KR20070077228A - Appratus and method for antenna which estimates direction of arrival and frequency of arrival - Google Patents

Abstract

An antenna apparatus for estimating a direction of arrival and a frequency of arrival and an estimating method thereof are provided to estimate the direction of arrival and the frequency of arrival by using a three-dimensional antenna array structure and to reduce operation complexity in comparison with SVD(singular value decomposition) and EVD(cross spectral matrix eigenvalue decomposition). An antenna unit(200,202,224) includes three array antennas composed in a three-dimensional manner. A signal reception unit(300) receives a narrow band signal from the antenna unit and transmits the narrow band signal to a matrix calculation unit(302). The matrix calculation unit calculates a data matrix or a mutual spectrum matrix by using the received signal. A matrix decomposition unit(304) decomposes the data matrix or the mutual spectrum matrix. A propagator estimated matrix calculation unit(306) calculates the propagator estimated matrix by using the data matrix or the mutual spectrum matrix. A propagator estimated matrix decomposition unit(308) decomposes the propagator estimated matrix. A phase matrix estimation unit(310) estimates a phase matrix by using the propagator estimated matrix. An estimation unit(312) estimates a directional of arrival, a vertical angle, and a frequency of arrival by using the phase matrix.

Description

TECHNICAL APPARATUS AND METHOD FOR Estimate Directional Arrival Angle and Arrival Frequency {APPRATUS AND METHOD FOR ANTENNA WHICH ESTIMATES DIRECTION OF ARRIVAL AND FREQUENCY OF ARRIVAL}

1 is a diagram illustrating an array of antennas having a general two-dimensional array;

2 is a view showing the structure of a three-dimensional array antenna constructed in accordance with an embodiment of the present invention,

3 is a diagram illustrating a configuration of an antenna device for estimating a direction angle of arrival and an arrival frequency configured according to an embodiment of the present invention;

4 is a flowchart illustrating a flow of estimating a direction arrival angle and an arrival frequency in an antenna device constructed according to an embodiment of the present invention.

The present invention relates to an antenna device and method for estimating the direction angle, the vertical angle and the arrival frequency of a signal received by a three-dimensional array antenna.

Estimation of direction-of-arrival (DOA) and arrival frequency (FOA) of multiple signals arriving at the array antenna received a lot of attention. Estimation of the direction and angle of arrival of the signal received by these antennas plays an important role in areas such as radar, sonar, radio astronomy, seismic data processing, and mobile communication systems.

The direction angle of arrival can be divided into two directions: the direction angle and the vertical angle. By using the existing two-dimensional hitter arrangement, only two of the direction angle, the vertical angle, and the arrival frequency can be estimated. Next, a commonly used two-dimensional hit or array will be described with reference to FIG. 1 below.

1 is a diagram illustrating an array of antennas having a general two-dimensional array.

Referring to FIG. 1, a general direction angle of arrival and arrival frequency estimating apparatus uses three linear array antennas having a plurality of antennas 100 to 114 and having an antenna interval d, and the number of antennas of each array is N or; N + 1. One antenna array is located on the xy plane, one antenna array is located on the x-axis, and X (100-104), Y (102-106), Z (110-114) consisting of N antennas using the antenna array. ), And estimates two of the direction angle, the vertical angle, and the arrival frequency using the signal received by the subarray antenna.

Representative methods for estimating the direction of arrival angle and arrival frequency include a single value decomposition (SVD) method and a cross spectral matrix eigenvalue decomposition (EVD) method of a data matrix, but the SVD and EVD must perform singular value decomposition of a covariance matrix of a received signal. Because it requires extensive calculations. For a discussion of SVD and EVD, see the article "S. Wang, J. Caffery, and X. Zhou," Analysis of a joint space time DOA / FOA estimator using MUSIC, "IEEE Internation Symposium on Personal, Indoor and Mobile Radio Communications, pp. . B138-B142, Sept. 2001. ", and detailed description thereof is omitted.

Therefore, there is a need for an antenna apparatus and method for estimating both directional angles of up and down angles and arrival frequencies, and estimating directional arrival angles and arrival frequencies with low computational complexity.

SUMMARY OF THE INVENTION An object of the present invention is to provide an antenna device and method for estimating a direction angle, a vertical angle, and an arrival frequency.

Another object of the present invention is to provide an antenna apparatus and method for estimating the direction of arrival angle and arrival frequency with a three-dimensional antenna array structure.

It is still another object of the present invention to provide an antenna device and a method in which the estimation of the direction of arrival angle and the arrival frequency has a relatively lower computational complexity than the conventional single value decomposition (SVD) and cross spectral matrix eigenvalue decomposition (EVD) methods.

An apparatus of the present invention for achieving the above object, in the antenna device for estimating the direction of arrival angle and the arrival frequency, an antenna unit consisting of three array antennas in three dimensions, by receiving a narrowband signal from the antenna unit A signal receiver provided to a matrix calculator, a matrix calculator to calculate a data matrix or a mutual spectrum matrix by using the received signal, and decompose the matrix calculator, a data matrix or the mutual spectrum matrix to a matrix resolver, and a propagator The propagator estimation matrix calculation unit calculating a propagator estimation matrix using the matrix decomposition unit, a decomposed data matrix, or a mutual spectrum matrix, and providing the propagator estimation matrix decomposition unit to a propagator estimation matrix decomposition unit; The propagator estimation matrix is decomposed and fed to a phase matrix estimator. A phase matrix estimator for estimating a phase matrix using the decomposed propagator estimation matrix and providing it to an estimator, and the phase matrix estimated by the phase matrix estimator. The present invention provides an apparatus including the estimator for estimating a direction angle, a vertical angle, and an arrival frequency.

In the method of the present invention for achieving the above object, in the method of estimating the direction of arrival angle and the arrival frequency, when receiving a narrowband signal from the antenna, calculating a data matrix or a mutual spectrum matrix using the received signal, Decomposing the data matrix or the mutual spectrum matrix, calculating a propagator estimation matrix using the decomposed data matrix or the mutual spectrum matrix, decomposing the propagator estimation matrix, and decomposing the decomposed matrix. The method includes estimating a phase matrix using a propagator estimation matrix, and estimating a direction angle, an upper and lower angle, and an arrival frequency using the estimated phase matrix.

Hereinafter, exemplary embodiments of the present invention will be described in detail with reference to the accompanying drawings. In the following description of the present invention, if it is determined that a detailed description of a related known function or configuration may unnecessarily obscure the subject matter of the present invention, the detailed description thereof will be omitted.

The present invention relates to an antenna device and a method for estimating the direction angle, the vertical angle, and the arrival frequency of the signal received by the array antenna, and the three-dimensional array antenna for estimating all the direction angle, the vertical angle, and the arrival frequency. It has a structure and will be described with reference to FIG. 2 below.

2 is a view showing the structure of a three-dimensional array antenna configured in accordance with an embodiment of the present invention.

Referring to FIG. 2, three linear array antennas are used at predetermined intervals d for a plurality of antennas 200 to 224, and the number of array antennas is N, N + 1, and N. One antenna array is in the x-y plane, one antenna array is in the y-axis, and the other antenna array is in the y-z plane. X (200 ~ 204), Y (202 ~ 206), Z (220 ~ 224), W (210 ~ 214) are subarrays of array antenna structure, and each subarray antenna is N antennas. Configure.

FIG. 2 is an example of an array antenna structure capable of simultaneously estimating a direction angle, an up-down angle, and an arrival frequency. Generally, the sub-array antennas X, Y, and W are arranged in the xy plane, and the Z sub-array antenna is disposed. When placed in parallel with equal intervals, the direction angle, vertical angle, and arrival frequency can all be measured.

In the present invention, a derivation process for estimating all directions, up and down angles, and arrival frequencies will be described by using equations. The K narrowband signals received by the antennas included in the sub-array antennas of FIG. It is expressed as Equation 1>.

Prior to the description of the present invention, the parameters of the equations of the present invention will be described in unified manner, and the description of the parameters described in the above equations will be omitted.

Here, K is the number of narrowband signals received through the antenna, θ _k is the rising angle of the direction of arrival of the signal, φ _k is the direction of the angle of arrival of the received signal, f _k is the received signal Is the arrival frequency.

The equations of Equation 1 can be expressed in a matrix form as shown in Equation 2 below.

이고, S(t)=[s₁(t), s₂(t), …, s_K(t)]^T 이고, θ=[θ₁,…θ_K]^T 이고, φ=[φ₁,…φ_K]^T 이고, f=[f₁,…f_K]^T 이고, n_x, n_y, n_z, n_w는 시간 t에서 N×1의 평균이 0이고 분산이 σ²인 부가성 백색 가우시안 잡음 벡터이고, c는 전파 전송속도이고, 윗첨자 T는 전치행렬을 의미한다.Where X (t) = [x ₁ (t), x ₂ (t),... , x _N (t)] ^T , Y (t) = [y ₁ (t), y ₂ (t),... , y _{N + 1} (t)] ^T , and Z (t) = [z ₁ (t), z ₂ (t),... , z _N (t)] ^T , W (t) = [w ₁ (t), w ₂ (t),... , w _N (t)] ^T , and A ( θ , φ , f ) = [ a (θ ₁ , φ ₁ , f ₁ ), a (θ ₂ , φ ₂ , f ₂ ),. , a (θ _k , φ _k , f _k )] and a (θ ₂ , φ ₂ , f ₂ ) = [1, u _k ,. , u _k ^{N -1} ], k = 1,... , K,

And S (t) = [s ₁ (t), s ₂ (t),... , s _K (t)] ^T , and θ = [θ ₁ ,. θ _K ] ^T and φ = [φ ₁ ,. φ _K ] ^T and f = [f ₁ ,... f _K ] ^T , n _x , n _y , n _z , n _w are additive white Gaussian noise vectors with an average of N × 1 and variance σ ² at time t, c is the propagation rate, and The subscript T stands for transpose.

In Equation 2, Φ ₁ ( θ , φ , f ), Φ ₂ ( θ , f ), and Φ ₃ ( θ , φ , f ) are K × K diagonal matrices, θ _k , It includes information about φ _k and f _k and can be expressed as Equation 3 below.

Where diag [xi] means that each element in the diagonal matrix is xi.

In the description of the present invention, the Φ ₁ ( θ , φ , f ), Φ ₂ ( θ , f ), Φ ₃ ( θ , φ , f ) are denoted by Φ ₁ , Φ ₂ , Φ ₃ , respectively, and the arrangement response The array response matrix A ( θ , φ , f ) is denoted by A.

Then, referring to the article "S. Marcos, A. Marsal, M. Benidir," The propagator method for source bearing estimation, "Signal Processing 42 (1995), pp. 121-138." The response response matrix A can be expressed as Equation 4 below.

Here, A ₁ is a sub-matrix of K × K, and A ₂ is a sub-matrix of (NK) × K.

Then, the propagator matrix P of K × (4N-K) is applied to each of the received output vectors, X, Y, Z, and W of Equation 2, and D is represented by Equation 5 below. Define as

If Equation 5 is expressed as Equation 4, Equation 6 below may be expressed.

이다.here,

to be.

When N≥2K, assuming that A ₁ is a non-K × K non-singular matrix, then the propagator matrix P of K × (4N-K) satisfies Equation 7 below. It is the only linear operator.

Where H is a Hermitian operation.

Meanwhile, the data vector Q (t) of 4N × 1 is expressed as in Equation 8 below.

If a 4N × L data matrix of L data vectors is F, F can be expressed as Equation 9 below.

은 아래 <수학식 10>과 같이 표기할 수 있다.And a 4N × 4N mutual spectral matrix

Can be written as in Equation 10 below.

Then, when the data matrix of Equation 9 and the mutual spectrum matrix of Equation 10 are decomposed, Equation 11 and Equation 12 may be expressed, respectively.

Here, F ₁ is a sub-matrix of K × L, and F ₂ is a sub-matrix of (4N-K) × L.

Here, E is a submatrix of 4N × K, and J is a submatrix of 4N × (4N-K).

이라고 하고, K×(4N-K) 크기의 상호 스팩트럼(spectral) 행렬

의 프로퍼게이터 추정행렬을

라고 하면, 상기 프로퍼게이터 추정행렬

와

는 아래 <수학식 13>의 비용함수가 최소화 되도록 정한다.Then, the propagator estimation matrix of the data matrix F of size K × (4N-K)

And a spectral matrix of size K × (4N-K)

The estimator matrix of the

Speaking, the estimator matrix

Wow

Is set to minimize the cost function in Equation 13 below.

는 프로베니우스 기준(Frobenius norm)이다.here,

Is the Frobenius norm.

와

를 아래 <수학식 14>과 같이 구할 수 있다.When the least square method is applied to Equation 13, the estimator matrix

Wow

Can be obtained as shown in Equation 14 below.

또는

는 각각 아래 <수학식 15>와 같이 분해할 수 있다.Estimator Matrix of Equation 14

or

Can be decomposed as shown in Equation 15 below.

의 차원은 각각

here

Dimension of each

의 차원과 일치한다. 그러면, 상기 <수학식 6>, <수학식 7>, <수학식 15>에 의하면 아래 <수학식 16>와 같이 표현할 수 있다.

Coincides with the dimension of. Then, according to Equation 6, Equation 7, and Equation 15, Equation 16 may be expressed.

Equation 16 may be expressed as Equation 17 below.

Where # is a pseudo inverse.

By using Equation 17, phase matrices Φ ₁ , Φ ₂ , and Φ ₃ are expressed as in Equation 18 below.

The phase matrices Φ ₁ , Φ ₂ , and Φ ₃ obtained in Equation 18 are applied to Eq. 19 below to estimate the up-down angle, the direction angle, and the arrival frequency. Estimate the arrival frequency.

의 추정은

의 추정식을 이용하여 얻은 값을 이용하여 추정하고, 주파수

의 추정은

의 추정식을 이용하여 추정한다.Referring to Equation 19, the upper and lower angles

Estimate of

Estimate using the value obtained using the equation

Estimate of

Estimate using

영역에 1대 1함수 임으로, arc-tangent 연산은 x가 실수 영역에 존재하면 추정에 실패하지 않는다.Estimation of the upper and lower angles and the direction angle of the present invention is estimated through the arc-tangent operation, if y = tan ^-1 (x), which is a characteristic of the arc-tangent operation, exists in the real area (R), for all x∈R

Because it is a one-to-one function in the domain, the arc-tangent operation does not fail to estimate if x is in the real domain.

Next, the antenna device of the present invention for estimating an up angle, an up and down angle, and an arrival frequency using the array antenna of FIG. 2 will be described below with reference to FIG. 3.

3 is a diagram illustrating a configuration of an antenna device for estimating a direction arrival angle and an arrival frequency configured according to an exemplary embodiment of the present invention.

Referring to FIG. 3, the antenna device of the present invention includes a plurality of antennas 200 to 224, a signal receiver 300, a matrix calculator 302, a matrix resolver 304, and a propagator estimation matrix calculation. The unit 306 includes a propagator estimation matrix decomposition unit 308, a phase matrix estimation unit 310, and an estimation unit 312.

Antennas 200 to 224 are the same as the description of FIG. 2 and receive K narrowband signals and provide them to the signal receiver 300.

The signal receiver 300 receives K narrowband signals from the antennas 200 to 224 and provides them to the matrix calculator 302 in subarray antenna units.

The matrix calculator 302 calculates a data matrix or a mutual spectrum matrix using the signal received from the signal receiver 300, and provides the matrix matrix to the matrix resolver 304.

은 상기 <수학식 10>을 통해 계산할 수 있다.The data matrix F may be calculated through Equation 9, and the mutual spectrum matrix

May be calculated through Equation 10.

The matrix decomposition unit 304 decomposes the data matrix or the mutual spectrum matrix received from the matrix calculation unit 302 and provides it to the propagator matrix calculation unit 306.

The decomposition of the data matrix is decomposed through Equation 11, and the decomposition of the mutual spectrum matrix is decomposed through Equation 12.

또는

를 계산하여 상기 프로퍼게이터(Propagator) 추정행렬 분해부(308)로 제공한다.The propagator estimation matrix calculator 306 uses the decomposed data matrix or the mutual spectrum matrix to estimate the propagator matrix.

or

Is calculated and provided to the propagator estimation matrix decomposition unit 308.

또는

는 상기 <수학식 14>과 같다.Proportional Estimation Matrix

or

Is as shown in Equation 14 above.

를 상기 <수학식 15>와 같이 분해여 위상(Phase) 행렬 추정부(310)로 제공한다.A propagator estimation matrix decomposition unit 308 may determine the propagator estimation matrix. or

Is then provided to the phase matrix estimator 310 by decomposition as shown in Equation 15.

The phase matrix estimator 310 estimates the phase matrix using the decomposed propagator estimation matrix and provides the estimated phase matrix to the estimator.

The phase matrix estimation is estimated using Equation 18.

The estimator 312 estimates the direction angle, the upper and lower angles, and the arrival frequency using the phase matrix estimated by the phase matrix estimator 310.

The direction angle, the vertical angle, and the estimation of the arrival frequency are estimated using Equation (19).

Hereinafter, a method of estimating the direction of arrival angle and the arrival frequency using the antenna device constructed according to the present invention configured as described above will be described with reference to FIG. 4.

4 is a flowchart illustrating a flow of estimating a direction arrival angle and an arrival frequency in an antenna device constructed according to an embodiment of the present invention.

Referring to FIG. 4, the antenna device of the present invention proceeds to step 400 and checks whether K narrowband signals are received from an array antenna.

In step 400, when the test result signal is received, the data matrix or the mutual spectrum matrix is calculated by using the received signal. In step 404, the received data matrix or the mutual spectrum matrix is decomposed. The propagator estimation matrix is calculated by using the decomposed data matrix or the mutual spectrum matrix, and the process proceeds to step 408 to decompose the propagator estimation matrix, and the process proceeds to step 410 to estimate the decomposed propagator. The phase matrix is estimated using the matrix, and the direction angle, the vertical angle, and the arrival frequency are estimated using the estimated phase matrix in step 412.

은 상기 <수학식 10>을 통해 계산할 수 있다.In step 402, the data matrix F may be calculated through Equation (9), and the mutual spectrum matrix

May be calculated through Equation 10.

In step 404, the decomposition of the data matrix is decomposed through Equation (11), and the decomposition of the mutual spectrum matrix is decomposed through Equation (12).

또는

는 상기 <수학식 14>과 같다.The propagator estimation matrix in step 406

or

Is as shown in Equation 14 above.

The propagator estimation matrix decomposition in step 408 is decomposed as shown in Equation 15 above.

The phase matrix estimation in step 410 is estimated using Equation 18.

The direction angle, the vertical angle, and the arrival frequency of step 412 are estimated using Equation 19.

Meanwhile, in the detailed description of the present invention, specific embodiments have been described, but various modifications are possible without departing from the scope of the present invention. Therefore, the scope of the present invention should not be limited to the described embodiments, but should be determined not only by the scope of the following claims, but also by the equivalents of the claims.

As described above, the present invention relates to an antenna device and a method for estimating the direction of arrival angle and the arrival frequency, and estimates the direction angle, the upper and lower angles, and the arrival frequency. Provided are an antenna device and a method for estimating a direction of arrival angle and arrival frequency having a relatively low computational complexity compared to a cross spectral matrix eigenvalue decomposition (EVD) method.

Claims (22)

In the antenna device for estimating the direction of arrival angle and the arrival frequency, An antenna unit configured to three array antennas in three dimensions; A signal receiver for receiving a narrowband signal from the antenna unit and providing the narrowband signal to a matrix calculator; The matrix calculation unit calculating a data matrix or a mutual spectrum matrix using the received signal and providing the matrix matrix to a matrix decomposition unit; The matrix decomposing unit decomposing the data matrix or the mutual spectrum matrix and providing the data matrix to a propagator matrix calculator; A propagator estimation matrix calculation unit calculating a propagator estimation matrix using the decomposed data matrix or the mutual spectrum matrix and providing the propagator estimation matrix decomposition unit to a propagator estimation matrix decomposition unit; The propagator estimation matrix decomposition unit decomposing the propagator estimation matrix and providing the result to a phase matrix estimation unit; A phase matrix estimator for estimating a phase matrix using the decomposed proparator estimate matrix and providing the estimated phase matrix to the estimator; And And an estimator for estimating a direction angle, an upper and lower angle, and an arrival frequency using the phase matrix estimated by the phase matrix estimator. The method of claim 1, The antenna unit, Three linear array antennas are used, and each array antenna is composed of N, N + 1, N, and one array antenna consisting of N is in the xy plane and the other array antenna composed of N + 1 y And the other one array antenna of which N is arranged on the axis is located in the yz plane. The method of claim 2, Each of the array antennas composed of N antennas consists of one sub-array antenna, and in the array antenna composed of N + 1 antennas, N other than the first antenna are composed of other sub-array antennas, and N + 1 antennas In the array antenna consisting of the N, except for the last antenna is configured with another sub-array antenna to configure a total of four sub-array antenna. The method of claim 1, The matrix calculation unit. Wherein the data matrix F is calculated through Equation 20 below.

Q (t) is a data vector when time t is from 1 to L. The method of claim 1, The matrix calculation unit. The mutual spectrum matrix

The device characterized in that calculated by the following equation (21).

Where F is a data matrix, L is the number of data vectors Q (t), and H is a Hermitian operation. According to claim 4 or Equation 5, And the data vector Q (t) of Equation 20 and Equation 21 is represented by Equation 22 below.

Here, X (t), Y (t), Z (t), and W (t) are matrixes of signals received through respective subarray antennas at time t, and the superscript T is a transpose matrix. The method of claim 1, The matrix decomposition unit, Decomposition of the data matrix F or the mutual spectrum matrix

A device characterized in that the decomposition of the following equation (23) below.

Where F ₁ is a sub-matrix of K (number of narrowband signals) × L (number of narrow-band signals received), F ₂ is a sub-matrix of (4N (number of sub-array antennas) -K) × L, and E Is a submatrix of 4N × K, and J is a submatrix of 4N × (4N-K). The method of claim 1, The propagator estimation matrix calculation unit, Proportional Estimation Matrix

or

Is estimated by Equation 24 below.

here,

Is a predictor estimate matrix of the data matrix,

Proportional estimation matrix of the mutual spectrum matrix, H is a Hermitian operation, F ₁ is a sub-matrix of K (number of narrowband signals) × L (number of narrowband signal reception), F ₂ is (4N (number of sub-array antennas) -K) x L sub-matrix, E is 4N x K sub-matrix, J is 4N x (4N-K) sub-matrix. The method of claim 1, The propagator estimation matrix decomposition unit, Proportional Estimation Matrix

or

The device characterized in that the decomposition as shown in Equation 25 below.

Where H is a Hermitian operation and superscript T is a transpose matrix. The method of claim 1, The phase matrix estimator, And estimating the phase matrices [phi] ₁ , [phi] _2, and [phi] ₃ using Equation (26) below.

Where

Is an eigenbalue of the propagator estimation matrix obtained by decomposing the propagator estimation matrix, and # is a pseudo inverse. The method of claim 1, The estimating unit, the direction angle of the kth narrowband signal (

), Top and bottom angles

) And arrival frequency (

) Is estimated using Equation 27 below.

Where Φ ₁ , Φ ₂ , and Φ ₃ phase matrices. In the method of estimating the direction of arrival angle and the arrival frequency, Calculating a data matrix or a mutual spectrum matrix using the received signal when receiving a narrowband signal from an antenna; Decomposing the data matrix or the mutual spectrum matrix; Calculating a propagator estimation matrix using the decomposed data matrix or the mutual spectrum matrix; Decomposing the propagator estimation matrix; Estimating a phase matrix using the decomposed propagator estimation matrix; And Estimating a direction angle, a vertical angle, and an arrival frequency using the estimated phase matrix. The method of claim 12, The antenna, Three linear array antennas are used, and each array antenna is composed of N, N + 1, N, and one array antenna consisting of N is in the xy plane and the other array antenna composed of N + 1 y And one remaining array antenna consisting of N elements on the yz plane. The method of claim 13, Each of the array antennas composed of N antennas consists of one sub-array antenna, and in the array antenna composed of N + 1 antennas, N other than the first antenna are composed of other sub-array antennas, and N + 1 antennas The method of claim 4, wherein the array antennas are configured as N other than the last antenna as another sub-array antenna and are configured as a total of four sub-array antennas. The method of claim 12, The data matrix F is calculated by Equation 28 below.

Q (t) is a data vector when time t is from 1 to L. The method of claim 12, The mutual spectrum matrix

Is calculated by Equation 29 below.

Where F is a data matrix, L is the number of data vectors Q (t), and H is a Hermitian operation. The method according to claim 15 or 16, The data vector Q (t) of Equation 28 and Equation 29 is expressed as Equation 30 below.

Here, X (t), Y (t), Z (t), and W (t) are matrixes of signals received through respective subarray antennas at time t, and the superscript T is a transpose matrix. The method of claim 12, Decomposition of the data matrix F or the mutual spectrum matrix

The decomposition of the method characterized in that the decomposition through <Equation 31> below.

Where F ₁ is a sub-matrix of K (number of narrowband signals) × L (number of narrow-band signals received), F ₂ is a sub-matrix of (4N (number of sub-array antennas) -K) × L, and E Is a submatrix of 4N × K, and J is a submatrix of 4N × (4N-K). The method of claim 12, Proportional Estimation Matrix

or

Equation (32) below is estimated by the method.

here,

Is a predictor estimate matrix of the data matrix,

A propagator estimate matrix of the mutual spectrum matrix, H is a Hermitian operation, F ₁ is a sub-matrix of K (number of narrowband signals) × L (number of narrowband signal receptions), and F ₂ Is a submatrix of (4N (number of subarray antennas) -K) × L, E is a submatrix of 4N × K, and J is a submatrix of 4N × (4N-K). The method of claim 12, Proportional Estimation Matrix

or

The decomposition of the method characterized in that the decomposition as shown in Equation 33 below.

Where H is a Hermitian operation and superscript T is a transpose matrix. The method of claim 12, The estimation of the phase matrices Φ ₁ , Φ ₂ and Φ ₃ is estimated using Equation 34 below.

Where

Is an eigenbalue of the propagator estimation matrix obtained by decomposing the propagator estimation matrix, and # is a pseudo inverse. The method of claim 12, the direction angle of the kth narrowband signal (

), Top and bottom angles

) And arrival frequency (

) Is estimated using Equation 35 below.

Where Φ ₁ , Φ ₂ , and Φ ₃ phase matrices.

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