A two-dimensional DOA estimation method for single snapshot data

Abstract

The present invention discloses a two-dimensional DOA estimation method for single snapshot data, including: setting a large-scale uniform parallel array, performing single snapshot sampling on the received signal; dividing the entire large-scale uniform parallel array into a number of overlapping and identical sub-parallel arrays, calculating the autocorrelation matrix and cross-correlation matrix of each sub-parallel array, averaging the sub-correlation matrix to obtain an estimate of the correlation matrix of the entire array; constructing a generalized DOA matrix, decomposing its eigenvalues ​​to estimate the direction matrix and phase rotation matrix; estimating the two-dimensional direction of arrival based on the estimated direction matrix and phase rotation matrix. The present invention adopts a spatial smoothing method, and only needs single snapshot data to effectively estimate the DOA of the signal, does not require spatial spectrum search, and reduces the complexity of the algorithm; fully utilizes the autocorrelation information and cross-correlation information of the single snapshot received data of the dual parallel arrays, and the obtained DOA estimation angle can be automatically paired, with better DOA estimation performance.

Description

Technical Field

[0001] The invention belongs to array signal processing, and in particular relates to a two-dimensional DOA estimation method for single snapshot data. Background Art

[0002] Direction of Arrival (DOA) estimation is an important direction of array signal processing. It is a technology that estimates the source position through the signal received by the sensor array. The application of DOA technology in large-scale antenna arrays can quickly and accurately estimate the source position, which will play an important role in sonar, radar and 5G communication systems. Traditional subspace DOA estimation methods, such as the MUSIC (Multiple Signal Classification) algorithm and the ESPRIT (Estimating Signal Parameters via Rotational Invariance Techniques, ESPRIT) algorithm, use rotational invariance to estimate signal parameters. It requires a lot of snapshots of received data to estimate the signal subspace, resulting in slow algorithm estimation speed. In addition, many algorithms require full-space spectrum peak search, which is very complex when directly applied to large-scale arrays. Although the DOA matrix method can completely avoid spectrum peak search and has a relatively low complexity, it does not fully utilize the received data information, has a relatively low estimation accuracy, and requires multiple snapshots of received data to construct the DOA matrix. Summary of the invention

[0003] Purpose of the invention: The purpose of the present invention is to provide a two-dimensional DOA estimation method for single snapshot data in a large-scale uniform parallel array, reduce the algorithm complexity, and only need one snapshot of received data to efficiently estimate the two-dimensional DOA, make full use of the received information, and improve the two-dimensional DOA angle estimation performance.

[0004] Technical solution: The present invention provides a two-dimensional DOA estimation method for single snapshot data, which specifically includes the following steps:

[0005] Step 1: Set up a large-scale uniform parallel array to perform single-snap sampling on the received signal;

[0006] Step 2: Divide the entire large-scale uniform parallel array into several overlapping and identical sub-parallel arrays, calculate the autocorrelation matrix and cross-correlation matrix of each sub-parallel array, and average the sub-correlation matrices to obtain the correlation matrix estimate of the entire array;

[0007] Step 3: Construct a generalized DOA matrix and estimate the direction matrix and phase rotation matrix by eigenvalue decomposition; estimate the two-dimensional direction of arrival based on the estimated direction matrix and phase rotation matrix.

[0008] Furthermore, in step 1, a first array and a second array of large-scale uniform linear arrays are provided, each array comprises M+N-1 array elements, the distance between adjacent array elements is half a wavelength, and the arrays are placed parallel to the x-axis.

[0009] Furthermore, step 1 specifically includes:

[0010] Suppose there are K incoherent far-field narrowband independent signal sources s k (t), where 1≤k≤K, s k (t) is incident on this array, the signal wavelength is λ, and the angle between the kth signal wave direction and the x-axis is α k , the angle with the y-axis is β k , each sub-array has M array elements; the output expression of the nth sub-array of the first array is:

[0011] x n (t) = [x n (t),x n+1 (t),…,x n+M (t)] T =A M D m-1 s(t)+n1(t)

[0012] Where n1(t) is additive white Gaussian noise, x n (t) is the output of the nth element in the first array, A M It is a (M+1)×K dimensional direction matrix:

[0013]

[0014] D is the phase rotation matrix between sub-arrays used for smoothing:

[0015]

[0016] Where d≤λ / 2 represents the spacing between adjacent array elements. The output expression of the nth subarray of the second array is:

[0017] y n (t) = [y n (t),y n+1 (t),…,y n+M (t)] T =A M D m-1 Φs(t)+n2(t)

[0018] Among them, n2(t) is the noise, y n (t) is the output of the nth element of the second array, and Φ is the rotation matrix between the first array and the second array:

[0019]

[0020] Furthermore, step 2 specifically includes:

[0021] The autocorrelation matrix of the nth sub-array received data of the first array is:

[0022]

[0023] Among them, R S =E[s(t)s H (t)] is the signal covariance matrix, I is the identity matrix, σ 2 represents the additive white Gaussian noise power received by the array;

[0024] The cross-correlation matrix of the nth forward sub-matrix of the second array and the nth forward sub-matrix of the first array is:

[0025]

[0026] The autocorrelation matrix of the nth forward sub-matrix of the second array is:

[0027]

[0028] The cross-correlation matrix between the nth forward sub-array of the first array and the nth forward sub-array of the second array is:

[0029]

[0030] By using spatial smoothing, the single snapshot signal of a large-scale antenna array is virtualized into multiple snapshot signals of a larger-scale signal.

[0031] Define the spatially smoothed autocorrelation matrix of the first array as:

[0032]

[0033] The spatially smoothed cross-correlation matrix of the second array and the first array is:

[0034]

[0035] The forward spatially smoothed autocorrelation matrix of the second array is:

[0036]

[0037] The spatially smoothed cross-correlation matrix of the first and second arrays is:

[0038]

[0039] R 11Perform eigenvalue decomposition and let ε1,…,ε K is the matrix R 11 Under the assumption of white noise, the noise variance σ is obtained by averaging the MK small eigenvalues. 2 Estimates.

[0040] Furthermore, the generalized DOA matrix construction method in step 3 is:

[0041]

[0042] in,(·) + represents the MP pseudo-inverse operation of the matrix, R 12 and R 21 are the spatially smoothed cross-covariance matrices of the first and second arrays, respectively, Among them, R S =E[s(t)s H (t)] is the signal covariance matrix, I is the identity matrix, σ 2 is the noise variance, R 11 and R 22 are the spatially smoothed autocovariance matrices of the first and second arrays respectively; R is obtained by spatial smoothing 11 , R 22 , R 12 , R 21 , the expression is:

[0043]

[0044]

[0045]

[0046]

[0047] Furthermore, the implementation process of step 3 is as follows:

[0048] RA E =A E Φ

[0049] in,

[0050] Perform eigendecomposition on the DOA matrix R, where the eigenvector is A E The eigenvalue is an estimate of Φ, and the eigenvalue is obtained according to the eigenvalue:

[0051]

[0052] where angle(·) represents the complex phase operation, φ krepresents the kth eigenvalue of R; the first M rows of the eigenvector of R Post-M behavior definition:

[0053]

[0054]

[0055] Define c1 = [c 01 ,u 1k ] T , c2=[c 02 ,u 2k ] T , where u 1k =cosα 1k ,u 2k =cosα 2k ,

[0056]

[0057] Bc1=t 1k , Bc2=t 2k , where t 1k is the kth column of T1, t 2k is the kth column of T2. Solving the above equation using the least squares method yields:

[0058]

[0059]

[0060] in, and All are for cosα k The estimation of DOA angle α k The estimated expression of is:

[0061]

[0062] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:

[0063] (1) Compared with the traditional DOA matrix method, the method proposed in the present invention fully utilizes the autocorrelation information and cross-correlation information of the array single snapshot received signal, and has better DOA estimation performance;

[0064] (2) Compared with the traditional subspace method, the method of the present invention has lower complexity;

[0065] (3) The method of the present invention only requires a single snapshot received signal to estimate the two-dimensional DOA. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 is a flow chart of the present invention;

[0067] Figure 2 It is a schematic diagram of the structure of a large-scale uniform parallel array in the present invention;

[0068] Figure 3 It is a scatter plot of two-dimensional DOA estimation in the present invention;

[0069] Figure 4 The performance comparison between the method of the present invention and the traditional DOA estimation method at different signal-to-noise ratios and the angle between the direction of arrival and the x-axis is shown;

[0070] Figure 5 The performance of the method of the present invention and the traditional DOA estimation method under different signal-to-noise ratios is compared with respect to the angle between the direction of arrival and the y-axis. DETAILED DESCRIPTION

[0071] Symbols: In the present invention, (·) T represents the matrix transpose, (·) H represents the conjugate transpose of the matrix, (·) * represents matrix conjugate, capital letter X represents matrix, lowercase letter x(·) represents vector, I M Represented as an M×M identity matrix, represents the Hadamard product, diag(v) represents the diagonal matrix composed of the elements in v, E[·] represents the expectation of the matrix, and angle(·) represents the phase angle operation.

[0072] like Figure 1 As shown, this embodiment provides a two-dimensional DOA estimation method using only a single snapshot signal in a large-scale uniform parallel array, specifically:

[0073] Step 1: Arrange a large-scale uniform parallel antenna array in space to collect single snapshot signals;

[0074] In this embodiment, the large-scale uniform parallel antenna array in step 1 is as follows: Figure 2 As shown, it contains two large-scale uniform linear arrays placed along the x-axis, called array 1 and array 2. Each array contains M+N-1 array elements, which can be divided into N identical and overlapping sub-arrays, and the distance between adjacent array elements is half a wavelength. Array 1 and array 2 are parallel to each other with a spacing of half a wavelength. The receiving model of the entire large-scale uniform parallel array can be expressed as follows:

[0075] Assume that there are K incoherent far-field narrowband independent signal sources s in space k (t)(1≤k≤K) is incident on this array, the signal wavelength is λ, and the angle between the kth signal wave direction and the x-axis is α k, the angle with the y-axis is β k , each sub-array has M array elements; the output of the nth sub-array of array 1 is:

[0076] x n (t) = [x n (t),x n+1 (t),…,x n+M (t)] T =A M D m-1 s(t)+n1(t)

[0077] Where n1(t) is additive white Gaussian noise, x n (t) is the output of the nth element of array 1, A M It is a (M+1)×K dimensional direction matrix:

[0078]

[0079] D is the phase rotation matrix between sub-arrays used for smoothing:

[0080]

[0081] Similarly, the output for the nth subarray of array 2 is:

[0082] y n (t) = [y n (t),y n+1 (t),…,y n+M (t)] T =A M D m-1 Φs(t)+n2(t)

[0083] Among them, n2(t) is the noise, y n (t) is the output of the nth element of array 2, and Φ is the rotation matrix between arrays 1 and 2:

[0084]

[0085] Step 2: If Figure 2 As shown, the dual parallel array is divided into N identical sub-arrays, each sub-array contains M array elements, of which M-1 array elements are the same as the previous sub-array, and the autocorrelation matrix and cross-correlation matrix of each sub-parallel array are calculated, and the sub-correlation matrices are averaged to obtain the correlation matrix estimate of the entire array;

[0086] When the number of snapshots is sufficient, the autocorrelation matrix of the received data of the nth subarray of array 1 is:

[0087]

[0088] Among them, R S =E[s(t)s H (t)] is the signal covariance matrix, and I is the identity matrix.

[0089] When the number of snapshots is sufficient, the cross-correlation matrix between the nth forward subarray of array 2 and the nth forward subarray of array 1 is:

[0090]

[0091] Similarly, when there are enough snapshots, the autocorrelation matrix of the nth forward subarray of array 2 is:

[0092]

[0093] When the number of snapshots is sufficient, the cross-correlation matrix between the nth forward subarray of array 1 and the nth forward subarray of array 2 is:

[0094]

[0095] However, in the case of a single snapshot, the signal and noise are not statistically independent, so the result of the above expression cannot be used directly. In this case, the spatial smoothing technique can be used to virtualize the single snapshot signal of the large-scale antenna array into a multi-block signal of a larger-scale signal. The spatial smoothing autocorrelation matrix of array 1 is defined as:

[0096]

[0097] The spatial smoothed cross-correlation matrix of array 2 and array 1 is defined as:

[0098]

[0099] Similarly, the forward spatial smoothed autocorrelation matrix of array 2 is:

[0100]

[0101] The spatially smoothed cross-correlation matrix of array 1 and array 2 is:

[0102]

[0103] R 11 Perform eigenvalue decomposition (EVD) and let ε1,…,ε K is the matrix R 11 Under the assumption of white noise, the noise variance σ can be obtained by averaging the K small eigenvalues. 2 Estimates.

[0104] Step 3: Construct a generalized DOA matrix, decompose its eigenvalues ​​to estimate the direction matrix and phase rotation matrix, and estimate the two-dimensional direction of arrival.

[0105] Definition C 11 =R 11 -σ 2 I, C 22 =R 22 -σ 2 I. Define the DOA matrix as

[0106]

[0107] For incoherent sources, A M and R S If the matrix is ​​full rank, Φ has no identical diagonal elements. Then the K non-zero eigenvalues ​​of the DOA matrix R are equal to the K diagonal elements in Φ, and the eigenvectors corresponding to these values ​​are equal to the corresponding signal direction vectors, that is,

[0108] RA E =A E Φ

[0109] in,

[0110] Obviously, by performing eigendecomposition on the DOA matrix R, we can obtain A E and an estimate of Φ, where the eigenvector is A E The eigenvalue is an estimate of Φ, and the eigenvalue is obtained according to the eigenvalue:

[0111]

[0112] where angle(·) represents the complex phase operation, φ k represents the kth eigenvalue of R. The first M rows of the eigenvector of R are recorded as Post-M behavior The DOA angle is estimated by using the Vandermonde characteristic of the direction matrix.

[0113] definition

[0114]

[0115]

[0116] Define c1 = [c 01 ,u 1k ] T , c2=[c 02 ,u 2k ] T , where u 1k =cosα 1k ,u 2k=cosα 2k definition

[0117]

[0118] Obviously Bc1=t 1k , Bc2=t 2k , where t 1k is the kth column of T1, t 2k is the kth column of T2. Using the least squares method to solve the above equation, we have

[0119]

[0120]

[0121] in, and All are for cosα k The DOA angle α is estimated k Estimates:

[0122]

[0123] Figure 3 This is a scatter plot of the two-dimensional DOA estimation of the method of the present invention; the simulation parameters are set to the angles between the wave direction and the x-axis are 50°, 60°, and 70°, and the angles between the wave direction and the y-axis are 55°, 65°, and 75°, respectively. The two large-scale uniform linear arrays along the x-axis each contain 128 array elements, and the signal-to-noise ratio SNR = 20dB. It can be seen from the figure that the two-dimensional angle matching is successful, the DOA estimation value is accurately distributed near the real angle, the error is very small, and the algorithm has good stability.

[0124] Figure 4 The performance comparison of the angle between the direction of arrival and the x-axis under different signal-to-noise ratios between the method of the present invention and the traditional DOA method is shown in the figure. The simulation parameters are set to the angle between the direction of arrival and the x-axis to be 50°, 60°, and 70°, respectively. The two large-scale uniform linear arrays along the x-axis each contain 128 array elements. As can be seen from the figure, the algorithm has good stability, and estimation can be achieved even at low signal-to-noise ratios. There is no accuracy threshold at high signal-to-noise ratios. As the signal-to-noise ratio increases, the estimation error of the angle between the direction of arrival and the x-axis of the present invention decreases, and the estimation accuracy is higher than the traditional DOA matrix method and DFT-least squares method, and slightly worse than the spatial smoothing ESPRIT algorithm.

[0125] Figure 5The performance comparison of the angle between the direction of arrival and the x-axis under different signal-to-noise ratios between the method of the present invention and the traditional DOA method; the simulation parameters are set to the angle between the direction of arrival and the y-axis of 55°, 65°, and 75°, respectively, and the two large-scale uniform linear arrays along the x-axis each contain 128 array elements. It can be seen from the figure that the algorithm has good stability, and the estimation can be achieved at a low signal-to-noise ratio, and there is no accuracy threshold at a high signal-to-noise ratio. With the increase of the signal-to-noise ratio, the estimation error of the angle between the direction of arrival and the y-axis of the present invention decreases, and the estimation accuracy is significantly higher than the DFT-least squares method, and slightly better than the traditional DOA matrix method and the spatial smoothing ESPRIT algorithm.

Claims

1. A two-dimensional DOA estimation method for single snapshot data, characterized in that: The specific steps include: Step 1: Set up a large-scale uniform parallel array to perform single-snap sampling on the received signal; Step 2: Divide the entire large-scale uniform parallel array into a number of overlapping and identical sub-parallel arrays, calculate the autocorrelation matrix and cross-correlation matrix of each sub-parallel array, and average the sub-correlation matrices to obtain an estimate of the correlation matrix of the entire array, where the sub-correlation matrices are the autocorrelation matrices and cross-correlation matrices of the sub-parallel arrays; Step 3: Construct a generalized DOA matrix and use its eigenvalue decomposition to estimate the direction matrix and phase rotation matrix; Estimate the two-dimensional direction of arrival based on the estimated direction matrix and the phase rotation matrix; The step 2 specifically includes: the autocorrelation matrix of the nth sub-array receiving data of the first array is: Among them, R S =E[s(t)s H (t)] is the signal covariance matrix, I is the identity matrix, σ 2 represents the additive white Gaussian noise power received by the array; The cross-correlation matrix of the nth forward sub-matrix of the second array and the nth forward sub-matrix of the first array is: The autocorrelation matrix of the nth forward sub-matrix of the second array is: The cross-correlation matrix between the nth forward sub-array of the first array and the nth forward sub-array of the second array is: By using spatial smoothing, the single snapshot signal of a large-scale antenna array is virtualized into a multi-snapshot signal of a larger-scale signal. Define the spatially smoothed autocorrelation matrix of the first array as: The spatially smoothed cross-correlation matrix of the second array and the first array is: The forward spatially smoothed autocorrelation matrix of the second array is: The spatially smoothed cross-correlation matrix of the first and second arrays is: R 11 Perform eigenvalue decomposition and let ε1,…,ε K is the matrix R 11 Under the assumption of white noise, the noise variance σ is obtained by averaging the MK small eigenvalues. 2 estimates; In step 1, a first array and a second array of large-scale uniform linear arrays are provided, each of the arrays comprises M+N-1 array elements, the distance between adjacent array elements in the arrays is half a wavelength, and the arrays are placed parallel to the x-axis; The step 1 specifically includes: Suppose there are K incoherent far-field narrowband independent signal sources s k (t), where 1≤k≤K, s k (t) is incident on this array, the signal wavelength is λ, and the angle between the kth signal wave direction and the x-axis is α k , the angle with the y-axis is β k , each sub-array has M+1 array elements; the output expression of the nth sub-array of the first array is: x n (t)=[x n (t),x n+1 (t),…,x n+M (t)] T =A M D m-1 s(t)+n1(t) Where n1(t) is additive white Gaussian noise, x n (t) is the output of the nth element in the first array, A M It is a (M+1)×K dimensional direction matrix: D is the phase rotation matrix between sub-arrays used for smoothing: Where d = λ / 2 represents the spacing between adjacent array elements. The output expression of the nth subarray of the second array is: y n (t)=[y n (t),y n+1 (t),…,y n+M (t)] T =A M D m-1 Φs(t)+n2(t) Among them, n2(t) is the noise, y n (t) is the output of the nth element of the second array, and Φ is the rotation matrix between the first array and the second array:

2. According to claim 1, a two-dimensional DOA estimation method for single snapshot data is characterized in that: The generalized DOA matrix construction method in step 3 is: in,(·) + represents the MP pseudo-inverse operation of the matrix, R 12 is the spatially smoothed cross-correlation matrix of the first and second arrays, R 21 is the spatially smoothed cross-correlation matrix of the second array and the first array, Among them, R S =E[s(t)s H (t)] is the signal covariance matrix, I is the identity matrix, σ 2 is the noise variance, R 11 and R 22 are the spatially smoothed autocovariance matrices of the first and second arrays, respectively; R 11 , R 22 , R 12 , R 21 It is obtained by spatial smoothing, and the expression is as follows:

3. The two-dimensional DOA estimation method for single snapshot data according to claim 1, characterized in that: The implementation process of step 3 is as follows: RA E =A E Φ in, Perform eigendecomposition on the DOA matrix R, where the eigenvector is A E The eigenvalue is an estimate of Φ, and the eigenvalue is obtained according to the eigenvalue: Where angle() represents the complex phase operation, φ k represents the kth eigenvalue of R; the first M rows of the eigenvector of R Post-M behavior definition: c1 = [c 01 , u 1k T , c2 = [c 02 , u 2k T , where u 1k = cosα 1k , u 2k = cosα 2k ,​​ Bc1=t 1k , Bc2=t 2k , where t 1k is the kth column of T1, t 2k is the kth column of T2. Solving the above equation using the least squares method yields: in, and All are for cosα k The estimation of DOA angle α k The estimated expression of is:

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