An improved coprime array structure, an improved DOA estimation method for coprime arrays, a computer, and a storage medium.

Abstract

This invention provides an improved coprime array structure, an improved DOA estimation method for coprime arrays, a computer, and a storage medium, relating to the field of array signal processing. It solves the problems of insufficient continuous virtual array portions, low continuous degrees of freedom, and insufficient array aperture in existing array structures. The invention provides the following scheme: an improved coprime array structure comprising three subarrays, namely subarray 1, subarray 2, and subarray 3. The elements in subarray 1 and subarray 2 are arranged alternately. The first element of subarray 3 is Nd away from the last element of subarray 2. Subarray 3 is considered to be formed by shifting subarray 1 to the right by (MN+N-M)d units. Subarray 3 is superimposed with subarrays 1 and 2 to obtain the improved coprime array structure. An improved DOA estimation method for coprime arrays is also provided, implemented using the aforementioned improved coprime array structure, and is suitable for array signal processing experiments.

Description

Technical Field

[0001] The present invention belongs to the technical field of array signal processing. Background Art

[0002] Direction of Arrival (DOA) estimation is to utilize the geometric structure of an antenna array and signal processing algorithms to process the received signals and obtain the incident directions of signal sources. The accuracy of DOA estimation is affected by the array aperture. The larger the array aperture, the higher the DOA estimation accuracy. Limited by the Nyquist sampling theorem, the element spacing between traditional antennas cannot be greater than half of the wavelength of the incident signal, the array aperture will be restricted, and mutual coupling effects will occur between elements. In addition, the number of targets that can be identified by traditional antenna elements is also limited by the number of elements in the array, that is, the number of targets cannot exceed the number of antenna elements. Sparse arrays can break through the limitation of the element spacing of the incident signal half wavelength, have a larger array aperture and a lower coupling degree. Common sparse arrays include minimum redundancy arrays, nested arrays and co-prime arrays. The minimum redundancy array has no closed-form expression, and the size of the degrees of freedom of the array cannot be determined with a fixed number of elements. Nested arrays and co-prime arrays have closed-form solutions for the array and higher degrees of freedom. During the process of DOA estimation of sparse arrays, a virtual array is constructed for the array. Usually, the continuous part of the virtual array is used. The corresponding continuous part of the traditional array structure for the virtual array is less, resulting in waste of degrees of freedom and virtual arrays.

[0003] The traditional co-prime array structure consists of two sub-arrays. Sub-array 1 is a uniform linear array with an element spacing of Nd and an element number of M. Sub-array 2 is a uniform linear array with an element spacing of Md and an element number of N. M and N are co-prime integers, M < N, d ≤ λ / 2. The two uniform linear arrays are combined into an array with an element number of M + N - 1 in the way of sharing the first element, which is the traditional co-prime array. On this basis, some scholars have proposed an extended co-prime array structure. By increasing the M elements of sub-array 1 to 2M on the basis of the traditional co-prime array and keeping the number of elements of sub-array 2 unchanged, the total number of elements is 2M + N - 1. The continuous parts of the virtual elements of these two array structures are not enough. Summary of the Invention

[0004] The present invention solves the problems that the continuous part of the virtual array of the existing array structure is not enough, the continuous degrees of freedom are low, and the array aperture is not large enough.

[0005] The present invention provides the following technical solutions:

[0006] Scheme 1. An improved co-prime array structure. The improved co-prime array includes three sub-arrays, namely sub-array 1, sub-array 2, and sub-array 3. Sub-array 1 is a uniform linear array with an element spacing of Nd and an element number of M. Sub-array 2 is a uniform linear array with an element spacing of Md and an element number of N. Sub-array 3 is a uniform linear array with an element spacing of Nd and an element number of M. M and N are co-prime integers, and M < N. The elements in sub-array 1 and sub-array 2 are arranged alternately. Sub-array 3 is supplemented on the superimposed sub-array. The distance between the first element of the supplemented sub-array 3 and the last element of the formed array after superposition is Nd, thus obtaining an improved co-prime array structure with an element number of 2M + N - 1.

[0007] Furthermore, a preferred implementation is provided. The position set of sub-array 1 is The position set of sub-array 2 is The position set of sub-array 3 is where l represents the l-th element in sub-array 3. Then the position set of the elements of the improved co-prime array is

[0008] Furthermore, a preferred implementation is provided, where M = 3 and N = 11.

[0009] Scheme 2. A DOA estimation method for an improved co-prime array. The DOA estimation method for the improved co-prime array is implemented using the improved co-prime array structure described in any one of Scheme 1. The DOA estimation method for the improved co-prime array is as follows:

[0010] S1. Calculate the difference of the element position sets in sub-array 1, sub-array 2, and sub-array 3 to obtain a difference virtual array:

[0011]

[0012] S2. Calculate the sum of the element position sets in sub-array 1, sub-array 2, and sub-array 3 to obtain a sum virtual array:

[0013]

[0014] Obtain the sum virtual array;

[0015] where, is the sum virtual array in the positive direction, is the sum virtual array in the negative direction; s ,

[0012] represents the position set of the improved co-prime array the position coordinate of the i-th element in it, s j represents the position set of the improved co-prime array the position coordinate of the j-th element in it.

[0016] S3. Merge the difference virtual array elements and the summation virtual array elements to obtain the set of positions of the summation and difference virtual array elements.

[0017]

[0018] S4. Using the improved coprime array from the above steps as a receiving array, receive K signal sources, vectorize the covariance matrix of the received signal sources to obtain the vector covariance matrix v, use the spatial smoothing method to obtain a new covariance matrix, and perform DOA estimation based on the obtained new covariance matrix.

[0019] Furthermore, a preferred embodiment is provided, wherein the differential virtual array element coordinates obtained in S1 The virtual array elements are located between -(2MN-M)d and (2MN-M)d, where the continuous virtual array elements are located between (-MN-N+1)d and (MN+N-1)d, where d<λ / 2 and λ is the wavelength of the incident signal.

[0020] Furthermore, a preferred embodiment is provided, wherein the summation virtual array obtained in S2 The coordinates of its array elements are between -(4MN-2M)d and (4MN-2M)d.

[0021] Option 3: A computer device, including a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the method described in any one of Option 2.

[0022] Option 4: A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described in any one of Options 2.

[0023] The difference between this invention and the prior art lies in:

[0024] The improved coprime array structure described in this invention is an improvement upon the extended coprime array structure. The original extended coprime array increases the number of array elements in subarray 1 from M to 2M elements. The improved coprime array in this invention adds these additional M elements to subarray 2, increasing the array aperture and the continuous degrees of freedom. The element coordinates, continuous degrees of freedom, and array aperture of the virtual array of the improved array structure are also provided.

[0025] The advantages of this invention are:

[0026] The present invention is improved based on the extended co-prime array structure, and a virtual array is constructed by means of summation and difference. When the number of array elements is 2M + N - 1 (M < N), the continuous degrees of freedom that can be obtained by the improved co-prime array are 4MN + 2N - 1, and the array aperture is M(2N - 1)d. Compared with the virtual array obtained by summation and difference of the extended co-prime array, the continuous degrees of freedom can be increased by 2(N - M), and the array aperture can be increased by (N - M)d. Under the experimental conditions of the same number of array elements, snapshots, and signal-to-noise ratio, the improved co-prime array can obtain higher DOA estimation accuracy compared with the traditional co-prime array and the extended co-prime array. Generally speaking, like the extended co-prime array, the improved co-prime array can make the element spacing not restricted by the Nyquist theorem, reduce the mutual coupling effect between elements. At the same time, the improved co-prime array can provide greater continuous degrees of freedom and continuous aperture, and has better performance in terms of estimation accuracy, angular resolution, etc.

[0027] The present invention is also applicable to array signal processing experiments. Brief Description of the Drawings

[0028] Figure 1 It is a flowchart of the DOA estimation method for an improved co-prime array according to the present invention.

[0029] Figure 2 It is a schematic structural diagram of a co-prime array in the prior art.

[0030] Figure 3 It is a schematic structural diagram of an extended co-prime array in the prior art.

[0031] Figure 4 It is a schematic structural diagram of an improved co-prime array according to the present invention.

[0032] Figure 5 It is a comparison diagram of the relationship between the root mean square error and the number of snapshots when performing DOA estimation on the array structures of the present invention and the prior art.

[0033] Figure 6 It is a comparison diagram of the relationship between the root mean square error and the signal-to-noise ratio when performing DOA estimation on the array structures of the present invention and the prior art.

[0034] Figure 7 It is a comparison diagram of the degrees of freedom and array aperture of different array structures of the present invention and the prior art. Detailed Embodiments

[0035] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present application. Apparently, the described embodiments are part of the embodiments of the present application, rather than all of the embodiments.

[0036] Embodiment 1. Refer to Figures 1-4 to describe this embodiment. This embodiment provides an improved co-prime array structure. The improved co-prime array includes three sub-arrays, namely sub-array 1, sub-array 2, and sub-array 3. Sub-array 1 is a uniform linear array with an element spacing of Nd and an element number of M. Sub-array 2 is a uniform linear array with an element spacing of Md and an element number of N. Sub-array 3 is a uniform linear array with an element spacing of Nd and an element number of M; M and N are co-prime integers, and M < N. The elements in sub-array 1 and the elements in sub-array 2 are arranged alternately. Sub-array 3 is supplemented on the superimposed sub-arrays. The distance between the first element of the supplemented sub-array 3 and the last element of the array formed after superimposition is Nd, thus obtaining an improved co-prime array structure with an element number of 2M + N - 1.

[0037] In this embodiment, when the element number is 2M + N - 1 (M < N), the continuous degrees of freedom that the improved co-prime array can obtain are 4MN + 2N - 1, and the array aperture is M(2N - 1)d. Compared with the virtual array obtained by summing and differencing of the extended co-prime array, the continuous degrees of freedom can be increased by 2(N - M), and the array aperture can be increased by (N - M)d. Under the experimental conditions of the same element number, snapshot number, and signal-to-noise ratio, the improved co-prime array can obtain higher DOA estimation accuracy compared with the traditional co-prime array and the extended co-prime array. Generally speaking, the improved co-prime array, like the extended co-prime array, can make the element spacing not restricted by the Nyquist theorem, reduce the mutual coupling effect between elements, and at the same time, the improved co-prime array can provide a larger continuous degree of freedom and a continuous aperture, and has better performance in terms of estimation accuracy, angular resolution, etc.

[0038] Embodiment 2. This embodiment further limits an improved co-prime array structure described in Embodiment 1. The position set of sub-array 1 is The position set of sub-array 2 is The position set of sub-array 3 is where l represents the l-th element in sub-array 3. Then the element position set of the improved co-prime array is

[0039] Embodiment 3. This embodiment further limits the improved co-prime array structure described in Embodiment 1, where M = 3 and N = 11. <000015​​​​Implementation Method 4: This implementation method proposes an improved DOA estimation method for coprime arrays. The improved DOA estimation method for coprime arrays is implemented using the improved coprime array structure described in any one of Implementation Methods 1 to 3. The improved DOA estimation method for coprime arrays is as follows:

[0042] S1. Obtain the difference virtual array by subtracting the set of array element positions in subarray 1, subarray 2, and subarray 3:

[0043]

[0044] S2. Summing the set of element positions in subarrays 1, 2, and 3 yields a summed virtual array:

[0045]

[0046] Obtain the summation virtual array.

[0047] in, For positive direction summation virtual array, A virtual array for summation in the negative direction; s i Represents the set of locations of an improved coprime array. The coordinates of the i-th element in the array are s j Represents the set of locations of an improved coprime array. The coordinates of the j-th array element.

[0048] S3. Merge the difference virtual array elements and the summation virtual array elements to obtain the set of positions of the summation and difference virtual array elements.

[0049]

[0050] S4. Using the improved coprime array from the above steps as a receiving array, receive K signal sources, vectorize the covariance matrix of the received signal sources to obtain the vector covariance matrix v, use the spatial smoothing method to obtain a new covariance matrix, and perform DOA estimation based on the obtained new covariance matrix.

[0051] Implementation Method 5: This implementation method further defines the improved DOA estimation method for coprime arrays described in Implementation Method 4. The differential virtual array element coordinates obtained in S1... The virtual array elements are located between -(2MN-M)d and (2MN-M)d, where the continuous virtual array elements are located between (-MN-N+1)d and (MN+N-1)d, where d<λ / 2 and λ is the wavelength of the incident signal.

[0052] Implementation Method Six: This implementation method further defines the improved DOA estimation method for coprime arrays described in Implementation Method Four. The summation virtual array obtained in S2... The coordinate positions of its array elements are between -(4MN - 2M)d and (4MN - 2M)d.

[0053] Embodiment 7: This embodiment proposes a computer device. A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor implements the method described in any one of Embodiments 4 to 6.

[0054] Embodiment 8: This embodiment proposes a computer-readable storage medium. The computer-readable storage medium stores a computer program. When the computer program is executed by a processor, the steps of the method described in any one of Embodiments 4 to 6 are implemented.

[0055] The following is a specific illustration with M = 3 and N = 11:

[0056] By improving the co-prime array structure, the array structure is composed of three uniform linear arrays. The number of elements in each sub-array is M, N, and M respectively, and the number of array elements is 2M + N - 1. Where M and N are co-prime integers, M < N, and the set of array element positions of each linear array is The virtual aperture is expanded by using the method of summation and difference to obtain a virtual array with a larger degree of freedom. The following is a specific illustration with M = 3 and N = 11:

[0057] Step 1: The array structure is composed of three sub-arrays. Among them, Sub-array 1 and Sub-array 3 are uniform linear arrays with 3 array elements, and Sub-array 2 is a uniform linear array with 11 array elements.

[0058] Step 2: The number of elements in Sub-array 1 is 3, and the element spacing is 11d. The set of its element positions is S1 = {11md, 0 ≤ m ≤  2}; the number of elements in Sub-array 2 is 11, and the element spacing is 3d. The set of its element positions is S2 = {3nd, 0 ≤ n ≤ 10}; the number of elements in Sub-array 3 is 3, and the element spacing is 11d. The set of its element positions is S3 = {30d + 11ld, 1 ≤ l ≤ 3}; the total number of elements in the improved co-prime array is 16, and the overall position set is S = S1US2US3.

[0059] Step 3: Calculate the difference of the element coordinate positions. The difference array can be expressed as follows: Z = Z 31 UZ 21 UZ 11 [ UZ 32 UZ 22 UZ 33 ,Z 31 = S3 - S1 = {30d + 11ld - 11md, 1 ≤ l ≤ 3, 0 ≤ m ≤ 2}, Z 21=S2-S1={3nd-11md,0≤n≤10,0≤m≤2},Z 11 =S1-S1={11m1d-11m2d,0≤m1,m2≤2}, Z 32 =S3-S2={30d+11ld-3nd,1≤l≤3,0≤n≤10}, Z 22 =S2-S2={3n1d-3n2d,0≤n1,n2≤10}, Z 33 =S3-S3={11l1d-11l2d,1≤l1,l2≤3} After calculation, the positions of the difference array elements are between (-63d,63d), and the set of coordinate positions of the continuous array elements is (-43d,43d).

[0060] Step 4: Summate the coordinates of the element positions. The summation array can be represented as follows: Q = Q 31 YQ 21 YQ 11 YQ 32 YQ 22 YQ 33 Q 31 =S3+S1={30d+11ld+11md,1≤l≤3,0≤m≤2}, Q 21 =S2+S1={3nd+11md,0≤n≤10,0≤m≤2}, Q 11 =S1+S1={11m1d-11m2d,0≤m1,m2≤2}、Q 32 =S3+S2={30d+11ld+3nd,1≤l≤3,0≤n≤10}, Q 22 =S2+S2={3n1d+3n2d,0≤n1,n2≤10}、Q 33 =S3+S3={60d+11l1d+11l2d,1≤l1,l2≤3},C=-Q The summation array element set is H=CUQ, and it is calculated that its summation array element position is between (-126d,126d).

[0061] Step 5: Merge the difference array and the summation array to obtain the virtual array R = ZUH, whose element position coordinates are between (-126d, 126d), and the virtual continuous array element coordinates are between (-76d, 76d).

[0062] Step Six: To verify the superiority of the constructed array structure, spatial smoothing is used to estimate the DOA of the traditional coprime array, the extended coprime array, and the improved coprime array, respectively, and their estimation performance is compared and analyzed. The improved coprime array from the previous step is used as the receiving array to receive K uncorrelated far-field narrowband signal sources, θ kLet θ be the angle of the incident source. k If ∈[-π / 2,π / 2], then the signal data reception model is:

[0063]

[0064] Where t = 1, 2, LT, and T is the number of snapshots:

[0065] A(θ)=[a(θ1),...,a(θ k ),...,a(θ K (2)

[0066]

[0067] a(θ k Let λ represent the steering vector of the k-th incoming signal. λ is the wavelength of the incident signal, and n(t) is the Gaussian white noise vector. Then the covariance matrix of the received signal is:

[0068]

[0069] The received signal covariance matrix is ​​vectorized to obtain the vector covariance matrix v.

[0070] v = vec(R) x (5)

[0071] Construct a virtual array element weight function, defining the number of times the q-th virtual array element is repeated as the weight function w of the virtual array element.

[0072]

[0073] If J is the redundancy integration matrix, then the row vector of the q-th virtual element in J can be represented as:

[0074] <j> q:,: =vec(I(q)) (7)

[0075] Matrix I(q) can be represented as:

[0076]

[0077] The resulting deredundant signal reception expression is:

[0078] z = Jv (9)

[0079] Because the rank of vector z is 1, the subspace algorithm cannot be directly applied. Therefore, a spatial smoothing method is used to obtain a new covariance matrix, and then the subspace decomposition method is used for DOA estimation. Specifically, this involves processing the continuous portion of the virtual aperture, extracting the vector z corresponding to the continuous aperture portion of z. U Assume the continuous part of v is U = [-P] U ,P U ], then z U The CCP corresponds to 2P U +1 element. Each time P is selected... U If +1 element is used for smoothing, then a total of P elements are selected. U +1 times, the element selected in the i-th selection is represented by z. Ui This represents the covariance matrix after spatial smoothing. This matrix is ​​a full-rank matrix, and therefore it can be used for DOA estimation.

[0080] See Figures 5 to 7 To illustrate this embodiment and verify the effectiveness of the invention, the rationality of the proposed array structure is verified by comparing it with traditional coprime arrays and extended coprime array structures, as well as by conducting simulation experiments.

[0081] The coprime array constructed in this invention has improved in terms of continuous degrees of freedom and array aperture compared to traditional coprime arrays and extended coprime arrays. Figure 5 , Figure 6 The relationships between the root mean square error (RMSE), snapshot number, and signal-to-noise ratio (SNR) for DOA estimation are presented for three array structures. The traditional coprime array has M=6 and N=11, while the extended coprime array and the coprime array constructed in this invention have M=3 and N=11. All three array structures have a total of 16 array elements and 5 signal sources. Figure 5 The number of corresponding experimental snapshots increased uniformly from 50 to 1000, the signal-to-noise ratio was 10dB, the number of Monte Carlo simulations was 100, and a spatial smoothing-based method was used for DOA estimation. Figure 6 The corresponding experimental snapshot count was 500, the signal-to-noise ratio increased uniformly from -10dB to 30dB, the Monte Carlo simulation was 100, and spatial smoothing was used for DOA estimation. Both experimental results show that the improved coprime array structure yielded the lowest root mean square error in DOA estimation, indicating more accurate results.

[0082] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0083] Those skilled in the art will understand that the above description is merely a preferred embodiment of the present invention, and the features described in the various embodiments and / or claims of this disclosure can be combined or combined in various ways, even if such combinations or combinations are not explicitly described in this disclosure. This is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0084] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention. Clearly, those skilled in the art can make various alterations and modifications to the invention without departing from its spirit and scope. Thus, if these modifications and modifications of the invention fall within the scope of the claims and their equivalents, the invention is also intended to include these modifications and modifications.< / j>

Claims

1. An improved coprime array structure, the improved coprime array comprising three subarrays, namely subarray 1, subarray 2 and subarray 3, wherein subarray 1 has an element spacing of... Nd The number of array elements is M A uniform linear array, subarray 2 has an element spacing of... Md The number of array elements is N A uniform linear array, subarray 3 has an element spacing of . Nd The number of array elements is M A uniform linear array; M and N They are coprime integers. Its characteristics are, The array elements in subarray 1 and subarray 2 are arranged alternately, and the first array element of subarray 3 is spaced apart from the last array element of subarray 2. Nd Subarray 3 is considered as subarray 1 shifted to the right. (MN+NM)d The units are formed by superimposing subarray 3 with subarray 1 and subarray 2 to obtain an improved coprime array structure. The set of positions of subarray 1 is The set of positions for subarray 2 is The set of positions for subarray 3 is ;in l Indicates the third subarray l The improved coprime array element position set is: .

2. The improved coprime array structure according to claim 1, characterized in that, The M =3, N =11.

3. An improved method for estimating the DOA of coprime arrays, characterized in that, The improved coprime array DOA estimation method is implemented using the improved coprime array structure described in any one of claims 1-2. The improved coprime array DOA estimation method is as follows: S1. Obtain the difference virtual array by subtracting the set of array element positions in subarray 1, subarray 2, and subarray 3: ； S2. Summing the set of element positions in subarrays 1, 2, and 3 yields a summed virtual array: S sum+ ={ s i +s j |i,j= 1,2,...2 M+N- 1}， S sum- ={- s i -s j |i,j= 1,2,...2 M+N- 1}, obtain the summation virtual array; in, S sum+ For positive direction summation virtual array, S sum- A virtual array for summation in the negative direction; s i This represents the coordinates of the i-th element in the improved coprime array position set S. s j This represents the coordinates of the j-th element in the improved coprime array position set S; S3. Merge the difference virtual array elements and the summation virtual array elements to obtain the set of positions of the summation and difference virtual array elements. ; S4. Using the improved coprime array from the above steps as the receiving array, receive... K For each signal source, the received signal source covariance matrix is ​​vectorized to obtain the vector covariance matrix. v A new covariance matrix is ​​obtained by using a spatial smoothing method, and DOA estimation is performed based on the obtained new covariance matrix.

4. The improved DOA estimation method for coprime arrays according to claim 3, characterized in that, The differential virtual array element coordinates S obtained in S1 differ In -(2MN-M)d arrive (2MN-M)d Between, where continuous virtual array elements are in (-MN-N+ 1)d arrive (MN+N-1)d Between, among them, , The wavelength of the incident signal is 1.

5. The improved DOA estimation method for coprime arrays according to claim 4, characterized in that, The summation virtual array obtained in S2 S sum+ Its array element position coordinates are located at -(4MN-2M)d arrive (4MN-2M)d between.

6. A computer device, including a memory and a processor, characterized in that, The memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor performs the method described in any one of claims 3-5.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method according to any one of claims 3-5.

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