High-precision positioning method of multi-user multi-mode system
By constructing a spatial-modal reception model and dividing it into subarray groups using UCCAs in a multi-user multimodal system, and combining it with the ESPRIT method, the problem of limited DOA estimation accuracy of multi-target base stations is solved, achieving high-precision multi-user positioning and reducing computational complexity.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- NORTHWESTERN POLYTECHNICAL UNIV
- Filing Date
- 2026-02-09
- Publication Date
- 2026-05-12
AI Technical Summary
Existing DOA estimation methods for multi-user multimodal systems are costly during the training phase, and their estimation accuracy is limited by the number of modes in the training sequence, failing to effectively address the accuracy issues caused by the different location angles of multiple target base stations.
A spatial-modal receiver model is constructed using uniform concentric circular arrays (UCCAs), subarrays are divided, the spatial-modal manifold matrix relationship of the subarrays is derived, and DOA estimation is performed using the ESPRIT method. By utilizing the degrees of freedom in the array space and modal domain, computational complexity is reduced and estimation accuracy is improved.
It effectively solves the multi-user localization problem, improves the multi-user estimation accuracy, reduces computational complexity, and enables high-precision DOA estimation at a lower cost.
Smart Images
Figure CN122017733A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of communication technology, specifically relating to a high-precision positioning method for a multi-user, multi-modal system. Background Technology
[0002] Multimode systems have the potential to improve communication channel capacity. However, if the transmit and receive beams are misaligned, it will affect the accuracy of mode reception detection and severely reduce channel capacity. Therefore, it is necessary to ensure perfect beam alignment between the transmit and receive antennas. Thus, how the receiver can accurately locate base station users and accurately estimate the direction of arrival (DOA) during the training phase is a key step in achieving beam alignment, thereby ensuring the system performance of wireless communication.
[0003] Existing methods for DOA estimation in multi-user, multimodal systems involve sending known training sequences for DOA estimation during the training phase. Single-channel signals are obtained by summing the signals received by each array element. Subspace algorithms are used to estimate parameters based on the degrees of freedom in the modal domain. However, due to the varying positions and angles of multiple target base stations, the estimation performance of current methods depends heavily on the number of modes or the mode / frequency ratio in the training sequence, leading to high training costs. In contrast, existing DOA estimation methods for array signals are well-developed, including subspace algorithms and sparse reconstruction algorithms, which can achieve higher accuracy in DOA estimation. Summary of the Invention
[0004] To overcome the shortcomings of existing technologies, this invention provides a high-precision positioning method for multi-user multimodal systems. The method derives the observation vectors of the receiving array elements, constructs a space-modal receiving model, divides the system into subarray groups, derives the relationship between the space-modal manifold matrices of the subarrays, substitutes the relationship into the subarray space-modal manifold matrices, and uses the ESPRIT method to obtain the DOA estimation for multiple users. Compared with existing DOA estimation schemes for multimodal systems, this invention estimates a greater number of interference sources, effectively solves the multi-user positioning problem, improves multi-user estimation accuracy, and reduces computational complexity.
[0005] The technical solution adopted by this invention to solve its technical problem is as follows: Step 1: Derive the observation vector of the receiving array element; Step 2: Construct a spatial-modal reception model; Step 3: Divide the subarrays into subarray groups and derive the relationship between the subarray space and the modal manifold matrix; Step 4: Substitute the relationship between the subarray space and modal manifold matrix, and use the ESPRIT method to obtain the DOA estimates for multiple base station users.
[0006] Preferably, step 1 specifically comprises: The array model used is A uniform concentric circular array UCCAs with 4 antenna elements consists of 3 uniform circular arrays UCA with 4 elements and 1 element with a common center. The elements of the UCCAs are numbered in order from top to bottom and from left to right. Establish a rectangular coordinate system with the center of the circle as the origin in the plane where the antenna array is located. The array elements of the innermost and outermost UCA layers are located at... and A circle with radius and and At the intersection; the array element of the middle UCA is located at the intersection of the two arrays. On a circle with radius , and the line connecting the array element and the origin is shaft and The included angle between the axes is 45°; The receiver array uses UCCAs, assuming that there are [missing information] in the far field. Each base station user is an independent entity, and each base station user is equipped with... There are OAM modes, among which For the number of modes used, , Let be the modal value; where the th The position parameters of the array elements relative to the origin of the transmission array are expressed as follows: ,in Expressed as azimuth, Expressed as pitch angle; Using element 7 at the center of UCCAs as the reference element, the first... The element receives the first One base station The expression for the observation vector of a mode:
[0007] in, For the constant term, in the formula The amplitude of the dipole constant current density, The imaginary unit, Permeability in vacuum Angular frequency, The length of the electric dipole. waveguide number, For the receiving array UCCAs The distance between each array element and the center of the circle For the first Individual elements and The angle between the positive and negative axes. for The first kind of Bessel function of order 1, For the first The distance from each base station user to the center of the receiving array UCCAs is... For the first Each array element receives the first Each base station user Gaussian white noise in the modal channel To determine the radius of the uniform circular array, For the first The training signals of each base station user, and the different signal sources are uncorrelated, satisfy the following formula:
[0008] During the training phase, all user base stations simultaneously send training sequences to the receiving base station; therefore, each element of the receiving array is in mode . The observation vector is the element pair The superposition of observation vectors from the training sequences of each base station, and the observation vector of each array element. After compensating for the constant term, we obtain the first... The receiving mode of each array element is: The expression for the observation vector is:
[0009] in For the first After compensating the constants of each array element, the mode is: The Gaussian white noise vector of the channel.
[0010] Preferably, step 2 specifically comprises: The array element receiving mode is The observation vectors are arranged in the order of the array element numbers of UCCAs, resulting in the mode as follows: Observation matrix:
[0011] in Let be the spatial manifold matrix, the first... The spatial steering vector for each base station user is:
[0012] in , Indicates the index of an array element in UCCAs. It is the first in UCCAs The distance from each numbered array element to the origin; Let be the modal manifold matrix, the first... The modal steering vector for each base station user is:
[0013] in express The OK, This indicates that a row vector is converted into a diagonal matrix; Define user matrix It is related to the base station user training matrix and the distance from the base station user to the receiving base station. To receive the number of snapshots of the training sequence, It is the base station user training sequence matrix, where After compensating for the constant, the mode is The Gaussian white noise matrix of the channel; The array observation data are stacked according to mode, and the observation matrix is represented as follows:
[0014] in Describes the Khatri-Rao product, defined For space-modal manifold matrix, This is a Gaussian white noise matrix.
[0015] Preferably, step 3 specifically comprises: Based on the rotation invariance between UCCAs elements, the UCCAs are divided into three subarrays, with each subarray containing the number of elements. Subarray 1: {1 2 3 4 7 8}, subarray 2: {2 5 6 7 10 11}, subarray 3: {3 6 78 11 12}; Define the space-modal manifold matrix corresponding to the three subarrays as follows: , and Combining the spatial-modal manifold matrix defined in step 2, the spatial-modal manifold matrices of subarray 1, subarray 2, and subarray 3 are expressed as follows: , , ,in The spatial manifold matrix of subarray 1, i.e. , Subarray 1 to the first The spatial steering vector for each base station user is:
[0016] The spatial manifold matrix of subarray 2, , Subarray 2 pairs The spatial steering vector for each base station user is:
[0017] This is the spatial manifold matrix of subarray 3. , Subarray 3 pairs The spatial steering vector for each base station user is:
[0018] Will Substituting the spatial array manifolds of the subarrays, the following rotation-invariant relationship is satisfied between the spatial array manifolds of the subarrays:
[0019] in , Both are diagonal matrices, where the diagonal elements are respectively , ; Therefore, the spatial-modal manifold of the subarray , , satisfy: .
[0020] Preferably, step 4 specifically comprises: For the observation matrix in step 2, calculate its covariance matrix:
[0021] in For the user covariance matrix, Here is the noise covariance matrix; right Eigenvalue decomposition yields:
[0022] in It is a diagonal matrix with diagonal elements as follows: eigenvalues, for eigenvector matrix; for Arrange the eigenvalues in descending order Take the largest The diagonal matrix of eigenvalues is Their corresponding eigenvectors constitute the signal subspace. Therefore, from Extract the corresponding rows of the corresponding elements of the three subarrays respectively, and form the signal subspaces respectively. , , ; According to subspace theory and The spaces spanned by the two elements are identical, that is, they satisfy the condition that the two elements are equal. Therefore, there exists a non-singular matrix. , making Therefore, the subarray signal subspace corresponding to the subarray also satisfies , and ; Calculate using the least squares method and get:
[0023] Substituting the rotation invariance relation from step 3 into the above equation, we get:
[0024] Therefore, for , Perform eigenvalue decomposition separately to obtain two eigenvalue diagonal matrices including the parameters. , , and ; Based on the property that the eigenvectors corresponding to different eigenvalues are mutually orthogonal, a sorting matrix is constructed. as follows:
[0025] Will According to After matching the order, reorder as ,make:
[0026] in for The first diagonal One element, for The first on the diagonal One element; Get the first The estimated DOA for each base station user is as follows:
[0027] Similarly, the estimated DOA values for all base station users are obtained. .
[0028] An electronic device includes a processor and a memory; the memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to enable the electronic device to perform the high-precision positioning method described above.
[0029] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the above-described high-precision positioning method.
[0030] A chip includes a processor for retrieving and running a computer program from a memory, causing a device equipped with the chip to perform the aforementioned high-precision positioning method.
[0031] A computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the aforementioned high-precision positioning method.
[0032] The beneficial effects of this invention are as follows: Compared with existing DOA estimation schemes for multimodal systems, this invention estimates a greater number of interference sources, effectively solves the multi-user localization problem, improves multi-user estimation accuracy, and reduces computational complexity. Attached Figure Description
[0033] Figure 1 A schematic diagram of the receiver array structure and numbering; Figure 2 A schematic diagram of subarray partitioning; Figure 3 The following are the estimation results for the number of modes of 3 under the noiseless ideal model of the method of the present invention: (a) 18 users, (b) 19 users; Figure 4 This is a schematic diagram showing the angle estimation results of two closely distributed interference sources using the method of the present invention when the number of modes is 3; Figure 5 This is a schematic diagram illustrating the relationship between the estimation accuracy and signal-to-noise ratio of the method of the present invention; Figure 6 This is a schematic diagram of the geometric model of the multi-user, multi-modal system according to the method of the present invention; Figure 7 This is a flowchart illustrating the implementation of the method of the present invention. Detailed Implementation
[0034] The present invention will be further described below with reference to the accompanying drawings and embodiments.
[0035] Current multimodal localization methods primarily rely on single-channel algorithms using the receiving array, neglecting to consider the array's spatial degrees of freedom. To address these shortcomings, this invention provides a multi-user localization method that combines the spatial and modal domain degrees of freedom of the receiving array. The aim of this invention is to solve the problem that the estimation accuracy of existing algorithms for multimodal multi-user base stations is limited by the number of modes in the training sequence. This invention proposes a high-precision spatial-modal domain multi-user localization method using a concentric circular array as the receiving array, combining spatial and modal domain degrees of freedom to achieve high-precision estimation performance at a relatively low cost.
[0036] This invention proposes a multi-user precise positioning scheme for multimodal systems, which achieves precise positioning of multiple users by estimating angles based on the spatial structural characteristics and modal domain of the receiving array.
[0037] The technical solution of this invention is as follows: Step 1: Derive the observation vector of the receiving array element.
[0038] The first array model used is A uniform concentric circular array (UCCA) consists of three 4-element uniform circular arrays (UCAs) and one element at a common center. The elements of the UCCAs are numbered from top to bottom and from left to right. The specific array structure and numbering are shown in the figure below. A Cartesian coordinate system is established in the plane containing the antenna array, with the center as the origin. The array elements of the innermost and outermost UCA layers are located at... and A circle with radius and and At the intersection. The array element of the middle UCA is located at the intersection of... On a circle with radius , and the line connecting the array element and the origin is shaft and The included angle between the axes is 45°.
[0039] The receiver array uses UCCAs, assuming that there are [missing information] in the far field. Each base station user is an independent entity, and each base station user is equipped with... There are OAM modes, among which For the number of modes used, , Let be the modal value; where the th The position parameters of the array elements relative to the origin of the transmission array are expressed as follows: ,in Expressed as azimuth, Expressed as pitch angle; Taking element 7 at the center of UCCAs as the reference element, the element receiving model is shown in the figure below, i.e., the 7th element. The element receives the first One base station The expression for the observation vector of a mode:
[0040] in, For the constant term, in the formula The amplitude of the dipole constant current density, The imaginary unit, Permeability in vacuum Angular frequency, The length of the electric dipole. waveguide number, For the receiving array UCCAs The distance between each array element and the center of the circle For the first Individual elements and The angle between the positive and negative axes. for The first kind of Bessel function of order 1, For the first The distance from each base station user to the center of the receiving array UCCAs is... For the first Each array element receives the first Each base station user Gaussian white noise in the modal channel To determine the radius of the uniform circular array, For the first The training signals of each base station user, and the different signal sources are uncorrelated, satisfy the following formula:
[0041] During the training phase, all user base stations simultaneously send training sequences to the receiving base station; therefore, each element of the receiving array is in mode . The observation vector is the element pair The superposition of observation vectors from the training sequences of each base station, and the observation vector of each array element. After compensating for the constant term, we obtain the first... The receiving mode of each array element is: The expression for the observation vector is:
[0042] in For the first After compensating the constants of each array element, the mode is: The Gaussian white noise vector of the channel.
[0043] Step 2: Construct a spatial-modal reception model.
[0044] The array element receiving mode is The observation vector is according to Figure 1 The array elements of UCCAs are numbered sequentially to obtain the modes. Observation matrix:
[0045] in Let be the spatial manifold matrix, the first... The spatial steering vector for each base station user is:
[0046] in , Indicates the index of an array element in UCCAs. It is the first in UCCAs The distance from each numbered array element to the origin. Let be the modal manifold matrix, the first... The modal steering vector for each base station user is:
[0047] in express The OK, This indicates that a row vector is converted into a diagonal matrix. Define the user matrix. It is related to the base station user training matrix and the distance from the base station user to the receiving base station. To receive the number of snapshots of the training sequence, It is the base station user training sequence matrix, where After compensating for the constant, the mode is The Gaussian white noise matrix of the channel.
[0048] The array observation data are stacked according to mode, and the observation matrix is represented as follows:
[0049] in Describes the Khatri-Rao product, defined For space-modal manifold matrix, This is a Gaussian white noise matrix.
[0050] Step 3: Divide the subarrays into subarray groups and derive the relationship between the subarray space and the modal manifold matrix.
[0051] Based on the rotation invariance between UCCAs elements, the UCCAs are divided into three subarrays, with each subarray containing the number of elements. Subarray 1: {1 2 3 4 7 8}, subarray 2: {2 5 6 7 10 11}, subarray 3: {3 6 7 8 11 12}. The specific subarray division method is shown in the figure below.
[0052] Based on the subarray partitioning method shown in the diagram above, the space-modal manifold matrix corresponding to the three subarrays is defined as follows: , and Combining the spatial-modal manifold matrix defined in step 2, the spatial-modal manifold matrices of subarray 1, subarray 2, and subarray 3 are expressed as follows: , , ,in The spatial manifold matrix of subarray 1, i.e. , Subarray 1 to the first The spatial steering vector for each base station user is:
[0053] The spatial manifold matrix of subarray 2, , Subarray 2 pairs The spatial steering vector for each base station user is:
[0054] This is the spatial manifold matrix of subarray 3. , Subarray 3 pairs The spatial steering vector for each base station user is:
[0055] Will Substituting the spatial array manifolds of the subarrays, the following rotation-invariant relationship is satisfied between the spatial array manifolds of the subarrays:
[0056] in , Both are diagonal matrices, where the diagonal elements are respectively , .
[0057] Therefore, the spatial-modal manifold of the subarray , , satisfy:
[0058] Step 4: Substitute the relationship between the subarray space and modal manifold matrix, and use the ESPRIT method to obtain the DOA estimates for multiple base station users.
[0059] For the observation matrix of UCCAs in step 2, calculate its covariance matrix:
[0060] in For the user covariance matrix, Let be the noise covariance matrix.
[0061] right Eigenvalue decomposition yields:
[0062] in It is a diagonal matrix with diagonal elements as follows: eigenvalues, for The eigenvector matrix. For Arrange the eigenvalues in descending order Take the largest The diagonal matrix of eigenvalues is Their corresponding eigenvectors constitute the signal subspace. Therefore, from Extract the corresponding rows of the corresponding elements of the three subarrays respectively, and form the signal subspaces respectively. , , .
[0063] According to subspace theory and The spaces spanned by the two elements are identical, that is, they satisfy the condition that the two elements are equal. Therefore, there exists a non-singular matrix. , making Therefore, the subarray signal subspace corresponding to the subarray also satisfies , and .
[0064] Calculate using the least squares method and get:
[0065] Substituting the rotation-invariant relationship between the subarray space and modal manifold in step 3 into the above equation, we can obtain:
[0066] Therefore, for , Perform eigenvalue decomposition separately to obtain two eigenvalue diagonal matrices including the parameters. , , and Because the eigenvalue decomposition was performed separately, it resulted in and , and It doesn't match.
[0067] Based on the property that the eigenvectors corresponding to different eigenvalues are mutually orthogonal, a sorting matrix is constructed. as follows:
[0068] Will According to After matching the order, reorder as ,make
[0069] in for The first diagonal One element, for The first on the diagonal Therefore, we can obtain the nth element. The estimated DOA for each base station user is as follows:
[0070] Similarly, the estimated DOA values for all base station users can be obtained. .
[0071] Example: Basic experimental setup: The array model used is a 13-element receiver array structure, as shown in the diagram. Figure 1 As shown.
[0072] Experiment 1: This experiment investigates how effectively this scheme can estimate the maximum number of users. Ignoring noise, three modes are used, and a 32-element UCA antenna array is employed. Figure 3 A scatter plot is given to estimate the number of interference sources by the algorithm. As can be seen from the figure, the proposed method makes full use of the degrees of freedom in the modal domain and the spatial domain, and the upper limit of the interference sources that can be estimated in theory is the product of the number of modes and the number of subarray elements, i.e., 18.
[0073] Experiment 2: Investigating the angular resolution capability of this scheme. The basic experimental assumptions are the same as above, assuming that there are two users to be tested in the hypothetical space located at... = (120°, 40°) and = (121°, 45°), input signal-to-noise ratio (SNR) = 10dB. Results of 100 angle estimations performed on two closely distributed targets using the proposed two methods. From... Figure 4 It can be observed that all proposed methods can successfully distinguish the angles of the targeted users, and the angle resolution is good.
[0074] Experiment 3: Investigate the relationship between the estimation accuracy and signal-to-noise ratio of this scheme. Set the input signal-to-noise ratio to increase from -5dB to 25dB in 5dB increments. Figure 5 The relationship between the estimation accuracy and signal-to-noise ratio of the proposed method is given, along with a comparison with traditional methods. The figure shows that the accuracy of the proposed method is better than the existing Unitary ESPRIT method, recursive ESPRIT method, and MUSIC method with a spectral search step size of 0.1.
Claims
1. A high-precision positioning method for a multi-user, multi-modal system, characterized in that, Includes the following steps: Step 1: Derive the observation vector of the receiving array element; Step 2: Construct a spatial-modal reception model; Step 3: Divide the subarrays into subarray groups and derive the relationship between the subarray space and the modal manifold matrix; Step 4: Substitute the relationship between the subarray space and modal manifold matrix, and use the ESPRIT method to obtain the DOA estimates for multiple base station users.
2. The high-precision positioning method for a multi-user, multi-modal system according to claim 1, characterized in that, Step 1 specifically involves: The array model used is A uniform concentric circular array UCCAs with 4 antenna elements consists of 3 uniform circular arrays UCA with 4 elements and 1 element with a common center. The elements of the UCCAs are numbered in order from top to bottom and from left to right. Establish a rectangular coordinate system with the center of the circle as the origin in the plane where the antenna array is located. The array elements of the innermost and outermost UCA layers are located at... and A circle with radius and and At the intersection; the array element of the middle UCA is located at the intersection of the two arrays. On a circle with radius , and the line connecting the array element and the origin is shaft and The included angle between the axes is 45°; The receiver array uses UCCAs, assuming that there are [missing information] in the far field. Each base station user is an independent entity, and each base station user is equipped with... There are OAM modes, among which For the number of modes used, , Let be the modal value; where the th The position parameters of the array elements relative to the origin of the transmission array are expressed as follows: ,in Expressed as azimuth, Expressed as pitch angle; Using element 7 at the center of UCCAs as the reference element, the first... The element receives the first One base station The expression for the observation vector of a mode: in, For the constant term, in the formula The amplitude of the dipole constant current density, The imaginary unit, Permeability in vacuum Angular frequency, The length of the electric dipole. waveguide number, For the receiving array UCCAs The distance between each array element and the center of the circle For the first Individual elements and The angle between the positive and negative axes. for The first kind of Bessel function of order 1, For the first The distance from each base station user to the center of the receiving array UCCAs is... For the first Each array element receives the first Each base station user Gaussian white noise in the modal channel To determine the radius of the uniform circular array, For the first The training signals of each base station user, and the different signal sources are uncorrelated, satisfy the following formula: During the training phase, all user base stations simultaneously send training sequences to the receiving base station; therefore, each element of the receiving array is in mode . The observation vector is the array element pair The superposition of observation vectors from the training sequences of each base station, and the observation vector of each array element. After compensating for the constant term, we obtain the first... The receiving mode of each array element is: The expression for the observation vector is: in For the first After compensating the constants of each array element, the mode is: The Gaussian white noise vector of the channel.
3. The high-precision positioning method for a multi-user, multi-modal system according to claim 2, characterized in that, Step 2 specifically involves: The array element receiving mode is The observation vectors are arranged in the order of the array element numbers of UCCAs, resulting in the mode as follows: Observation matrix: in Let be the spatial manifold matrix, the first... The spatial steering vector for each base station user is: in , Indicates the index of an array element in UCCAs. It is the first in UCCAs The distance from each numbered array element to the origin; Let be the modal manifold matrix, the first... The modal steering vector for each base station user is: in express The OK, This indicates that a row vector is converted into a diagonal matrix; Define user matrix It is related to the base station user training matrix and the distance from the base station user to the receiving base station. To receive the number of snapshots of the training sequence, It is the base station user training sequence matrix, where After compensating for the constant, the mode is as follows The Gaussian white noise matrix of the channel; The array observation data are stacked according to mode, and the observation matrix is represented as follows: in Describes the Khatri-Rao product, defined For space-modal manifold matrix, This is a Gaussian white noise matrix.
4. The high-precision positioning method for a multi-user multimodal system according to claim 3, characterized in that, Step 3 specifically involves: Based on the rotation invariance between UCCAs elements, the UCCAs are divided into three subarrays, with each subarray containing the number of elements. Subarray 1: {1 2 3 4 7 8}, subarray 2: {2 5 6 7 10 11}, subarray 3: {3 6 7 8 1112}; Define the space-modal manifold matrix corresponding to the three subarrays as follows: , and Combining the spatial-modal manifold matrix defined in step 2, the spatial-modal manifold matrices of subarray 1, subarray 2, and subarray 3 are expressed as follows: , , ,in The spatial manifold matrix of subarray 1, i.e. , Subarray 1 to the first The spatial steering vector for each base station user is: The spatial manifold matrix of subarray 2, , Subarray 2 pairs The spatial steering vector for each base station user is: This is the spatial manifold matrix of subarray 3. , Subarray 3 pairs The spatial steering vector for each base station user is: Will Substituting the spatial array manifolds of the subarrays, the following rotation-invariant relationship is satisfied between the spatial array manifolds of the subarrays: in , Both are diagonal matrices, where the diagonal elements are respectively , ; Therefore, the spatial-modal manifold of the subarray , , satisfy: 。 5. The high-precision positioning method for a multi-user multimodal system according to claim 4, characterized in that, Step 4 specifically involves: For the observation matrix in step 2, calculate its covariance matrix: in For the user covariance matrix, Here is the noise covariance matrix; right Eigenvalue decomposition yields: in It is a diagonal matrix with diagonal elements as follows: eigenvalues, for eigenvector matrix; for Arrange the eigenvalues in descending order Take the largest The diagonal matrix of eigenvalues is Their corresponding eigenvectors constitute the signal subspace. Therefore, from Extract the corresponding rows of the corresponding elements of the three subarrays respectively, and form the signal subspaces respectively. , , ; According to subspace theory and The spaces spanned by are identical, that is, they satisfy... Therefore, there exists a non-singular matrix. , making Therefore, the subarray signal subspace corresponding to the subarray also satisfies , and ; Calculate using the least squares method and get: Substituting the rotation invariance relation from step 3 into the above equation, we get: Therefore, for , Perform eigenvalue decomposition separately to obtain two eigenvalue diagonal matrices including the parameters. , , and ; Based on the property that the eigenvectors corresponding to different eigenvalues are mutually orthogonal, a sorting matrix is constructed. as follows: Will According to After matching the order, reorder as ,make: in for The diagonal of One element, for The first on the diagonal One element; Get the first The estimated DOA for each base station user is as follows: Similarly, the estimated DOA values for all base station users are obtained. .
6. An electronic device, characterized in that, include: Processor and memory; The memory is used to store a computer program, and the processor is used to execute the computer program stored in the memory to cause the electronic device to perform the method as described in any one of claims 1 to 5.
7. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1 to 5.
8. A chip, characterized in that, include: A processor for retrieving and running a computer program from memory, causing a device on which the chip is mounted to perform the method as described in any one of claims 1 to 5.
9. A computer program product, characterized in that, The computer program product includes a computer storage medium storing a computer program, the computer program including instructions executable by at least one processor, which, when executed by the at least one processor, implement the method as described in any one of claims 1 to 5.