Signal frequency and direction of arrival estimation method based on undersampled metasurface array

Abstract

This invention discloses a signal frequency and direction-of-arrival (AOA) estimation algorithm based on an undersampled metasurface array, primarily addressing the high cost and low accuracy of simultaneous frequency and AOA estimation under ultra-wideband signal conditions. The implementation scheme is as follows: A metasurface array is constructed, and the received signal is acquired after space-time coding; the coded signal is delayed through a time-delay channel, and then sampled to obtain the output signal; a direction vector matrix is ​​constructed based on the coded signal; two propagation operator matrices are obtained from the output signal, and the frequency solution matrix is ​​derived from these propagation operator matrices; the frequency solution matrix is ​​decomposed to obtain eigenvalues, and the signal frequency is calculated; the frequency is substituted into the direction vector matrix to obtain the angle solution matrix, and its eigenvalues ​​are decomposed to calculate the signal AOA. This invention offers low sampling cost and can simultaneously and accurately estimate the signal frequency and AOA, making it suitable for ultra-wideband signal reconnaissance and processing.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, and specifically relates to a frequency and direction of arrival estimation method that can be used for signal reconnaissance and processing of metasurface arrays. 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 estimations 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 azimuth 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, among others. However, existing traditional array estimation methods typically require large and costly equipment.

[0003] Patent document CN116184308A discloses a method for estimating the direction of arrival (DOA) of a signal based on a distributed 1-bit coded metasurface array. The implementation involves constructing a distributed 1-bit coded metasurface array U, obtaining the received signal Y(t) through U, constructing a measurement vector for the received signal Y(t), constructing an array manifold dictionary for U, and solving for the target vector X using compressed sensing based on the measurement vector and the array manifold dictionary. The DOA estimate is obtained by searching the spectral peaks of the target vector X. However, this method can only be used for DOA estimation of the metasurface array, not for frequency estimation, thus failing to fully utilize the array and wasting array resources. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a joint estimation method for frequency and direction of arrival based on undersampled metasurface arrays, so as to reduce the estimation cost of signal frequency and direction of arrival angle and improve measurement accuracy.

[0005] To achieve the above objectives, the technical solution of the present invention includes the following steps:

[0006] (1) Construct an undersampled metasurface array containing M array elements with a spacing of d between adjacent array elements;

[0007] (2) Let the signal encoded by the m-th array element in the q-th iteration be x. m，q (l), after superposition, the received signal X of the qth encoding of the metasurface array with M array elements is obtained. q (l);

[0008] (3) Based on X obtained in (2) q (l) Obtain the undersampled model output signal Z(l) with N time-delay channels:

[0009] Z(l) = [Z1(l), ..., Z n (l), ..., Z N (l)] T

[0010] Among them, Z n (l)=X q (l)Φ n-1 (f)+n(l) is the undersampled model output signal of the nth time delay channel, Φ is the rotation invariant matrix of the undersampled model output signal of the nth time delay channel, and n(l) is Gaussian white noise;

[0011] (4) Two propagation operator matrices P1 and P2 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 P1 and P2.

[0012] (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;

[0013] (6) Using K eigenvalues ​​μ K Calculate the signal frequency f k :

[0014]

[0015] Where angle(·) is the obtained phase angle, and τ is the time delay of the first delay channel;

[0016] (7) Based on the received signal X in (2) q The rotation-invariant matrix Φ in (l) and (3) is used to construct the direction vector matrix.

[0017]

[0018] Where f is the signal frequency vector;

[0019] (8) Based on the signal frequency f k Calculate the direction of arrival angle θ of the signal k :

[0020] (8a) The frequency f k Substitute the direction vector matrix into (7) In the process, the angle solution matrix D(θ) is obtained, and the first K largest eigenvalues ​​α1, ..., α2 are obtained by eigenvalue decomposition of D(θ). k ;

[0021] (8b) Using K eigenvalues ​​α k Calculate the direction of arrival angle θ of the signal k :

[0022]

[0023] Compared with the prior art, the present invention has the following advantages:

[0024] First, by constructing an undersampled metasurface array, this invention can alleviate the strict frequency limitation imposed by the Nyquist sampling law in the sampling operation and reduce sampling costs.

[0025] Secondly, the present invention improves the quantity and accuracy of frequency measurements by performing time delay operations through N time delay channels.

[0026] Third, by constructing an angle solution matrix and a propagation operator matrix, this invention can simultaneously and accurately estimate the direction of arrival (DOA) and frequency of a signal. Attached Figure Description

[0027] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0028] Figure 2 This is a schematic diagram of the undersampling metasurface array constructed in this invention. Detailed Implementation

[0029] The embodiments of the invention will be described in further detail below with reference to the accompanying drawings.

[0030] Reference Figure 1 The implementation steps for this example are as follows:

[0031] Step 1: Construct a metasurface array and set up an undersampling model.

[0032] Reference Figure 2 The specific implementation of this step is as follows:

[0033] The metasurface is configured to have M array elements, with a spacing of d between adjacent array elements, and the array receives K spatially incoherent far-field narrowband radiated signals.

[0034] The signal received by each array element of the metasurface is spatially encoded, and the encoded value of each received signal is 0 or 1;

[0035] In the undersampling stage, the encoded signal is first input into N delay channels for delay operation, with delay time lengths of 0, τ, ..., (N-1)τ, where τ is the unit time delay. Then, sampling operation is performed to obtain the sampled output.

[0036] 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.

[0037] Step 2: Obtain the q-th encoded received signal X from the M-element metasurface array. q (l).

[0038] (2.1) The direction vector element a of the signal received by the m-th array element m (f k θ k The following is represented:

[0039]

[0040] Where, 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.

[0041] (2.2) Adjust the encoding parameter value to 1 bit to obtain the encoded value b of the m-th array element in the q-th encoding. m，q (-1) 0 and (-1) 1 These two encoded values ​​are 1 and -1;

[0042] (2.3) Based on the above a m (f k θ k ) and b m，q The signal x received by snapshot l is obtained by the qth encoding of the m-th array element. m，q (l):

[0043]

[0044] Among them, s k (l) represents the k-th complex signal;

[0045] (2.4) The signals x received on a total of M array elements m，q (l) Summation is performed to obtain the q-th encoded received signal X of the entire metasurface array. q (l):

[0046]

[0047] Step 3: Obtain the output signal Z(l) of the undersampled model.

[0048] (3.1) Construct the rotation-invariant matrix Φ of the output signal of the undersampled model for the nth time-delay channel:

[0049]

[0050] Where diag[·] is the diagonal matrix symbol;

[0051] (3.2) Obtain the undersampled model output signal Z of the nth time-delay channel. n (l):

[0052]

[0053] in, Let n(l) be the sampled signal, and n(l) be Gaussian white noise.

[0054] (3.3) Use a time delay device to process the received signal X obtained in step 2. q (l) Perform a time delay operation and sampling to obtain the undersampled model output signal Z(l) with N time delay channels:

[0055] Z(l) = [Z1(l), ..., Z n (l), ..., Z N (l)] T

[0056] in,[·] T This represents the matrix transpose operation.

[0057] Step 4, construct the direction vector matrix

[0058] According to the received signal X in step 2 q (l) and the rotation-invariant matrix Φ in step 3, construct the direction vector matrix.

[0059]

[0060] Where f is the signal frequency vector.

[0061] Step 5: Construct the frequency solution matrix Ψ.

[0062] (5.1) Two propagation operator matrices P1 and P2 are obtained from the output signal Z(l) acquired in step 3:

[0063] P1 = [Z1(l), Z2(l), ..., Z n (l), ..., Z N-1(l)] T

[0064] P2 = [Z2(l), Z3(l), ..., Z n′ (l), ..., Z N (l)] T

[0065] Among them, Z n (l) represents the undersampled model output signal of the nth time-delay channel in the first propagation operator matrix P1, where n∈{1,2,…,N-1}; Z n′ (l) represents the undersampled model output signal of the n′-th time-delay channel in the second propagation operator matrix P2, where n′∈{2, 3, ..., N}, [·] T Represents the matrix transpose operation;

[0066] (5.2) Based on the two propagation operator matrices P1 and P2, the frequency solution matrix Ψ is obtained:

[0067]

[0068] in,[·] H This represents the conjugate transpose symbol.

[0069] Step 6: Obtain the K largest eigenvalues ​​μ1, ..., μ of matrix Ψ. K .

[0070] The eigenvalue decomposition of the frequency solution matrix Ψ is as follows:

[0071] Ψ=YΛY H

[0072] Where Λ is the eigenvalue diagonal matrix of the frequency solution matrix Ψ, Y is the subspace matrix, [·] H This represents the conjugate transpose symbol.

[0073] Sort the eigenvalues ​​in the eigenvalue diagonal matrix Λ in descending order, and take the first K largest eigenvalues ​​μ1, ..., μ2. K .

[0074] Step 7: Solve for the signal frequency and calculate the signal direction of arrival angle θ. k .

[0075] (7.1) Using the K eigenvalues ​​μ obtained in step 6 K Calculate the signal frequency f k :

[0076]

[0077] Where angle(·) is the corresponding phase angle obtained;

[0078] (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 D(θ):

[0079]

[0080] in, This is a vector of frequency constants.

[0081] The eigenvalue decomposition of D(θ) is as follows:

[0082]

[0083] in, To find the eigenvalues ​​of the angle matrix D(θ), we need to find the diagonal matrix of the eigenvalues. Let be the subspace matrix, [·] H This represents the conjugate transpose symbol.

[0084] For eigenvalue diagonal matrices The eigenvalues ​​in the array are sorted in descending order, and the first K largest eigenvalues ​​α1, ..., α2 are selected. k ;

[0085] (8.3) Using K eigenvalues ​​α k Calculate the direction of arrival angle θ of the signal k ,

[0086]

[0087] This completes the estimation of frequency and direction of arrival for the undersampled metasurface array received signal.

[0088] 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 signal frequency and direction of arrival based on an undersampled metasurface array, characterized in that, Includes the following steps: (1) Construct an undersampled metasurface array containing M array elements with a spacing of d between adjacent array elements; (2) Let the signal encoded by the m-th array element in the q-th iteration be x. m,q (l), the received signal of the qth encoding of the metasurface array with M elements after superposition is X. q (l); (3) Based on the information obtained in (2) Obtain the undersampled model output signal with N time delay channels. : ； in, The output signal of the undersampled model for the nth time-delay channel is... Let n be the rotation-invariant matrix of the undersampled model output signal of the nth time-delay channel. 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 matrix is ​​solved by decomposing its eigenvalues. 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 the frequency of the k-th signal : ； in, The corresponding phase angle obtained is... Delay per unit of time; (7) Based on the received signal X in (2) q Rotation invariant matrices in (l) and (3) Construct the direction vector matrix : ； in, It is the signal frequency 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 (2) is encoded for the qth time. q (l) represents the following: ； in, The signal received in snapshot l is the q-th encoding of the m-th array element. 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 element in the q-th encoding, where j is the imaginary unit. Let m be the distance between the m-th array element and the first array element.

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

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) special The eigenvalues ​​are decomposed and represented as follows: ； in, Solving the matrix for frequency The eigenvalue diagonal matrix, For subspace matrices, This represents the conjugate transpose symbol.

7. The method according to claim 1, characterized in that, The angle solution matrix is ​​obtained in (8a). Specifically, it is to Substitute the direction vector matrix The first M(N-1) rows and the last M(N-1) rows of the resulting matrix form two submatrices. Multiplying these two submatrices yields the angle solution matrix. .

8. The method according to claim 1, characterized in that, In (8a), the solution matrix is... Eigenvalue decomposition is performed, as follows: ； in, Solving the matrix for frequency The eigenvalue diagonal matrix, For subspace matrices, This represents the conjugate transpose symbol.

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