A design method for multi-level sub-array extended nested array to reduce mutual coupling effect

Abstract

The present invention relates to a multi-level sub-array extended nested array design method for reducing mutual coupling effect. The method comprises the following steps: determining a unit length between array elements of an augmented multi-level extended nested array; determining array parameters of the augmented multi-level extended nested array; setting the augmented multi-level extended nested array to be composed of a uniform sparse array ULA(0), X uniform arrays ULA(x.1) with a spacing of 2d, and X uniform arrays ULA(x.2) with a spacing of 2d; the augmented 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, sets the spacing between the dense uniform arrays, and symmetrically migrates some array elements of the dense uniform arrays compared to ULA(0), so that under the condition of satisfying differential no-holes, a higher degree of freedom is obtained compared to the original nested array, and the mutual coupling effect between array elements is greatly reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of array design, and in particular to a multi-level sub-array extended nested array design method for reducing mutual coupling effects. Background Art

[0002] Array signal processing refers to the formation of a sensor array by arranging several sensors in a certain form and distributed at 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), in which the spacing between elements is constant and does not exceed half a wavelength to avoid spatial aliasing. For a uniform array (ULA) with N sensors, in theory, the traditional subspace-based array signal processing method can resolve up to N-1 signal sources; however, in practical applications, there is mutual coupling between sensors, and the smaller the spacing, the greater the mutual coupling, so the mutual coupling between ULAs is often large. Therefore, in practical applications, the mutual coupling between sensors in ULAs will have a certain impact on the estimation results. Compared with the traditional uniform array, there are fewer pairs of sensors with small spacing in a sparse array with the same number of array elements.

[0003] At present, by vectorizing the covariance matrix obtained by observing the sparse array receiving data, an equivalent differential array is generated. Although the degree of freedom of direction finding can be improved, its mutual coupling effect cannot be ignored when designing the array. The high mutual coupling array will limit its application in many engineering projects, such as radar, sonar, wireless communication, etc. Therefore, how to ensure that the designed sparse array can improve the degree of freedom while minimizing its mutual coupling effect are two principles that need to be considered in the design process. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a multi-level sub-array extended nested array design method for reducing mutual coupling effects, which can greatly reduce the influence of mutual coupling between array elements while maintaining an increase in the degree of freedom.

[0005] The technical solution adopted by the present invention is a multi-level sub-array extended nested array design method for reducing mutual coupling effect, the method comprising the following steps:

[0006] S1. Determine the unit length between array elements of the augmented 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;

[0007] S2, determining the array parameters of the augmented multi-level extended nested array, the array parameters are represented by D, X, N1, then the total number of array elements of the augmented multi-level extended nested array is: N = DX + N1-1;

[0008] S3, set the augmented multi-level extended nested array to The augmented multi-level extended nested array It consists of a uniform sparse array ULA(0), X uniform arrays ULA(x.1) with a spacing of 2d, and X uniform arrays ULA(x.2) with a spacing of 2d. Its expression is: And satisfy the following formula:

[0009] in,

[0010] ULA(x.1)=ULA((x-2).1)-2(N1D+D-1)d, (x>2),

[0011] ULA(x.2)=ULA((x-2).2)+2(N1D+D-1)d, (x>2); ULA(0) is a uniform sparse array with N1 array elements and Dd array element spacing, ULA(x.1) and ULA(x.2) are uniform arrays with a spacing of 2d, and the total number of the two is D; ULA(x.1) is equivalent to all the array elements of ULA((x-2).1) translated in the negative direction by 2(N1D+D-1)d, and ULA(x.2) is equivalent to all the array elements of ULA((x-2).2) translated in the positive direction by 2(N1D+D-1)d;

[0012] S4, Augmented 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: when the parity of D and X is the same, L=N1XD+DX-D-X+1; when the parity of D and X is different, L=N1XD+DX-DX.

[0013] The beneficial effect of the present invention is that: by adopting the above-mentioned nested array design method for multi-level sub-array expansion for reducing mutual coupling effect, on the basis of the traditional nested array, a number of identical dense uniform arrays are expanded, the spacing between the dense uniform arrays is set, and part of the array elements of the dense uniform array are symmetrically migrated compared to ULA (0), so that under the condition of differential hole-free, a higher degree of freedom is obtained compared to the original nested array, and the mutual coupling effect between the array elements is greatly reduced.

[0014] Preferably, in step S4, the augmented multi-level extended nested array The specific process of using a differential array to generate continuous virtual array elements includes the following steps:

[0015] S4.1. Assume that K incoherent far-field narrowband targets are incident on the augmented 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;

[0016] 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 Generates augmented multi-level extended nested arrays The differential array (A * ⊙A) represents a virtual differential array The flow matrix of

[0017] As a preference, when array parameter D≥2 and N1≥2, augment the multi-level extended nested array The weight function is as follows: w(1)=1

[0018]

[0019] BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a schematic diagram of the structure of the augmented multi-level extended nested array in the present invention;

[0021] Figure 2 It is a result diagram of the symmetric migration of ULA(x.2) about ULA(0) in the augmented multi-level extended nested array of the present invention;

[0022] Figure 3 It is a partial enlarged view of the parameter pending time ULA(0) in the augmented multi-level extended nested array of the present invention;

[0023] Figure 4It is a comparison diagram of the angle estimation error changing with the signal-to-noise ratio of the augmented multi-stage extended nested array in the present invention and other commonly used arrays under the same mutual coupling condition. DETAILED DESCRIPTION

[0024] 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.

[0025] The present invention relates to a multi-level sub-array extended nested array design method for reducing mutual coupling effect, the method comprising the following steps:

[0026] S1. Determine the unit length between array elements of the augmented multi-stage 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;

[0027] S2, determining the array parameters of the augmented multi-level extended nested array, the array parameters are represented by D, X, N1, then the total number of array elements of the augmented multi-level extended nested array is: N = DX + N1-1;

[0028] S3, set the augmented multi-level extended nested array to The augmented multi-level extended nested array It consists of a uniform sparse array ULA(0), X uniform arrays ULA(x.1) with a spacing of 2d, and X uniform arrays ULA(x.2) with a spacing of 2d. Its expression is: And satisfy the following formula:

[0029] in,

[0030] ULA(x.1)=ULA((x-2).1)-2(N1D+D-1)d, (x>2),

[0031] ULA(x.2)=ULA((x-2)·2)+2(N1D+D-1)d, (x>2); ULA(0) is a uniform sparse array with N elements and Dd spacing, ULA(x.1) and ULA(x.2) are uniform arrays with 2d spacing, and the total number of the two is D; ULA(x.1) is equivalent to all the elements of ULA((x-2).1) shifted in the negative direction by 2(N1D+D-1)d, and ULA(x.2) is equivalent to all the elements of ULA((x-2).2) shifted in the positive direction by 2(N1D+D-1)d;

[0032] The leftmost end of ULA(0) is the origin, the spacing is Dd, and the number of elements is N1; the rightmost end of ULA(1.1) is the origin, the spacing is 2d, and the number of elements is The leftmost end of ULA (1.2) is (N1-1)D+1, the spacing is 2d, and the number of array elements is The rightmost end of ULA (2.1) is -(N1D+D), the spacing is 2d, and the number of array elements is The leftmost end of ULA (2.2) is (2N1D-1), the spacing is 2d, and the number of array elements is From ULA(x.1)=ULA((x-2).1)-2(N1D+D-1) and ULA(x.2)=ULA((x-2).2)+2(N1D+D-1), all other ULA(x.1) and ULA(x.2) can be deduced;

[0033] In the embodiment of the present invention, refer to Figure 1 As shown, it is an augmented multi-level extended nested array with D=3 and N1=5, so ULA(0)={0, 3, 6, 9, 12}, ULA(1.1)={0, -2}, ULA(1.2)={13}, ULA(2.1)={-18}, ULA(2.2)={29, 31}; ULA(x.1)=ULA((x-2).1)-2(N1D+D-1), ULA(x.2)=ULA((x-2).2)+2(N1D+D-1), and the entire array structure of the augmented multi-level extended nested array can be obtained in the same way;

[0034] See also Figure 2 and Figure 3 It can be seen that the number of array elements of ULA(0) is N1; the total number of array elements of ULA(1.1) and ULA(1.2) is D, and all the array elements of ULA(2.2) with respect to all the symmetric array elements of ULA(0) just form the set {0, -1, ..., -(D-1)} with ULA(1.1); similarly, the total number of array elements of ULA(x.1) and ULA(x.2) is D, and all the array elements of ULA(x.2) with respect to all the symmetric array elements of ULA(0) just form the set {0, -1, ..., -(D-1)} with ULA(x.1) The set is {0, -1, ..., -(D-1)}-(x-1)(N1D+D-1); Since the total number of array elements of ULA(x.1) and ULA(x.2) is D, and x is any value from 1 to X, ULA(x)=ULA(x.1)∪ULA(x.2), and the total number of array elements of x=1, 2, ...X is N2=DX; Since there is the same array element 0 in ULA(0) and ULA(1.1), the total number of array elements of AMDNA is N=N1+N2=N1+DX-1;

[0035] S4. Introduce the concept of differential array, (·) TExpressed 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; augments multi-level nested arrays 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: when the parity of D and X is the same, L=N1XD+DX-D-X+1; when the parity of D and X is different, L=N1XD+DX-DX; the augmented multi-level extended nested array The specific process of using a differential array to generate continuous virtual array elements includes the following steps:

[0036] S4.1. Assume that K incoherent far-field narrowband targets are incident on the augmented 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;

[0037] S4.2. The covariance matrix R x Vectorize it and get: in,

[0038] 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 Generates augmented multi-level extended nested arrays The differential array (A * ⊙A) represents a virtual differential array The flow matrix of

[0039] The present invention can obtain more virtual array elements by utilizing a differential array, thereby increasing the degree of freedom, and can improve the accuracy of angle estimation by combining a spatial smoothing algorithm.

[0040] See also Figure 1 As shown, the augmented multi-level extended nested array is defined and the array element positions are determined; the array element position set is defined as It is called augmented multi-level extended nested array, or AMDNA; the total number of array elements is N = DX + N1-1, and AMDNA is defined as follows: And satisfy the following formula: When D is an odd number:

[0041] ULA(1.1)={0,-2,...,-(D-1)};

[0042] ULA(1.2)=(N1-1)D-{-1,-3,…,-(D-2)};

[0043] ULA(2.1)={-1,-3,...,-(D-2)}-(N1D+D-1);

[0044] ULA(2.2)=(N1-1)D-{{0,-2,...,-(D-1)}-(N1D+D-1)}

[0045] =(2N1D-1)-{0,-2,...,-(D-1)};

[0046] When D is an even number:

[0047] ULA(1.1)={0,-2,…,-(D-2)};

[0048] ULA(1.2)=(N1-1)D-{-1,-3,…,-(D-1)};

[0049] ULA(2.1)={-1,-3,…,-(D-1)}-(N1D+D-1);

[0050] ULA(2.2)=(N1-1)D-{{0,-2,...,-(D-2)}-(N1D+D-1)}

[0051] =(2N1D-1)-{0,-2,...,-(D-2)};

[0052] Regardless of the parity of D, it holds:

[0053] ULA(x.1)=ULA((x-2).1)-2(N1D+D-1), (x>2);

[0054] ULA(x.2)=ULA((x-2).2)+2(N1D+D-1), (x>2).

[0055] The range of continuous virtual array elements generated by using the concept of differential array is [-L, L], the continuous degree of freedom is 2L+1, and when the parity of D and X is different, L=N1DX+DX-DX; when the parity of D and X is the same, L=N1XD+DX-D-X+1; the proof is as follows:

[0056] Since all the array elements of ULA(x.2) with respect to all the symmetric array elements of ULA(0) just form a set with ULA(x.1) Therefore, the difference between ULA(x) and ULA(0) is directly equivalent to the difference between ULA(0) and The difference of

[0057] First, we focus 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), and we get:

[0058] diff[ULA(0),ULA(1)]=[0,N1D-1];

[0059] Similarly, we can get:

[0060] diff[ULA(0), ULA(X)]=diff[ULA(0), ULA(1)]+(X-1)(N1D+D-1)

[0061] =[0,N1D-1]+(X-1)(N1D+D-1) (1)

[0062] Further we get:

[0063]

[0064] Observe formula (2) and we can get: The hole in the above formula is

[0065] When D is an odd number:

[0066] If x is an odd number, where x>1, we get:

[0067]

[0068]

[0069] If x is an even number, where x>1, we get:

[0070]

[0071]

[0072] Therefore, it can be seen that when D is an odd number, AMDNA can form a continuous segment of [-L, L] after differentiation, where L = N1DX + DX - DX.

[0073] Similarly, when D is an even number:

[0074] If x is an odd number, where x>1, we get:

[0075]

[0076]

[0077] If x is an even number, where x>1, we get:

[0078]

[0079]

[0080] Therefore, it can be seen that when D is an even number, the AMDNA can form a continuous segment of [-L, L] after differentiation, where L = N1DX + DX-DX. When the parity of D and x is the same, the leftmost array element of AMDNA is exactly -(D-1)-(X-1)(N1D+D-1), and the difference with (N1-1)D+1 in ULA (1.2) can obtain the virtual array element N1DX+DX-D-X+1. Therefore, when the parity of D and X is the same, the maximum aperture of the virtual array is L = N1DX+DX-D-X+1.

[0081] 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 AMDNA can obtain the best degrees of freedom. The additional degrees of freedom when the parity of D and X is the same will not be discussed here.

[0082] Given N=N1+N2=N1+DX-1, we can substitute it into L=(N1+1)(N+1-N1)-DX. In this case, N1 is the independent variable about L, N is a constant, and D and X are considered constants. We can find the partial derivative of L with independent variable N1 and get: Therefore When , the maximum degree of freedom can be obtained: At this time, we get:

[0083] It can be seen that the maximum aperture at N is determined by D and 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 from them, calculate the best degree of freedom that can be obtained, and obtain the parameters;

[0084] When D≥2, N1≥2, and m=1, 2, 3, the weight function of AMDNA is as follows:

[0085] w(1)=1

[0086]

[0087] The proof is as follows:

[0088] Pay attention to the value of w(1): For self-differentiation, the array element spacing of ULA(0) is D, and the array element spacing of the other ULAs is 2. Therefore, since D≠1, if only the self-differentiation between arrays is considered, w(1)=0. Considering the mutual difference between ULAs, the mutual difference between ULA(1)~ULA(X), the minimum spacing is N1D>1, which is obviously true. Therefore, considering only the difference between ULA(1.1), ULA(1.2) and ULA(0), it can be found that only w(1)=1 exists.

[0089] Pay attention to the value of w(2): It is known that the array element spacing of ULA(0) is D, and the array element spacing of the other ULAs is 2. When D>2, first count the self-differences. Obviously, the cumulative sum of w(2) in ULA(x.1) and ULA(x.2) is D-2, where x is any value from 1 to X. Similarly, since the mutual difference between ULA(1) to ULA(X) has a minimum spacing of N1D>2, only considering the difference between ULA(1.1), ULA(1.2) and ULA(0), it can be found that w(2)=1 exists. However, it should be noted that w(2)=1 at this time is the difference between 0 and -2, and array element 0 is also included in ULA(1.1), so w(2)=1 at this time is included in the self-difference of ULAx.1. Therefore, when D>2, w(2)=(D-2)*X holds.

[0090] When D=2, the array element spacing in ULA(0) is 2, then the cumulative sum of w(2) in the self-checking score adds N1-1 items of the self-differential score in ULA(0) compared to when D>2. Note that when D=2, the cumulative sum of w(2) in ULA(x.1) and ULA(x.2) is D-2=0, so when D=2, w(2)=N1-1.

[0091] Pay attention to the value of w(3): When D≠3, since the mutual difference between ULA(1)~ULA(X) has a minimum spacing of N1D≥4, for the value of w(3), only the difference between ULA(1.1), ULA(1.2) and ULA(0) is considered in the mutual difference. It can be found that no matter D=2 or D>3, the difference term w(3) between ULA(0) and ULA(1.2) is 1. Considering the self-difference of ULA, it is obvious that only when D≠3, the self-difference of ULA0 has w(3)=0. Therefore, when D≠3, w(3)=1.

[0092] Considering the case when D=3, w(3)=N1-1 in the self-differentiation of ULA0; similarly, considering only the difference between ULA(1.1), ULA(1.2) and ULA(0) in the mutual difference, it can be found that when D=3, since ULA1.2 contains only one array element, w(3)=0 in the difference term between ULA(0) and ULA(1.2). Therefore, when D=3, w(3)=N1-1.

Claims

1. A multi-level sub-array extended nested array design method for reducing mutual coupling effects, characterized by: The method comprises the following steps: S1. Determine the unit length between array elements of the augmented 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; S2, determining the array parameters of the augmented multi-level extended nested array, the array parameters are represented by D, X, N1, then the total number of array elements of the augmented multi-level extended nested array is: N = DX + N1-1; S3, set the augmented multi-level extended nested array to The augmented multi-level extended nested array It consists of a uniform sparse array ULA(0), X uniform arrays ULA(x.1) with a spacing of 2d, and X uniform arrays ULA(x.2) with a spacing of 2d. Its expression is: And satisfy the following formula: in, ULA(x.1)=ULA((x-2).1)-2(N1D+D-1)d,(x>2), ULA(x.2)=ULA((x-2).2)+2(N1D+D-1)d,(x>2); ULA(0) is a uniform sparse array with N1 elements and Dd spacing, ULA(x.1) and ULA(x.2) are uniform arrays with 2d spacing, and the total number of the two is D; ULA(x.1) is equivalent to all the elements of ULA((x-2).1) shifted in the negative direction by 2(N1D+D-1)d, and ULA(x.2) is equivalent to all the elements of ULA((x-2).2) shifted in the positive direction by 2(N1D+D-1)d; S4, Augmented 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], and the continuous degree of freedom is 2L+1. When the parity of D and X is the same, L=N1XD+DX-D-X+1; when the parity of D and X is different, L=N1XD+DX-DX; In step S4, the augmented 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. Assume that K incoherent far-field narrowband targets are incident on the augmented 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 Η (t)] = diag{p}, where is the noise power, I M is the M-order unit matrix; 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 Generates augmented multi-level extended nested arrays The differential array (A * A) Represented as a virtual differential array The flow matrix of 2. A multi-level sub-array extended nested array design method for reducing mutual coupling effect according to claim 1, characterized in that: When array parameter D≥2 and N1≥2, augment multi-level extended nested array The weight function is as follows: w(1)＝1

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