L-shaped mutual-coupling-resistant sparse array and far-field information source direction finding method thereof

Abstract

The invention relates to an L-shaped mutual-coupling-resistant sparse array and a far-field information source direction finding method thereof, the L-shaped mutual-coupling-resistant sparse array comprises a first sparse linear array and a second sparse linear array, and the first sparse linear array and the second sparse linear array are perpendicular to each other and intersect to form an L-shaped array; each of the first sparse linear array and the second sparse linear array is formed by a first sub-array, a second sub-array and a third sub-array which are distributed at intervals along the extension direction of the linear array, and the first sub-array is arranged at the intersection of the first sparse linear array and the second sparse linear array; and the first sub-array, the second sub-array and the third sub-array are formed by equidistantly distributing a plurality of sensor array elements. According to the L-shaped mutual-coupling-resistant sparse array, the aperture of the array can be effectively increased, and the estimation resolution is improved; the continuous virtual array element length can be increased, the physical hardware expenditure is reduced, and the freedom degree of the array is improved; meanwhile, during design, the distance between the array elements in the array can be increased in advance, the mutual coupling effect is reduced, and the estimation effect of the array is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of signal processing, and in particular relates to a method for direction finding of a signal source based on an L-type anti-mutual coupling sparse array and a far-field signal source thereof. Background Art

[0002] Direction Of Arrival Estimation (DOA) is one of the important topics in the fields of radar, seismic survey, sonar, wireless communication, microphone array voice localization, etc. In the past few decades, researchers have conducted a lot of research on one-dimensional DOA estimation, but one-dimensional DOA estimation can only estimate the azimuth, not the elevation. Fortunately, two-dimensional DOA estimation can solve the above problems. At present, the two-dimensional direction of arrival estimation problem is widely used in Internet of Vehicles (IOV) and fifth-generation (5G) mobile communications, and many algorithms have been developed to solve the DOA estimation problem, such as the improved reduced-dimensionality MUSIC algorithm (IRD-MUSIC), reduced-dimensionality multi-signal classification algorithm, etc. Compared with two-dimensional planar arrays, L-type sparse arrays have the advantages of lower cost and better adaptability. It can be flexibly arranged and adjusted according to specific requirements to meet the needs of specific tasks. Therefore, it is of great practical significance to develop an L-type sparse array with a more reasonable structure and higher degree of freedom.

[0003] At present, most of the far-field source direction finding technologies based on L-type arrays are based on uniform linear arrays, and the situation of non-uniform linear arrays is rarely considered. The far-field source direction finding technology based on L-type arrays is performed on uniform linear arrays. There are three main problems with such array configurations:

[0004] First, for existing uniform linear arrays, the array aperture is determined by the number of physical sensors. In order to increase the array aperture, the number of sensors needs to be increased proportionally, resulting in a significant increase in hardware costs. As the number of sensors increases, the volume and weight of the array also increase accordingly, making the layout and maintenance of the array more cumbersome and expensive in practical applications, consuming a lot of hardware costs.

[0005] Secondly, for the existing uniform linear array based on L-type array far-field source direction finding, the degrees of freedom that the array can provide are limited by the number of physical sensors. The array cannot perform underdetermined estimation and the estimation of the source is limited. Since the degrees of freedom of the array directly depend on the number of physical sensors, when the number of sensors is limited, the degrees of freedom of the array are also limited, making it difficult to adapt to the situation where the number of sources exceeds the number of sensors. This underdetermined estimation problem is particularly prominent in the face of complex scenes or densely distributed sources. The array may not be able to accurately capture the information of all sources, resulting in limited or even distorted source estimation.

[0006] Finally, for the existing uniform linear array based on L-shaped array far-field source direction finding, the distance between array elements in the array is relatively small, and there is serious mutual coupling. The mutual coupling effect at a small distance makes it difficult for the array to effectively distinguish signals from different sources, especially when the signal strength is similar. The mutual coupling effect will cause signal aliasing and interference, which significantly affects the accuracy of source estimation.

[0007] Therefore, the existing L-type array far-field source direction finding technology based on uniform linear array has the problems of high hardware cost, low source estimation resolution, and serious mutual coupling effect, which leads to poor source estimation effect. Summary of the invention

[0008] In order to solve the above problems existing in the prior art, the present invention provides an L-type anti-mutual coupling sparse array and a far-field source direction finding method thereof. The technical problem to be solved by the present invention is achieved by the following technical solutions:

[0009] An embodiment of the present invention provides an L-shaped anti-mutual coupling sparse array for realizing far-field source direction finding, comprising: a first sparse linear array and a second sparse linear array, wherein the first sparse linear array and the second sparse linear array are perpendicular to each other and intersect to form an L-shaped array;

[0010] The first sparse linear array and the second sparse linear array are both formed by a first sub-array, a second sub-array and a third sub-array which are spaced apart along the extension direction of the linear arrays, and the first sub-array is arranged at the intersection of the first sparse linear array and the second sparse linear array;

[0011] The first sub-array, the second sub-array and the third sub-array are all formed by a number of sensor array elements distributed at equal intervals.

[0012] In one embodiment of the present invention, the relationship between the total number Q of sensor array elements of the L-type anti-mutual coupling sparse array and the number T of sensor array elements of each sparse linear array is: Q=2T-1, where T is the number of sensor array elements of the first sparse linear array or the second sparse linear array;

[0013] The first optimal array configuration parameter N of the L-type anti-mutual coupling sparse array is:

[0014] The second optimal array configuration parameter of the L-type anti-mutual coupling sparse array is M:

[0015] When the first optimal array configuration parameter N is an even number, the number of continuous virtual array elements of the first sparse linear array or the second sparse linear array is: 2(2N-1)(T-2N+2)-1;

[0016] When the first optimal array configuration parameter N is an odd number, the number of continuous virtual array elements of the first sparse linear array or the second sparse linear array is: 2(2N-1)(T-2N+2)+2N-3;

[0017] The aperture of the first sparse linear array or the second sparse linear array is: (2N-1)(T-2N)-(N-1) 2 +(2M+N)(N-1); T>1, T is an integer.

[0018] In one embodiment of the present invention, the first subarray includes N-1 sensors with a spacing of (N-1)d; the second subarray includes T-2N+2 sensors with a spacing of (2N-1)d; and the third subarray includes N sensors with a spacing of Nd; wherein d is 1 / 2 of the wavelength λ.

[0019] In one embodiment of the present invention, the position of each sensor on the first sparse linear array or the second sparse linear array is:

[0020]

[0021] in, is the position set of each sensor in the first sparse linear array or the second sparse linear array, represents a set of position elements of each sensor in the first sparse linear array or the second sparse linear array, p i d represents the position of the i-th sensor, i∈[0,…,T-1,T]; represents the first subarray, represents the second subarray, represents the third subarray;

[0022] The optimal array structure of the first subarray is:

[0023]

[0024] The optimal array structure of the second subarray is:

[0025]

[0026] The optimal array structure of the third subarray is:

[0027]

[0028] In one embodiment of the present invention, the first sparse line array extends along the X-axis, and the second sparse line array extends along the Z-axis.

[0029] Another embodiment of the present invention provides a far-field source direction finding method based on an L-type anti-mutual coupling sparse array, comprising the steps of:

[0030] A receiving signal model is established based on the optimal array structure of an L-type anti-mutual coupling sparse array, and a receiving signal that conforms to the receiving signal model is obtained according to a source signal; wherein the L-type anti-mutual coupling sparse array adopts the L-type anti-mutual coupling sparse array described in the above embodiment;

[0031] The azimuth angle of each received signal is estimated by using the DOA estimation method of the second-order cumulant to obtain an azimuth angle estimation value;

[0032] Constructing a cross covariance matrix including azimuth information and elevation angle information using the received signal model, estimating an array manifold related to the elevation angle based on the cross covariance matrix, and calculating a covariance matrix corresponding to the elevation angle using the array manifold related to the elevation angle;

[0033] estimating the elevation angle of each received signal by combining the azimuth angle estimation value and a covariance matrix corresponding to the elevation angle to obtain an elevation angle estimation value;

[0034] The azimuth angle estimation value and the elevation angle estimation value are matched to achieve far-field source direction finding.

[0035] In one embodiment of the present invention, the received signal of each array element in the optimal array structure of the L-type anti-mutual coupling sparse array is:

[0036]

[0037] Where i represents the i-th array element, t represents time t, K represents the number of narrowband signals incident on the array, and s k (t) represents the kth narrowband signal, n k (t) represents the Gaussian white noise of the k-th narrowband signal, τ ik represents the delay of the k-th narrowband signal;

[0038] The receiving signal model of the optimal array structure of the L-type anti-mutual coupling sparse array is:

[0039] x(t)=A X s X (t)+n(t);

[0040] z(t)=A Z s Z (t)+n(t);

[0041] Where x(t) represents the received signal model of the first sparse linear array, A X represents the array manifold of the first sparse linear array related to the azimuth angle, θ represents the azimuth, A Z represents the array manifold of the second sparse linear array related to the pitch angle, β represents the pitch angle, n(t) represents Gaussian white noise, n(t) = [n -T (t),…,n0(t),…,n T (t)] T .

[0042] In one embodiment of the present invention, the azimuth angle of each received signal is estimated by using the DOA estimation method of the second-order cumulant to obtain an azimuth angle estimation value, including:

[0043] The received signal is used to construct a second-order cumulant matrix:

[0044]

[0045] Among them, R X represents the second-order cumulant matrix, x(t) represents the received signal of the first sparse linear array, A X represents the array manifold of the first sparse linear array and the azimuth angle, R S represents the covariance matrix of the source signal, Represents the power of Gaussian white noise, I T represents the identity matrix;

[0046] Based on the second-order cumulant matrix, the azimuth of each received signal is estimated using the MUSIC method to obtain an azimuth estimation value:

[0047]

[0048] in, is the estimated azimuth angle, θ is the variable for spatial spectrum search, and a x (θ) represents the azimuth vector containing azimuth information, a x (θ) H Indicates a x The conjugate transpose of (θ), U n represents the eigenvector matrix of the noise subspace, Indicates U n The conjugate transpose of n It is calculated by the second-order cumulant matrix, where K is the number of information sources.

[0049] In one embodiment of the present invention, the received signal model is used to construct a cross covariance matrix containing azimuth information and elevation angle information, and the cross covariance matrix is ​​used to estimate an array manifold related to the elevation angle, and the array manifold related to the elevation angle is used to calculate a covariance matrix corresponding to the elevation angle, including:

[0050] The received signal model is used to construct a cross-covariance matrix containing azimuth information and elevation angle information:

[0051]

[0052] Among them, R XZ represents the cross covariance matrix, x(t) represents the received signal of the first sparse linear array, z(t) represents the received signal of the second sparse linear array, A X represents the array manifold of the first sparse linear array and the azimuth angle, R S Represents the covariance matrix of the source signal, A Z represents the covariance matrix of the second sparse linear array related to the pitch angle;

[0053] The cross-covariance matrix is ​​converted into a least squares problem of the covariance matrix of the pitch angle and solved to obtain the array manifold related to the pitch angle:

[0054]

[0055] in, represents the estimated value of the array manifold associated with the pitch angle of the second sparse subarray;

[0056] The covariance matrix corresponding to the pitch angle is calculated using the array manifold associated with the pitch angle:

[0057]

[0058] in, represents the covariance matrix corresponding to the pitch angle, Represents the power of Gaussian white noise, I T Represents the identity matrix.

[0059] In one embodiment of the present invention, estimating the elevation angle of each received signal in combination with the azimuth angle estimation value and the elevation angle covariance matrix to obtain the elevation angle estimation value includes:

[0060] Combining the azimuth angle estimate value and the covariance matrix corresponding to the elevation angle, the elevation angle of each received signal is estimated by searching the spatial spectrum function to obtain an elevation angle estimate value:

[0061]

[0062] in, is the estimated value of the azimuth angle, β represents the variable for spatial spectrum search, a z (β) represents the pitch angle vector containing the pitch angle information, U n represents the eigenvector matrix of the noise subspace, Indicates Un is the conjugate transpose of , where K is the number of information sources.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] The L-type anti-mutual coupling sparse array of the present invention is based on the L-type array far-field source direction finding requirements, and designs a first sparse linear array and a second sparse linear array that are perpendicular and intersecting to each other. In each sparse linear array, a first sub-array, a second sub-array and a third sub-array are formed by spaced-apart distribution, and each sub-array is formed by a number of sensor array elements that are equally spaced, which can effectively increase the aperture of the array and improve the estimation resolution. The L-type anti-mutual coupling sparse array can increase the length of continuous virtual array elements, reduce physical hardware expenses, and increase the degree of freedom of the array. At the same time, during the design, the spacing between array elements in the array can be increased in advance to reduce the mutual coupling effect and improve the estimation effect of the array. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 A schematic diagram of the structure of an L-type anti-mutual coupling sparse array provided by an embodiment of the present invention;

[0066] Figure 2 A schematic diagram of the optimal array structure arrangement of an L-shaped anti-mutual coupling sparse array provided in an embodiment of the present invention;

[0067] Figure 3 A schematic flow chart of a far-field source direction finding method based on an L-type anti-mutual coupling sparse array provided in an embodiment of the present invention;

[0068] Figure 4 A schematic diagram of azimuth spatial spectrum estimation for far-field source direction finding based on an L-type anti-mutual coupling sparse array provided in an embodiment of the present invention;

[0069] Figure 5a-5c A schematic diagram of elevation angle spatial spectrum estimation for far-field source direction finding based on an L-type anti-mutual coupling sparse array provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0070] The present invention is further described in detail below with reference to specific embodiments, but the embodiments of the present invention are not limited thereto.

[0071] Embodiment 1

[0072] Most of the current hybrid source positioning technologies in which far-field signal sources and near-field signal sources coexist are based on uniform linear arrays. In this embodiment, an L-type anti-mutual coupling sparse array is designed in consideration of the situation of non-uniform linear arrays.

[0073] See also Figure 1 and Figure 2 , Figure 1 A schematic diagram of the structure of an L-type anti-mutual coupling sparse array provided by an embodiment of the present invention, Figure 2A schematic diagram of the optimal array structure arrangement of an L-type anti-mutual coupling sparse array provided in an embodiment of the present invention.

[0074] The L-shaped anti-mutual coupling sparse array of the present embodiment is used to realize far-field source direction finding, including: a first sparse linear array and a second sparse linear array, the first sparse linear array and the second sparse linear array are perpendicular to each other and intersect to form an L-shaped array; the first sparse linear array and the second sparse linear array are both formed by a first sub-array, a second sub-array and a third sub-array spaced apart along an extension direction of the linear array, and the first sub-array is arranged at the intersection of the first sparse linear array and the second sparse linear array; the first sub-array, the second sub-array and the third sub-array are all formed by a plurality of sensor array elements spaced apart.

[0075] Specifically, the first sparse linear array extends along a first direction, the second sparse linear array extends along the first direction, the first direction and the second direction are perpendicular and intersecting, the first direction includes but is not limited to the X-axis, and the second direction includes but is not limited to the Z-axis.

[0076] Specifically, the relationship between the total number Q of sensor elements of the L-type anti-mutual coupling sparse array and the number T of sensor elements of each sparse linear array is: Q=2T-1, where T is the number of sensor elements of the first sparse linear array or the second sparse linear array.

[0077] The first optimal array configuration parameter N of the L-type anti-mutual coupling sparse array is:

[0078] The second best array configuration parameter of L-type anti-mutual coupling sparse array is M:

[0079] When the first optimal array configuration parameter N is an even number, the number of continuous virtual array elements of the first sparse linear array or the second sparse linear array is: 2(2N-1)(T-2N+2)-1; when the first optimal array configuration parameter N is an odd number, the number of continuous virtual array elements of the first sparse linear array or the second sparse linear array is: 2(2N-1)(T-2N+2)+2N-3.

[0080] The aperture of the first sparse linear array or the second sparse linear array is: (2N-1)(T-2N)-(N-1) 2 +(2M+N)(N-1); T>1, T is an integer.

[0081] Specifically, the first sub-array is arranged at the intersection of the sparse linear arrays, the second sub-array is arranged in the middle of the sparse linear array, and the third sub-array is arranged at a position of the sparse linear array away from the intersection.

[0082] The first subarray, the second subarray and the third subarray form a sparse linear array on the X axis or the Z axis. The sparse linear array on the X axis and the sparse linear array on the Z axis are arranged vertically to form an optimal array structure of an L-type anti-mutual coupling sparse array.

[0083] Specifically, the first subarray includes N-1 sensors with a spacing of (N-1)d; the second subarray includes T-2N+2 sensors with a spacing of (2N-1)d; and the third subarray includes N sensors with a spacing of Nd; wherein d is 1 / 2 of the wavelength λ.

[0084] Specifically, the positions of the sensors on the first sparse linear array or the second sparse linear array are:

[0085]

[0086] in, is the position set of each sensor in the first sparse linear array or the second sparse linear array, represents a set of position elements of each sensor in the first sparse linear array or the second sparse linear array, p i d represents the position of the i-th sensor, i∈[0,…,T-1,T]; represents the first subarray, represents the second subarray, represents the third subarray;

[0087] The optimal array structure for the first subarray is:

[0088]

[0089] The optimal array structure of the second subarray is:

[0090]

[0091] The optimal array structure of the third subarray is:

[0092]

[0093] Taking the first sparse linear array extending along the X-axis and the second sparse linear array extending along the Z-axis as an example, this embodiment further provides a design method for an L-type anti-mutual coupling sparse array, including the steps of:

[0094] The L-type anti-mutual coupling sparse array of this embodiment is based on the L-type array far-field source direction finding requirements, and designs a first sparse linear array and a second sparse linear array that are perpendicular and intersecting to each other. In each sparse linear array, it is formed by a first sub-array, a second sub-array and a third sub-array that are distributed at intervals, and each sub-array is formed by a number of sensor array elements that are distributed at equal intervals, which can effectively increase the aperture of the array and improve the estimation resolution; the L-type anti-mutual coupling sparse array can increase the length of continuous virtual array elements, reduce physical hardware expenses, and improve the degree of freedom of the array. It can also enhance the robustness of the array, adapt to the electromagnetic environment of strong mutual coupling interference, improve the estimation resolution, and enhance the estimation effect of the array; at the same time, when designing, the spacing of the array elements in the array can be increased in advance to reduce the mutual coupling effect and improve the estimation effect of the array. Therefore, the L-type anti-mutual coupling sparse array has the advantages of large array aperture, low hardware cost, high degree of freedom and weak mutual coupling effect between sensors, and can be applied to far-field source direction finding.

[0095] Embodiment 2

[0096] See also Figure 3 , Figure 3 A flow chart of a far-field source direction finding method based on an L-type anti-mutual coupling sparse array provided in an embodiment of the present invention. The far-field source direction finding method based on an L-type anti-mutual coupling sparse array comprises the following steps:

[0097] S1. Establish a received signal model based on the optimal array structure of the L-type anti-mutual coupling sparse array, and obtain a received signal that conforms to the received signal model according to the source signal. The L-type anti-mutual coupling sparse array adopts the L-type anti-mutual coupling sparse array described in Example 1.

[0098] Step S1 includes the steps of:

[0099] S11, presetting the total number Q of sensor array elements in the L-type anti-mutual coupling sparse array, and determining the position relationship and the number of sensors of each sub-array in the first sparse linear array or the second sparse linear array of the L-type anti-mutual coupling sparse array according to the total number Q of sensor array elements.

[0100] First, according to the total number Q of sensor array elements, the values ​​of the first optimal array configuration parameter N and the second optimal array configuration parameter M that provide the best degree of freedom are obtained.

[0101] Then, according to the values ​​of M and N, a difference set is constructed for the X-axis or Z-axis of the L-type anti-mutual coupling sparse array, and the difference set is P D = {l = p ρ -p q ,ρ,q∈[-L,L]}, the virtual differential array of the L-type anti-mutual coupling sparse array can be obtained, and the number of continuous virtual array elements is obtained from the maximum number of continuous array elements in the virtual differential array.

[0102] Furthermore, the X-axis or Z-axis aperture of the array structure and the optimal degree of freedom of the array structure can also be calculated. The calculation of the optimal degree of freedom belongs to the prior art and will not be described in detail here.

[0103] Next, the positional relationship among the first sub-array, the second sub-array, and the third sub-array and the number of sensors in each sub-array may be determined according to the values ​​of M and N.

[0104] S12. Obtain the optimal array structure of the first sparse linear array and the second sparse linear array in the L-type anti-mutual coupling sparse array according to the positional relationship among the first sub-array, the second sub-array and the third sub-array and the number of sensors in each sub-array.

[0105] Specifically, the set of positions of each sensor is obtained according to the position relationship of each sub-array and the number of sensors. Then we get the set of position elements of each sensor Will Split into corresponding to the first sub-matrix, the second sub-matrix and the third sub-matrix and As the optimal array structure of the L-type anti-mutual coupling sparse array X-axis or Z-axis, it is used for direction finding of far-field sources.

[0106] For the relationship between the parameters in steps S11 and S12, please refer to the first embodiment, which will not be described in detail in this embodiment.

[0107] S13. Establish a receiving signal model based on the optimal array structure of the L-type anti-mutual coupling sparse array.

[0108] Specifically, let the sensor array element at position 0 be the phase reference point, and the received signal of each array element of any axis in the optimal array structure of the L-type anti-mutual coupling sparse array is:

[0109]

[0110] Where i represents the i-th array element, t represents time t, K represents the number of narrowband signals incident on the array, and s k (t) represents the kth narrowband signal, n k (t) represents the Gaussian white noise of the k-th narrowband signal, τ ik represents the delay of the kth narrowband signal.

[0111] The received signal model is obtained according to the expression of the received signal. The received signal model of the optimal array structure of the L-type anti-mutual coupling sparse array is:

[0112] x(t)=A X s X (t)+n(t);

[0113] z(t)=A Z s Z(t)+n(t);

[0114] Where x(t) represents the received signal model of the first sparse linear array, A X represents the array manifold of the first sparse linear array and the azimuth angle, A X =[a(θ1),…,a(θ Kn )], θ represents the azimuth, A Z A represents the array manifold of the second sparse linear array related to the pitch angle, Z =[a(β1),…,a(β Kn )], β represents the pitch angle, n(t) represents Gaussian white noise, n(t) = [n -T (t),…,n0(t),…,n T (t)] T Array Manifold A X and A Z It can be obtained from the relevant parameters of the L-type anti-mutual coupling sparse array in the first embodiment.

[0115] Furthermore, a received signal that conforms to the above-mentioned received signal model is obtained based on the signal of the far-field source. In this embodiment, a second-order cumulant algorithm is used to estimate the azimuth and elevation angles of the received signal to achieve far-field source direction finding. The second-order cumulant algorithm has the characteristics of low complexity and high resolution in the signal processing process. The process of far-field source direction finding based on the second-order cumulant algorithm includes the following steps: (1) using the received signal to construct a second-order cumulant matrix containing only azimuth information; (2) applying a DOA estimation method such as MUSIC or ESPRIT to the newly obtained matrix to estimate the azimuth of all sources; (3) constructing a new second-order cumulant matrix containing azimuth information; (4) using the estimated azimuth information, bringing it into a new cross-covariance matrix to estimate the elevation distance information; (5) completing the pairing of azimuth and elevation angles to complete the three-dimensional spatial direction finding of the far-field source.

[0116] Specifically for the present application, far-field source direction finding based on the second-order cumulant algorithm includes steps S2, S3, S4, and S5.

[0117] S2. Use the DOA estimation method of the second-order cumulant to estimate the azimuth of each received signal to obtain an azimuth estimation value.

[0118] Specifically, the second-order cumulant matrix is ​​constructed using the received signal:

[0119]

[0120] Among them, R X represents the second-order cumulant matrix, x(t) represents the received signal of the first sparse linear array, A Xrepresents the array manifold of the first sparse linear array and the azimuth angle, R S represents the covariance matrix of the source signal, Represents the power of Gaussian white noise, I T Represents the identity matrix.

[0121] Then, based on the second-order cumulant matrix, the MUSIC method is used to estimate the azimuth of each received signal to obtain an azimuth estimation value. It can be understood that by using the second-order cumulant matrix as the input of the MUSIC method, the azimuth estimation value corresponding to each received signal can be output:

[0122]

[0123] in, is the estimated value of the azimuth angle, θ is the variable for spatial spectrum search, and a x (θ) represents the azimuth vector containing azimuth information, a x (θ) H Indicates a x The conjugate transpose of (θ), U n represents the eigenvector matrix of the noise subspace, Indicates U n The conjugate transpose of n It is calculated by the second-order cumulant matrix, where K is the number of information sources.

[0124] S3. Construct a cross covariance matrix containing azimuth information and elevation angle information using the received signal model, estimate the array manifold related to the elevation angle based on the cross covariance matrix, and calculate the covariance matrix corresponding to the elevation angle using the array manifold related to the elevation angle.

[0125] Specifically, a covariance matrix R containing distance information is constructed according to the received signal model. The expression of the covariance matrix R is R = {x(t)x H (t)}. Based on the form of the covariance matrix R, a cross covariance matrix containing azimuth information and elevation angle information can be constructed:

[0126]

[0127] Among them, R XZ represents the cross covariance matrix, x(t) represents the received signal of the first sparse linear array, and z(t) represents the received signal of the second sparse linear array.

[0128] Then, the cross covariance matrix is ​​converted into a least squares problem of the covariance matrix of the pitch angle and solved to obtain the array manifold related to the pitch angle. Specifically, since A X Each column element corresponds to A Z, so the steering matrix A needs to be estimated Z It is equivalent to its corresponding matrix A X By solving the following least squares problem, the array manifold related to the pitch angle is obtained:

[0129]

[0130] in, Represents the estimate of the array manifold for the second sparse subarray as a function of the elevation angle.

[0131] Find the covariance matrix corresponding to the pitch angle calculated using the array manifold related to the pitch angle:

[0132]

[0133] in, Represents the covariance matrix corresponding to the pitch angle.

[0134] S4. Estimate the elevation angle of each received signal by combining the azimuth angle estimate value and the elevation angle covariance matrix to obtain an elevation angle estimate value.

[0135] Specifically, the azimuth angle estimate and the covariance matrix corresponding to the elevation angle are combined, and the DOA estimation method is used to estimate the elevation angle of each received signal by searching the spatial spectrum function to obtain the elevation angle estimate expression:

[0136]

[0137] in, is the estimated value of the azimuth angle, β represents the variable for spatial spectrum search, a z (β) represents the pitch angle vector containing the pitch angle information, U n represents the eigenvector matrix of the noise subspace, Indicates U n is the conjugate transpose of , K is the number of information sources.

[0138] S5. Match the azimuth angle estimate value and the elevation angle estimate value to achieve far-field source direction finding.

[0139] Specifically, according to the value of k, and By matching and corresponding, the direction of the far-field signal source is obtained, and the three-dimensional spatial direction finding of the far-field signal source is realized.

[0140] Furthermore, this embodiment further verifies the far-field source direction finding method based on the L-type anti-mutual coupling sparse array through experiments. The simulation conditions are: for the optimal array when the number of array elements Q is 23, N=4, M=2. In the experiment, the mutual coupling coefficient is 0.2 and the SNR value is 5dB. The number of snapshots is T=2000. Assume that there are K=3 far-field sources in space, {θ1=-50°, β1=70°}, {θ1=10°, β1=20°}, {θ1=70°, β1=-30°}.

[0141] See also Figure 4 , Figure 4 A schematic diagram of azimuth spatial spectrum estimation for far-field source direction finding based on an L-type anti-mutual coupling sparse array provided in an embodiment of the present invention. Figure 4 In the figure, the three peaks of the spectrum diagram correspond to the three azimuth information of the far-field source. The application of this array structure can effectively estimate the three-dimensional spatial direction-finding information of the three signals with high accuracy.

[0142] See also Figure 5a-5c , Figure 5a-5c A schematic diagram of elevation angle spatial spectrum estimation for far-field source direction finding based on an L-type anti-mutual coupling sparse array provided in an embodiment of the present invention. Figure 5a-5c In the figure, three clear spectrum peaks correspond to three far-field signal sources in sequence. The array structure can be used to estimate the three-dimensional spatial direction finding information of the three signals with high precision, with matching azimuth and elevation angles. This can realize the three-dimensional spatial direction finding of far-field signal sources.

[0143] In the method of this embodiment, according to the three-dimensional spatial direction finding requirements of far-field signal sources, an L-shaped anti-mutual coupling sparse array is designed, which can effectively increase the aperture of the array and improve the estimation resolution; the obtained optimal array structure can increase the length of continuous virtual array elements, reduce physical hardware expenses, increase the degree of freedom of the array, reduce the mutual coupling effect, and improve the estimation effect of the array.

[0144] The above contents are further detailed descriptions of the present invention in combination with specific preferred embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the protection scope of the present invention.

Claims

1. An L-type anti-mutual coupling sparse array, characterized in that: Used to realize far-field source direction finding, comprising: a first sparse linear array and a second sparse linear array, wherein the first sparse linear array and the second sparse linear array are perpendicular to each other and intersect to form an L-shaped array; The first sparse linear array and the second sparse linear array are both formed by a first sub-array, a second sub-array and a third sub-array which are spaced apart along the extension direction of the linear arrays, and the first sub-array is arranged at the intersection of the first sparse linear array and the second sparse linear array; The first sub-array, the second sub-array and the third sub-array are all formed by a number of sensor array elements distributed at equal intervals.

2. The L-type anti-mutual coupling sparse array according to claim 1, characterized in that: The relationship between the total number Q of sensor array elements of the L-type anti-mutual coupling sparse array and the number T of sensor array elements of each sparse linear array is: Q=2T-1, where T is the number of sensor array elements of the first sparse linear array or the second sparse linear array; The first optimal array configuration parameter N of the L-type anti-mutual coupling sparse array is: The second optimal array configuration parameter of the L-type anti-mutual coupling sparse array is M: When the first optimal array configuration parameter N is an even number, the number of continuous virtual array elements of the first sparse linear array or the second sparse linear array is: 2(2N-1)(T-2N+2)-1; When the first optimal array configuration parameter N is an odd number, the number of continuous virtual array elements of the first sparse linear array or the second sparse linear array is: 2(2N-1)(T-2N+2)+2N-3; The aperture of the first sparse linear array or the second sparse linear array is: (2N-1)(T-2N)-(N-1) 2 +(2M+N)(N-1); T>1, T is an integer.

3. The L-type anti-mutual coupling sparse array according to claim 1, characterized in that: The first subarray includes N-1 sensors with a spacing of (N-1)d; the second subarray includes T-2N+2 sensors with a spacing of (2N-1)d; the third subarray includes N sensors with a spacing of Nd; wherein d is 1 / 2 of the wavelength λ.

4. The L-type anti-mutual coupling sparse array according to claim 1, characterized in that: On the first sparse linear array or the second sparse linear array, the position of each sensor is: in, is the position set of each sensor in the first sparse linear array or the second sparse linear array, represents a set of position elements of each sensor in the first sparse linear array or the second sparse linear array, p i d represents the position of the i-th sensor, i∈[0,…,T-1,T]; 1 represents the first subarray, represents the second subarray, represents the third subarray; The optimal array structure of the first subarray is: The optimal array structure of the second subarray is: The optimal array structure of the third subarray is:

5. The L-type anti-mutual coupling sparse array according to claim 1, characterized in that: The first sparse line array extends along the X-axis, and the second sparse line array extends along the Z-axis.

6. A far-field source direction finding method based on an L-type anti-mutual coupling sparse array, characterized in that: Includes steps: A receiving signal model is established based on the optimal array structure of an L-type anti-mutual coupling sparse array, and a receiving signal that conforms to the receiving signal model is obtained according to a source signal; wherein the L-type anti-mutual coupling sparse array adopts the L-type anti-mutual coupling sparse array according to any one of claims 1 to 5; The azimuth angle of each received signal is estimated by using the DOA estimation method of the second-order cumulant to obtain an azimuth angle estimation value; Constructing a cross covariance matrix including azimuth information and elevation angle information using the received signal model, estimating an array manifold related to the elevation angle based on the cross covariance matrix, and calculating a covariance matrix corresponding to the elevation angle using the array manifold related to the elevation angle; estimating the elevation angle of each received signal by combining the azimuth angle estimation value and a covariance matrix corresponding to the elevation angle to obtain an elevation angle estimation value; The azimuth angle estimation value and the elevation angle estimation value are matched to achieve far-field source direction finding.

7. The far-field source direction finding method based on L-type anti-mutual coupling sparse array according to claim 6, characterized in that: The received signal of each array element in the optimal array structure of the L-type anti-mutual coupling sparse array is: Where i represents the i-th array element, t represents time t, K represents the number of narrowband signals incident on the array, sk(t) represents the k-th narrowband signal, nk(t) represents the Gaussian white noise of the k-th narrowband signal, τ ik represents the delay of the k-th narrowband signal; The receiving signal model of the optimal array structure of the L-type anti-mutual coupling sparse array is: x(t)=A X s X (t)+n(t); z(t)=A Z s Z (t)+n(t); Where x(t) represents the received signal model of the first sparse linear array, A X represents the array manifold of the first sparse linear array related to the azimuth angle, θ represents the azimuth, A Z represents the array manifold of the second sparse linear array related to the pitch angle, β represents the pitch angle, n(t) represents Gaussian white noise, n(t) = [n -T (t),…,n0(t),…,n T (t)] T .

8. The far-field source direction finding method based on L-type anti-mutual coupling sparse array according to claim 6, characterized in that: The DOA estimation method of the second-order cumulant is used to estimate the azimuth angle of each received signal to obtain an azimuth angle estimation value, including: The received signal is used to construct a second-order cumulant matrix: Among them, R X represents the second-order cumulant matrix, x(t) represents the received signal of the first sparse linear array, A X represents the array manifold of the first sparse linear array and the azimuth angle, R S represents the covariance matrix of the source signal, Represents the power of Gaussian white noise, I T represents the identity matrix; Based on the second-order cumulant matrix, the azimuth of each received signal is estimated using the MUSIC method to obtain an azimuth estimation value: in, is the estimated value of the azimuth angle, θ is the variable for spatial spectrum search, and a x (θ) represents the azimuth vector containing azimuth information, a x (θ) H Indicates a x The conjugate transpose of (θ), U n represents the eigenvector matrix of the noise subspace, Indicates U n The conjugate transpose of n It is calculated by the second-order cumulant matrix, where K is the number of information sources.

9. The far-field source direction finding method based on L-type anti-mutual coupling sparse array according to claim 6, characterized in that: The method comprises: constructing a cross covariance matrix including azimuth information and elevation angle information by using the received signal model, estimating an array manifold related to the elevation angle by using the cross covariance matrix, and calculating a covariance matrix corresponding to the elevation angle by using the array manifold related to the elevation angle, including: The received signal model is used to construct a cross-covariance matrix containing azimuth information and elevation angle information: Among them, R XZ represents the cross covariance matrix, x(t) represents the received signal of the first sparse linear array, z(t) represents the received signal of the second sparse linear array, A X represents the array manifold of the first sparse linear array and the azimuth angle, R S Represents the covariance matrix of the source signal, A Z represents the covariance matrix of the second sparse linear array related to the pitch angle; The cross-covariance matrix is ​​converted into a least squares problem of the covariance matrix of the pitch angle and solved to obtain the array manifold related to the pitch angle: in, represents the estimated value of the array manifold associated with the pitch angle of the second sparse subarray; The covariance matrix corresponding to the pitch angle is calculated using the array manifold associated with the pitch angle: in, represents the covariance matrix corresponding to the pitch angle, Represents the power of Gaussian white noise, I T Represents the identity matrix.

10. The far-field source direction finding method based on L-type anti-mutual coupling sparse array according to claim 6, characterized in that: The elevation angle of each received signal is estimated by combining the azimuth angle estimate value and the elevation angle covariance matrix to obtain the elevation angle estimate value, including: Combining the azimuth angle estimate value and the covariance matrix corresponding to the elevation angle, the elevation angle of each received signal is estimated by searching the spatial spectrum function to obtain an elevation angle estimate value: in, is the estimated value of the azimuth angle, β represents the variable for spatial spectrum search, a z (β) represents the pitch angle vector containing the pitch angle information, U n represents the eigenvector matrix of the noise subspace, Indicates U n is the conjugate transpose of , where K is the number of information sources.

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