CN111381208B - Method for estimating direction of arrival of known waveform information source - Google Patents

Method for estimating direction of arrival of known waveform information source Download PDF

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CN111381208B
CN111381208B CN201811644418.0A CN201811644418A CN111381208B CN 111381208 B CN111381208 B CN 111381208B CN 201811644418 A CN201811644418 A CN 201811644418A CN 111381208 B CN111381208 B CN 111381208B
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董阳阳
董春曦
饶鲜
孙霆
毕斯威
叶强
刘明明
唐峥钊
畅鑫
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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
    • G01S3/02—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 using radio waves
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Abstract

The invention relates to a method for estimating the direction of arrival of a known waveform information source, which comprises the following steps: acquiring an array receiving data matrix of a known waveform signal containing a known waveform signal source; acquiring an initial space domain characteristic matrix and an initial rotation invariant vector according to the array received data matrix; calculating a high-precision rotation invariant vector according to the initial airspace feature matrix and the initial rotation invariant vector; and obtaining an angle estimation value of the known waveform signal according to the high-precision rotation invariant vector. The direction-of-arrival estimation method can effectively realize the direction-of-arrival estimation of the known waveform information source under the condition of small snapshot number, and overcomes the problem of larger angle estimation error under the condition of small snapshot number in the existing method, thereby effectively reducing the positioning error of targets such as radar or communication systems.

Description

Method for estimating direction of arrival of known waveform information source
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a direction of arrival estimation method of a known waveform information source.
Background
Direction of arrival (DOA) refers to the Direction of arrival of spatial signals (the Direction angle of each signal to an array reference array element, called Direction of arrival for short), and estimation of the Direction of arrival is an important component of an intelligent antenna, and can be used for determining target positioning of systems such as an array radar and a communication base station. In practical application, due to the cooperative nature of communication, the situation of known waveform information sources is very common, and the introduction of waveform prior information can effectively improve the direction-finding performance. Therefore, the method for estimating the direction of arrival of a waveform source is known and has been paid attention to by a plurality of researchers over the years.
Gu et al, in its published article "Fast and Efficient DOA Estimation Method for Signals with Known waveform Using non-Linear Arrays" ("Signal Processing 2015, pp:265-276), proposed a LR (Linear regression) Method, which comprises the first step: receiving a target signal by adopting a one-dimensional uniform antenna array consisting of M antennas, and sampling the target signal received by each antenna according to the Nyquist sampling theorem to obtain an array receiving data matrix; the second step is that: receiving a data matrix by using an array, and estimating a regression coefficient covariance matrix; the third step: and estimating the direction of arrival of the known waveform information source by using a regression coefficient covariance matrix and combining a generalized least square principle. Although the method has the arrival direction estimation performance close to the Clalmelo boundary, the method still has the defect that when the snapshot number of the known waveform information source is small, the angle estimation performance is seriously deteriorated, so that the positioning error of targets such as a radar or a communication system is large.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention provides a method for estimating the direction of arrival of a known waveform source. The technical problem to be solved by the invention is realized by the following technical scheme:
the invention provides a method for estimating the direction of arrival of a known waveform information source, which comprises the following steps:
s1: acquiring an array receiving data matrix of a known waveform signal containing a known waveform signal source;
s2: acquiring an initial space domain characteristic matrix and an initial rotation invariant vector according to the array received data matrix;
s3: calculating a high-precision rotation invariant vector according to the initial airspace feature matrix and the initial rotation invariant vector;
s4: and obtaining an angle estimation value of the known waveform signal according to the high-precision rotation invariant vector.
In an embodiment of the present invention, the S1 includes:
s11: receiving Q known waveform signals from Q known waveform information sources by using a one-dimensional uniform antenna array consisting of M antennas;
s12: and sampling the Q known waveform signals received by each antenna according to the Nyquist sampling theorem to generate an array received data matrix X.
In an embodiment of the present invention, the S2 includes:
s21: calculating to obtain the initial space domain characteristic matrix B according to the array received data matrix X0The calculation formula is as follows:
B0＝XST(SST)-1，
wherein, S is a known waveform matrix, the superscript T represents the matrix conjugate transpose operation, and the superscript-1 represents the matrix inversion operation;
s22: according to the initial spatial domain feature matrix B0Calculating to obtain the initial rotation invariant vector phi0The calculation formula is as follows:
φ0＝invdiag{(J1B0)#J2B0}，
wherein invdiag {. denotes constructing a column vector by taking diagonal elements of the matrix, J1The selection matrix on the representation: j. the design is a square1＝[IM-1,0(M-1)×1]，J2The following selection matrix is represented: j. the design is a square2＝[0(M-1)×1,IM-1]，IM-1An identity matrix having dimensions of (M-1) × (M-1), 0(M-1)×1Represents the zero matrix with dimension (M-1) x 1, and the superscript # represents the pseudo-inverse of the matrix.
In an embodiment of the present invention, the S3 includes:
s31: according to the initial spatial domain feature matrix B0And said initial rotation invariant vector phi0And calculating an increment vector g by the following calculation formula:
g＝-H#f，
wherein, H is a coefficient matrix, f is a differential vector, and superscript # represents the pseudo-inverse operation of the matrix;
s32: and calculating a rotation-invariant increment vector delta phi according to the increment vector g, wherein the calculation formula is as follows:
Δφ＝g(1:Q)+j·g(Q+1:2Q)，
wherein Q represents the number of the known waveform signals, j represents an imaginary unit, g (1: Q) represents a vector constructed by selecting the 1 st element to the Q th element of the incremental vector g, and g (Q +1:2Q) represents a vector constructed by selecting the Q +1 st element to the 2Q nd element of the incremental vector g.
S33: according to the initial rotation invariant vector phi0And calculating the high-precision rotation invariant vector phi according to the rotation invariant increment vector delta phi, wherein the calculation formula is as follows:
φ＝φ0+Δφ。
in an embodiment of the present invention, the expression of the coefficient matrix H is:
Figure BDA0001931766050000041
wherein, IQAn identity matrix of dimension Q × Q, a matrix Khatri-Rao product, superscript
Figure BDA0001931766050000045
Constructing new matrix or vector by real part of matrix or vector, and superscripting
Figure BDA0001931766050000046
Representing the construction of a new matrix or vector by taking the imaginary part of the matrix or vector, and diag {. cndot } representing the placement of each data element in the vector in a diagonal construction pair of the matrixThe operation of the angle matrix is such that,
Figure BDA0001931766050000047
representing the matrix Kronecker product, 0Q×MQA zero matrix of dimension Q × MQ.
In one embodiment of the present invention, the delta vector f is expressed as:
Figure BDA0001931766050000042
where vec {. cndot } represents an operation of straightening a matrix along a column into a vector, IQIs an identity matrix of dimension Q x Q,
Figure BDA0001931766050000048
is a matrix Hadamard product, 1Q×1A vector in which all elements of dimension Q × 1 are 1.
In an embodiment of the present invention, the S4 includes:
and calculating the angle estimation value of the known waveform information source by using the high-precision rotation invariant vector phi, wherein the calculation formula is as follows:
Figure BDA0001931766050000043
wherein,
Figure BDA0001931766050000044
for the angle estimate of the qth of the known waveform signal, arcsin {. cndot.) represents an arcsine function, and angle {. cndot.) represents the phase angle of the complex number, φqAnd Q is the Q element of the high-precision rotation invariant vector phi, Q is 1,2, …, Q, lambda represents the wavelength of the known waveform signal, and d is the spacing between adjacent antennas in the one-dimensional uniform antenna array.
Compared with the method in the prior art, the method has the beneficial effects that: the method for estimating the direction of arrival of the known waveform information source fully considers the problem of strong correlation between the known waveform signal and noise under the condition of small snapshot number, can effectively realize the direction of arrival estimation of the known waveform information source under the condition of small snapshot number, overcomes the problem of large angle estimation error under the condition of small snapshot number, and well solves the problem of large target positioning error of radar, communication and other systems.
The foregoing description is only an overview of the technical solutions of the present invention, and in order to make the technical means of the present invention more clearly understood, the present invention may be implemented in accordance with the content of the description, and in order to make the above and other objects, features, and advantages of the present invention more clearly understood, the following preferred embodiments are described in detail with reference to the accompanying drawings.
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Fig. 1 is a flowchart of a method for estimating a direction of arrival of a known waveform source according to an embodiment of the present invention;
fig. 2 is a graph of the root mean square error of the DOA estimate as a function of the signal-to-noise ratio using the inventive method and the prior art LR algorithm, respectively, for a fast beat number of 10.
Detailed Description
To further illustrate the technical means and effects of the present invention adopted to achieve the predetermined object, a method for estimating a direction of arrival according to the present invention is described in detail below with reference to the accompanying drawings and the detailed description.
The foregoing and other technical matters, features and effects of the present invention will be apparent from the following detailed description of the embodiments, which is to be read in connection with the accompanying drawings. The technical means and effects of the present invention adopted to achieve the predetermined purpose can be more deeply and specifically understood through the description of the specific embodiments, however, the attached drawings are provided for reference and description only and are not used for limiting the technical scheme of the present invention.
Referring to fig. 1, fig. 1 is a flowchart of a method for estimating a direction of arrival of a known waveform source according to an embodiment of the present invention. The direction of arrival estimation method comprises the following steps:
s1: converting a known waveform signal of a known waveform signal source into an array receiving data matrix;
s2: acquiring an initial space domain characteristic matrix and an initial rotation invariant vector according to the array received data matrix;
s3: calculating a high-precision rotation invariant vector according to the initial airspace feature matrix and the initial rotation invariant vector;
s4: and obtaining an angle estimation value of the known waveform signal according to the high-precision rotation invariant vector.
The direction-of-arrival estimation method of the embodiment can be used for estimating the direction-of-arrival (DOA) of a known waveform information source by a communication antenna under the condition of small snapshot number, so as to improve the reaction speed of a communication system and improve the direction-finding performance under the condition of small snapshot number.
Specifically, the S1 includes:
s11: receiving Q known waveform signals from Q known waveform information sources by using a one-dimensional uniform antenna array consisting of M antennas;
specifically, the Q known waveform sources each transmit a signal having a known waveform.
S12: and sampling the Q known waveform signals received by each antenna according to the Nyquist sampling theorem to generate an array received data matrix X.
In this embodiment, the distances d between adjacent antennas in the one-dimensional uniform antenna array are all equal, and the array reception data matrix X is a matrix of dimension M × N, where M is the number of antennas in the one-dimensional uniform antenna array, and N is the number of fast beats.
The array receive data matrix X may be represented as:
X＝BS+W，
where B denotes a spatial domain feature matrix of dimension M × Q, S denotes a known waveform matrix of dimension Q × N, that is, S is a matrix of dimension Q × N in which all elements are known, and W denotes a noise matrix of dimension M × N.
The spatial domain feature matrix B is in the following specific form:
B＝A·diag{γ1,γ2,…,γq,…,γQ}，
wherein, A is an array manifold matrix, and diag {. cndot } represents the vector in the vectorIs placed on the diagonal of the matrix to construct a diagonal matrix, gammaqThe amplitude of the qth known waveform signal is shown, Q is the serial number of the known waveform signal, and Q is 1,2, …, Q, and Q is the number of the known waveform signals.
The specific form of the array manifold matrix A is as follows:
Figure BDA0001931766050000071
wherein e represents an exponential function, j represents an imaginary unit, d represents a distance between adjacent antennas in the one-dimensional uniform antenna array, and thetaqThe angle of the qth known waveform signal is shown, Q is the serial number of the known waveform signal, Q is 1,2, …, Q is the number of the known waveform signals, λ is the wavelength of the known waveform signal, M is the serial number of the antenna in the one-dimensional uniform antenna array, and M is 1,2, …, M is the number of the antenna in the one-dimensional uniform antenna array.
It is an object of embodiments of the present invention to calculate the angle θ of all known waveform signals from the known waveform sourceqQ is 1,2, …, Q.
Further, the S2 includes:
s21: calculating to obtain the initial space domain characteristic matrix B according to the array received data matrix X0The calculation formula is as follows:
B0＝XST(SST)-1，
wherein, S is a known waveform matrix, the superscript T represents the matrix conjugate transpose operation, and the superscript-1 represents the matrix inversion operation;
s22: according to the initial spatial domain feature matrix B0Calculating to obtain the initial rotation invariant vector phi0The calculation formula is as follows:
φ0＝invdiag{(J1B0)#J2B0}，
wherein invdiag {. denotes constructing a column vector by taking diagonal elements of the matrix, J1The selection matrix on the representation: j. the design is a square1＝[IM-1,0(M-1)×1]，J2The following selection matrix is represented: j. the design is a square2＝[0(M-1)×1,IM-1]，IM-1An identity matrix having dimensions of (M-1) × (M-1), 0(M-1)×1Represents the zero matrix with dimension (M-1) x 1, and the superscript # represents the pseudo-inverse of the matrix.
Next, the S3 includes:
s31: according to the initial spatial domain feature matrix B0And said initial rotation invariant vector phi0And calculating an increment vector g by the following calculation formula:
g＝-H#f，
wherein, H is a coefficient matrix, f is a differential vector, and superscript # represents the pseudo-inverse operation of the matrix;
specifically, the specific form of the coefficient matrix H is:
Figure BDA0001931766050000081
wherein, IQAn identity matrix of dimension Q × Q, a matrix Khatri-Rao product, superscript
Figure BDA0001931766050000082
Constructing new matrix or vector by real part of matrix or vector, and superscripting
Figure BDA0001931766050000083
Representing the construction of a new matrix or vector taking the imaginary part of the matrix or vector, diag {. cndot } representing the operation of placing each data element in the vector on the diagonal of the matrix to construct a diagonal matrix,
Figure BDA0001931766050000092
representing the matrix Kronecker product, 0Q×MQA zero matrix of dimension Q × MQ.
The specific form of the delta vector f is:
Figure BDA0001931766050000091
where vec {. cndot } represents an operation of straightening a matrix along a column into a vector, IQIs an identity matrix of dimension Q x Q,
Figure BDA0001931766050000093
is a matrix Hadamard product, 1Q×1Vectors with elements of dimension Q1 all being 1, superscript
Figure BDA0001931766050000094
Constructing new matrix or vector by real part of matrix or vector, and superscripting
Figure BDA0001931766050000095
The expression takes the imaginary part of the matrix or vector to construct a new matrix or vector.
S32: and calculating a rotation-invariant increment vector delta phi according to the increment vector g, wherein the calculation formula is as follows:
Δφ＝g(1:Q)+j·g(Q+1:2Q)，
wherein Q represents the number of the known waveform signals, j represents an imaginary unit, g (1: Q) represents a vector constructed by selecting the 1 st element to the Q th element of the incremental vector g, and g (Q +1:2Q) represents a vector constructed by selecting the Q +1 st element to the 2Q nd element of the incremental vector g.
S33: according to the initial rotation invariant vector phi0And calculating the high-precision rotation invariant vector phi according to the rotation invariant increment vector delta phi, wherein the calculation formula is as follows:
φ＝φ0+Δφ。
next, the S4 includes:
and calculating the angle estimation value of the known waveform information source by using the high-precision rotation invariant vector phi, wherein the calculation formula is as follows:
Figure BDA0001931766050000101
wherein,
Figure BDA0001931766050000102
for the angle estimate of the qth of the known waveform signal, arcsin {. cndot.) represents an arcsine function, and angle {. cndot.) represents the phase angle of the complex number, φqAnd Q is the Q element of the high-precision rotation invariant vector phi, Q is 1,2, …, Q, lambda represents the wavelength of the known waveform signal, and d is the spacing between adjacent antennas in the one-dimensional uniform antenna array.
Therefore, according to the method, the angles theta of all the known waveform signals of the known waveform source can be calculatedqAngle estimate of
Figure BDA0001931766050000103
The method for estimating the direction of arrival of the known waveform information source can be used for solving the problem of target positioning of systems such as array radars and 5G communication base stations, fully considers the problem of strong correlation between the known waveform signal and noise under the condition of small snapshot number, can effectively realize the estimation of the direction of arrival of the known waveform information source under the condition of small snapshot number, and overcomes the problem of large angle estimation error under the condition of small snapshot number.
The effect of the direction of arrival estimation method of the present embodiment is further described below with reference to simulation experiments.
1. Simulation conditions are as follows:
in the simulation experiment of this embodiment, the computer configuration environment is an intel (R) Core (i7-7700K)4.20GHZ cpu, and the memory 16G, WINDOWS 7 operating system, and the computer simulation software adopts MATLAB R2017a software.
Simulation parameters: assuming that the number of antennas of a one-dimensional uniform antenna array is 4, the distance between adjacent antennas is 1cm, two known waveform signals of a known waveform information source are received, the wavelength is 2cm, and the angles are respectively as follows: 0 ° and 20 °. The Root Mean Square Error (RMSE) of the DOA estimate is expressed as:
Figure BDA0001931766050000111
wherein omega represents the number of Monte Carlo simulation experiments,
Figure BDA0001931766050000112
showing the simulation angle theta of the q known waveform signal obtained by the gamma Monte Carlo simulation experimentqAnd (3) representing the actual angle of the qth known waveform signal, q being 1, 2.
2. Simulation content:
when the fast beat number is 10, under the condition of different signal-to-noise ratios, the DOA estimation is performed by adopting the DOA estimation method of the invention and the LR method of the prior art, 1000 Monte Carlo simulation experiments are respectively performed under each signal-to-noise ratio to obtain the root mean square error of the DOA estimation, and the simulation result is shown in FIG. 2.
3. And (3) simulation result analysis:
fig. 2 is a graph of the rms error of the DOA estimate as a function of the snr obtained using the method of the present invention and the LR algorithm of the prior art, respectively, for a fast beat number of 10, where the x-axis represents the snr in decibels and the y-axis represents the rms error of the DOA estimate in degrees. In fig. 2, the curve marked by a square represents the change curve of the DOA estimation root mean square error along with the signal-to-noise ratio of the direction-of-arrival estimation method of the present invention, and the curve marked by a circle represents the change curve of the DOA estimation root mean square error along with the signal-to-noise ratio of the LR algorithm of the prior art. As can be seen from fig. 2, compared with the LR algorithm of the prior art, the method of the present invention has a smaller root mean square error of DOA estimation, indicating that the present invention has a better DOA estimation performance when the number of snapshots is smaller.
The method for estimating the direction of arrival of the known waveform information source fully considers the problem of strong correlation between the known waveform signal and noise under the condition of small snapshot number, can effectively realize the direction of arrival estimation of the known waveform information source under the condition of small snapshot number, and overcomes the problem of large angle estimation error under the condition of small snapshot number.
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 (4)

1. A method for estimating a direction of arrival of a known waveform source, comprising:
s1: acquiring an array receiving data matrix of a known waveform signal containing a known waveform signal source;
s2: acquiring an initial space domain characteristic matrix and an initial rotation invariant vector according to the array received data matrix;
s3: calculating a high-precision rotation invariant vector according to the initial airspace feature matrix and the initial rotation invariant vector;
s4: obtaining an angle estimation value of the known waveform signal according to the high-precision rotation invariant vector;
the S1 includes:
s11: receiving Q known waveform signals from Q known waveform information sources by using a one-dimensional uniform antenna array consisting of M antennas;
s12: sampling the Q known waveform signals received by each antenna according to the Nyquist sampling theorem respectively to generate an array receiving data matrix X;
the S2 includes:
s21: calculating to obtain the initial space domain characteristic matrix B according to the array received data matrix X0The calculation formula is as follows:
B0＝XST(SST)-1，
wherein, S is a known waveform matrix, the superscript T represents the matrix conjugate transpose operation, and the superscript-1 represents the matrix inversion operation;
s22: according to the initial spatial domain feature matrix B0Calculating to obtain the initial rotation invariant vector phi0The calculation formula is as follows:
φ0＝invdiag{(J1B0)#J2B0}，
wherein invdiag {. denotes a momentArray diagonal elements construct column vectors, J1The selection matrix on the representation: j. the design is a square1＝[IM-1,0(M-1)×1]，J2The following selection matrix is represented: j. the design is a square2＝[0(M-1)×1,IM-1]，IM-1An identity matrix having dimensions of (M-1) × (M-1), 0(M-1)×1A zero matrix with dimension (M-1) multiplied by 1 is represented, and superscript # represents the pseudo-inverse of the matrix;
the S3 includes:
s31: according to the initial spatial domain feature matrix B0And said initial rotation invariant vector phi0And calculating an increment vector g by the following calculation formula:
g＝-H#f，
wherein, H is a coefficient matrix, f is a differential vector, and superscript # represents the pseudo-inverse operation of the matrix;
s32: and calculating a rotation-invariant increment vector delta phi according to the increment vector g, wherein the calculation formula is as follows:
Δφ＝g(1:Q)+j·g(Q+1:2Q)，
wherein Q represents the number of the known waveform signals, j represents an imaginary unit, g (1: Q) represents a vector constructed by selecting the 1 st element to the Q th element of the incremental vector g, and g (Q +1:2Q) represents a vector constructed by selecting the Q +1 st element to the 2Q nd element of the incremental vector g;
s33: according to the initial rotation invariant vector phi0And calculating the high-precision rotation invariant vector phi according to the rotation invariant increment vector delta phi, wherein the calculation formula is as follows:
φ＝φ0+Δφ。
2. the method as claimed in claim 1, wherein the coefficient matrix H is expressed as:
Figure FDA0003288276900000021
wherein, IQAn identity matrix of dimension Q × Q, a matrix Khatri-Rao product, superscript
Figure FDA0003288276900000022
Constructing new matrix or vector by real part of matrix or vector, and superscripting
Figure FDA0003288276900000023
Representing the construction of a new matrix or vector taking the imaginary part of the matrix or vector, diag {. cndot } representing the operation of placing each data element in the vector on the diagonal of the matrix to construct a diagonal matrix,
Figure FDA0003288276900000031
representing the matrix Kronecker product, 0Q×MQA zero matrix of dimension Q × MQ.
3. The method according to claim 2, wherein the delta vector f is expressed as:
Figure FDA0003288276900000032
where vec {. cndot } represents an operation of straightening a matrix along a column into a vector, IQIs an identity matrix of dimension Q x Q,
Figure FDA0003288276900000033
is a matrix Hadamard product, 1Q×1A vector in which all elements of dimension Q × 1 are 1.
4. The direction-of-arrival estimation method according to any one of claims 1 to 3, wherein the S4 includes:
and calculating the angle estimation value of the known waveform information source by using the high-precision rotation invariant vector phi, wherein the calculation formula is as follows:
Figure FDA0003288276900000034
wherein,
Figure FDA0003288276900000035
for the angle estimate of the qth of the known waveform signal, arcsin {. cndot.) represents an arcsine function, and angle {. cndot.) represents the phase angle of the complex number, φqAnd Q is the Q element of the high-precision rotation invariant vector phi, Q is 1,2, …, Q, lambda represents the wavelength of the known waveform signal, and d is the spacing between adjacent antennas in the one-dimensional uniform antenna array.
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