Sparse-delay-based metasurface array signal frequency and direction of arrival estimation method

Abstract

The application discloses a kind of based on sparse time delay's metasurface array signal frequency and direction of arrival estimation method, mainly solve the problem of high cost and low precision in the condition of ultra-wideband signal, frequency and direction of arrival angle simultaneous estimation.It is as follows: the implementation scheme is: constructing metasurface array, and the received signal is space-time coded;The coded signal is time-delayed to meet the nested sequence, and the time delay is increased by Q times of nested time delay, and the output signal of a total of QN times of time delay is obtained after sampling;Frequency solving matrix is obtained according to the output signal, and the eigenvalue is obtained by decomposition, to calculate the frequency of received signal;Direction vector matrix is constructed according to the coded signal, angle solving matrix is obtained using frequency and direction vector matrix, and the eigenvalue is solved by eigenvalue decomposition, to calculate signal direction of arrival angle.The application increases the time delay of undersampling model, improves the precision of simultaneous estimation of signal frequency and direction of arrival angle, and can be used for ultra-wideband signal reconnaissance processing.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and specifically relates to a method for estimating the signal frequency and direction of arrival of a metasurface array, which can be used for processing signals received by a metasurface array. Background Technology

[0002] Traditional array signal processing, as an important signal processing technology, has seen rapid development in various fields such as communications, radar, sonar, and seismic exploration. Array signal processing involves constructing sensor arrays with different geometric structures in space and using these arrays to detect and process incoming signals, achieving estimation of the number of signal sources, direction of arrival (DOA), and accurate frequency. The DOA refers to the direction of arrival of a spatial signal, i.e., the directional angle at which each signal reaches the array's reference element. DOA is a crucial component of array signal processing, primarily studying the ability of array processing systems to accurately estimate the DOA of spatial signals. It has significant application value in parameter estimation, military electronic warfare, signal recognition, mobile communications, and medical diagnostics. However, existing traditional array estimation methods typically require large equipment and do not fully utilize equipment resources, resulting in high costs.

[0003] Patent document CN114879136A discloses a method for estimating the direction of arrival (DOA) of a signal based on a non-uniformly arranged metasurface array. It first constructs a non-uniform metasurface array and obtains the array manifold by decomposing the received signal from the array. Then, it constructs a Topplitz matrix based on the covariance matrix of the received signal. Next, it performs eigenvalue decomposition on the Topplitz matrix to obtain a noise subspace matrix and constructs a steering vector. Finally, it constructs a spatial spectrum function based on the noise subspace matrix, array manifold, and steering vector obtained from these operations. The final DOA estimation result is obtained by plotting the amplitude spectrum of the spatial spectrum function. However, this method has the following shortcomings:

[0004] First, the construction of the Pritzker matrix and subsequent calculations are highly complex, and the construction of non-uniformly arranged metasurface arrays is also quite complex. Second, it can only estimate the direction of arrival angle and cannot estimate the signal frequency. Third, it does not fully utilize the resources of the metasurface array model. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the existing technology by proposing a method for estimating the signal frequency and direction of arrival of a metasurface array based on sparse time delay, so as to make full use of array resources, reduce costs, reduce computational complexity, and improve the accuracy of measuring signal frequency and direction of arrival angle.

[0006] To achieve the above objectives, the technical solution of the present invention includes the following steps:

[0007] (1) Construct a metasurface array containing M array elements with a spacing of d between adjacent array elements;

[0008] (2) Encode and delay the received signal Y of each array element at the same sampling time multiple times;

[0009] (2a) Set the encoding parameter adjustment value to 1 bit, and each array element encodes the received signal Y multiple times at the same sampling time. The encoding value can be 1 or -1. Obtain the received signal X after the rth encoding of the metasurface array composed of M array elements. r (l);

[0010] (2b) N time delay channels for the received signal X after the r-th encoding r (l) The time lengths are 0, τ1, ..., τ N-1 The delays, which satisfy the nested sequence pattern, are τ. N-1 =h (N-1) τ, where h (N-1) The sequence is a nested sequence, and τ is the unit time delay.

[0011] (2c) The received signal X after the r-th encoding r (l) Perform Q nested time delays, where the qth time delay corresponds to the output signal of each of the N time delay channels. in,

[0012] (3) Sample the signal in (2) after the time delay to obtain the sampled signal Z(l):

[0013] Z(l) = [Z1(l), Z2(l), ..., Z n (l),,Z QN (l)] T

[0014] Among them, Z n (l)=X r (l)Φ n-1 (f)+n(l) is the undersampled signal of the nth time-delay channel, n∈{1,2,…,QN}, Φ is the rotation-invariant matrix of the undersampled output signal, and n(l) is Gaussian white noise;

[0015] (4) Two propagation operator matrices F1 and F2 are obtained from the output signal Z(l) obtained in (3), and the frequency solution matrix Ψ is obtained based on these two propagation operator matrices F1 and F2.

[0016] (5) Decompose the eigenvalues ​​of the frequency solution matrix Ψ and solve for the K largest eigenvalues ​​μ1,…,μ of the matrix Ψ. K Where K is the number of incoherent far-field narrowband radiation signals in space, 0 <K<M;

[0017] (6) Using K eigenvalues ​​μ K Calculate the signal frequency f k :

[0018]

[0019] Where angle(·) is the corresponding phase angle obtained;

[0020] (7) Based on the received signal X after the rth encoding in (2) r The rotation-invariant matrix Φ in (l) and (3) is used to construct the direction vector matrix.

[0021]

[0022] Where f is the signal frequency vector, X r (l)Φ i (f) is the i-th direction vector, i∈{0,1,…,QN-1};

[0023] (8) Based on the signal frequency f k Calculate the direction of arrival angle θ of the signal k :

[0024] (8a) The frequency f k Substitute the direction vector matrix into (7) In the process, the angle solution matrix E(θ) is obtained, and the first K largest eigenvalues ​​α1,…,α are obtained by eigenvalue decomposition of E(θ). k ;

[0025] (8b) Using K eigenvalues ​​α k Calculate the direction of arrival angle θ of the signal k :

[0026]

[0027] Compared with the prior art, the present invention has the following advantages:

[0028] First, by constructing an undersampled metasurface array, this invention can alleviate the strict limitations on broadband signal sampling operations and reduce sampling costs.

[0029] Secondly, by applying multiple time delays to the encoded received signal, this invention can fully utilize the array time delay channel and reduce measurement costs; at the same time, by increasing the number of delays through Q-time nested time delays, the accuracy of frequency measurement can be improved.

[0030] Third, by constructing the angle solution matrix and the propagation operator matrix of the signal, the present invention can simultaneously and accurately estimate the direction of arrival angle and the frequency of the signal. Attached Figure Description

[0031] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0032] Figure 2 This is a schematic diagram of the nested time-delay metasurface array structure of the present invention. Detailed Implementation

[0033] The embodiments of the invention will be described in further detail below with reference to the accompanying drawings.

[0034] Reference Figure 1 The implementation steps for this example are as follows:

[0035] Step 1: Construct a metasurface array and set up an undersampling model.

[0036] Reference Figure 2 The specific implementation of this step is as follows:

[0037] 1.1) Set the metasurface to have M array elements, and the spacing between adjacent array elements is d. The number of spatially incoherent far-field narrowband radiated signals received by the array is K.

[0038] 1.2) Perform multiple space-time encodings on the signal received by each array element of the metasurface, with each received signal having an encoding value of -1 or 1;

[0039] 1.3) Set up N delay channels, and input the encoded signal into the N delay channels for delay times of 0, τ1, ..., τ. N-1 The delay;

[0040] 1.4) The received signal is subjected to Q nested time delays, and the q-th time delays corresponding to the output signals of the N time delay channels are respectively...

[0041] In this example, under the overall length constraint of the metasurface array, the number of array elements M and the spacing d between adjacent array elements are set to any reasonable values, and the number of radiation signals received by the metasurface array satisfies 0. <K<M。

[0042] Step 2: Obtain the r-th encoded received signal X from the M-element metasurface array. r (l).

[0043] (2.1) Obtain the direction vector element a of the signal received by the m-th array element. m (f k ,θ k ):

[0044]

[0045] Among them, f k Let θ be the signal frequency. k Let d be the direction of arrival angle of the signal, c be the speed of light, and d be the direction of arrival angle. m The distance between the m-th array element and the first array element is denoted by j, where j is the imaginary unit.

[0046] (2.2) Adjust the encoding parameter value to 1 bit to obtain the encoded value b of the m-th array element in the r-th encoding. m,r For (-1)0 and (-1) 1 These two encoded values ​​are 1 and -1;

[0047] (2.3) Based on the above a m (f k ,θ k ) and b m,r The signal x received by snapshot l is obtained by the r-th encoding of the m-th array element. m,r (l):

[0048]

[0049] Among them, s k (l) represents the k-th complex signal;

[0050] (2.4) The signals x received on a total of M array elements m,r (l) Summation is performed to obtain the r-th encoded received signal X of the entire metasurface array. r (l):

[0051]

[0052] Step 3: Obtain the sampled output signal Z(l) through undersampling operation.

[0053] (3.1) Set the rotation-invariant matrix Φ for the undersampled output signal of the delay channel:

[0054]

[0055] Where, diag[·] is the diagonal matrix symbol, and τ is the unit time delay;

[0056] (3.2) Receive signal X according to the r-th encoding. r (l) and the rotation-invariant matrix Φ of the nth time delay channel n-1 Obtain the undersampled output signal Z of the nth time-delay channel. n (l):

[0057]

[0058] in, Let n(l) be the sampled signal, and n(l) be Gaussian white noise.

[0059] (3.3) Based on the undersampled output signal Z of the nth time-delay channel n (l) and Q nested time delays, to obtain a total of QN time delays for the sampled output signal Z(l):

[0060] Z(l) = [Z1(l), Z2(l), ..., Z n (l),,Z QN (l)] T

[0061] in,[·] T This represents the matrix transpose operation.

[0062] Step 4, construct the direction vector matrix

[0063] According to the received signal X in step 2 r (l) and the rotation-invariant matrix Φ in step 3, construct the direction vector matrix.

[0064]

[0065] Where f is the signal frequency vector, X r (l)Φ i (f) is the i-th direction vector, i∈{0,1,…,QN-1}.

[0066] Step 5: Construct the frequency solution matrix Ψ.

[0067] (5.1) Two propagation operator matrices F1 and F2 are obtained from the output signal Z(l) acquired in step 3:

[0068] F1=[Z1(l),Z2(l),…,Z n (l),…,Z QN-1 (l)] T

[0069] F2=[Z2(l),Z3(l),…,Z n' (l),…,Z QN-1 (l)] T

[0070] Among them, Z n (l) represents the undersampled output signal of the nth time-delayed channel in the first propagation operator matrix F1, where n∈{1,2,…,QN-1}; Z n'(l) represents the undersampled output signal of the n'-th time-delayed channel in the second propagation operator matrix F2, where n'∈{2,3…,QN-1}, [·] T Represents the matrix transpose operation;

[0071] (5.2) Based on the two propagation operator matrices F1 and F2, calculate the frequency solution matrix Ψ:

[0072] Ψ=(F1 H F1) -1 F1 H F2

[0073] in,[] H This represents the conjugate transpose symbol.

[0074] Step 6: Obtain the K largest eigenvalues ​​μ1,…,μ of the frequency solution matrix Ψ. K .

[0075] The eigenvalue decomposition of the frequency solution matrix Ψ is as follows:

[0076] Ψ=YΛY H

[0077] Where Λ is the eigenvalue diagonal matrix of the frequency solution matrix Ψ, Y is the subspace matrix, [·] H Indicates the conjugate transpose symbol;

[0078] Sort the eigenvalues ​​in the eigenvalue diagonal matrix Λ in descending order, and take the K largest eigenvalues ​​to obtain the eigenvalues ​​μ1,…,μ K .

[0079] Step 7: Solve for the signal frequency and calculate the signal direction of arrival angle θ. k .

[0080] (7.1) Using the K eigenvalues ​​μ obtained in step 6 K Calculate the signal frequency f k :

[0081]

[0082] Where angle(·) is the corresponding phase angle obtained;

[0083] (7.2) The frequency f k Substitute the direction vector matrix from step 4 Then, take the first M(N-1) rows and multiply the last M(N-1) rows to obtain the angle solution matrix E(θ):

[0084]

[0085] in, is the frequency constant vector of the signal.

[0086] (7.3) The eigenvalue decomposition of E(θ) is as follows:

[0087]

[0088] in, To find the eigenvalues ​​of the angle matrix E(θ), find the diagonal matrix. Let be the subspace matrix, [·] H This represents the conjugate transpose symbol.

[0089] (7.4) For the eigenvalue diagonal matrix The eigenvalues ​​in the array are sorted in descending order, and the first K largest eigenvalues ​​α1,…,α are selected. k ;

[0090] (7.5) Using K eigenvalues ​​α k The direction of arrival angle θ of the signal wave is calculated. k :

[0091]

[0092] Thus, the estimation of signal frequency and direction of arrival of metasurface array based on sparse time delay is completed.

[0093] The above description is merely a specific example of the present invention and does not constitute any limitation on the present invention. Obviously, those skilled in the art, after understanding the content and principles of the present invention, may make various modifications and changes in form and details without departing from the principles and structure of the present invention. However, these modifications and changes based on the ideas of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A method for estimating the signal frequency and direction of arrival of a metasurface array based on sparse time delay, characterized in that, Includes the following steps: (1) Construct a metasurface array containing M array elements with a spacing of d between adjacent array elements; (2) Received signals of each array element at the same sampling time Perform multiple encodings and time delays; (2a) Set the encoding parameter adjustment value to 1 bit, and each array element samples the received signal at the same sampling time. Multiple encodings are performed, with the encoded value being 1 or -1, to obtain the received signal X after the r-th encoding of the metasurface array composed of M superimposed array elements. r (l); (2b) The received signal X after the r-th encoding by N time delay channels r (l) The durations are respectively The delays, these time delays satisfy the nested sequence pattern, that is... ,in It is a nested sequence. The unit time delay; the nested sequence It is expressed as follows: ； Where a is the number of elements in the first subsequence and b is the number of elements in the second subsequence; (2c) The received signal X after the r-th encoding r (l) Perform Q nested time delays, where the qth time delay corresponds to the output signal of each of the N time delay channels. ,in, ; (3) Sample the signal in (2) after the time delay to obtain the sampled signal. : ； in, For the sampled signal of the nth time-delay channel, , For the rotation-invariant matrix of the undersampled output signal, It is Gaussian white noise; (4) Two propagation operator matrices are obtained from the output signal Z(l) obtained in (3). , And based on these two propagation operator matrices , Obtain the frequency solution matrix ; (5) Solve for the frequency matrix The eigenvalues ​​are decomposed to solve the matrix. K larger eigenvalues Where K is the number of incoherent far-field narrowband radiation signals in space, 0 <K<M; (6) Using K eigenvalues Calculate signal frequency : ； in, The corresponding phase angle obtained; (7) Based on the received signal X after the rth encoding in (2) r Rotation invariant matrices in (l) and (3) Construct the direction vector matrix : ； in, It is the signal frequency vector. For the (i+1)th direction vector, ; (8) Based on the signal frequency Calculate the direction of arrival angle of the signal : (8a) Frequency Substitute the direction vector matrix in (7) In the process, the angle solution matrix is ​​obtained. and to Perform eigenvalue decomposition to obtain the top K largest eigenvalues. ; (8b) Using K eigenvalues Calculate the direction of arrival angle of the signal : 。 2. The method according to claim 1, characterized in that, The received signal X of the metasurface array with M elements obtained in (2a) after the r-th encoding. r (l) represents the following: ； in, The signal received by the m-th array element in snapshot l. For frequency f k and the direction of arrival angle θ k The changing direction vector elements, Let c be the k-th complex signal, and c be the speed of light. Let j be the encoded value of the m-th array element in the r-th encoding, where j is the imaginary unit.

3. The method according to claim 1, characterized in that, The rotation-invariant matrix in (3) , means as follows: ； in, This is a diagonal matrix representation.

4. The method according to claim 1, characterized in that, The two propagation operator matrices obtained in (4) , They are represented as follows: ； ； in, The first propagation operator matrix The undersampled model output signal of the nth time-delay channel. ; For the second propagation operator matrix The Middle The undersampled model output signal of each time-delayed channel. , This represents the matrix transpose operation.

5. The method according to claim 1, characterized in that, The frequency solution matrix obtained in (4) is represented as follows: ； in, This represents the conjugate transpose symbol.

6. The method according to claim 1, characterized in that, The frequency solution matrix in (5) Perform eigenvalue decomposition to obtain the top K largest eigenvalues. The implementation is as follows: (5a) Solving the frequency matrix Perform eigenvalue decomposition: ； in, Solving the matrix for frequency The eigenvalue diagonal matrix, For subspace matrices, Indicates the conjugate transpose symbol; (5b) For the frequency eigenvalue diagonal matrix Arrange the diagonal elements of the array in descending order, and take the K largest eigenvalues, denoted as: .

7. The method according to claim 1, characterized in that, The angle solution matrix obtained in (8a) , means as follows: ； in, This is a vector of frequency constants.

8. The method according to claim 1, characterized in that, The angle solution matrix in (8a) Perform eigenvalue decomposition to obtain the top K largest eigenvalues. The implementation is as follows: (8a1) Solve the matrix for the angle. Perform the following eigenvalue decomposition: ； in, Solving the matrix for frequency The eigenvalue diagonal matrix, For subspace matrices, Indicates the conjugate transpose symbol; (8a2) Diagonal matrix of angular eigenvalues Arrange the diagonal elements of the array in descending order, and take the K largest eigenvalues, denoted as: .

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