Double-side multi-subarray filling co-prime array design method

Abstract

The invention discloses a double-side multi-subarray filling co-prime array design method, which comprises the following steps of: on the basis of an original co-prime array, taking a subarray I as a reference subarray, keeping the subarray I unchanged, dividing a subarray II into two parts, and respectively copying the two parts on two sides of the reference subarray for multiple times, so that a virtual aperture is expanded; meanwhile, the mutual coupling effect is effectively reduced by increasing the array element distance between the copied left subarray and the copied right subarray, then a supplementary subarray is introduced into the obtained double-side multi-subarray co-prime array, a double-side multi-subarray filling co-prime array is formed, a hole in the central part of a differential co-array of the double-side multi-subarray co-prime array is filled, and the double-side multi-subarray co-prime array is formed. Therefore, the continuous range of the differential common array is enlarged, and the degree of freedom and the uniform degree of freedom are remarkably improved. Besides, the double-side multi-subarray filling co-prime array shows an obvious sparse structure, the mutual coupling effect is obviously reduced, a balance can be obtained in high degree of freedom and low mutual coupling, and the DOA estimation performance is improved.

Description

Technical Field

[0001] The present invention belongs to the field of array signal processing, and relates to a sparse array design technology, in particular to a design method of a Bilateral Multi-Subarray Padded Coprime Array (BMSPCA). Background Art

[0002] DOA (Direction of Arrival) estimation is an important part of array signal processing and has been widely used in various fields such as radar, positioning, wireless communication, etc. In DOA estimation, the most commonly used array structure is the Uniform Liner Array (ULA). However, since the degree of freedom (DOF) is limited by the total number of array elements, it is difficult for the uniform linear array to achieve signal estimation in the underdetermined case. The non-uniform sparse array significantly improves the overall degree of freedom (DOF) through the virtual array element expansion technology and has low mutual coupling characteristics, which can significantly improve the DOA estimation performance and has received extensive attention. Two relatively common non-uniform sparse array structures are the nested array and the coprime array. Due to the existence of dense subarrays, the nested array has a high mutual coupling, which reduces the DOA estimation performance. Although the coprime array has a low mutual coupling effect, there are holes in its difference coarray, resulting in limited uniform degree of freedom (uDOF), which in turn affects the performance of the continuous segment. Based on these two non-uniform sparse arrays, two types of variants have emerged, namely the improved nested array and the improved coprime array, which make up for the shortcomings of the original arrays and improve the DOA estimation performance from two aspects of reducing mutual coupling and increasing the degree of freedom (DOF) respectively.

[0003] For the improved coprime array, some array structures have improved the uniform degree of freedom to a certain extent. However, compared with the improved nested array, the improvement of its uniform degree of freedom is still relatively limited. The key problem in non-uniform sparse arrays is to consider both the uniform degree of freedom and the mutual coupling effect of the array. Although the improved coprime array has a strong anti-mutual coupling ability, there are a large number of holes in its difference coarray, resulting in limited uniform degree of freedom. Therefore, filling the holes in the difference coarray can increase the uniform degree of freedom and thus improve the DOA estimation performance. Summary of the Invention

[0004] Aiming at the deficiencies of the existing coprime arrays, the present invention provides a design method of a bilateral multi-subarray padded coprime array. This method can significantly improve the degree of freedom (DOF) and uniform degree of freedom (uDOF) of the designed coprime array, and can effectively reduce the mutual coupling effect, thereby greatly improving the DOA estimation performance.

[0005] The technical solution adopted by the present invention to solve the above technical problems is as follows: A design method for a bilateral multi-subarray filled coprime array, which is characterized by including the following steps:

[0006] Step 1: Set the element spacing of subarray one in the original coprime array to Md and the number of elements to N, the element spacing of subarray two to Nd and the number of elements to M. Subarray one and subarray two share the first element, which is used as a reference element, and the reference element is located at the origin of the coordinate system, that is, the position of the reference element is 0. Among them, 3 ≤ M < N, and M and N are coprime numbers, d represents the reference spacing unit, λ represents the wavelength of the incident signal incident on the original coprime array;

[0007] Step 2: On the basis of the original coprime array, construct a bilateral multi-subarray coprime array. The specific process is as follows: Keep subarray one unchanged and use it as the reference subarray; then extract subarray two, and divide all the elements of subarray two into two parts. The first part contains M1 elements, and the second part contains M2 elements, where, M1 > 1, M2 ≥ 1, M = M1 + M2, is the ceiling symbol, is the floor symbol; then deploy the M1 elements of the first part on the left side of the reference subarray at an element spacing of 2Nd to form a left subarray, and deploy the M2 elements of the second part on the right side of the reference subarray at an element spacing of 2Nd to form a right subarray; then copy and add several identical left subarrays on the left side of the left subarray, and copy and add several identical right subarrays on the right side of the right subarray, so that there are k left subarrays on the left side of the reference subarray and k right subarrays on the right side. Set the spacing between the reference subarray and its adjacent left subarray to L1, the spacing between the reference subarray and its adjacent right subarray to L2, the spacing between two adjacent left subarrays to L3, and the spacing between two adjacent right subarrays to L4. Thus, a new sparse array is constructed and defined as a bilateral multi-subarray coprime array, where k ≥ 1;

[0008] Step 3: Obtain the position set formed by the positions of all the elements of the bilateral multi-subarray coprime array representation of, where, ∪ is the union operation symbol, represents the position set formed by the positions of all the elements of the reference subarray, <·> represents taking all integers within the range, represents the position set formed by the positions of all the elements of k left subarrays, represents the position set formed by the positions of all the elements of the i-th left subarray. The left subarray closest to the reference subarray is the first left subarray, Denote the position set formed by the positions of all the array elements of k right sub-arrays. Denote the position set formed by the positions of all the array elements of the i-th right sub-array. The right sub-array closest to the reference sub-array is the 1st right sub-array.

[0009] Step 4: Determine the values of L1, L2, L3, and L4 to determine the positions of each array element of the bilateral multi-sub-array co-prime array. Among them, the determination method of the values of L3 and L4 is as follows: If M is even, then L3 = L4 = M + 2N; if M is odd, then L3 = M + N, L4 = M + 3N; the values of L1 and L2 satisfy the condition: to obtain the difference co-array with the largest continuous range, that is, L1 = M + N, L2 = M + 2N.

[0010] Step 5: On the basis of Step 4, determine the position set formed by the positions of all the holes in the interval [0, Q] in the difference co-array of the bilateral multi-sub-array co-prime array, denoted as where a ∈ <1, N - 2>, b ∈ <1, M - 1>, c ∈ <0, M2 - 1>, g ∈ <1, M2 - 1>, \ means exclusion. If M is even, then Q = k(MN + M) + MN - M. If M is odd, then Q = k(MN + M) + MN, h3 = {N + M(N + 1) < 1, k>, k(MN + M) + 2N < 1, M2}.

[0011] Step 6: Construct a supplementary sub-array, and set the position set formed by the positions of all the array elements of the supplementary sub-array as where, when M = 3, b1 ∈ <1, M2 + 1>; when M ≥ 4, b1 ∈ <1, M2>.

[0012] Step 7: Incorporate the supplementary sub-array into the bilateral multi-sub-array co-prime array to form a bilateral multi-sub-array filled co-prime array, and denote the position set formed by the positions of all the array elements of the bilateral multi-sub-array filled co-prime array as

[0013]

[0014] Compared with the prior art, the advantages of the present invention are as follows: Based on the original co-prime array, sub-array one is used as the reference sub-array and remains unchanged. By dividing sub-array two into two parts and replicating them multiple times on both sides of the reference sub-array, the virtual aperture is expanded. At the same time, the mutual coupling effect is effectively reduced by increasing the element spacing of the replicated left sub-array and right sub-array. Then, a supplementary sub-array is introduced into the obtained bilateral multi-sub-array co-prime array to fill the holes in the central part of the difference co-array of the bilateral multi-sub-array co-prime array, thereby increasing the continuous range of the difference co-array and significantly improving the degrees of freedom and the uniform degrees of freedom. In addition, the bilateral multi-sub-array filled co-prime array exhibits a significant sparse structure, significantly reducing the mutual coupling effect. The bilateral multi-sub-array filled co-prime array can achieve a balance between high degrees of freedom and low mutual coupling, improving the DOA estimation performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is the overall implementation block diagram of the method of the present invention;

[0016] Figure 2 is the schematic diagram of the two-dimensional representation structure of the original co-prime array;

[0017] Figure 3 is the schematic diagram of the composition of the bilateral multi-sub-array co-prime array;

[0018] Figure 4 is the two-dimensional representation structure and the difference co-array schematic diagram of the bilateral multi-sub-array co-prime array and the bilateral multi-sub-array filled co-prime array when M = 4, N = 5, and k = 2;

[0019] Figure 5 is the result of the change of RMSE with the number of snapshots under the mutual coupling condition when observing different configurations of the bilateral multi-sub-array filled co-prime array with the same total number of array elements using the SS-MUSIC algorithm. Among them, the array configurations (M, N, k) of BMSPCA1 and BMSPCA2 are (9, 10, 1) and (5, 11, 2) respectively, the total number of array elements is 23, the mutual coupling coefficient |c1| = 0.3, the coupling threshold B = 100, the number of signal sources K = 26, and the number of Monte Carlo times is set to J = 1000. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0020] The present invention will be further described below with reference to the accompanying drawings and embodiments, so that those skilled in the art can implement it according to the description in the specification. The protection scope of the present invention is not limited to this specific implementation.

[0021] A design method of a bilateral multi-sub-array filled co-prime array proposed by the present invention, the overall implementation block diagram of which is as Figure 1 shown, and it includes the following steps:

[0022] Step 1: Set the element spacing of Subarray 1 in the original coprime array as Md and the number of elements as N, the element spacing of Subarray 2 as Nd and the number of elements as M. Subarray 1 and Subarray 2 share the first element, which is used as the reference element, and the reference element is located at the origin of the coordinate system, that is, the position of the reference element is 0. Among them, 3 ≤ M < N, and M and N are coprime numbers, and d represents the reference spacing unit. λ represents the wavelength of the incident signal incident on the original coprime array. Both Subarray 1 and Subarray 2 are uniform linear arrays. Since Subarray 1 and Subarray 2 share the first element, the total number of elements in the original coprime array is M + N - 1.

[0023] Figure 2 The two-dimensional representation structure schematic diagram of the original coprime array is given.

[0024] Step 2: On the basis of the original coprime array, construct a Bilateral Multi-Subarray Coprime Array (BMSCA). The specific process is as follows: Keep Subarray 1 unchanged and use it as the reference subarray; then extract Subarray 2, and divide all the elements of Subarray 2 into two parts. The first part contains M1 elements, and the second part contains M2 elements, where, M1 > 1, M2 ≥ 1, M = M1 + M2, is the ceiling symbol, is the floor symbol; then deploy the M1 elements of the first part on the left side of the reference subarray with an element spacing of 2Nd to form the left subarray, and deploy the M2 elements of the second part on the right side of the reference subarray with an element spacing of 2Nd to form the right subarray; then copy and add several identical left subarrays on the left side of the left subarray, and copy and add several identical right subarrays on the right side of the right subarray, so that there are k left subarrays on the left side of the reference subarray and k right subarrays on the right side. Set the spacing between the reference subarray and its adjacent left subarray as L1, the spacing between the reference subarray and its adjacent right subarray as L2, the spacing between two adjacent left subarrays as L3, and the spacing between two adjacent right subarrays as L4. Thus, a new sparse array is constructed and defined as the Bilateral Multi-Subarray Coprime Array. Among them, k ≥ 1, and the total number of elements in the Bilateral Multi-Subarray Coprime Array is kM + N.

[0025] Since the Bilateral Multi-Subarray Coprime Array has multiple left subarrays copied on the left side of the reference subarray and multiple right subarrays copied on the right side, the virtual aperture is expanded. Figure 3The composition schematic diagram of the constructed bilateral multi-subarray co-prime array is given. In the figure, the array represented by the triangular symbol is the reference subarray, that is, subarray one that remains in the original position unchanged. The array represented by the circular symbol on the left side of the triangular symbol is the left subarray, and the array represented by the circular symbol on the right side of the triangular symbol is the right subarray.

[0026] Step 3: Obtain the position set formed by the positions of all the array elements of the bilateral multi-subarray co-prime array representation where, ∪ is the union operation symbol represents the position set formed by the positions of all the array elements of the reference subarray <·> represents taking all integers within the range. <0, N - 1> is equivalent to taking 0, 1, 2, ……, N - 1 represents the position set formed by the positions of all the array elements of k left subarrays represents the position set formed by the positions of all the array elements of the i-th left subarray. The left subarray closest to the reference subarray is the 1st left subarray represents the position set formed by the positions of all the array elements of k right subarrays represents the position set formed by the positions of all the array elements of the i-th right subarray. The right subarray closest to the reference subarray is the 1st right subarray

[0027] Step 4: Determine the values of L1, L2, L3, and L4 to determine the position of each array element of the bilateral multi-subarray co-prime array. Among them, the determination method of the values of L3 and L4 is: if M is even, then L3 = L4 = M + 2N; if M is odd, then L3 = M + N, L4 = M + 3N; the values of L1 and L2 satisfy the condition: so as to obtain the difference co-array with the largest continuous range, that is, L1 = M + N, L2 = M + 2N.

[0028] Step 5: On the basis of Step 4, determine the position set formed by the positions of all the holes within the interval [0, Q] in the difference co-array of the bilateral multi-subarray co-prime array, denoted as where h 11 、h 12 、h 13 、h 21 、h 22 、h3 are all introduced intermediate variables. a ∈ <1, N - 2>, b ∈ <1, M - 1>, c ∈ <0, M2 - 1>, g ∈ <1, M2 - 1>, \ represents exclusion. If M is even, then Q = k(MN + M) + MN - M If M is odd, then Q = k(MN + M) + MN, h3 = {N + M(N + 1) < 1,k>, k(MN + M) + 2N < 1,M2>}.

[0029] Step 6: Construct a supplementary subarray, and set the position set formed by the positions of all the array elements of the supplementary subarray as where, when M = 3, b1 ∈ <1,M2 + 1>; when M ≥ 4, b1 ∈ <1,M2>.

[0030] Here, the constructed supplementary subarray can completely fill the holes in the difference coarray of the bilateral multi-subarray coprime array whose positions belong to When M is even, it can also completely fill the holes whose positions belong to of the holes.

[0031] Step 7: Incorporate the supplementary subarray into the bilateral multi-subarray coprime array to form a bilateral multi-subarray padded coprime array (BMSPCA), and denote the position set formed by the positions of all the array elements of the bilateral multi-subarray padded coprime array as where, when 3 < M < N, the total number of array elements of the bilateral multi-subarray padded coprime array is When N > M = 3, the total number of array elements of the bilateral multi-subarray padded coprime array is

[0032] Using the method of the present invention, based on the original coprime array, taking subarray one of the original coprime array as the reference subarray and keeping it unchanged, and by dividing subarray two into two parts and replicating them multiple times on both sides of the reference subarray to expand the virtual aperture, and at the same time effectively reducing the mutual coupling effect by increasing the element spacing of the replicated left subarray and right subarray, a bilateral multi-subarray coprime array is obtained; then a supplementary subarray is introduced to fill the holes in the central part of the difference coarray of the bilateral multi-subarray coprime array, increasing the continuous range of the difference coarray, significantly improving the degrees of freedom and the uniform degrees of freedom, thereby improving the DOA estimation performance.

[0033] Figure 4 The (a) part of Figure 4 The upper figure of Figure 4 The (b) part of Figure 4 The lower figure of Figure 4Among them, sub1 represents the elements in the reference subarray, sub2 represents the elements in the left subarray, sub3 represents the elements in the right subarray, lags represents the virtual elements in the difference coarray, and sub4 represents the elements in the supplementary subarray. From Figure 4 It can be found that after incorporating the supplementary subarray into the bilateral multi-subarray co-prime array, the holes in the central part of the difference coarray are filled, and the continuous range of the difference coarray increases, significantly improving the degrees of freedom and the uniform degrees of freedom.

[0034] Calculate the degrees of freedom and the uniform degrees of freedom of the bilateral multi-subarray filled co-prime array as follows: When M is even, the degrees of freedom DOF = 2k(MN + 2M - 1) + (M + 1)(N - 1) + 2M^2 + 1; when M is odd, the degrees of freedom DOF = 2k(MN + 2M - 1) + (M + 1)(N - 1) + 2M^2 + 3. The continuous range of the difference coarray of the bilateral multi-subarray filled co-prime array is [-k(MN + M) - M - N + 1, k(MN + M) + M + N - 1], that is, the uniform degrees of freedom uDOF of the bilateral multi-subarray filled co-prime array = 2k(MN + M) + 2M + 2N - 1.

[0035] In an actual mutually coupled environment, calculate the first three weight functions w(1), w(2), and w(3) of the difference coarray of the bilateral multi-subarray filled co-prime array. These three weight functions will have a negative impact on DOA estimation. It can be found that the values of w(1), w(2), and w(3) are small, reducing the mutual coupling; and as the number of elements N increases, only the value of w(3) changes when M = 3, and w(1), w(2), and w(3) when M > 3 remain unchanged. This means that the bilateral multi-subarray filled co-prime array designed by the present invention does not have the problem that the mutual coupling effect increases significantly with the increase in the number of elements like the existing improved co-prime array. This will be a unique advantage of the bilateral multi-subarray filled co-prime array designed by the present invention. The bilateral multi-subarray filled co-prime array designed by the present invention achieves a balance between high degrees of freedom and low mutual coupling, improving the DOA estimation performance.

[0036] Figure 5 The results of the change of RMSE with the number of snapshots under mutual coupling conditions for different configurations of the bilateral multi-subarray filled co-prime array with the same total number of observed elements when using the SS-MUSIC algorithm are given. Among them, the array configurations (M, N, k) of BMSPCA1 and BMSPCA2 are (9, 10, 1) and (5, 11, 2) respectively, the total number of elements is 23, the mutual coupling coefficient |c1| = 0.3, the coupling threshold B = 100, the number of signal sources K = 26, and the number of Monte Carlo runs is set to J = 1000. From Figure 5It can be found that the RMSE of BMSPCA1 decreases relatively slowly, while for BMSPCA2, due to the combination of a large uniform degree of freedom and low mutual coupling, its RMSE reaches the lowest value at a large number of snapshots.

Claims

1. A design method for a bilateral multi-subarray filling co-prime array, characterized in that Including the following steps: Step 1: Set the element spacing of Sub-array 1 in the original coprime array as Md and the number of elements as N, the element spacing of Sub-array 2 as Nd and the number of elements as M. Sub-array 1 and Sub-array 2 share the first element, which is used as the reference element, and the reference element is located at the origin of the coordinate system, that is, the position of the reference element is 0. Among them, 3 ≤ M < N, and M and N are coprime numbers, and d represents the reference spacing unit. λ represents the wavelength of the incident signal incident on the original coprime array; Step 2: Based on the original co-prime array, construct a bilateral multi-subarray co-prime array. The specific process is as follows: Keep subarray one unchanged and use it as the reference subarray. Then extract subarray two and divide all the elements of subarray two into two parts. The first part contains M1 elements, and the second part contains M2 elements, where, M1 > 1, M2 ≥ 1, M = M1 + M2, is the ceiling symbol, is the floor symbol; then deploy the M1 elements of the first part on the left side of the reference subarray with an element spacing of 2Nd to form the left subarray, and deploy the M2 elements of the second part on the right side of the reference subarray with an element spacing of 2Nd to form the right subarray; then copy and add several identical left subarrays on the left side of the left subarray, and copy and add several identical right subarrays on the right side of the right subarray, so that there are k left subarrays on the left side of the reference subarray and k right subarrays on the right side of the reference subarray, and set the spacing between the reference subarray and its adjacent left subarray as L1, the spacing between the reference subarray and its adjacent right subarray as L2, the spacing between two adjacent left subarrays as L3, and the spacing between two adjacent right subarrays as L4. Thus, a new sparse array is constructed and defined as a bilateral multi-subarray co-prime array, where, k ≥ 1; Step 3: Obtain the position set formed by the positions of all the array elements of the bilateral multi-subarray co-prime array representation, where ∪ is the union operation symbol, denotes the position set formed by the positions of all the array elements of the reference subarray, ·> denotes all the integers within the range, denotes the position set formed by the positions of all the array elements of the k left subarrays, denotes the position set formed by the positions of all the array elements of the i-th left subarray, and the left subarray closest to the reference subarray is the 1st left subarray, denotes the position set formed by the positions of all the array elements of the k right subarrays, denotes the position set formed by the positions of all the array elements of the i-th right subarray, and the right subarray closest to the reference subarray is the 1st right subarray, Step 4: Determine the values of L1, L2, L3, and L4 to determine the position of each element of the bilateral multi-subarray coprime array. Among them, the determination method of the values of L3 and L4 is as follows: If M is even, then L3 = L4 = M + 2N; if M is odd, then L3 = M + N, L4 = M + 3N; the values of L1 and L2 satisfy the condition: enabling the largest continuous range of difference coarray to be obtained, that is, L1 = M + N, L2 = M + 2N; Step 5: On the basis of Step 4, determine the position set formed by the positions of all holes in the difference coarray of the bilateral multi-subarray co-prime array within the interval [0, Q], denoted as where a ∈ <1, N - 2>, b ∈ <1, M - 1>, c ∈ <0, M2 - 1>, g ∈ <1, M2 - 1>, \ represents exclusion. If M is even, then Q = k(MN + M) + MN - M; if M is odd, then Q = k(MN + M) + MN, h3 = {N + M(N + 1)<1, k>, k(MN + M) + 2N<1, M2>}; Step 6: Construct a supplementary subarray, and set the position set formed by the positions of all elements of the supplementary subarray as where, when M = 3, b1 ∈ <1, M2 + 1>; when M ≥ 4, b1 ∈ <1, M2>; Step 7: Incorporate the supplementary subarray into the bilateral multi-subarray co-prime array to form a bilateral multi-subarray filled co-prime array, and denote the position set formed by the positions of all the array elements of the bilateral multi-subarray filled co-prime array as

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