A nested array design method based on multi-level subarray expansion with enhanced degrees of freedom

Abstract

The present invention relates to a nested array design method based on multi-level sub-array expansion with enhanced degree of freedom, comprising: determining the unit length between array elements of the multi-level extended nested array; determining array parameters of the multi-level extended nested array; setting the multi-level extended nested array to be composed of a uniform sparse array ULA(0) and X identical uniform dense arrays ULA(x), and the expression thereof is: determining the array element positions of the multi-level extended nested array according to the multi-level extended nested array; the multi-level extended nested array uses a differential array to generate continuous virtual array elements. The present invention expands a plurality of identical dense uniform arrays and sets the spacing between the dense uniform arrays, thereby making full use of the differences between the dense uniform arrays, so that under the condition of satisfying the differential no-hole condition, a higher degree of freedom is obtained compared with the original nested array, and the mutual coupling influence between the array elements is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of array design, and in particular to a nested array design method based on multi-level sub-array expansion with enhanced degree of freedom. Background Art

[0002] Array signal processing refers to forming a sensor array with several sensors arranged in a certain form and distributed in different positions in space. All array elements in the sensor array sense the signals from space and then perform specific processing on them. The most commonly used sensor array is the traditional uniform linear array (ULA). The spacing between array elements in the array is constant and does not exceed half a wavelength to avoid spatial aliasing. For a uniform array (ULA) with N sensors, the traditional subspace-based array signal processing method can resolve up to N-1 signal sources. If you want to increase the number of resolved signal sources, additional sensors are required, which leads to increased cost and system complexity. Sparse arrays are an effective solution to this problem.

[0003] Compared with traditional uniform arrays, sparse arrays have been widely used in array signal processing due to their high degrees of freedom and low mutual coupling. In recent years, the design of sparse arrays has attracted more and more attention. The method of using sparse arrays for array signal processing in the prior art is to vectorize the covariance matrix of the array signal received by the sparse array to obtain a single-snap virtual received data, which is equivalent to the array signal received by the virtual differential array of the original array, thereby achieving an increase in the degree of freedom; although in theory a sparse array of N sensors can obtain at most N 2 Compared with the ULA with the same number of array elements, the ULA can analyze more signal sources. However, in actual situations, the theoretical highest degree of freedom is often not achieved due to differential redundancy, and there is still mutual coupling between the array elements.

[0004] The nested array is a typical sparse array. The traditional nested array is composed of two uniform arrays with different spacings. The two uniform arrays can form a hole-free uniform array after differentiation. The degrees of freedom of the nested array designed by this method still have room for improvement, and there is still mutual coupling between the array elements. Summary of the invention

[0005] The technical problem to be solved by the present invention is to provide a nested array design method based on multi-level sub-array expansion with enhanced degree of freedom, which can improve the degree of freedom of the array and reduce the influence of mutual coupling between array elements.

[0006] The technical solution adopted by the present invention is a nested array design method based on multi-level subarray expansion with enhanced degrees of freedom, comprising the following steps:

[0007] S1. Determine the unit length between array elements of the multi-stage extended nested array, where the unit length between array elements is represented by d, d satisfies d≤λ / 2, and λ represents the wavelength of the incident signal incident on the array;

[0008] S2, determining array parameters of the multi-level extended nested array, the array parameters are represented by D, X, N1, then the total number of array elements of the sparse array is: N = DX + N1-1;

[0009] S3, set the multi-level extended nested array to The multi-level extended nested array It consists of a uniform sparse array ULA(0) and X identical uniform dense arrays ULA(x), and its expression is: And satisfy the following formula: Among them, ULA(0) represents a uniform sparse array with N1 array elements and Dd array element spacing, and ULA(x) represents a uniform dense array with D array elements and d array element spacing. ULA(x) is equivalent to ULA(x-1) with all elements shifted in the negative direction by (N1D+D-1)d. Determine the array element positions of the multi-level extended nested array;

[0010] S4, multi-level extended nested array A differential array is used to generate continuous virtual array elements, the range of the virtual array elements is [-L, L], the continuous degree of freedom is 2L+1, and L=N1XD+DX-DX.

[0011] The beneficial effect of the present invention is that: by adopting the above-mentioned nested array design method based on multi-level sub-array expansion with enhanced degrees of freedom, on the basis of the traditional nested array, a number of identical dense uniform arrays are expanded, and the spacing between the dense uniform arrays is set, so as to make full use of the differences between the dense uniform arrays, so that under the condition of differential hole-free, a higher degree of freedom is obtained compared with the original nested array, and the mutual coupling effect between array elements is reduced.

[0012] Preferably, in step S4, the multi-level extended nested array The specific process of using a differential array to generate continuous virtual array elements includes the following steps:

[0013] S4.1. Assume that K incoherent far-field narrowband targets are incident on the multi-stage extended nested array. The covariance matrix of the received signal of the array element is expressed as: Where x(t) = As(t) + n(t), A represents the array flow matrix, s(t) and n(t) represent the source vector and noise vector respectively, R s=E[s(t)s H (t)] = diag{p}, where is the noise power, I M is the M-order unit matrix;

[0014] S4.2. The covariance matrix R x Vectorize it and get: Among them, 1 M =vec(I M ), is the noise power; (A * The ((x-1)*M+v,i)th element in ⊙A) is Where 1≤v≤M, which is equivalent to v The virtual flow matrix at the p1 position is obtained by vectorizing the covariance matrix R x Generate multi-level extended nested arrays The differential array (A * ⊙A) represents a virtual differential array The flow matrix of BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a schematic diagram of the structure of the multi-level extended nested array in the present invention;

[0016] Figure 2 It is a partial enlarged view of the subarray ULA(0) of the multi-level extended nested array in the present invention;

[0017] Figure 3 It is a partial enlarged view of a subarray set ULA(x) of a multi-level extended nested array in the present invention, where x=1, 2...X;

[0018] Figure 4 The error of angle estimation of the multi-stage extended nested array in the present invention and other commonly used arrays varies with the signal-to-noise ratio under the same conditions. DETAILED DESCRIPTION

[0019] The invention will be further described below with reference to the accompanying drawings and in combination with specific implementations, so that those skilled in the art can implement the invention with reference to the description. The protection scope of the invention is not limited to the specific implementations.

[0020] The present invention relates to a nested array design method based on multi-level subarray expansion with enhanced degrees of freedom, comprising the following steps:

[0021] S1. Determine the unit length between array elements of the multi-level extended nested array, where the unit length between array elements is represented by d, where d satisfies d≤λ / 2, where λ represents the wavelength of an incident signal incident on the array; in the embodiment of the present invention, d defaults to 1 unit length;

[0022] S2, determining array parameters of the multi-level extended nested array, the array parameters are represented by D, X, N1, then the total number of array elements of the sparse array is: N = DX + N1-1;

[0023] S3, set the multi-level extended nested array to The multi-level extended nested array It consists of a uniform sparse array ULA(0) and X identical uniform dense arrays ULA(x), and its expression is: And satisfy the following formula: Among them, ULA(0) represents a uniform sparse array with N1 array elements and Dd array element spacing, and ULA(x) represents a uniform dense array with D array elements and d array element spacing. ULA(x) is equivalent to ULA(x-1) with all elements shifted in the negative direction by (N1D+D-1)d. Determine the array element position of the multi-level extended nested array; in the embodiment of the present invention, refer to Figure 1 As shown, it is a multi-level extended nested array with D = 3, N1 = 4; therefore, ULA(0) = {0, 3, 6, 9}, ULA(1) = {0, -1, -2}, and ULA(2) = ULA(1) - (N1D + D-1) = {-14, -15, -16}; similarly, it can be extended to ULA(X); see Figure 2 and Figure 3 It can be seen that the number of array elements in ULA(0) is N1, the number of array elements in ULA(1) is D, and the structures of ULA(2) to ULA(X) are exactly the same as ULA(1), only the positions are different, so the total number of array elements in ULA(x), x=1,2…X is N2=DX; since ULA(0) and ULA(1) have the same array element 0, the total number of array elements in MDNA is N=DX+N1-1;

[0024] The array provided by the present invention is composed of a uniform sparse array ULA(0) and X identical uniform dense arrays ULA(x); the leftmost end of ULA(0) is the origin, the spacing is Dd, and the number is N1; the rightmost end of ULA(1) is the origin, the spacing is d, and the number of array elements is D; ULA(2) is equivalent to ULA(1) translated in the negative direction (N1D+D-1-d, and the same is true for ULA(x) and ULA(x-1); the total number of array elements in ULA(x), x=1,2...X is N2=DX; since ULA(0) and ULA(1) contain repeated array element 0 at the origin, The number of array elements is N = DX + N1-1;

[0025] Here we introduce the concept of differential array, (·) T Expressed as transpose, (·) H is the conjugate transpose, (·) -1 To seek the inverse, (·) * represents the conjugate operation, ⊙ represents the Khatri-Rao product, vec() represents the vectorization of the matrix, E(·) represents the mathematical expectation, represents the smallest integer greater than x;

[0026] S4, multi-level extended nested array A differential array is used to generate continuous virtual array elements, the range of the virtual array elements is [-L, L], the continuous degree of freedom is 2L+1, and L=N1XD+DX-DX; the multi-level extended nested array The specific process of using a differential array to generate continuous virtual array elements includes the following steps:

[0027] S4.1. Assume that K incoherent far-field narrowband targets are incident on the multi-stage extended nested array. The covariance matrix of the received signal of the array element is expressed as: Where x(t) = As(t) + n(t), A represents the array flow matrix, s(t) and n(t) represent the source vector and noise vector respectively, R s =E[s(t)s H (t)] = diag{p}, where is the noise power, I M is the M-order unit matrix;

[0028] S4.2. The covariance matrix R x Vectorize it and get: Among them, 1 M =vec(I M ), is the noise power; (A * The ((x-1)*M+v,i)th element in ⊙A) is Where 1≤v≤M, which is equivalent to v The virtual flow matrix at the p1 position is obtained by vectorizing the covariance matrix R x Generate multi-level extended nested arrays The differential array (A * ⊙A) represents a virtual differential array The flow matrix of

[0029] By designing a better array The corresponding differential array can be Having more virtual array elements and increasing the degree of freedom can improve the accuracy of angle estimation by combining with the spatial smoothing algorithm.

[0030] See also Figure 1 As shown, a multi-level extended nested array is defined and the array element position is determined. The sparse array of the present invention is composed of X+1 uniform sub-arrays. The first sub-array ULA(0) is a uniform sparse sub-array, and the remaining X sub-arrays are all the same uniform dense sub-arrays. The collection of all sub-arrays is defined as It is called multi-level extended nested array, or MDNA.

[0031] The total number of array elements is N = DX + N1-1, and MDNA is defined as follows: And satisfy the following formula:

[0032] ULA(0)={0,D,...,(N1-1)D}

[0033] ULA(1)={0,-1,...,-(D-1)}

[0034] ULA(X)=ULA(X-1)-(N1D+D-1),(X>2);

[0035] The range of continuous virtual array elements generated by using the concept of differential array is [-L, L], and L = N1XD + DX-DX, which is proved as follows:

[0036] Focusing on the difference between ULA(0) and ULA(1) (due to the symmetric nature of the differential array, only the positive half is considered here), we can obtain: diff[ULA(0),ULA(1)]=[0,N1D-1];

[0037] Similarly, we get:

[0038] diff[ULA(0),ULA(X)]=diff[ULA(0),ULA(1)]+(X-1)(N1D+D-1)

[0039] =[0,N1D-1]+(X-1)(N1D+D-1) (1)

[0040] diff[ULA(1),ULA(X)]=diff[ULA(1),ULA(1)]+(X-1)(N1D+D-1)

[0041] =[-(D-1),D-1]+(X-1)(N1D+D-1) (2)

[0042] Combining the above equations (1) and (2), we can get the set: L X =[-(D-1),N1D-1]+(X-1)(N1D+D-1);

[0043] Similarly, we get:

[0044] diff[ULA(0),ULA(X+1)]=diff[ULA(0),ULA(1)]+X(N1D+D-1)

[0045] =[0,N1D-1]+X(N1D+D-1) (3)

[0046] diff[ULA(1),ULA(X+1)]=diff[ULA(1),ULA(1)]+X(N1D+D-1)

[0047] =[-(D-1),D-1]+X(N1D+D-1) (4)

[0048] Combining the above equations (3) and (4), we can get the set L X+1 =[-(D-1),N1D-1]+X(N1D+D-1);

[0049] Comparison L X+1 The minimum value of X(N1D+D-1)-(D-1)=XN1D+(X-1)(D-1) and L X The maximum value can be obtained: (X-1)(N1D+D-1)+N1D-1=XN1D+(X-1)(D-1)-1;

[0050] Obviously L X With L X+1 There is no gap between them, where X≥2, so it is proved that after the array is differentiated, a completely hole-free virtual array can be obtained.

[0051] The maximum aperture can be directly calculated by the array element with the largest distance in the array. The rightmost end of the array is D(N1-1), and the leftmost end is -(D-1)-(X-1)(N1D+D-1), so L=N1XD+DX-DX;

[0052] When comparing different array degrees of freedom, it must be based on the condition that the number of array elements is the same; therefore, for a given total number of array elements N, we explore how to allocate the array elements so that MDNA can obtain the best degrees of freedom.

[0053] Given N=N1+N2=N1+DX-1, L=(N1+1)(N+1-N1)-DX; N1 is the independent variable with respect to L, N is a constant, first consider D and X as constants, and take the partial derivative of L with independent variable N1, we can get: Therefore The maximum degree of freedom can be obtained when . It can be seen that the maximum aperture in N is determined by D,X; In order to make L as large as possible, it is obvious that The longest L can be obtained when , but because D and X need to be integers, the theoretical optimal value may not be obtained, so it is only necessary to select D and X as close as possible; considering Therefore, when N is determined, the value of N1 does not necessarily have to be exist Select it, calculate the best degree of freedom that can be obtained, and obtain the parameters.

Claims

1. A nested array design method based on multi-level subarray expansion with enhanced degrees of freedom, characterized by: Includes the following step: S1, determine the unit length between the array elements of the multi-level extended nested array, the unit length between the array elements is expressed as express, satisfy , represents the wavelength of the incident signal incident on the array; S2, determining the array parameters of the multi-level extended nested array, the array parameters are used Represented by, the total number of array elements in the sparse array is: ; S3, set the multi-level extended nested array to , the multi-level extended nested array A uniformly sparse array and The same uniformly dense array Composition, its expression is: , and satisfies the following formula: ;in, Indicates the number of array elements , the array element spacing is A uniformly sparse array of Indicates the number of array elements , the spacing is A uniformly dense array of ; Equivalent to All array elements are shifted in the negative direction Result; According to the multi-level expansion nested array Determine the array element positions of the multi-level extended nested array; S4, multi-level extended nested array A differential array is used to generate continuous virtual array elements. The range of the virtual array elements is , the continuous degrees of freedom are ,and .

2. The nested array design method based on multi-level subarray expansion with enhanced degrees of freedom according to claim 1, characterized in that: The multi-level extended nested array The specific process of using a differential array to generate continuous virtual array elements includes the following steps: S4.

1. Setting An incoherent far-field narrowband target is incident on a multi-stage extended nested array. The covariance matrix of the received signal of the array element is expressed as: ,in, , represents the array flow matrix, and represent the source vector and the noise vector respectively, , is the M-order unit matrix; S4.

2. The covariance matrix Vectorize it and get: ;in, , is the noise power; The The elements are ,in , which is equivalent to The virtual manifold matrix at position is obtained by vectorizing the covariance matrix Generate multi-level extended nested arrays The differential array , Represented as a virtual difference array The flow matrix of .

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