A sparse array layout method for direction of arrival estimation

Abstract

The present invention discloses a sparse array arrangement method for wave direction estimation. Based on the nested array, the method retains the dense sub-array with a spacing of half the wavelength of the incident signal on the left side, rearranges the sparse sub-array on the right side, and sets a larger interval between the left and right sub-arrays, and the size of the interval is determined by the arrangement of the right sub-array. The basic steps for its implementation are: determining the number of array elements of the array, obtaining the parameters of the array through the configuration formula for maximizing the array aperture, and then substituting the parameters into the general formula of the array to determine the spacing set of each array element, and finally converting the array element spacing set into the array element position set. Compared with the traditional sparse array improved based on the nested array, the present design method effectively improves the aperture of the array under the condition of the same number of array elements, and at the same time improves the accuracy of the array for wave direction estimation. It is particularly pointed out that the design method of the present invention has a more obvious improvement in the array direction finding performance for the arrangement with a large number of array elements (greater than or equal to 26).

Description

Technical Field

[0001] The present invention belongs to the field of array antenna design, and specifically is a sparse array arrangement method for wave direction estimation, which can be used for active and passive multi-target direction finding. By virtual transformation of the sparse array response, the physical array can be converted into a virtual array with additional array elements, thereby improving the direction finding performance of the array. Background Art

[0002] The traditional subspace-based DOA estimation algorithm uses a uniform linear array of N elements to find the direction of up to N-1 targets at the same time, and is limited by the Nyquist sampling theorem, which means that in the spatial domain, the spacing between adjacent elements cannot be greater than half the wavelength of the incident signal. In practical applications, the spacing between elements of a uniform linear array is fixed at half a wavelength, which leads to a strong mutual coupling effect between elements, and the array aperture is severely limited by the number of elements. In increasingly complex real environments, there are often many source signals, mutual interference between elements, and array element sensors are relatively expensive. Therefore, a uniform linear array is not the best choice for a direction finding array.

[0003] Unlike uniform linear arrays, sparse linear arrays allow the element spacing to be larger than half the wavelength of the incident signal. We can think of a sparse array as a sparse arrangement of linear arrays, or as an arrangement based on the original uniform linear array by removing elements at certain locations. Sparse arrays have many advantages. First, because the spacing between adjacent elements can be larger than half the wavelength, the mutual coupling effect between elements is greatly reduced, and the aperture of the array is also increased. In fact, with the same number of elements, the aperture of some sparse arrays is several times that of a uniform linear array. The increase in aperture also means an improvement in the direction-finding accuracy of the array. In addition, by performing a virtual transformation on the physical array response, the resulting virtual array allows for simultaneous direction-finding of more signals than the number of physical elements. Most sparse arrays can utilize O(N) physical elements to perform O(N) direction-finding on O(N) physical elements. 2 ) source signals for direction finding.

[0004] Research on sparse arrays can be traced back to the 1960s. Minimum redundancy arrays and minimum hole arrays were the first to be proposed and are representative sparse arrays. Although they have sufficiently low redundancy and can realize the underdetermined direction of arrival estimation of the array, the two are mainly defined in the form of explanations. The specific arrangement of the given number of array elements is completely obtained by computer search or table lookup. When the number of array elements is large, the time for computer exhaustive enumeration increases exponentially, and it is difficult to determine the specific arrangement of the array elements. In recent years, nested arrays and coprime arrays with closed mathematical expressions have been proposed. They can construct appropriate autocorrelation matrices that satisfy the Hermitian, Toplitz, and semi-positive definite characteristics through the second-order statistics of the array response, and realize the underdetermined direction of arrival estimation of the array. Their degrees of freedom and aperture have been significantly improved compared to uniform linear arrays. After that, researchers have proposed a variety of low-redundancy sparse arrays based on nested array improvements, such as improved nested arrays, augmented nested arrays, and unilateral sparse nested arrays, and the corresponding array apertures have also gradually increased. However, these arrays often show performance close to that of minimum redundant arrays in the case of small array element numbers, but when the number of array elements is large, the aperture growth is significantly different from that of minimum redundant arrays or sparse arrays with the largest known aperture. Therefore, designing an array with a closed mathematical form that is suitable for the case of a large number of array elements is of great significance for practical applications. Summary of the invention

[0005] The main purpose of the present invention is to provide a sparse array arrangement method for DOA estimation, which can significantly improve the array aperture and degree of freedom when the number of array elements is large. At the same time, by processing the physical array response, the corresponding virtual array response can be obtained, and the underdetermined DOA estimation can be performed using the virtual array response, which can obtain better DOA performance than the traditional sparse array.

[0006] To achieve the above purpose, the design ideas of the present invention are as follows:

[0007] A sparse array arrangement method for direction of arrival estimation, the sparse array arrangement comprising:

[0008] The left side shows a uniform linear array with uniform element spacing, where the element spacing is 1 times the half wavelength of the incident signal of the sparse array;

[0009] The right side shows sparse linear arrays with various array element spacings, where the array element spacings are all greater than 1 times the half wavelength of the incident signal of the sparse array and less than or equal to m times the half wavelength of the incident signal of the sparse array;

[0010] The spacing between the uniform linear array and the sparse linear array is ((t+2)m-5) times the half wavelength of the incident signal of the sparse array;

[0011] Determine the number of array elements M of the sparse array, obtain the array parameters m, t and c through the configuration formula of maximizing the array aperture, then substitute the array parameters m, t and c into the general formula of the array to determine the spacing set P of each array element, and finally convert the array element spacing set P into the array element position set P.

[0012] Optionally, the array general formula is:

[0013] P = {p1, p2, ..., p i ,…,p M-2 , p M-1}×d

[0014] ={1 m-1 , (t+2)m-5, (m-1) 2 ,m-2,m t , 2 c , m-1, (m-2) c}×d'

[0015] The i-th element of the set is P i , which represents the spacing between the i-th array element and the i+1-th array element in the sparse array, and the unit is d=λ / 2, where λ represents the wavelength of the incident signal of the sparse array; the set P is an ordered set, in which the superscript of the element represents the number of repetitions of the element;

[0016] The configuration formula for maximizing the array aperture is as follows:

[0017]

[0018] Optionally, converting the array element spacing set P into the array element position set S includes:

[0019] Place the first array element at position d, and place the remaining M-1 array elements in the order of the elements in the array element spacing set P; let S = {s1, s2, ..., s j , ..., s M-1 ,s M}, then the position of the jth array element

[0020] Optionally, by processing the second-order statistics of the sparse array response, the response of each element of the corresponding virtual array can be obtained. The position of the virtual array element is determined by the difference set D, and D is obtained by taking the difference between any two elements in the array element position set S, which can be written as follows:

[0021] D = {mn|m, n∈S};

[0022] m and n are any elements in the set S, and m=n is allowed; after deduplication, sorting and discarding the negative part of the difference set, a position set U of the virtual array element is formed.

[0023] Optionally, for a given number of array elements M and m>3, let the parameter value of the maximum aperture of the sparse array be m≈(9+4M) / 14, m is an odd number, t=M-2m; the resulting array aperture L is:

[0024]

[0025] Optionally, the parameter m of the sparse array determines the hole characteristics of the corresponding virtual array. When m=5 or m=7, the virtual array corresponding to the physical array has a hole at ((2m-4)×d), and the virtual arrays in other cases are hole-free; for every increase of 1 in the array parameter t, the aperture L of the sparse array increases by at least 2m×d; the parameter c depends on the parameter m, which is related to the number and arrangement of array elements of the sparse sub-array on the right.

[0026] Compared with the traditional sparse array structure, the present invention has the following advantages:

[0027] (1) When the number of array elements is large, such as an array with more than 26 elements, the design method described in the present invention can make the array have a larger aperture, which can effectively improve the accuracy and resolution of array direction finding;

[0028] (2) According to the number of array elements M, the optimal array parameters can be directly obtained through the formula, and the array aperture can also be directly calculated.

[0029] (3) In the DOA estimation of the sparse array, the physical array is first converted into a virtual array, and the DOA estimation algorithm is completed based on the virtual array. The number of signals that the virtual array can simultaneously measure depends on the number of array elements in the virtual array. The structure proposed in the present invention can generate more virtual array elements than the traditional sparse array structure, so it can achieve simultaneous direction finding of more signals. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] The accompanying drawings are used to provide a further understanding of the present disclosure and constitute a part of the specification. Together with the following specific embodiments, they are used to explain the present disclosure but do not constitute a limitation of the present disclosure. In the accompanying drawings:

[0031] Figure 1 2mg-SLA array structure schematic diagram proposed by the present invention, omitting the basic unit d, d is the half wavelength of the incident signal;

[0032] Figure 2 This is an array element weight distribution diagram of the extended nested array structure proposed by the present invention when the number of array elements is 34;

[0033] Figure 3 A comparison diagram of the aperture ratio of the structure designed by the present invention and six types of nested arrays with the number of array elements;

[0034] Figure 4 A comparison diagram of the root mean square error of the direction of arrival estimation of the structure designed by the present invention and six sparse arrays versus the signal-to-noise ratio;

[0035] Figure 5 The figure is a comparison of the root mean square error of the direction of arrival estimation of the structure designed by the present invention and six sparse arrays as a function of the signal sampling number. DETAILED DESCRIPTION

[0036] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments, and it cannot be determined that the specific implementation of the present invention is limited to these descriptions. For ordinary technicians in the technical field to which the present invention belongs, several simple deductions or substitutions can be made without departing from the concept of the present invention, which should be regarded as falling within the scope of protection of the present invention.

[0037] The unit of the array element spacing and sub-array spacing of the present invention is d=λ / 2, where λ represents the wavelength of the incident signal of the sparse array; that is, the half wavelength of the incident signal of the sparse array is used as the spacing unit.

[0038] The sparse array arrangement method for wave direction estimation of the present invention is a 2mgrowth Sparse Linear Array (2mg-SLA). The biggest feature of the array is that the array aperture increases by at least 2m×d when the number of array elements increases by d, where m is an array parameter. On the basis of the original nested array, a dense subarray with a spacing of 1 and a half wavelength on the left is retained, and the sparse subarray on the right is rearranged, and a larger interval is set between the left and right subarrays, and the size of the interval is determined by the arrangement of the right subarray. The entire array arrangement satisfies certain characteristics mathematically, so that it can be filled and restored by the response of the physical array elements, corresponding to the response of the virtual array elements, and constructing a virtual array response covariance matrix with a larger dimension (greater than the number of physical array elements). The fitted virtual covariance matrix satisfies the positive definite, Toplitz and Hermitian properties, so the wave direction of the source signal can be obtained using a traditional subspace algorithm (such as the MUSIC algorithm).

[0039] The steps for building the specific structure are as follows:

[0040] Step 1: Determine the number of array elements M of the sparse array, and obtain the parameters m, t and c of the sparse array through the configuration formula of maximizing the aperture of the sparse array. The parameter selection method is as follows:

[0041] And m is an odd number;

[0042] (1) Let (9+4M) / 14≈m0, with m0 rounded to one decimal place. If the integer part of m0 is an odd number, then m is the integer part of m0. If it is an even number, then m is the integer part of m0 plus 1.

[0043] (2) When m = 3, t = Mm-5 and c = 0. When m>3, t = M-2m and c = (m-5) / 2.

[0044] Step 2: Substitute the parameters m, t, and c into the general formula for the sparse array to determine the spacing of each array element. The general formula for the array is given in the form of an integer set P, where the i-th element of the set is P i , which represents the spacing between the i-th array element and the i+1-th array element in the sparse array, and the unit is d=λ / 2, where λ represents the wavelength of the incident signal of the array. The form of the set P is as follows:

[0045] P = {p1, p2, ..., p i , ..., p M-2 , p M-1}×d

[0046] ={1 m-1 , (t+2)m-5, (m-1) 2 ,m-2,m t , 2 c , m-1, (m-2) c}×d;

[0047] It is specially pointed out that the set is an ordered set, the superscript of the element indicates the number of repetitions of the element, and the value of the parameter is the value determined in step 1.

[0048] Step 3, convert the array element spacing set P into the array element position set S. Put the first array element at d. The left sub-array has m elements, so the position of the left sub-array is {1, 2, ..., m}×d. The right sub-array is larger than the left sub-array. The position of the first array element of the right sub-array is ((t+3)m-5)×d, and the sub-array includes 3 or 4 array element spacings, depending on the value of c=(m-5) / 2. When m=3 and m=5, c=0, including 3 spacings, namely m-1, m-2 and m, and the unit is d. Let The position s of the jth array element in the right subarray j for When m ≥ 7, c ≥ 1, including 4 spacings, namely m-1, m-2, m and 2, the unit is d. Similarly, the position of the jth element of the right subarray is

[0049] Step 4: By processing the second-order statistics of the sparse array response, the responses of each element of the corresponding virtual array can be obtained. The position of the virtual array element is determined by the difference set D, which is obtained by taking the difference between any two elements in the array element position set S, which can be written as follows:

[0050] D = {mn|m, n∈S};

[0051] m and n are any elements in the set S, and m=n is allowed; after deduplication, sorting and discarding the negative part of the difference set, a virtual array element position set U is formed. Assuming that the aperture of the virtual array is K×d, when m>7 or m=3, U=[0,K]×d, that is, the virtual array has no holes (array elements are missing); when m=5, U={[0,5]∪[7,K]}×d, that is, the virtual array has holes, and the position is 6d (the first array element is at 0d); when m=7, U={[0,9]∪[11,K]}×d, that is, the virtual array has holes, and the position is 10d. The interval here should be understood as a discrete numerical sequence, such as [0,K]={0,1,2,...,K}, and usually K+1>M, K+1 is the number of array elements in the virtual array, and M is the number of array elements in the physical array.

[0052] Step 5: Based on the sparse array position set S obtained in steps 3 and 4, the array position difference set D can be obtained. After removing duplicates, sorting, and discarding the negative parts of the set D, the position set of the virtual array element can be obtained. The sparse array proposed in the present invention mainly considers the case where the number of array elements is large. When m=9, combined with the optimal parameter configuration under a given number of array elements, the total number of array elements is reversely deduced to be 26. Therefore, the performance of the proposed sparse array is better when the number of array elements is greater than or equal to 26.

[0053] Step 6: further analyze the aperture L of the sparse array. When m=3, L=(10+6t)×d; when m>3,

[0054] Taking the incident signal frequency of 20 GHz and the total number of array elements M = 34 as an example, the construction process of 2mg-SLA is further explained and the sparse array aperture formula and the non-porousness of the sparse array corresponding to the virtual array are explained.

[0055] (1) Calculate the wavelength of the incident signal λ = c / f = (3.0 × 10 8 ) / (20×10 9 )=1.5cm; d is used to represent the unit of array element spacing, which is half wavelength, that is, d=λ / 2=7.5mm.

[0056] (2) According to the total number of array elements M=34 and M=2m+t given by the sparse array, when the virtual array aperture is maximum, m≈(9+4×M) / 14, m is the nearest odd number, so in this implementation, m=11, t=12.

[0057] (3) According to the parameter values ​​obtained in (2) and Figure 1 The schematic diagram of the 2mg-SLA sparse array structure shown can be used to obtain the interval set P of the array elements, as follows:

[0058] P={1,1,1,1,1,1,1,1,1,1,149,10,10,9,11,11,11,11,11,11,11,11,11,11,11,11,2,2,2,10,9,9,9}×d;

[0059] (4) Convert the array element spacing set P to the array element position S, place the first array element at position d, and then place the remaining array elements from left to right using the elements in the set P as spacing, with the basic unit of spacing being 7.5 mm. Therefore, the actual array element placement position is:

[0060] S={1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 160, 170, 180, 189, 200, 211, 222, 233, 244, 255, 266, 277, 288, 299, 310, 321, 323, 325, 327, 337, 346, 355, 364}×7.5mm;

[0061] (5) Based on the aperture formula for a given number of array elements M And the parameters obtained in (2) can be obtained as L = 363 × 7.5mm. The result is exactly the difference between the maximum element and the minimum element of the array element position set S obtained in (4). We further obtain the difference set D corresponding to the position set S through D = {mn|m, n∈S}, and make the following Figure 2 In the needle diagram shown, since the elements of D are symmetrically distributed about 0, only the non-negative half axis is shown. Its horizontal axis represents the different virtual array element positions (the unit d is omitted), and the vertical axis is the number of virtual array elements at the same position. For example, there are 34 virtual array elements at 0, because 0 can only be obtained by subtracting the 34 elements in S from itself, so there are only 34 virtual array elements, and the principle is the same for the rest of the cases. At the same time, the entire virtual array is hole-free, and the position of the virtual array elements starts from 0 and ends at L.

[0062] The direction finding performance of the sparse array proposed in the present invention is further described below in conjunction with a simulation example.

[0063] Embodiment 1:

[0064] The purpose of this example is to verify that the sparse array proposed in the present invention has a larger aperture and higher spatial freedom than the other five arrays under the same array elements, and is closer to the performance of ANAII-1. It should be supplemented that for a uniform linear array with M array elements and a spacing of half a wavelength, it can simultaneously find the direction of up to M-1 source signals, and M-1 is the size of its spatial freedom. The definition of the aperture of a linear array is the maximum array element spacing, which is equal to (M-1)×d in the above-mentioned uniform linear array. We find that the two differ in value by only unit d. For a sparse array, its spatial freedom is determined by the corresponding virtual array. The arrays proposed in this article and all the comparison arrays are physical arrays that are sparse arrays. After virtual changes, a virtual array with the same aperture as the original physical array can be obtained, and it is a uniform linear array with an array element spacing of d. Therefore, in this example, the aperture and degree of freedom of the sparse array also differ in value by only unit d. To some extent, the spatial freedom and aperture can be considered to be the same indicator. This example first compares the apertures of 7 arrays and the changes in aperture as the number of array elements increases for a given number of array elements M, and the results are shown in Table 1. The concept of aperture ratio is introduced, which characterizes the redundancy of the proposed sparse array. The smaller the aperture ratio, the lower the redundancy of the elements in the differential set D corresponding to the sparse array, that is, the more different elements in D, the larger the aperture of the array, or the higher the degree of freedom. Set M to vary from 20 to 800, with a step size of 80 array elements, and add a case where the number of array elements is 34. The aperture ratios γ of NA, ENA, ANAI-1, MISC, OS-SNA, 2mg-SLA and ANAII-1 are statistically analyzed, where γ = M 2 / L(M), where L(M) represents the array aperture formed by M array elements, and the comparison diagram is plotted on Figure 3 .

[0065] Table 1 Sparse array characteristics comparison table

[0066]

[0067] As shown in Table 1, the array proposed in the present invention is compared with 6 types of sparse arrays, all of which have corresponding virtual arrays without holes, and increasing the array aperture is one of their design purposes. The corresponding relationship between the array names and their abbreviations is as follows: Nested Array (NA), Enhanced Nested Array (ENA), Augmented Nested Array (ANAI-1), Maximum Inter-element Spacing Constraint (MISC), One-side Sparse Nested Array (OS-SNA), Augmented Nested Array (ANAII-1), and the array proposed in the present invention, 2m growth Sparse Linear Array (2mg-SLA). It is worth mentioning that the ANAII-1 array is the sparse array with the largest aperture under a given number of array elements (M>17) known so far. In the table, M is the total number of array elements, and L is the aperture of the linear array, in units of d. ΔL refers to the increment of the array aperture for each additional array element. The δ in the table represents a constant, which is mainly used to approximate a certain value. It does not affect the order of magnitude of the approximated value, but it can avoid too much discussion. It can be seen from the table that the parameter values, array aperture L, and aperture change ΔL of the seven sparse arrays are all functions of the number of array elements M, and they are different. The aperture of all arrays is M 2 After discarding the low-order terms and constant terms, the pore size of 2mg-SLA is Second only to the largest known sparse array aperture, ANAII-1 The rest of the arrays are ΔL reflects the change in the virtual array aperture of the sparse array as the number of array elements increases. As shown in Table 1, the ΔL of the proposed array is second only to that of ANAII-1.

[0068] from Figure 3 It can be seen that the aperture ratios of NA and ENA are always very similar, because their aperture formulas are almost the same. As the number of array elements increases, the aperture ratio of ANAI-1, MISC and OS-SNA increases significantly, which means that with each additional array element, the corresponding aperture increase rate decreases significantly. However, when the number of array elements is large, the aperture ratio of 2mg-SLA and ANAII-1 changes less, which has a clear advantage over other array aperture ratios. It is worth mentioning that when the number of array elements continues to increase, the aperture ratio of 2mg-SLA is maintained at around 3.5, and that of ANAII-1 is maintained at around 3, both of which are better than the aperture ratio of 4 of other arrays.

[0069] Embodiment 2:

[0070] The purpose of this example is to verify that the array proposed by the present invention has better direction finding performance than the other five arrays under the same array elements, and is closer to the performance of ANAII-1. Assume that there are 61 unrelated signal sources incident on the above sparse array in space, and the incident angle is uniformly distributed between -60° and 60°. The signal-to-noise ratio of the incident signal changes from -20dB to 20dB, the step size is 2dB, there are 21 points in total, the number of samples is K=1000, and 100 Monte Carlo experiments are performed.

[0071] The optimal parameter settings and apertures of each array with 34 elements are as follows:

[0072]

[0073] The results of the root mean square error of the seven sparse arrays for the direction of arrival estimation as the signal-to-noise ratio changes are as follows: Figure 4 As shown. It can be seen that for all arrays, when the signal-to-noise ratio is between -20dB and 0dB, the root mean square error decreases significantly with the increase of the signal-to-noise ratio. After 0dB, the root mean square error gradually stabilizes with the increase of the signal-to-noise ratio. The root mean square error curves after stabilization are NA, ENA, ANAI-1, MISC, OS-SNA, 2mg-SLA, and ANAII-1 from top to bottom. This is because, as described above, when the number of array elements is the same, ANAII-1 has the largest aperture, reaching 396, followed by the 2mg-SLA mentioned in the present invention, reaching 363, and the apertures of the remaining arrays are smaller than these two arrays. The aperture plays an important role in the estimation of the array's direction of arrival. When other experimental conditions are the same, the size of the aperture directly determines the direction-finding accuracy of the array.

[0074] Embodiment 3:

[0075] The purpose of this example is to verify that the array proposed in the present invention has better direction finding performance than the other five arrays under the same array elements, and is closer to the performance of ANAII-1. Assume that there are 61 unrelated signal sources in space incident on the above sparse array, and the incident angle is uniformly distributed between -60° and 60°. The signal-to-noise ratio of the incident signal is 0dB, and 100 Monte Carlo experiments are performed. The change of the sampling number is set to uneven sampling. The method of multi-sampling with small steps in the interval of low sampling number and large steps in the interval of high sampling number is adopted. The final set of sampling numbers is:

[0076] {50,100,150,200,250,300,400,600,800,1000,1300,1600,1900,2400,2800}, a total of 15 points.

[0077] The array parameter settings are the same as those in Experimental Example 2.

[0078] The results of the root mean square error of the seven sparse arrays for the direction of arrival estimation as the number of samples changes are shown in the figure below: Figure 5 As shown in the figure. After the sampling number reaches 500, all curves tend to be stable. The 2mg-SLA proposed by the present invention has the closest estimation error to ANAII-1 and is lower than the root mean square error of the other five structures. This is because 2mg-SLA and ANAII-1 have larger apertures than other arrays when the number of array elements is the same, which directly determines that they have better direction finding capabilities than other arrays.

[0079] In summary, the design method proposed in the present invention can obtain the optimal parameters of the array for arranging the array by formula calculation when only the total number of array elements is given. The array structure is similar to the nested array, and also includes a dense subarray on the left and a sparse subarray on the right. In addition to the type II augmented nested array, the array structure of the present invention has a higher aperture and better direction finding performance than the five popular sparse arrays. This advantage is particularly obvious when the number of array elements is large.

[0080] The preferred embodiments of the present disclosure are described in detail above in conjunction with the accompanying drawings; however, the present disclosure is not limited to the specific details in the above embodiments. Within the technical concept of the present disclosure, a variety of simple modifications can be made to the technical solution of the present disclosure, and these simple modifications all fall within the protection scope of the present disclosure.

[0081] It should also be noted that the various specific technical features described in the above specific embodiments can be combined in any suitable manner without contradiction. In order to avoid unnecessary repetition, the present disclosure will not further describe various possible combinations.

[0082] In addition, various embodiments of the present disclosure may be arbitrarily combined, and as long as they do not violate the concept of the present disclosure, they should also be regarded as the contents disclosed by the present disclosure.

Claims

1. A sparse array arrangement method for direction of arrival estimation, characterized in that: The sparse array setting includes: The left side shows a uniform linear array with uniform element spacing, where the element spacing is 1 times the half wavelength of the incident signal of the sparse array; The right side shows sparse linear arrays with various array element spacings, where the array element spacings are all greater than 1 times the half wavelength of the incident signal of the sparse array and less than or equal to m times the half wavelength of the incident signal of the sparse array; The spacing between the uniform linear array and the sparse linear array is ((t+2)m-5) times the half wavelength of the incident signal of the sparse array; Determine the number of array elements M of the sparse array, obtain the array parameters m, t and c through the configuration formula of maximizing the array aperture, then substitute the array parameters m, t and c into the general formula of the array to determine the spacing set P of each array element, and finally convert the array element spacing set P into the array element position set S.

2. The sparse array arrangement method for direction of arrival estimation according to claim 1, characterized in that: The general formula of the array is: The i-th element of the set is p i , which represents the spacing between the i-th array element and the i+1-th array element in the sparse array, and the unit is d=λ / 2, where λ represents the wavelength of the incident signal of the sparse array; the set P is an ordered set, in which the superscript of the element represents the number of repetitions of the element; The configuration formula for maximizing the array aperture is as follows: m>3 and m is an odd number; 3. The sparse array arrangement method for direction of arrival estimation according to claim 2, characterized in that: Converting the array element spacing set P into the array element position set S includes: Place the first array element at position d, and place the remaining M-1 array elements in the order of the elements in the array element spacing set P; let S = {s1, s2, ..., s j , ..., s M-1 ,s M }, then the position of the jth array element 4. The sparse array arrangement method for DOA estimation according to claim 2 or 3, characterized in that: By processing the second-order statistics of the sparse array response, the response of each element of the corresponding virtual array can be obtained. The position of the virtual array element is determined by the difference set D, which is obtained by taking the difference between any two elements in the array element position set S, which can be written as follows: D = {mn|m, n∈S}; m and n are any elements in the set S, and m=n is allowed; after deduplication, sorting and discarding the negative part of the difference set, a position set U of the virtual array element is formed.

5. The sparse array arrangement method for DOA estimation according to claim 2, characterized in that: For a given number of array elements M and m>3, let the parameter value of the maximum aperture of the sparse array be m≈(9+4M) / 14, m is an odd number, t=M-2m; the resulting array aperture L is:

6. The sparse array arrangement method for direction of arrival estimation according to claim 2, characterized in that: The parameter m of the sparse array determines the hole characteristics of the corresponding virtual array. When m=5 or m=7, the virtual array corresponding to the physical array has a hole at ((2m-4)×d), and the virtual arrays in other cases are hole-free; for every increase of 1 in the array parameter t, the aperture L of the sparse array increases by at least 2m×d; the parameter c depends on the parameter m, which is related to the number and arrangement of the array elements of the sparse subarray on the right.

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