A direction finding method based on array received data reconstruction

Abstract

The application relates to a direction-finding method based on array-received data reconstruction, and belongs to the technical field of array signal processing. The application first calculates the covariance matrix of array-received signals, then combines the array flow characteristics to use the elements in the covariance matrix to perform array-received data reconstruction, and finally performs direction finding based on the reconstructed received data matrix, so that the processing gain and the direction-finding precision are further improved. The application can improve the processing gain of array signals and the spatial resolution of array direction finding without increasing the number of array elements and the array aperture. Compared with the traditional beam synthesis method, the application has higher direction-finding precision and sidelobe suppression ratio.

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 array received data reconstruction. Background Technology

[0002] Array signal processing is a crucial branch of modern signal processing, and DOA estimation has always been considered a key research area within this field. In traditional direction-finding methods, achieving higher spatial resolution requires increasing the number of array elements or the array aperture, thus increasing the system's hardware and software costs. However, spatial spectrum algorithms such as MUSIC and ESPRIT often involve eigenvalue decomposition and matrix inversion, resulting in substantial computational demands. These limitations restrict their applicability in engineering applications. Summary of the Invention

[0003] The technical problem to be solved by this invention is to provide a direction finding method based on array received data reconstruction in the field of array signal processing.

[0004] The technical problem to be solved by this invention is achieved by the following technical solution:

[0005] A direction-finding method based on array received data reconstruction includes the following steps:

[0006] Step 1: Calculate the covariance matrix R of the array signal:

[0007]

[0008] In the formula, X is the received data matrix with M elements, and the superscript [·] H Let r(m,p) denote the conjugate transpose of a matrix, where N is the number of sampling points, and r(m,p) is the element in the m-th row and p-th column of R.

[0009] Step 2: Select the elements in the first column of matrix R to form vector Y1, and select the elements in the first row of matrix R to form vector Y2.

[0010] Y1=[r(1,1),r(2,1),r(3,1),…,r(M,1)]

[0011] Y2=[r(1,1),r(1,2),r(1,3),…,r(1,M)]

[0012] Step 3: Remove redundant elements from Y1 and Y2, rearrange the element order, and merge them to reconstruct the array received data vector matrix Y:

[0013] Y=[r(1,M),r(1,M-1),…,r(1,2),r(1,1),r(2,2),…,r(M,1)] T ;

[0014] in,[·] T This is the transpose of the matrix;

[0015] Step 4: In the spatial set θ = {θ i |θ i =θ1,θ2,…,θ I The weighted vector w is constructed within the inner structure. i :

[0016]

[0017] Where θ is the set of I spatial scanning angles, f is the signal frequency, and c is the speed of light. and The reconstructed array element coordinates:

[0018] The x and y coordinates of the array elements in the original array are as follows:

[0019] x = [0, x1, x2, ..., x M-1 ] T

[0020] y = [0, y1, y2, ..., y M-1 ] T

[0021] The reconstructed array element coordinates are:

[0022]

[0023]

[0024] Where, x -(M-1) The value is x (M-1) The opposite number;

[0025] Step 5: Use the weighted vector w i Perform a spatially weighted scan of Y within the spatial set θ to construct the spatial spectral function P(θ):

[0026] P(θ i ) = w i H ·Y

[0027] Step 6: In P(θ) i Find K spectral peaks and their corresponding angle set θ d ={θ k |θ k =θ1,θ2,…,θ K} represents the azimuth angles of the K signals.

[0028] Compared with the prior art, the present invention has the following advantages:

[0029] 1. It can improve the processing gain of array signals without increasing the number of array elements or the array aperture;

[0030] 2. It can improve the spatial resolution of array direction finding without increasing the number of array elements or the array aperture;

[0031] 3. Compared with traditional beamforming methods, this invention has higher direction finding accuracy and sidelobe suppression ratio. Attached Figure Description

[0032] Figure 1 This is the overall flowchart of the present invention.

[0033] Figure 2 This is the direction-finding spatial spectrum of the present invention and conventional beamforming algorithms in the case of a single source.

[0034] Figure 3 This invention provides the direction-finding spatial spectrum of the present invention compared to conventional beamforming algorithms when there are multiple signal sources. Detailed Implementation

[0035] A direction-finding method based on array received data reconstruction is proposed. This method first calculates the covariance matrix of the array received data, then takes the first row and first column elements, performs redundancy removal, sorting, and merging to obtain the reconstructed array received data vector. Subsequently, a weighted vector is constructed in the spatial domain using the reconstructed array element coordinates. This weighted vector is then used to perform a spatial weighted scan of the reconstructed array received data vector in the spatial domain to obtain the direction-finding spatial spectrum. Finally, by locating the positions of spectral peaks in the spatial spectrum, the azimuth angle set of the signal is obtained, completing high-precision array direction finding after virtual aperture extension.

[0036] Reference Figure 1 The method specifically includes the following steps:

[0037] Step 1: Calculate the covariance matrix R of the array signal:

[0038]

[0039] In the above formula, N is the number of sampling points, X is the received data matrix of M elements, [·] H The received data matrix, being the conjugate transpose of the matrix, can be represented as follows when noise is ignored:

[0040] X = AS

[0041] A is an array manifold, A = [a1, a2, ..., a...]. K], K is the number of signals, when the array is a one-dimensional uniform linear array and the spacing d between adjacent array elements is half a wavelength, a i for:

[0042]

[0043] in,[·] T Let f be the transpose of the matrix, f be the signal frequency, and c be the speed of light;

[0044] S is the source matrix, S = [S1, S2, ..., S2] K If the received data of the i-th element in the array is:

[0045]

[0046] Let r(m,p) be the element in the m-th row and p-th column of R, then E{·} represents the expected value, [·] * To obtain conjugates, for m, p = 1, 2, ..., M, then we have:

[0047]

[0048] When the signals in S are uncorrelated, then E{S} i ·S * m}=0, i≠m, the above formula can be simplified to:

[0049]

[0050] In the above formula, δ k 2 Let be the power of the k-th signal;

[0051] Step 2: Select the elements in the first column of matrix R to form vector Y1, and select the elements in the first row of matrix R to form vector Y2.

[0052] Y1=[r(1,1),r(2,1),r(3,1),…,r(M,1)]

[0053] Y2=[r(1,1),r(1,2),r(1,3),…,r(1,M)];

[0054] Step 3: Remove redundant elements from Y1 and Y2, rearrange the element order, and merge them to reconstruct the array received data vector Y:

[0055]

[0056] In the above formula:

[0057]

[0058]

[0059] Step 4: In the spatial set θ = {θ i |θ i =θ1,θ2,…,θ I The weighted vector w is constructed within the inner structure. i :

[0060]

[0061] in, and The reconstructed array element coordinates:

[0062] The x and y coordinates of the array elements in the original array are:

[0063] x = [0, x1, x2, ..., x M-1 ] T = [0,d,2d,…,(M-1)d] T

[0064] y = [0, y1, y2, ..., y M-1 ] T =[0,0,0,…,0] T

[0065] The reconstructed array element coordinates are:

[0066]

[0067]

[0068] Then the weighted vector w i It can be rewritten as:

[0069]

[0070] Step 5: Use the weighted vector w i Perform a spatially weighted scan of Y within the spatial set θ to construct the spatial spectral function P(θ):

[0071] P(θ i ) = w i H ·Y

[0072] Step 6: In P(θ) i Find K spectral peaks and their corresponding angle set θ d ={θ k |θ k =θ1,θ2,…,θ K} represents the azimuth angles of the K signals.

[0073] Simulation verification:

[0074] Figure 2 Simulation conditions: 1 signal source, 1.8 GHz carrier frequency, 1 MHz bandwidth, 5° azimuth angle, 15 dB signal-to-noise ratio, 1024 sampling points, and a uniform linear array with half-wavelength arrangement. Figure 2 As can be seen, compared with conventional beamforming algorithms, the direction finding method based on array received data reconstruction proposed in this invention has higher spatial resolution and higher sidelobe suppression ratio.

[0075] Figure 3 Simulation conditions: 3 signal sources with azimuth angles of -60°, 5°, and 55°; carrier frequency of 1.8 GHz; bandwidth of 10 MHz; signal-to-noise ratio of 15 dB; 1024 sampling points; and a uniform linear array with half-wavelength arrangement. Figure 3 It can be seen that conventional beamforming algorithms are no longer able to determine the direction of -60° and 55° signals. However, the direction finding method based on array received data reconstruction proposed in this invention can still accurately estimate the azimuth of the three signal sources, and has higher direction finding accuracy than conventional beamforming algorithms.

Claims

1. A direction-finding method based on array received data reconstruction, characterized in that, The array consists of M array elements and includes the following steps: Step 1: Calculate the covariance matrix R of the array signal: In the formula, X is the received data matrix with M elements, and the superscript [·] H Let r(m,p) denote the conjugate transpose of a matrix, where N is the number of sampling points, and r(m,p) is the element in the m-th row and p-th column of R. Step 2: Select the elements in the first column of matrix R to form vector Y1, and select the elements in the first row of matrix R to form vector Y2. Y1 = [r(1,1), r(2,1), r(3,1),…, r(M,1)] Y2 = [r(1,1), r(1,2), r(1,3),…, r(1,M)] Step 3: Remove redundant elements from Y1 and Y2, rearrange the element order, and merge them to reconstruct the array received data vector matrix Y: Y = [r(1,M), r(1,M-1),…, r(1,2), r(1,1), r(2,1),…, r(M,1)] T ; in,[·] T This is the transpose of the matrix; Step 4: In the spatial set θ={θ i | θ i =θ1, θ2,…, θ I Constructing a weighted vector within the inner layer : Where θ is a set of I spatial scanning angles. Where c is the signal frequency and c is the speed of light; The x and y coordinates of the array elements in the original array are as follows: x=[0,x1, x2,…, x M-1 ] T y=[0,y1, y2,…, y M-1 ] T The reconstructed array element coordinates are: Where, x -(M-1) The value is x (M-1) The opposite number; Step 5: Use weighted vectors Perform a spatially weighted scan of Y within the spatial set θ to construct the spatial spectral function P(θ): P(θ i ) = H ·Y Step 6: In P(θ) i Find K spectral peaks and their corresponding angle set θ d ={θ k | θ k =θ1, θ2,…, θ K } represents the azimuth angles of the K signals.

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