KR101414574B1 - A Spatially Smoothed Auto-convolution based DOA Estimating Method for Correlated Signals in the Presence of Correlated Antenna Noises - Google Patents

Abstract

A method for predicting a signal arrival direction angle (DOA) in a receiver that receives a signal from a plurality of signal sources via an antenna array, the method comprising: (a) Expressing a complex envelope expression as a linear vector; (b) performing an auto convolution on the received signal to obtain a new signal; (c) transforming the first signal represented by a linear vector (hereinafter, signal vector) into frequency domain data through Fourier transform; (d) expressing a new signal vector in a frequency domain through Fourier transform; (e) extracting a first spectral density matrix using an operator for performing an element-by-element multiplication between two matrices (hereinafter referred to as a delta element); And (f) spatially smoothing the first spectral density matrix to obtain a second spectral density matrix.
According to the above-described signal arrival direction angle predicting method, it is possible to effectively predict the signal arrival direction angle (DOA) even when a plurality of correlated signals arriving at the antenna array with the additional correlated noise in the environment of the correlated noise region.

Description

[0001] The present invention relates to a spatially smoothed self-convolution based DOA Estimating Method for Correlated Signals in Correlated Antenna Noises for Correlated Signals in the Presence of Correlated Antenna Noise,

The present invention relates to a method for predicting a spatially smoothed self-convolutional direction-of-arrival angle in a receiver that receives cross-correlated signals obtained from a plurality of signal sources via an antenna array having correlated antenna noise.

Array signal processing can be defined as the field of analyzing and processing the structure of data received from an antenna array that is spatially dispersed in the presence of noise. Estimation of the direction of arrival (DOA) of a signal using array signal processing has been dealt with as a very important research topic in radar, sonar detection, and mobile communication fields [Non-Patent Documents 1-3].

The MUSIC (Multiple Signal Classification) method is based on a proprietary structure algorithm and uses array signal processing, which is considered as a benchmark for DOA estimation methods to be developed later. The MUSIC method provides better resolution with less complexity in the DOA estimation [Non-Patent Documents 4 and 5] than the spectral estimation method [Non-Patent Document 6,7].

However, MUSIC has some crucial limitations in application in real situations. That is, the MUSIC degrades the DOA prediction performance when a plurality of signals arriving at the antenna array are correlated or added to each other and the antenna noise is correlated.

For DOA prediction of coherent or partially correlated signals, a spatial smoothing (SS) pre-processing structure has been proposed [Non-Patent Document 8]. This structure is based on the idea that correlation between signals can be eliminated by processing coherent signals using spatially overlapping and dispersed antenna sub-arrays.

On the other hand, most of the DOA estimation algorithms including MUSIC and spatial smoothing (SS) assume that the added array antenna noise is not correlated with each other in general. Obviously, if these algorithms are used to predict the DOA in environments where the array antenna noise is correlated, the DOA prediction results obtained will be poor.

In the non-patent document 9, the present invention proposes an algorithm for eliminating correlation between correlated antenna additive noise with known or estimated noise correlation coefficients. This algorithm, called "SO (second order)" algorithm, performs the self-convolution of the original data composed of multiple signals and noise arriving at a given antenna, do. Because these new magnetized data can retain information for all other data points with a constant delay, the SO algorithm that utilizes these new sample data can be used in both correlated noise environments and low S / N (signal to noise ratio) environments And provides improved DOA prediction resolution.

In summary, the array signal processing method can provide a high resolution for predicting the DOA of a signal due to the conceptual increase of the signal-to-noise ratio (S / N). Unique structure based array signal processing algorithms such as MUSIC and Root MUSIC provide effective DOA results when multiple signals are not coherent. The class of the spatial smoothing (SS) algorithm spatially removes the correlation of coherent signals using redundant sub-arrays distributed in space. On the other hand, the second order (SO) algorithm has been found to de-correlate correlated antenna noise with known or estimated noise correlation coefficients.

From a practical point of view, it is possible to consider a situation in which multiple signals arriving at the antenna array are correlated with each other, and additional noises in the array antenna are correlated with each other.

Therefore, there is a need for a method that can effectively analyze correlated multiple signals arriving at an antenna array with additional correlation noise.

D.G. Manolakis, et al .: Statistical and Adaptive Signal Processing, Artech House, Inc., Norwood, (2005) [Non-Patent Document 2] X. Zhang, et al .: Digital Processing System for Digital Beam Forming Antenna, IEEE International Symposium on Microwave, Antenna Propagation and EMC Technologies (2005) [Non-Patent Document 3] T.B. Lavate, et al .: Performance Analysis of MUSIC and ESPIT DOA Estimation Algorithms for Adaptive Array Smart Antenna in Mobile Communication: International Journal of Computer Networks (IJCN), Vol. 2, Issue 3, pp. 152-158 (2009) [Non-patent Document 4] R.O. Schmidt: A Signal Subspace Approach to Multiple Source Location and Spectral Estimation: Ph.D. Dissertation, Stanford University, Stanford (1981) [Non-Patent Document 5] R.O. Schmidt: Multiple Emitter Location and Signal Parameter Estimation: IEEE Trans. on Antennas and Propagation, Vol. AP-34, pp. 276-280 (1986) [Non-Patent Document 6] E.H. Satorius, et al .: Maximum Entropy Spectral Analysis of Multiple Sinusoids in Noise: Geophysics, Vol. 43, pp. 1111-1118 (1978) [Non-Patent Document 7] T. Thorvldsen, Maximum Entropy Spectral analysis in Antenna Spatial Filtering: IEEE Trans. on Antennas and Propagation, Vol. AP-28, pp. 552-560 (1980) [Non-Patent Document 8] T. Shan, et al .: On Spatial Smoothing for Direction-of-Arrival Estimation of Coherent Signals: IEEE Trans. on Acoust., Speech, and Signal Processing, Vol-ASSP-33, No. 4, pp.801-811 (1985) [Non-Patent Document 9] Ill-Keun Rhee: Performance Analysis of Highly Effective Proposed Direction Finding Method: The Journal of the Acoustical Society of Korea, Vol. 14, No. 1E, pp. 88-97 (1995). [Non-Patent Document 10] Ill-Keun Rhee: Highly Effective Direction Finding Method under the Particular Circumstances: The Journal of the Korean Institute of Communication Sciences, Vol. 18, No. 3, pp. 439-448 (1993).

It is an object of the present invention to provide a method and apparatus for estimating a signal arrival direction angle (DOA) in a receiver that receives signals from multiple signal sources via an antenna array, The present invention provides a space-smoothed self-convolution-based direction-of-arrival estimation method that combines an SO algorithm and an SS algorithm based on spatially smoothed self-convolution.

In order to achieve the above object, the present invention relates to a spatial smoothing self-convolutional approach angle predicting method for predicting an incoming direction angle (DOA) in a receiver which receives a signal from a plurality of signal sources through an antenna array, Obtaining a received signal (hereinafter referred to as a first signal) when transmission signals from multiple signal sources are received through an antenna array; (b) performing a self-convolution on the first signal to obtain a new signal (hereinafter referred to as a second signal); (c) transforming the first signal represented by a linear vector (hereinafter referred to as a first signal vector) into frequency domain data through Fourier transform; (d) expressing the second signal as a linear vector (hereinafter referred to as a second signal vector) in a frequency domain through Fourier transform; (e) extracting a first spectral density matrix using an operator for performing an element-by-element multiplication between two matrices (hereinafter referred to as a delta element); (f) spatially smoothing the first spectral density matrix to obtain a second spectral density matrix; And (g) decomposing the second spectral density matrix by eigenvalness, and extracting an incoming direction angle using an eigenvector corresponding to the minimum eigenvalue.

The present invention also provides a spatial smoothing magnetic-convolution-based direction-of-gaze estimation method, wherein the first spectral density matrix is obtained by using a spectral density matrix obtained from data in the frequency domain of the first and second signal vectors .

Further, the present invention is characterized in that, in the spatially smoothed self-convolutionary direction-of-arrival-angle predicting method, the first spectral density matrix L _{(2) R} is defined by [Expression 1].

[Equation 1]

Here, L ₍₁₎ and L ₍₂₎ are spectral density matrices obtained from data in the frequency domain of the first and second signal vectors, respectively, and? Is delta-specific.

According to another aspect of the present invention, there is provided a method for predicting a direction-of-arrival angular deviation based on a spatially smoothed self-convolution, the antenna array comprising a plurality of antennas, And is a linear array (ULA).

Further, the present invention is characterized in that, in the spatially smoothed self-convolution-based direction-of-arrival-angle predicting method, the second spectral density matrix is obtained by [Expression 2].

[Equation 2]

Where ( L _{(2) R} ) _p is the first spectral density matrix of the pth subarray,

P is the number of sub-arrays.

Further, the present invention is characterized in that, in the spatially smoothed self-convolution-based direction-of-arrival-angle predicting method, the arrival direction angle is obtained by using the orthogonality of the eigenvector and the steering vector.

In the method of predicting the arrival direction angle based on the spatially smoothed magnetic convolution, the arrival direction angle is obtained by the following [Expression 3], and the Ps _sso value in the course of changing θ from 0 to 360 degrees Is obtained as &thetas; when it becomes infinite.

[Equation 3]

V _{M + 1} , v _{M +2} , ..., v _L are the eigenvectors corresponding to the minimum eigenvalues, and a _s (θ) is the steering vector.

Further, the present invention is characterized in that, in the spatially smoothed self-convolution-based direction-of-arrival-angle predicting method, the steering vector a _s (θ) is obtained by the following [Expression 4].

[Equation 4]

Where D is the distance between the antennas, and [lambda] is the wavelength of the transmitted signal.

As described above, according to the spatially smoothed self-convolutionary directional angle estimation method of the present invention, even if a plurality of correlated signals arriving at the antenna array with additional correlated noise effectively predict the DOA The effect can be obtained.

1 is an overall system configuration diagram for implementing the present invention.
FIG. 2 is a flowchart illustrating a spatial smoothed self-convolution based approach angle prediction method according to an embodiment of the present invention.
3 shows a ULA antenna configuration according to the present invention.
Fig. 4 is a diagram showing the delta characteristic according to the present invention.
Figure 5 illustrates a subarray configuration for spatial smoothing according to the present invention.
FIGS. 6 and 7 are graphs showing DOA evaluation for the SS method according to the experiment of the present invention and the method of the present invention. FIG.
FIGS. 8 and 9 are tables showing the SS method according to the experiment of the present invention and the performance of the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Hereinafter, the present invention will be described in detail with reference to the drawings.

In the description of the present invention, the same parts are denoted by the same reference numerals, and repetitive description thereof will be omitted.

First, the overall system configuration for carrying out the present invention will be described with reference to Fig.

1 shows an example of a receiver 10 that communicates with a plurality of signal sources 20 with an array antenna. For example, the source may be a plurality of user terminals and the receiver may be a base station.

Referring to Fig. 1, the receiver 10 has an array antenna 40 composed of M (for example, four) antenna elements r1, r2, r3, r4. There are Q (for example, five) signal sources s1, s2, ..., s5 in the service area of the receiver 10. [ Receiver 10 receives signals from signal sources 20 from M (or four) antenna channels.

The signal arrival direction angle predicting device 30 receives the signals coming from the antenna 40 and analyzes the received signals to predict the signal arrival direction angle (DOA).

As an example for implementing the signal arrival direction angle predicting device 30, a program system device installed in a computer device. That is, each function of the signal arrival direction angle predicting device 30 is implemented by a computer program and installed in the computer device, receives the received signal through the input device of the computer device, processes the processed result, Output. Data required by the signal arrival direction angle predicting device 30 can be stored in a storage space such as a hard disk of a computer terminal.

As another embodiment, a computing function is provided in the receiver 10, and the signal arrival direction angle predicting device 30 can be operated and operated through the computing function in the receiver 10. [ As another embodiment, the signal arrival direction angle predicting device 30 may be implemented by a dedicated IC chip formed by a microprogram and driven by a microprocessor, or by an electronic circuit such as an ASIC (application-specific semiconductor) . In other words, it may be configured in the form of software, an electronic circuit composed of an FPGA chip or a plurality of circuit elements. Other possible forms may also be practiced. However, for convenience of explanation, the signal arrival direction angle predicting device 30 implemented in the computing apparatus will be described below.

Next, a spatially smoothed self-convolution based approach angle prediction method according to an embodiment of the present invention will be described with reference to FIG.

First, a reception signal (hereinafter referred to as a first signal) when transmission signals from multiple signal sources are received through an antenna array with additional noise is obtained (S10).

As shown in Fig. 1, M remote signal source signals are transmitted in directions {&thetas; ₁ , &thetas; ₂ , ... θ _M } to a uniform linear array ULA having Q antennas. At this time, the signal received from the i-th antenna can be expressed as Equation (1).

[Equation 1]

Here, s _m (t) = signal radiated from the m-th signal source,

D = distance between antennas,

lambda = wavelength of transmitted signal,

θ _m = DOA from the mth signal source,

x _i (t) = additive noise at the ith antenna.

When a complex envelope expression is applied to the m-th transmission signal s _m (t), the signal received in [Non-Patent Document 9] and [Equation 1] can be expressed by Equation (2).

&Quot; (2) "

The signals received from the Q antennas can be described in the vector form of (3) or (4). This is called a first signal vector.

&Quot; (3) "

or,

&Quot; (4) "

here,

r ^T (t) = [r ₁ (t), r ₂ (t), ..., r _Q (t)

s ^t (t) = s ₁ (t), s ₂ (t), ..., s _M (t)

x ^T (t) = [x ₁ (t), x ₂ (t), ..., x _Q (t)],

And the column of the QxM steering matrix A ([theta]) is composed of a steering vector which can be expressed by the following equation (5).

&Quot; (5) "

Next, a new signal (hereinafter referred to as a second signal) is obtained by performing an auto convolution on the received signal (or the first signal) (S20).

That is, a new signal (or a second signal) r _{(2) i} (t) is obtained by performing a magnetic convolution operation on the signal (or the first signal) received by the i-th antenna as in Equation (6).

&Quot; (6) "

는 콘볼루션 연산자를 나타낸다.only,

Represents a convolution operator.

At this time, new signals of Q antennas can be represented as vectors as described above. This is called a new signal vector (or a second signal vector).

Next, the first signal represented by a linear vector (or a first signal vector) is transformed into frequency domain data through Fourier transform (S30).

The spectral density matrix required for predicting the signal arrival direction angle used in the present invention should be obtained. For this purpose, it is convenient to apply the Fourier transform to the received data and use the data in the frequency domain as in Equation (3) or (4), so that the signal vector is transformed through Fourier transform Into frequency domain data. That is, the Fourier-transformed received signal vector (or first signal vector) in [Equation 3] or [Equation 4] has the form of [Equation 7].

&Quot; (7) "

F = AS  + X

Here, F = F [ r ], S = F [ s ], X = F [ x ], and " F " denotes a Fourier transform operator.

Therefore, the spectral density matrix of F (hereinafter 0-1 spectral density matrix) L ₍₁₎ is obtained as follows.

[Equation 7-2]

Next, the second signal represented by a linear vector (hereinafter referred to as a second signal vector) is expressed in the frequency domain through Fourier transform (S40). That is, a new signal vector (or a second signal vector) composed of the new signal (or the second signal) of Equation (6) can be expressed in the frequency domain as follows through Fourier transform.

&Quot; (8) "

Here, the spectral density matrix of F ₍₂₎ (hereinafter referred to as a 0-2 spectral density matrix) L ₍₂₎ is expressed as follows.

&Quot; (9) "

Introduces a new operator? Called "delta product " that performs multiplication of each corresponding element of the matrix to efficiently handle the spectral density matrix in [Equation 9].

Next, a first spectral density matrix is extracted using an operator (hereinafter referred to as a delta element) for performing multiplication of the corresponding elements of the two matrices (S50). In particular, the first spectral density matrix is obtained using a spectral density matrix obtained from data in the frequency domain of the first and second signal vectors.

The delta product operation is defined as:

&Quot; (10) "

However, the matrices A, B, and C all have the same dimension.

The characteristics of? Are as shown in FIG.

By the definition above, the spectral density matrix for the new signal is expressed as

&Quot; (11) "

In Equation (11), each element in the Expectation Bracket is equal to the square of the corresponding element. In general, since the source signal and the noise are uncorrelated to each other, they are expressed by Equation (12).

&Quot; (12) "

The Fourier transform of the Stationary random process X _q (t) = a _q (t) + jb _q (t), where a _q (t) and b _q when (t) is independent of each other, X _q (t) is X _q = X _qr + jX _qi . The following results are obtained for the complex Gaussian random process.

[Equation 12-2]

Therefore, using the above results,

&Quot; (13) "

&Quot; (14) "

Using this, we can write the remaining term in [15] as follows.

&Quot; (15) "

When the source signals are independent of each other, they can be obtained by the following process.

&Quot; (16) "

를 구한다.next

.

&Quot; (17) "

For example, for a Sinusoidal Source with or without a Uniformly Distributed Random Phase, the following holds:

&Quot; (18) "

Substituting Equations (16), (17), and (18) into Equation (15) yields the following.

&Quot; (19) "

From Equation 17,

&Quot; (20) "

Substituting equation (20) into equation (19) now yields:

&Quot; (21) "

here,

&Quot; (22) "

By definition,

&Quot; (23) "

A new first spectral density matrix L _{(2) R} is obtained.

The first spectral density matrix L _{(2) R} expressed theoretically is as shown in Equation (23), and in reality, the first spectral density matrix L _{(2) R} obtained using Equation (22 ₎ Spatial Smoothing) technique.

Next, the first spectral density matrix is spatially smoothed to obtain a second spectral density matrix (S60).

According to the method of applying the SO algorithm to the SS method, a ULA having Q identical antennas divided into P (= Q - L + 1) overlapping sub-arrays of size L as shown in FIG. 5 is considered .

First, the SS technique (non-patent document 8) will be briefly described as follows.

은 수학식 24와 같이 얻어진다.As shown in FIG. 5, when the total number of antennas is Q and the number of antennas per sub-array is L , sub-arrays S ₁ , S ₂ , and S ₃ The total number P of ... becomes Q - L + 1. Suppose that the signals from the M signal sources coming into each sub-array and the sample array antenna covariance matrix by the antenna noise are R _k , then a spatial smoothing (SS) covariance matrix

Is obtained as shown in equation (24).

&Quot; (24) "

는 다중 신호의 상관관계에 무관하게 항상 rank가 M이 된다.
At this time, a spatially smoothed signal covariance matrix

The rank is always M regardless of the correlation of the multiple signals.

대신에 [수학식 25]와 같은 제 2 스펙트럼 밀도 행렬을 구하여 MUSIC과 유사한 부공간 기법[비특허문헌 5]에 적용한다. In the present invention, instead of obtaining the array antenna covariance matrix, the array antenna first spectral density matrix L _{(2) R} is obtained and used. In addition, a spatially smoothed covariance matrix

Instead, a second spectral density matrix as shown in [Equation 25] is obtained and applied to a subspace method similar to MUSIC [Non-Patent Document 5].

&Quot; (25) "

That is, L _{(2) R} in the above equation (22 ₎ is obtained by calculating as a difference between 2L ₍₁₎ ^{? 2} and L ₍₂₎ .

In order to combine the SO (Second Order) technique with the SS (Spatial Smoothing) technique, the SS (Spatial Smoothing) technique is applied to the spectral density matrices of F ₍₂₎ The spectral density matrix of the SS-SO (Spatial Smoothed Second Order) technique can be obtained by performing calculations such as Equations (22) and (25).

Next, the second spectral density matrix is subjected to eigenvalue decomposition, and an incoming direction angle is extracted using an eigenvector corresponding to the minimum eigenvalue (S70).

을 고유치 분해(eigenvalue decomposition)한다. 즉, 고유치 분해를 통하여 L개의 고유치와 고유벡터를 얻을 수 있다.The obtained L x L second spectral density matrix

Eigenvalue decomposition. That is, L eigenvalues and eigenvectors can be obtained through eigenvalue decomposition.

이 된다.Assuming that the number of signals is M and the eigenvalues are arranged in the order of magnitude, Equation (26) is obtained. Where the M eigenvalue components are by signal components and the LM minimum eigenvalues are

.

&Quot; (26) "

The eigenvectors corresponding to the LM minimum eigenvalues become a noise subspace matrix V _n as shown in Equation (27) by the same principle as the MUSIC technique (see Non-Patent Document 5). And [Equation 22] linearly column vector of independent A ^₂ = A ^△ ₂ matrix shown in (the search (searching) vector la called) is equal to Equation (28), which is V _n and a quadrature (orthogonal ).

&Quot; (27) "

&Quot; (28) "

Using the orthogonality of V _n and a _s ^T (?) Described above, the vertices selected on the function graph of the incoming directional angle expressed by the formula of (29) become the predicted incoming directional angles from the signal source.

&Quot; (29) "

값들은 0이 되고 [수학식 29]의 식으로 표현되는 가상 함수값은 이론적으로 무한대가 된다. 이들 꼭지점들이 신호원으로부터의 예측된 도래방향각들이 된다.
Here, in the process of changing the angle θ from 0 ° to 360 °, in the vicinity of the actual LM arrival direction angles

The values become 0 and the virtual function value expressed by the equation of (29) becomes theoretically infinite. These vertices are the predicted direction angles from the source.

The effects of the present invention will be described in more detail with reference to Figs. 6 to 9. Fig.

The following example shows that SS-SO is superior to SS in predicting the direction of arrival of correlated signals when correlated antenna noise is present.

The two 70% correlated signals coming from the 5 ° and 12 ° directions respectively are analyzed using the SS and the proposed SS-SO method. A ULA consisting of twelve antenna elements divided into three overlapping subarrays of size 10 is considered. Of the antennas, the two antennas have fully correlated antenna noise and the rest of the antenna has uncorrelated noise. The resolution performance is tested with the number of sample data N = 512 and S / N = 5 dB as shown in FIG. In this case, only the SS-SO method analyzes two peak values without error, and the SS method fails to detect two signal directions.

Next, FIG. 7 reflects the tests performed to determine how well the two DOA estimation methods predict DOAs when the two 70% correlated signals arrive in directions of 5 and 10 degrees, respectively. The method according to the invention clearly shows that in this case it also gives an accurate result with an error of about 0.25 [deg.].

For more accurate evaluation and comparison of the experimental results, the RMS error and the multiple signal detection probability of the DOAs of the correlated multiple signals were investigated through statistical analysis.

A comparison between the SS and the proposed SS-SO algorithm is statistically performed to analyze the accuracy of the prediction of the direction angle of arrival of the 70% correlated multiple signals in the presence of fully correlated antenna noise. The ULA consists of 10 antennas divided into three redundant sub-arrays of size 8 with a distance between half-wave antennas. The number of independent experiments performed is 100, the number of sample data used is 256, and the S / N is 5 dB.

As shown in FIG. 8, in the DOA prediction using the SS algorithm, the RMS errors decrease as the angular spacing between multiple signals increases, but the detection probability does not exceed 12% even if the separation between the two signals is extended to 17 degrees. However, in Fig. 8, the RMS errors increase as the angular separation between multiple signals decreases in the DOA prediction using the SS-SO algorithm, but the RMS error does not exceed 0.2 degrees even if the separation between the two signals is narrowed to 3 degrees The detection probability is 100% in all cases.

The SS-SO algorithm can completely detect multiple correlated signals with very low RMS error in perfectly correlated antenna noise environments. However, SS can not predict correctly correlated multiple signals in fully correlated antenna noise environments. Thus, it can be seen that the SS-SO algorithm provides very good resolution for DOA prediction of correlated multiple signals under correlated antenna noise environments.

In the present invention, a very reliable spatially smoothed self-convolution-based directional angle estimation method called "Spatially Smoothed Secondary (SS-SO)" algorithm is proposed. The prediction method according to the present invention has been developed by combining the SO and SS algorithms and is very effective even when the multiple signals arriving at the antenna array are correlated with each other in the presence of correlated additional noise, Respectively.

The method proposed in the present invention will contribute to the development of a direction detection system equipped with an antenna array which can be easily exposed to an environment such as an airwave with an antenna noise correlated with a correlated signal.

The invention made by the present inventors has been described concretely with reference to the embodiments. However, it is needless to say that the present invention is not limited to the embodiments, and that various changes can be made without departing from the gist of the present invention.

10: receiver 20: signal source
30: DOA prediction device 40: Antenna array

Claims (8)

A spatial smoothed self-convolutional approach angle predicting method for predicting an incoming direction angle (DOA) at a receiver that receives a signal from a plurality of signal sources via an antenna array,
(a) obtaining a reception signal (hereinafter referred to as a first signal) when transmission signals from multiple signal sources are received through an antenna array;
(b) performing a self-convolution on the first signal to obtain a new signal (hereinafter referred to as a second signal);
(c) transforming the first signal represented by a linear vector (hereinafter referred to as a first signal vector) into frequency domain data through Fourier transform;
(d) expressing the second signal as a linear vector (hereinafter referred to as a second signal vector) in a frequency domain through Fourier transform;
(e) extracting a first spectral density matrix using an operator for performing an element-by-element multiplication between two matrices (hereinafter referred to as a delta element);
(f) spatially smoothing the first spectral density matrix to obtain a second spectral density matrix; And
(g) decomposing the second spectral density matrix by eigenvalness, and extracting an arrival direction angle using an eigenvector corresponding to the minimum eigenvalue, and estimating an arrival direction angle based on the spatially smoothed self-convolution.
The method according to claim 1,
Wherein the first spectral density matrix is obtained using a spectral density matrix obtained from data of a frequency domain of the first and second signal vectors.
3. The method of claim 2,
Wherein the first spectral density matrix L _{(2) R} is defined by < _{RTI ID} = _{0.0 > (1). &} Lt _{; / RTI &gt};
[Equation 1]

Here, L ₍₁₎ and L ₍₂₎ are spectral density matrices obtained from data in the frequency domain of the first and second signal vectors, respectively, and? Is delta-specific.
The method according to claim 1,
Characterized in that the antenna array is a uniform linear array (ULA) having Q identical antennas divided into P (= Q - L + 1) overlapping sub-arrays of size L. The spatially smoothed self- Each prediction method.
The method of claim 3,
Wherein the second spectral density matrix is obtained by [Expression 2]. ≪ EMI ID = 2.0 >
[Equation 2]

Where ( L _{(2) R} ) _p is the first spectral density matrix of the pth subarray,
P is the number of sub-arrays.
The method of claim 3,
Wherein the arrival direction angle is obtained using the orthogonality of the eigenvector and the steering vector.
The method according to claim 6,
The arrival direction angle is obtained by the following equation 3 and is obtained as? When the value of _Psso is infinite in the process of changing the angle of 0 from 0 to 360 degrees, based on the spatially smoothed self-convolution Direction angle prediction method.
[Equation 3]

V _{M + 1} , v _{M +2} , ..., v _L are the eigenvectors corresponding to the minimum eigenvalues, and a _s (θ) is the steering vector.
8. The method of claim 7,
Wherein the steering vector a _s (&thetas;) is obtained by the following equation (4).
[Equation 4]

Where D is the distance between the antennas, and [lambda] is the wavelength of the transmitted signal.

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