A Weak Signal DOA Estimation Method Based on Weighted Sparse Reconstruction

Abstract

The present invention discloses a weak signal DOA estimation method based on weighted sparse reconstruction. First, the received array data is subjected to dimensionality reduction and optimization processing to obtain a new sparse reconstruction model; secondly, according to the array data, a weight matrix is ​​constructed by combining the phase group delay spectrum with the amplitude spectrum; finally, the weight matrix is ​​combined with the new sparse reconstruction model to perform second-order cone programming to solve the DOA estimation. This method has high resolution and strong robustness when finding the direction of weak signals, a sharp main lobe of the spectrum, lower side lobes, fewer pseudo peaks, and fewer snapshots required, and can accurately and stably estimate the signal arrival direction and improve the system sensitivity. This is conducive to improving the calculation time of the equipment, reducing hardware overhead, and to a certain extent reducing the system operating cost.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication technology, and relates to radio astronomy detection, sonar underwater detection, electromagnetic detection, passive positioning and radio monitoring management technology. Specifically, it relates to a weak signal DOA estimation method based on weighted sparse reconstruction. Background Art

[0002] Direction finding is one of the most important technologies in the field of detection. It is often used in astronomy, radar, electronic reconnaissance, earthquake monitoring, acoustic detection and other fields. At present, passive direction finding faces the following challenges: (1) With the update and iteration of communication technology, the power of the radiated signal becomes smaller, and the long-distance detection signal is weak; (2) With the increasing number of frequency / sound-generating devices, the signal spectrum in the environment is crowded, interference is superimposed, and noise is enhanced; (3) People’s rich production and life lead to a complex propagation environment (obstruction, reflection), which affects signal propagation. These will cause the received signal to weaken and the noise to increase, thereby affecting the direction finding accuracy and resolution, resulting in poor system detection performance. Therefore, the research on weak signal direction finding methods is of great significance to improving system sensitivity and breaking through the detection limit.

[0003] In order to obtain higher direction finding accuracy, domestic and foreign researchers have proposed a large number of algorithms, such as: Multiple Signal Classification (MUSIC), Rotation Invariant Subspace (ESPRIT), Maximum Likelihood Estimation (ML), etc. The MUSIC algorithm estimates the direction of arrival (DOA) based on the principle of orthogonality between the signal subspace and the noise subspace. It decomposes the signal received by the array into the signal subspace and the noise subspace, and then uses the orthogonality of the two subspaces to construct the spatial spectrum function. Finally, the direction of the signal is determined by searching the peak of the spatial spectrum. It has the advantages of high resolution and strong applicability. However, the computational complexity is high, especially when the number of array elements is large or the search angle range is large. It also depends on the accurate estimation of the number of signal sources. In order to obtain a stable subspace division, more snapshot data is usually required. The ESPRIT algorithm uses the geometric characteristics of the array structure, especially when there are two or more sub-arrays with the same rotational invariance in the array, the phase difference between the signals received by the two sub-arrays is used to estimate the direction of arrival of the signal. Compared with the MUSIC algorithm, it does not need to perform full-angle search, has high computational efficiency, low computational complexity, and good real-time performance. However, the ESPRIT algorithm has requirements for the array structure, that is, the array needs to have specific rotational invariance, and usually requires multiple snapshot data to construct the covariance matrix or correlation matrix, and then perform eigenvalue decomposition and other processing. In addition, its estimation accuracy is largely affected by the array structure and the accurate estimation of the number of signal sources. The maximum likelihood estimation estimates the parameters of the signal source by maximizing the probability density function of the received signal, including the direction of arrival, signal strength, etc., considering all possible signal and noise configurations to find the parameter set that best fits the observed data. It has strong adaptability and can flexibly handle various noise and signal models, but the computational complexity is extremely high and sensitive to the initial value. In summary, although these methods have shown excellent direction finding performance, they generally require multiple array elements and snapshots, which seriously restricts the engineering application of direction finding algorithms.

[0004] In recent years, sparse reconstruction direction finding methods have attracted widespread attention due to their better direction finding performance with fewer array elements and fewer snapshots. The essence of sparse reconstruction is the l0 norm problem. Since the l0 norm is an NP-hard problem, researchers often use l pInstead of using the \(L_0\) (where \(0 < p\leq1\)) norm to solve for an approximate result, the FOCUSS algorithm uses the \(L_p\) (where \(0 < p < 1\)) norm as the objective function. Its objective function is mainly optimized by an iterative approximation method, and the computational complexity increases with the increase in the number of snapshots. During optimization, it is troubled by local extrema. The \(L_1\) norm can satisfy the sparsity constraint and eliminate the possibility of local convergence of the objective function. Therefore, the most typical one is the \(L_1\) sparse representation DOA estimation algorithm. This method has good performance at high signal-to-noise ratios. However, since the \(L_1\) norm is used to replace the \(L_0\) norm during solution, at low signal-to-noise ratios, the sparsity of the solution deteriorates, the number of false peaks increases, and the direction-finding performance drops significantly. To address this issue, researchers increase the sparsity of the solution by weighting the sparse signal, thereby suppressing false peaks and improving the direction-finding accuracy. Common weighting methods in these approaches include the MUSIC spectrum, Capon spectrum, etc. They can improve the solution of the \(L_1\) norm, effectively suppress false peaks, enhance the robustness of the \(L_1\) sparse representation algorithm to noise, and estimate the direction of arrival. However, the MUSIC spectrum and Capon spectrum generally require multiple array elements and snapshots, which reduces the multi-signal direction-finding resolution. Especially when the signal-to-noise ratio (SNR) decreases, the sparsity of the solution will become worse, the direction-finding accuracy and resolution will decrease significantly, and more spurious peaks will appear in the spatial spectrum, resulting in a worse direction-finding effect and even direction-finding failure.

[0005] Therefore, it is necessary to study a weight with better accuracy and resolution to form a weak signal direction-finding method based on weighted sparse reconstruction to address the deficiencies of current methods. Summary of the Invention

[0006] In view of this, the present invention proposes a weak signal DOA estimation method based on weighted sparse reconstruction, aiming to solve the problems of low direction-finding accuracy and resolution for weak signals, as well as the presence of many spurious peaks.

[0007] To achieve the above object, the technical solution of the present invention is as follows: A weak signal DOA estimation method based on weighted sparse reconstruction is provided, including the following steps:

[0008] First, perform dimensionality reduction and optimization processing on the received array data to obtain a new sparse reconstruction model; secondly, according to the array data, construct a weight matrix by combining the phase group delay spectrum and the amplitude spectrum, which is the reciprocal of the sum of the phase group delay spectra of the noise and signal subspace spectra, multiplied by the ratio of the amplitude spectra of the noise and signal subspaces; finally, combine the weight matrix with the new sparse reconstruction model and perform second-order cone programming to solve for the DOA estimation.

[0009] Further, the reciprocal of the sum of the phase group delay spectra of the noise and signal subspace spectra, multiplied by the ratio of the amplitude spectra of the noise and signal subspaces, specifically means constructing the following weight matrix:

[0010] ;

[0011] ;

[0012] In the formula, is the direction vector, is the conjugate transpose, E n = span{e K+1 , e K+2 , …, e M} is the noise subspace, E s = span{e1, e2, …, e K} is the signal subspace, θ k is the incident angle of the desired signal, is the group delay of the inner product of the noise subspace and the direction vector, is the group delay of the inner product of the signal subspace and the direction vector:

[0013] ;

[0014] ;

[0015] where θ is the DOA variable, that is, the traversal space search angle, is the phase spectrum of the inner product of the noise subspace and the direction vector, is the phase spectrum of the inner product of the signal subspace and the direction vector:

[0016] ;

[0017] .

[0018] Furthermore, the dimension reduction and optimization processing are specifically as follows: establish a mathematical model of the received array signal, replace the l0 norm with the l1 norm sparse representation for solution, and perform singular value decomposition on the received array data to obtain a dimension reduction matrix.

[0019] Furthermore, the establishment of the mathematical model of the received array signal is specifically as follows: establish a data model of the received signal at a certain moment t, as follows:

[0020] ;

[0021] where K is the number of far-field narrowband signals, the number of array elements is M, satisfying K < M, the array element spacing is half a wavelength, then the desired signal direction vector is a vector, d is the spacing between adjacent array elements, is the wavelength of the signal, T is the snapshot, s k (t) is the signal envelope, and n(t) is Gaussian white noise;

[0022] If the above equation is written in vector form, the mathematical model of the receiving array signal is:

[0023] ;

[0024] in, , is an M×K expected signal array manifold matrix, the expected signal matrix is a K×T matrix, where T is the number of snapshots; is zero and has a variance of The additive white Gaussian noise matrix of . For the convenience of description, the above formula can be simplified as:

[0025] ;

[0026] According to the mathematical model of the receiving array signal, the l0 norm is replaced by the l1 norm sparse representation to obtain:

[0027] ;

[0028] in, is a column vector consisting of the l2 norm of the row vector of each row in S: , is a regularization parameter affected by noise, usually a small constant; The matrix The result of straightening by column and taking the l2 norm is:

[0029] .

[0030] Furthermore, the singular value decomposition of the received array data is specifically performed as follows: assuming that the singular value decomposition of X is:

[0031] ;

[0032] The sparse model after dimensionality reduction is:

[0033] ;

[0034] in, , , , is a The identity matrix of The zero matrix of .

[0035] Preferably, the method further comprises: preprocessing the sparse model after dimensionality reduction to reduce calculation and obtain better sparsity, specifically: , , is the original signal vector The covariance matrix of , we get the new sparse reconstruction model after preprocessing:

[0036] .

[0037] Furthermore, the weight matrix is ​​combined with the sparse reconstruction new model to obtain:

[0038] .

[0039] Furthermore, the second-order cone programming is specifically:

[0040] ;

[0041] To estimate the DOA value.

[0042] As a second aspect, the present invention also provides a weak signal DOA estimation device based on weighted sparse reconstruction, including multiple sensors, a multi-channel receiver and a processor, for implementing the above-mentioned weak signal DOA estimation method based on weighted sparse reconstruction.

[0043] Furthermore, the weak signal DOA estimation device based on weighted sparse reconstruction described in the present invention can be divided into a hardware part and a software part. The hardware part mainly includes a sensor array and a receiver, wherein the sensor array can be a linear array, a circular array, a body array, etc., the sensor can be an acoustic sensor, an electromagnetic signal sensor, etc., and the receiver can be a zero intermediate frequency receiver, a frequency conversion receiver, a superheterodyne receiver, etc. The software part mainly includes a data processing part, which mainly includes a processor, a memory, a network interface, and a non-volatile memory, etc.

[0044] As a third aspect, the present invention further provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the weak signal DOA estimation method as described above.

[0045] The beneficial effects of the present invention are:

[0046] (1) A new direction finding method based on weighted sparse reconstruction is proposed. This method has a sharp main lobe, low average noise spectrum value, few pseudo peaks, and requires few snapshots. It has high direction finding accuracy, high resolution, and strong robustness under weak signals. (2) This method can improve the problems of many pseudo peaks and low direction finding resolution in the traditional method under weak signals and low signal-to-noise ratio, which is beneficial to improve system sensitivity, reduce hardware overhead, and reduce system operating costs to a certain extent. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the implementation cases. By referring to the drawings, the features and advantages of the present invention will be more clearly understood. The drawings are schematic and should not be understood as limiting the present invention in any way. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative work, among which:

[0048] Figure 1 is a flow chart of the method of the present invention;

[0049] Figure 2 This is the simulation diagram of the normalized spectrum of the two spatial sources;

[0050] Figure 3 This is a comparison chart of SNR and RMSE under two spatial sources;

[0051] Figure 4 This is a comparison chart of snapshots and RMSE under two spatial sources;

[0052] Figure 5 This is a comparison chart of the number of array elements and RMSE under two spatial sources;

[0053] Figure 6 This is a diagram of the equipment for the method of the present invention. DETAILED DESCRIPTION

[0054] In order to more clearly understand the above-mentioned purpose, features and advantages of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments. It should be noted that the embodiments of the present invention and the features in the embodiments can be combined with each other without conflict.

[0055] In the following description, many specific details are set forth to facilitate a full understanding of the present invention, but the present invention may also be implemented in other ways different from those described herein, and therefore, the scope of protection of the present invention is not limited by the specific embodiments disclosed below. The singular forms of "a", "said" and "the" used in the present invention and the appended claims are also intended to include plural forms, unless the context clearly indicates other meanings. It should also be understood that the term "and / or" used herein refers to and includes any or all possible combinations of one or more associated listed items.

[0056] Due to the disadvantage of low resolution of the traditional weight matrix solution method at low SNR, to solve this problem, we propose a method of combining the phase group delay spectrum and the amplitude spectrum to construct the weight matrix, that is: the reciprocal of the sum of the phase group delay spectra of the noise and signal subspace spectra, and then multiplied by the ratio of the amplitude spectra of the noise and signal subspaces. Since the phase group delay spectrum is sensitive to peak changes and has additivity, while the amplitude spectrum has multiplicativity, the combined weight matrix has high resolution and accuracy.

[0057] Specifically, for weak signal direction finding, the present invention proposes a new high-resolution and strong-robustness direction finding method for weak signals based on weighted sparse reconstruction. As Figure 1 shown, it is a schematic flow diagram of the above-mentioned direction finding method for weak array signal phase enhancement. First, the received array data is dimension-reduced and optimized to obtain a new sparse reconstruction model; secondly, according to the array data, a method of combining the phase group delay spectrum and the amplitude spectrum is used to construct a weight matrix; finally, the weight matrix is combined with the new sparse reconstruction model, and second-order cone programming is performed to solve the DOA estimation. The weak signal DOA estimation method based on weighted sparse reconstruction described in the present invention has high resolution and strong robustness for weak signal direction finding, the main lobe of the spectrogram is sharp, the side lobes are lower, there are fewer false peaks, fewer snapshots are required, and it can accurately and stably estimate the signal arrival direction, and improve the system sensitivity. This is beneficial to improving the device calculation time, reducing the overhead, and reducing the system operation cost to a certain extent.

[0058] The present invention will be described in detail below with reference to the accompanying drawings. Without conflict, the features in the following embodiments and implementation manners can be combined with each other.

[0059] Embodiment 1: For a weak signal DOA estimation method based on weighted sparse reconstruction, it includes the following steps:

[0060] S1, dimension-reduce and optimize the received array data to obtain a new sparse reconstruction model;

[0061] Assume that K far-field narrowband signals are incident on a uniform array with M array elements (K < M), and the element spacing is half a wavelength. Then, at a certain moment t, the data model of the received signal is

[0062] ;

[0063] Where is an desired signal direction vector, d is the spacing between adjacent elements, is the wavelength of the signal, is the incident angle, T is the snapshot, s k (t) is the signal envelope, and n(t) is Gaussian white noise.

[0064] If the above equation is written in vector form, the mathematical model of the receiving array signal is:

[0065] ;

[0066] in, , is an M×K expected signal array manifold matrix, the expected signal matrix is a K×T matrix, where T is the number of snapshots. is zero and has a variance of The additive white Gaussian noise matrix of . For the convenience of description, the above formula can be simplified as:

[0067] ;

[0068] if Can recover , then according to The position of the non-zero rows in is used to determine the DOA estimate of the source, which is the l0 norm problem. However, the optimization of the l0 norm is an NP-hard problem, and its l1 norm approximate solution is

[0069] ;

[0070] in, It is a column vector composed of the l2 norm of the row vector of each row in S, that is: , is a regularization parameter affected by noise and is usually a small constant. The matrix The result of straightening by column and calculating the l2 norm is:

[0071] ;

[0072] When the snapshot T is large, the amount of computation will inevitably be too large. Therefore, the singular value decomposition of the received array data can be obtained The dimension reduction matrix . Let the singular value decomposition of X be:

[0073] ;

[0074] The sparse model after dimensionality reduction is:

[0075] ;

[0076] in, , , , is a The identity matrix 0 is The zero matrix of .

[0077] In order to reduce calculation and obtain better sparsity, the above formula can be preprocessed. , , is the original signal vector The covariance matrix of .

[0078] At this point, the new sparse reconstruction model after preprocessing is obtained:

[0079] .

[0080] S2, based on the array data, a weight matrix is ​​constructed by combining the phase group delay spectrum with the amplitude spectrum;

[0081] Since the l0 norm is replaced by the l1 norm sparse representation, its sparsity deteriorates, resulting in more pseudo peaks in the spectrum when the signal is weak, resulting in poor direction finding accuracy and resolution. At this time, the present invention proposes to weight the sparse signal S to improve the sparsity of the solution. Traditional weight matrices often use MUSIC and Capon spectrum methods, which can improve the l1 norm solution, effectively suppress pseudo peaks, and enhance the robustness of the l1 sparse representation algorithm to noise. However, MUSIC spectrum and Capon spectrum generally require multiple array elements and snapshots, which will lead to reduced resolution at low SNR.

[0082] The group delay spectrum is often used for high-resolution signal time-frequency processing, which coincides with the goal of improving the resolution of direction finding angles. In addition, the classic MUSIC algorithm only uses the amplitude spectrum of the noise subspace spectrum, while ignoring the useful information of the phase spectrum and the signal subspace spectrum. To this end, the present invention makes full use of the information of the phase group delay spectrum and the signal subspace, and proposes a new weight matrix construction equation:

[0083] ;

[0084] ;

[0085] In the formula is the direction vector, is the conjugate transpose, E n = span{e K+1 , e K+2 , …, e M} is the noise subspace, E s = span{e1, e2, …, e K} is the signal subspace. is the group delay of the inner product of the noise subspace and the direction vector, is the group delay of the inner product of the signal subspace and the direction vector, that is:

[0086] ;

[0087] ;

[0088] Among them, θ is the DOA variable, that is, the search angle of the traversal space, is the phase spectrum of the inner product of the noise subspace and the direction vector, is the phase spectrum of the inner product of the signal subspace and the direction vector, that is:

[0089] ;

[0090] .

[0091] S3, combining the weight matrix with the new sparse reconstruction model, performing second-order cone programming, and solving the DOA estimation.

[0092] The weight of step S3 Combined with the l1 norm sparse representation new model in step S1:

[0093] ;

[0094] The above formula uses second-order cone programming

[0095] ;

[0096] The DOA value can be estimated from the above formula.

[0097] Embodiment 2: Corresponding to the aforementioned embodiment 1 of a weak signal DOA estimation method based on weighted sparse reconstruction, the present invention also provides an embodiment of a weak signal DOA estimation device based on weighted sparse reconstruction.

[0098] See also Figure 6 A weak signal DOA estimation device based on weighted sparse reconstruction provided in an embodiment of the present invention includes multiple sensors, a multi-channel receiver and a processor, which is used to implement a weak signal DOA estimation method based on weighted sparse reconstruction in the above embodiment.

[0099] The embodiment of the weak signal DOA estimation device based on weighted sparse reconstruction of the present invention can be divided into a hardware part and a software part. The hardware part mainly includes a sensor array and a receiver, wherein the sensor array can be a linear array, a circular array, a body array, etc., the sensor can be an acoustic sensor, an electromagnetic signal sensor, etc., and the receiver can be a zero intermediate frequency receiver, a frequency conversion receiver, a superheterodyne receiver, etc. The software part mainly includes a data processing part, mainly including a processor, a memory, a network interface, and a non-volatile memory, etc.

[0100] The software part can be applied to any device with data processing capability, which can be a device or apparatus such as a computer. The software part in the device embodiment can be implemented by software, or by hardware or a combination of software and hardware. Taking software implementation as an example, as a device in a logical sense, it is formed by the processor of any device with data processing capability in which it is located reading the corresponding computer program instructions in the non-volatile memory into the memory and running them. From the hardware level, if Figure 6 As shown, it is a structural diagram of a device with data processing capability in which a device for estimating weak signal DOA based on weighted sparse reconstruction is located in the present invention, except Figure 6 In addition to the processor, memory, network interface and non-volatile memory shown, any device with data processing capabilities in which the apparatus in the embodiments is located may also include other hardware, generally based on the actual functions of the device with data processing capabilities, which will not be described in detail.

[0101] The implementation process of the functions and effects of each unit in the above-mentioned device is specifically described in the implementation process of the corresponding steps in the above-mentioned method, and will not be repeated here.

[0102] For the device embodiment, since it basically corresponds to the method embodiment, the relevant parts can refer to the partial description of the method embodiment. The device embodiment described above is only schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of the present invention. Ordinary technicians in this field can understand and implement it without paying creative work.

[0103] It should also be noted that the terms "include", "comprises" or any other variations thereof are intended to cover non-exclusive inclusion, so that a process, method, commodity or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, commodity or device. In the absence of more restrictions, the elements defined by the sentence "comprises a ..." do not exclude the existence of other identical elements in the process, method, commodity or device including the elements.

[0104] Embodiment 3: The embodiment of the present invention further provides a computer-readable storage medium, on which a program is stored. When the program is executed by a processor, a weak signal DOA estimation method based on weighted sparse reconstruction in the above embodiment is implemented. The computer-readable storage medium may be an internal storage unit of any device with data processing capability described in any of the above embodiments, such as a hard disk or a memory. The computer-readable storage medium may also be an external storage device of any device with data processing capability, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), an SD card, a flash card (Flash Card), etc. equipped on the device. Furthermore, the computer-readable storage medium may also include both an internal storage unit and an external storage device of any device with data processing capability. The computer-readable storage medium is used to store the computer program and other programs and data required by any device with data processing capability, and may also be used to temporarily store data that has been output or is to be output.

[0105] Example 4: This example uses simulation experiments to compare the method of the present invention with the existing MUSIC, L1-SVD and the MUSIC-L1-SVD method proposed by Wentao Li et al. (see: W. Li, Y. Lei, X. Shi. DOA estimation of time-modulated linear array based on sparse signal recovery [J]. IEEE Antennas & Wireless Propagation Letters, vol. 16, pp. 2336-2340, 2017. hereinafter referred to as M-L1-SVD) to verify the effectiveness of the method of the present invention by comparing the DOA estimation performance of two spatial sources under low SNR, the resolution comparison under different SNRs, the relationship between different snapshots of two spatial sources and RSME, and the relationship between different numbers of array elements of two spatial sources and RSME.

[0106] First, the DOA estimation performance of two spatial sources under low SNR of various methods is compared. In simulation, the SNR of the two signals is -9dB, the directions of the incoming waves are 46° and 52° respectively, an 8-element uniform linear array is used, the distance between adjacent antennas is half a wavelength, the snapshot is 200 during data processing, and the regularization parameter h of the method of the present invention is 220. Figure 2 It is the normalized spectra of the four methods when SNR=-9 dB. The circles in the figure are actual signals. It can be seen from the figure that when the signal-to-noise ratio is low, other methods cannot effectively find the direction of two signals. The method of the present invention can suppress pseudo peaks, its main lobe is the sharpest, the side lobe is the lowest, and the DOA of two adjacent signals can be estimated.

[0107] Secondly, the resolution of each method is compared under different SNR. During the simulation, the SNR range of the two signals is [-15, 6] dB, the interval is 3 dB, the incoming wave directions are 46° and 52° respectively, an 8-element uniform linear array is used, and the distance between adjacent antennas is half a wavelength. The snapshot is 200 during data processing, and the regularization parameter h corresponding to the method of the present invention under different SNRs is [400, 300, 220, 150, 120,110, 100, 90]. 200 Monte Carlo simulations are used, and the direction finding accuracy is expressed by the root mean square error (RMSE):

[0108] ;

[0109] in is the number of Monte Carlo simulations, and the true angle of the signal is , is the signal source n c Monte Carlo DOA estimation. Figure 3 This is a comparison of SNR and RMSE under two spatial sources. It can be seen from the figure that the RMSE of each method decreases as the SNR increases. The method of the present invention has the lowest RMSE for direction finding under different SNRs, the highest resolution, and the best effect.

[0110] Again, the relationship between different snapshots and RSME under two spatial sources of each method is compared. During simulation, the SNR of the two signals is -3 dB, the directions of the incoming waves are 46° and 52° respectively, an 8-element uniform linear array is used, the distance between adjacent antennas is half a wavelength, and the snapshots during data processing are 50, 200, 600, 1200, and 2000 respectively. The regularization parameter h of the method of the present invention is 120. Figure 4 It is a comparison of snapshots and RMSE under two spatial sources. From the figure, we can see that with the increase of the number of snapshots, the RMSE of the method of the present invention and M-L1-SVD decreases, while the RMSE of the MUSIC and L1-SVD methods is almost unchanged due to the low SNR. The direction finding accuracy of the method of the present invention is high when there are few snapshots, and the effect is the best, which is conducive to improving the calculation time and reducing the system operation cost to a certain extent.

[0111] Finally, the relationship between the number of different array elements and RSME under two spatial sources of each method is compared. During simulation, the SNR of the two signals is -9dB, the directions of the incoming waves are 46° and 52° respectively, the distance between adjacent antennas is half a wavelength, the snapshots during data processing are 200 respectively, the antennas use 4, 6, 8, 10, and 20-element uniform linear arrays respectively, and the regularization parameter h of the method of the present invention is 220. Figure 5 It is a comparison between the number of array elements and RMSE under two spatial sources. From the figure, it can be seen that as the number of array elements increases, the RMSE of the method of the present invention and the other two methods decreases, and the method of the present invention has the best effect, especially when the number of array elements is small, the direction finding accuracy is high, which is conducive to reducing the antenna array overhead and reducing the system operating cost to a certain extent.

[0112] Based on this embodiment, it can be concluded that the method of the present invention has high resolution and strong robustness when weak signal direction finding, sharp main lobe of spectrum, lower side lobe, fewer pseudo peaks, fewer snapshots required, and can accurately and stably estimate the direction of arrival of the signal and improve the sensitivity of the system. This is conducive to improving the computing time of the equipment, reducing hardware overhead, and reducing the system operation cost to a certain extent.

[0113] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A weak signal DOA estimation method based on weighted sparse reconstruction, characterized in that: The following steps are involved: The received array data is processed by dimensionality reduction and optimization to obtain a sparsely reconstructed new model; According to the array data, the weight matrix is ​​constructed by combining the phase group delay spectrum with the amplitude spectrum: the inverse of the sum of the phase group delay spectrum of the noise and signal subspace spectra is multiplied by the ratio of the noise to signal subspace amplitude spectrum; The weight matrix is ​​combined with the new sparse reconstruction model to perform second-order cone programming to solve the DOA estimation.

2. The method according to claim 1, characterized in that The inverse of the sum of the phase group delay spectra of the noise and signal subspace spectra is multiplied by the ratio of the noise to signal subspace amplitude spectra. Specifically, the following weight matrix is ​​constructed: ； ； In the formula, is the direction vector, is the conjugate transpose, E n = span{e K+1 , e K+2 , …, e M } is the noise subspace, E s = span{e1, e2, …, e K } is the signal subspace, θ k is the expected signal incident angle, is the group delay of the inner product of the noise subspace and the direction vector, is the group delay of the inner product of the signal subspace and the direction vector: ； ； Among them, θ is the DOA variable, traversing the space to search for angles, is the phase spectrum of the inner product of the noise subspace and the direction vector, is the phase spectrum of the inner product of the signal subspace and the direction vector: ； 。 3. The method according to claim 1, characterized in that The dimension reduction and optimization processing specifically includes: establishing a mathematical model of the receiving array signal, replacing the l0 norm with the l1 norm sparse representation to solve, performing singular value decomposition on the receiving array data, and obtaining a dimension reduction matrix.

4. The method according to claim 3, characterized in that The establishment of the mathematical model of the receiving array signal is specifically: establishing a data model of the signal received at a certain time t, ； where K is the number of far-field narrowband signals, the number of array elements is M, satisfying K < M, the array element spacing is half a wavelength, and the desired signal direction vector is a vector, d is the spacing between adjacent array elements, is the wavelength of the signal, T is the number of snapshots, s k (t) is the signal envelope, and n(t) is Gaussian white noise; If the above equation is written in vector form, the mathematical model of the receiving array signal is: ； in, , is an M×K expected signal array manifold matrix, the expected signal matrix is a K×T matrix, where T is the number of snapshots; is zero and has a variance of The additive white Gaussian noise matrix of ; According to the mathematical model of the receiving array signal, the l0 norm is replaced by the l1 norm sparse representation to obtain: ； in, is a column vector consisting of the l2 norm of the row vector of each row in S: , is the regularization parameter affected by noise; The matrix The result of straightening by column and taking the l2 norm is: 。 5. The method according to claim 3, characterized in that: Specifically, the singular value decomposition of the received array data is as follows: Suppose the singular value decomposition of X is: ； The sparse model after dimensionality reduction is: ； in, , , , is a The identity matrix of for The zero matrix of .

6. The method according to claim 5, characterized in that Also includes: The sparse model after dimensionality reduction is preprocessed, specifically: , , is the original signal vector The covariance matrix of , we get the new sparse reconstruction model after preprocessing: 。 7. The method according to claim 6, characterized in that The weight matrix is ​​combined with the sparse reconstruction new model to obtain: 。 8. The method according to claim 6, characterized in that The second-order cone programming is specifically: ； To estimate the DOA value.

9. A weak signal DOA estimation device based on weighted sparse reconstruction, comprising a plurality of sensors, a multi-channel receiver and a processor, characterized in that: Used to implement the weak signal DOA estimation method based on weighted sparse reconstruction as described in any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps in the weak signal DOA estimation method according to any one of claims 1 to 8 are implemented.

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