High-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL

Abstract

The invention discloses a high-precision sub-Nyquist DOA (Direction of Arrival) estimation method based on multi-configuration virtual space-time compression and UAMP-SBL (Uniform Amplitude Modulation Point-Square Binary Receiving the signal through sub-Nyquist sampling of the MWC; multi-configuration airspace angle compression and virtual array mapping: firstly performing airspace angle compression, and then performing virtual array phase compensation and virtual sampling value construction; sparse Bayesian DOA rough estimation based on UAMP-SBL: firstly constructing a sparse representation model, then performing unitary transformation and model transformation, and finally performing UAMP-SBL iterative estimation to obtain a DOA rough estimation value; and off-grid DOA fine estimation and multi-configuration ambiguity resolution: performing off-grid correction, constructing an off-grid model, and performing multi-configuration ambiguity resolution. According to the invention, an MWC sub-Nyquist sampling structure is combined with airspace compression, the ADC sampling rate is reduced from a Nyquist rate exceeding 10 G to a 100M sampling rate level, the complexity of an estimation algorithm is reduced, the implementation difficulty, system power consumption and hardware cost of the ADC are greatly reduced, the radio frequency front end design is simplified, and the system performance is improved. And the sampling rate and the hardware complexity are greatly reduced.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of signal processing, in particular to a high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL. BACKGROUND

[0002] In the field of array signal processing, direction of arrival (DOA) estimation is a core technology in many applications such as cognitive radio, radar reconnaissance, and autonomous driving.

[0003] However, with the rapid increase in signal bandwidth, traditional DOA estimation methods based on the Nyquist sampling theorem (such as MUSIC, ESPRIT, and other subspace algorithms) face severe challenges. The high sampling rate leads to a large amount of data, which puts high demands on the performance of analog-to-digital converters (ADCs) and the real-time processing capability of the system.

[0004] Although the sub-Nyquist sampling strategy combining the theory of compressed sensing with the sparse recovery framework can effectively reduce the sampling rate and computational complexity, the existing technical solutions still have defects. The sparse recovery method based on matching pursuit (MP) usually requires a large number of measurements and is sensitive to noise, and its performance deteriorates severely in coherent signal scenarios. The estimation accuracy of the traditional SBL method depends on discrete grid search, and specifically, when the number of grids increases and spatial compression is not performed, the computational complexity may increase exponentially.

[0005] Approximate message passing (AMP) has a lower complexity and has been proposed for low-complexity implementation of SBL. However, AMP performs poorly when facing non-zero mean, rank deficiency, correlation, or ill-conditioned matrices, which may lead to divergence or poor performance, severely limiting its application in complex signal scenarios.

[0006] A mutual coupling array DOA estimation method based on an improved LAMP network is disclosed in Chinese patent document CN114415106B. The mutual coupling array DOA estimation method based on the improved LAMP network improves the estimation accuracy, maintains a low computational complexity, and realizes DOA estimation. It solves the divergence problem of traditional approximate message passing methods for high-correlation matrices and improves efficiency. The mutual coupling array DOA estimation method based on the improved LAMP network of the present application comprises the following steps: determining the array signal vector model received, using the divergence compensation complex simplified learning approximate message passing DCCS-LAMP network to process the received signal, and obtaining the DOA estimation value. The present application is mainly applied to the direction of arrival estimation occasion, but the mutual coupling array DOA estimation method based on the improved LAMP network usually requires a large number of measurements and is sensitive to noise.

[0007] A DOA estimation method based on compressed sensing time modulation arrays is disclosed in Chinese patent document CN106772226B. This method addresses the technical problem of low estimation accuracy in existing time modulation array DOA estimation methods due to limited snapshots, close indexing, or coherent signals. The implementation steps are as follows: optimizing the pulse start time and pulse duration; establishing a sideband signal receiving model; expanding and sparsifying the array manifold in the sideband signal receiving model; performing singular value decomposition and dimensionality reduction on the sideband signals in the sparse receiving model of the time modulation array sideband signals; obtaining a sparse recovery problem model of the time modulation array based on compressed sensing; and solving for the direction of arrival (DOA) angle of the target signal. This invention, based on compressed sensing theory, fully utilizes the high-resolution characteristics of sparse reconstruction methods to improve the DOA estimation accuracy of the target wave. However, the performance of this DOA estimation method based on compressed sensing time modulation arrays deteriorates significantly in coherent signal scenarios.

[0008] A method for estimating the Direction of Arrival (DOA) of a nested multi-input multi-output (MIMO) radar based on compressed sensing is disclosed in Chinese patent document CN103886207B. The implementation process of this method is as follows: (1) the transmitting and receiving arrays of the nested multi-input multi-output radar are determined by the element arrangement of the nested array; (2) the echo signal is matched and filtered in each pulse repetition period of the radar; (3) the covariance matrix of the matched filter output data is vectorized; (4) the noise subspace is obtained by matrix reconstruction and singular value decomposition; (5) the L1 norm constraint term and L2 norm constraint term in the sparse recovery problem are constructed; and (6) the target direction of arrival is determined by solving the sparse recovery problem. This invention utilizes the degree of freedom extension characteristics of the nested array and the high resolution characteristics of compressed sensing, and can be used for the precise positioning of targets with more than the total number of virtual array elements. However, the computational complexity of this method for estimating the DOA of a nested multi-input multi-output radar based on compressed sensing may increase exponentially when the number of grids increases and spatial compression is not performed.

[0009] Existing hardware architectures are too complex, making it difficult to achieve a good balance between accuracy, efficiency, and practicality. Therefore, there is an urgent need for an innovative DOA solution that can balance high-precision estimation, low computational complexity, strong robustness, and hardware friendliness, in order to overcome current technological bottlenecks and meet the urgent needs of modern electronic systems for high-precision parameter estimation.

[0010] To address the shortcomings of the existing technologies, it is worthwhile to explore a high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL. Summary of the Invention

[0011] The purpose of this invention is to overcome the difficulty in achieving a good balance between accuracy, efficiency and practicality, and to provide a high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL, which achieves the technical effect of balancing high-precision estimation, low computational complexity, strong robustness and hardware friendliness.

[0012] The objective of this invention is achieved through the following technical solution:

[0013] A high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL includes the following steps:

[0014] Step 1: MWC-based sub-Nyquist sampling signal reception;

[0015] Step 2: Multi-configuration spatial angle compression and virtual array mapping: First, perform spatial angle compression, then perform virtual array phase compensation and virtual sample value construction;

[0016] Step 3: Sparse Bayesian DOA coarse estimation based on UAMP-SBL: First, construct a sparse representation model, then perform unitary transformation and model transformation, and finally perform UAMP-SBL iterative estimation to obtain a coarse estimate of DOA.

[0017] Step 4: Off-network DOA fine estimation and multi-configuration deblurring: Off-network correction, construction of off-network model, and multi-configuration deblurring. This invention has strong robustness and can maintain stable and excellent estimation performance in low signal-to-noise ratio (SNR>-3dB), few snapshots (K=100) and coherent source scenarios, and has wide applicability.

[0018] Optionally, the signal reception in step one is achieved by utilizing... The spacing is ULA uniform linear array receiver composed of array elements Each array element is connected to an independent MWC modulated wideband converter sampling channel, which transmits signals from a far-field narrowband signal source. The MWC channel sequentially performs pseudo-random sequence mixing, low-pass filtering, and low-speed analog-to-digital conversion (ADC) sampling on the received signals to obtain an under-Nyquist sampling sequence matrix. ;

[0019] in, It's the number of snapshots. The m-th element is The matrix, yes Inverse Fourier transform, The array steering matrix is ​​represented as...

[0020] (1),

[0021] By employing the MWC sub-Nyquist sampling structure, the ADC sampling rate is reduced from the Nyquist rate (typically exceeding 20 GS / s) to the hundreds of megabits per second, significantly reducing the implementation difficulty, system power consumption, and hardware cost of the ADC. Each array element requires only a single sampling channel, simplifying the RF front-end design and greatly reducing the sampling rate and hardware complexity.

[0022] Optionally, the spatial angle compression in step two involves adjusting the equivalent element spacing of the virtual array based on the spatial aliasing phenomenon caused by the periodicity of spatial phase difference. To compress the unambiguous angle measurement range, the spatial phase difference between adjacent array elements is:

[0023] (2)

[0024] Where λ is the signal wavelength and θ is the direction of the incident signal;

[0025] make The corresponding spatial aliasing interval is obtained by solving. for:

[0026] (3)

[0027] Then the half-width of the main lobe without ambiguity intervals , is represented as:

[0028] (4)

[0029] To precisely control the working range of the gridless lobe The element spacing should be designed as follows:

[0030] (5)

[0031] This represents the spacing between adjacent elements of the virtual array in the p-th compression mode. Let be the critical compression angle in the p-th compression mode, when the virtual array element spacing is When adjusted to a specific value, the angle measurement range is compressed to... This achieves angle compression by using multi-configuration spatial compression, reducing the required spatial range from the entire space (-90° to 90°) to a few finite sub-regions (e.g., ±21°, ±25°), significantly reducing the number of grid points G required for sparse recovery. Combined with the UAMP-SBL algorithm, which eliminates the need for matrix inversion, the computational complexity is reduced from O(G³) of traditional SBL to O(NG²+NGK), improving computational efficiency by over 50% and significantly reducing computational complexity.

[0032] Optionally, in step two, the virtual array phase compensation and virtual sample value construction extract accurate phase difference information through subspace rotation invariance, construct the virtual array's steering vector and sampling sequence, and realize an effective mapping from the physical array to the virtual array.

[0033] The covariance of the physical array sample values ​​is eigenvalues ​​obtained by eigendecomposition Then the signal subspace This is the column vector corresponding to the first M largest eigenvalues;

[0034] To extract the phase difference of each signal source, Decomposed into two overlapping subarrays , ,satisfy , It is a rotation matrix, and its eigenvalues ​​are... Least squares estimation solution for

[0035] (6)

[0036] right Perform eigenvalue decomposition , Then the phase gradient is

[0037] (7)

[0038] When the array element spacing , ,lead to Only return the main value To resolve the ambiguity, a multi-period search mechanism is introduced for each... Consider candidate sets ,in For positive integers, choose the one that minimizes the residual.

[0039] (8)

[0040] The relationship between the virtual array phase difference and the physical array phase difference in the p-th mode is as follows:

[0041] (9)

[0042] Then the steering vector of the virtual array in the p-th mode is

[0043] (10)

[0044] Then the virtual array sampling sequence in mode p is

[0045] (11)

[0046] in , ;

[0047] In coherent signal source scenarios, the rank of the array covariance matrix may drop to 1, causing subspace estimation to fail. To restore the rank, spatial smoothing technology is used to divide the array into multiple subarrays, allowing each subarray to receive coherent signals separately. The average value of these subarrays is used to replace the coherence matrix of the original received data, thereby obtaining the phase difference of the coherent physical array sample values. Then, the virtual array sample values ​​are solved. By using rotation-invariant subspace (ESPRIT-like) technology to extract the accurate phase difference from the physical array data and combining it with a multi-period search mechanism to solve the phase ambiguity problem, virtual array data of different modes are constructed. This achieves the equivalent acquisition of multiple virtual arrays with different apertures and characteristics without increasing the number of physical array elements, providing a data foundation for multi-configuration deambiguity.

[0048] Optionally, the sparse representation model in step three is established by sparsifying the sampled data of the physical array and the virtual array in the spatial domain:

[0049] (12)

[0050] in It is a complete dictionary matrix consisting of the guide vectors of G grid points. , The signal matrix to be estimated has joint sparsity. By discretizing the continuous spatial domain into an overcomplete dictionary, the DOA estimation problem is transformed into a sparse signal recovery problem. High-resolution DOA estimation is achieved by utilizing the spatial sparse prior of the signal.

[0051] Optionally, the unitary transformation and model transformation in step three are first performed on... Performing a unitary transformation on a matrix, the matrix Decomposed into singular value decomposition by SVD ,in , diagonal array , then the formula It can be written as

[0052] (13)

[0053] in ,

[0054] ,

[0055] ,

[0056] By performing a unitary transformation on the observation model, the problem is transformed into an equivalent estimation model with whitened noise, which enhances the numerical stability of the algorithm and avoids the divergence of AMP-type algorithms caused by ill-conditioned matrices.

[0057] Optionally, in step three, the UAMP-SBL iterative estimation, based on the probabilistic graphical model and the SVMP structured variational inference framework, derives the message passing process on the transformed model; it uses the UAMP unitary approximation message passing rule to approximate the marginal distribution, avoiding high-dimensional matrix inversion; and it automatically learns noise accuracy during iteration. and signal hyperparameters Finally, the sparse matrix of the signal is obtained. The estimated value; the peak position of its power spectrum is the coarse estimate of DOA in the compression angle domain. By employing the UAMP-SBL algorithm for sparse recovery, the high accuracy and robustness of the SBL method and the low complexity and high stability of the UAMP algorithm are combined. It can still obtain a coarse estimate of DOA stably and accurately in scenarios with low signal-to-noise ratio, few snapshots and coherent sources, while avoiding the huge computational overhead caused by high-dimensional matrix inversion in traditional SBL.

[0058] Optionally, the off-network correction in step four, based on the coarse estimation results obtained in step three, retains non-zero rows to reduce the dimensionality of the model and constructs an off-network model:

[0059] (14)

[0060] The signal matrix is ​​alternately optimized using a low-complexity Jacobi iterative method. and guiding matrix By eliminating grid mismatch errors through root-finding operations, a higher-precision DOA estimate is obtained, defined as... The estimated value of DOA is:

[0061] (15)

[0062] The innovative UAMP-SBL framework exhibits excellent noise resistance and the ability to process coherent signals. Combined with an off-grid correction mechanism, it effectively eliminates quantization errors introduced by the discrete grid. Simulations show that its root mean square error (RMSE) performance is 30%-40% higher than traditional methods such as MUSIC, MWC_SOMP, and untrimmed_SBL, achieving ultra-high estimation accuracy.

[0063] Optionally, the multi-configuration defuzzification in step four utilizes multiple different The estimated compression angle obtained under the set compression mode, and the phase ambiguity relation are solved. Solving for the true angle By reasonably setting the spacing between virtual array elements in each mode, the spacing between virtual array elements in different modes can be adjusted. The irrational number ensures that the true DOA is determined from the measurements of multiple modes. By comprehensively utilizing the local unambiguous estimation results of multiple compressed modes and taking advantage of the characteristic that the virtual element spacing ratio is an irrational number for joint calculation, the compressed angle estimates of each mode are uniquely and unambiguously mapped back to the true full-space DOA, and finally outputting a high-precision, globally unambiguous DOA estimation result.

[0064] Positive and beneficial effects: 1. Significantly reduced sampling rate and hardware complexity: By adopting the MWC sub-Nyquist sampling structure, the ADC sampling rate is reduced from a high Nyquist rate (typically exceeding 20GS / s) to the hundreds of megabits per second level, greatly reducing the implementation difficulty, system power consumption, and hardware cost of the ADC. Each array element requires only a single sampling channel, simplifying the RF front-end design.

[0065] 2. Significantly Reduced Computational Complexity: By using multi-configuration spatial compression, the spatial range to be calculated is reduced from the entire space (-90° to 90°) to a few finite sub-regions (e.g., ±17°, ±21°, ±25°), significantly reducing the number of grid points G required for sparse recovery. Combined with the UAMP-SBL algorithm, which does not require matrix inversion, the computational complexity is reduced from O(G³) of the traditional SBL to O(NG²+NGK), improving computational efficiency by more than 50%.

[0066] 3. Achieving Ultra-High Estimation Accuracy: The innovative UAMP-SBL framework exhibits excellent noise resistance and the ability to process coherent signals. Combined with an off-grid correction mechanism, it effectively eliminates quantization errors caused by discrete grids. Simulations show that its root mean square error (RMSE) performance is 30%-40% higher than traditional methods such as MUSIC, MWC_SOMP, and untrimmed_SBL.

[0067] 4. Strong robustness: The method of this invention can still maintain stable and excellent estimation performance in scenarios with low signal-to-noise ratio (SNR>-3dB), few snapshots (K=100), and coherent sources, and has wide applicability. Attached Figure Description

[0068] Figure 1 This is a schematic diagram of the multi-configuration compressed array model of the present invention;

[0069] Figure 2 This is a schematic diagram of the ULA-MWC sampling channel structure of the present invention;

[0070] Figure 3 This is a comparison of the simulation experimental performance of the relationship between RMSE and SNR under the incoherent source condition of the present invention;

[0071] Figure 4 This is a comparison of the simulation experimental performance of the relationship between RMSE and SNR under the coherent source condition of this invention;

[0072] Figure 5 This is a comparison of the simulation experimental performance of the relationship between RMSE and the number of array elements under the incoherent source condition of the present invention;

[0073] Figure 6 This is a comparison of the simulation experimental performance of the relationship between RMSE and the number of array elements under the coherent source condition of the present invention;

[0074] Figure 7 This is a comparison of the simulation experimental performance of the relationship between RMSE and snapshot number under the incoherent source condition of the present invention;

[0075] Figure 8 This is a comparison of the simulation performance of the relationship between RMSE and snapshot number under the coherent source condition of the present invention;

[0076] Figure 9 This is a flowchart of the UAMP-SBL algorithm of the present invention. Figure 10 This invention relates to a multi-mode spatial compression DOA estimation method. Detailed Implementation

[0077] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0078] Example 1

[0079] like Figures 1 to 9 As shown, a high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL includes the following steps:

[0080] Step 1: MWC-based sub-Nyquist sampling signal reception;

[0081] Step 2: Multi-configuration spatial angle compression and virtual array mapping: First, perform spatial angle compression, then perform virtual array phase compensation and virtual sample value construction;

[0082] Step 3: Sparse Bayesian DOA coarse estimation based on UAMP-SBL: First, construct a sparse representation model, then perform unitary transformation and model transformation, and finally perform UAMP-SBL iterative estimation to obtain a coarse estimate of DOA.

[0083] Step 4: Off-network DOA fine estimation and multi-configuration deblurring: Off-network correction, construction of off-network model, and multi-configuration deblurring. This invention has strong robustness and can maintain stable and excellent estimation performance in low signal-to-noise ratio (SNR>-3dB), few snapshots (K=100) and coherent source scenarios, and has wide applicability.

[0084] The signal reception in step one is achieved by using the signal received from the source. The spacing is ULA uniform linear array receiver composed of array elements Each array element is connected to an independent MWC modulated wideband converter sampling channel, which transmits signals from a far-field narrowband signal source. The MWC channel sequentially performs pseudo-random sequence mixing, low-pass filtering, and low-speed analog-to-digital conversion (ADC) sampling on the received signals to obtain an under-Nyquist sampling sequence matrix. ;

[0085] in, It's the number of snapshots. The m-th element is The matrix, yes Inverse Fourier transform, The array steering matrix is ​​represented as...

[0086] (1),

[0087] By employing the MWC sub-Nyquist sampling structure, the ADC sampling rate is reduced from high Nyquist rates (typically exceeding 20 GS / s) to the hundreds of megabits per second (Mbps) level, significantly reducing the implementation difficulty, system power consumption, and hardware cost of the ADC. Each array element requires only a single sampling channel, simplifying the RF front-end design and greatly reducing the sampling rate and hardware complexity.

[0088] In step two, spatial angle compression adjusts the equivalent element spacing of the virtual array based on the spatial aliasing phenomenon caused by the periodicity of spatial phase difference. To compress the unambiguous angle measurement range, the spatial phase difference between adjacent array elements is:

[0089] (2)

[0090] Where λ is the signal wavelength and θ is the direction of the incident signal;

[0091] make The corresponding spatial aliasing interval is obtained by solving. for:

[0092] (3)

[0093] Then the half-width of the main lobe without ambiguity intervals , is represented as:

[0094] (4)

[0095] To precisely control the working range of the gridless lobe The element spacing should be designed as follows:

[0096] (5)

[0097] This represents the spacing between adjacent elements of the virtual array in the p-th compression mode. Let be the critical compression angle in the p-th compression mode, when the virtual array element spacing is When adjusted to a specific value, the angle measurement range is compressed to... This achieves angle compression by using multi-configuration spatial compression, reducing the required spatial range from the entire space (-90° to 90°) to a few finite sub-regions (e.g., ±21°, ±25°), significantly reducing the number of grid points G required for sparse recovery. Combined with the UAMP-SBL algorithm, which eliminates the need for matrix inversion, the computational complexity is reduced from O(G³) of traditional SBL to O(NG²+NGK), improving computational efficiency by over 50% and significantly reducing computational complexity.

[0098] In step two, virtual array phase compensation and virtual sample value construction extract accurate phase difference information through subspace rotation invariance, construct the virtual array's steering vector and sampling sequence, and achieve effective mapping from physical array to virtual array;

[0099] The covariance of the physical array sample values ​​is eigenvalues ​​obtained by eigendecomposition Then the signal subspace This is the column vector corresponding to the first M largest eigenvalues;

[0100] To extract the phase difference of each signal source, Decomposed into two overlapping subarrays , ,satisfy , It is a rotation matrix, and its eigenvalues ​​are... Least squares estimation solution for

[0101] (6)

[0102] right Perform eigenvalue decomposition , Then the phase gradient is

[0103] (7)

[0104] When the array element spacing , ,lead to Only return the main value To resolve the ambiguity, a multi-period search mechanism is introduced for each... Consider candidate sets Choose the one that minimizes the residual.

[0105] (8)

[0106] The relationship between the virtual array phase difference and the physical array phase difference in the p-th mode is as follows:

[0107] (9)

[0108] Then the steering vector of the virtual array in the p-th mode is

[0109] (10)

[0110] Then the virtual array sampling sequence in mode p is

[0111] (11)

[0112] in , ;

[0113] In coherent signal source scenarios, the rank of the array covariance matrix may drop to 1, causing subspace estimation to fail. To restore the rank, spatial smoothing technology is used to divide the array into multiple subarrays, allowing each subarray to receive coherent signals separately. The average value of these subarrays is used to replace the coherence matrix of the original received data, thereby obtaining the phase difference of the coherent physical array sample values. Then, the virtual array sample values ​​are solved. By using rotation-invariant subspace (ESPRIT-like) technology to extract the accurate phase difference from the physical array data and combining it with a multi-period search mechanism to solve the phase ambiguity problem, virtual array data of different modes are constructed. This achieves the equivalent acquisition of multiple virtual arrays with different apertures and characteristics without increasing the number of physical array elements, providing a data foundation for multi-configuration deambiguity.

[0114] The sparse representation model in step three is established by sparsifying the sampled data from the physical and virtual arrays in the spatial domain.

[0115] (12)

[0116] in It is a complete dictionary matrix consisting of the guide vectors of G grid points. , The signal matrix to be estimated has joint sparsity. By discretizing the continuous spatial domain into an overcomplete dictionary, the DOA estimation problem is transformed into a sparse signal recovery problem. By utilizing the spatial sparse prior of the signal, the Rayleigh limit is broken, and super-resolution DOA estimation is achieved.

[0117] In step three, the unitary transformation and model transformation first involve... Performing a unitary transformation on a matrix, the matrix Decomposed into singular value decomposition by SVD ,in , diagonal array , then the formula It can be written as

[0118] (13)

[0119] in ,

[0120] ,

[0121] ,

[0122] By performing a unitary transformation on the observation model, the problem is transformed into an equivalent estimation model with whitened noise, which enhances the numerical stability of the algorithm and avoids the divergence of AMP-type algorithms caused by ill-conditioned matrices.

[0123] In step three, the UAMP-SBL iterative estimation derives the message passing process based on the probabilistic graphical model and the SVMP structured variational inference framework on the transformed model; it approximates the marginal distribution using the UAMP unitary approximation message passing rule to avoid high-dimensional matrix inversion; and it automatically learns noise accuracy during iteration. and signal hyperparameters Finally, the sparse matrix of the signal is obtained. The estimated value; the peak position of its power spectrum is the coarse estimate of DOA in the compression angle domain. By employing the UAMP-SBL algorithm for sparse recovery, the high accuracy and robustness of the SBL method and the low complexity and high stability of the UAMP algorithm are combined. It can still obtain a coarse estimate of DOA stably and accurately in scenarios with low signal-to-noise ratio, few snapshots and coherent sources, while avoiding the huge computational overhead caused by high-dimensional matrix inversion in traditional SBL.

[0124] In step four, the off-network correction, based on the coarse estimation results obtained in step three, retains the non-zero rows to reduce the dimensionality of the model and constructs the off-network model:

[0125] (14)

[0126] The signal matrix is ​​alternately optimized using a low-complexity Jacobi iterative method. and guiding matrix By eliminating grid mismatch errors through root-finding operations, a higher-precision DOA estimate is obtained, defined as... The estimated value of DOA is:

[0127] (15)

[0128] The innovative UAMP-SBL framework exhibits excellent noise resistance and the ability to process coherent signals. Combined with an off-grid correction mechanism, it effectively eliminates quantization errors introduced by the discrete grid. Simulations show that its root mean square error (RMSE) performance is 30%-40% higher than traditional methods such as MUSIC, MWC_SOMP, and untrimmed_SBL, achieving ultra-high estimation accuracy.

[0129] Step four involves multi-configuration deblurring, utilizing multiple different... The estimated compression angle obtained under the set compression mode, and the phase ambiguity relation are solved. Solving for the true angle By reasonably setting the spacing between virtual array elements in each mode, the spacing between virtual array elements in different modes can be adjusted. The irrational number ensures that the true DOA is determined from the measurements of multiple modes. By comprehensively utilizing the local unambiguous estimation results of multiple compressed modes and taking advantage of the characteristic that the virtual element spacing ratio is an irrational number, the compressed angle estimates of each mode are uniquely and unambiguously mapped back to the true full-space DOA, and finally outputting a high-precision, globally unambiguous DOA estimation result.

[0130] The flowchart of the high-precision DOA estimation algorithm based on multi-configuration spatial domain compression is as follows:

[0131]

[0132] Example 2

[0133] Step 1: Signal Acquisition

[0134] Sampling is performed using a uniform linear array (spacing greater than λ / 2) MWC sampling structure to obtain time-domain sampled data for each channel. ,in For the snapshot index.

[0135] Step 2: Multiple configurations for spatial angle compression:

[0136] To compress the angle search range and reduce computational complexity, a multi-configuration array consisting of one physical array and two virtual arrays was adopted, mainly including the following steps:

[0137] 1. Calculate the virtual array steering matrix. Accurate phase difference information is extracted using subspace rotation invariance, thereby constructing the steering matrix of the virtual array.

[0138]

[0139] 2. Generate virtual array data. Using formula 11, obtain the virtual array sampling data for the p-th mode using the physical array sampling value Y:

[0140]

[0141] 3. Construct a sparse dictionary matrix. The compression angle range of the p-th mode is [− ,+ Within a given range, divide the area into G grid points at predetermined intervals (e.g., 0.5∘), and construct a complete guide dictionary matrix accordingly.

[0142] Step 3: Sparse Recovery and Coarse Estimation Based on UAMP-SBL

[0143] Virtual array data for each mode p and dictionary The UAMP-SBL algorithm is used for sparse recovery, and the process is as follows:

[0144] 1. Unitary Transformation: Singular Value Decomposition (SVD) of a dictionary matrix. Furthermore, the observed data were unitarily transformed to enhance numerical stability. .

[0145] 2. Initialization: Set the iteration index Initialize variables , , , and hyperparameters , .

[0146] 3. Iterative Update: Following the process of Algorithm 1, iteratively calculate and update the intermediate variables until the convergence condition is met. and .

[0147] 4. Extracting the coarse estimation angle: Find the M largest peaks in the power spectrum of each row of the sparse matrix X^. The corresponding grid angles are the coarse estimation results for this mode. .

[0148] Step 4: Offline Precision Estimation and Multi-Configuration Defuzzing

[0149] 1. Off-grid correction: For the coarse estimation results of each mode, non-zero rows are retained to construct a dimensionality reduction model, and the Jacobi iterative method is used to alternately optimize the signal matrix and steering vector. The grid mismatch error is eliminated by root-finding operation to obtain a more accurate compression angle estimate.

[0150] 2. Multi-configuration deblurring: Collect the set of angles after precise estimation of all P modes. According to the formula:

[0151]

[0152] Due to the ratio of virtual array element spacing in each mode Since it is an irrational number, the true direction of arrival can be uniquely determined by solving the above system of equations. This outputs the final high-precision DOA estimation result.

[0153] Examples and Performance Verification

[0154] To verify the effectiveness of the invention, tests were conducted under the following conditions:

[0155] Test signals: M = 2 far-field narrowband signals, which may be incoherent or coherent sources (correlation coefficient K = 0.2588 − 0.9659i), Nyquist frequency 10 GHz, bandwidth B = 50 MHz.

[0156] Comparison algorithms: MUSIC, untrimmed_SBL, real_VBI, MWC_ESPRIT, MWC_SOMP.

[0157] Performance metric: Root Mean Square Error (RMSE).

[0158] Extensive simulation experiments demonstrate that the method described in this invention (CMWC_UAMP-SBL) under the given conditions exhibits significantly better RMSE performance than all comparative algorithms. As shown in the figure, regardless of whether the signal-to-noise ratio (SNR), number of array elements (N), or number of snapshots (K) is changed, the curve of this invention remains at the bottom. Furthermore, it demonstrates high accuracy and robust performance even in challenging scenarios such as low SNR, few snapshots, and coherent sources, fully proving its superiority.

[0159] The above is only used to illustrate the technical solution of the present invention and not to limit it. Any other modifications or equivalent substitutions made by those skilled in the art to the technical solution of the present invention, as long as they do not depart from the spirit and scope of the technical solution of the present invention, should be covered within the scope of the claims of the present invention.

Claims

1. A high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL, characterized in that, Includes the following steps: Step 1: Receiving sub-Nyquist sampling signals based on MWC architecture; Step 2: Multi-configuration spatial angle compression and virtual array mapping: First, perform spatial angle compression, then perform virtual array phase compensation and virtual sample value construction; Step 3: Sparse Bayesian DOA coarse estimation based on UAMP-SBL: First, construct a sparse representation model, then perform unitary transformation and model transformation, and finally perform UAMP-SBL iterative estimation to obtain a coarse estimate of DOA. Step 4: Offline DOA Precision Estimation and Multi-Configuration Defuzzing: Offline correction, construction of the offline model, and then multi-configuration defuzzing.

2. The high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL according to claim 1, characterized in that: The signal reception in step one is achieved by utilizing... The spacing is ULA uniform linear array receiver composed of array elements Each array element is connected to an independent MWC modulated wideband converter sampling channel, which transmits signals from a far-field narrowband signal source. The MWC channel sequentially performs pseudo-random sequence mixing, low-pass filtering, and low-speed analog-to-digital conversion (ADC) sampling on the received signals to obtain an under-Nyquist sampling sequence matrix. ; in, It's the number of snapshots. The m-th element is The matrix, yes Inverse Fourier transform, The array steering matrix is ​​represented as... （1）。 3. The high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL according to claim 1, characterized in that: The spatial angle compression in step two involves adjusting the equivalent element spacing of the array based on the spatial aliasing phenomenon caused by the periodicity of the spatial phase difference. To compress the unambiguous angle measurement range, the spatial phase difference between adjacent array elements is: （2） Where λ is the signal wavelength and θ is the direction of the incident signal; make The corresponding spatial aliasing interval is obtained by solving. for: （3） Then the half-width of the unambiguous interval , is represented as: （4） To precisely control the working range of the gridless lobe The element spacing should be designed as follows: （5）。 4. The high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL according to claim 1, characterized in that: In step two, the virtual array phase compensation and virtual sample value construction extract accurate phase difference information through subspace rotation invariance, construct the virtual array's steering vector and sampling sequence, and realize an effective mapping from the physical array to the virtual array. The covariance of the physical array sample values ​​is eigenvalues ​​obtained by eigendecomposition Then the signal subspace This is the column vector corresponding to the first M largest eigenvalues; To extract the phase difference of each signal source, Decomposed into two overlapping subarrays , ,satisfy , It is a rotation matrix, and its eigenvalues ​​are... Least squares estimation solution for （6） right Perform eigenvalue decomposition , Then the phase gradient is （7） When the array element spacing , ,lead to Only return the main value To resolve the ambiguity, a multi-period search mechanism is introduced for each... Consider candidate sets Choose the one that minimizes the residual. （8） The relationship between the virtual array phase difference and the physical array phase difference in the p-th mode is as follows: （9） Then the steering vector of the virtual array in the p-th mode is （10） Then the virtual array sampling sequence in mode p is （11） in , ; In the case of coherent signal sources, the rank of the array covariance matrix may drop to 1, causing the subspace estimation to fail. To restore the rank, a spatial smoothing technique is used to divide the array into multiple subarrays, so that each subarray receives the coherent signal separately. The average value of these subarrays is used to replace the coherent matrix of the original received data, thereby obtaining the phase difference of the coherent physical array sample values, and then solving for the virtual array sample values.

5. The high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL according to claim 1, characterized in that: The sparse representation model in step three is established by sparsifying the sampled data of the physical array and the virtual array in the spatial domain: （12） in It is a complete dictionary matrix consisting of the guide vectors of G grid points. , It is a signal with joint sparsity to be estimated.

6. The high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL according to claim 1, characterized in that: The unitary transformation and model transformation in step three first involve... Performing a unitary transformation on a matrix, the matrix Decomposed into singular value decomposition by SVD ,in , diagonal array , then the formula It can be written as （13） in , ， ， 。 7. The high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL according to claim 1, characterized in that: In step three, the UAMP-SBL iterative estimation derives the message passing process based on the probabilistic graphical model and the SVMP structured variational inference framework on the transformed model. Marginal distributions are approximated using the UAMP unitary approximation message-passing rule, avoiding high-dimensional matrix inversion; noise accuracy is automatically learned during iteration. and signal hyperparameters Finally, the sparse matrix of the signal is obtained. The estimated value; the peak position of its power spectrum is the coarse estimate of DOA in the compression angle domain. .

8. The high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL according to claim 1, characterized in that: The off-network correction in step four, based on the coarse estimation results obtained in step three, retains non-zero rows to reduce the dimensionality of the model and constructs the off-network model: （14） The signal matrix is ​​alternately optimized using a low-complexity Jacobi iterative method. and guiding matrix By eliminating grid mismatch errors through root-finding operations, a higher-precision DOA estimate is obtained, defined as... The estimated value of DOA is: （15）。 9. A high-precision sub-Nyquist DOA estimation method based on multi-configuration virtual space-time compression and UAMP-SBL according to claim 1, characterized in that: The multi-configuration defuzzification in step four utilizes multiple different... The estimated compression angle obtained under the set compression mode, and the phase ambiguity relation are solved. Solving for the true angle By reasonably setting the spacing between virtual array elements in each mode, the spacing between virtual array elements in different modes can be adjusted. It is an irrational number, thus ensuring that the true direction of arrival can be determined from measurements of multiple modes.

Images