Complementary co-prime array and DOA estimation method thereof
By designing complementary and mutually exclusive arrays, the virtual array holes are filled with the arrangement and translation of the sub-arrays, the problem of uncontrollable freedom and mutual coupling leakage of nested arrays and mutually exclusive arrays is solved, and the accuracy of DOA estimation is improved.
Patent Information
- Application Number
- CN202411201580.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-08-29
- Publication Date
- 2024-12-27
AI Technical Summary
The degree of freedom and mutual coupling leakage of nested class arrays and coefficient class arrays are uncontrollable, resulting in low accuracy of DOA estimation.
Design a complementary and mutually exclusive array, through the first sub-array, the second sub-array, the third sub-array and the fourth sub-array arranged from left to right, the first sub-array includes the first sparse sub-array and the first Unit sub-array, the second sub-array includes U1+1 array element, the third sub-array and the fourth sub-array both include 2 array elements, and the fourth sub-array is formed by translation of the third sub-array and adding it to the mutual In the mass array, virtual array holes are filled to build a complementary mutually qualitative array to improve freedom and reduce mutually coupled leakage.
The controllable balance between the degrees of freedom of complementary and mutually coupled leakage of the complementary and mutually coupled leakage is achieved, and the accuracy of DOA estimation is improved, which is more efficient than traditional methods.
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Figure CN119199717A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of array signal processing, and in particular to a complementary coprime array and a direction of arrival (DOA) estimation method thereof. Background Art
[0002] As a key research direction in the field of array signal processing, spatial spectrum estimation refers to distinguishing multiple signals that arrive at a certain area at the same time in space and determining the location of these signals, also known as DOA estimation or direction finding. In practical application scenarios, target signals are usually diverse, so it is of great significance to adopt a suitable array structure and corresponding DOA estimation algorithm. The DOA estimation algorithm based on uniform array requires that the array element spacing cannot exceed half the wavelength of the incident signal. In order to increase the array aperture, the commonly used method is to increase the number of array elements. However, the more array elements there are, the longer the array takes to process the received data, which increases the complexity of the system. When the array element spacing is too small, too many array elements will cause mutual coupling, and the processing method is also more complicated. In response to the above problems, researchers proposed the concept of sparse array. Sparse array adopts a non-uniform distribution arrangement between array elements, which can increase the array aperture and improve the array degree of freedom, so that DOA estimation can be performed for sources greater than the number of array elements. However, the structural design of coprime arrays in sparse arrays is not mature enough, and there are still many problems that deserve further study, such as the discontinuity of the constructed virtual array and the existence of holes. Therefore, improving the coprime array structure has important research significance and value in both theory and practical application.
[0003] At present, the array used for DOA estimation is a classical sparse array, which includes nested arrays and coprime arrays. Nested arrays can be uniquely determined by analytical expressions, but there are many small-pitch array element pairs in nested arrays, which are easily affected by mutual coupling effects; the K-times extended coprime array (KECA) in the coprime array increases the physical array aperture, analyzes the hole positions in the KECA virtual array, and constructs a hole-free mutual difference virtual array by configuring two dense subarrays to fill the holes, which improves the degree of freedom. However, the introduction of dense subarrays also increases the mutual coupling leakage of the array; this leads to an uncontrollable imbalance between the degree of freedom and mutual coupling leakage of nested arrays and coprime arrays, which in turn makes the accuracy of the estimated DOA low. Summary of the invention
[0004] The purpose of the embodiment of the present invention is to provide a complementary coprime array and a DOA estimation method thereof, so as to solve the problem of uncontrollable imbalance between degrees of freedom and mutual coupling leakage of nested arrays and coprime arrays, and low accuracy of estimated DOA.
[0005] To solve the above technical problems, the embodiments of the present invention provide the following technical solutions:
[0006] A first aspect of the present invention provides a complementary coprime array, the complementary coprime array comprising a first subarray, a second subarray, a third subarray and a fourth subarray arranged in sequence from left to right; the first subarray comprises a first sparse subarray and a first unit subarray, the first sparse subarray comprises N array elements, and the N array elements are evenly arranged, the array element spacing of the first sparse subarray is M, and the first unit subarray comprises 1 array element; the second subarray comprises U1+1 array elements, and the array element spacing of the second subarray is N d ; The third sub-array and the fourth sub-array each include 2 array elements, and the array element spacing of the third sub-array and the fourth sub-array is N d +3; the distance between the first subarray and the second subarray is N d +3, the distance between the second sub-array and the third sub-array is N d , the distance between the third sub-array and the fourth sub-array is N d -5, the fourth sub-matrix is formed by translating the third sub-matrix to the right by 2N distance units, and N and M are relatively prime numbers.
[0007] A second aspect of the present invention provides a DOA estimation method for a complementary coprime array, the DOA estimation method comprising:
[0008] According to the coprime arrays, the first unit sub-array and the third sub-array are constructed;
[0009] Add the first unit sub-matrix and the third sub-matrix to the coprime array to obtain a filled array;
[0010] Shift the third sub-array to the right by 2N distance units to obtain the fourth sub-array;
[0011] Add the fourth subarray to the filled array to generate a complementary coprime array;
[0012] According to the complementary coprime array, a receiving signal model is established, and a receiving signal is obtained according to the source signal, and the receiving signal is an actual signal that conforms to the receiving signal model;
[0013] The DOA of the received signal is estimated based on the spatial smoothing multiple signal classification algorithm.
[0014] Compared with the prior art, the complementary coprime array provided by the present invention includes a first subarray, a second subarray, a third subarray and a fourth subarray arranged from left to right in sequence; the first subarray includes a first sparse subarray and a first unit subarray, the first sparse subarray includes N array elements, and the N array elements are evenly arranged, the array element spacing of the first sparse subarray is M, and the first unit subarray includes 1 array element; the second subarray includes U1+1 array elements, and the array element spacing of the second subarray is N d; The third sub-array and the fourth sub-array each include 2 array elements, and the array element spacing of the third sub-array and the fourth sub-array is N d +3; the distance between the first subarray and the second subarray is N d +3, the distance between the second sub-array and the third sub-array is N d , the distance between the third sub-array and the fourth sub-array is N d -5, and the fourth subarray is formed by translating the third subarray to the right by 2N distance units. In this way, by using the first subarray, the second subarray, the third subarray and the fourth subarray arranged from left to right, the original coprime array can be expanded to fill the virtual array holes corresponding to the original coprime array, so that the degree of freedom of the complementary coprime array and the controllable balance of the mutual coupling leakage are achieved, thereby making the estimated DOA more accurate. BRIEF DESCRIPTION OF THE DRAWINGS
[0015] By reading the detailed description below with reference to the accompanying drawings, the above and other objects, features and advantages of the exemplary embodiments of the present invention will become readily understood. In the accompanying drawings, several embodiments of the present invention are shown in an exemplary and non-limiting manner, and the same or corresponding reference numerals represent the same or corresponding parts, wherein:
[0016] Figure 1 A schematic diagram of the structure of a complementary coprime array is shown;
[0017] Figure 2 The structure diagram of the target complementary coprime array is schematically shown;
[0018] Figure 3 A flow chart of a DOA estimation method for a complementary coprime array is schematically shown;
[0019] Figure 4 A schematic diagram showing the comparison of degrees of freedom for sparse arrays is shown schematically;
[0020] Figure 5 A schematic diagram of sparse array mutual coupling leakage comparison is schematically shown;
[0021] Figure 6 The diagram schematically shows the variation of the root mean square error with the signal-to-noise ratio under the condition of mutual coupling;
[0022] Figure 7 The diagram schematically shows the variation of the root mean square error with the number of snapshots in the presence of mutual coupling. DETAILED DESCRIPTION
[0023] The exemplary embodiments of the present invention will be described in more detail below with reference to the accompanying drawings. Although the exemplary embodiments of the present invention are shown in the accompanying drawings, it should be understood that the present invention can be implemented in various forms and should not be limited by the embodiments described herein. On the contrary, these embodiments are provided in order to enable a more thorough understanding of the present invention and to fully convey the scope of the present invention to those skilled in the art.
[0024] It should be noted that, unless otherwise specified, the technical terms or scientific terms used in the present invention should have the common meanings understood by those skilled in the art to which the present invention belongs.
[0025] The method in the embodiment of the present invention is described in detail below.
[0026] Figure 1 is a structural diagram of a complementary coprime array in an embodiment of the present invention, see Figure 1 As shown, the complementary coprime array may include:
[0027] The first sub-array, the second sub-array, the third sub-array and the fourth sub-array are arranged from left to right; the first sub-array includes the first sparse sub-array and the first unit sub-array, the first sparse sub-array includes N array elements, and the N array elements are evenly arranged, the array element spacing of the first sparse sub-array is M, and the first unit sub-array includes 1 array element; the second sub-array includes U1+1 array elements, and the array element spacing of the second sub-array is N d ; The third sub-array and the fourth sub-array each include 2 array elements, and the array element spacing of the third sub-array and the fourth sub-array is N d +3; the distance between the first subarray and the second subarray is N d +3, the distance between the second sub-array and the third sub-array is N d , the distance between the third sub-array and the fourth sub-array is N d -5, the fourth sub-matrix is formed by translating the third sub-matrix to the right by 2N distance units, and N and M are relatively prime numbers.
[0028] The total number of array elements in the complementary coprime array is Q.
[0029] In this embodiment, the set of physical array element positions of the complementary coprime array is:
[0030]
[0031] in, is the set of physical element positions of complementary coprime arrays, is the set of physical array element positions of the first subarray, is the set of physical array element positions of the second subarray, is the set of physical array element positions of the third subarray, is the set of physical element positions of the fourth sub-array, n1∈{0,1,2,…,N-1}, n1 is the number of any one of the N elements, n2∈{0,1,2,…,U1}, n2 is the number of any one of the U1+1 elements, n3∈{0,1}, n3 is the number of any one of the 2 elements, n4∈{0,1}, n4 is the number of any one of the 2 elements, U1=QN-6≥2, U1 is the number of elements of the second sub-array minus one, U2=(QN-1)N, U2 is the starting position of the third sub-array, Q is the total number of elements of the complementary coprime array, and N is the number of elements of the first sparse sub-array.
[0032] Specifically, the first sub-array includes a first sparse sub-array and a first unit sub-array, and the physical array element position set of the first sub-array is expressed as is the set of physical array element positions of the first sparse sub-array, is the set of physical array element positions of the first unit subarray.
[0033] Figure 1 The structure diagram of the complementary coprime array is schematically shown, where Figure (a) is a complementary coprime array, array parameters (Q, N) = (17, 8), the total number of array elements of the complementary coprime array Q = 17, and the blue squares, hollow triangles, diamonds, hexagons and solid triangles represent as well as The black circles represent the virtual elements of the complementary coprime array, and the red crosses represent the holes in the equivalent differential array corresponding to the complementary coprime array. The set of physical element positions of the complementary coprime array The physical array element position set of the first sparse subarray The physical array element position set of the first unit subarray The physical element position set of the second subarray The physical array element position set of the third subarray The physical array element position set of the fourth subarray Figure (b) is The position of the elements in the difference set, it can be seen The middle and both ends of the difference set are discontinuous, and the location set of the holes is Figure (c) is The elements of the difference set, Figure (d) is The elements of the difference set, the hole position set Depend on Fill the elements of the difference set and set the position of the hole Depend on The elements of the difference set are filled, so, All the holes in the mutual difference array interval are filled, so the continuous virtual array element interval is [-56,56]. The mutual difference array can be seen from Figure (d) and Figure (e) Holes with positions greater than 56 in the differential set interval can be The elements in the difference set are filled. Therefore, the available continuous virtual array element interval is extended to [-80,80].
[0034] In this embodiment, the position range of the continuous virtual array elements corresponding to the complementary coprime array is [-U2-N-8, U2+N+8], and the number of continuous virtual array elements corresponding to the complementary coprime array is 2U2+2N+17, where U2 is the starting position of the third sub-array, and N is the number of array elements of the first sparse sub-array.
[0035] In this embodiment, the second subarray, the third subarray and the fourth subarray are all translated to the right by 3 unit spacings to obtain the target second subarray, the target third subarray and the target fourth subarray respectively; the first subarray, the target second subarray, the target third subarray and the target fourth subarray form a target complementary coprime array, and the spacing between the first subarray and the second subarray is N d +6.
[0036] Specifically, the target complementary coprime array includes the first subarray, the target second subarray, the target third subarray and the target fourth subarray arranged from left to right; the first subarray includes the first sparse subarray and the first unit subarray, the first sparse subarray includes N array elements, and the N array elements are evenly arranged, the array element spacing of the first sparse subarray is M, and the first unit subarray includes 1 array element; the target second subarray includes U1+1 array elements, and the array element spacing of the target second subarray is N d ; The third target sub-array and the fourth target sub-array each include 2 array elements, and the array element spacing between the third target sub-array and the fourth target sub-array is N d +3; the distance between the first target subarray and the second target subarray is N d +6, the distance between the second target subarray and the third target subarray is N d , the distance between the third target subarray and the fourth target subarray is N d -5, N and M are coprime numbers.
[0037] In this embodiment, the physical array element position set of the target complementary coprime array is:
[0038]
[0039] in, is the set of physical array element positions of the target complementary coprime array, is the set of physical array element positions of the first subarray, is the set of physical array element positions of the second subarray of the target, is the set of physical array element positions of the third subarray of the target, is the set of physical element positions of the target fourth sub-array, n1∈{0,1,2,…,N-1}, n1 is the number of any one of the N elements, n2∈{0,1,2,…,U1}, n2 is the number of any one of the U1+1 elements, n3∈{0,1}, n3 is the number of any one of the 2 elements, n4∈{0,1}, n4 is the number of any one of the 2 elements, U1=QN-6≥2, U1 is the number of elements of the second sub-array minus one, U2=(QN-1)N, U2 is the starting position of the third sub-array, Q is the total number of elements in the complementary coprime array, and N is the number of elements in the first sparse sub-array.
[0040] Specifically, the position range of the target continuous virtual array elements corresponding to the target complementary coprime array is [-U2+N-3, U2-N+3], and the number of the target continuous virtual array elements corresponding to the target complementary coprime array is 2U2+2N+23.
[0041] Figure 2 The structure diagram of the target complementary coprime array is schematically shown, the array parameters (Q, N) = (17, 8), the total number of array elements of the target complementary coprime array Q = 17, the target complementary coprime array can provide 167 continuous virtual array elements, and the number of continuous virtual array elements generated by the complementary coprime array under the same configuration parameters is 161. Compared with the complementary coprime array, the target complementary coprime array has a larger physical array aperture and a higher degree of freedom.
[0042] Based on the above Figure 1 It can be seen from the implementation method that the complementary coprime array in the embodiment of the present invention includes a first sub-array, a second sub-array, a third sub-array and a fourth sub-array arranged from left to right; the first sub-array includes a first sparse sub-array and a first unit sub-array, the first sparse sub-array includes N array elements, and the N array elements are evenly arranged, the array element spacing of the first sparse sub-array is M, and the first unit sub-array includes 1 array element; the second sub-array includes U1+1 array elements, and the array element spacing of the second sub-array is N d ; The third sub-array and the fourth sub-array each include 2 array elements, and the array element spacing of the third sub-array and the fourth sub-array is N d +3; the distance between the first subarray and the second subarray is N d +3, the distance between the second sub-array and the third sub-array is N d , the distance between the third sub-array and the fourth sub-array is N d-5, and the fourth subarray is formed by translating the third subarray to the right by 2N distance units. In this way, by using the first subarray, the second subarray, the third subarray and the fourth subarray arranged from left to right, the original coprime array can be expanded to fill the virtual array holes corresponding to the original coprime array, so that the degree of freedom of the complementary coprime array and the controllable balance of the mutual coupling leakage are achieved, thereby making the estimated DOA more accurate.
[0043] Based on the same inventive concept, as an implementation of the above-mentioned complementary coprime array, an embodiment of the present invention further provides a DOA estimation method for a complementary coprime array. Figure 3 The flowchart of the DOA estimation method of the complementary coprime array in the embodiment of the present invention is schematically shown. Figure 3 As shown, the DOA estimation method may include:
[0044] S301. Construct a first unit sub-array and a third sub-array according to a coprime array.
[0045] Specifically, according to the hole positions in the equivalent differential array corresponding to the coprime array, the first unit sub-array and the third sub-array are constructed to fill the holes in the equivalent differential array.
[0046] The coprime array consists of a first sparse sub-matrix and a preset sub-matrix.
[0047] Let the element spacing of the first sparse subarray in the coprime array be M=3, the number of elements in the first sparse subarray be N>4, and N and M be coprime numbers. Then the set of physical element positions corresponding to the coprime array is:
[0048]
[0049] in, is the set of physical array element positions corresponding to the coprime array, and the set of physical array element positions of the first sparse subarray is The physical array element position set of the preset subarray is {n2N d +N+3+3(N-1)|n2∈[0,U1]}, N is the number of array elements in the first sparse sub-array, and the array element spacing of the preset sub-array is N d , n1∈{0,1,2,…,N-1}, n1 is the number of any array element in the N array elements, n2∈{0,1,2,…,U1}, n2 is the number of any array element in the U1+1 array elements, and U1 is the number of array elements of the preset sub-array minus one.
[0050] The first sparse sub-array includes N array elements, and the array element spacing of the first sparse sub-array is M=3. The preset sub-array includes U1+1 array elements, and the array element spacing of the preset sub-array is N. d , N d =N.
[0051] Since the middle and both ends of the equivalent differential array corresponding to the coprime array are discontinuous, the existence of holes in the equivalent differential array will reduce the number of continuous virtual array elements, thereby reducing the array degree of freedom and affecting the coprime array performance. Therefore, according to the position of the holes in the equivalent differential array, sparse subarrays, namely the first unit subarray and the third subarray, can be constructed to fill the holes in the equivalent differential array.
[0052] The set of physical array element positions corresponding to the first unit subarray is: The set of physical array element positions corresponding to the third subarray is:
[0053] S302: Add the first unit sub-array and the third sub-array to the coprime array to obtain a filled array.
[0054] The first unit subarray and the third subarray are added to the coprime array to obtain a filled array, so that the coprime array can be subarray expanded to fill the virtual array holes.
[0055] Specifically, the first unit sub-matrix and the third sub-matrix are added to the coprime array to obtain a filled array, including:
[0056] Step A1: Add the first unit sub-matrix to the first sparse sub-matrix to generate the first sub-matrix.
[0057] The first unit subarray is added to the first sparse subarray to generate the first subarray to fill the hole in the middle of the differential array corresponding to the coprime array. The set of physical array element positions corresponding to the first subarray is
[0058] Step A2: The preset sub-array is used as the second sub-array and arranged on the right side of the first sub-array.
[0059] The set of physical array element positions corresponding to the second subarray is:
[0060] Step A3: Arrange the third sub-array on the right side of the second sub-array to obtain a filled array.
[0061] The third subarray is arranged on the right side of the second subarray to realize adding the third subarray into the coprime array and filling the holes at both ends of the differential array corresponding to the coprime array. At this time, all the holes in the differential array corresponding to the coprime array are filled to obtain a filled array.
[0062] The set of physical array element positions corresponding to the filled array is:
[0063]
[0064] in, is the set of physical array element positions corresponding to the filled array, is the set of physical array element positions of the first subarray, is the set of physical array element positions of the second subarray, is the set of physical element positions of the third sub-array, n1∈{0,1,2,…,N-1}, n1 is the number of any one of the N elements, n2∈{0,1,2,…,U1}, n2 is the number of any one of the U1+1 elements, n3∈{0,1}, n3 is the number of any one of the 2 elements, U1=QN-6≥2, U1 is the number of elements of the second sub-array minus one, U2=(QN-1)N, U2 is the starting position of the third sub-array, Q is the total number of elements of the complementary coprime array, and N is the number of elements of the first sparse sub-array.
[0065] By adding the first unit sub-array and the third sub-array in the coprime array, the holes in the differential array corresponding to the coprime array are filled, and the number of virtual array elements in the array is increased.
[0066] S303 , translate the third sub-array to the right by 2N distance units to obtain a fourth sub-array.
[0067] Since there are holes at both ends of the array after filling, it is necessary to introduce a fourth sub-array obtained by translating the third sub-array to fill the holes existing in the array after filling.
[0068] The set of physical array element positions corresponding to the fourth subarray is Where n4∈{0,1}, n4 is the number of any one of the two array elements, U2=(QN-1)N, U2 is the starting position of the third sub-array, N is the number of array elements of the first sparse sub-array, N d is the element spacing of the second subarray.
[0069] By translating the third subarray, the array degree of freedom can be improved and the array aperture can be increased.
[0070] S304: Add the fourth subarray to the filled array to generate a complementary coprime array.
[0071] Specifically, assuming that the number of array elements N of the first sparse subarray and the array element spacing M of the first sparse subarray are coprime numbers, let M=3, N>4, then the expression of the set of physical array element positions corresponding to the complementary coprime array is:
[0072]
[0073] in, is the set of physical element positions of complementary coprime arrays, is the set of physical array element positions of the first subarray, is the set of physical array element positions of the second subarray, is the set of physical array element positions of the third subarray, is the set of physical element positions of the fourth sub-array, n1∈{0,1,2,…,N-1}, n1 is the number of any one of the N elements, n2∈{0,1,2,…,U1}, n2 is the number of any one of the U1+1 elements, n3∈{0,1}, n3 is the number of any one of the 2 elements, n4∈{0,1}, n4 is the number of any one of the 2 elements, U1=QN-6≥2, U1 is the number of elements of the second sub-array minus one, U2=(QN-1)N, U2 is the starting position of the third sub-array, Q is the total number of elements of the complementary coprime array, and N is the number of elements of the first sparse sub-array.
[0074] The first sub-array, the second sub-array, the third sub-array and the fourth sub-array in the complementary coprime array, namely the Replished Coprime Array, RCA-I, are arranged in sequence from left to right.
[0075] Adding the fourth subarray to the filled array can fill the holes in the filled array, further improving the array degree of freedom and increasing the array aperture.
[0076] Specifically, the difference set of the complementary coprime array can provide a position range of continuous virtual array elements in the range of [-U2-N-8, U2+N+8]. The physical aperture of the complementary coprime array is U2+3N+3. The expression for the number of continuous virtual array elements that can be provided by the mutual difference array corresponding to the complementary coprime array is 2U2+2N+17.
[0077] From the expression of the number of continuous virtual array elements, it can be seen that the array degree of freedom is closely related to the total number of array elements Q and the number of array elements in the first sparse subarray N. When the number of array elements Q is constant, how to determine the value of N to maximize the number of continuous virtual array elements can be modeled as the following optimization problem:
[0078]
[0079] Among them, gcd(N,3)=1 means that N and 3 are prime numbers to each other.
[0080] The solution to this optimization problem is:
[0081] When Q is even:
[0082]
[0083] When Q is an odd number:
[0084]
[0085] Among them, N1 optis the optimal solution for the number of elements N of the first sparse sub-matrix when Q is an even number, N2 opt is the optimal solution for the number of elements N of the first sparse submatrix when Q is an odd number, and mod means taking the remainder.
[0086] In order to further increase the aperture of the continuous virtual array, the structure was improved by translating some subarrays in the RCA-I array to obtain the target complementary coprime array, namely the Replished Coprime Array, RCA-II.
[0087] Specifically, after adding the fourth subarray to the filled array to generate a complementary coprime array, the DOA estimation method further includes:
[0088] Step B1: Shift the second sub-array, the third sub-array and the fourth sub-array to the right by 3 unit intervals to obtain the target second sub-array, the target third sub-array and the target fourth sub-array respectively.
[0089] The set of physical array element positions corresponding to the second subarray is: The set of physical array element positions corresponding to the third subarray is: The set of physical array element positions corresponding to the fourth subarray is
[0090] Step B2: forming a target complementary coprime array according to the first sub-array, the target second sub-array, the target third sub-array and the target fourth sub-array.
[0091] The expression of the set of physical array element positions corresponding to the target complementary coprime array is:
[0092]
[0093] in, is the set of physical array element positions of the target complementary coprime array, is the set of physical array element positions of the first subarray, is the set of physical array element positions of the second subarray of the target, is the set of physical array element positions of the third subarray of the target, is the set of physical array element positions of the fourth subarray of the target.
[0094] Specifically, the expression of the set of physical array element positions corresponding to the target complementary coprime array is:
[0095]
[0096] in, is the set of physical array element positions of the target complementary coprime array, is the set of physical array element positions of the first subarray, is the set of physical array element positions of the second subarray of the target, is the set of physical array element positions of the third subarray of the target, is the set of physical element positions of the target fourth sub-array, n1∈{0,1,2,…,N-1}, n1 is the number of any one of the N elements, n2∈{0,1,2,…,U1}, n2 is the number of any one of the U1+1 elements, n3∈{0,1}, n3 is the number of any one of the 2 elements, n4∈{0,1}, n4 is the number of any one of the 2 elements, U1=QN-6≥2, U1 is the number of elements of the second sub-array minus one, U2=(QN-1)N, U2 is the starting position of the third sub-array, Q is the total number of elements in the complementary coprime array, and N is the number of elements in the first sparse sub-array.
[0097] The physical aperture of the target complementary coprime array is U2+3N+6, the differential array of the target complementary coprime array can provide a position range of continuous virtual array elements in the interval [-U2+N-3, U2-N+3], and the number of continuous virtual array elements corresponding to the target complementary coprime array is 2U2+2N+23.
[0098] S305: Establish a receiving signal model according to the complementary coprime array, and obtain a receiving signal according to the source signal.
[0099] The received signal is an actual signal that conforms to the received signal model.
[0100] Specifically, consider a Q-element complementary coprime array or a Q-element target complementary coprime array, where the position of the i-th array element is l i d, where i∈[1,Q], is a set of integers, l i is any integer, d represents the unit interval, and λ / 2 is equal to half the wavelength. Assume that there are K uncorrelated far-field narrowband signals s(t) = [s1(t), s2(t), ..., s k (t)] T , where s k (t) is the kth uncorrelated far-field narrowband signal, and the incoming wave direction is θ=[θ1,θ2,...,θ k ], where θ k is the kth incoming wave direction, then the received signal model is:
[0101] x(t)=As(t)+n(t),t=1,2,...,T;
[0102] Where x(t) is the received signal model, T is the number of snapshots, t is any snapshot number, s(t) is k uncorrelated far-field narrowband signals, A = [a(θ1), a(θ2), ..., a(θ k )], A is the steering vector matrix, p1 is the power of the first received signal, n(t) is the covariance matrix of additive white Gaussian noise, is the power of additive white Gaussian noise, I Q is the Q×Q identity matrix.
[0103] The covariance matrix of the received signal x(t) can be expressed as:
[0104]
[0105] Where R is the covariance matrix of the received signal, x H (t) is the conjugate transpose of the received signal, p k is the power of the kth received signal.
[0106] Vectorize the covariance matrix:
[0107]
[0108] Where z is the vectorized covariance matrix, vec is the vectorized covariance matrix, ⊙ represents the Khatri-Rao product, and p = [p1, p2, ..., p K ] T , G=[g(θ1),g(θ2),...,g(θ K )], g(θ K )for is the steering vector of the virtual array, G is the array manifold of the virtual array, p is the power of the received signal, l i for Any element in l j for Any element in is the set of physical element positions of the complementary coprime array.
[0109] Considering the mutual coupling between array elements, the corresponding target receiving signal model is:
[0110] x′(t)=CAs(t)+n(t), t=1,2,...,T;
[0111] Among them, C is the mutual coupling coefficient matrix of M1×M1, where M1 is the number of array elements. For a uniform linear array, C can be expressed as:
[0112]
[0113] Among them, C m,n is the element in the mth row and nth column of the mutual coupling coefficient matrix C, c0,c1,...,c B is the mutual coupling coefficient and satisfies the relationship c0=1>|c1|>|c2|>...>|c B |, B represents the maximum range of the mutual coupling effect, c B is the minimum mutual coupling coefficient.
[0114] S306: Perform DOA estimation on the received signal according to a spatial smoothing multiple signal classification algorithm.
[0115] After DOA estimation of the received signal is performed according to the spatial smoothing multiple signal classification algorithm, the performance of the complementary coprime array or the target complementary coprime array, such as degree of freedom, mutual coupling leakage and DOA estimation accuracy, is evaluated through simulation experiments.
[0116] To verify the performance of complementary coprime array or target complementary coprime array, the spatial spectra of complementary coprime array, target complementary coprime array and comparison array, and the root mean square error under different mutual coupling strengths are simulated respectively. All simulations assume that the number of signal sources is known, and the spatial smoothing multiple signal classification (SS-MUSIC) algorithm is used to achieve DOA estimation.
[0117] The definition of Root Mean Square Error (RMSE) is as follows:
[0118]
[0119] Among them, RMSE is the root mean square error, Υ is the Monte Carlo number, K1 is the number of target sources, is the arrival azimuth of the k1th source estimated by the m1th Monte Carlo experiment, θ k1 is the true arrival azimuth of the k1th source.
[0120] Eight typical sparse arrays were selected as comparison arrays, namely, Nested Array (NA), Super Nested Array (Super NA), Thinned Coprime Array (TCA), Coprime Array with Prime integer 3 (CAP3), Coprime Array with a two-hole Difference Co-array (CATHDC), Complementary Co-array, Augmented Nested Array (Augumented Nested Array) type I, and Augmented Nested Array (Augumented Nested Array) type II.
[0121] One of the significant advantages of sparse linear arrays over uniform linear arrays is that Q array elements can be used to estimate O(Q 2 ) sources. Therefore, the degree of freedom is an important indicator to measure the potential of sparse arrays. Figure 4 The schematic diagram of the comparison of the degrees of freedom of sparse arrays is shown schematically, and the curves of the degrees of freedom of ten sparse arrays varying with the number of array elements are given, where the total number of array elements Q∈[13,30]. Figure 4 It can be inferred that the degrees of freedom of the complementary coprime array, RCA-I, and the target complementary coprime array, RCA-II, are higher than those of TCA, CCA, CAP3, and CATHDC coprime arrays, and are close to those of NA, SNA, and ANA nested arrays.
[0122] Figure 5 The schematic diagram of the comparison of mutual coupling leakage of sparse arrays is shown schematically, and the mutual coupling leakage simulation diagrams of ten sparse arrays are given when the total number of array elements Q changes from 13 to 30. Figure 5 It can be seen that the mutual coupling leakage of the complementary coprime array, i.e., RCA-I, and the target complementary coprime array, i.e., RCA-II, is slightly higher than that of the simplified coprime array, but lower than that of the other eight sparse arrays. This is because the complementary coprime array and the target complementary coprime array have fewer array element pairs with array element spacing of 1, 2, and 3.
[0123] Figure 6The diagram schematically shows the variation of the root mean square error with the signal-to-noise ratio under the condition of mutual coupling, and the variation of the RMSE of DOA estimation with the signal-to-noise ratio under the condition of mutual coupling effect. The simulation sets the number of snapshots T=1000. The RMSE curves of the complementary coprime array, i.e., RCA-I, and the TCA array are close. This is because the degree of freedom of the complementary coprime array is higher than that of the TCA. It can be seen that the complementary coprime array has a stronger anti-mutual coupling ability. In addition, the number of small-pitch array element pairs of the target complementary coprime array, i.e., RCA-II, is equal to that of the complementary coprime array, but the degree of freedom of the target complementary coprime array is higher than that of the complementary coprime array, so the target complementary coprime array provides the lowest RMSE among all arrays.
[0124] Figure 7 The diagram schematically shows the change of the root mean square error with the number of snapshots under the condition of mutual coupling, and gives the change of the DOA estimation RMSE with the number of snapshots based on different sparse arrays. The simulation sets the signal-to-noise ratio SNR = 10dB. Figure 7 It can be seen that the RMSE of all arrays shows an overall downward trend with the increase of snapshot number. In addition, the target complementary coprime array, i.e., RCA-II, has the highest accuracy compared to the other nine types, because the target complementary coprime array has a higher degree of freedom and a more sparse array structure.
[0125] Based on the above Figure 3 It can be seen from the implementation method that the embodiment of the present invention constructs the first unit subarray and the third subarray according to the coprime array; adds the first unit subarray and the third subarray to the coprime array to obtain the filled array; translates the third subarray to the right by 2N distance units to obtain the fourth subarray; adds the fourth subarray to the filled array to generate a complementary coprime array; establishes a receiving signal model according to the complementary coprime array, and obtains the receiving signal according to the source signal, and the received signal is an actual signal that conforms to the receiving signal model; and estimates the DOA of the received signal according to the spatial smoothing multiple signal classification algorithm. In this way, the coprime array is expanded to fill the virtual array holes, and the array degree of freedom is effectively improved at the cost of a slight decrease in mutual coupling leakage performance, achieving a controllable balance between the degree of freedom and mutual coupling leakage, the mutual coupling between array elements is weak, and the DOA estimation accuracy is high. Compared with the nested array, the complementary coprime array has lower mutual coupling leakage, and compared with the coprime array, the complementary coprime array has higher degrees of freedom.
[0126] It should be noted here that: the above description of the DOA estimation method embodiment for complementary coprime arrays is similar to the description of the complementary coprime array embodiment described above, and has similar beneficial effects as the complementary coprime array embodiment. For technical details not disclosed in the embodiment of the DOA estimation method for complementary coprime arrays of the embodiment of the present invention, please refer to the description of the complementary coprime array embodiment of the present invention for understanding.
[0127] The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art who is familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.
Claims
1. A complementary coprime array, characterized in that: The complementary coprime array includes a first subarray, a second subarray, a third subarray and a fourth subarray arranged in sequence from left to right; the first subarray includes a first sparse subarray and a first unit subarray, the first sparse subarray includes N array elements, and the N array elements are evenly arranged, the array element spacing of the first sparse subarray is M, and the first unit subarray includes 1 array element; the second subarray includes U1+1 array elements, and the array element spacing of the second subarray is N d ; The third sub-array and the fourth sub-array each include 2 array elements, and the array element spacing of the third sub-array and the fourth sub-array is N d +3; the distance between the first sub-array and the second sub-array is N d +3, the distance between the second sub-array and the third sub-array is N d , the distance between the third sub-array and the fourth sub-array is N d -5, the fourth sub-matrix is formed by translating the third sub-matrix to the right by 2N distance units, and N and M are coprime numbers.
2. The complementary coprime array according to claim 1, characterized in that: The physical array element position set of the complementary coprime array is: in, is the set of physical element positions of complementary coprime arrays, is the set of physical array element positions of the first subarray, is the set of physical array element positions of the second subarray, is the set of physical array element positions of the third subarray, is the set of physical element positions of the fourth sub-array, n1∈{0,1,2,…,N-1}, n1 is the number of any one of the N elements, n2∈{0,1,2,…,U1}, n2 is the number of any one of the U1+1 elements, n3∈{0,1}, n3 is the number of any one of the 2 elements, n4∈{0,1}, n4 is the number of any one of the 2 elements, U1=QN-6≥2, U1 is the number of elements of the second sub-array minus one, U2=(QN-1)N, U2 is the starting position of the third sub-array, Q is the total number of elements of the complementary coprime array, and N is the number of elements of the first sparse sub-array.
3. The complementary coprime array according to claim 2, characterized in that: The position range of the continuous virtual array elements corresponding to the complementary coprime array is [-U2-N-8, U2+N+8], and the number of continuous virtual array elements corresponding to the complementary coprime array is 2U2+2N+17, where U2 is the starting position of the third sub-array, and N is the number of array elements of the first sparse sub-array.
4. The method according to claim 2, characterized in that: The second sub-array, the third sub-array and the fourth sub-array are all translated to the right by 3 unit spacings to obtain the target second sub-array, the target third sub-array and the target fourth sub-array respectively; the first sub-array, the target second sub-array, the target third sub-array and the target fourth sub-array form a target complementary coprime array, and the spacing between the first sub-array and the second sub-array is N d +6.
5. The method according to claim 4, characterized in that The physical array element position set of the target complementary coprime array is: in, is the set of physical array element positions of the target complementary coprime array, is a set of physical array element positions of the first subarray, is the set of physical array element positions of the second subarray of the target, is the set of physical array element positions of the third subarray of the target, is the physical element position set of the target fourth sub-array, n1∈{0,1,2,…,N-1}, n1 is the number of any one of the N elements, n2∈{0,1,2,…,U1}, n2 is the number of any one of the U1+1 elements, n3∈{0,1}, n3 is the number of any one of the 2 elements, n4∈{0,1}, n4 is the number of any one of the 2 elements, U1=QN-6≥2, U1 is the number of elements of the second sub-array minus one, U2=(QN-1)N, U2 is the starting position of the third sub-array, Q is the total number of elements of the complementary coprime array, and N is the number of elements of the first sparse sub-array.
6. A DOA estimation method for complementary coprime arrays, characterized in that: The DOA estimation method is implemented by using the complementary coprime array described in any one of claims 1 to 5, and the DOA estimation method comprises: According to the coprime arrays, the first unit sub-array and the third sub-array are constructed; Adding the first unit sub-array and the third sub-array to the coprime array to obtain a filled array; Shifting the third sub-array to the right by 2N distance units to obtain a fourth sub-array; adding the fourth sub-array to the filled array to generate a complementary coprime array; A receiving signal model is established according to the complementary coprime array, and a receiving signal is obtained according to the source signal, wherein the receiving signal is an actual signal that conforms to the receiving signal model; The DOA of the received signal is estimated according to a spatial smoothing multiple signal classification algorithm.
7. The DOA estimation method according to claim 6, characterized in that: The coprime array is composed of a first sparse sub-matrix and a preset sub-matrix, and the first unit sub-matrix and the third sub-matrix are added to the coprime array to obtain a filled array, including: Adding the first unit sub-matrix to the first sparse sub-matrix to generate a first sub-matrix; The preset sub-array is used as the second sub-array and arranged on the right side of the first sub-array; The third sub-array is arranged on the right side of the second sub-array to obtain the filled array.
8. The DOA estimation method according to claim 6, characterized in that: The expression of the set of physical array element positions corresponding to the complementary coprime array is: in, is the set of physical element positions of complementary coprime arrays, is the set of physical array element positions of the first subarray, is the set of physical array element positions of the second subarray, is the set of physical array element positions of the third subarray, is the set of physical element positions of the fourth sub-array, n1∈{0,1,2,…,N-1}, n1 is the number of any one of the N elements, n2∈{0,1,2,…,U1}, n2 is the number of any one of the U1+1 elements, n3∈{0,1}, n3 is the number of any one of the 2 elements, n4∈{0,1}, n4 is the number of any one of the 2 elements, U1=QN-6≥2, U1 is the number of elements of the second sub-array minus one, U2=(QN-1)N, U2 is the starting position of the third sub-array, Q is the total number of elements of the complementary coprime array, and N is the number of elements of the first sparse sub-array.
9. The DOA estimation method according to claim 8, characterized in that: After adding the fourth sub-array to the padded array to generate a complementary coprime array, the DOA estimation method further includes: The second sub-array, the third sub-array and the fourth sub-array are all translated to the right by 3 unit spacings to obtain a target second sub-array, a target third sub-array and a target fourth sub-array respectively; A target complementary coprime array is formed according to the first sub-array, the target second sub-array, the target third sub-array and the target fourth sub-array.
10. The DOA estimation method according to claim 9, characterized in that: The expression of the physical array element position set corresponding to the target complementary coprime array is: in, is the set of physical array element positions of the target complementary coprime array, is a set of physical array element positions of the first subarray, is the set of physical array element positions of the second subarray of the target, is the set of physical array element positions of the third subarray of the target, is the physical element position set of the target fourth sub-array, n1∈{0,1,2,…,N-1}, n1 is the number of any one of the N elements, n2∈{0,1,2,…,U1}, n2 is the number of any one of the U1+1 elements, n3∈{0,1}, n3 is the number of any one of the 2 elements, n4∈{0,1}, n4 is the number of any one of the 2 elements, U1=QN-6≥2, U1 is the number of elements of the second sub-array minus one, U2=(QN-1)N, U2 is the starting position of the third sub-array, Q is the total number of elements of the complementary coprime array, and N is the number of elements of the first sparse sub-array.