CN105445696A - Nested L-shaped antenna array structure and direction of arrival estimation method thereof - Google Patents

Abstract

The invention relates to a nested L-shaped antenna array structure and a direction of arrival estimation method thereof. The direction of arrival estimation method includes the following steps that: a nested L-shaped antenna array structure is constructed, and the received signals of a physical array antenna structure is determined based on the nested L-shaped antenna array structure; the high-order cumulant matrix of the received signals of the physical array antenna structure is obtained through using a high-order cumulant DOA algorithm; vectorization calculation is performed on the high-order cumulant matrix, so that a vectorized high-order cumulant matrix can be obtained, and the information of maximum continuous virtual square matrixes is extracted, and equivalent received signals can be obtained; two-dimensional spatial smoothing processing is performed on the equivalent received signals, so that an equivalent autocorrelation matrix can be obtained, eigenvalue decomposition is performed on the equivalent autocorrelation matrix, so that a signal feature vector matrix and a noise feature vector matrix can be obtained; and the signal feature vector matrix and the noise feature vector matrix are utilized to construct a spectral peak searching relational expression, and direction of arrival estimation is carried out, and the estimated value of the direction of arrival of the received signals is obtained. According to the nested L-shaped antenna array structure and the direction of arrival estimation method thereof adopted, a larger effective aperture can be realized when few array elements are adopted, and direction of arrival estimation precision can be improved.

Description

Nested L-shaped antenna array structure and arrival direction estimation method thereof

Technical Field

The invention relates to an antenna array structure and a two-dimensional direction of arrival estimation technology, in particular to a nested L-shaped antenna array structure and a direction of arrival estimation method thereof.

Background

In the past two decades, many high-order cumulant array processing-based direction-of-arrival estimation methods for non-gaussian sources have been rapidly developed, and the fourth-order cumulant-based method is the most typical method. Compared with a second-order statistic method, the direction of arrival estimation method of the fourth-order cumulant has the following advantages: 1) statistically independent non-Gaussian sources with more than physical array elements can be processed; 2) the aperture of the array is enlarged; 3) gaussian noise is suppressed; 4) and the estimation precision is higher. To further increase the number of virtual array elements and improve the accuracy of the estimation, Pascal Chevalier, Laurent Albera et al extend the fourth order cumulant to higher orders. Meanwhile, the concept of the fourth-order virtual array element is also expanded to the concept of the high-order virtual array element, and the essence that the estimation accuracy can be improved by the high-order cumulative quantity algorithm is that the number of the virtual array elements is increased. However, this method cannot fully utilize the formed virtual array elements.

In 2012, PiyaPal, p.p.vaidyanathan et al applied the method of high-order cumulant to a one-dimensional non-uniform array structure, so that virtual array elements are arranged into a uniform linear array to the maximum extent. However, this study is limited to linear arrays.

In 2012, PiyaPal, p.p. vaidyanathan et al proposed a two-dimensional non-uniform array on a grid, and using the proposed array, two-dimensional direction-of-arrival estimation was performed on the signal. However, with this structure, the estimation performance (the maximum number of signals that can be estimated and the accuracy of the direction of arrival estimation) is significantly improved only in the case where there are many array elements.

Disclosure of Invention

The invention aims to provide a nested L-shaped antenna array structure and a direction of arrival estimation method thereof, so as to make up for the defects of the prior art that the number of estimated information sources is small and the estimation precision is low for limited array elements.

The invention is realized by the following technical scheme:

the invention provides a nested L-shaped antenna array structure, which comprises:

physical array antenna structure RL in the x-axis_xAnd physical array antenna structure RL in the y-axis_y；

Physical array antenna structure RL on the x-axis_xThe array comprises a two-level nested array consisting of two uniform linear arrays, wherein the ith level kth physical array element is expressed as:

$RE(m,0),(m=k(\underset{i=1}{\overset{2}{\Π}}{N}_i)d,N_1=1,N_2=N/4+1)$

d is the array element spacing of the first stage, d is lambda/2, and lambda is the wavelength of an incident signal; i is 1, 2; k is 1,2, …, N/4; n is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, …; physical array antenna structure RL on the x-axis_xThe array element number of (2) is N/2;

physical array antenna structure RL on the y-axis_yThe system comprises a two-level nested array consisting of two uniform linear arrays, wherein the nth physical array element of the ith level is represented as:

$RE(0,m),(m=k(\underset{i=1}{\overset{2}{\Π}}{N}_i)d,N_1=1,N_2=N/4+1)$

d is the array element spacing of the first stage, d is lambda/2, and lambda is the wavelength of an incident signal; i is 1, 2; k is 1,2, …, N/4; n is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2, …, N/4; a physical array antenna structure on the y-axisRL_yThe number of array elements is N/2.

The invention also provides a direction of arrival estimation method of the nested L-shaped antenna array structure, which comprises the following steps:

step S101, constructing a nested L-shaped antenna array structure, and determining a receiving signal of a physical array antenna structure based on the nested L-shaped antenna array structure; the received signal of the physical array antenna structure is:

$z\left(t\right)=\left[\begin{array}{c}x\left(t\right)\\ y\left(t\right)\end{array}\right]=As\left(t\right)+n\left(t\right),$ z(t)＝[z₁(t),z₂(t),…,z_N(t)]^T；

wherein x (t) is the physical array antenna structure RL on the x-axis_xThe received signal of (1); y (t) is the physical array antenna structure RL on the y axis_yThe received signal of (1); a ═ a₁,a₂,…,a_D]Is an array flow pattern of the array antenna structure RL, a_d(D ═ 1, …, D) is the steering vector of the signal on the physical array antenna structure RL, as a function of the direction of arrival (θ, Φ), θ is the pitch angle, Φ is the azimuth angle, and s (t) is the transmitted signal;for the physical array antenna structure RLNoise, n_x(t) is the physical array antenna structure RL on the x-axis_xNoise of (2), n_y(t) is the physical array antenna structure RL on the y-axis_xNoise on (□)^TA transpose operation representing a matrix;

step S102, obtaining a high-order cumulant matrix C of the physical array antenna structure receiving signal z (t) by using a high-order cumulant DOA algorithm_2q,zSaid high order cumulant matrix C_2q,zThe expression of (a) is:

wherein,is the ith of the physical array antenna structure_kReceived signal of array element, 1 ≦ i_kN is not less than 1, k is not less than 2 q; l is a direction index parameter, which is any positive integer;which represents the product of the Kronecker reaction,denotes l a_dPerforming Kronecker product operation to obtain N^l× 1 column vector of dimension a_d(D ═ 1, …, D) is the steering vector of the signal on the physical array antenna structure RL, as a function of the direction of arrival (θ, Φ), θ is the pitch angle and Φ is the azimuth angle, (□) dirac function;

step S103, aiming at the high-order cumulant matrix C_2q,zVectorizing operation is carried out to obtain vectorized c_2q,zSaid vectorized c_2q,zInformation containing all virtual array elements; extracting the information of the maximum continuous virtual square matrix to obtain an equivalent received signal

The equivalent received signalThe expression of (a) is:

${\tilde{c}}_{2q,z}=\[{\tilde{a}}_1,{\tilde{a}}_2,...,{\tilde{a}}_d,...,{\tilde{a}}_D\]p_{2q,s}$

for equivalent signal steering vectors, p, on said physical array antenna structure RL_2q,sIs an equivalent transmit signal;

step S104, for the equivalent received signalPerforming two-dimensional spatial smoothing to obtain equivalent autocorrelation matrixFor the equivalent autocorrelation matrixDecomposing the eigenvalue to obtain a signal eigenvector matrix U_sSum noise eigenvector matrix U_n；

The equivalent autocorrelation matrixThe expression of (a) is:

$\tilde{R}=U_s{\mathrm{\Σ}}_s{U}_s^H+U_n{\mathrm{\Σ}}_n{U}_n^H$

wherein, U_sIs a signal feature vector matrix; u shape_nIs a noise eigenvector matrix; sigma_sSum-sigma_nDiagonal arrays respectively formed by signal and noise characteristic values; (□)^HRepresenting a conjugate transpose operation;

step S105, utilizing the noise characteristic vector matrix U_nAnd said equivalent signal steering vectorConstructing a spectral peak search relation by adopting a two-dimensional MUSIC algorithm, and estimating the direction of arrival by using the spectral peak search relation to obtain an estimated value of the direction of arrival of the received signal

The spectral peak searching relation is as follows:

$P(\widehat{\mathrm{\θ}},\widehat{\mathrm{\φ}})=\frac{1}{{\tilde{a}}^H{U}_n{U}_n^H\tilde{a}}$

wherein,for the purpose of the pitch angle estimation,is an azimuth angle estimated value;a conjugate transpose operation for the equivalent signal steering vector; u shape_nIs a noise eigenvector matrix;performing conjugate transpose operation on the noise characteristic vector matrix;the equivalent signal is directed to the vector.

Further, the process of determining the received signal of the physical array antenna structure in step S101 includes:

determining a physical array antenna structure RL on the x axis based on the number N/2 of the array elements on the x axis of the constructed nested L-shaped antenna array structure and the distance d between two adjacent virtual array elements in each row or each column_yAnd determining the physical array antenna structure RL in said x-axis based on the received signal steering vector_xThe expression of (1) is:

x(t)＝A_xs(t)+n_x(t)；

wherein x (t) is the physical array antenna structure RL on the x-axis_xA received signal of_xFor the physical array antenna structure RL in the x-axis_xS (t) is a transmission signal, n_x(t) is the physical array antenna structure RL on the x-axis_xNoise on;

determining a received signal steering vector of a physical array antenna structure on a y axis based on the number N/2 of array elements of the constructed nested L-shaped antenna array structure on the y axis and the distance d between two adjacent virtual array elements in each row or each column, and determining a received signal of the physical array antenna structure on the y axis based on the received signal steering vector, wherein the expression is as follows:

y(t)＝A_ys(t)+n_y(t)；

wherein y (t) is the physical array antenna structure RL on the y-axis_yA received signal of_yFor the physical array antenna structure RL in the y-axis_yS (t) is a transmission signal, n_y(t) is the physical array antenna structure RL on the y-axis_yNoise on;

according to the physical array antenna structure RL on the x axis_xAnd a physical array antenna structure RL in the y-axis_yThe received signal of the physical array antenna structure RL is obtained as follows:

$z\left(t\right)=\left[\begin{array}{c}x\left(t\right)\\ y\left(t\right)\end{array}\right]=As\left(t\right)+n\left(t\right),$ z(t)＝[z₁(t),z₂(t),…,z_N(t)]^T

wherein x (t) is the physical array antenna structure RL on the x-axis_xThe received signal of (1); y (t) is the physical array antenna structure RL on the y axis_yThe received signal of (1); a ═ a₁,a₂,…,a_d,…,a_D]Is an array flow pattern of the array antenna structure RL, a_d(D ═ 1, …, D) is the steering vector of the signal on the physical array antenna structure RL, as a function of the direction of arrival (θ, Φ), θ is the pitch angle, Φ is the azimuth angle, and s (t) is the transmitted signal;for noise on the physical array antenna structure RL, n_x(t) is the physical array antenna structure RL on the x-axis_xNoise of (2), n_y(t) is the physical array antenna structure RL on the y-axis_xNoise on (□)^TRepresenting a transpose operation of the matrix.

Further, it is characterized byDetermining a physical array antenna structure RL on the x axis based on the number N/2 of the array elements on the x axis of the constructed nested L-shaped antenna array structure and the distance d between two adjacent virtual array elements in each row or each column_yThe process of receiving a signal steering vector, comprising:

obtaining an MXM uniform virtual plane array antenna structure VP through processing the received signal of the nested L-shaped antenna array structure RL;

setting a distance d between two adjacent virtual array elements in each row or each column, wherein any virtual array element in the mxm uniform virtual planar array antenna structure VP is represented as:

$VE(m,n),(m,n=-\frac{M-1}{2},-\frac{M-1}{2}+1,...,0,...,\frac{M-1}{2}-1,\frac{M-1}{2})$

wherein M is N²N is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N，n＝1,2,3,…；

By a physical array antenna structure RL in the x-axis_xN/2 and the distance d between two adjacent virtual array elements in each row or column determine the physical array antenna structure RL on the x-axis_xOf the received signal steering vector a_x,d(θ, φ), expressed as:

$a_{x,d}(\mathrm{\θ},\mathrm{\φ})={\[{\mathrm{\β}}_x(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_x^{N/4}(\mathrm{\θ},\mathrm{\φ}),{\mathrm{\β}}_x^{N/4+1}(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_x^{(N/4)(N/4+1)}(\mathrm{\θ},\mathrm{\φ})\]}^T$

wherein, β_x(theta, phi) is the physical array antenna structure RL in the x-axis_xThe phase difference between adjacent inner array elements, θ is the pitch angle of the received signal, Φ is the azimuth angle of the received signal, N is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, ….

Further, the physical array antenna structure RL in the x-axis_xPhase difference β between adjacent array elements_x(θ, φ) is determined by the following process:

far field signal s_d(t) physical array antenna Structure RL incident on the x-axis_xSelecting the kth array element from the array elements, mapping the received signal to the RL plane of the physical array antenna structure, and then mapping the received signal to the RL plane of the physical array antenna structure on the x axis_xObtaining the phase difference of the kth array element on the x axis relative to a reference point:

β_k＝e^{-j2πkcosθcosφ/λ}(1≤k≤N/4)

or,

β_k＝e^{-j2πk(N/4+1)cosθcosφ/λ}(N/4+1≤k≤(N/4)(N/4+1))

in the formula, j is an imaginary unit; theta is the pitch angle of the received signal; phi is the azimuth angle of the received signal; λ is the wavelength of the received signal; n is the array element number of the array antenna structure RL;

phase expressed in formulaDifference β_kEqual to the physical array antenna structure RL on the x-axis_xPhase difference β between adjacent array elements_x(θ,φ)。

Furthermore, the process of determining the received signal steering vector of the physical array antenna structure on the y axis based on the number N/2 of the array elements of the constructed nested L-shaped antenna array structure on the y axis and the distance d between two adjacent virtual array elements in each row or each column comprises:

obtaining an MXM uniform virtual plane array antenna structure VP through processing the received signal of the nested L-shaped antenna array structure RL;

setting a distance d between two adjacent virtual array elements in each row or each column, wherein any virtual array element in the mxm uniform virtual planar array antenna structure VP is represented as:

$VE(m,n),(m,n=-\frac{M-1}{2},-\frac{M-1}{2}+1,...,0,...,\frac{M-1}{2}-1,\frac{M-1}{2})$

wherein M is N²N is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, …;

by physical array antenna structure RL in the y-axis_yN/2 and the distance d between two adjacent virtual array elements in each row or each column can determine the physical array antenna structure RL on the y-axis_yThe upper received signal steering vector is a_y,d(θ, φ), expressed as:

$a_{y,d}\left(\mathrm{\θ},\mathrm{\φ}\right)={\[{\mathrm{\β}}_y(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_y^{N/4}(\mathrm{\θ},\mathrm{\φ}),{\mathrm{\β}}_y^{N/4+1}(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_y^{(N/4)(N/4+1)}(\mathrm{\θ},\mathrm{\φ})\]}^T$

wherein, β_y(theta, phi) is the physical array antenna structure RL on the y-axis_yThe phase difference between adjacent array elements in the receiving device is equal to theta, and theta is the pitch angle of the received signal; phi is the azimuth angle of the received signal; and N is the array element number of the array antenna structure RL.

Further, the physical array antenna structure RL in the y-axis_yPhase difference β between adjacent array elements_y(θ, φ) is determined by the following process:

far field signal s_d(t) physical array antenna Structure RL incident on the y-axis_ySelecting the kth array element from the array elements, mapping the received signal to the RL plane of the physical array antenna structure, and then mapping the received signal to the RL plane of the physical array antenna structure on the y axis_yIn the method, the phase difference of the kth array element relative to a reference point can be obtained:

β_k＝e^{-j2πkcosθsinφ/λ}(1≤k≤N/4)

or,

β_k＝e^{-j2πk(N/4+1)cosθsinφ/λ}(N/4+1≤k≤(N/4)(N/4+1))；

wherein j is an imaginary unit, and θ is a pitch angle of the received signal; phi is the azimuth angle of the received signal; λ is the wavelength of the received signal; n is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, …;

phase difference β expressed by the above formula_kEqual to the physical array antenna structure RL on the y-axis_yPhase difference β between adjacent array elements_y(θ,φ)。

Further, the pair of high-order cumulant matrices C in step S103_2q,zVectorizing operation is carried out to obtain vectorized c_2q,zThe process comprises the following steps:

using the following formula, a high-order cumulant matrix C of the received signals of the physical array antenna structure RL_2q,zVectorizing operation is carried out to obtain vectorized c_2q,z：

$\begin{array}{c}{c}_{2q,z}=\[a_1^{*\⊗q}\⊗{a_1}^{\⊗q},\mathrm{...},a_d^{*\⊗q}\⊗{a_d}^{\⊗q},\mathrm{...},a_d^{*\⊗q}\⊗{a_D}^{\⊗q}\]p_{2q,s}=\[b_1,\mathrm{...},b_d,\mathrm{...},b_D\]p_{2q,s}\\ ,b_d=a_d^{*\⊗q}\⊗{a_d}^{\⊗q}={\left[\begin{array}{c}{a}_{x,d}\\ a_{y,d}\end{array}\right]}^{*\⊗q}\⊗{\left[\begin{array}{c}{a}_{x,d}\\ a_{y,d}\end{array}\right]}^{\⊗q}\end{array}$

Wherein, b_dComprises ${\tilde{a}}_d={\tilde{a}}_{x,d}\⊗{\tilde{a}}_{y,d},{\tilde{a}}_{x,d}=a_{x,d}^{*}\⊗a_{x,d},{\tilde{a}}_{y,d}=a_{y,d}^{*}\⊗a_{y,d},$ For an equivalent signal steering vector on the physical array antenna structure RL,for the physical array antenna structure RL in the x-axis_xThe above equivalent signal-steering vector is,for the physical array antenna structure RL in the y-axis_yThe above equivalent signal steering vector, q is 1,2,3, …, which is a parameter of order; said vectorised c_2q,zContaining information of all virtual array elements.

Or,

using the following formula, the high-order cumulant matrix C is obtained_2q,zVectorizing operation is carried out to obtain vectorized c_2q,z(ii) a Said vectorised c_2q,zThe expression of (a) is:

wherein l is a direction index parameter which is any positive integer; a is_d(D-1, …, D) is the steering vector of the signal on the physical array antenna structure RL as a function of the direction of arrival (θ, Φ), θ is the pitch angle, Φ is the azimuth angle,denotes l a_dPerforming Kronecker product operation to obtain N^lColumn vectors of dimension × 1.

The technical scheme of the invention can show that the invention has the following technical effects:

the invention has simple structure and is easier to realize; under the condition of using less array elements, the method has larger effective aperture and stronger method applicability, and solves the problem of low accuracy of estimation of the direction of arrival in the prior art.

Drawings

The present invention, however, both as to organization, principles, operation, and advantages thereof, may best be understood by reference to the following description, taken in conjunction with the accompanying drawings, which are included to further explain the present invention, the drawings being described and illustrated herein for purposes of better understanding the present invention and are not to be considered as limiting, in which:

fig. 1 is a flowchart of a direction of arrival estimation method for a nested L-shaped antenna array structure according to the present invention;

fig. 2 is a diagram of the relationship between the nested L-shaped antenna array structure and the mxm uniform virtual planar array antenna structure VP according to the present invention;

FIG. 3 is a schematic structural diagram of a physical array antenna structure according to the present disclosure;

FIG. 4 is a diagram of a direction of arrival estimation spectrum according to the present disclosure;

FIG. 5 is a diagram of the variation of the RMS error with the SNR for the estimation of the direction of arrival disclosed in the present invention;

FIG. 6 is a graph of the variation of the RMS error along with the sampling snapshot number for the direction of arrival estimation disclosed in the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings.

Hereinafter, a specific embodiment of the present invention will be described with reference to fig. 1 to 6.

The first embodiment is as follows:

the invention provides a nested L-shaped antenna array structure, marked as RL, which comprises: physical array antenna structure RL in the x-axis_xAnd physical array antenna structure RL in the y-axis_y。

Physical array antenna structure RL on the x-axis_xThe array comprises a two-level nested array consisting of two uniform linear arrays, wherein the ith level kth physical array element is expressed as:

$RE(m,0),(m=k(\underset{i=1}{\overset{2}{\Π}}{N}_i)d,N_1=1,N_2=N/4+1)$ equation 1

The parameter d is the array element interval of the first stage, d is lambda/2, and lambda is the wavelength of an incident signal; i is 1, 2; k is 1,2, L, N/4; n is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, …; physical array antenna structure RL on the x-axis_xThe array element number of (2) is N/2;

physical array antenna structure RL on the y-axis_yThe system comprises a two-level nested array consisting of two uniform linear arrays, wherein the nth physical array element of the ith level is represented as:

$RE(0,m),(m=k(\underset{i=1}{\overset{2}{\Π}}{N}_i)d,N_1=1,N_2=N/4+1)$ equation 2

D is the array element spacing of the first stage, d is lambda/2, and lambda is the wavelength of an incident signal; i is 1, 2; k is a number of bits of 1,2, …,n/4; n is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2, …, N/4; physical array antenna structure RL on the y-axis_yThe number of array elements is N/2.

Example two:

the invention also provides a two-dimensional direction of arrival estimation method of the nested L-shaped antenna array structure, the implementation flow of which is shown in figure 1, and the method comprises the following steps:

step S101, constructing a nested L-shaped antenna array structure RL, and determining a received signal of the physical array antenna structure RL based on the nested L-shaped antenna array structure RL.

The nested L-shaped antenna array structure RL is constructed as in the first embodiment and will not be described in detail here.

In step S101, a process of determining a received signal of the physical array antenna structure RL based on the constructed nested L-shaped antenna array structure RL is specifically as follows:

obtaining an M × M uniform virtual planar array antenna structure VP through processing the received signal of the nested L-shaped antenna array structure RL, where the M × M uniform virtual planar array antenna structure VP is formed by M rows and M columns of virtual array element square arrays (M ═ N)²/2+ N-1), the center of the M × M uniform virtual planar array antenna structure VP being the origin, thThe straight line of the line virtual array element is the x axisThe straight line of the row of virtual array elements is the y axis, and a rectangular coordinate system is established according to the straight line, so as to obtain a relation diagram of the nested L-shaped antenna array structure RL and the uniform virtual planar array antenna structure VP of M × M as shown in FIG. 2_xAnd physical array antenna structure RL in the y-axis_yDoes not have a true at the intersection pointAnd in order to obtain more virtual array elements, the intersection point is taken as a reference point, and the forward extension is carried out along the x axis and the y axis to obtain more virtual array elements in the physical array antenna structure RL.

Setting a distance d between two adjacent virtual array elements in each row or each column, wherein any virtual array element in the mxm uniform virtual planar array antenna structure VP is represented as:

$VE(m,n),(m,n=-\frac{M-1}{2},-\frac{M-1}{2}+1,...,0,...,\frac{M-1}{2}-1,\frac{M-1}{2})$ equation 3

Wherein M is N²And/2 + N-1, where N is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, and N is 1,2,3, and ….

By a physical array antenna structure RL in the x-axis_xThe number of the array elements N/2 and the distance d between two adjacent virtual array elements in each row or each column can determine the physical array antenna structure on the x-axisRL_xOf the received signal steering vector a_x,d(θ, φ), expressed as:

$a_{x,d}(\mathrm{\θ},\mathrm{\φ})={\[{\mathrm{\β}}_x(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_x^{N/4}(\mathrm{\θ},\mathrm{\φ}),{\mathrm{\β}}_x^{N/4+1}(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_x^{(N/4)(N/4+1)}(\mathrm{\θ},\mathrm{\φ})\]}^T$ equation 4

Wherein, β_x(theta, phi) is the physical array antenna structure RL in the x-axis_xThe phase difference between adjacent inner array elements, θ is the pitch angle of the received signal, Φ is the azimuth angle of the received signal, N is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, ….

Physical array antenna structure RL in the x-axis_xPhase difference β between adjacent array elements_xThe process of (θ, φ) determination is specifically as follows:

far field signal s_d(t) physical array antenna Structure RL incident on the x-axis_xSelecting the kth array element from the array elements, mapping the received signal to the RL plane of the physical array antenna structure, and then mapping the received signal to the RL plane of the physical array antenna structure on the x axis_xThe phase difference of the kth array element on the x axis relative to a reference point can be obtained:

β_k＝e^{-j2πkcosθcosφ/λ}(1. ltoreq. k. ltoreq.N/4) formula 5

Or,

β_k＝e^{-j2πk(N/4+1)cosθcosφ/λ}(N/4+ 1. ltoreq. k. ltoreq. N/4 (N/4+1)) formula 6

In equations 5 and 6, j is an imaginary unit; theta is the pitch angle of the received signal; phi is the azimuth angle of the received signal; λ is the wavelength of the received signal; n is the array element number of the array antenna structure RL;

the phase difference expressed by the above equation 5 or equation 6 is the physical array antenna structure RL on the x-axis_xPhase difference β between adjacent array elements_x(theta, phi). Substituting this into equation 4, the physical array antenna structure RL in the x-axis can be determined_xIs received by the receiving stationNumber-oriented vector a_x,d(θ,φ)。

By physical array antenna structure RL in the y-axis_yN/2 and the distance d between two adjacent virtual array elements in each row or each column can determine the physical array antenna structure RL on the y-axis_yThe upper received signal steering vector is a_y,d(θ, φ), expressed as:

$a_{y,d}\left(\mathrm{\θ},\mathrm{\φ}\right)={\[{\mathrm{\β}}_y(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_y^{N/4}(\mathrm{\θ},\mathrm{\φ}),{\mathrm{\β}}_y^{N/4+1}(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_y^{(N/4)(N/4+1)}(\mathrm{\θ},\mathrm{\φ})\]}^T$ equation 7

Wherein, β_y(theta, phi) is the physical array antenna structure RL on the y-axis_yThe phase difference between adjacent array elements in the receiving device is equal to theta, and theta is the pitch angle of the received signal; phi is the azimuth angle of the received signal; and N is the array element number of the array antenna structure RL.

Physical array antenna structure RL in the y-axis_yPhase difference β between adjacent array elements_yThe process of (θ, φ) determination is specifically as follows:

far field signal s_d(t) physical array antenna Structure RL incident on the y-axis_ySelecting the kth array element from the array elements, mapping the received signal to the RL plane of the physical array antenna structure, and then mapping the received signal to the RL plane of the physical array antenna structure on the y axis_yIn the method, the phase difference of the kth array element relative to a reference point can be obtained:

β_k＝e^{-j2πkcosθsinφ/λ}(1. ltoreq. k. ltoreq.N/4) formula 8

Or,

β_k＝e^{-j2πk(N/4+1)cosθsinφ/λ}(N/4+ 1. ltoreq. k. ltoreq. N/4) (N/4+ 1)); equation 9

Wherein j is an imaginary unit, and θ is a pitch angle of the received signal; phi is the azimuth angle of the received signal; λ is the wavelength of the received signal; n is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, ….

The phase difference expressed by the above equation 8 or equation 9 is the physical array antenna structure RL on the y-axis_yPhase difference β between adjacent array elements_y(theta, phi). Substituting this into equation 7, the physical array antenna structure RL in the y-axis can be determined_yThe upper received signal steering vector is a_y,d(θ,φ)。

Physical array antenna structure RL on the x-axis based on the determination in equation 4_xOf the received signal steering vector a_x,d(theta, phi) determining the physical array antenna structure RL in the x-axis_xThe received signals of (a) are:

x(t)＝A_xs(t)+n_x(t)

and,

x(t)＝[x₁(t),x₂(t),…,x_d(t),…,x_D(t)]^T；

A_x＝[a_x,1,a_x,2,…,a_x,d,…,a_x,D]；

s(t)＝[s₁(t),s₂(t),…,s_d(t),…,s_D(t)]^T；

n_x(t)＝[n₁(t),n₂(t),…,n_d(t),…,n_D(t)]^T

equation 10

Wherein x (t) is the physical array antenna structure RL on the x-axis_xA received signal of_xFor the physical array antenna structure RL in the x-axis_xArray flow pattern of a_x,d(D-1, …, D) is a physical array antenna structure RL with signals on the x-axis_xAn upper steering vector is a function of the direction of arrival (θ, φ), and $a_{x,d}(\mathrm{\θ},\mathrm{\φ})={\[{\mathrm{\β}}_x(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_x^{N/4}(\mathrm{\θ},\mathrm{\φ}),{\mathrm{\β}}_x^{N/4+1}(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_x^{(N/4)(N/4+1)}(\mathrm{\θ},\mathrm{\φ})\]}^T,$ β_x(θ,φ)＝e^{-j2πkcosθsinφ/λ}(1. ltoreq. k. ltoreq.N/4) or β_x(θ,φ)＝e^{-j2πk(N/4+1)cosθsinφ/λ}(N/4+ 1. ltoreq. k. ltoreq. N/4) (N/4+ 1)); j is an imaginary unit, N is the number of elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, …. λ is the wavelength of the received signal, θ is the pitch angle, φ is the azimuth angle, s (t) is the transmitted signal, n_x(t) is the physical array antenna structure RL on the x-axis_xThe noise of (2).

Based on the physical array antenna structure RL on the y-axis determined in equation 7_yThe upper received signal steering vector is a_y,d(theta, phi) determining the physical array antenna structure RL on the y-axis_yThe received signals of (a) are:

y(t)＝A_ys(t)+n_y(t)

and,

y(t)＝[y₁(t),y₂(t),…,y_d(t),…,y_D(t)]^T；

A_y＝[a_y,1,a_y,2,…,a_y,d,…,a_y,D]；

s(t)＝[s₁(t),s₂(t),…,s_d(t),…,s_D(t)]^T；

n_y(t)＝[n₁(t),n₂(t),…,n_d(t),…,n_D(t)]^T

equation 11

Wherein y (t) is the physical array antenna structure RL on the y-axis_yA received signal of_yFor the physical array antenna structure RL in the y-axis_yArray flow pattern of a_y,d(D-1, …, D) is a physical array antenna structure RL with signals on the y-axis_yAn upper steering vector is a function of the direction of arrival (θ, φ), and $a_{y,d}\left(\mathrm{\θ},\mathrm{\φ}\right)={\[{\mathrm{\β}}_y(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_y^{N/4}(\mathrm{\θ},\mathrm{\φ}),{\mathrm{\β}}_y^{N/4+1}(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_y^{(N/4)(N/4+1)}(\mathrm{\θ},\mathrm{\φ})\]}^T,$ β_y(θ,φ)＝e^{-j2πkcosθsinφ/λ}(1≤k is less than or equal to N/4) or β_y(θ,φ)＝e^{-j2πk(N/4+1)cosθsinφ/λ}(N/4+ 1. ltoreq. k. ltoreq. N/4) (N/4+ 1)); j is an imaginary unit, N is the number of elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, …. λ is the wavelength of the received signal, θ is the pitch angle, φ is the azimuth angle, s (t) is the transmitted signal, n_y(t) is the physical array antenna structure RL on the y-axis_yThe noise of (2).

Physical array antenna structure RL on x axis obtained according to the above_yAnd physical array antenna structure RL in the y-axis_yThe received signal of the physical array antenna structure RL shown in fig. 2 can be obtained, and the expression is:

$z\left(t\right)=\left[\begin{array}{c}x\left(t\right)\\ y\left(t\right)\end{array}\right]=As\left(t\right)+n\left(t\right)$

and,

z(t)＝[z₁(t),z₂(t),…,z_N(t)]^Tequation 12

Wherein x (t) is the physical array antenna structure RL on the x-axis_xThe received signal of (1); y (t) is the physical array antenna structure RL on the y axis_yThe received signal of (1); $A=\left[\begin{array}{c}{A}_x\\ A_y\end{array}\right]$ for the array flow pattern on the array antenna structure RL, A_x＝[a_x,1,a_x,2,…,a_x,d,…,a_x,D]，A_y＝[a_y,1,a_y,2,…,a_y,d,…,a_y,D]，a_x,dAnd a_x,dPhysical array antenna structure RL with signals on the x-axis respectively_xPhysical array antenna structure RL with steering vector sum signal on y-axis_yThe upper steering vector is a function of the direction of arrival (theta, phi), theta is a pitch angle, phi is an azimuth angle, and s (t) is a transmitting signal;for noise on the physical array antenna structure RL, n_x(t) physical array antenna Structure RL in the x-axis_xNoise of (2), n_y(t) physical array antenna Structure RL in the y-axis_xNoise on (□)^TRepresenting a transpose operation of the matrix.

Step S102, obtaining a high-order cumulant matrix of the received signal z (t) of the physical array antenna structure RL by using a high-order cumulant DOA algorithm.

Obtaining a high-order cumulant matrix C of the received signals of the physical array antenna structure RL according to the DOA algorithm of a high-order cumulant formula by using the received signals z (t)_2q,zSaid high order cumulant matrix C_2q,zThe expression of (a) is:

equation 13

Wherein,is the ith of the physical array antenna structure RL_kReceived signal of array element, 1 ≦ i_kN is not less than 1, k is not less than 2 q; l is a direction index parameter which can be any positive integer;a parameter representing the Kronecker product, q ═ 1,2,3, …, for the order;denotes l a_dPerforming Kronecker product operation to obtain N^l× 1 column vector of dimension a_dIs a function of the direction of arrival (θ, φ); theta is a pitch angle; phi is an azimuth angle; (□) a dirac function;

step S103, aiming at the high-order cumulant matrix C_2q,zVectorizing, and according to c after vectorization_2q,zExtracting the information of the most continuous virtual array elements to obtain equivalent received signals

For the high-order cumulant matrix C_2q,zVectorizing to obtain vectorized c_2q,z：

Equation 14

Wherein, a_d(D-1, …, D) is the steering vector of the signal on the physical array antenna structure RL as a function of the direction of arrival (θ, Φ), θ is the pitch angle, Φ is the azimuth angle,denotes l a_dPerforming Kronecker product operation to obtain N^lColumn vector of dimension × 1, p_2q,sIs an equivalent transmitted signal.

C after vectorization as described above_2q,zExtracting the information of the most continuous virtual array elements to obtain equivalent received signalsComprises the following steps:

${\tilde{c}}_{2q,z}=\[{\tilde{a}}_1,{\tilde{a}}_2,...,{\tilde{a}}_d,...,{\tilde{a}}_D\]p_{2q,s}$ equation 15

Wherein,for an equivalent signal steering vector to be used,middle (k)₂-1)(2N′-1)+k₁) The elements of the row are:k₁＝1,2,…,2N′-1，k₂1,2, …,2N '-1, 2N' -1 is the number of virtual array elements of x-axis and y-axis, u_d＝cosθ_dcosφ_d，v_d＝cosθ_dsinφ_d， $p_{2q,s}={\[{\mathrm{\γ}}_{2q,s_1},{\mathrm{\γ}}_{2q,s_2},...,{\mathrm{\γ}}_{2q,s_d},...,{\mathrm{\γ}}_{2q,s_D}\]}^T,{\mathrm{\γ}}_{2q,s_d},(d=1,2,...,D)$ Is the power of the signal.

The equivalent array receiving signal described in the above step S103The determination method of (2) may also be obtained by:

a high-order cumulant matrix C for the received signals of the physical array antenna structure RL_2q,zPerforming vectorization operations can yield:

equation 16

Wherein, a_d(D ═ 1, …, D) is the steering vector of the signal on the physical array antenna structure RL, as a function of the direction of arrival (θ, Φ), θ being the pitch angle and Φ being the azimuth angle;denotes a_d(D ═ 1, …, D) conjugate operations; p is a radical of_2q,sIs an equivalent transmitted signal.

The equation can also be written as:

$c_{2q,z}=\[a_1^{*\⊗q}\⊗{a_1}^{\⊗q},\mathrm{...},a_d^{*\⊗q}\⊗{a_d}^{\⊗q},\mathrm{...},a_d^{*\⊗q}\⊗{a_D}^{\⊗q}\]p_{2q,s}=\[b_1,\mathrm{...},b_d,\mathrm{...},b_D\]p_{2q,s}$ equation 17

Wherein, $b_d=a_d^{*\⊗q}\⊗{a_d}^{\⊗q}={\left[\begin{array}{c}{a}_{x,d}\\ a_{y,d}\end{array}\right]}^{*\⊗q}\⊗{\left[\begin{array}{c}{a}_{x,d}\\ a_{y,d}\end{array}\right]}^{\⊗q},$ obviously, b_dComprises ${\tilde{a}}_d={\tilde{a}}_{x,d}\⊗{\tilde{a}}_{y,d},$ Anda_x,d(D-1, …, D) is a physical array antenna structure RL with signals on the x-axis_xThe upper steering vector, a, is a function of the direction of arrival (θ, φ)_y,d(D-1, …, D) is a physical array antenna structure RL with signals on the y-axis_yThe steering vector above, being a function of the direction of arrival (θ, φ), θ being the pitch angle and φ being the azimuth angle, (□)^*The vectorized M × M uniform virtual planar array antenna structure VP is obtained;

then extracting the maximum continuous virtual array elements in the vectorized virtual plane array antenna structure VP, and constructing the equivalent receiving signal of the physical array antenna structure RL according to the vectorized continuous virtual array elements

Step S104, for the equivalent received signalPerforming two-dimensional spatial smoothing to obtain equivalent autocorrelation matrixSignal eigenvector matrix U_sSum noise eigenvector matrix U_n. The specific implementation steps are as follows:

using said equivalent received signalObtaining equivalent autocorrelation matrix by two-dimensional space smoothing methodThe expression is as follows:

$\tilde{R}=U_s{\mathrm{\Σ}}_s{U}_s^H+U_n{\mathrm{\Σ}}_n{U}_n^H$ equation 18

Wherein, sigma_sSum-sigma_nDiagonal arrays respectively formed by signal and noise characteristic values; u shape_sAnd U_nRespectively a signal eigenvector matrix and a noise eigenvector matrix. For the equivalent autocorrelation matrixDecomposing the eigenvalue to obtain a signal eigenvector matrix U_sSum noise eigenvector matrix U_n。

Wherein the equivalent autocorrelation matrixThe determination method specifically includes:

the equivalent received signal obtained aboveIs divided into N^′2A sub-rectangular array (called sub-array for short) with the size of N '× N',the array element distribution of the (m, n) th sub-array can be expressed as:

{((n_x+m-N′)λ/2,(n_y+ N-N') λ/2) } equation 19

Wherein n is_x＝0,1,…,N′-1，n_yWhere λ is the wavelength of the received signal, 0,1, …, N' -1.

The output of the (m, n) th sub-array is:

${\stackrel{\‾}{z}}_{m,n}={\stackrel{\‾}{A}}_{m,n}{p}_{2q,s}$ equation 20

ThereinIs an array flow pattern of the (m, n) th sub-array, and the expression is as follows: ${\stackrel{\‾}{A}}_{m,n}=\[{\tilde{a}}_{m,n}^1,...{\left({\tilde{a}}_{m,n}^d\right)}_{(n_y-1)*N^{\′}+n_x}...,{\tilde{a}}_{m,n}^D\],$ therein ${\left({\tilde{a}}_{m,n}^d\right)}_{(n_y-1)*N^{\′}+n_x}=e^{j\mathrm{\π}\[(n_x+m-N^{\′})u_d+(n_y+n-N^{\′})v_d\]}.$ The remaining parameters in the formula have the same meaning as the same parameters described above and will not be described in detail here.

Obtaining an autocorrelation matrix of an (m, n) th sub-array output signal according to the following formula:

${\stackrel{\‾}{R}}_{m,n}={\stackrel{\‾}{A}}_{m,n}{p}_{2q,s}{p}_{2q,s}^H{\stackrel{\‾}{A}}_{m,n}^H$ equation 21

Wherein, $p_{2q,s}={\[{\mathrm{\γ}}_{2q,s_1},{\mathrm{\γ}}_{2q,s_2},...,{\mathrm{\γ}}_{2q,s_d},...,{\mathrm{\γ}}_{2q,s_D}\]}^T,{\mathrm{\γ}}_{2q,s_d},(d=1,2,...,D)$ is the power of the signal (□)^TIndicating the transpose operation of the matrix (□)^HRepresenting a conjugate transpose operation of the matrix. The remaining parameters in the formula have the same meaning as the same parameters described above and will not be described in detail here.

To N^′2After the autocorrelation matrixes of the output signals of the subarrays are summed and averaged, the following can be obtained:

$\stackrel{\‾}{R}=\frac{1}{N^{\′2}}\underset{n=1}{\overset{N^{\′}}{\Σ}}\underset{m=1}{\overset{N^{\′}}{\Σ}}{\stackrel{\‾}{R}}_{m,n}=\frac{1}{N^{\′2}}{\left({\stackrel{\‾}{A}}_{1,1}{\mathrm{\Λ}}_{2q,s}{\stackrel{\‾}{A}}_{1,1}^H\right)}^2$ equation 22

Wherein, Λ_2q,s＝diag(p_2q,s)，The array flow pattern of the (m, n) th subarray is shown. The remaining parameters have the same meanings as described above.

To pairAfter the evolution, the following can be obtained:

$\tilde{R}=\frac{1}{N^{\′}}\left({\stackrel{\‾}{A}}_{1,1}{\mathrm{\Λ}}_{2q,s}{\stackrel{\‾}{A}}_{1,1}^H\right)=U_s{\mathrm{\Σ}}_s{U}_s^H+U_n{\mathrm{\Σ}}_n{U}_n^H$ equation 23

Wherein, sigma_sSum-sigma_nDiagonal arrays respectively formed by signal and noise characteristic values; u shape_sAnd U_nRespectively a signal characteristic vector matrix and a noise characteristic vector matrix; (□)^HRepresenting a conjugate transpose operation; the remaining parameters in the formula have the same meaning as the same parameters described above and will not be described in detail here.

Step S105, utilizing the noise characteristic vector matrix U_nAnd said equivalent signal steering vectorAnd constructing a spectral peak search relational expression by adopting a two-dimensional MUSIC algorithm, and estimating the direction of arrival by using the spectral peak search relational expression to obtain an estimated value of the received signal. The specific implementation conditions are as follows:

for the equivalent autocorrelation matrixDecomposing the eigenvalue, wherein the matrix formed by the eigenvectors corresponding to the large eigenvalue is a signal subspace U_sThe matrix formed by the eigenvectors corresponding to the small eigenvalues is the noise subspace U_nUsing equivalent signal steering vectorsAnd equivalent noise subspace matrix U_nConstructing a spectrum peak search relation, wherein the expression is as follows:

$P(\widehat{\mathrm{\θ}},\widehat{\mathrm{\φ}})=\frac{1}{{\tilde{a}}^H{U}_n{U}_n^H\tilde{a}}$ equation 24

Wherein,for the purpose of the pitch angle estimation,is an azimuth angle estimated value;a conjugate transpose operation for the equivalent signal steering vector; u shape_nIs a noise eigenvector matrix;performing conjugate transpose operation on the noise characteristic vector matrix;is an equivalent signal directorAn amount;

performing two-dimensional ordinary peak search by using the spectral peak search relation to obtain an estimated value of the received signal

The performance of the physical array antenna structure RL and its DOA estimation algorithm is explained by simulation experiments below. And respectively applying a high-order cumulant algorithm to the physical array antenna structure RL, wherein the simulation conditions in the test are q is 2, L is 1, and the array element number N is 12, the minimum array element distance d of the first-stage array in the physical array antenna structure RL is lambda/2, and lambda is the wavelength of a signal. In the uniform L-shaped array, the minimum array element spacing d is lambda/2. In a two-dimensional nested array, a dense lattice N is randomly generated^(d)And is and $P=\left(\begin{array}{cc}3& 0\\ 0& 3\end{array}\right),$ the number of array elements N on the lattice^(d)＝det(P)＝9，N^(s)＝4。

Simulation 1: fig. 4 shows a spectrogram of the direction of arrival estimation disclosed in the present invention, where 36 mutually independent signal sources are emitted into three different array models, where the SNR is 10dB and the snapshot number T is 1000.

As can be seen from fig. 4, the L-shaped nested array can accurately estimate 36 signals in the case of using only 12 array elements.

Simulation 2: fig. 5 shows a diagram of the variation of the root mean square error of the direction of arrival estimation with the signal-to-noise ratio disclosed in the present invention. Wherein the signal to noise ratioFrom-6 dB to 14dB, six from [ theta ]₁,θ₂,θ₃,θ₄,θ₅,θ₆]＝[60°,45°,8°,30°,75°,15°]And [ phi ]₁,φ₂,φ₃,φ₄,φ₅,φ₆]＝[13°,60°,36°,50°,5°,25°]The Root Mean Square Error (RMSE) was calculated from the independent non-gaussian signal sources for the direction by N-1000 monte carlo experiments, and the other simulation conditions were the same as above.

Defining a root mean square error of

$RMSE=\sqrt{\frac{1}{ND}\underset{k=1}{\overset{D}{\Σ}}\underset{i=1}{\overset{N}{\Σ}}({\left({\widehat{\mathrm{\θ}}}_k^{\left(i\right)}-{\mathrm{\θ}}_k\right)}^2+{\left({\widehat{\mathrm{\φ}}}_k^{\left(i\right)}-{\mathrm{\φ}}_k\right)}^2)}$ Equation 24

Wherein,andare each theta_kAnd phi_kAn estimated value of an ith Monte Carlo experiment; n is the number of independent Monte Carlo experiments; d is the number of signals.

Simulation 3: referring to fig. 6, a graph of variation of the root mean square error of the direction of arrival estimation with the sampling snapshot number is shown. The number of sample points varies from 400 to 2900, with other simulation conditions being the same.

As can be seen from fig. 5 and 6, the physical array antenna structure RL has the best performance, and then is a two-dimensional nested array, and the uniform L-shaped array has the worst performance, because the nested array forms a virtual uniform rectangular array with more array elements, the aperture of the array is further enlarged, and the direction finding precision is improved. Also, in planar arrays, the performance of L-shaped arrays is superior to other arrays.

Although the present invention has been described in terms of the preferred embodiment, it is not intended that the invention be limited to the embodiment. Any equivalent changes or modifications made without departing from the spirit and scope of the present invention also belong to the protection scope of the present invention. The scope of the invention should therefore be determined with reference to the appended claims.

Claims (8)

1. A nested L-shaped antenna array structure, the nested L-shaped antenna array structure comprising:

physical array antenna structure RL in the x-axis_xAnd physical array antenna structure RL in the y-axis_y；

Physical array antenna structure RL on the x-axis_xThe array comprises a two-level nested array consisting of two uniform linear arrays, wherein the ith level kth physical array element is expressed as:

$RE(m,0)(m=k(\underset{i=1}{\overset{2}{\Π}}{N}_i)d,N_1=1,N_2=N/4+1)$

d is the array element spacing of the first stage, d is lambda/2, and lambda is the wavelength of an incident signal; i is 1, 2; k is 1,2, …, N/4; n is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, …; physical array antenna structure RL on the x-axis_xThe array element number of (2) is N/2;

physical array antenna structure RL on the y-axis_yThe system comprises a two-level nested array consisting of two uniform linear arrays, wherein the nth physical array element of the ith level is represented as:

$RE(0,m)(m=k(\underset{i=1}{\overset{2}{\Π}}{N}_i)d,N_1=1,N_2=N/4+1)$

d is the array element spacing of the first stage, d is lambda/2, and lambda is the wavelength of an incident signal; i is 1, 2; k is 1,2, …, N/4; n is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2, …, N/4; physical array antenna structure RL on the y-axis_yThe number of array elements is N/2.

2. A method for estimating a direction of arrival of a nested L-shaped antenna array structure, the method comprising:

step S101, constructing a nested L-shaped antenna array structure, and determining a receiving signal of a physical array antenna structure based on the nested L-shaped antenna array structure; the received signal of the physical array antenna structure is:

$z\left(t\right)=\left[\begin{array}{c}x\left(t\right)\\ y\left(t\right)\end{array}\right]=As\left(t\right)+n\left(t\right),z\left(t\right)={\[z_1\left(t\right),z_2\left(t\right),...,z_N\left(t\right)\]}^T;$

wherein x (t) is the physical array antenna structure RL on the x-axis_xThe received signal of (1); y (t) is the physical array antenna structure RL on the y axis_yThe received signal of (1); a ═ a₁,a₂,…,a_D]Is an array flow pattern of the array antenna structure RL, a_d(D ═ 1, …, D) is the steering vector of the signal on the physical array antenna structure RL, as a function of the direction of arrival (θ, Φ), θ is the pitch angle, Φ is the azimuth angle, and s (t) is the transmitted signal;for noise on the physical array antenna structure RL, n_x(t) is the physical array antenna structure RL on the x-axis_xNoise of (2), n_y(t) is the physical array antenna structure RL on the y-axis_xNoise on (□)^TA transpose operation representing a matrix;

step S102, obtaining a high-order cumulant matrix C of the physical array antenna structure receiving signal z (t) by using a high-order cumulant DOA algorithm_2q,zSaid high order cumulant matrix C_2q,zThe expression of (a) is:

wherein,is the ith of the physical array antenna structure_kReceived signal of array element, 1 ≦ i_kN is not less than 1, k is not less than 2 q; l is a direction index parameter, which is any positive integer;which represents the product of the Kronecker reaction,denotes l a_dPerforming Kronecker product operation to obtain N^l× 1 column vector of dimension a_d(D ═ 1, …, D) is the steering vector of the signal on the physical array antenna structure RL, as a function of the direction of arrival (θ, Φ), θ is the pitch angle and Φ is the azimuth angle, (□) dirac function;

step S103, aiming at the high-order cumulant matrix C_2q,zVectorizing operation is carried out to obtain vectorized c_2q,zSaid vectorized c_2q,zInformation containing all virtual array elements; extracting the information of the maximum continuous virtual square matrix to obtain an equivalent received signal

The equivalent received signalThe expression of (a) is:

${\tilde{c}}_{2q,z}=\[{\tilde{a}}_1,{\tilde{a}}_2,...,{\tilde{a}}_d,...,{\tilde{a}}_D\]p_{2q,s}$

for equivalent signal steering vectors, p, on said physical array antenna structure RL_2q,sIs an equivalent transmit signal;

step S104, for the equivalent received signalPerforming two-dimensional spatial smoothing to obtain equivalent autocorrelation matrixFor the equivalent autocorrelation matrixDecomposing the eigenvalue to obtain a signal eigenvector matrix U_sSum noise eigenvector matrix U_n；

The equivalent autocorrelation matrixThe expression of (a) is:

$\tilde{R}=U_s{\mathrm{\Σ}}_s{U}_s^H+U_n{\mathrm{\Σ}}_n{U}_n^H$

wherein, U_sIs a signal feature vector matrix; u shape_nIs a noise eigenvector matrix; sigma_sSum-sigma_nDiagonal arrays respectively formed by signal and noise characteristic values; (□)^HRepresenting a conjugate transpose operation;

step S105, utilizing the noise characteristic vector matrix U_nAnd said equivalent signal steering vectorConstructing a spectral peak search relation by adopting a two-dimensional MUSIC algorithm, and estimating the direction of arrival by using the spectral peak search relation to obtain an estimated value of the direction of arrival of the received signal

The spectral peak searching relation is as follows:

$P(\widehat{\mathrm{\θ}},\widehat{\mathrm{\φ}})=\frac{1}{{\tilde{a}}^H{U}_n{U}_n^H\tilde{a}}$

wherein,for the purpose of the pitch angle estimation,is an azimuth angle estimated value;a conjugate transpose operation for the equivalent signal steering vector; u shape_nIs a noise eigenvector matrix;performing conjugate transpose operation on the noise characteristic vector matrix;the equivalent signal is directed to the vector.

3. The method of estimating the direction of arrival of a nested L-shaped antenna array structure of claim 2, wherein the step S101 of determining the received signal of the physical array antenna structure comprises:

determining a physical array antenna structure RL on the x axis based on the number N/2 of the array elements on the x axis of the constructed nested L-shaped antenna array structure and the distance d between two adjacent virtual array elements in each row or each column_yAnd determining the physical array antenna structure RL in said x-axis based on the received signal steering vector_xThe expression of (1) is:

x(t)＝A_xs(t)+n_x(t)；

wherein x (t) is the physical array antenna structure RL on the x-axis_xA received signal of_xFor the physical array antenna structure RL in the x-axis_xS (t) is a transmission signal, n_x(t) is the physical array antenna structure RL on the x-axis_xNoise on;

determining a received signal steering vector of a physical array antenna structure on a y axis based on the number N/2 of array elements of the constructed nested L-shaped antenna array structure on the y axis and the distance d between two adjacent virtual array elements in each row or each column, and determining a received signal of the physical array antenna structure on the y axis based on the received signal steering vector, wherein the expression is as follows:

y(t)＝A_ys(t)+n_y(t)；

wherein y (t) is the physical array antenna structure RL on the y-axis_yA received signal of_yFor the physical array antenna structure RL in the y-axis_yS (t) is a transmission signal, n_y(t) is the physical array antenna structure RL on the y-axis_yNoise on;

according to the physical array antenna structure RL on the x axis_xAnd a physical array antenna structure RL in the y-axis_yThe received signal of the physical array antenna structure RL is obtained as follows:

$z\left(t\right)=\left[\begin{array}{c}x\left(t\right)\\ y\left(t\right)\end{array}\right]=As\left(t\right)+n\left(t\right),z\left(t\right)={\[z_1\left(t\right),z_2\left(t\right),...,z_N\left(t\right)\]}^T$

wherein x (t) is the physical array antenna structure RL on the x-axis_xThe received signal of (1); y (t) is the physical array antenna structure RL on the y axis_yThe received signal of (1); a ═ a₁,a₂,…,a_d,…,a_D]Is an array flow pattern of the array antenna structure RL, a_d(D ═ 1, …, D) is the steering vector of the signal on the physical array antenna structure RL, as a function of the direction of arrival (θ, Φ), θ is the pitch angle, Φ is the azimuth angle, and s (t) is the transmitted signal;for noise on the physical array antenna structure RL, n_x(t) is the physical array antenna structure RL on the x-axis_xNoise of (2), n_y(t) is the physical array antenna structure RL on the y-axis_xNoise on (□)^TRepresenting a transpose operation of the matrix.

4. The method as claimed in claim 3, wherein the physical array antenna structure RL on the x-axis is determined based on the number N/2 of the array elements on the x-axis of the nested L-shaped antenna array structure and the distance d between two adjacent virtual array elements in each row or each column_yThe process of receiving a signal steering vector, comprising:

obtaining an MXM uniform virtual plane array antenna structure VP through processing the received signal of the nested L-shaped antenna array structure RL;

setting a distance d between two adjacent virtual array elements in each row or each column, wherein any virtual array element in the mxm uniform virtual planar array antenna structure VP is represented as:

$VE(m,n)(m,n=-\frac{M-1}{2},-\frac{M-1}{2}+1,...,0,...,\frac{M-1}{2}-1,\frac{M-1}{2})$

wherein M is N²N is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, …;

by a physical array antenna structure RL in the x-axis_xN/2 and the distance d between two adjacent virtual array elements in each row or column determine the physical array antenna structure RL on the x-axis_xOf the received signal steering vector a_x,d(θ, φ), expressed as:

$a_{x,d}(\mathrm{\θ},\mathrm{\φ})={\[{\mathrm{\β}}_x(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_x^{N/4}(\mathrm{\θ},\mathrm{\φ}),{\mathrm{\β}}_x^{N/4+1}(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_x^{(N/4)(N/4+1)}(\mathrm{\θ},\mathrm{\φ})\]}^T$

wherein, β_x(theta, phi) is the physical array antenna structure RL in the x-axis_xThe phase difference between adjacent array elements in the array is theta, theta is the pitch angle of the received signal, phi is the azimuth angle of the received signalN is the number of elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, ….

5. The method of estimating the direction of arrival of a nested L-shaped antenna array structure of claim 4, in which the physical array antenna structure RL in the x-axis_xPhase difference β between adjacent array elements_x(θ, φ) is determined by the following process:

far field signal s_d(t) physical array antenna Structure RL incident on the x-axis_xSelecting the kth array element from the array elements, mapping the received signal to the RL plane of the physical array antenna structure, and then mapping the received signal to the RL plane of the physical array antenna structure on the x axis_xObtaining the phase difference of the kth array element on the x axis relative to a reference point:

β_k＝e^{-j2πkcosθcosφ/λ}(1≤k≤N/4)

or,

β_k＝e^{-j2πk(N/4+1)cosθcosφ/λ}(N/4+1≤k≤(N/4)(N/4+1))

in the formula, j is an imaginary unit; theta is the pitch angle of the received signal; phi is the azimuth angle of the received signal; λ is the wavelength of the received signal; n is the array element number of the array antenna structure RL;

phase difference β expressed in the formula_kEqual to the physical array antenna structure RL on the x-axis_xPhase difference β between adjacent array elements_x(θ,φ)。

6. The method for estimating direction of arrival of a nested L-shaped antenna array structure of claim 3, wherein the step of determining the received signal steering vector of the physical array antenna structure on the y-axis based on the number of elements N/2 of the constructed nested L-shaped antenna array structure on the y-axis and the distance d between two adjacent virtual elements in each row or each column comprises:

obtaining an MXM uniform virtual plane array antenna structure VP through processing the received signal of the nested L-shaped antenna array structure RL;

setting a distance d between two adjacent virtual array elements in each row or each column, wherein any virtual array element in the mxm uniform virtual planar array antenna structure VP is represented as:

$VE(m,n)(m,n=-\frac{M-1}{2},-\frac{M-1}{2}+1,...,0,...,\frac{M-1}{2}-1,\frac{M-1}{2})$

wherein M is N²N is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, …;

by physical array antenna structure RL in the y-axis_yN/2 and the distance d between two adjacent virtual array elements in each row or each column can determine the physical array antenna structure RL on the y-axis_yThe upper received signal steering vector is a_y,d(θ, φ), expressed as:

$a_{y,d}\left(\mathrm{\θ},\mathrm{\φ}\right)={\[{\mathrm{\β}}_y(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_y^{N/4}(\mathrm{\θ},\mathrm{\φ}),{\mathrm{\β}}_y^{N/4+1}(\mathrm{\θ},\mathrm{\φ}),...,{\mathrm{\β}}_y^{(N/4)(N/4+1)}(\mathrm{\θ},\mathrm{\φ})\]}^T$

wherein, β_y(theta, phi) isPhysical array antenna structure RL in the y-axis_yThe phase difference between adjacent array elements in the receiving device is equal to theta, and theta is the pitch angle of the received signal; phi is the azimuth angle of the received signal; and N is the array element number of the array antenna structure RL.

7. The method of claim 6, wherein the physical array antenna structure RL in the y-axis is a direction of arrival estimation method of a nested L-shaped antenna array structure_yPhase difference β between adjacent array elements_y(θ, φ) is determined by the following process:

far field signal s_d(t) physical array antenna Structure RL incident on the y-axis_ySelecting the kth array element from the array elements, mapping the received signal to the RL plane of the physical array antenna structure, and then mapping the received signal to the RL plane of the physical array antenna structure on the y axis_yIn the method, the phase difference of the kth array element relative to a reference point can be obtained:

β_k＝e^{-j2πkcosθsinφ/λ}(1≤k≤N/4)

or,

β_k＝e^{-j2πk(N/4+1)cosθsinφ/λ}(N/4+1≤k≤(N/4)(N/4+1))；

wherein j is an imaginary unit, and θ is a pitch angle of the received signal; phi is the azimuth angle of the received signal; λ is the wavelength of the received signal; n is the number of array elements of the nested L-shaped antenna array structure RL, and N is 4N, N is 1,2,3, …;

phase difference β expressed by the above formula_kEqual to the physical array antenna structure RL on the y-axis_yPhase difference β between adjacent array elements_y(θ,φ)。

8. The method according to any one of claims 2 to 7, wherein said step S103 is characterized in that said high-order cumulant matrix C_2q,zVectorizing operation is carried out to obtain vectorized c_2q,zThe process comprises the following steps:

for receiving signals by said physical array antenna structure RL by using the following formulaHigh order cumulant matrix C_2q,zVectorizing operation is carried out to obtain vectorized c_2q,z：

$c_{2q,z}=\[a_1^{*\⊗q}\⊗{a_1}^{\⊗q},\mathrm{...},a_d^{*\⊗q}\⊗{a_d}^{\⊗q},\mathrm{...},a_D^{*\⊗q}\⊗{a_D}^{\⊗q}\]p_{2q,s}=\[b_1,\mathrm{...},b_d,\mathrm{...},b_D\]p_{2q,s}$

$,b_d=a_d^{*\⊗q}\⊗{a_d}^{\⊗q}={\left[\begin{array}{c}{a}_{x,d}\\ a_{y,d}\end{array}\right]}^{*\⊗q}\⊗{\left[\begin{array}{c}{a}_{x,d}\\ a_{y,d}\end{array}\right]}^{\⊗q},$

Wherein, b_dComprises ${\tilde{a}}_d={\tilde{a}}_{x,d}\⊗{\tilde{a}}_{y,d},{\tilde{a}}_{x,d}=a_{x,d}^{*}\⊗a_{x,d},{\tilde{a}}_{y,d}=a_{y,d}^{*}\⊗a_{y,d},$ ${\tilde{a}}_d(d=1,...,D)$ For an equivalent signal steering vector on the physical array antenna structure RL,for the physical array antenna structure RL in the x-axis_xThe above equivalent signal-steering vector is,for the physical array antenna structure RL in the y-axis_yThe above equivalent signal steering vector, q is 1,2,3, …, which is a parameter of order; said vectorised c_2q,zContaining information of all virtual array elements.

Or,

using the following formula, the high-order cumulant matrix C is obtained_2q,zVectorizing operation is carried out to obtain vectorized c_2q,z(ii) a Said vectorised c_2q,zThe expression of (a) is:

wherein l is a direction index parameter which is any positive integer; a is_d(D-1, …, D) is the steering vector of the signal on the physical array antenna structure RL as a function of the direction of arrival (θ, Φ), θ is the pitch angle, Φ is the azimuth angle,denotes l a_dPerforming Kronecker product operation to obtain N^lColumn vectors of dimension × 1.