CN112731272A - Coherent signal DOA estimation method - Google Patents

Coherent signal DOA estimation method Download PDF

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CN112731272A
CN112731272A CN202011356468.6A CN202011356468A CN112731272A CN 112731272 A CN112731272 A CN 112731272A CN 202011356468 A CN202011356468 A CN 202011356468A CN 112731272 A CN112731272 A CN 112731272A
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representing
doa
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朱圣棋
王祎
房云飞
许京伟
曾操
刘婧
刘永军
兰岚
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Xidian University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received

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Abstract

The invention discloses a coherent signal DOA estimation method, which comprises the steps of establishing a coherent signal model, and obtaining received signal data according to the coherent signal model; calculating a covariance matrix of the received signal data using the coherent signal model; calculating noiseless received signal data according to the covariance matrix; establishing an equivalent source vector according to the noiseless received signal data; and establishing a weight vector, and performing DOA estimation according to the weight vector and the equivalent source vector. The invention considers the space domain correlated Gaussian noise and the coherent signal, and carries out DOA estimation by utilizing the designed weight vector and the equivalent source vector, thereby improving the performance of the DOA estimation and having relatively low calculation cost.

Description

Coherent signal DOA estimation method
Technical Field
The invention belongs to the technical field of radar signal processing, and particularly relates to a coherent signal DOA estimation method.
Background
Direction-Of-Arrival (DOA) estimation Of signals is an important research topic in array signal processing, and has been widely used in the military field (radar, sonar, communication) and the economic field (unmanned). With the rapid development of the unmanned technology, in a complex urban traffic environment (such as scattering effect of large-area trees and buildings), it is an extremely important task to improve the detection performance and the positioning resolution of a stationary target.
At present, classical DOA estimation algorithms of Signal subspace, such as Multiple Signal Classification Algorithm (MUSIC) and estimation of Signal parameter by rotation invariant technique Algorithm (estimation Signal Parameters via Rotational estimation Techniques, ESPRIT), can provide high resolution DOA estimation in case of uncorrelated and partially correlated signals. The classical signal subspace algorithm represented by MUSIC makes the direction-finding positioning technology break through the limitation of resolution, but the algorithm has the defects of large calculation amount, poor performance under the condition of low signal-to-noise ratio and the like, the algorithm cannot directly process coherent signals, and the coherent solution by using a space smoothing method can lose a certain array aperture. Furthermore, one key assumption typically employed by conventional subspace algorithms is the establishment of uncorrelated or incoherent signal models. In practical circumstances, however, coherent signals tend to be generated due to multipath propagation or intentional interference of the transmitted signal. In this case, since the signal covariance matrix is not full rank, the subspace-based DOA estimation method will fail. Compared with the classical spatial spectrum estimation method, the DOA estimation method based on sparse representation has very high estimation precision, does not need any preprocessing, and can be directly applied to coherent signals, thereby gaining wide attention of domestic and foreign scholars. M.M. Han and X.D.Zhang, "An ESPRIT-like algorithm for coherent DOA estimation," IEEE Antennas Wireless Propag.Lett., vol.4, pp.443-446, Dec.2005, propose a DOA estimation method (hereinafter referred to as similar ESPRIT algorithm for short), this method utilizes symmetrical array transducer structure, obtain An equivalent signal Toeplitz matrix that rank and coherence between the input signals are irrelevant, utilize this equivalent signal Toeplitz matrix to realize DOA estimation; s.u. pilai and b.h.kwon, "Forward/backward spatial smoothing techniques for coherent Signal identification," IEEE trans.initial, Speech, Signal process, vol.37, No.1, pp.8-15, jan.1989, proposes a weighted spatial smoothing method (hereinafter referred to as FBSS algorithm) that achieves DOA estimation by creating a smoothed array output covariance matrix in combination with a feature-based technique without considering Signal correlation; qian, L.Huang, Y.Xiao, and H.C.so, "Localization of signals with out source number knowledge in unknown spatial correlated Gaussian noise," Signal Process, vol.111, pp.170-178, Jun.2015, which proposes a Signal Localization method (hereinafter referred to as Qian algorithm) without source number knowledge, which respectively decorrelates coherent signals and suppresses unknown spatial correlated noise by using a symmetric array model and a fourth-order cumulant, and then realizes DOA estimation by using a joint diagonalization algorithm.
However, the above-mentioned similar Esprit algorithm does not effectively utilize all information of the covariance matrix of the received signal, and the DOA estimation performance is relatively poor; the FBSS algorithm works normally only under conditions where the signal is highly correlated, and signal cancellation may occur to affect DOA estimation performance; the Qian algorithm, while suppressing noise, results in a considerable amount of computation and requires a lot of time.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention provides a coherent signal DOA estimation method.
One embodiment of the present invention provides a coherent signal DOA estimation method, including the following steps:
step 1, establishing a coherent signal model, and obtaining received signal data according to the coherent signal model;
step 2, calculating a covariance matrix of the received signal data by using the coherent signal model;
step 3, calculating noiseless received signal data according to the covariance matrix;
step 4, establishing an equivalent source vector according to the noiseless received signal data;
and 5, establishing a weight vector, and performing DOA estimation according to the weight vector and the equivalent source vector.
In one embodiment of the present invention, the received signal data x (t) in step 1 is represented as:
Figure BDA0002802753110000031
wherein the content of the first and second substances,
Figure BDA0002802753110000032
representing a flow pattern matrix, M representing the number of linear arrays, 2M +1 linear arrays shared by received signal data, L representing the number of coherent signals, a (theta)l)＝[ejMβ，ej(M-1)β，...，1，...，e-j(M-1)β，e-jMβ]TDenotes a guide vector of 2M +1 dimensions, β ═ 2 π dsin (θ)l) λ represents the l-th direction of arrival, θlThe ith DOA estimation angle is shown, d and lambda respectively represent the array element spacing and wavelength,
Figure BDA0002802753110000033
and alpha is1＝1，
Figure BDA0002802753110000034
Representing a coherent signal waveform vector, n (t) ═ n-M(t)，...，n0(t)，...，nM(t)]TRepresenting unknown spatial correlated gaussian noise; wherein the content of the first and second substances,
received signal data x of corresponding m-th array element at time tm(t) is expressed as:
Figure BDA0002802753110000041
wherein the content of the first and second substances,
Figure BDA0002802753110000042
representing a non-zero complex constant, plAnd delta philAmplitude attenuation factor and phase change, respectively, nmAnd (t) represents the noise signal received by the m array elements.
In one embodiment of the present invention, the covariance matrix R of the received signal data in step 2 is represented as:
R＝E[x(t)xH(t)]＝ARsAH+Q；
wherein R iss＝E[s(t)sH(t)]A covariance matrix representing the coherent signal, Q represents a covariance matrix of the noise signal, (-)HRepresents a hermitian matrix;
the (m, k) th term Q (m, k) of the covariance matrix Q is represented as:
q(m，k)＝Qmk＝σnρ|m-k|ej((m-k)π/2)；
wherein M and k respectively represent an index of an array element, wherein M, k ═ MnRepresenting the desired signal-to-noise ratio, p representing the regression coefficient;
the (m, k) th term R (m, k) of the covariance matrix R is expressed as:
Figure BDA0002802753110000051
wherein the content of the first and second substances,
Figure BDA0002802753110000052
and is
Figure BDA0002802753110000053
(·)*Representing a complex conjugate.
In one embodiment of the present invention, the noiseless received signal data γ (m, k) calculated in step 3 is represented as:
Figure BDA0002802753110000054
wherein the content of the first and second substances,
Figure BDA0002802753110000055
and q (m, k) is q*(-m，-k)＝q*(k，m)。
In one embodiment of the invention, the equivalent source vector established in step 4
Figure BDA0002802753110000056
Expressed as:
Figure BDA0002802753110000057
wherein the content of the first and second substances,
Figure BDA0002802753110000058
and is
Figure BDA0002802753110000059
Figure BDA00028027531100000510
In a corresponding manner, the first and second electrodes are,
Figure BDA00028027531100000511
expressed as:
Figure BDA0002802753110000061
in a corresponding manner, the first and second electrodes are,
Figure BDA0002802753110000062
represents a switching matrix represented as:
Figure BDA0002802753110000063
wherein e isjThis represents an (M +1) × 1-dimensional column vector having a j-th position of 1 and the remaining positions of 0.
In one embodiment of the present invention, step 5 comprises:
step 5.1, establishing a weight vector;
step 5.2, constructing a sparse representation function of the equivalent source vector according to the weight vector;
and 5.3, solving the sparse representation function to carry out DOA estimation.
In one embodiment of the invention, the weight vector established in step 5.1 is represented as:
ω＝[ω1，ω2，...，ωK]T；
wherein, ω iskIs denoted by ωk＝(aH(θk)UUHa(θk))1/2，a(θk) Representing DOA estimation angle thetakU represents a noise subspace obtained by performing eigen decomposition on the covariance matrix Q.
In one embodiment of the invention, the sparse representation function of the equivalent source vector constructed in step 5.2 is represented as:
Figure BDA0002802753110000064
wherein the content of the first and second substances,
Figure BDA0002802753110000065
representing an overcomplete dictionary, K representing the number of directions of arrival of the potential signal,
Figure BDA0002802753110000066
representing a vector of equivalent sources
Figure BDA0002802753110000067
Is used to represent the coefficients of the image,
Figure BDA0002802753110000071
representing the intelligent product of elements, wherein,
Figure BDA0002802753110000072
representing overcomplete dictionariesk steering vectors.
In one embodiment of the invention, solving the sparse representation function in step 5.3 is represented as:
Figure BDA0002802753110000073
wherein | · | purple sweet0Is represented by0Norm, θ, represents the final DOA estimation angle.
In one embodiment of the invention, solving the sparse representation function in step 5.3 is represented as:
Figure BDA0002802753110000074
wherein xi > 0 and is a constant, | | ·| Erythroc1Is represented by1The norm of the number of the first-order-of-arrival,
Figure BDA0002802753110000075
is represented by2The square of the norm.
Compared with the prior art, the invention has the beneficial effects that:
the coherent signal DOA estimation method provided by the invention considers the spatial domain correlated Gaussian noise and the coherent signal, and carries out DOA estimation by utilizing the designed weight vector and the equivalent source vector, thereby improving the performance of DOA estimation and having relatively low calculation cost.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
Fig. 1 is a schematic flowchart of a coherent signal DOA estimation method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram illustrating a comparison between DOA estimation results in different directions of arrival between the DOA estimation method provided by the embodiment of the present invention and three conventional DOA estimation methods;
fig. 3 is a schematic diagram showing a comparison of root mean square errors of DOA estimation under different signal-to-noise ratios between the DOA estimation method provided by the embodiment of the present invention and three conventional DOA estimation methods.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
Example one
To solve the problem that the existing DOA estimation cannot achieve both DOA estimation performance and operation time, please refer to fig. 1, where fig. 1 is a schematic structural diagram of a coherent signal DOA estimation method according to an embodiment of the present invention. The embodiment provides a coherent signal DOA estimation method, which includes the following steps:
step 1, establishing a coherent signal model, and obtaining received signal data according to the coherent signal model.
Specifically, the coherent signal model is set as: l far-field narrow-band coherent signals
Figure BDA0002802753110000081
At an unknown angle
Figure BDA0002802753110000082
To one-dimensional symmetric equidistant lines, e.g. Sparse Uniform Line Array (SULA), consisting of
Figure BDA0002802753110000083
The array elements are arranged in all directions, and the input signal is uncorrelated with noise. Assuming that the central array element of the array is the reference array element, the received signal data x (t) of the array at time t is represented as:
Figure BDA0002802753110000084
wherein the content of the first and second substances,
Figure BDA0002802753110000085
representing a flow pattern matrix, M representing the number of linear arrays, 2M +1 linear arrays shared by received signal data, L representing the number of coherent signals, a (theta)l)＝[ejMβ，ej(M-1)β，...，1，...，e-j(M-1)β，e-jMβ]TDenotes a guide vector of 2M +1 dimensions, β ═ 2 π dsin (θ)l) λ represents the l-th direction of arrival, θlThe ith DOA estimation angle is shown, d and lambda respectively represent the array element spacing and wavelength,
Figure BDA0002802753110000086
and alpha is1＝1，
Figure BDA0002802753110000091
Representing a coherent signal waveform vector, n (t) ═ n-M(t)，...，n0(t)，...，nM(t)]TRepresenting unknown spatial correlated gaussian noise; wherein the content of the first and second substances,
received signal data x of corresponding m-th array element at time tm(t) is expressed as:
Figure BDA0002802753110000092
wherein the content of the first and second substances,
Figure BDA0002802753110000093
representing a non-zero complex constant, plAnd delta philAmplitude attenuation factor and phase change, respectively, nmAnd (t) represents the noise signal received by the m array elements.
And 2, calculating a covariance matrix of the received signal data by using a coherent signal model.
Specifically, the covariance matrix R of the received signal data of the present embodiment is expressed as:
R＝E[x(t)xH(t)]＝ARsAH+Q (3)
wherein R iss＝E[s(t)sH(t)]A covariance matrix representing the coherent signal, Q represents a covariance matrix of the noise signal, (-)HRepresenting the hermitian matrix.
Correspondingly, the (m, k) th term Q (m, k) of the covariance matrix Q of the noise signal is expressed as:
q(m，k)＝Qmk＝σnρ|m-k|ej((m-k)π/2) (4)
where M and k respectively represent an index of an array element, specifically, a row index and a column index of the noise covariance matrix Q, where M, k ═ M,. 0.. M, σ ·nRepresenting a desired signal-to-noise ratio, which can be obtained by adjustment, wherein rho represents a regression coefficient and is used for controlling the relative height of a noise space spectrum peak;
correspondingly, the (m, k) th term R (m, k) of the covariance matrix R of the coherent signal is represented as:
Figure BDA0002802753110000101
where M and k also represent the indices of the array elements, respectively, and here specifically the row index and the column index of the covariance matrix R of the coherent signal, where M, k is-M, 0, M,
Figure BDA0002802753110000102
and is
Figure BDA0002802753110000103
(·)*Representing a complex conjugate.
And 3, calculating the noiseless received signal data according to the covariance matrix.
Specifically, the noiseless received signal data γ (m, k) calculated by the present embodiment is expressed as:
Figure BDA0002802753110000104
when q (m, k) is q*(-m，-k)＝q*(k, m), gaussian noise can be removed, and the noiseless received signal data γ (m, k) can be updated by substituting equation (6) as:
Figure BDA0002802753110000111
wherein the content of the first and second substances,
Figure BDA0002802753110000112
and 4, establishing an equivalent source vector according to the noiseless received signal data.
Specifically, in order to use all rows of the covariance matrix R to the received signal data in the calculation, thereby improving the estimation performance of the direction of arrival, the present embodiment establishes an equivalent source vector, specifically an equivalent source vector
Figure BDA0002802753110000113
Expressed as:
Figure BDA0002802753110000114
wherein the content of the first and second substances,
Figure BDA0002802753110000115
and is
Figure BDA0002802753110000116
Figure BDA0002802753110000117
In a corresponding manner, the first and second electrodes are,
Figure BDA0002802753110000118
expressed as:
Figure BDA0002802753110000119
in a corresponding manner, the first and second electrodes are,
Figure BDA00028027531100001110
represents a switching matrix represented as:
Figure BDA00028027531100001111
wherein e isjThis represents an (M +1) × 1-dimensional column vector having a j-th position of 1 and the remaining positions of 0.
And 5, establishing a weight vector, and performing DOA estimation according to the weight vector and the equivalent source vector.
Specifically, step 5 of this embodiment includes step 5.1, step 5.2, and step 5.3:
and 5.1, establishing a weight vector.
Specifically, for better sparse reconstruction performance, the present embodiment establishes a weight vector ω, and the real signal direction is assigned with a smaller weight, which can significantly amplify the corresponding signal power, and according to the MUSIC spatial spectrum, the weight vector ω established in the present embodiment is represented as:
ω＝[ω1，ω2，...，ωK]T (11)
wherein, ω iskIs denoted by ωk＝(aH(θk)UUHa(θk))1/2，a(θk) Representing DOA estimation angle thetakU represents a noise subspace obtained by performing eigen decomposition on the covariance matrix Q.
And 5.2, constructing a sparse representation function of the equivalent source vector according to the weight vector.
Specifically, a weight vector ω is established, and the embodiment is equivalent to the source vector
Figure BDA0002802753110000121
The problem of deterministic DOA (direction of arrival) estimation is seen as a problem of sparse reconstruction, building an equivalent source vector from the weight vector ω
Figure BDA0002802753110000122
Before the sparse representation function, the embodiment first constructs a sparse representation function of the equivalent source vector, where the constructed sparse representation function of the equivalent source vector is represented as:
Figure BDA0002802753110000123
wherein the content of the first and second substances,
Figure BDA0002802753110000124
representing the sparse signal power vector, K representing the number of directions of arrival of the potential signal,
Figure BDA0002802753110000125
represents an overcomplete dictionary and satisfies the constraint isometry property, (2M +1) < K, the kth steering vector of the overcomplete dictionary in equation (12) can be expressed as:
Figure BDA0002802753110000126
further, sparse representation of p is achieved by using the established weight vector omega. According to the signal subspace theory, it can be seen from the formula (11) that ω is the spatial frequency spectrum of the correlation signal, when θkAngle close to the true signal, ωkIs very small. According to this characteristic, the present embodiment implements a sparse representation of p with a weight vector ω as:
Figure BDA0002802753110000127
wherein the content of the first and second substances,
Figure BDA0002802753110000131
representing a vector of equivalent sources
Figure BDA0002802753110000132
Is a non-zero term ratio of p
Figure BDA0002802753110000133
Is much smaller than the corresponding position of (A) and
Figure BDA0002802753110000134
the sparsity of the correlation is enhanced and,
Figure BDA0002802753110000135
representing the element intelligence product. Substituting equation (13) into equation (12) results in an updated sparse representation function of the equivalent source vector, which is expressed as:
Figure BDA0002802753110000136
and 5.3, solving the sparse representation function to carry out DOA estimation.
Specifically, the present implementation ultimately converts the DOA estimate into a sparse representation function that solves for the equivalent source vector, and by solving for
Figure BDA00028027531100001311
Minimum values to achieve an estimate of DOA, in particular:
the solving sparse representation function of the present embodiment is expressed as:
Figure BDA0002802753110000137
wherein | · | purple sweet0Is represented by0Norm, θ, represents the final DOA estimation angle.
Similarly, the solving sparse representation function of the present embodiment is expressed as:
Figure BDA0002802753110000138
wherein xi > 0 and is a constant, | | ·| Erythroc1Is represented by1The norm of the number of the first-order-of-arrival,
Figure BDA0002802753110000139
is represented by2The square of the norm.
The present embodiment is solved by formula (15) or formula (16)
Figure BDA00028027531100001310
And (3) corresponding to the minimum value through a formula (14) to obtain a DOA estimation angle theta, so as to realize final DOA estimation.
To verify the effectiveness of the coherent signal DOA estimation method proposed in this embodiment, the following simulation experiments are used to further prove the effectiveness of the coherent signal DOA estimation method.
The simulation assumes that M is 11, the interval of array elements is half wavelength, and xi is 10 in the one-dimensional symmetrical uniform linear array-4. To measure the performance of DOA estimation, the Root Mean Square Error (RMSE) of the direction of arrival estimation is defined as:
Figure BDA0002802753110000141
wherein, N represents the Monte Carlo experiment times, and L represents the number of related signals.
In this embodiment, similar Esprit algorithm, FBSS algorithm, and Qian algorithm are respectively adopted to compare with the method provided by the present invention, where similar Esprit is a similar technical algorithm (An Esprit-like algorithm for coherent DOA estimation, for short) that estimates signal parameters by using a subspace rotation method, and a Forward/Backward Spatial Smoothing algorithm (FBSS, for short), and a Qian algorithm is a signal localization algorithm that does not need to know the source number.
Simulation experiment I:
three coherent signals acting on the one-dimensional symmetrical equidistant linear array are considered, and the arrival directions of the three coherent signals are as follows: -12 °, 2 °, 16 ° }, colored noise ρ ═ 0.8 and SNR ═ 5 dB. Referring to fig. 2, fig. 2 is a schematic diagram illustrating a comparison between DOA estimation results in different directions of arrival of the DOA estimation method provided by the embodiment of the present invention and three traditional DOA estimation methods, as shown in fig. 2: the DOA estimation performance similar to Esprit algorithm and FBSS algorithm is significantly degraded; although colored noise can be eliminated by utilizing the fourth-order cumulant mentioned by the Qian algorithm, the Qian algorithm can only estimate a signal with the arrival direction of 16 degrees under the background of low signal-to-noise ratio; the DOA estimation can be well carried out on the algorithms under the conditions of-12 degrees, 2 degrees and 16 degrees, and the algorithms have good performance.
And (2) simulation experiment II:
three coherent signals acting on a one-dimensional symmetrical equidistant linear array are considered, the arrival directions of the three coherent signals are { -12 °, 2 °, 16 ° }, the signal-to-noise ratio varies from-5 dB to 20dB, and the SNR is 0dB and the ρ is 0.8. The RMSE of the directions of arrival of three coherent signals calculated by 500 monte carlo experiments, please refer to fig. 3, a schematic diagram showing the root mean square error comparison of the DOA estimation method provided in the embodiment of the present invention and the conventional three DOA estimation methods under different signal-to-noise ratios, and the embodiment evaluates the DOA estimation performance under different signal-to-noise ratios. As can be seen from fig. 3: the colored noise is not processed, so that the estimation performance of the FBSS algorithm and the similar Esprit algorithm DOA is particularly poor; the DOA estimation performance of the algorithm provided by the invention is superior to that of other methods in the whole signal-to-noise ratio range, and particularly under the condition of low signal-to-noise ratio, the estimation performance of the algorithm provided by the invention is the best.
Meanwhile, the embodiment also counts the time required by the algorithm to realize DOA estimation under different array element numbers, and concretely refers to Table 1.
TABLE 1 simulation time required for different algorithms under different array element numbers
Number of array elements 11 13 15 17 19 21 23 25
Operation time(s) 0.8028 0.8031 0.7483 0.7759 0.7787 0.8388 0.8062 0.8467
As can be seen from Table 1, the algorithm provided by the invention is short in time consumption, and the execution time change is increased less with the increase of the number of array elements.
In summary, the coherent signal DOA estimation method provided in this embodiment considers spatial domain correlated gaussian noise and coherent signals, and performs DOA estimation by using the designed weight vector and equivalent source vector, specifically: the embodiment establishes a coherent signal model, eliminates the Gaussian noise related to the space domain based on a one-dimensional symmetrical equidistant linear array, reconstructs the noiseless item in the covariance matrix to calculate the noiseless received signal data, then constructs an equivalent source vector according to the noiseless received signal data, thereby simulating the received signal data in the extended virtual array without considering the coherence among the received signal data, enhancing the sparsity of the signal by using the obtained equivalent source vector and the weight vector designed by using the signal subspace theory, the weight vector can realize more robust DOA estimation of sparse reconstruction performance, improve the performance of the DOA estimation, particularly obviously improve the DOA estimation performance under the condition of low signal-to-noise ratio, and the computing cost is relatively low, the computing efficiency is high, and the method is crucial to a large array/real-time data processing system.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (10)

1. A coherent signal DOA estimation method is characterized by comprising the following steps:
step 1, establishing a coherent signal model, and obtaining received signal data according to the coherent signal model;
step 2, calculating a covariance matrix of the received signal data by using the coherent signal model;
step 3, calculating noiseless received signal data according to the covariance matrix;
step 4, establishing an equivalent source vector according to the noiseless received signal data;
and 5, establishing a weight vector, and performing DOA estimation according to the weight vector and the equivalent source vector.
2. A method of estimating a DOA of a coherent signal according to claim 1, wherein said received signal data x (t) in step 1 is represented by:
Figure FDA0002802753100000011
wherein the content of the first and second substances,
Figure FDA0002802753100000012
representing a flow pattern matrix, wherein the data of the received signals share 2M +1 linear arrays, L represents the number of coherent signals, a (theta)l)＝[ejMβ，ej(M-1)β，…，1，…，e-j(M-1)β，e-jMβ]TDenotes a guide vector of 2M +1 dimensions, β ═ 2 π dsin (θ)l) λ represents the l-th direction of arrival, θlThe first DOA estimation angle is shown, and d and lambda respectively represent the array element spacing and the wavelength，
Figure FDA0002802753100000013
And alpha is1＝1，
Figure FDA0002802753100000014
Representing a coherent signal waveform vector, n (t) ═ n-M(t)，…，n0(t)，…，nM(t)]TRepresenting unknown spatial correlated gaussian noise; wherein the content of the first and second substances,
received signal data x of corresponding m-th array element at time tm(t) is expressed as:
Figure FDA0002802753100000015
wherein the content of the first and second substances,
Figure FDA0002802753100000021
representing a non-zero complex constant, plAnd delta philAmplitude attenuation factor and phase change, respectively, nmAnd (t) represents the noise signal received by the m array elements.
3. A method of estimating a DOA of a coherent signal according to claim 2, wherein the covariance matrix R of the received signal data in step 2 is represented as:
R＝E[x(t)xH(t)]＝ARsAH+Q；
wherein R iss＝E[s(t)sH(t)]A covariance matrix representing the coherent signal, Q represents a covariance matrix of the noise signal, (-)HRepresents a hermitian matrix;
the (m, k) th term Q (m, k) of the covariance matrix Q is represented as:
q(m，k)＝Qmk＝σnρ|m-k|ej((m-k)π/2)；
where M and k represent the indices of the array elements, respectively, where M, k ═ M, …, 0, …, M, σnWhich is indicative of a desired signal-to-noise ratio,ρ represents a regression coefficient;
the (m, k) th term R (m, k) of the covariance matrix R is expressed as:
Figure FDA0002802753100000022
wherein the content of the first and second substances,
Figure FDA0002802753100000023
and is
Figure FDA0002802753100000024
(·)*Representing a complex conjugate.
4. A coherent signal DOA estimation method according to claim 3, characterized in that the noiseless received signal data γ (m, k) calculated in step 3 is represented as:
Figure FDA0002802753100000031
wherein the content of the first and second substances,
Figure FDA0002802753100000032
and q (m, k) is q*(-m，-k)＝q*(k，m)。
5. A method of DOA estimation of a coherent signal according to claim 4, characterized in that said equivalent source vector established in step 4 is
Figure FDA0002802753100000033
Expressed as:
Figure FDA0002802753100000034
wherein the content of the first and second substances,
Figure FDA0002802753100000035
and is
Figure FDA0002802753100000036
Figure FDA0002802753100000037
In a corresponding manner, the first and second electrodes are,
Figure FDA0002802753100000038
expressed as:
Figure FDA00028027531000000311
in a corresponding manner, the first and second electrodes are,
Figure FDA0002802753100000039
represents a switching matrix represented as:
Figure FDA00028027531000000310
wherein e isjThis represents an (M +1) × 1-dimensional column vector having a j-th position of 1 and the remaining positions of 0.
6. A method of DOA estimation of a coherent signal according to claim 5, characterized in that step 5 comprises:
step 5.1, establishing a weight vector;
step 5.2, constructing a sparse representation function of the equivalent source vector according to the weight vector;
and 5.3, solving the sparse representation function to carry out DOA estimation.
7. A method of estimation of a DOA of a coherent signal according to claim 6, characterized in that the weight vector established in step 5.1 is represented as:
ω＝[ω1，ω2，…，ωK]T；
wherein, ω iskIs denoted by ωk＝(aH(θk)UUHa(θk))1/2，a(θk) Representing DOA estimation angle thetakU represents a noise subspace obtained by performing eigen decomposition on the covariance matrix Q.
8. A method of estimation of a DOA of coherent signals according to claim 7, characterized in that the sparse representation function of the equivalent source vectors constructed in step 5.2 is represented as:
Figure FDA0002802753100000041
wherein the content of the first and second substances,
Figure FDA0002802753100000042
representing an overcomplete dictionary, K representing the number of directions of arrival of the potential signal,
Figure FDA0002802753100000043
representing a vector of equivalent sources
Figure FDA0002802753100000044
Represents the coefficient of sparsity, wherein,
Figure FDA0002802753100000045
the kth steering vector representing an overcomplete dictionary.
9. A method of estimation of a DOA of a coherent signal according to claim 8, characterized in that the solving of the sparse representation function in step 5.3 is represented by:
Figure FDA0002802753100000046
Figure FDA0002802753100000048
Figure FDA0002802753100000047
wherein | · | purple sweet0Is represented by0Norm, θ, represents the final DOA estimation angle.
10. A method of estimation of a DOA of a coherent signal according to claim 8, characterized in that the solving of the sparse representation function in step 5.3 is represented by:
Figure FDA0002802753100000051
Figure FDA0002802753100000052
Figure FDA0002802753100000053
wherein xi > 0 and is a constant, | | ·| Erythroc1Is represented by1The norm of the number of the first-order-of-arrival,
Figure FDA0002802753100000054
is represented by2The square of the norm.
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Citations (2)

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Publication number Priority date Publication date Assignee Title
US5262789A (en) * 1992-04-30 1993-11-16 General Electric Company Source identification system for closely separated spatial sources
CN108957388A (en) * 2018-05-21 2018-12-07 南京信息工程大学 A kind of MIMO radar coherent DOA estimation method based on covariance matching SL0 algorithm

Patent Citations (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US5262789A (en) * 1992-04-30 1993-11-16 General Electric Company Source identification system for closely separated spatial sources
CN108957388A (en) * 2018-05-21 2018-12-07 南京信息工程大学 A kind of MIMO radar coherent DOA estimation method based on covariance matching SL0 algorithm

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Title
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