CN110208736B - Non-circular signal uniform array direction-of-arrival angle estimation method based on fourth-order cumulant - Google Patents
Non-circular signal uniform array direction-of-arrival angle estimation method based on fourth-order cumulant Download PDFInfo
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Abstract
The invention discloses a method for estimating the direction of arrival angle of a non-circular signal uniform array based on fourth-order cumulant, which mainly solves the problems that array elements are fixed in the estimation of the direction of arrival angle, and virtual array elements are not fully excavated, so that the number of estimated target signals is small. The implementation steps are as follows: constructing a non-circular signal uniform linear array; acquiring output signals of a non-circular signal uniform linear array and calculating two groups of fourth-order cumulants of the output signals; constructing two groups of fourth-order cumulant matrixes by using two groups of fourth-order cumulant; constructing a final fourth-order cumulant matrix, calculating a noise subspace of the final fourth-order cumulant matrix, and constructing a non-circular signal uniform linear array steering vector to calculate a spatial spectrum; and drawing an amplitude spectrogram according to the space spectrum to obtain a direction of arrival angle. The invention adopts the fourth order cumulant to estimate the direction of arrival angle of the target signal and calculates two groups of fourth order cumulants of the non-circular signal uniform linear array. The array element number greatly improves the number of array measurable noncircular signals at a certain time, and is suitable for target reconnaissance and passive positioning.
Description
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to array signal direction-of-arrival angle estimation of electromagnetic signals, in particular to a non-circular signal uniform linear array direction-of-arrival angle estimation method based on fourth-order cumulant, which can be used for reconnaissance and passive positioning of moving targets of airplanes and ships.
Background
The DOA estimation of the direction of arrival of a signal is an important branch in the field of array signal processing, and the DOA estimation is characterized in that space acoustic signals and electromagnetic signals are received by an antenna array in an induction mode, then the direction of a signal source is rapidly and accurately estimated by using a modern signal processing method, and the DOA estimation has important application value in the fields of radar, sonar, wireless communication and the like. With the continuous progress of science and technology, there is a higher and higher requirement on the degree of freedom of the array in estimating the direction of arrival of signals.
Aiming at the research of the problem, an early model with a multi-signal classification MUSIC subspace appears, and the number of detectable information sources of a typical linear uniform array of Q array elements in the traditional MUSIC calculation method is Q-1. Most of the latter algorithms are generated using the model, for example, signal parameter estimation rotation invariant technique ESPRIT. These algorithms, due to the use of a typical linear uniform array, result in an estimated number of signals lower than the number of array elements, and even fail to identify when the number of targets is large, resulting in a failure in target acquisition.
At present, most of actually used signals are non-circular signals, and the angle degree of freedom can be improved and more information sources can be detected under the condition of limited array elements by utilizing the properties of the non-circular signals. Feifei Gao et al, in its published article "Improved Multi Under the Cooperation of Both Circuit and non-Circular Sources" ("IEEE TRANSACTIONS Signal PROCESSING, VOL.56, NO.7, JULY 2008), disclose a method for estimating DOA based ON a uniform array of second order cumulant non-Circular SIGNALs, which can use M array elements to obtain a plurality of virtual array elements using second order cumulant between output SIGNALs of M array elements, and has the capability of estimating a target number of SIGNALs more than the number of array elements, but the method still has the disadvantage that, in the case of a certain number of array elements, the number of obtained virtual array elements is not sufficient, i.e., the maximum number of obtained virtual array elements is not enough to be ideal, i.e., the number of target SIGNALs that can be measured is directly less than the number of SIGNALs that can be measured in an ideal situation.
Disclosure of Invention
The present invention is directed to provide a method for estimating direction-of-arrival of a non-circular signal uniform linear array based on a fourth order cumulant, which is capable of estimating more non-circular target signals, in view of the above-mentioned shortcomings of the prior art.
The invention relates to a method for estimating the direction of arrival angle of a non-circular signal uniform linear array based on fourth-order cumulant, which is characterized by comprising the following steps:
(1) Constructing a non-circular signal uniform linear array: each antenna receiver is called an array element, M antenna receivers are used for forming a non-circular signal uniform linear array Q, the array element interval of the non-circular signal uniform linear array Q is d, the first array element of the uniform linear array Q is defined as a starting array element, the array origin is 0, the position of the starting array element is d, and the positions of all array elements of the non-circular signal uniform linear array Q are d,2d,3d, 8230, md, and Md; wherein M is more than or equal to 1, d is more than 0 and less than or equal to lambda/2, and lambda is the wavelength of the narrow-band signal incident to the array;
(2) Obtaining a target non-circular signal uniform linear array output signal Y (t): assuming that there are K non-circular target signals in space, Y (t) = [ Y = 1 (t),y 2 (t),…,y i (t),…,y M (t)]Wherein y is i (t) the output signal of the ith array element of the non-circular signal uniform linear array is represented, i is the array element serial number in the non-circular signal uniform linear array, and the value range of i is more than or equal to 1 and less than or equal to M; sampling and filtering through an antenna receiver to obtain a non-circular signal uniform linear array output signal Y (t);
(3) Respectively calculating two groups of fourth-order cumulants of the output signal Y (t) of the non-circular signal uniform linear array: solving a first set of fourth order cumulants c for the non-circular signal uniform linear array output signal Y (t) 1 (k 1, k2, k3, k 4), solving a second set of fourth order cumulants c for the non-circular signal uniform linear array output signal Y (t) 2 (k1,k2,k3,k4)；
(4) Two sets of four-order cumulant matrices G are constructed respectively 1 、G 2 : respectively constructing a first group of fourth-order cumulant matrixes G corresponding to the first group of fourth-order cumulant according to two groups of fourth-order cumulant of the output signal Y (t) of the non-circular signal uniform linear array 1 A second group of fourth order cumulant matrices G corresponding to the second group of fourth order cumulant 2 ；
(5) Using two sets of fourth order cumulant matrices G 1 、G 2 Generating a final fourth order cumulant matrix G of the antenna receiver:
(6) Computing the noise subspace U of the final fourth order cumulant matrix G n (ii) a After the final fourth-order cumulant matrix G is subjected to feature decomposition, a noise subspace U is constructed according to the feature vectors n ；
(7) Constructing a non-circular signal uniform linear array guide vector alpha (theta); two (4D + 1) multiplied by 1 dimensional 0 vectors participate in constructing a non-circular signal uniform linear array guide vector alpha (theta);
(8) Noise subspace U based on non-circular signal uniform linear array steering vector α (θ) and final fourth order cumulant matrix G n Calculating a target signal space spectrum P (theta);
(9) Obtaining the angle value of the direction of arrival of the target: and (3) taking the value of the angular range theta of the direction of arrival as an x-axis coordinate, taking the amplitude value of the spatial spectrum P (theta) as a y-axis coordinate, drawing an amplitude spectrogram, searching K spectral peaks in the front of the amplitude from the amplitude spectrogram in a sequence from high to low, wherein K represents the number of spatial target signals of the uniform linear array, K is more than or equal to 1, and the x-axis coordinate corresponding to the peak points of the spectral peaks is the angle value of the direction of arrival of the target.
The invention is based on the fact that the phenomenon and the current situation that the number of the obtained virtual array elements is not enough under the condition that the number of the array elements is certain in the prior art are known in the research, and the invention further excavates through analysis research on the basis, provides a method for estimating the direction angle of arrival of a non-circular signal uniform linear array based on four-order cumulant, which expands the number space of the virtual array elements, improves the number of the virtual array elements, can estimate more target signal numbers and greatly improves the estimation precision of the direction angle of arrival.
Compared with the prior art, the invention has the following advantages:
the technical scheme capable of improving the estimation precision of the angle of arrival is provided: the invention adopts a fourth-order cumulative array model to estimate the direction of arrival angle, overcomes the defect that the number of estimated signals is lower than the number of array elements because a typical linear uniform array is adopted in the prior art, and improves the number of array identifiable information sources under the condition of the same number of array elements.
The number of the obtained virtual array elements is more, and the number of the captured targets is more: compared with the prior art, the method adopts the second-order cumulant to estimate the direction of arrival angle of the non-circular signal, so that the number of virtual array elements cannot reach the maximum number of virtual array elements which can be reached under the ideal condition, and the number of the measured target signals is small. By calculating two groups of four-order cumulant of the non-circular signal uniform linear array, 2 (4M-3) continuous virtual array elements can be obtained by using M array elements, the array utilization rate is greatly improved, more virtual array elements are obtained at the same time, and the number of information sources which can be identified by the array is further increased.
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FIG. 1 is a flow chart of an implementation of the present invention.
Detailed Description
The technical solution and effects of the present invention will be described in detail below with reference to the accompanying drawings.
Example 1
In the technical field of signal processing, particularly, estimation of an array signal direction of arrival of an electromagnetic signal is very important, and the method plays an important role in reconnaissance and passive positioning of moving targets of airplanes and ships. In practice, the arrival angle of a target signal is estimated, in the prior art, under the condition of a certain array element number, second-order cumulant is adopted to estimate the arrival direction angle of a non-circular signal, so that the number of virtual array elements cannot reach the maximum number of virtual array elements which can be reached under the ideal condition, and the number of the measured target signals is small.
The invention discloses a method for estimating the direction of arrival angle of a non-circular signal uniform linear array based on fourth-order cumulant, which is shown in figure 1 and comprises the following steps:
(1) Constructing a non-circular signal uniform linear array: each antenna receiver is called an array element, M antenna receivers are used for forming a non-circular signal uniform linear array Q, the array element interval of the non-circular signal uniform linear array Q is d, the first array element of the uniform linear array Q is defined as a starting array element, the array origin is 0, the position of the starting array element is d, and the positions of the array elements of the non-circular signal uniform linear array Q are d,2d,3d, 8230;, md, \8230;, and Md. Wherein M is more than or equal to 1, d is more than 0 and less than or equal to lambda/2, and lambda is the narrow-band signal wavelength incident to the array.
(2) Obtaining a target non-circular signal uniform linear array output signal Y (t): assuming that there are K non-circular target signals in space, Y (t) = [ Y = 1 (t),y 2 (t),…,y i (t),…,y M (t)]Wherein y is i And (t) the output signal of the ith array element of the non-circular signal uniform linear array is shown, i is the array element serial number in the non-circular signal uniform linear array, and the value range of i is more than or equal to 1 and less than or equal to M. And obtaining a non-circular signal uniform linear array output signal Y (t) through sampling and filtering of an antenna receiver.
(3) Respectively calculating two groups of fourth-order cumulants of the output signal Y (t) of the non-circular signal uniform linear array: firstly, a non-circular signal uniform linear array is constructed and formed, then the non-circular signal uniform of a target signal is obtained through filtering and sampling of an antenna receiver, a linear array output signal Y (t) is obtained, and then two groups of four-order cumulants of the non-circular signal uniform linear array output signal Y (t) are calculated. It can also be expressed as solving a first set of fourth order cumulants c for the non-circular signal uniform linear array output signal Y (t) 1 (k 1, k2, k3, k 4), solving a second set of fourth order cumulants c for the non-circular signal uniform linear array output signal Y (t) 2 (k1,k2,k3,k4)。
(4) Two sets of four-order cumulant matrices G are constructed respectively 1 、G 2 : respectively constructing a first group of fourth-order cumulant matrixes G of the non-circular signal uniform linear array corresponding to a first group of fourth-order cumulant of the non-circular signal uniform linear array according to two groups of fourth-order cumulant of the output signal Y (t) of the non-circular signal uniform linear array 1 The non-circular signal uniform linear array second group fourth order cumulant matrix G corresponding to the non-circular signal uniform linear array second group fourth order cumulant 2 。
(5) Utilizing two groups of fourth order cumulant matrixes G of the non-circular signal uniform linear array obtained in the step (4) 1 、G 2 Generating a final fourth order cumulant matrix G of the antenna receiver:
(6) Computing the noise subspace U of the final fourth order cumulant matrix G n : after the final fourth-order cumulant matrix G is subjected to feature decomposition, a noise subspace U is constructed according to the feature vectors n 。
(7) Constructing a non-circular signal uniform linear array guide vector alpha (theta); two (4D + 1) multiplied by 1 dimensional 0 vectors are used for constructing the non-circular signal uniform linear array guiding vector alpha (theta).
(8) Noise subspace U based on non-circular signal uniform linear array steering vector α (θ) and final fourth order cumulant matrix G n And calculating a target signal space spectrum P (theta).
(9) Obtaining the angle value of the direction of arrival of the target: and taking the value of the angular range theta of the direction of arrival as an x-axis coordinate, taking the amplitude value of the space spectrum P (theta) as a y-axis coordinate, drawing an amplitude spectrogram, searching K spectral peaks in front of the amplitude value from the amplitude spectrogram from high to low, wherein K represents the number of space target signals of the uniform linear array, K is more than or equal to 1, and the x-axis coordinate corresponding to the peak value points of the spectral peaks is the angle value of the direction of arrival of the target.
In order to solve the problems that the number of virtual array elements obtained by estimating the arrival direction angle of a target signal under the condition that the array element number is fixed by using second-order cumulant in the prior art cannot reach the maximum virtual array element number obtained under the ideal condition, and the number of the target signals which can be measured is less than the number of the signals which can be measured under the ideal condition, the invention adopts fourth-order cumulant to estimate the arrival direction angle of the target signal, and obtains two groups of fourth-order cumulant of a non-circular signal uniform linear array, thereby greatly increasing the number of the virtual array elements, increasing the number of the target signals which can be estimated, and avoiding the waste of the array elements.
In the invention, the target signal is estimated by adopting the four-order cumulant, and two groups of four-order cumulant of the non-circular signal uniform linear array are calculated, so that the number of virtual array elements is greatly increased, and the number of the target signals which can be measured is increased.
The invention adopts a fourth-order accumulation array model to estimate the direction of arrival angle, overcomes the defect that the number of estimated signals is lower than that of array elements because a typical linear uniform array is adopted in the prior art, and improves the number of array identifiable information sources under the condition of the same number of array elements. The present invention applies the fourth order cumulants to the DOA estimation of the non-circular signal uniform linear array and calculates two sets of fourth order cumulants for the non-circular signal uniform linear array. By using the fourth order cumulant, M array elements can be used to obtain 2 (4M-3) continuous virtual array elements, thereby greatly improving the array utilization rate, and simultaneously, by obtaining more virtual array elements, the number of information sources which can be identified by the array is further increased.
Example 2
The method for estimating direction of arrival angles of a non-circular signal uniform linear array based on the fourth-order cumulant is the same as that in embodiment 1, and the two groups of fourth-order cumulants based on the output signal Y (t) of the non-circular signal uniform linear array in the step (3) of the invention specifically comprise the following steps:
(3a) Solving a first set of fourth order cumulants c for the non-circular signal uniform linear array output signal Y (t) 1 (k1,k2,k3,k4)：
c 1 (k1,k2,k3,k4)＝cum(y k1 (t),y k2 * (t),y k3 (t),y k4 * (t))，
Wherein k1, k2, k3 and k4 are the serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, k1 is not less than 1, k2, k3 and k4 are not less than M, y k1 (t),y k2 (t),y k3 (t),y k4 (t) output signal of output signal Y (t) of non-circular signal uniform linear array under array element number of k1, k2, k3 and k4The number, cum, represents the solving of the fourth order cumulant operation, (. C) * Representing the conjugate operation of the vector.
(3b) Solving a second set of fourth order cumulants c for the non-circular signal uniform linear array output signal Y (t) 2 (k1,k2,k3,k4)：
c 2 (k1,k2,k3,k4)＝cum(y k1 (t),y k2 * (t),y k3 * (t),y k4 * (t))，
Wherein k1, k2, k3 and k4 are the serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, k1 is not less than 1, k2, k3 and k4 are not less than M, y k1 (t),y k2 (t),y k3 (t),y k4 (t) output signals of output signals Y (t) of the non-circular signal uniform linear array under the array element numbers of k1, k2, k3 and k4, cum represents the operation of solving the fourth order cumulant, (. Cndot) * Representing the conjugate operation of the vector.
K1, k2, k3 and k4 used for comparing and calculating the first group of fourth-order cumulant of the non-circular signal uniform linear array and the second group of fourth-order cumulant to calculate the two groups of fourth-order cumulant of the non-circular signal uniform linear array are the serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, wherein k1 is not less than 1, k2, k3 and k4 are not less than M, and k1, k2, k3 and k4 used for calculating the first group of fourth-order cumulant of the non-circular signal uniform linear array are the same as k1, k2, k3 and k4 used for calculating the second group of fourth-order cumulant of the non-circular signal uniform linear array.
For example, in this example, if M is 2, the intermediate value D of the first group of fourth order cumulant of the non-circular signal uniform linear array is 1, the minimum value L of the fourth order cumulant of the second group of the non-circular signal uniform linear array is-5, the maximum value S is-1, and the number of the virtual array elements which can be obtained is 10, so that the array utilization rate is greatly improved, more virtual array elements are obtained, and the number of the information sources which can be identified by the array is further increased.
Compared with the prior art, the invention adopts the second-order cumulant to estimate the direction of arrival angle of the non-circular signal, which causes the problem that the number of virtual array elements cannot reach the maximum number of virtual array elements under the ideal condition, so that the number of measured target signals is less, applies the fourth-order cumulant to DOA estimation of the non-circular signal uniform linear array, and calculates two groups of fourth-order cumulant of the non-circular signal uniform linear array. By calculating two groups of four-order cumulant of the non-circular signal uniform linear array, M array elements can be used for obtaining 2 (4M-3) continuous virtual array elements, the array utilization rate is greatly improved, more virtual array elements are obtained, and the number of information sources which can be identified by the array is further increased.
Example 3
The method for estimating direction of arrival angles of a non-circular signal uniform linear array based on fourth-order cumulant is the same as that in embodiment 1-2, and two groups of fourth-order cumulant matrixes G are obtained through respective calculation in step (4) of the invention 1 、G 2 Respectively constructing two groups of four-order cumulant matrixes of corresponding non-circular signal uniform linear arrays according to two groups of four-order cumulant of non-circular signal uniform linear array output signals Y (t) of an antenna receiver target signal, and specifically comprising the following steps of:
(4a) Constructing a first group of fourth-order cumulant matrix G of a non-circular signal uniform linear array 1 : defining the intermediate value of the fourth order cumulant of the first group of the non-circular signal uniform linear array as D, D = M-1, and defining the fourth order cumulant c of the first group of the non-circular signal uniform linear array 1 And (k 1, k2, k3, k 4) finding out the fourth-order cumulant with k1, k2, k3, k4 satisfying the following conditions in sequence:
k1+k3-k2-k4＝-2D,-2D+1,…,0,…,2D-1,2D，
first group of fourth order cumulants c of uniform linear array for non-circular signals 1 (k 1, k2, k3, k 4) are sequentially defined as four-order cumulant elements G (-2D), G (-2D + 1), \8230;, G (0), \8230;, G (2D-1), G (2D), four-order cumulant elements G (-2D), \8230;, G (-1), G (0), G (1), \8230;, and G (2D) are arranged to form a first group of four-order cumulant matrices G of a non-circular signal uniform linear array 1 ：
k1, k2, k3 and k4 are serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, k1 is not less than 1, k2, k3 and k4 are not less than M, and g (·) represents a fourth-order cumulant element. In the first group of fourth-order cumulant of the non-circular signal uniform linear array, D is the middle value of the first group of fourth-order cumulant of the non-circular signal uniform linear array, the maximum value of the first group of fourth-order cumulant of the non-circular signal uniform linear array is 2D, and the minimum value is-2D.
(4b) Constructing a first group of fourth-order cumulant matrix G of a non-circular signal uniform linear array 2 : defining the second group of fourth order cumulants of the non-circular signal uniform linear array as L, L =1-3M and S, S = M-3, and defining the second group of fourth order cumulants c of the non-circular signal uniform linear array 2 And (k 1, k2, k3, k 4) finding out the fourth-order cumulant with k1, k2, k3 and k4 meeting the following conditions in sequence:
k1-k2-k3-k4＝L,L+1,…,S-1,S，
second group of fourth order cumulants c of the non-circular signal uniform linear array 2 The (k 1, k2, k3, k 4) are sequentially defined as four-order cumulant elements G (L), G (L + 1), \ 8230;, G (S-1), G (S), and the four-order cumulant elements G (L), G (L + 1), \ 8230;, G (S-1), G (S) are arranged to form a second group of four-order cumulant matrixes G of the non-circular signal uniform linear array 2 ：
k1, k2, k3 and k4 are serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, k1 is not less than 1, k2, k3 and k4 are not less than M, and g (·) represents a fourth-order cumulant element. In the second group of fourth-order cumulant of the non-circular signal uniform linear array, L is the minimum value of the second group of fourth-order cumulant of the non-circular signal uniform linear array, and S is the maximum value of the second group of fourth-order cumulant of the non-circular signal uniform linear array.
Compared with the prior art that the second-order cumulant is adopted to estimate the direction-of-arrival angle of the target signal, the method adopts the fourth-order cumulant to estimate the direction-of-arrival angle of the target, calculates two groups of fourth-order cumulants of the non-circular signal uniform linear array, can generate more virtual array elements, and constructs the second group of fourth-order cumulant matrixes G of the non-circular signal uniform linear array by arranging the second group of fourth-order cumulant matrixes 2 Thus, the virtual array element is fully utilized, and the number of the target signals which can be measured is increased.
Example 4
Based on fourth-order accumulationThe method for estimating the direction of arrival angle of the non-circular signal uniform linear array is the same as that in the embodiments 1 to 3, and the noise subspace U of the final fourth-order cumulant matrix G of the non-circular signal uniform linear array is calculated in the step (6) of the invention n The method comprises the following steps:
(6a) And (3) performing the following characteristic decomposition on the final fourth-order cumulant matrix G:
G＝U·Λ·U H ，
wherein, Λ is the eigenvalue matrix of the final fourth order cumulant matrix G, and U is the eigenvector matrix corresponding to the eigenvalue of the final fourth order cumulant matrix G (·) H Representing a conjugate transpose operation of the matrix.
(6b) Sorting the eigenvalues in the eigenvalue matrix Lambda from large to small, taking the eigenvector matrix corresponding to the next 2 (2D + 1) -K smaller eigenvalues as the noise subspace U of the final fourth order cumulant matrix G of the non-circular signal uniform linear array n And K represents the number of space target signals of the non-circular signal uniform linear array.
Example 5
The method for estimating the direction of arrival angle of the non-circular signal uniform linear array based on the fourth-order cumulant is the same as that in the embodiments 1 to 4, and the guide vector alpha (theta) of the non-circular signal uniform linear array constructed in the step (7) of the invention comprises the following steps:
(7a) Non-circular signal uniform linear array steering vector α (θ):
wherein Z is a vector in which all of the elements of dimension (4D + 1) × 1 are 0.
(7b) First group of fourth-order cumulant guide component vectors alpha of non-circular signal uniform linear array 1 (theta) and a second set of fourth order cumulant steering component vectors alpha of a non-circular signal uniform linear array 2 (θ) is calculated as follows:
wherein D is the middle value of the first group of fourth order cumulant of the non-circular signal uniform linear array, L is the minimum value of the second group of fourth order cumulant of the non-circular signal uniform linear array, and S is the maximum value of the second group of fourth order cumulant of the non-circular signal uniform linear array, (.) T Representing a matrix transpose operation, j being an imaginary unit.
In summary, the invention adopts the fourth order cumulant to estimate the arrival angle of the target signal, and calculates two groups of fourth order cumulants of the non-circular signal uniform linear array, thereby greatly improving the number of virtual array elements and increasing the number of target signals which can be estimated. The problems of low utilization rate of array elements, small number of identified information sources and large passive positioning estimation error in the prior art are solved, the requirement on the number of the array elements is reduced, the use flexibility of the number of the array elements is ensured, and the estimation performance of the number of the array identifiable information sources and the estimation performance of the signal direction angle under low signal-to-noise ratio are improved.
Compared with the prior art, the method adopts second-order cumulant to estimate the arrival angle of the target signal, and under the condition of certain array element quantity, the obtained number of virtual array elements cannot reach the maximum virtual array element number which can be obtained under the ideal condition, thereby directly causing the problem that the number of the target signal which can be measured is less than the number of the signal which can be measured under the ideal condition. The invention adopts the fourth-order cumulant to estimate the arrival angle of the target signal, and calculates two groups of fourth-order cumulant of the non-circular signal uniform linear array in the invention, and the arrival angle of the target signal can be estimated if only the first group of fourth-order cumulant of the non-circular signal uniform linear array is calculated, but the effect is not good if the two groups of fourth-order cumulant are calculated in the invention. The invention calculates two groups of four-order cumulant of the non-circular signal uniform linear array, so that the number of the virtual array elements is greatly increased, compared with the prior art, the invention does not increase much calculation amount, but greatly increases the number of the virtual array elements, has obvious effect, and greatly increases the number of the measured target signals.
A more detailed example is given below to further illustrate the invention
Example 6
The method for estimating the direction of arrival angle of the non-circular signal uniform linear array based on the fourth-order cumulant is the same as the embodiment 1-5, and referring to the attached figure 1, and the method comprises the following specific steps:
Step 1:
constructing a non-circular signal uniform linear array: the method comprises the steps of referring each antenna receiver as an array element, taking M antenna receivers as M array elements, enabling the distance between each array element to be d, forming a non-circular signal uniform linear array Q, defining the first array element of the non-circular signal uniform linear array Q as a starting array element, enabling the array origin to be 0, enabling the position of the starting array element to be d, enabling the position of the last array element to be Md, and enabling the positions of all array elements of the non-circular signal uniform linear array Q to be d,2d,3d, 8230, md, 8230and Md. Wherein M is more than or equal to 1, d is more than 0 and less than or equal to lambda/2, and lambda is the wavelength of the narrow-band signal incident to the array.
Step 2:
obtaining a non-circular signal uniform linear array output signal: a narrow-band signal with the wavelength of lambda is incident into the non-circular signal uniform linear array Q, and an antenna receiver in the non-circular signal uniform linear array Q samples a space target signal to obtain a non-circular signal uniform linear array output signal:
Y(t)＝[y 1 (t),…,y i (t),…,y M (t)]，
wherein y is i (t) an output signal of the ith array element of the non-circular signal uniform linear array is represented, i is the array element serial number in the non-circular signal uniform linear array, and the value range of i is more than or equal to 1 and less than or equal to M.
And 3, step 3:
calculating two groups of fourth-order cumulants of the output signal Y (t) of the non-circular signal uniform linear array: the method comprises the following steps of constructing and forming a non-circular signal uniform linear array, then obtaining a non-circular signal uniform linear array output signal Y (t) through sampling and filtering of a target signal by an antenna receiver, and then respectively calculating two groups of four-order cumulants of the non-circular signal uniform linear array output signal Y (t), wherein the method specifically comprises the following steps:
(3a) Solving a first set of fourth order cumulants c for the non-circular signal uniform linear array output signal Y (t) 1 (k1,k2,k3,k4)：
c 1 (k1,k2,k3,k4)＝cum(y k1 (t),y k2 * (t),y k3 (t),y k4 * (t))，
Wherein k1, k2, k3 and k4 are the serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, k1 is not less than 1, k2, k3 and k4 are not less than M, y k1 (t),y k2 (t),y k3 (t),y k4 (t) output signals of output signals Y (t) of the non-circular signal uniform linear array under the array element numbers of k1, k2, k3 and k4, cum represents the operation of solving the fourth-order cumulant, (.) * Representing the conjugate operation of the vector.
(3b) Solving a second group of fourth-order cumulants c of the output signal Y (t) of the non-circular signal uniform linear array 2 (k1,k2,k3,k4)：
c 2 (k1,k2,k3,k4)＝cum(y k1 (t),y k2 * (t),y k3 * (t),y k4 * (t))，
Wherein k1, k2, k3 and k4 are the serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, k1 is not less than 1, k2, k3 and k4 are not less than M, y k1 (t),y k2 (t),y k3 (t),y k4 (t) output signals of output signals Y (t) of the non-circular signal uniform linear array under the array element numbers of k1, k2, k3 and k4, cum represents the operation of solving the fourth-order cumulant, (.) * Representing the conjugate operation of the vector.
K1, k2, k3 and k4 used for calculating two groups of fourth-order cumulants of the non-circular signal uniform linear array are the serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, wherein k1 is not less than 1, and k2, k3 and k4 are not less than M, and k1, k2, k3 and k4 used for calculating the first group of fourth-order cumulants of the non-circular signal uniform linear array are the same as k1, k2, k3 and k4 used for calculating the second group of fourth-order cumulants of the non-circular signal uniform linear array.
(3c) The fourth order cumulant operation cum of calculating the non-circular signal uniform linear array output signal Y (t) is performed as follows: assuming that A (t), B (t), C (t) and D (t) are required fourth-order cumulant signals, the fourth-order cumulant obtained by calculating A (t), B (t), C (t) and D (t) by using cum is as follows:
wherein, T is the signal acquisition fast beat number, the product operation is represented, (-) * Which represents the operation of the conjugate of the vector,
representing a summation operation.
And 4, step 4:
two groups of fourth-order cumulants c of the output signal Y (t) of the non-circular signal uniform linear array in the step (3) 1 (k1,k2,k3,k4)、c 2 (k 1, k2, k3, k 4) respectively constructing corresponding fourth-order cumulant matrixes G 1 、G 2 。
(4a) Constructing a first group of fourth-order cumulant matrixes G of the non-circular signal uniform linear array 1 Defining a first set of fourth order cumulants of a uniform linear array of non-circular signals with a median value of D, D = M-1, and a first set of fourth order cumulants c of a uniform linear array of non-circular signals 1 And (k 1, k2, k3, k 4) finding out the fourth-order cumulant with k1, k2, k3, k4 satisfying the following conditions in sequence:
k1+k3-k2-k4＝-2D,-2D+1,…,0,…,2D-1,2D，
uniformly linear array first group fourth order cumulant c of non-circular signal 1 (k 1, k2, k3, k 4) are sequentially defined as the following fourth order cumulant elements: g (-2D), G (-2D + 1), \ 8230;, G (0), \ 8230;, G (2D-1), G (2D), and then the fourth order cumulant elements G (-2D), \ 8230;, G (-1), G (0), G (1), \ 8230;, G (2D) are arranged to form a first set of fourth order cumulant matrices G of a non-circular signal uniform linear array 1 ：
k1, k2, k3 and k4 are serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, k1 is not less than 1, k2, k3 and k4 are not less than M, and g (·) represents a fourth-order cumulant element. In the first group of fourth-order cumulant of the non-circular signal uniform linear array, D is the middle value of the first group of fourth-order cumulant of the non-circular signal uniform linear array, the maximum value of the first group of fourth-order cumulant of the non-circular signal uniform linear array is 2D, and the minimum value is-2D.
(4b) Constructing a second group of fourth-order cumulant matrixes G of the non-circular signal uniform linear array 2 A second group of fourth-order cumulant of the non-circular signal uniform linear array is defined, wherein the minimum value is L, L =1-3M, the maximum value is S, and S = M-3. Second set of fourth order cumulants c from non-circular signal uniform linear array 2 (k 1, k2, k3, k 4) all the fourth order cumulants find out the fourth order cumulant of which k1, k2, k3, k4 meet the following condition in turn:
k1-k2-k3-k4＝L,L+1,…,S-1,S，
second group of fourth order cumulants c of uniform linear array for non-circular signals 2 (k 1, k2, k3, k 4) are sequentially defined as four-order cumulant elements G (L), G (L + 1), \ 8230;, G (S-1), G (S), and then four-order cumulant elements G (L), G (L + 1), \ 8230;, G (S-1), G (S) are arranged as a second set of four-order cumulant matrices G of a non-circular signal uniform linear array 2 ：
k1, k2, k3 and k4 are serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, k1 is not less than 1, k2, k3 and k4 are not less than M, and g (·) represents a fourth-order cumulant element. In the second group of fourth-order cumulant of the non-circular signal uniform linear array, L is the minimum value of the second group of fourth-order cumulant of the non-circular signal uniform linear array, and S is the maximum value of the second group of fourth-order cumulant of the non-circular signal uniform linear array.
Compared with the prior art that the second-order cumulant is adopted to estimate the direction-of-arrival angle of the target signal, the method adopts the fourth-order cumulant to estimate the direction-of-arrival angle of the target, calculates two groups of fourth-order cumulants of the non-circular signal uniform linear array, can generate more virtual array elements, and constructs the second group of fourth-order cumulant matrixes G of the non-circular signal uniform linear array by arranging the second group of fourth-order cumulant matrixes 2 Therefore, the virtual array elements are fully utilized, the number of the target signals which can be measured is increased, and more target signals are estimated.
And 5:
utilizing two groups of fourth order cumulant matrixes G of the non-circular signal uniform linear array obtained in the step (4) 1 、G 2 Generating a final fourth-order cumulant matrix G, and using the first group of fourth-order cumulant matrices G of the first group of non-circular signal uniform linear arrays corresponding to the first group of fourth-order cumulant of the non-circular signal uniform linear arrays 1 And a second group of fourth-order cumulant matrixes G of the circular signal uniform linear array corresponding to the second group of fourth-order cumulant matrixes G of the non-circular signal uniform linear array 2 Forming a final fourth order cumulant matrix G for the antenna receiver:
wherein G is 2 H Is G 2 Conjugate transpose matrix of G 1 T Is G 1 The transposed matrix of (2). And the final fourth-order cumulant matrix is a square matrix, so that the feature decomposition and the noise subspace construction are facilitated.
Step 6:
computing the noise subspace U of the final fourth order cumulant matrix G n After the final fourth-order cumulant matrix G is subjected to feature decomposition, a noise subspace U is constructed according to the feature vectors n The method comprises the following steps:
(6a) And (3) performing the following characteristic decomposition on the final fourth-order cumulant matrix G:
G＝U·Λ·U H ，
wherein, Λ is the eigenvalue matrix of the final fourth order cumulant matrix G of the non-circular signal uniform linear array, U is the eigenvector matrix corresponding to the eigenvalue of the final fourth order cumulant matrix G (·) H Representing a conjugate transpose operation of the matrix.
(6b) Sorting eigenvalues in the eigenvalue matrix Lambda from large to small, taking the eigenvector matrix corresponding to the next 2 (2D + 1) -K smaller eigenvalues as the noise subspace U of the final fourth order cumulant G of the non-circular signal uniform linear array n ，U n ＝[U K+1 ,U K+2 ,…,U 2(2D+1) ]Wherein U is K+1 To U 2(2D+1) Eigenvector matrix corresponding to K +1 to 2 (2D + 1) position eigenvalues respectivelyAnd K represents the number of space target signals of the non-circular signal uniform linear array, wherein D is a middle value of a first group of fourth-order cumulants of the non-circular signal uniform linear array.
And 7:
a non-circular signal uniform linear array steering vector alpha (theta) is constructed. Two zero vectors of (4D + 1) multiplied by 1 dimension participate in constructing the non-circular signal uniform linear array guiding vector alpha (theta).
(7a) The non-circular signal uniform linear array guiding vector alpha (theta) is constructed according to the following formula:
wherein Z is a vector in which all of the elements of dimension (4D + 1) × 1 are 0. Where D is the median of the first set of fourth order cumulants for the non-circular signal uniform linear array.
(7b) First group of fourth-order cumulant guide component vectors alpha of non-circular signal uniform linear array 1 (theta) and a second set of fourth order cumulant steering component vectors alpha of a non-circular signal uniform linear array 2 (θ) is calculated as follows:
wherein D is the middle value of the first group of fourth order cumulant of the non-circular signal uniform linear array, L is the minimum value of the second group of fourth order cumulant of the non-circular signal uniform linear array, and S is the maximum value of the second group of fourth order cumulant of the non-circular signal uniform linear array, (.) T Representing a matrix transpose operation, j being an imaginary unit.
And step 8:
the spatial spectrum P (θ) is calculated. Noise subspace U based on non-circular signal uniform linear array steering vector α (θ) and final fourth order cumulant matrix G n And calculating a target signal space spectrum P (theta).
(8a) An observation airspace [ -90 degrees, 90 degrees ] is divided into E angles at equal intervals, and is defined as a direction-of-arrival angle range:
θ＝[θ 1 ,θ 2 ,…,θ e ,…,θ E ]，
wherein, theta e Denotes the E-th target direction of arrival angle, E =1,2, \8230;, E, E > M.
(8b) Calculating the spatial spectrum P (θ):
When direction angle of arrival range theta = [ theta ] 1 ,θ 2 ,…,θ e ,…θ E ]Time, corresponding spatial spectrum:
P(θ)＝[P(θ 1 ),P(θ 2 ),…,P(θ e ),…,P(θ E )]，
where α (θ) represents an array steering vector, P (θ) e ) Represents the e-th target spatial spectrum, (-) H Representing a conjugate transpose operation of a matrix, U n The noise subspace, det [. For representing the fourth order cumulant matrix G]Representing a determinant operation of matrix evaluation.
And step 9:
drawing an amplitude spectrogram:
(9a) And drawing an amplitude spectrogram by taking the value of the angular range theta of the direction of arrival as an x-axis coordinate and the amplitude value of the space spectrum P (theta) as a y-axis coordinate.
(9b) And sequencing all the spectral peak amplitude values from high to low in the drawn amplitude spectrogram, and taking x-axis coordinates corresponding to peak points of the first K spectral peaks as the direction-of-arrival angle values of the target, wherein K represents the number of spatial target signals of the uniform linear array, and the spatial target signals are supposed to be added with complex white Gaussian noise with the mean value of zero in the propagation process, and K is more than or equal to 1. The estimation of the angle of arrival of the target signal is completed.
Compared with the prior art, the method adopts second-order cumulant to estimate the arrival angle of the target signal, and under the condition of a certain array element number, the number of the obtained virtual array elements cannot reach the maximum virtual array element number which can be obtained under the ideal condition, thereby directly causing the problem that the number of the target signal which can be measured is less than the number of the signals which can be measured under the ideal condition. The invention adopts the fourth order cumulant to estimate the arrival angle of the target signal, and compared with the calculation of the second order cumulant, the calculation of the fourth order cumulant only slightly increases the calculation amount and does not influence the efficiency, but the adoption of the fourth order cumulant to estimate the arrival angle of the target signal greatly increases the number of virtual array elements, so that the number of the target signals which can be measured is increased. In the invention, two groups of four-order cumulant of the non-circular signal uniform linear array are calculated, if only the first group of four-order cumulant of the non-circular signal uniform linear array is calculated, the arrival angle estimation of the target signal can also be carried out, but the effect is not good in the invention, the two groups of four-order cumulant calculation effect is not good, and in the process of calculating the two groups of four-order cumulant of the non-circular signal uniform linear array, k1, k2, k3 and k4 are the serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, wherein k1 is less than or equal to k1, k2, k3 and k4 is less than or equal to M, so that the flexibility is very high, and the efficiency is very high. The invention calculates two groups of four-order cumulant of the non-circular signal uniform linear array, so that the number of the virtual array elements is greatly increased, compared with the prior art, the invention does not increase much calculation amount, but greatly increases the number of the virtual array elements, thereby increasing the number of the target signals which can be measured.
The effect of the present invention will be described below with reference to the simulation example.
Example 7
Method for estimating direction of arrival angle of non-circular signal uniform linear array based on fourth-order cumulant as in embodiments 1 to 6
Simulation example
And taking the M antenna receivers as M array elements to form a non-circular signal uniform linear array Q. Setting M =3 and the distance between each array element as d, constructing a non-circular signal uniform array, and simulating the following steps:
(1.1) array element position in the non-circular signal uniform linear array Q is [1,2,3] d.
And (1.2) calculating a first group of fourth-order cumulants of the non-circular signal uniform linear array. Firstly, summing the positions [1,2,3] d of the Q array elements of the non-circular signal uniform linear array pairwise to obtain the position [2,3,4,5,6] d of the virtual array element. And negating the obtained sum virtual array element position [2,3,4,5,6] d to obtain a negated sum virtual array element position of [ -6, -5, -4, -3, -2] d. And then, mutually summing the sum virtual array element position and the negation sum virtual array element position pairwise, and obtaining continuous numerical values to obtain a first group of fourth-order cumulant of the non-circular signal uniform linear array from-4 to 4. I.e., D = M-1=2 in this example, the first set of fourth order cumulants for the non-circular signal uniform linear array is-4 to 4. The results are shown in the second row and the third column of table 1.
And (1.3) calculating a second group of fourth-order cumulant of the non-circular signal uniform linear array. Firstly, summing the positions [1,2,3] d of the Q array elements of the non-circular signal uniform linear array pairwise to obtain the position [2,3,4,5,6] d of the virtual array element. Then, the positions [1,2,3] d of the Q array elements of the non-circular signal uniform linear array are mutually differenced pairwise to obtain the position of a differential virtual array element which is [ -2, -1,0,1,2] d. And then, mutually subtracting the difference virtual array element position and the sum virtual array element position pairwise, and obtaining continuous numerical values to obtain a second group of fourth-order accumulated quantities of the non-circular signal uniform linear array from-8 to 0. I.e., L =1-3M = -8,s = -3M = -0 in this example, the second group of fourth order cumulants for the non-circular signal uniform linear array is-8 to 0. The results are shown in the third row and fourth column of table 1.
TABLE 1 non-circular signal uniform linear array virtual array element based on fourth order cumulant
As can be seen from table 1, the non-circular signal uniform linear array structure based on the fourth-order cumulant can obtain more array element position information under the condition of a certain array element number, and compared with the prior art in which the second-order cumulant is adopted to estimate the arrival angle of a target signal, the number of virtual array elements generated by a uniform linear array formed by 3 array elements is limited, and the estimated target signal number is less. The non-circular signal uniform linear array formed by 3 array elements can obtain 18 virtual array elements, so that the number of the virtual array elements is greatly increased, and the number of identifiable information sources of the array is increased.
In summary, the method for estimating the direction of arrival angle of the non-circular signal uniform linear array based on the fourth-order cumulant disclosed by the invention mainly solves the problems that the number of estimated target signals is small because the number of virtual array elements is not fully excavated because the array elements in the estimation of the angle of arrival is fixed. The implementation steps are as follows: constructing a non-circular signal uniform linear array; acquiring output signals of a non-circular signal uniform linear array and calculating two groups of four-order cumulants of the output signals; respectively constructing two corresponding groups of non-circular signal uniform linear array fourth-order cumulant matrixes by using two groups of fourth-order cumulant of the non-circular signal uniform linear array; constructing a final fourth-order cumulant matrix, calculating a noise subspace of the final fourth-order cumulant matrix, and constructing a non-circular signal uniform linear array steering vector to calculate a spatial spectrum; and drawing an amplitude spectrogram according to the space spectrum to obtain a direction of arrival angle. The invention adopts the fourth order cumulant to estimate the direction of arrival angle of the target signal and calculates two groups of fourth order cumulants of the non-circular signal uniform linear array. The array element number greatly improves the number of array measurable non-circular signals at a certain time, and is suitable for target reconnaissance and passive positioning.
Claims (5)
1. A non-circular signal uniform linear array direction of arrival estimation method based on fourth-order cumulant is characterized by comprising the following steps:
(1) Constructing a non-circular signal uniform linear array: each antenna receiver is called an array element, M antenna receivers are used for forming a non-circular signal uniform linear array Q aiming at a target, the array element distance of the non-circular signal uniform linear array Q is d, the first array element of the non-circular signal uniform linear array Q is defined as a starting array element, the array origin is 0, the position of the starting array element is d, the positions of all array elements of the non-circular signal uniform linear array Q are d,2d,3d, 8230, md, 8230, md; wherein M is more than or equal to 1, d is more than 0 and less than or equal to lambda/2, and lambda is the wavelength of the narrow-band signal incident to the array;
(2) Obtaining a target non-circular signal uniform linear array output signal Y (t): assuming that there are K non-circular target signals in space, Y (t) = [ Y = 1 (t),y 2 (t),…,y i (t),…,y M (t)]Wherein y is i (t) represents the output signal of the ith array element of the non-circular signal uniform linear array, i is the array element serial number in the non-circular signal uniform linear array,the value range of i is more than or equal to 1 and less than or equal to M; obtaining a target non-circular signal uniform linear array output signal Y (t) through sampling and filtering of an antenna receiver;
(3) Respectively calculating two groups of fourth-order cumulants of the output signal Y (t) of the non-circular signal uniform linear array: solving a first group of fourth order cumulants c for the output signal Y (t) of the non-circular signal uniform linear array 1 (k 1, k2, k3, k 4), solving a second set of fourth order cumulants c for the non-circular signal uniform linear array output signal Y (t) 2 (k1,k2,k3,k4)；
(4) Two sets of four-order cumulant matrices G are constructed respectively 1 、G 2 : respectively constructing a first group of fourth-order accumulation matrixes G corresponding to the first group of fourth-order accumulation quantities according to two groups of fourth-order accumulation quantities of the output signals Y (t) of the non-circular signal uniform linear array 1 A second group of fourth order accumulation matrices G corresponding to a second group of fourth order cumulants 2 ；
(5) Using two sets of fourth order cumulant matrices G 1 、G 2 Generating a final fourth order cumulant matrix G of the antenna receiver:
(6) Computing the noise subspace U of the final fourth order cumulant matrix G n (ii) a After the final fourth-order cumulant matrix G is subjected to feature decomposition, a noise subspace U is constructed according to the feature vectors n ；
(7) Constructing a non-circular signal uniform linear array guide vector alpha (theta); two 0 vectors of (4D + 1) multiplied by 1 dimension participate in constructing a non-circular signal uniform linear array guide vector alpha (theta), D is a first group of fourth-order cumulant intermediate value of the non-circular signal uniform linear array;
(8) Noise subspace U based on non-circular signal uniform linear array steering vector α (θ) and final fourth order cumulant matrix G n Calculating a target signal space spectrum P (theta);
(9) Obtaining a direction of arrival angle value of the target: and taking the value of the angular range theta of the direction of arrival as an x-axis coordinate, taking the amplitude value of the space spectrum P (theta) as a y-axis coordinate, drawing an amplitude spectrogram, searching K spectral peaks in front of the amplitude value from the amplitude spectrogram in a sequence from high to low, wherein K represents the number of space target signals of the non-circular signal uniform linear array, K is more than or equal to 1, and the x-axis coordinate corresponding to the peak value points of the spectral peaks is the angular value of the direction of arrival of the target.
2. The method according to claim 1, wherein the step (3) of calculating two sets of fourth order cumulants of the output signal Y (t) of the non-circular signal uniform linear array comprises the steps of:
(3a) Solving a first set of fourth order cumulants c for the non-circular signal uniform linear array output signal Y (t) 1 (k1,k2,k3,k4)：
c 1 (k1,k2,k3,k4)＝cum(y k1 (t),y k2 * (t),y k3 (t),y k4 * (t))，
Wherein k1, k2, k3 and k4 are the serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, k1 is not less than 1, k2, k3 and k4 are not less than M, y k1 (t),y k2 (t),y k3 (t),y k4 (t) output signals of output signals Y (t) of the non-circular signal uniform linear array under the array element numbers of k1, k2, k3 and k4, cum represents the operation of solving the fourth order cumulant, (. Cndot) * A conjugate operation representing a vector;
(3b) Solving a second group of fourth-order cumulants c of the output signal Y (t) of the non-circular signal uniform linear array 2 (k1,k2,k3,k4)：
c 2 (k1,k2,k3,k4)＝cum(y k1 (t),y k2 * (t),y k3 * (t),y k4 * (t))，
Wherein k1, k2, k3 and k4 are the serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, k1 is not less than 1, k2, k3 and k4 are not less than M, y k1 (t),y k2 (t),y k3 (t),y k4 (t) the output signal of the output signal Y (t) of the non-circular signal uniform linear array under the array element serial numbers of k1, k2, k3 and k4, cum represents the operation of solving the fourth-order cumulant,(·) * a conjugate operation representing a vector;
k1, k2, k3 and k4 used for calculating two groups of four-point accumulated quantities of the non-circular signal uniform linear array are serial numbers of four array elements randomly selected from the non-circular signal uniform linear array, wherein k1 is not less than 1, k2, k3 and k4 are not less than M, and k1, k2, k3 and k4 used for calculating the first group of four-point accumulated quantities of the non-circular signal uniform linear array are the same as k1, k2, k3 and k4 used for calculating the second group of four-point accumulated quantities of the non-circular signal uniform linear array.
3. The method of claim 1, wherein the step (4) of computing two sets of fourth order cumulant matrices G 1 、G 2 The method comprises the following steps:
(4a) Constructing a first group of fourth-order cumulant matrix G of a non-circular signal uniform linear array 1 : defining the intermediate value of the fourth order cumulant of the first group of the non-circular signal uniform linear array as D, D = M-1, and defining the first group of the fourth order cumulant c of the non-circular signal uniform linear array as 1 And sequentially finding out the fourth-order cumulant of the k1, k2, k3 and k4 from all the fourth-order cumulant of the (k 1, k2, k3 and k 4) so as to meet the following conditions:
k1+k3-k2-k4＝-2D,-2D+1,…,0,…,2D-1,2D，
first group of fourth order cumulants c of uniform linear array for non-circular signals 1 (k 1, k2, k3, k 4) are sequentially defined as four-order cumulant elements, G (-2D), G (-2D + 1), \8230;, G (0), \8230;, G (2D-1), G (2D), and the four-order cumulant elements G (-2D), \8230;, G (-1), G (0), G (1), \8230;, and G (2D) are arranged to form a first set of four-order cumulant matrices of a non-circular signal uniform linear array 1 ；
(4b) Constructing a first group of fourth-order cumulant matrix G of a non-circular signal uniform linear array 2 : defining the minimum value of the fourth-order cumulant of the second group of the non-circular signal uniform linear array as L, L =1-3M, defining the maximum value of the fourth-order cumulant of the second group of the non-circular signal uniform linear array as S, S = M-3, and calculating the maximum value of the fourth-order cumulant of the second group of the non-circular signal uniform linear array as L, L =1-3 Second group of fourth order cumulants c of signal uniform linear array 2 And (k 1, k2, k3, k 4) finding out the fourth-order cumulant with k1, k2, k3, k4 satisfying the following conditions in sequence:
k1-k2-k3-k4＝L,L+1,…,S-1,S
second group of fourth order cumulants c of the non-circular signal uniform linear array 2 (k 1, k2, k3, k 4) are sequentially defined as four-order cumulant elements G (L), G (L + 1), \ 8230;, G (S-1), G (S), and then four-order cumulant elements G (L), G (L + 1), \ 8230;, G (S-1), G (S) are arranged to form a second group of four-order cumulant matrices G of a non-circular signal uniform linear array 2 ：
4. The method of claim 1, wherein the noise subspace U of the final fourth order cumulant matrix G is calculated according to the step (6) n The method comprises the following steps:
(6a) And (3) performing the following characteristic decomposition on the final fourth-order cumulant matrix G:
G＝U·Λ·U H ，
wherein, Λ is the eigenvalue matrix of the final fourth order cumulant matrix G, and U is the eigenvector matrix corresponding to the eigenvalue of the final fourth order cumulant matrix G (·) H Representing a conjugate transpose operation of a matrix;
(6b) Sorting the eigenvalues in the eigenvalue matrix Lambda from large to small, and taking the eigenvector matrix corresponding to the next 2 (2D + 1) -K smaller eigenvalues as the noise subspace U of the final fourth order cumulant matrix G n And K represents the number of space target signals of the non-circular signal uniform linear array.
5. The method according to claim 1, wherein the array steering vector α (θ) constructed in step (7) comprises the following steps:
(7a) Non-circular signal uniform linear array steering vector α (θ):
wherein Z is a vector in which all the elements of dimension (4D + 1) x 1 are 0;
(7b) First group of fourth-order cumulant guide component vectors alpha of non-circular signal uniform linear array 1 (theta) and a second set of fourth order cumulant vectoring component vectors alpha 2 (θ) is calculated as follows:
(·) T representing a matrix transpose operation, j being an imaginary unit.
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