A matrix decomposition based direction finding method

Abstract

This invention relates to a direction-finding method based on matrix decomposition, belonging to the field of array signal processing technology. The invention first calculates the covariance matrix of the received data, then performs matrix decomposition and reconstruction based on the covariance matrix, and finally constructs a solution function by combining the spatial relationship between the reconstructed matrix and the array steering vector. The direction of arrival of the signal source is obtained from the mapping relationship between the peak value of the solution function and the signal incident angle. This invention utilizes the orthogonality between noise vectors to reduce the impact of noise on the direction of arrival (DOA), which can further improve the stability of the direction-finding algorithm.

Description

Technical Field

[0001] This invention relates to the field of array signal processing technology, and in particular to a direction finding method based on matrix decomposition. Background Technology

[0002] Spatial spectrum algorithms, as super-resolution direction-finding algorithms, are widely used due to their high spatial resolution. Their principle is to utilize the orthogonality between the noise subspace and the signal subspace, constructing a solution function and performing spatial traversal to obtain the distribution relationship of signal energy in each spatial domain, thereby completing the DOA estimation. Compared with traditional interferometer algorithms, they have certain advantages in terms of the number of signal sources that can be solved simultaneously and in direction-finding accuracy.

[0003] However, during the solution process of the above algorithm, the presence of received noise causes information leakage between the signal subspace and the noise subspace when performing eigenvalue decomposition on the covariance matrix. This disrupts the orthogonality of the two subspaces and reduces the direction-finding accuracy of the algorithm. Summary of the Invention

[0004] In view of this, this invention proposes a direction-finding method based on matrix decomposition. This invention utilizes the orthogonality between noise vectors to reduce the impact of noise on the Direction of Ability (DOA), thereby further improving the stability of the direction-finding algorithm.

[0005] The objective of this invention is achieved through the following technical solutions:

[0006] A direction-finding method based on matrix decomposition, applied to an array antenna, includes the following steps:

[0007] Step 1: Obtain the received signal from the array antenna, and calculate the time-averaged estimate of the covariance matrix using a finite number of sampled samples. ;

[0008] Step 2: For The decomposition yields matrices G and H.

[0009] Step 3: Reorganize the decomposed matrices G and H to obtain matrix Q:

[0010]

[0011] Wherein, the superscript H denotes the conjugate transpose of the matrix, and M is the number of array elements of the antenna array;

[0012] Step 4: Construct the solution function P, obtain the mapping relationship between the peak value of the solution function and the incident angle of the signal, and complete the DOA estimation.

[0013] Furthermore, in step 1, the time-averaged estimate of the covariance matrix is:

[0014]

[0015] in, Let N be the time-averaged estimate of the covariance matrix R, and N be the number of sampling points. This indicates the received signal of the array antenna.

[0016] Furthermore, in step 2, matrices G and H are respectively:

[0017]

[0018]

[0019] Where K is the number of information sources, Indicates taking the matrix Columns 1 to K, Indicates taking the matrix The K+1th column to the last column.

[0020] Furthermore, in step 4, the function P is solved as follows:

[0021]

[0022] Here, det(·) represents calculating the determinant of a matrix. and When the signal orientation is The A1 and A2 matrices at that time; This indicates taking rows 1 to K of matrix A. , which means taking the (K+1)th row to the last row of matrix A;

[0023] A is the array steering vector matrix:

[0024]

[0025] In the formula, j is the imaginary unit, f is the signal frequency, and d i Let be the distance between the i-th array element and the reference array element, where i = 1, 2, ..., M, and M is the total number of array elements. Let be the incident angle of the k-th signal, k = 1, 2, ..., K, where K is the total number of signals and c is the speed of light.

[0026] Compared with the prior art, the present invention has the following advantages:

[0027] 1. Compared with spatial spectrum direction finding algorithms, this invention reduces the impact of noise.

[0028] 2. Compared with spatial spectrum direction finding algorithms, this invention reduces the computational dimensionality through matrix decomposition. Attached Figure Description

[0029] Figure 1 This is a diagram showing the DOA estimation results of the method in the embodiment under single-source conditions, with a source azimuth of 20°, a signal-to-noise ratio of 15dB, a signal frequency of 500MHz, and a snapshot number of 1024.

[0030] Figure 2 The diagram shows the solution results of the method in the embodiment under dual source conditions, with source azimuths of -30° and 20° respectively, a signal-to-noise ratio of 15dB, a signal frequency of 500MHz, and a snapshot number of 1024. Detailed Implementation

[0031] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings.

[0032] A direction-finding method based on matrix decomposition first obtains an estimated covariance matrix from sampled snapshot data. Then, matrix decomposition and reconstruction are performed based on the covariance matrix. Finally, a solution function is constructed by combining the spatial relationship between the reconstructed matrix and the array steering vector. The direction of arrival of the signal source is obtained from the mapping relationship between the peak value of the solution function and the signal incident angle. Specifically, the method includes the following steps:

[0033] Step 1: Obtain the array received signal and calculate the time-averaged estimate of the covariance matrix using a finite number of sampled samples. :

[0034]

[0035] in, Let N be the time-averaged estimate of the covariance matrix R, and N be the number of sampling points. This indicates that the array is receiving signals.

[0036] Step 2: For Decomposition yields matrices G and H:

[0037]

[0038]

[0039] Where K is the number of information sources, Indicates taking The first to Kth columns of the matrix, Indicates taking The (K+1)th column to the last column of the matrix.

[0040] Step 3: Reorganize the decomposed matrices G and H to obtain matrix Q:

[0041]

[0042] Here, the superscript H denotes the conjugate transpose of the matrix, and M is the number of matrix elements.

[0043] Step 4: Construct the solution function P:

[0044]

[0045] Here, det(·) represents calculating the determinant of a matrix. and When the signal orientation is The A1 and A2 matrices at time; the A1 matrix is This indicates taking rows 1 to K of matrix A, and matrix A2 is... , which means taking the (K+1)th row to the last row of matrix A.

[0046] When A is the array steering vector matrix, we have:

[0047]

[0048] In the above formula, f is the signal frequency, and d i Let i be the distance between the i-th (i=1,2,…,M) array element and the reference array element. Let be the incident angle of the k-th (k=1,2,…,K) signal, and c be the speed of light.

[0049] After solving, the mapping relationship between the peak value of the solution function P and the incident angle of the signal is obtained, thus completing the DOA estimation.

[0050] Here is a more specific example:

[0051] A direction-finding method based on matrix decomposition includes the following steps:

[0052] Step 1: Obtain the array received signal and calculate the time-averaged estimate of the covariance matrix using a finite number of sampled samples. :

[0053]

[0054] in, Let N be the time-averaged estimate of the covariance matrix R, and N be the number of sampling points. This indicates that the array is receiving signals.

[0055] Step 2: For Decomposition yields matrices G and H:

[0056] The known array receiving data model is as follows:

[0057] X = AS+N

[0058] In the above formula, X represents the array received data.

[0059] For array space guide vector,

[0060] f is the signal frequency, d i Let i be the distance between the i-th (i=1,2,…,M) array element and the reference array element. Let be the incident angle of the k-th (k=1,2,…,K) signal, and c be the speed of light.

[0061] For source vector, This is the noise vector.

[0062] If A is decomposed into ,in , , This means taking rows 1 to K of matrix A. Let represent taking the (K+1)th row to the last row of matrix A. Then, the covariance matrix can be expressed as:

[0063] Since the noise vector and the signal steering vector are orthogonal, the above equation can be rearranged as:

[0064] ,in

[0065] At this time, ,

[0066] Further deduction can be made:

[0067]

[0068] Since the noise vector and the signal steering vector are orthogonal, the above equation can be rearranged as:

[0069]

[0070] It can be seen that the above formula still contains a noise factor. and Further deduction leads to Then we have:

[0071]

[0072] Since the noise vector and the signal steering vector are orthogonal, and different noise vectors are orthogonal to each other, the above equation can be rewritten as:

[0073]

[0074] From the above formula, we can see that the matrix Independent of noise, subsequent steps can be based on the matrix. Construct a solution function to reduce the impact of noise on the direction finding results.

[0075] Step 3: Reorganize the decomposed matrices G and H to obtain matrix Q:

[0076]

[0077] Here, the superscript H denotes the conjugate transpose of the matrix, and M is the number of matrix elements.

[0078] Step 4: Construct the solution function P:

[0079]

[0080] Here, det(·) represents calculating the determinant of a matrix. and When the signal orientation is The A1 and A2 matrices at that time.

[0081] A detailed derivation of the solution function P yields the following:

[0082]

[0083]

[0084] Easy to know Let it be a constant value. Then the above equation can be further simplified to:

[0085]

[0086] From the above formula, it can be seen that only when When the azimuth of the incoming signal wave is consistent (i.e. ), Take the maximum value:

[0087]

[0088] at this time, Also take the maximum value.

[0089] After solving, the mapping relationship between the peak value of the solution function P and the incident angle of the signal is obtained, thus completing the DOA estimation.

[0090] To verify the effectiveness of this method, simulations can be performed.

[0091] Simulation conditions: M=16 element uniform linear array, signal frequency of 500MHz, bandwidth B=1MHz, number of snapshots N=1024, signal-to-noise ratio SNR=15dB.

[0092] Figure 1This is a graph showing the DOA estimation results of this method under single-source conditions, with the source azimuth at 20°. As can be seen from the graph, the source arrival direction calculated by this method is 20°.

[0093] Figure 2 This figure shows the solution results of this method under dual-source conditions, with source azimuths of -30° and 20° respectively. As can be seen from the figure, the source arrival directions calculated by this method are -29.6° and 19.6° respectively.

[0094] Simulation results show that this method can obtain accurate spatial distribution information of the information source.

[0095] This invention utilizes the orthogonality between noise vectors to reduce the impact of noise on DOA, which can further improve the stability of the direction finding algorithm.

Claims

1. A matrix decomposition based direction finding method applied to an array antenna, characterized in that, Includes the following steps: Step 1: Obtain the received signal of the array antenna, calculate the time average estimation matrix of the covariance matrix with limited sampling samples ; Step 2: For The decomposition yields matrices G and H. Step 3: Reorganize the decomposed matrices G and H to obtain matrix Q: Wherein, the superscript H denotes the conjugate transpose of the matrix, and M is the number of array elements of the antenna array; Step 4: Construct the solution function P, obtain the mapping relationship between the peak value of the solution function and the incident angle of the signal, and complete the DOA estimation.

2. The direction finding method based on matrix decomposition according to claim 1, characterized in that, In step 1, the time-averaged estimate of the covariance matrix is: in, Let N be the time-averaged estimate of the covariance matrix R, and N be the number of sampling points. This indicates the received signal of the array antenna.

3. The direction finding method based on matrix decomposition according to claim 1, characterized in that, In step 2, matrices G and H are respectively: Where K is the number of information sources, Indicates taking the matrix Columns 1 to K, Indicates taking the matrix The K+1th column to the last column.

4. The direction finding method based on matrix decomposition according to claim 1, characterized in that, In step 4, the function P is solved as follows: Here, det(·) represents calculating the determinant of a matrix. and When the signal orientation is The A1 and A2 matrices at that time; This indicates taking rows 1 to K of matrix A. , which means taking the (K+1)th row to the last row of matrix A; A is the array steering vector matrix: In the formula, j is the imaginary unit, f is the signal frequency, and d i Let be the distance between the i-th array element and the reference array element, where i = 1, 2, ..., M, and M is the total number of array elements. Let be the incident angle of the k-th signal, k = 1, 2, ..., K, where K is the total number of signals and c is the speed of light.

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