obtained by overwriting the DOA estimation result of one wave incidence. In order to perform equivalent element space conversion, it is necessary to accurately estimate the equivalent weight matrix W at reactance shown in Table 1. FIG. 7 shows 16 azimuth angles φ = 0 °, 30 °,..., 300 ° and φ = 45 °, 135 °, 225 °, 315 ° using a calibration signal with a zenith elevation angle θ = 90 °. It is an estimation result using the equivalent weight matrix W obtained from the calibration data. Although the estimation results of φ are both accurate, it can be seen that the zenith elevation angle θ has a large deviation (bias) as it moves away from the θ = 90 ° direction (horizontal plane direction) used for calibration. In FIG. 8, the zenith elevation angle θ of the calibration signal is 80 °. It can be seen that the estimation result is improved in the region where the zenith elevation angle θ = 80 ° or more. As can be seen from equation (4), the row of the equivalent weight matrix W is a function of mutual coupling between elements. The array antenna apparatus 100 forms a beam using strong mutual coupling between elements. As shown in Non-Patent Document 13, the equivalent circuit model of the mutual coupling matrix between elements is strictly established for all DOAs when the current distribution on the element such as a minute dipole can be regarded as constant. However, when the element length reaches a certain level, the arrival direction dependency appears even in the case of single mode operation. In the electronically controlled waveguide array antenna device handled in this embodiment, the azimuth angle φ direction dependency is small, but it can be seen that the influence of the zenith elevation angle θ direction cannot be ignored. However, as these results show, improvement can be made by appropriately setting the DOA of the calibration signal.

[Numerical calculation result 2: Incoherent two-wave estimation]
9 and 10 show three examples of incoherent two-wave estimation results (data 1, data 2, data 3). Since it is incoherent, the bias tendency of the estimation error is basically similar to the one-wave estimation, and a deviation depending on the θ direction of the calibration wave is seen.

[Numerical calculation result 3: Coherent two-wave estimation]
FIG. 11 shows the coherent two-wave estimation result corresponding to FIG. In the case of a coherent wave, since an estimation is made from one signal subspace in which two waves are combined, an error increase of 2 to 3 ° is recognized also in the azimuth angle φ direction, but they are detected separately without using SSP. FIG. 12 shows an estimation result in which only the calibration signals of the azimuth angles φ = 45 °, 135 °, 225 °, and 315 ° are set to θ = 80 ° in the calibration of FIG. Although the entire data is shifted with respect to the data 2, the data 1 and the data 3 are improved. Although it is difficult to eliminate the deviation in all directions, it can be seen that improvement in characteristics can be expected by optimizing the arrival direction of the calibration signal. In addition, although the reactance value set shown in Table 1 is used here, it is expected that the setting of the reactance value set also has a great influence on the estimation performance.

  As described above, by using the concept of equivalent element space conversion, various array signal processing algorithms can be applied to the array antenna apparatus 100 that is an electronically controlled waveguide array antenna apparatus. In the present embodiment, as an example, a simulation result of the MODE method using the array antenna apparatus 100 which is a nine-element rectangular monopole array antenna is shown. Good results were obtained for DOA estimation in the horizontal plane direction for both coherent and incoherent waves. However, when the elevation angle is large (that is, the zenith elevation angle θ is small), the deviation may increase.

  In the above embodiment, a nine-element rectangular electronically controlled waveguide array antenna device is used as an example. However, the present invention is not limited to this, and at least the non-excitation elements A1, A2, A4 and the excitation element A5. A radio wave arrival direction detecting device can be realized using a rectangular electronically controlled waveguide array antenna device having at least four elements. That is, the number of elements may be an integer of 4 or more.

Appendix: eigenvalues of the signal subspace, the eigenvectors eh _k, when using the eigenvalues lambda _k and eigenvector _{e k} is defined by the following equation, the main part ^B H eh _k of formula (17a) can be modified as: .

Here, the matrices P, Q, and R are matrices defined by the following modifications.

It is a block diagram which shows the structure of the radio wave arrival direction detection apparatus which concerns on embodiment of this invention. It is sectional drawing which shows the detailed structure of the array antenna apparatus 100 of FIG. It is a flowchart which shows the radio wave arrival direction estimation process which is the main routine performed by the radio wave arrival direction detection computer 20 of the radio wave arrival direction detection device of FIG. It is a flowchart which shows the process (step S1) which calibrates and calculates the equivalent weight matrix which is a subroutine of FIG. It is a flowchart which shows the eigenvalue decomposition | disassembly process (step S2) which is a subroutine of FIG. It is a flowchart which shows the arrival direction estimation process (step S3) which is a subroutine of FIG. It is a simulation result of the radio wave arrival direction detection device according to the present embodiment, and includes one wave arrival direction estimation results in various directions (using a calibration signal with a zenith elevation angle θ = 90 degrees; including a set value ○ and an estimated value × .). It is a simulation result of the radio wave arrival direction detection device according to the present embodiment, and includes one wave arrival direction estimation results in various directions (using a calibration signal with a zenith elevation angle θ = 80 degrees; including a set value ○ and an estimated value × .). FIG. 7 is a graph showing simulation results of the radio wave arrival direction detection device according to the present embodiment and showing incoherent two-wave estimation results (using a calibration signal with a zenith elevation angle θ = 90 degrees; including a set value ○ and an estimated value x); It is. FIG. 6 is a simulation result of the radio wave arrival direction detection apparatus according to the present embodiment, and is a graph showing incoherent two-wave estimation results (using a calibration signal with a zenith elevation angle θ = 80 degrees; including a set value ○ and an estimated value x); It is. It is a simulation result of the radio wave arrival direction detection apparatus according to the present embodiment, and is a graph showing a coherent two-wave estimation result (using a calibration signal with a zenith elevation angle θ = 90 degrees; including a set value ○ and an estimated value x). is there. It is a simulation result of the radio wave arrival direction detection apparatus according to the present embodiment, and is a graph showing a coherent two-wave estimation result (using a calibration signal with a zenith elevation angle θ = 80 degrees; including a set value ○ and an estimated value x). is there.

Explanation of symbols

A5 ... Excitation element,
A1, A2, A3, A4, A6, A7, A8, A9 ... non-excited elements,
1 ... Low noise amplifier (LNA),
2 ... down converter,
3 ... A / D converter,
4 ... Wireless receiver,
9 ... Coaxial cable,
10: Reactance value controller,
11: Ground conductor,
12-1, 12-2, 12-3, 12-4, 12-6, 12-7, 12-8, 12-9 ... variable reactance elements,
13 ... Reactance value table memory,
20 ... A direction-of-arrival detection computer,
21 ... CRT display
30 ... rotation mechanism,
100: Array antenna device.

Claims (6)

An excitation element for receiving a radio signal and at least three non-excitation elements are arranged in a lattice shape, and each element includes a variable reactance element connected to each of the non-excitation elements, and a reactance value of each of the variable reactance elements By changing the above, each non-excited element is operated as a director or a reflector to change the directivity, and the radio wave arrival direction detection method using a square array array antenna,
Receiving each radio signal by the array antenna using a plurality of different radiation patterns respectively set by a plurality of sets of reactance values of each variable reactance element, detecting each received signal received, and detecting the received A correlation matrix R _y indicating a correlation between the plurality of received signals is calculated, and eigenvalues and eigenvectors for the received signals for each azimuth are calculated using the eigenvalue decomposition method based on the calculated correlation matrix R _y. , Using an eigenvector corresponding to the eigenvalue of the maximum value for each direction of each azimuth angle, an equivalent weight matrix consisting of equivalent vectors representing weights for each direction vector of the radiation pattern by each variable reactance element of the array antenna Calibrating, and
When a plurality of sets of reactance values of the different variable reactance elements are set, the received signals received by the array antenna are detected, and a correlation matrix R _y representing the correlation between the received signals is calculated. Eigenvalue decomposition of each calculated correlation matrix R _y to calculate eigenvalues and eigenvectors of each correlation matrix R _y with respect to the received signal, and the calculated correlation matrix R _y and noise power estimate σ ² Calculating a correlation matrix R _s converted into a predetermined element space in which inter-element coupling is canceled, and calculating eigenvalues and eigenvectors of the calculated correlation matrix R _s using an eigenvalue decomposition method;
Based on the eigenvalues and eigenvectors of the calculated correlation matrix R _s , the angle of the radio wave arrival direction is estimated by solving a polynomial rooted in a parameter corresponding to the one-dimensional or two-dimensional radio wave arrival direction using the MODE method. And calculating the direction of arrival of the radio wave. The step of estimating and calculating the angle of the radio wave arrival direction includes a matrix B in a matrix B (B ^H B) ⁻¹ B ^H spanning a noise subspace which is a space orthogonal to the signal subspace Es composed of eigenvalues of signals. The radio wave arrival direction detecting method according to claim 1, wherein the angle of the radio wave arrival direction is estimated and calculated by solving a one-way polynomial having a relationship with the arrival direction. The step of estimating and calculating the angle of the radio wave arrival direction includes a matrix B in a matrix B (B ^H B) ⁻¹ B ^H spanning a noise subspace which is a space orthogonal to the signal subspace Es composed of eigenvalues of signals. , Define a matrix Wn ^1/2 obtained by performing Cholesky decomposition on the normalization matrix Wn for eliminating the bias of the parameter matrix B that is a function of each coefficient vector in the binary polynomial having a relation with the arrival direction, and Wn = ( When B ^H B) ⁻¹ , the likelihood function including the matrix B (B ^H B) ⁻¹ B ^H that extends the noise subspace that is orthogonal to the signal subspace Es composed of the eigenvalues of the signal is substantially The coefficient vectors of the two polynomials are calculated by an iterative operation so that the two angles of the radio wave arrival direction are estimated and calculated by solving the binary polynomials so as to be minimized. 1 DOA finder method of mounting. An excitation element for receiving a radio signal and at least three non-excitation elements are arranged in a lattice shape, and each element includes a variable reactance element connected to each of the non-excitation elements, and a reactance value of each of the variable reactance elements A radio wave arrival direction detector using a square array array antenna that changes the directivity by operating each of the non-excitation elements as a director or a reflector,
Receiving each radio signal by the array antenna using a plurality of different radiation patterns respectively set by a plurality of sets of reactance values of each variable reactance element, detecting each received signal received, and detecting the received A correlation matrix R _y indicating a correlation between the plurality of received signals is calculated, and eigenvalues and eigenvectors for the received signals for each azimuth are calculated using the eigenvalue decomposition method based on the calculated correlation matrix R _y. , Using an eigenvector corresponding to the eigenvalue of the maximum value for each direction of each azimuth angle, an equivalent weight matrix consisting of equivalent vectors representing weights for each direction vector of the radiation pattern by each variable reactance element of the array antenna Means to calibrate;
When a plurality of sets of reactance values of the different variable reactance elements are set, the received signals received by the array antenna are detected, and a correlation matrix R _y representing the correlation between the received signals is calculated. , each correlation matrix R _y, which is calculated above to calculate the eigenvalues and eigenvectors of the above correlation matrix R _y with respect to eigenvalue decomposition to the received signal, the estimated value sigma ² of the calculated correlation matrix R _y and noise power means for calculating and used to calculate the correlation matrix R _s, which is converted to a predetermined element space cancels the inter element coupling, the eigenvalue decomposition method eigenvalues and eigenvectors of the calculated correlation matrix R _s based,
Based on the eigenvalues and eigenvectors of the calculated correlation matrix R _s , the angle of the radio wave arrival direction is estimated by solving a polynomial rooted in a parameter corresponding to the one-dimensional or two-dimensional radio wave arrival direction using the MODE method. And a radio wave arrival direction detecting device. The means for estimating and calculating the angle of the direction of arrival of the radio wave includes a matrix B in a matrix B (B ^H B) ⁻¹ B ^H that spans a noise subspace that is orthogonal to the signal subspace Es composed of eigenvalues of the signal, and 5. The radio wave arrival direction detecting device according to claim 4, wherein the radio wave arrival direction angle is estimated and calculated by solving a one-way polynomial having a relationship with the arrival direction. The means for estimating and calculating the angle of the direction of arrival of the radio wave includes a matrix B in a matrix B (B ^H B) ⁻¹ B ^H that spans a noise subspace that is orthogonal to the signal subspace Es composed of eigenvalues of the signal, and , Define a matrix Wn ^1/2 obtained by performing Cholesky decomposition on the normalization matrix Wn for eliminating the bias of the parameter matrix B that is a function of each coefficient vector in the binary polynomial having a relation with the arrival direction, and Wn = ( When B ^H B) ⁻¹ , the likelihood function including the matrix B (B ^H B) ⁻¹ B ^H that extends the noise subspace that is orthogonal to the signal subspace Es composed of the eigenvalues of the signal is substantially The coefficient vectors of the two polynomials are calculated by an iterative operation so that the two angles of the radio wave arrival direction are estimated and calculated by solving the binary polynomials so as to be minimized. 4 description Radio wave arrival direction sensing devices.

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