A monostatic symmetric nested array MIMO system and near-field positioning method

Abstract

This invention discloses a monostatic symmetric nested array MIMO system and a near-field positioning method, belonging to the field of monostatic MIMO near-field positioning technology. This invention can effectively improve the positioning performance during near-field estimation. The monostatic symmetric nested array MIMO system proposed in this invention has a symmetrically distributed transmit and receive arrays. Compared to other symmetric MIMO systems, its differential array is a positionally continuous array with more degrees of freedom. With the same physical array aperture, fewer physical array elements are actually used, reducing costs. The near-field positioning method proposed in this invention calculates the fourth-order statistics of the signal and quantizes them to obtain a virtual differential array of the differential array, achieving accurate near-field positioning of sparse MIMO structure arrays. Furthermore, it can be extended to more sparse MIMO symmetric systems.

Description

Technical Field

[0001] This invention belongs to the field of monostatic MIMO near-field positioning technology, specifically relating to a monostatic symmetric nested array MIMO system and a near-field positioning method. Background Technology

[0002] Near-field target localization has received widespread attention in recent years for its applications in automotive driving, speech enhancement, and indoor positioning. Combining near-field localization technology with Multiple-Input Multiple-Output (MIMO) technology can improve the accuracy and anti-interference capability of target localization. Unlike the far-field assumption, near-field target localization presents a greater challenge because the near-field source is located in the Fresnel zone of the antenna array, where the wavefront transforms from a plane wave to a spherical wavefront. Furthermore, the simultaneous determination of the direction of arrival (DOA) and distance to the identifiable target is required.

[0003] The first problem to solve in achieving near-field target localization with monostatic MIMO is determining the structure of the monostatic MIMO device. Currently, the mainstream monostatic MIMO devices include: 1) symmetrical and uniformly dense antenna arrays (ULMA) for both transmit and receive arrays. The disadvantages of this structure are high cost and severe coupling between antennas, resulting in poor localization accuracy. 2) Nested MIMO localization devices based on sparse structure technology, which can achieve more degrees of freedom and a larger array aperture while maintaining the same number of antennas. 3) Introducing coprime structures into monostatic MIMO further reduces the mutual coupling effect between antennas, thereby achieving higher parameter estimation performance. 4) Further optimizing the MIMO transmit and receive arrays based on method 3), using nested arrays for the transmit array and nested arrays with significantly increased spacing for the receive array, and utilizing differential co-arrays of co-arrays in the localization method, which provides more degrees of freedom compared to co-arrays. However, none of the above three types of monostatic MIMO localization devices can meet the requirement of symmetrical transmit and receive array antenna structures under near-field conditions. To address this, a positioning method based on symmetric nested MIMO (SDNMA) has emerged. Its device structure meets the near-field requirements, but it only achieves far-field positioning.

[0004] In the process of realizing the technical solution of this invention, the inventors discovered that current research on monostatic MIMO systems for near-field positioning focuses on the structure and working methods of MIMO positioning devices. Near-field positioning research on monostatic MIMO devices is mainly based on ULMA, and structural sparsity techniques are mostly used for far-field positioning in monostatic MIMO. Research on introducing structural sparsity techniques into monostatic MIMO for near-field positioning is scarce, but compared to ULMA, it can bring a significant improvement in near-field positioning accuracy. Therefore, designing a monostatic symmetric nested array MIMO system and near-field positioning method based on nesting theory and combined with structural sparsity techniques is of great significance. Summary of the Invention

[0005] This invention provides a monostatic symmetric nested array MIMO system and a near-field positioning method to achieve near-field positioning for monostatic MIMO positioning devices with sparse structures.

[0006] On one hand, the present invention provides a monostatic symmetric nested array MIMO system, which includes three subarrays linearly distributed and located on the same straight line. Subarray 1 is a uniform linear array with 2M1-1 array elements, and the element spacing of subarray 1 is d = λ / 4, where λ is the carrier wavelength. Subarrays 2 and 3 have the same structure, both being uniform linear arrays with M2-1 array elements and an element spacing of (M1+1)d. Subarrays 2 and 3 are located on both sides of subarray 1, and the spacing between them and subarray 1 is d. Subarray 1 constitutes a transmitting array, and the central array elements of subarrays 2, 3, and 1 constitute a receiving array. Wherein, positive integers M1≥2 and M2≥1.

[0007] Furthermore, the total number of array elements Q in the monobase symmetric nested array MIMO system is set to positive integers M1 and M2: if Q is divided by 4 and leaves a remainder of 1, then M1 = (Q+3) / 4 and M2 = (Q-1) / 4; if Q is divided by 4 and leaves a remainder of 3, then M1 = (Q+1) / 4 and M2 = (Q+1) / 4.

[0008] On the other hand, the present invention also provides a near-field positioning method, which includes the following steps:

[0009] Step 1: Arrange the antenna array based on the monostatic symmetric nested array MIMO system provided by the present invention to obtain a monostatic MIMO positioning device with a sparse structure;

[0010] A linear number line is established to represent the position coordinates. The central array element is defined as the origin, and the position coordinates of each element in the transmitting and receiving arrays are obtained. The position index of each element in the transmitting array is denoted as p. tm The position index of each element in the receiving array is p. rnWhere m∈[-M,M], n∈[-N,N], M=M1-1, N=M2-1;

[0011] Step 2: The transmitting array emits a radiated signal outward, and the receiving array receives the returned signal and obtains the received signal x(t) through matched filtering;

[0012] The received signal x(t) is represented as:

[0013] x(t)=A N s N (t)+n(t)

[0014] Among them, s N (t) represents the near-field signal source vector, n(t) represents the noise vector, and A N =A Nt ⊙A Nr Let A represent the array manifold matrix. Nt This represents the steering vectors of the transmission arrays corresponding to the target signals of K targets (sources). A-dimensional near-field emission array manifold matrix Nr This represents the steering vectors of the receiving arrays corresponding to the target signals of K targets. dimensional receiver array manifold matrix, parameters parameter K represents the target number;

[0015] Step 3: Perform redundancy removal processing on the received array signal based on the harmonic array:

[0016] Based on the element position index p tm p rn Obtain the element position index h = p of the harmonic array. tm +p rn ;

[0017] Based on the element position index h, from A N Extract the rows that are identical to the item corresponding to the current element position index h. For several extracted rows, in A... N Keep only one row in the array, and the element value of that row is the mean of all extracted rows. Repeat this operation until A is obtained. N The signal does not contain duplicates corresponding to the element position index h, thus obtaining the deredundant signal. Let h be the sum and concord array after removing redundancy. k ,k∈[-Q s Q s ], 2Q s +1 indicates The number of sampling points;

[0018] Furthermore, the continuous segment of the element index of the difference array of the harmonic array is: [-2(M2+1)(M1+1)+6,2(M2+1)(M1+1)-6];

[0019] Step 4: Calculate the fourth-order statistic and construct a spatial smoothing matrix for the vectorized signal:

[0020] calculate The fourth-order statistics are used to generate a virtual array composed of the difference matrix of the covariance array. The received signal vector of the virtual array is spatially smoothed, and then its covariance matrix is ​​calculated based on the spatially smoothed received signal vector to obtain the smoothing matrix R. ss ;

[0021] Step 5, for the smoothing matrix R ss Eigenvalue decomposition is performed, and the signal subspace is obtained based on the diagonal matrix formed by the first K largest eigenvalues. The first 2Q... s The diagonal matrix composed of +1-K minimum eigenvalues ​​yields the noise subspace;

[0022] Based on the signal subspace and noise subspace, the MUSIC algorithm is used to perform spectrum search, and the near-field DOA estimation result is obtained based on the K largest peaks in the spectrum peak search results.

[0023] Step 6: Near-field range estimation:

[0024] Remove from the received signal x(t) Obtain the received signal x′(t) and calculate the covariance matrix R′ corresponding to the received signal x′(t);

[0025] Perform eigenvalue decomposition on matrix R', and obtain the signal subspace based on the diagonal matrix formed by the first K largest eigenvalues. Then, based on the first 2Q... s The diagonal matrix composed of +1-K minimum eigenvalues ​​yields the noise subspace;

[0026] Based on the signal subspace and noise subspace, the MUSIC algorithm is used for spectrum search, and the near-field distance estimation result is obtained based on the K largest peaks in the spectrum peak search results.

[0027] The technical solution provided by this invention brings at least the following beneficial effects:

[0028] This invention proposes a monostatic symmetric nested array MIMO system and a near-field localization method that can effectively improve the localization performance during near-field estimation. The monostatic symmetric nested array MIMO system proposed in this invention features a symmetrically distributed transmit and receive arrays. Compared to other symmetric MIMO systems, its differential array is a positionally continuous array with more degrees of freedom, requiring fewer physical array elements for the same physical array aperture, thus reducing costs. The near-field localization method proposed in this invention calculates the fourth-order statistics of the signal and quantizes them to obtain a virtual differential array of the differential array, achieving accurate near-field localization of sparse MIMO structure arrays. Furthermore, this method can be extended to more sparse MIMO symmetric systems. Attached Figure Description

[0029] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0030] Figure 1 This is a schematic diagram of the transceiver array of a monobase symmetric nested array MIMO system proposed in an embodiment of the present invention.

[0031] Figure 2 The angle estimation effect of the working method of the monostatic symmetric nested array MIMO system proposed in the embodiments of the present invention.

[0032] Figure 3 The distance estimation effect of the working method of the monostatic symmetric nested array MIMO system proposed in the embodiments of the present invention.

[0033] Figure 4 The graph shows the variation of near-field positioning angle RMSE with SNR for different monostatic MIMO positioning devices.

[0034] Figure 5 The graph shows the variation of near-field positioning distance (RMSE) with SNR for different monostatic MIMO positioning devices.

[0035] Figure 6 The graph shows the variation of near-field positioning angle RMSE with the number of snapshots for different monostatic MIMO positioning devices.

[0036] Figure 7 The graph shows the variation of near-field positioning distance (RMSE) with the number of snapshots for different monostatic MIMO positioning devices. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0038] To effectively improve near-field positioning accuracy, one embodiment of the present invention provides a monostatic symmetric nested array MIMO system, comprising three linearly distributed subarrays located on the same straight line, such as... Figure 1 As shown, subarray 1 is a uniform linear array comprising 2M1-1 elements, with an element spacing of d = λ / 4, where λ is the carrier wavelength. Subarrays 2 and 3 have the same structure, both being uniform linear arrays comprising M2-1 elements with an element spacing of (M1+1)d. Subarrays 2 and 3 are located on opposite sides of subarray 1, with a spacing of d between them and subarray 1. Subarray 1 constitutes the transmitting array, and the central elements of subarrays 2, 3, and 1 (e.g., ...) are... Figure 1 The array elements at the origin 0 position in the array constitute the receiving array; where positive integers M1≥2 and M2≥1.

[0039] In this embodiment of the invention, both the transmitting array and the receiving array are linear arrays located on a one-dimensional number axis. The transmitting array is a uniformly dense array symmetrical about the origin, and the receiving array is uniformly distributed on both sides of the transmitting array except for the antenna at the origin. The set of positions of the transmitting array can be represented as St = S1 = {l|l = m1}d, where ld represents the position of each element of the transmitting array, and m1∈[-M1+1,M1-1]. The set of positions of the receiving array can be represented as Sr = S2∪S3∪{0}, where S2 = {l|l = M1+m2(M1+1)}d, S3 = {l|l = -M1-m2(M1+1)}d, and m2∈[0,M2-1].

[0040] As one possible implementation, the transmitting array and the receiving array reuse the central array element at the origin, and the total number of array elements is Q (Q = 2M1 + 2M2 - 1). The process of determining the preferred value is as follows: Since Q is an odd number, there are two cases. If Q is divided by 4 and leaves a remainder of 1, then take M1 = (Q + 3) / 4 and M2 = (Q - 1) / 4; if Q is divided by 4 and leaves a remainder of 3, then take M1 = (Q + 1) / 4 and M2 = (Q + 1) / 4.

[0041] The transceiver arrays of the monostatic symmetric nested array MIMO system provided in this embodiment of the invention are both symmetric structures, and during the positioning process, its virtual array is generated by the differential array of its sum and co-array, which is a uniform and dense linear array. The continuous segment of the differential array of its sum and co-array is [-2(M2+1)(M1+1)+6, 2(M2+1)(M1+1)-6], which can significantly improve the positioning accuracy of near-field positioning.

[0042] On the other hand, embodiments of the present invention also provide a near-field localization method based on the monostatic symmetric nested array MIMO system, which may specifically include the following steps:

[0043] Step S1: Establish a linear number line to represent position coordinates (unit interval d = λ / 4, where λ is the carrier wavelength). Set as follows... Figure 1 The position coordinates of the transmitting and receiving arrays shown, based on the selected parameters, are expressed as follows:

[0044] St=S1 (1)

[0045] Sr=S2∪S3∪{0} (2)

[0046] S1={l|l=m1}d (3)

[0047] S2={l|l=M1+m2(M1+1)}d (4)

[0048] S3={l|l=-M1-m2(M1+1)}d (5)

[0049] Where m1∈[-M1+1,M1-1], m2∈[0,M2-1].

[0050] Step S2: The transmitting array emits a radiated signal, and the receiving array receives the returned signal. The output data through the matched filter is used to construct a near-field monostatic MIMO transceiver signal model. The specific process is as follows:

[0051] Suppose there are K near-field narrowband targets located at (θ) k ,r k ), k=1,2,...,K,θ k ,r k Let p represent the target's angle of arrival and range, respectively. The position of the transmitted signal in a monostatic symmetric nested array MIMO system is represented by p. tm d, where p tm d∈St, m∈[-M,M], the position of the receiving array is represented as p rn d, where p rn d∈Sr, n∈[-N,N]; let M = M1-1, N = M2-1; noise interference will occur during the process, which needs to be considered. The variance is The signal consists of independent, identically distributed additive white Gaussian noise, uncorrelated with the target signal; the received array signal after matched filtering is:

[0052]

[0053] in,

[0054] s N (t)=[s1(t),…,s K (t)] T Represents the signal source vector;

[0055] It is an array manifold matrix;

[0056] This is the array manifold matrix of the transmitting array;

[0057] Let θ be the steering vector of the transmitting array, and θ be the value of the k-th near-field signal. k ,r k Correspondingly;

[0058] The array manifold matrix of the receiving array;

[0059] The guide vector of the receiving array, and θ of the k-th near-field signal. k ,r k Correspondingly;

[0060] Parameter w k and φ k The values ​​are respectively:

[0061] In the above formula, ⊙ represents the Khatri-Rao product.

[0062] Step S3: Perform redundancy removal processing on the received array signal based on the harmonic array:

[0063] Harmony array and A in equation (6) N It contains The terms have a corresponding relationship, and the formula for calculating the coarray is: h = p tm +p rn The A corresponding to the repeated sum and coarray. N Let it be A N1 ,...,A Ni The corresponding row descriptor in equation (6) is x1(t),...,x i (t), use x1(t)=(x1(t)+x2(t)+...+x i Replace x1(t) with x2(t),...,x i (t) corresponds to the row in equation (6), up to A. N It does not contain duplicates. This step completes the redundancy removal of the harmonic array; the signal after this operation is the redundancy-removed signal. The concatenated array after removing redundancy is denoted as h. k ,k∈[-Qs Q s ].

[0064] Step S4: Calculation The fourth-order statistics matrix is ​​used to perform spatial smoothing on the vectorized signal:

[0065] The matrix form of a fourth-order statistic can be expressed as:

[0066] C = BC 4s B H (7)

[0067] in:

[0068]

[0069] in, These are terms in a fourth-order statistics matrix.

[0070]

[0071] B = [b(θ1), b(θ2), ..., b(θ)] K )];

[0072]

[0073] Vectorizing C yields the received signal vector z of the virtual array:

[0074] z = vec(C) = (B * ⊙B)p (8)

[0075] in, B is the signal vector of the virtual array; * ⊙B is the array manifold matrix of the virtual array composed of the difference matrices of the harmonic array, which contains Term, k,k'∈[-Q s Q s ], h k -h k' Let the difference matrix of the concordant column be in the range [-L]. u ,L u ], L u =2(M2+1)(M1+1)-6, find the corresponding row in equation (8) and rearrange it to form the result. in Corresponding to the row of B in equation (8), take L from it. u -i+2 lines to 2L u The -i+2 row yields the spatial smoothing matrix:

[0076]

[0077] Step S5: Smooth the spatial matrix R ss Perform eigenvalue decomposition and construct the search spectrum using the array manifold matrix corresponding to the redundancy-free sum and coarray:

[0078]

[0079] in, They are respectively composed of R ss The sum of the first K largest eigenvalues ​​and the first 2Q after eigenvalue decomposition s A diagonal matrix consisting of +1-K smallest eigenvalues These are matrices composed of their corresponding eigenvectors, and the search spectrum is constructed as follows:

[0080]

[0081] Where, a(θ,r) H yes After removing the redundancy of the co-array according to the method described in step 3, h k The corresponding array manifold matrix, This represents the Kronecker product. A spectral peak search is performed, and the K largest peaks in the result correspond to the near-field DOA estimation results.

[0082] Step S6: Eigenvalue decomposition of the signal x(t) without redundancy removal in equation (3) yields:

[0083]

[0084] in, These are the first K largest eigenvalues ​​and the first 2Q values ​​after R' eigenvalue decomposition. s A diagonal matrix consisting of +1-K smallest eigenvalues These are matrices composed of their corresponding eigenvectors, and the spectrum is constructed as follows:

[0085]

[0086] Perform a spectral peak search, and the distances corresponding to the top K largest peaks in the results are the near-field distance estimates.

[0087] To further verify the positioning performance of the near-field positioning method proposed in this embodiment of the invention, the following three sets of simulation experiments are conducted:

[0088] Simulation Experiment 1: Near Field Positioning Capability.

[0089] The parameters selected for this simulation experiment are: Q = 19, M1 = 5, M2 = 5. Assuming that there are four approach signals located in the Fresnel zone of the monostatic symmetric nested array MIMO system of this embodiment of the invention, respectively at (-30°, 35λ), (-20°, 38λ), (-10°, 40λ), and (10°, 42λ), with a signal-to-noise ratio of 10dB and a snapshot count of 500, the near-field localization results obtained using the monostatic symmetric nested array MIMO system proposed in this embodiment of the invention are as follows: Figure 2 and Figure 3 As shown, all four near-field signals were successfully identified and accurately estimated, and the spectral peaks were quite sharp, especially the spectral peaks for angle estimation.

[0090] Simulation Experiment 2: Mean Square Error (RMSE) as a function of signal-to-noise ratio.

[0091] This simulation experiment adopts a control experiment method. The parameter settings of the monostatic symmetric nested array MIMO system in this embodiment are the same as those in Simulation Experiment 1. The performance of the monostatic MIMO positioning devices ULMA (M1=9, N1=9) and SNMA (M1=3, N1=5) with the same number of transmit and receive antennas is compared. The monostatic symmetric nested array MIMO system proposed in this embodiment is used to locate two near-field signals. In the experiment, the number of snapshots is set to 600, the signal-to-noise ratio (SNR) is increased by 5dB at a time from -5dB to 30dB, and the number of Monte Carlo experiments is 500. The changes in the RMSE of the estimated angle and distance with the SNR are shown below. Figure 4 and Figure 5 As shown, ULMA has the worst positioning performance, followed by SNMA. The monostatic symmetric nested array MIMO system proposed in this embodiment of the invention has the smallest RMSE and the highest positioning accuracy.

[0092] Simulation Experiment 3: The variation of mean square error (RMSE) with the number of snapshots.

[0093] The setup for this experiment is the same as Experiment 2, but the signal-to-noise ratio is fixed at 5dB. The number of snapshots is simulated starting from 100 and increasing by 100 each time until it reaches 1000. The changes in the RMSE of angle and distance estimations with the number of snapshots are shown below. Figure 6 and Figure 7 As shown, the positioning error of each experimental result decreases with the increase of the number of snapshots. The RMSE of the monostatic symmetric nested array MIMO system proposed in this embodiment is the smallest, much smaller than ULMA, and the change in RMSE tends to be gradual when the number of snapshots is 900, achieving optimal positioning performance.

[0094] In summary, the near-field positioning method proposed in this embodiment of the invention can achieve high-precision near-field positioning.

[0095] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

[0096] The above descriptions are merely some embodiments of the present invention. Those skilled in the art can make various modifications and improvements without departing from the inventive concept of the present invention, and these all fall within the scope of protection of the present invention.

Claims

1. A near-field positioning method, characterized in that, Includes the following steps: Step 1: Deploy the antenna array based on the monostatic symmetric nested array MIMO system; The monostatic symmetric nested array MIMO system includes three linearly distributed subarrays located on the same straight line; subarray 1 includes... A uniform linear array of n elements, with the element spacing of subarray 1 being... , The carrier wavelength; subarray 2 and subarray 3 have the same structure, both including A uniform linear array of n elements, with an element spacing of 1. The array elements are arranged such that subarray 2 and subarray 3 are located on either side of subarray 1, and the distance between them and subarray 1 is 1 / 2. Subarray 1 forms the transmitting array, and subarrays 2, 3, and the central element of subarray 1 form the receiving array; where positive integers , ; A linear number line is established with the central array element as the origin to obtain the position coordinates of each element in the transmitting and receiving arrays. The position index of each element in the transmitting array is denoted as... The position index of each element of the receiving array is ,in , , , ; Step 2: The transmitting array emits a radiated signal, and the receiving array receives the returned signal and performs matched filtering to obtain the received signal. ; Received signal Represented as: in, Represents the near-field signal source vector. Represents the noise vector. Represents the array manifold matrix. express The steering vector of the transmission array corresponding to the target signal of each target constitutes the... 3D near-field emission array manifold matrix, express The steering vector of the receiving array corresponding to the target signal of each target constitutes the... dimensional receiver array manifold matrix, parameters ,parameter , Indicates the target number; Step 3: Perform redundancy removal processing on the received array signal based on the harmonic array: Based on array element position index , Obtain the element position index of the harmonic array. ; Based on array element position index ,from Extract the index of the current array element position For rows with the same corresponding items, for several extracted rows, in Keep only one row, and the element value of that row is the mean of all extracted rows. Repeat this process until... It does not contain the element position index. The corresponding duplicate terms are used to obtain the redundancy-free signal. And denote the redundancy-free concordance array as , express The number of sampling points; Furthermore, the continuous segment of the element index of the difference matrix of the harmonic array is: [Continued segment is...] ; Step 4: Calculate the fourth-order statistic and construct a spatial smoothing matrix for the vectorized signal: calculate The fourth-order statistics are used to generate a virtual array composed of the difference matrix of the covariance array. The received signal vector of the virtual array is spatially smoothed, and then its covariance matrix is ​​calculated based on the spatially smoothed received signal vector to obtain the smoothing matrix. ; Step 5, smooth the matrix Perform feature decomposition based on the previous The signal subspace is obtained by forming a diagonal matrix of the largest eigenvalues, based on the previous... The diagonal matrix formed by the smallest eigenvalues ​​yields the noise subspace; Based on the signal subspace and noise subspace, the MUSIC algorithm is used for spectrum search, and the search results are based on the corresponding peaks. The largest peak value yields the near-field DOA estimation result; Step 6: Near-field range estimation: From the received signal Remove from Received signal And calculate the received signal The corresponding covariance matrix ; For matrix Perform feature decomposition based on the previous The signal subspace is obtained by forming a diagonal matrix of the largest eigenvalues, based on the previous... The diagonal matrix formed by the smallest eigenvalues ​​yields the noise subspace; Based on the signal subspace and noise subspace, the MUSIC algorithm is used for spectral search, and the peaks in the search results are compared with the peaks in the signal subspace and noise subspace. The largest peak value yields the near-field distance estimate.

2. The method as described in claim 1, characterized in that, Step 4 specifically involves: Will The fourth-order statistics matrix is ​​represented as: ; in, diagonal array , , ; matrix , ~ express The guiding vector of each covariance matrix; Vectorized fourth-order statistics matrix Obtain vector ,in For the signal vector of the virtual array, The array manifold matrix of a virtual array composed of the difference matrices of a harmonic array; exist Find the row composition vector corresponding to a continuous segment of the difference matrix of the concordance array. ; Based on vectors Calculate the smoothing matrix ,in, Representing vectors The i-th row, .

3. The method as described in claim 1, characterized in that, Based on the total number of array elements The value is set to a positive integer. and :like If the remainder when divided by 4 is 1, then take... , ;like If the remainder when divided by 4 is 3, then take... , .

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