Method and system for direction of arrival estimation based on grouping of rectangular array sub-arrays

Abstract

The application discloses a direction of arrival estimation method and system based on rectangular array subarray grouping, according to the row and column distribution of the rectangular array, array elements are divided into multiple linear subarrays along two orthogonal directions respectively, and a steering vector is constructed for the linear subarrays of the two directions respectively; the received data of the subarrays in the same direction is rearranged and combined to construct a received signal data matrix corresponding to the direction; then, the included angle between the direction of arrival and two orthogonal coordinate axes is estimated respectively, and the direction of arrival of the signal in the three-dimensional space is obtained according to the angle estimation result. The application fully utilizes the array element data of the rectangular array, converts the multi-dimensional angle joint estimation problem into multiple one-dimensional angle estimation problems, reduces the calculation complexity, uses the data collected by all array elements to estimate a single dimension parameter, improves the stability of the angle estimation and the array aperture utilization rate, is suitable for array signal processing scenes such as communication, radar and acoustics, and improves the estimation performance and practical value.

Description

Technical Field

[0001] This invention belongs to the field of array signal processing and parameter estimation technology, specifically relating to a method and system for estimating direction of arrival (DOA) based on rectangular array subarray grouping. Background Technology

[0002] Direction of arrival (DOA) estimation is a crucial research area in array signal processing, widely applied in communications, radar, acoustic detection, and other fields. By analyzing the phase difference, time delay difference, or spatial spectrum characteristics of the received signal from the array, the incident direction of the signal can be estimated, providing important information for target localization and beamforming. Existing DOA estimation methods mainly include beamforming methods, subspace methods, and sparse reconstruction methods. These methods typically require establishing a steering vector based on the array structure and obtaining the angle estimation result through spatial spectrum search, eigenvalue decomposition, or sparse reconstruction.

[0003] Rectangular arrays are a common array structure in array signal processing. Compared to linear arrays, rectangular arrays can acquire the directional information of signals in three-dimensional space. Existing methods for direction-of-arrival (DOA) estimation using rectangular arrays typically require joint searches across multiple angular dimensions. For example, with an azimuth search range of 360°, an elevation search range of 180°, and an angle search step size of 1°, a joint azimuth and elevation grid search would require traversing approximately 360 × 180 candidate angle combinations, or 64,800 possible cases. As search accuracy increases, the number of candidate angle combinations continues to rise, leading to high computational complexity. Furthermore, joint scanning requires obtaining three-dimensional angle parameters based on limited sampled data. Limited sampling is equivalent to maximum likelihood estimation of the true signal; to obtain more accurate three-dimensional angle estimation results simultaneously, a larger amount of data is needed.

[0004] In summary, the large computational cost and insufficient estimation stability of multi-dimensional angle joint search are common problems encountered in the existing process of estimating direction of arrival based on rectangular arrays. Summary of the Invention

[0005] To overcome the shortcomings of existing technologies and achieve the goals of fully utilizing all array elements of the rectangular array to receive data, reducing the computational complexity of multidimensional direction of arrival estimation, improving the stability of angle estimation, and enhancing engineering applicability, this invention adopts the following technical solution:

[0006] The direction-of-arrival estimation method based on rectangular array subarray grouping is as follows:

[0007] Based on the rectangular array of received signals, the array is divided into subarrays along the horizontal axis of the array rows and the vertical axis of the array columns. According to the element spacing of the subarrays, the guide vectors of the direction of arrival and the angle between the horizontal axis and the vertical axis are constructed respectively.

[0008] Acquire the received signal data of each element in the rectangular array, and construct received signal data matrices in the horizontal and vertical directions according to different axes;

[0009] Based on the steering vector and the received signal data matrix, estimate the one-dimensional angle between the direction of arrival and the horizontal and vertical axes;

[0010] Based on the estimated angles of the horizontal and vertical axes, the angle between the direction of arrival and the vertical axis is calculated, thus obtaining the three-dimensional direction of arrival.

[0011] Furthermore, each row of sensors parallel to the horizontal axis in the rectangular array is divided into a separate horizontal axis linear subarray, and each column of sensors parallel to the vertical axis in the array is divided into a separate vertical axis linear subarray.

[0012] Select one element in the rectangular array as a reference point to calculate the distance between each element and the reference point;

[0013] Based on the distance to the reference point, the angle between the wave direction and the signal frequency, a guide vector is constructed that includes the horizontal and vertical axis angles.

[0014]

[0015]

[0016] Where e represents the base of the exponential function, and j represents the imaginary number. Indicates signal frequency. Indicates the x-direction The distance between each array element and the reference point, where c represents the speed of light. Indicates the angle with the horizontal axis. Indicates the angle with the vertical axis. Indicates the first position in the y-direction The distance between each array element and the reference point, here The column number of the array element antenna is indicated. This indicates the row number of the array element antenna.

[0017] Furthermore, data from multiple snapshots of the rectangular array are acquired. Based on the number of rows in the array, the received data from the linear subarrays along the horizontal axis are merged in snapshot form to construct a horizontal axis received signal data matrix. Based on the number of columns in the array, the received data from the vertical axis linear subarrays are combined in snapshot form to construct a vertical axis received signal data matrix. .

[0018]

[0019]

[0020] in, This indicates the data received by the rectangular array:

[0021]

[0022] here, Represents the first in a rectangular array Column, number The sampling data of the nth snapshot of the array element. Indicates the number of snapshots.

[0023] For rectangular arrays, after grouping according to the proposed x-direction, although there are multiple subarrays in the x-direction, the element arrangement in the x-direction of each subarray is consistent. Therefore, the basic shape of these subarrays is consistent. Thus, in step 2, the data of each subarray can be integrated into the array in snapshot form. In this approach, it's equivalent to transforming a rectangular array into a one-dimensional linear array, where each element contains multiple sensors, except that the data from these sensors is stored in snapshot form to create a data matrix. ,and Each row is equivalent to the data acquired by an array element; the proposed grouping by the y-direction is based on the same principle; based on this, the angle between the direction of arrival and the horizontal and vertical axes can be estimated separately using corresponding algorithms.

[0024] Furthermore, a beamforming algorithm is used to assign a weight to each array element that is related to the one-dimensional angle between the direction of arrival and the axis. The weights of each array element are used to form a weight vector along a certain axis.

[0025] Calculate the covariance of the received signal data matrix along a certain axis;

[0026] When the weight vector is equal to the guide vector of the corresponding angle, the spectral function of the beamforming algorithm is constructed based on the guide vector and the covariance. The peak value of the spectral function is the estimated one-dimensional angle between the direction of arrival and the corresponding axis direction.

[0027] Furthermore, the Capon algorithm is employed, with the lossless output of the target direction signal as a constraint, to minimize the array output power, solve for the optimal beam weight vector, and then construct the spectral function of the Capon algorithm to estimate the one-dimensional angle.

[0028] Furthermore, a multiple signal classification algorithm is employed to perform eigenvalue decomposition on the covariance of the received signal data matrix along a certain axis. Large eigenvalues ​​and eigenvectors represent the signal component, while small eigenvalues ​​and eigenvectors represent the noise component. By utilizing the orthogonality of the eigenvectors corresponding to different eigenvalues, a spectral function of the multiple signal classification algorithm based on the steering vector and noise subspace is constructed. The angles of all corresponding axes are scanned according to the step size, and the peak value of the spectral function is the estimated one-dimensional angle between the direction of arrival and the corresponding axis direction.

[0029] Furthermore, a sparse reconstruction-type OMP algorithm is adopted to divide all directions in space equally to obtain equal-division angles, and the number of equal-division angles is much larger than the number of general signals. A dictionary matrix is ​​constructed based on the values ​​of the steering vector at different equal-division angles. The dictionary matrix contains all possible signal directions of arrival in space. Within a limited range, the larger the number of uniform divisions, the higher the corresponding angular resolution. For the received signal data matrix, the inner product is calculated with each atom in the dictionary matrix to obtain the angle corresponding to the atom with the largest inner product.

[0030] After removing the reconstructed signal component of the atom from the original signal, the inner product is calculated on the remaining residual part to perform iterative calculations until the expected conditions are met and then the iteration stops.

[0031] The angle corresponding to the most relevant atom obtained through iteration is the estimated one-dimensional angle.

[0032] Furthermore, the OMP algorithm only requires signal data from a single snapshot to estimate the direction of arrival, but single snapshot data may have a large error. Using signal data from multiple snapshots can obtain more accurate results. For multi-snapshot data, the data of each snapshot is multiplied by all atoms, and then the results of each snapshot are combined using the L2 norm. The largest value in the combined result is selected to determine the most relevant atom.

[0033] Furthermore, based on the property that the magnitude of the unit direction vector is 1, that is... By using the angles between the horizontal and vertical axes, the angles between the positive and negative wave arrival directions and the vertical axis can be obtained, i.e. Since the sine function is an odd function, the square root needs to be distinguished between positive and negative cases. The correct value is determined based on the radiation pattern of the rectangular array. If the antenna radiation direction is consistent with the vertical axis, then a positive number is taken; otherwise, a negative number is taken.

[0034] The direction-of-arrival estimation system based on rectangular array subarray grouping includes a steering vector construction module, a received signal data matrix construction module, and a direction-of-arrival and axis angle generation module. The direction-of-arrival estimation method based on rectangular array subarray grouping is used to estimate the direction of arrival.

[0035] The advantages and beneficial effects of this invention are as follows:

[0036] This invention utilizes the regular distribution of a rectangular array in two orthogonal directions to divide the array into multiple linear subarrays in orthogonal directions. The received data from subarrays in the same direction are rearranged and merged, allowing the received data from different subarrays to participate as equivalent snapshots in the estimation of corresponding directional angle parameters. This improves the utilization rate of the received data from the rectangular array elements and the stability of angle estimation without increasing the actual number of samplings. The invention described herein... and All are one-dimensional estimates, determined and Then, calculate based on the vector relationships. This yields a three-dimensional angle estimation result. By decomposing the meshed angle parameter scanning in the three-dimensional joint estimation into multiple one-dimensional angle estimation problems, the number of variables to be estimated is reduced with the same number of sampling snapshots, theoretically leading to more accurate results. Furthermore, the scheme described in this invention, which obtains the complete direction of arrival in three-dimensional space by separately estimating the angle between the direction of arrival and two orthogonal directions, can significantly reduce the complexity of joint direction of arrival estimation. Analyzing the computational complexity with a resolution of 1°, for a one-dimensional linear array, the recognizable angle range is... , and Total Existence One possibility is that if azimuth and elevation angles are used, the range of azimuth angles is... The range of pitch angles is The joint estimation method requires a gridded scan, and a total of One possibility; in comparison, the complexity of the solution of the present invention is only one-third of that of the original solution. Therefore, this invention can achieve faster calculation speed, higher accuracy, and better engineering applicability. Attached Figure Description

[0037] Figure 1 This is a flowchart of the method of the present invention.

[0038] Figure 2 This is a schematic diagram of the linear subarray grouping of the rectangular array in the x-direction in this invention.

[0039] Figure 3 This is a schematic diagram of the linear subarray grouping of the rectangular array in the y-direction in this invention.

[0040] Figure 4 This is a schematic diagram of a rectangular array that is not uniformly distributed in the x and y directions in this invention.

[0041] Figure 5This is a schematic diagram of a rectangular array uniformly distributed in the x and y directions in this invention.

[0042] Figure 6 This is a schematic diagram of the one-dimensional angle between the wave direction and the linear subarray in the x-direction in this invention.

[0043] Figure 7 This is a schematic diagram showing the angle between the direction of arrival and the normal direction of the linear subarray in the x-direction in this invention.

[0044] Figure 8 In this invention, the angles between the direction of arrival and the x, y, and z directions, and the azimuth angles are... and pitch angle A schematic diagram of the geometric relationship between them.

[0045] Figure 9 This is a schematic diagram of the simulation results of the estimated angle in the x-direction in Embodiment 1 of the present invention.

[0046] Figure 10 This is a schematic diagram of the simulation results of the included angle in the y-direction estimated in Embodiment 1 of the present invention.

[0047] Figure 11 This is a comparison diagram of the x-direction angle estimated by the method of the present invention and a single linear array in Embodiment 2 of the present invention with the theoretical value.

[0048] Figure 12 This is a comparison chart of the y-direction angle estimated by the method of the present invention and a single linear array in Embodiment 2 of the present invention with the theoretical value. Detailed Implementation

[0049] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0050] like Figure 1 As shown, the direction-of-arrival (DOA) estimation method based on rectangular array subarray grouping is applicable to communication, radar, and acoustic applications where signals are received using rectangular arrays and their DOA is estimated. The method includes the following steps:

[0051] Step 1: Divide the rectangular array into subarrays based on the rows and columns and construct the guide vector.

[0052] Let the rectangular array have a total of List, Line, that is, shared Each array element can then be sampled in a snapshot to obtain... Data. For example... Figure 2 As shown, the rectangular array is divided into multiple "x-direction linear subarrays" along the x-direction. Each row of the rectangular array is considered a subarray, and there are a total of Okay, that is Similarly, a "linear subarray in the x-direction", such as Figure 3 As shown, the rectangular array is divided into multiple "linear subarrays along the y-direction". Each column of the rectangular array is considered a subarray, and there are a total of Okay, that is A “y-direction linear subarray”.

[0053] Figure 4 In this invention, for a regular rectangular array, a reference point is determined. For ease of description, the reference point is defined as the position of the first element of the rectangular array. The selection of the reference point is only for the convenience of establishing the coordinate system and has no impact on the method of this invention. The horizontal and vertical axes, i.e., the x-axis and y-axis directions in the figure, are determined with the reference point as the origin. The distance from each column of elements in the x-direction to the reference point is determined and denoted as [missing information]. Determine the distance from each row of array elements in the y-direction to the reference point, denoted as: This method is applicable to both uniformly distributed and non-uniformly distributed rectangular arrays. The guiding vector matrices with angles to the x-axis and y-axis, respectively, are constructed based on the element spacing as follows:

[0054] (1)

[0055] (2)

[0056] Where e represents the base of the exponential function, and j represents the imaginary number. Indicates signal frequency. Indicates the x-direction The distance between each array element and the reference point, where c represents the speed of light. Indicates the angle between the horizontal axis and the horizontal axis. Indicates the angle between the vertical axis and the vertical axis. Indicates the first position in the y-direction The distance between each array element and the reference point, here The column number of the array element antenna is indicated. This indicates the row number of the array element antenna.

[0057] Figure 5 In a rectangular array, if the rows and columns are uniformly distributed (i.e., the spacing is equal), the element spacing in the x-direction is... If the reference point is taken as the location of the first array element, then the distance between each array element along the horizontal axis and the reference point becomes... The element spacing in the y-direction is Similarly, taking the first array element as the reference point, the distance from each array element along the vertical axis to the reference point is... The specific formula is as follows:

[0058] (3)

[0059] (4)

[0060] Step 2: Obtain the received signal data of each element in the rectangular array and rearrange and merge the received data of multiple linear subarrays in the same direction.

[0061] for The data collected in the second snapshot, the array in the [number]th [time frame]. Data received by each array element for:

[0062] (5)

[0063] Among them, here, Represents the first in a rectangular array Column, number The sampling data of the nth snapshot of the array element. Indicates the number of snapshots;

[0064] Will The received data from each "x-direction linear subarray" are combined in snapshot form to construct the x-direction received signal data matrix. Here, merging in the form of snapshots refers to directly splicing together multiple snapshot data matrices received by different subarrays in the same direction. Let the first snapshot be... The data received by the linear subarrays are:

[0065] (6)

[0066] No. The data matrix received by the linear subarrays is:

[0067] (7)

[0068] No. The linear subarray and the first The data received by the linear subarrays, after being combined, are:

[0069] (8)

[0070] Similarly, by merging the data from all the "x-direction linear subarrays", the constructed received signal data matrix can be obtained. for:

[0071] (9)

[0072] Will The received data from each "y-direction linear subarray" is combined in snapshot form to construct a y-direction received signal data matrix. Accordingly, let the first The data received by the linear subarrays are:

[0073] (10)

[0074] No. The data matrix received by the linear subarrays is:

[0075] (11)

[0076] No. The linear subarray and the first The data received by the linear subarrays, after being combined, are:

[0077] (12)

[0078] The received signal data matrix can be obtained by merging the data from all the "y-direction linear subarrays". for:

[0079] (13)

[0080] in, and In As long as the indices are the same, it means that the content is the same. In the process of combination, the first... The linear subarray and the first The order of the first linear subarray can be arbitrarily sorted. The linear subarray and the first The order of the linear subarrays can be arbitrary, and different orders have no effect on the method of this invention. Matrix sum matrix The data includes all the sampled snapshots of the array. In the subsequent estimation of the direction of arrival, all the data are used to estimate the angle in one dimension, rather than the angle in three-dimensional space. This means that the number of variables to be solved is reduced under the condition of limited data, so the data utilization rate can be fully improved. According to the basic principle of spatial spectrum estimation, the discrete data after multiple consecutive snapshots can be regarded as the maximum likelihood estimate of the real data. The more samples, the closer the result will be to the real value, and thus the more accurate the result of the direction of arrival estimation will be.

[0081] Step 3: Based on the constructed received signal data matrix and Guide vector and Estimate the one-dimensional angle between the direction of arrival and the x and y directions. and .

[0082] Taking a "linear array in the x-direction" as an example, the data matrix obtained according to the method of this invention... Total Okay, the method of this invention is proposed for rectangular arrays. After grouping by the x-direction, although there are multiple subarrays in the x-direction, the array element arrangement in the x-direction of each subarray is consistent. Therefore, the basic shape of these subarrays is consistent. Step 2 integrates the data of each subarray in the form of snapshots. In this approach, a rectangular array is equivalent to a one-dimensional linear array, where each element contains multiple sensors, and the data from these sensors are presented as snapshots to form a data matrix. Based on this, the angle between the direction of arrival and the x-direction. Existing algorithms can be used for estimation, and the angle between the direction of arrival and the y-direction can be obtained in the same way. .

[0083] The angles with the x (horizontal axis), y (vertical axis), and z (vertical axis) directions mentioned in this invention refer to the geometric relationship between the direction of arrival and the x, y, and z directions. Taking the angle with the x direction as an example, for instance... Figure 6 As shown, this invention uses the angle with the x-direction for description, and its path difference is... ,like Figure 7 As shown, if the path difference is expressed using the angle with the normal, then it becomes... Since the geometric relationship is ultimately converted into the path difference of the incoming wave reaching different array elements, the final effect is consistent regardless of the description method. Therefore, the expression that changes the steering vector by only altering the description of the geometric relationship of the included angle should be considered an equivalent expression of this invention.

[0084] Algorithms for estimating the one-dimensional angle between the direction of arrival (DOA) and the x and y directions include, but are not limited to, beamforming (CBF), multiple signal classification (MUSIC), rotation-invariant subspace (ESPRIT), and sparse reconstruction-type OMP algorithms. Steps 1 and 2 provide a method for constructing the received signal matrix adapted to the above angle estimation algorithms. The following further explains how to estimate the one-dimensional angle between the DOA and the x and y directions after constructing the received signal data matrix and steering vector according to the steps of this invention. and .

[0085] Beamforming (CBF) algorithm:

[0086] To estimate the one-dimensional angle between the direction of arrival and the x-direction. For example, a weight is assigned to each array element. , Weights and angles Regarding the weights of each array element It can form a weight vector ,here, This indicates transpose.

[0087] Find the received data matrix Covariance:

[0088] (14)

[0089] in, H represents the mean operation, and H represents the conjugate transpose operation.

[0090] when hour, = Combined with the covariance of received data and weight vector The spectral function of the beamforming algorithm is obtained as follows:

[0091] (15)

[0092] Apply step size to all values ​​within the range The peak value of the spectral function obtained by scanning is the estimated angle between the direction of arrival and the x-direction. Similarly, the angle between the direction of arrival and the y-direction can be obtained. .

[0093] Capon algorithm:

[0094] To estimate the one-dimensional angle between the direction of arrival and the x-direction. For example, regarding the weight vector in the aforementioned classic beamforming algorithm, in order to ensure... If signals from one direction can be correctly received, while signals from other directions are suppressed, then:

[0095] (16)

[0096] The spectral function of Capon's algorithm can be obtained by solving using the Lagrange multiplier method:

[0097] (17)

[0098] Apply step size to all values ​​within the range The peak value of the spectral function obtained by scanning is the estimated angle between the direction of arrival and the x-direction. Similarly, the angle between the direction of arrival and the y-direction can be obtained. .

[0099] MUSIC algorithm:

[0100] To estimate the one-dimensional angle between the direction of arrival and the x-direction. For example, regarding the received data matrix covariance Then to Perform eigenvalue decomposition and sort the eigenvalues, where larger eigenvalues ​​and eigenvectors represent the signal component, and smaller eigenvalues ​​and eigenvectors represent the noise component. Based on this, we can obtain:

[0101] (18)

[0102] in, This represents the signal subspace composed of signal eigenvectors. Represents the characteristic values ​​of the signal. This represents the noise subspace formed by noise feature vectors. Let represent the eigenvalues ​​of the noise. Ideally, the eigenvectors corresponding to different eigenvalues ​​are orthogonal to each other; therefore, the spectral function of the MUSIC algorithm can be obtained as:

[0103] (19)

[0104] Among them, because of the theoretical noise subspace It cannot be obtained precisely; it is obtained through sampling calculations. This represents the maximum likelihood estimate of the noise subspace.

[0105] Apply step size to all values ​​within the range The peak value of the spectral function obtained by scanning is the estimated angle between the direction of arrival and the x-direction. Similarly, the angle between the direction of arrival and the y-direction can be obtained. .

[0106] OMP algorithm:

[0107] To estimate the one-dimensional angle between the direction of arrival and the x-direction. For example, in compressed sensing theory, the dictionary matrix for sparse reconstruction can be generated based on the steering vector. All directions in space are equally divided into... Divide into equal parts, and the set of angle indices after division is: Typical signal quantity Much smaller than the number of equally divided angles The dictionary matrix is ​​defined as follows:

[0108] (20)

[0109] in, Indicates the guide vector In the The specific values ​​from each dividing perspective are also known as the atoms of a dictionary. dictionary matrix It includes all possible directions of arrival of signals within space, and evenly divides the number of signals within a finite range. The larger the value, the higher the corresponding angular resolution.

[0110] For the received signal to The inner product of each atom in the algorithm is calculated. The atom with the largest inner product is the steering vector corresponding to the direction most relevant to the incoming wave signal. This atom is used to reconstruct the original signal, and the reconstructed signal components are then removed from the original signal. Iterative calculations are performed on the remaining residual until the expected conditions are met, at which point the iteration stops. The angle corresponding to the most relevant atom obtained through calculation is the estimated value. In principle, the OMP algorithm only requires a single snapshot of signal data to estimate DOA, but single snapshot data may contain significant errors. Using multi-snapshot signal data can obtain more accurate results. For processing multi-snapshot data, the general approach is to multiply the data from each snapshot by all atoms, then combine the results from each snapshot using the L2 norm, and select the largest value from the combined result to determine the most relevant atom. Therefore, the specific steps of the OMP algorithm are as follows:

[0111] 1) Constructing a dictionary matrix ;

[0112] 2) Initialize parameters, including: number of iterations: Residual: Reconstruct the atomic set: Index set: Reconstructed signal: ;

[0113] 3) Calculate the dictionary matrix Each atom and the current residual Find the index corresponding to the largest inner product. The index corresponds to the angle of the atom. This is the estimate from this iteration. ;

[0114] 4) Update the index set Update and reconstruct the atomic set: ;

[0115] 5) Reconstruct the signal using the least squares method: ;

[0116] 6) Update residuals: ;

[0117] 7) Stop iteration when the number of iterations is reached or the residual is less than the limit value; otherwise, update the number of iterations: Then proceed to step 3).

[0118] Similarly, using the same method, the angle between the direction of arrival and the y-direction can be obtained. Note that the estimations here are all for one-dimensional angles, which have lower complexity compared to joint estimation of two-dimensional angles.

[0119] This invention uses the Capon algorithm, MUSIC algorithm, and OMP algorithm as examples to demonstrate how to estimate the one-dimensional angle between the direction of arrival and a set x and y directions. Besides these algorithms, other algorithms are also applicable to the signal matrix constructed in this invention. and and guide vector and Examples of algorithms include the Smoothing MUSIC algorithm, the ESPRIT algorithm, and the L1-SVD algorithm, which will not be listed here. After step 3, the angle between the x-axis and the x-axis in three-dimensional space is obtained. and the angle with the y-axis The next step will be to calculate the angle with the z-axis based on this. .

[0120] Step 4: Based on the estimated angle with the x-direction and the angle with the y direction Calculate the angle between the direction of arrival and the z-direction. .

[0121] like Figure 8 As shown, for the description of the direction of arrival in a three-dimensional spatial coordinate system, this invention uses the angles between the direction of arrival and the x, y, and z directions. Azimuth angle can also be used. and pitch angle To represent it. From a geometric perspective, these two representations are consistent. According to the principle of unit direction vectors, if the angle with the x, y, and z directions is used, its direction-of-arrival vector is represented as: The direction of arrival at this time includes These three-dimensional parameters can be referred to as three-dimensional angular parameters. If azimuth and elevation angles are used, the direction of arrival can be expressed as: At this time, it includes Two dimensional parameters (also called two-dimensional parameters) are used, each uniquely representing the direction of arrival in three-dimensional space. Based on the principle of unit direction vector equivalence, the angles with the x, y, and z directions are used. The representation method, compared with the use of azimuth angle and pitch angle The conversion relationship between the representation methods is as follows:

[0122] (twenty one)

[0123] This invention converts the direction of arrival in three-dimensional space into an estimated angle with the x-direction. The angle between and the y-direction Then based on the estimated and Calculate the angle between the direction of arrival and the z-direction. The z-direction is a direction in three-dimensional space that is orthogonal to both the x- and y-directions. It is equivalent to the positive directions of the x-axis, y-axis, and z-axis in a three-dimensional Cartesian coordinate system. Based on the property that the magnitude of a unit direction vector is 1, we have:

[0124] (twenty two)

[0125] according to The transformation yields:

[0126] (twenty three)

[0127] Further, we can obtain for:

[0128] (twenty four)

[0129] Since the sine function is an odd function, for Taking the square root yields two cases: positive and negative. Similarly, there are two cases: positive and negative. The correct value is determined by the radiation pattern of the rectangular array. If the antenna radiation direction is consistent with the z-direction, a positive value is taken; otherwise, a negative value is taken. Thus, the complete description of the direction of arrival in three-dimensional space is obtained as follows: .

[0130] In this invention, the algorithm only needs to estimate and It can be calculated This enables the estimation of the direction of arrival in three-dimensional space, whereby... and All estimates are one-dimensional. The computational complexity is analyzed with a resolution of 1°. For a one-dimensional linear array, the range of recognizable angles is... , and Total Existence One possibility, to determine and back, The result can be determined through calculation, without estimation. However, if azimuth and elevation angles are used, the range of azimuth angles is... The range of pitch angles is The joint estimation method requires a gridded scan, and a total of This presents several possibilities. In comparison, the complexity of the solution in this invention is only one-third that of the original solution. Therefore, the present invention can significantly reduce the complexity of joint estimation of direction of arrival.

[0131] The present invention will be further described in detail below through specific embodiments.

[0132] Example 1:

[0133] like Figure 9 , Figure 10 As shown, the structure of the rectangular array is defined by... Array element composition, namely , The signal frequency is 28GHz electromagnetic wave, and the array element spacing is 1 / 3 of the signal wavelength. The sampling snapshot count was 1000 times. The environment has a total of 4 channels, including 1 LOS channel and 3 NLOS channels that are reflected once. Channels with received signal power below 25 dB of the maximum received power are ignored, and channels reflected more than twice are also not considered. The path loss of multipath channels is calculated based on their distance and the dielectric constant of the electromagnetic wave and the reflecting surface. These factors can be calculated using finite element simulation with ray tracing software. To simplify the model, the transmitted signal power is set to 0 dBm. Since the path loss calculated by the simulation software is between 72.96 dB and 89.44 dB, the noise power is set to −90 dBm. Although this cannot simulate the noise of a real environment, its combination with path loss can control the SNR within a reasonable range, as shown in row 4 of Table 1. The SNR of different paths is calculated according to… Calculate, where, Indicates the signal transmission power. Indicates path loss. Indicates noise power.

[0134] Table 1 Ideal Multipath Channel Parameters

[0135]

[0136] The steps corresponding to this invention are as follows:

[0137] Step 1: Construct the guiding vectors after grouping the subarrays in the x and y directions. and ;

[0138] Step 2: Construct the data matrix after grouping the subarrays in the x and y directions. and ;

[0139] Step 3: Estimate the angles with the x and y directions respectively based on existing parameter estimation methods. and In this embodiment, the classical beamforming algorithm, Capon algorithm, classical MUSIC algorithm, smooth MUSIC algorithm and OMP algorithm were used to calculate the angle between the direction of arrival and the x and y directions. It can be seen that all kinds of algorithms can give corresponding estimation results, especially for the LOS channel, the error of all algorithms is very small.

[0140] Step 4: Based on the estimated and Calculate the angle between the direction of arrival and the z-direction. Taking the smoothing MUSIC algorithm as an example, the calculation results are shown in Table 2:

[0141] Table 2. Direction of Arrival Estimation Results

[0142]

[0143] As can be seen, the direction of arrival estimated by the method of this invention is very close to the true value, with a relatively small error. Although some angles of NLOS3 were not estimated, this is due to the extremely low signal-to-noise ratio of the multipath channel. In fact, being able to estimate NLOS2 already surpasses most methods.

[0144] Example 2:

[0145] For the same use In the case of a rectangular array of array elements, the subarray grouping method of the present invention and single subarray data pairs located in the x and y directions are respectively used. and The estimation process, including the steps and parameter settings, is consistent with Example 1, and the results obtained are, for example... Figure 11 , Figure 12 As shown, it can be seen that the estimation performance of the algorithm is improved after using the subarray grouping algorithm.

[0146] This invention also proposes a direction-of-arrival (DOA) estimation system based on rectangular array subarray grouping, including a steering vector construction module, a received signal data matrix construction module, and a direction-of-arrival and axis angle generation module. The system uses the aforementioned DOA estimation method based on rectangular array subarray grouping to estimate the DOA.

[0147] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features therein. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A direction-of-arrival estimation method based on rectangular array subarray grouping, characterized in that: Based on the rectangular array of received signals, the array is divided into subarrays along the horizontal axis of the array row and the vertical axis of the array column. Guide vectors with the direction of arrival forming angles with the horizontal axis and the vertical axis are constructed according to the element spacing of the subarrays. Each row of sensors parallel to the horizontal axis in the rectangular array is divided into a separate horizontal axis subarray, and each column of sensors parallel to the vertical axis in the array is divided into a separate vertical axis subarray. An array element in the rectangular array is selected as a reference point to calculate the distance between each array element and the reference line. Based on the distance, the angle between the direction of arrival and the signal frequency, a guide vector is constructed between the horizontal axis angle and the vertical axis angle. Acquire the received signal data of each element in the rectangular array, and construct received signal data matrices in the horizontal and vertical directions according to different axes; For data collected in multiple snapshots, obtain the data received by each element in the rectangular array in each snapshot. Based on the number of rows in the array, the received data from the horizontal axis subarrays are combined in snapshot form to construct a horizontal axis received signal data matrix. Based on the number of columns in the array, the received data from the vertical axis linear subarray are combined in snapshot form to construct a vertical axis received signal data matrix. ; in, This indicates the data received by the rectangular array: in, Represents the first in a rectangular array Column, number The sampling data of the nth snapshot of the array element. Indicates the number of snapshots; The data from each subarray is incorporated in snapshot form. In this approach, a rectangular array is equivalent to a one-dimensional linear array, where each element contains multiple sensors. The data from these sensors is stored in snapshot form to create a data matrix. , Each row is equivalent to the data acquired by an array element; Based on the steering vector and the received signal data matrix, estimate the one-dimensional angle between the direction of arrival and the horizontal and vertical axes; Based on the estimated angles of the horizontal and vertical axes, the angle between the direction of arrival and the vertical axis is calculated, thus obtaining the three-dimensional direction of arrival. Utilizing the property that the unit direction vector has a magnitude of 1, the angles between the positive and negative directions of arrival and the vertical direction are calculated using the angles between the horizontal and vertical directions. Based on the radiation pattern of the rectangular array, if the radiation direction is consistent with the vertical direction, a positive number is taken; otherwise, a negative number is taken.

2. The direction-of-arrival estimation method based on rectangular array subarray grouping according to claim 1, characterized in that: Each array element is assigned a weight related to the one-dimensional angle between the direction of arrival and the axis. The weights of each array element are used to form a weight vector along a certain axis. Calculate the covariance of the received signal data matrix along a certain axis; When the weight vector is equal to the steering vector of the corresponding angle, a spectral function is constructed based on the steering vector and the covariance. The peak value of the spectral function is the estimated one-dimensional angle between the direction of arrival and the corresponding axis direction.

3. The direction-of-arrival estimation method based on rectangular array subarray grouping according to claim 2, characterized in that: With the lossless output of the target direction signal as a constraint, the array output power is minimized, the optimal beam weight vector is solved, and then the spectral function is constructed to estimate the one-dimensional angle.

4. The direction-of-arrival estimation method based on rectangular array subarray grouping according to claim 1, characterized in that: Eigenvalue decomposition is performed on the covariance of the received signal data matrix along a certain axis. Large eigenvalues ​​and eigenvectors represent the signal part, while small eigenvalues ​​and eigenvectors represent the noise part. Based on the orthogonality of the eigenvectors corresponding to different eigenvalues, a spectral function is constructed based on the steering vector and the noise subspace estimation matrix. The angles of all corresponding axes are scanned by a step size, and the peak value of the spectral function is the estimated one-dimensional angle between the direction of arrival and the corresponding axis direction.

5. The direction-of-arrival estimation method based on rectangular array subarray grouping according to claim 1, characterized in that: Divide all directions in space equally to obtain equal angles, and make the number of equal angles greater than the number of signals. Construct a dictionary matrix based on the values ​​of the steering vector at different equal angles. For the received signal data matrix, take the inner product with each atom in the dictionary matrix to obtain the angle corresponding to the atom with the largest inner product. After removing the reconstructed signal component of the atom from the original signal, the inner product is calculated on the remaining residual part to perform iterative calculations until the expected conditions are met and then the iteration stops. The angle corresponding to the most relevant atom obtained through iteration is the estimated one-dimensional angle.

6. The direction-of-arrival estimation method based on rectangular array subarray grouping according to claim 5, characterized in that: For multi-snapshot data, the data of each snapshot is multiplied by all atoms, and then the results of each snapshot are combined using the L2 norm. The largest value in the combined result is selected to determine the most relevant atom.

7. A direction-of-arrival estimation system based on rectangular array subarray grouping, comprising a steering vector construction module, a received signal data matrix construction module, and a direction-of-arrival-axis angle generation module, characterized in that: The direction of arrival estimation method based on rectangular array subarray grouping as described in any one of claims 1 to 6 is used for direction of arrival estimation.

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