Novel non-uniform array DOA estimation method based on improved spatial smoothing

Abstract

The method comprises the following steps of: determining an approximate arraying position by combining the number of incoming wave signals and the wavelength of incoming waves according to a signal arrival destination and an available terrain, further adjusting a part of unreasonably arrayed array elements according to the terrain, and then calculating to obtain accurate and reasonable position coefficients of other array elements of a sparse array; carrying out difference processing on the sparse array position coefficient, and removing redundancy in combination with the existing non-uniform array position to obtain all virtual difference synthesis array position information; calculating a covariance matrix of the non-uniform array and performing vectorization processing, and then performing redundancy elimination and sorting on the data to obtain partial single-snapshot virtual array information; performing data processing on the single-snapshot virtual differential synthesis array information to obtain a signal correlation matrix; due to the influence of coherent signals, de-coherence processing is carried out on a signal correlation matrix for the first time; and an improved spatial smoothing algorithm is adopted again to further reduce the influence of coherent signals, and finally, a MUSIC spectral peak search algorithm is used to carry out DOA estimation on single-snapshot virtual differential synthesis array information.

Description

Technical Field

[0001] The present invention belongs to the field of array signal processing, and in particular relates to a non-uniform array design and a wave direction estimation method, which estimates the wave directions of multiple spatial target sources through flexible array arrangement. Background Art

[0002] Array signal processing plays a vital role in many fields such as radar, positioning, wireless communication, and the Internet of Things, and array measurements enable us to extract the essential characteristics of signals. DOA (direction of arrival) estimation is one of the traditional parameter estimation methods, and a uniform linear array is usually used for angle estimation. However, in order to avoid spatial aliasing, the element spacing of a uniform linear array is usually limited to half a wavelength, which will lead to serious mutual coupling effects and require complex calculations for decoupling. The aperture of the array will also be greatly limited. A uniform linear array with L+1 sensors can only identify L sources at most. Therefore, in modern communications, uniform linear arrays need to significantly increase the number of sensors and perform complex data processing to solve the problem of massive signals.

[0003] For this reason, scientists have introduced the concept of differential coaxial arrays and proposed sparse arrays such as coprime arrays, nested arrays, and minimum hole arrays. Although this expands the spacing between adjacent sensors so that more targets can be detected under the same sensor, the sensors are not fully utilized, resulting in a waste of some resources. At the same time, the position of the array arrangement has a greater impact on the signal reception effect. In the case of complex terrain environment, the array arrangement cannot find a reasonable position, and the expected effect can hardly be achieved at this time. The present invention proposes a new non-uniform array arrangement method, which uses the idea of ​​differential arrays to arrange the array according to the terrain environment and the received signal and the needs of the user. When the terrain of the signal receiving area is complex and it is impossible to arrange the array in detail, the method of the present invention can be used to find available terrain around the complex terrain environment. After measuring the distance between the complex terrain and the available terrain, and calculating with the predicted information of the signal to be received, the minimum number of sensors used and the optimal array position are obtained. At this time, the complex terrain can be avoided and the array can be arranged only in the available geographical environment. At the same time, the least sensors are used to obtain the most virtual arrays, which reduces the error while saving resources. Then, the signal received by the sensor is used to process and decorrelate the signal using an improved spatial smoothing algorithm. Since the array of the present invention is sparse, the coupling between signals is greatly reduced, which can greatly reduce the amount of calculation and improve the success rate of signal information extraction. Summary of the invention

[0004] To achieve the above purpose, the technical idea of ​​the present invention is: according to the signal arrival destination and the available terrain, combined with the number of incoming wave signals and the wavelength of the incoming wave, the position of the approximate non-uniform array is determined, and further according to the terrain, some unreasonable array elements are adjusted, and then the accurate and reasonable position coefficients of the remaining elements of the sparse array are obtained by calculation; the sparse array position coefficients are subjected to difference processing, combined with the existing non-uniform array position, and all virtual differential synthesis array position information is obtained by removing redundancy; the covariance matrix of the non-uniform array is calculated and vectorized, and then the data is de-redundant and sorted to obtain part of the single-snap virtual array information; the single-snap virtual differential synthesis array information is processed to obtain a signal correlation matrix; due to the influence of coherent signals, the signal correlation matrix is ​​first subjected to decorrelation processing; the improved spatial smoothing algorithm is used again to further reduce the influence of coherent signals, and finally the MUSIC spectrum peak search algorithm is used to perform DOA estimation on the single-snap virtual differential synthesis array information.

[0005] Step 1: Arrange the non-uniform array according to the signal arrival situation, avoid complex terrain, and calculate the specific position coefficients x1, x2, ..., x in the non-uniform array. M :

[0006] Select the array direction coordinate axis and the coordinate axis origin O to calculate the non-uniform array layout position Ensure that the dense sub-array S1 can be arranged reasonably:

[0007] It is known that there are K coherent and incoherent mixed wave signals arriving at a complex terrain, and the incident wave direction is θ k , the wavelength is λ, if and only if there are only M antenna sensors used to receive the incoming wave signals, and the number of antenna sensors M is equal to or slightly less than the number of incoming wave signals K, it is impossible to use the traditional uniform linear array and classical algorithm to calculate the direction of the incoming wave signals, and there is a problem of difficulty in reasonable array arrangement. In order to use a limited number of M antenna array elements to identify K incoming wave signals, a non-uniform array is used to receive the incoming wave signals. First, a direction suitable for array arrangement in the complex terrain is selected as the coordinate axis, and any point is taken as the origin O of the coordinate axis to ensure that the origin O can be reasonably arranged. The position coefficients of the M antenna sensors on the coordinate axis are x1, x2, ..., x M .

[0008] Then, the M antenna sensors are divided into a dense subarray S1 and a sparse subarray S2, a total of two antenna subarrays. The dense subarray S1 has P antenna sensors, and the sparse subarray S2 has Q antenna sensors, satisfying P+Q=M. The spacing between adjacent antenna array element sensors of the dense subarray S1 is d, satisfying The distance D1 between each antenna element in the dense subarray S1 and the center point O is D1 = d×{x1, x2, ..., x P}=d×{0,1,…,P-1}, and because the dense sub-array S1 is near the center point O, the array can be arranged reasonably; the spacing between adjacent array elements of the sparse sub-array S2 is P×d, and the distance D2 between the sparse sub-array S2 and the center point O is D2=d×{x P+1 , x P+2 , …, x M}=d×{P,P+P,…,P+(Q-1)×P}. Due to the complex terrain, it cannot be guaranteed that the sparse sub-array S2 can be arranged reasonably.

[0009] It is found that the array element spacing between the first antenna array element of the sparse subarray S2 and the last antenna array element of the dense subarray S1 is d, so the total non-uniform array layout position is The degree of freedom of the non-uniform array is the aperture of the array, that is, DOF=2×Q×P+1, at which time the aperture of the array antenna is lengthened.

[0010] Step 2: translate some antenna elements in the non-uniform array antenna so that the non-uniform array antenna can be arranged reasonably and meet x M >K:

[0011] 2.1) Determine whether the non-uniform array can reasonably estimate the angle of the incoming wave. If it is not reasonable, translate the sparse subarray S2 backward. The maximum translation distance is (P+1)d. The translation only needs to ensure that most of the array elements in the sparse subarray S2 are reasonably arranged or x M >K:

[0012] If the last antenna element position coefficient x of the non-uniform array M If it is still less than the number of incoming signals K, or some array elements in the sparse sub-array S2 cannot be reasonably arranged due to terrain reasons, it is still impossible to use the limited M antenna array elements to accurately estimate the arrival angles of the K incoming signals. In this case, it is necessary to first increase the spacing between the dense sub-array S1 and the sparse sub-array S2.

[0013] At present, the array element spacing between the first antenna array element of the sparse subarray S2 and the last antenna array element of the dense subarray S1 is d. The sparse subarray S2 can be shifted backward as a whole. After the shift, the position coefficient x of the last array element of the sparse subarray S2 is calculated. M The relationship between the incoming signal K and x M >K, because the larger the array degree of freedom DOF, the more accurate the estimation of the incoming wave angle, but there is an upper limit to the backward translation, that is, the sparse subarray S2 can only move a maximum distance of (P+1)×d. Assume that the sparse subarray S2 translates backward by a distance of Cd, where C is the position coefficient of the backward movement. At this time, the array position of the sparse array is

[0014] The degree of freedom of the sparse array increases to DOF = 2 × x M+1=2×(C+Q×P)+1.

[0015] Then determine x M The relationship between x and K is as follows: M >K, then proceed to the next step 2.21); if x is not satisfied at this time M >K then proceed to the next step 2.22).

[0016] 2.21) Check whether the array of each antenna element in the sparse subarray S2 is reasonable. If the array is unreasonable, the antenna unit of the array element and all the subsequent sparse subarray elements are shifted backward by a distance d:

[0017] The non-uniform array has preliminarily met the requirement of estimating K incoming signals with a limited number of M array antennas. However, due to the complex array terrain, the array positions of each array element in the sparse sub-array S2 cannot be completely guaranteed to be within the error range, resulting in large errors in subsequent calculations. It is necessary to check each antenna array element of the sparse sub-array S2 one by one.

[0018] If there is a lth array element in the sparse sub-matrix S2, its coordinate position coefficient is x P+l If the reasonable array cannot be satisfied, the position coefficient is x P+l The array element and all other array elements of the sparse sub-array S2 arranged behind it are shifted backward by d, that is, the position coefficient is x P+l , x P+l+1 , …, x M The array element is shifted backward by a distance d to meet the position coefficient x P+l The purpose of reasonable arrangement of array elements is to arrange the array elements reasonably. At this time, the array position of the sparse sub-array S2 is D2 = d × {C + P, C + 2 × P, ..., C + (l-1) × P, C + l × P + 1, ..., C + P × Q + 1}. After the entire operation process is completed, because the unreasonable array elements are operated by backward translation, the array degree of freedom is not reduced. At this time, DOF = 2 × x M +1=2×(C+P×Q)+3, still satisfying x M >K does not affect the non-uniform array's judgment on the number of incoming waves, but increases the array's degree of freedom DOF, thus greatly reducing the error in estimating the direction of the incoming wave signal.

[0019] 2.22) Further lengthen the sparse sub-matrix S2 so that the array satisfies x M >K:

[0020] If the sparse sub-array S2 is translated backward by a distance of (P+1)×d, then x is still not satisfied. m >K, then the sparse sub-array S2 is further moved one by one. At this time, the current position coefficient of the sparse sub-array S2 is D2 = d×{x P+1 , x P+2, …, x M}=d×{2×P,3×P,…,(Q+1)×P}, starting from the second antenna element of the sparse subarray S2 and ending with the second to last element, the antenna element and all subsequent antenna elements are translated backward by a distance of d, that is, the coordinate position coefficient is x m The antennas, m∈P+2, P+3, ..., M-1, starting from m=P+2, are respectively m , x m+1 , …, x M The array elements are translated backward by a distance of d until m = M-1. After the translation is completed, the array position of the sparse sub-array S2 is D2 = d×{x P+1 , x P+2 …, x M}=d×{2×P,3×P+1,…,Q×(P+1)-2,Q×(P+1)+P-2},at this time DOF=2×x M +1=2×(Q×(P+1)+P)-3,x M Extend back to x M >K, the arrangement of the non-uniform array ends.

[0021] Step 3: According to the total array element position coefficients x1, x2, ..., x M , calculate the virtual element position coefficients of the non-uniform antenna array Get the virtual differential synthesis array and its degrees of freedom:

[0022] First, the position coefficients x1, x2, ..., x of the non-uniform antenna array are M Perform difference processing to obtain the virtual differential array element position coefficient In order to ensure that the non-uniform antenna array of the present invention does not miss the virtual array element position after the difference processing, the matrix Y∈C is constructed. (M×M) The specific operation is to use the element position coefficient x of each non-uniform antenna array in turn. i , respectively subtract all array element position coefficients x1, x2, ..., x M , the difference matrix is:

[0023]

[0024] Arrange the elements in matrix Y by row, remove duplicates, and reorder them from small to large to obtain the virtual differential synthesis array position coefficients Due to the ingenuity of the translation array element, the position coefficients of each virtual array element in the virtual differential synthesis array obtained by difference are arranged continuously, and the largest virtual array element position coefficient y m Equal to the position coefficient x of the last element of the non-uniform array M , that is, the virtual differential synthesis array position coefficient There are 2×y m +1 virtual array element.

[0025] Step 4: Calculate the covariance matrix R of the non-uniform antenna array based on the incoming wave matrix, and solve the single-snapshot virtual differential synthesis array receiving information Z:

[0026] 4.1) Calculate the covariance matrix R of the non-uniform antenna array:

[0027] At any time t, the received signal model of the non-uniform array is: Where n(t) is the Gaussian white noise component, A(θ) = [a(θ2), a(θ2), ..., a(θ K )] is the non-uniform array flow matrix, where is the kth incident signal source θ k The non-uniform antenna array steering vector, a(θ k ) contains the direction information of the incoming signal, s(t) = [s1(t), s2(t), ..., s K (t)] T Represents the signal vector. Since the received signal Y(t) is a continuous signal, the computer cannot process it directly. We choose the point sampling method and take T sampling points for the continuous signal Y(t). The sampled received signal processed by the computer is Then the covariance matrix of the non-uniform array is:

[0028] 4.2) Define the elements in the covariance matrix R as the virtual array element receiving signal, and obtain the single snapshot virtual differential array information Z1:

[0029] Among them, the element in the uth row and vth column of the covariance matrix R is:

[0030]

[0031] And u, v = 1, 2, ..., M, r u，v Considered as the cross-correlation statistics of the received signals of the u-th and v-th antenna elements in the non-uniform antenna array, in the exponential term x u -x v It is expressed as the virtual element position coefficient of the non-uniform antenna array. According to the second-order statistics, r u，v It can be equivalent to the received signal at a virtual array element position. Establish a single-snapshot virtual differential synthesis array receiving information matrix Z, and the matrix Z and the virtual differential synthesis array position coefficient The same size, and then compare them one by one The virtual array element position coefficient y i , extract r from the covariance matrix R u，vThe exponential term of the same term as the virtual array element position coefficient, that is, x u -x v =y i After the average values ​​of these items are obtained, the average values ​​are sequentially put into the single-snapshot virtual differential synthesis array receiving information matrix Z to obtain the receiving signal Z of all virtual array element positions.

[0032] Step 5: Calculate the Toeplitz matrix R of the virtual signal z , through the Toeplitz matrix R z Constructing an unbiased estimate of the covariance matrix Introduce the anti-unit matrix J and calculate the unbiased covariance estimate

[0033] Since the single-shot pseudo-snapshot virtual signal contains the incoming wave information, the matrix Z is used for covariance processing. First, the first y of the single-shot virtual differential synthesis array receiving information matrix Z is taken. m +1 element to build the Toeplitz matrix Then calculate the covariance matrix of the single-snapshot virtual difference synthesis array In order to make full use of the received information and reduce the signal estimation error, the inverse unit matrix J is introduced to calculate the unbiased estimate of the covariance matrix of the single pseudo-snapshot virtual signal, that is, Since the signal subspace and noise subspace are divided later, Only the diagonal elements of the matrix are used. The unbiased covariance estimation matrix obtained by this operation is By using the diagonal elements and anti-diagonal elements at the same time, the influence between the coherent signals is reduced, and a more accurate result is obtained.

[0034] Step 6: Estimation matrix of unbiased covariance Perform eigendecomposition, construct the noise subspace, and use the MUSIC algorithm to obtain the incoming wave angle.

[0035] because Where Λ is the diagonal matrix of eigenvectors, and U is the eigenvector matrix corresponding to the eigenvalues, so first extract the eigenvectors of Λ into a vector and arrange them in ascending order, and then rearrange the eigenvector matrix according to the sorted eigenvalue order Finally, take the eigenvector matrix The first K columns of are the signal subspace, and the rest are the noise subspace.

[0036] Finally, the MUSIC algorithm is used to estimate DOA, and the signal vector is taken as γ changes from -90 to 90 with a step size of 0.01 degrees. Using the orthogonal relationship between the noise vector and the signal vector, Find the angle of arrival by peak searching.

[0037] Compared with the existing array structure, the present invention has the following advantages:

[0038] 1. Compared with the existing non-uniform array, the virtual array elements obtained by the present invention are continuously arranged without holes, and no hole filling operation is required, which simplifies the operation steps. Under the same sensor, more signals can be identified, which is more suitable for engineering;

[0039] 2. The present invention is less affected by terrain. In complex terrain, it is only necessary to find nearby available terrain, select the array coordinate axis and the coordinate origin, and then arrange the complete array according to the present invention, thereby expanding the array aperture and having better angle measurement performance;

[0040] 3. The present invention has more virtual array elements, and makes fuller use of the incoming wave information. It is not necessary to take multiple points for the virtual single snapshot information again. It only needs to use the anti-diagonal matrix to transform the covariance matrix to achieve the purpose of reducing the experimental error. Then, the improved spatial smoothing algorithm is used to reduce the influence of coherent waves on the experimental results. The traditional MUSIC algorithm is used to make the program more stable. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a diagram of a ten-element non-uniform array and a virtual array arrangement of the present invention:

[0042] Figure 2 A diagram showing a two-level nested array of ten array elements and the arrangement of a virtual array element array;

[0043] Figure 3 A diagram showing a two-level coprime array of ten array elements and the arrangement of the generated virtual array element array;

[0044] Figure 4 A flowchart for implementing the method of the present invention;

[0045] Figure 5 It is a scatter plot of DOA estimation of airspace targets under ten array elements of the method of the present invention;

[0046] Figure 6 A comparison diagram of the relationship between the root mean square error and the signal-to-noise ratio of DOA estimation for the present invention and the two-level nested array, the coprime array, and the uniform linear array;

[0047] Figure 7 A comparison diagram of the relationship between the root mean square error of DOA estimation and the number of snapshots for the present invention, a two-level nested array, a coprime array, and a uniform linear array; DETAILED DESCRIPTION

[0048] In order to make the above and other purposes, features and advantages of the present invention more obvious, the following is a detailed description of the embodiments of the present invention with reference to the accompanying drawings as follows:

[0049] Reference Figure 1 The non-uniform array of the ten-element array of the present invention and the virtual array arrangement diagram generated therefrom are shown in FIG. Figure 1 It can be seen that the array element position coefficients x are arranged continuously, so that the number of virtual array elements is the largest, and the array data can be used to the maximum extent. In the case of the same array elements, the present invention can identify more incoming wave signals;

[0050] Reference Figure 2 The diagram is a diagram of the arrangement of the coprime array and its virtual array under ten array elements. It can be seen that under the same array elements, the coprime array virtualizes fewer arrays than the present invention, and there is a problem of discontinuous position coefficients, so the coprime array cannot fully utilize the existing data, making the subsequent calculation complicated;

[0051] Reference Figure 3 The figure is a nested array and its virtual array arrangement diagram under a ten-element array. It can be seen that although the virtual array coefficients of the nested array are continuous, the total number of virtual array elements is still less than that of the present invention, so the performance of the present invention is better under the same array elements. For the convenience of description, it is assumed that the present invention and the coprime array have the same number of nested array elements, both of which are ten array elements. The steps of the method of the present invention are as follows:

[0052] Step 1: Arrange the non-uniform array according to the signal arrival situation, avoid complex terrain, and calculate the specific position coefficients x1, x2, ..., x in the non-uniform array. M :

[0053] Select the array direction coordinate axis and the coordinate axis origin O to calculate the non-uniform array layout position Ensure that the dense sub-array S1 can be arranged reasonably:

[0054] It is known that there are K coherent and incoherent mixed wave signals arriving at a complex terrain, and the incident wave direction is θ k , the wavelength is λ, if and only if there are only M antenna sensors used to receive the incoming wave signals, and the number of antenna sensors M is equal to or slightly less than the number of incoming wave signals K, it is impossible to use the traditional uniform linear array and classical algorithm to calculate the direction of the incoming wave signals, and there is a problem of difficulty in reasonable array arrangement. In order to use a limited number of M antenna array elements to identify K incoming wave signals, a non-uniform array is used to receive the incoming wave signals. First, a direction suitable for array arrangement in the complex terrain is selected as the coordinate axis, and any point is taken as the origin O of the coordinate axis to ensure that the origin O can be reasonably arranged. The position coefficients of the M antenna sensors on the coordinate axis are x1, x2, ..., x M .

[0055] Then, the M antenna sensors are divided into a dense subarray S1 and a sparse subarray S2, a total of two antenna subarrays. The dense subarray S1 has P antenna sensors, and the sparse subarray S2 has Q antenna sensors, satisfying P+Q=M. The spacing between adjacent antenna array element sensors of the dense subarray S1 is d, satisfying The distance D1 between each antenna element in the dense subarray S1 and the center point O is D1 = d×{x1, x2, ..., x P}=d×{0,1,…,P-1}, and because the dense sub-array S1 is near the center point O, the array can be arranged reasonably; the spacing between adjacent array elements of the sparse sub-array S2 is P×d, and the distance D2 between the sparse sub-array S2 and the center point O is D2=d×{x P+1 , x P+2 …, x M}=d×{P,P+P,…,P+(Q-1)×P}. Due to the complex terrain, it cannot be guaranteed that the sparse sub-array S2 can be arranged reasonably.

[0056] It is found that the array element spacing between the first antenna array element of the sparse subarray S2 and the last antenna array element of the dense subarray S1 is d, so the total non-uniform array layout position is The degree of freedom of the non-uniform array is the aperture of the array, that is, DOF=2×Q×P+1, at which time the aperture of the array antenna is lengthened.

[0057] Step 2: translate some antenna elements in the non-uniform array antenna so that the non-uniform array antenna can be arranged reasonably and meet x M >K:

[0058] 2.1) Determine whether the non-uniform array can reasonably estimate the angle of the incoming wave. If it is not reasonable, translate the sparse subarray S2 backward. The maximum translation distance is (P+1)d. The translation only needs to ensure that most of the array elements in the sparse subarray S2 are reasonably arranged or x M >K:

[0059] If the last antenna element position coefficient x of the non-uniform array M If it is still less than the number of incoming signals K, or some array elements in the sparse sub-array S2 cannot be reasonably arranged due to terrain reasons, it is still impossible to use the limited M antenna array elements to accurately estimate the arrival angles of the K incoming signals. In this case, it is necessary to first increase the spacing between the dense sub-array S1 and the sparse sub-array S2.

[0060] At present, the array element spacing between the first antenna array element of the sparse subarray S2 and the last antenna array element of the dense subarray S1 is d. The sparse subarray S2 can be shifted backward as a whole. After the shift, the position coefficient x of the last array element of the sparse subarray S2 is calculated. M The relationship between the incoming signal K and x M>K, because the larger the array degree of freedom DOF, the more accurate the estimation of the incoming wave angle, but there is an upper limit to the backward translation, that is, the sparse subarray S2 can only move a maximum distance of (P+1)×d. Assume that the sparse subarray S2 translates backward by a distance of Cd, where C is the position coefficient of the backward movement. At this time, the array position of the sparse array is The degree of freedom of the sparse array increases to DOF = 2 × x M +1=2×(C+Q×P)+1.

[0061] Then determine x M The relationship between x and K is as follows: M >K, then proceed to the next step 2.21); if x is not satisfied at this time M >K then proceed to the next step 2.22).

[0062] 2.21) Check whether the array of each antenna element in the sparse subarray S2 is reasonable. If the array is unreasonable, the antenna unit of the array element and all the subsequent sparse subarray elements are shifted backward by a distance d:

[0063] The non-uniform array has preliminarily met the requirement of estimating K incoming signals with a limited number of M array antennas. However, due to the complex array terrain, the array positions of each array element in the sparse sub-array S2 cannot be completely guaranteed to be within the error range, resulting in large errors in subsequent calculations. It is necessary to check each antenna array element of the sparse sub-array S2 one by one.

[0064] If there is a lth array element in the sparse sub-matrix S2, its coordinate position coefficient is x P+l If the reasonable array cannot be satisfied, the position coefficient is x P+l The array element and all other array elements of the sparse sub-array S2 arranged behind it are shifted backward by d, that is, the position coefficient is x P+l , x P+l+1 , …, x M The array element is shifted backward by a distance d to meet the position coefficient x P+l The purpose of reasonable arrangement of array elements is to arrange the array elements reasonably. At this time, the array position of the sparse sub-array S2 is D2 = d × {C + P, C + 2 × P, ..., C + (l-1) × P, C + l × P + 1, ..., C + P × Q + 1}. After the entire operation process is completed, because the unreasonable array elements are operated by backward translation, the array degree of freedom is not reduced. At this time, DOF = 2 × x M +1=2×(C+P×Q)+3, still satisfying x M >K does not affect the non-uniform array's judgment on the number of incoming waves, but increases the array's degree of freedom DOF, thus greatly reducing the error in estimating the direction of the incoming wave signal.

[0065] 2.22) Further lengthen the sparse sub-matrix S2 so that the array satisfies xM >K:

[0066] If the sparse sub-array S2 is translated backward by a distance of (P+1)×d, then x is still not satisfied. m >K, then the sparse sub-array S2 is further moved one by one. At this time, the current position coefficient of the sparse sub-array S2 is D2 = d×{x P+1 , x P+2 ,…,x M}=d×{2×P,3×P,…,(Q+1)×P}, starting from the second antenna element of the sparse subarray S2 and ending with the second to last element, the antenna element and all subsequent antenna elements are translated backward by a distance of d, that is, the coordinate position coefficient is taken as the xth m The antennas, m∈P+2, P+3, ..., M-1, starting from m=P+2, are respectively m , x m+1 , …, x M The array elements are translated backward by a distance of d until m = M-1. After the translation is completed, the array position of the sparse sub-array S2 is D2 = d×{x P+1 , x P+2 , …, x M}=d×{2×P,3×P+1,…,Q×(P+1)-2,Q×(P+1)+P-2},at this time DOF=2×x M +1=2×(Q×(P+1)+P)-3,x M Extend back to x M >K, the arrangement of the non-uniform array ends.

[0067] Step 3: According to the total array element position coefficients x1, x2, ..., x M , calculate the virtual element position coefficients of the non-uniform antenna array Get the virtual differential synthesis array and its degrees of freedom:

[0068] First, the position coefficients x1, x2, ..., x of the non-uniform antenna array are M Perform difference processing to obtain the virtual differential array element position coefficient In order to ensure that the non-uniform antenna array of the present invention does not miss the virtual array element position after the difference processing, the matrix Y∈C is constructed. (M×M) The specific operation is to use the element position coefficient x of each non-uniform antenna array in turn. i , respectively subtract all array element position coefficients x1, x2, ..., x M , the difference matrix is:

[0069]

[0070] Arrange the elements in matrix Y by row, remove duplicates, and reorder them from small to large to obtain the virtual differential synthesis array position coefficients Due to the ingenuity of the translation array element, the position coefficients of each virtual array element in the virtual differential synthesis array obtained by difference are arranged continuously, and the largest virtual array element position coefficient y m Equal to the position coefficient x of the last element of the non-uniform array M , that is, the virtual differential synthesis array position coefficient There are 2×y m +1 virtual array element.

[0071] Step 4: Calculate the covariance matrix R of the non-uniform antenna array based on the incoming wave matrix, and solve the single-snapshot virtual differential synthesis array receiving information Z:

[0072] 4.1) Calculate the covariance matrix R of the non-uniform antenna array:

[0073] At any time t, the received signal model of the non-uniform array is: Where n(t) is the Gaussian white noise component, A(θ) = [a(θ1), a(θ2), ..., a(θ K )] is the non-uniform array flow matrix, where is the kth incident signal source θ k The non-uniform antenna array steering vector, a(θ k ) contains the direction information of the incoming signal, s(t) = [s1(t), s2(t), ..., s K (t)] T Represents the signal vector. Since the received signal Y(t) is a continuous signal, the computer cannot process it directly. We choose the point sampling method and take T sampling points for the continuous signal Y(t). The sampled received signal processed by the computer is Then the covariance matrix of the non-uniform array is:

[0074] 4.2) Define the elements in the covariance matrix R as the virtual array element receiving signal, and obtain the single snapshot virtual differential array information Z1:

[0075] Among them, the element in the uth row and vth column of the covariance matrix R is:

[0076] And u, v = 1, 2, ..., M, r u，v Considered as the cross-correlation statistics of the received signals of the u-th and v-th antenna elements in the non-uniform antenna array, in the exponential term x u -x v It is expressed as the virtual element position coefficient of the non-uniform antenna array. According to the second-order statistics, r u，vIt can be equivalent to the received signal at a virtual array element position. Establish a single-snapshot virtual differential synthesis array receiving information matrix Z, and the matrix Z and the virtual differential synthesis array position coefficient The same size, and then compare them one by one The virtual array element position coefficient y i , extract r from the covariance matrix R u，v The exponential term of the same term as the virtual array element position coefficient, that is, x u -x v =y i After the average values ​​of these items are obtained, the average values ​​are sequentially put into the single-snapshot virtual differential synthesis array receiving information matrix Z to obtain the receiving signal Z of all virtual array element positions.

[0077] Step 5: Calculate the Toeplitz matrix R of the virtual signal z , through the Toeplitz matrix R z Constructing an unbiased estimate of the covariance matrix Introduce the anti-unit matrix J and calculate the unbiased covariance estimate

[0078] Since the single-shot pseudo-snapshot virtual signal contains the incoming wave information, the matrix Z is used for covariance processing. First, the first y of the single-shot virtual differential synthesis array receiving information matrix Z is taken. m +1 element to build the Toeplitz matrix Then calculate the covariance matrix of the single-snapshot virtual difference synthesis array In order to make full use of the received information and reduce the signal estimation error, the inverse unit matrix J is introduced to calculate the unbiased estimate of the covariance matrix of the single pseudo-snapshot virtual signal, that is, Since the signal subspace and noise subspace are divided later, Only the diagonal elements of the matrix are used. The unbiased covariance estimation matrix obtained by this operation is By using the diagonal elements and anti-diagonal elements at the same time, the influence between the coherent signals is reduced, and a more accurate result is obtained.

[0079] Step 6: Estimation matrix of unbiased covariance Perform eigendecomposition, construct the noise subspace, and use the MUSIC algorithm to obtain the incoming wave angle.

[0080] because Where Λ is the diagonal matrix of eigenvectors, and U is the eigenvector matrix corresponding to the eigenvalues, so first extract the eigenvectors of Λ into a vector and arrange them in ascending order, and then rearrange the eigenvector matrix according to the sorted eigenvalue order Finally, take the eigenvector matrix The first K columns of are the signal subspace, and the rest are the noise subspace.

[0081] Finally, the MUSIC algorithm is used to estimate DOA, and the signal vector is taken as γ changes from -90 to 90 with a step size of 0.01 degrees. Using the orthogonal relationship between the noise vector and the signal vector, The arrival angle is found by searching the spectrum peak. The specific implementation process of the present invention is as follows: Figure 4 shown.

[0082] To prove the superiority of the present invention, the method of the present invention is used to estimate the DOA of the spatial target under ten array elements. The results are as follows: Figure 5 As shown, it is found that the estimation accuracy of the present invention is accurate. Then the influence of the signal-to-noise ratio and the number of snapshots on the present invention is verified, and comparative experiments are performed using the present invention and a two-level nested array, a coprime array, and a uniform linear array. The results are shown in Figure 6 and Figure 7 As shown, it is found that the estimation accuracy of the present invention decreases with the increase of snapshot number and signal-to-noise ratio, and the estimation accuracy is higher than that of other arrays. At the same time, it has the best performance under low signal-to-noise ratio and low snapshot number, which verifies the excellent performance of the method of the present invention.

Claims

1. The specific steps of the new non-uniform array DOA estimation method based on improved spatial smoothing are as follows: 1a) Arrange the non-uniform array according to the signal arrival situation, avoid complex terrain, and calculate the specific position coefficients x1, x2, ..., x in the non-uniform array. M : It is known that there are K coherent and incoherent mixed wave signals arriving at a complex terrain, and the incident wave direction is θ k , the wavelength is λ, if and only if there are only M antenna sensors used to receive the incoming wave signal, then M≤K, so it is impossible to use the traditional uniform linear array and classical algorithm to calculate the direction of the incoming wave signal, and there is a problem of difficulty in reasonable array arrangement due to the complex terrain; in order to use the limited M antenna array elements to identify K incoming wave signals, a non-uniform array is used to receive the incoming wave signals. First, a direction suitable for array arrangement in the complex terrain is selected as the coordinate axis, and any point is taken as the origin O of the coordinate axis to ensure that the array can be reasonably arranged near the origin O. The position coefficients of the M antenna sensors on the coordinate axis are x1, x2, …, x M ; Then, the M antenna sensors are divided into a dense subarray S1 and a sparse subarray S2, with two antenna subarrays in total. The dense subarray S1 has P antenna sensors, and the sparse subarray S2 has Q antenna sensors, satisfying P+Q=M; the spacing between adjacent antenna array element sensors in the dense subarray S1 is d, satisfying The distance D1 between each antenna element in the dense subarray S1 and the center point O is D1 = d×{x1, x2, ..., x P }=d×{0,1,…,P-1}, and because the dense sub-array S1 is near the center point O, the array can be arranged reasonably; the spacing between adjacent array elements of the sparse sub-array S2 is P×d, and the distance D2 between the sparse sub-array S2 and the center point O is D2=d×{x P+1 ,x P+2 ,…,x M }=d×{P,P+P,…,P+(Q-1)×P}. Due to the complex terrain, it is impossible to ensure that the sparse sub-array S2 can be reasonably arranged. At this time, the array degree of freedom DOF=2×Q×P+1; 1b) Adjust some antenna elements in the non-uniform array antenna so that all antenna elements in the non-uniform array antenna can be arranged reasonably and achieve the purpose of using finite array elements to reasonably estimate the incoming wave signal: If the last antenna element position coefficient x of the non-uniform array M If the number of antenna elements in the sparse sub-array S2 is still less than the number of incoming signals K, or some of the array elements in the sparse sub-array S2 cannot be properly arranged due to terrain reasons, it is still impossible to accurately estimate the arrival angles of the K incoming signals using the limited M antenna array elements. In this case, the distance between the dense sub-array S1 and the sparse sub-array S2 needs to be increased first. At present, the array element spacing between the first antenna array element of the sparse subarray S2 and the last antenna array element of the dense subarray S1 is d. The sparse subarray S2 can be shifted backward as a whole. After the shift, the position coefficient x of the last array element of the sparse subarray S2 is calculated. M The relationship between the incoming signal K and x M >K, because the larger the array degree of freedom DOF, the more accurate the estimation of the incoming wave angle, but there is an upper limit to the backward translation, that is, the sparse subarray S2 can only move a distance of (P+1)×d at most; assuming that the sparse subarray S2 translates backward by a distance of Cd, C is the position coefficient of the backward movement, then the array position of the sparse array is The degree of freedom of the sparse array increases to DOF = 2 × x M +1=2×(C+Q×P)+1; Then determine x M The relationship between x and K is as follows: M >K, then check whether the array element layout is reasonable; if x is not satisfied at this time M >K, the length of the non-uniform array is lengthened to check whether the array elements are arranged reasonably; Check whether the array element layout is reasonable or not: The non-uniform array has preliminarily met the requirement of estimating K incoming wave signals with a limited number of M array antennas. However, due to the complex array terrain, the array positions of each array element in the sparse sub-array S2 cannot be completely guaranteed to be arranged within the error range, resulting in large errors in subsequent calculations. It is necessary to check each antenna array element of the sparse sub-array S2 one by one; if there is an l-th array element in the sparse sub-array S2, its coordinate position coefficient is x P+l If the reasonable array cannot be satisfied, the position coefficient is x P+l The array element and all other array elements of the sparse sub-array S2 arranged behind it are shifted backward by d, that is, the position coefficient is x P+l , x P+l+1 , …, x M The array element is shifted backward by a distance d to meet the position coefficient x P+l The purpose of reasonable arrangement of array elements is to arrange the array elements reasonably; at this time, the array position of the sparse sub-array S2 is D2 = d × {C + P, C + 2 × P, ..., C + (l-1) × P, C + l × P + 1, ..., C + P × Q + 1}. After the entire operation process is completed, because the unreasonable array elements are operated by backward translation, the array degree of freedom is not reduced. At this time, DOF = 2 × x M +1=2×(C+P×Q)+3, still satisfying x M >K does not affect the non-uniform array's judgment of the number of incoming waves, but increases the array's degree of freedom DOF, which greatly reduces the error in estimating the direction of the incoming wave signal; Lengthen the non-uniform array length and check whether the array element layout is reasonable. Operation: If the sparse subarray S2 is translated backward by a distance of (P+1)×d, then x is still not satisfied. m >K, the sparse sub-array S2 needs to be further moved one by one; at this time, the current position coefficient of the sparse sub-array S2 is D2 = d×{x P+1 , x P+2 …, x M }=d×{2×P,3×P,…,(Q+1)×P}, starting from the second antenna element of the sparse subarray S2 and ending with the second to last element, the antenna element and all subsequent antenna elements are translated backward by a distance of d, that is, the coordinate position coefficient is taken as the xth m The antennas, m∈P+2, P+3, ..., M-1, starting from m=P+2, are respectively m , x m+1 ,…,x M The array elements are translated backward by a distance of d until m = M-1. After the translation is completed, the array position of the sparse sub-array S2 is D2 = d×{x P+1 , x P+2 , …, x M }=d×{2×P,3×P+1,…,Q×(P+1)-2,Q×(P+1)+P-2},at this time DOF=2×x M +1=2×(Q×(P+1)+P)-3,x M Extend back to x M >K, the arrangement of the non-uniform array ends; 1c) According to the total array element position coefficients x1, x2, ..., x M , calculate the virtual element position coefficients of the non-uniform antenna array Get the virtual differential synthesis array and its degrees of freedom: First, the position coefficients x1, x2, ..., x of the non-uniform antenna array are M Perform difference processing to obtain the virtual differential array element position coefficient To ensure that the non-uniform antenna array does not miss the virtual array element position after the difference processing, the matrix Y∈C is constructed. (M×M) The specific operation is to use the element position coefficient x of each non-uniform antenna array in turn. i , respectively subtract all array element position coefficients x1, x2, ..., x M , the difference matrix is: Arrange the elements in matrix Y by row, remove duplicates, and reorder them from small to large to obtain the virtual differential synthesis array position coefficients Due to the ingenuity of the translation array element, the position coefficients of each virtual array element in the virtual differential synthesis array obtained by difference are arranged continuously, and the largest virtual array element position coefficient y m Equal to the position coefficient x of the last element of the non-uniform array M , that is, the virtual differential synthesis array position coefficient There are 2×y m +1 virtual array element; 1d) According to the incoming wave matrix, calculate the covariance matrix R of the non-uniform antenna array and solve the single-snapshot virtual differential synthesis array receiving information Z: First, the covariance matrix R of the non-uniform antenna array is calculated. At any time t, the received signal model of the non-uniform array is: Where n(t) is the Gaussian white noise component, A(θ) = [a(θ1), a(θ2), ..., a(θ K )] is the non-uniform array flow matrix, where is the kth incident signal source θ k The non-uniform antenna array steering vector, a(θ k ) contains the direction information of the incoming signal, s(t) = [s1(t), s2(t), ..., s K (t)] T Represents the signal vector; Since the received signal Y(t) is a continuous signal, the computer cannot process it directly. The point sampling method is selected to take T sampling points of the continuous signal Y(t). The sampled received signal processed by the computer is Then the covariance matrix of the non-uniform array is: Then, the elements in the covariance matrix R are defined as the virtual array element receiving signals, and the single-snapshot virtual differential array information Z1 is obtained; the elements in the uth row and the Vth column in the covariance matrix R are: And u, v = 1, 2, ..., M, r u，v Considered as the cross-correlation statistics of the received signals of the u-th and v-th antenna elements in the non-uniform antenna array, in the exponential term x u -x v It is expressed as the virtual element position coefficient of the non-uniform antenna array. According to the second-order statistics, r u，v It can be equivalent to the received signal at a virtual array element position; establish a single-snapshot virtual differential synthesis array receiving information matrix Z, matrix Z and virtual differential synthesis array position coefficient The same size, and then compare them one by one The virtual array element position coefficient y i , extract r from the covariance matrix R u，v The exponential term of the same term as the virtual array element position coefficient, that is, x u -x v =y i After the average values ​​of these items are obtained, the average values ​​are sequentially put into the single-snapshot virtual differential synthesis array receiving information matrix Z to obtain the receiving signal Z of all virtual array element positions; 1e) Calculate the Toeplitz matrix R of the virtual signal z , through the Toeplitz matrix R z Constructing an unbiased estimate of the covariance matrix Introduce the anti-unit matrix J and calculate the unbiased covariance estimate Since the single-shot pseudo-snapshot virtual signal contains the incoming wave information, the matrix Z is used for covariance processing. First, the first y of the single-shot virtual differential synthesis array receiving information matrix Z is taken. m +1 element to build the Toeplitz matrix Then calculate the covariance matrix of the single-snapshot virtual difference synthesis array In order to make full use of the received information and reduce the signal estimation error, the inverse unit matrix J is introduced to calculate the unbiased estimate of the covariance matrix of the single pseudo-snapshot virtual signal, that is, Since the signal subspace and noise subspace are divided later, Only the diagonal elements of the matrix are used. The unbiased covariance estimation matrix obtained by this operation is By using diagonal elements and anti-diagonal elements at the same time, the influence between coherent signals is reduced, and more accurate results are obtained; 1f) For the unbiased covariance estimation matrix Perform eigendecomposition, construct the noise subspace, and use the MUSIC algorithm to obtain the incoming wave angle: because Where Λ is the diagonal matrix of eigenvectors, and U is the eigenvector matrix corresponding to the eigenvalues, so first extract the eigenvectors of Λ into a vector and arrange them in ascending order, and then rearrange the eigenvector matrix according to the sorted eigenvalue order Finally, take the eigenvector matrix The first K columns of are the signal subspace, and the rest are the noise subspace. Finally, the MUSIC algorithm is used to estimate DOA, and the signal vector is taken as γ changes from -90 to 90 with a step size of 0.01 degrees. Using the orthogonal relationship between the noise vector and the signal vector, Find the angle of arrival by peak searching.

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