CN113238184B - Two-dimensional DOA estimation method based on non-circular signal - Google Patents
Two-dimensional DOA estimation method based on non-circular signal Download PDFInfo
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Abstract
The invention belongs to the technical field of array signal processing, relates to a DOA (direction of arrival) estimation technology, and particularly relates to a two-dimensional DOA estimation method when an incident signal is a non-circular signal. The method comprises the following steps that step 1, conjugation of L array received signals is utilized to expand a received signal vector, and an expanded signal vector is obtained; step 2, calculating a covariance matrix of the spread signal vector and carrying out feature decomposition on the covariance matrix; step 3, expanding covariance matrix feature decomposition to obtain a signal subspace and a noise subspace; step 4, defining a new phase angle theta k The method comprises the steps of carrying out a first treatment on the surface of the Step 5, constructing a one-dimensional spectrum peak search function by utilizing a signal subspace, and obtaining a phase angle theta through one-dimensional spectrum peak search; step 6, constructing a new spectral peak search function by the orthogonal relation between the signal subspace and the noise subspace, and passing the phase angle theta k Estimating gamma k The method comprises the steps of carrying out a first treatment on the surface of the Step 7, passing the phase angle theta k And gamma k Calculating pitch angle alpha k And azimuth angle beta k 。
Description
Technical Field
The invention belongs to the technical field of array signal processing, relates to a DOA (direction of arrival) estimation technology, and particularly relates to a two-dimensional DOA estimation method when an incident signal is a non-circular signal.
Background
The two-dimensional DOA estimation is always a research hot spot in the field of array signal processing, and has wide application in the fields of radar, sonar, mobile communication and the like. Conventional DOA estimation methods include multiple signal classification (MUSIC) and rotation invariant subspace (ESPRIT) algorithms based on subspace decomposition, which are very widely applied algorithms, but both algorithms are based on one-dimensional uniform linear arrays, and if the algorithms are directly extended to two-dimensional structural arrays, parameter pairing and complicated calculation problems (such as two-dimensional MUSIC search) can occur.
The two-dimensional structures of the array are various, and the array is represented by a planar array, a double parallel line array, a circular array and an L-shaped array. From the literature "An L-shaped array for estimating 2-D directions of wave arrival" published by Hua Y et al, it is known that L-arrays have better direction finding performance than arrays of other structures, and research on two-dimensional direction finding algorithms based on L-arrays has attracted a great deal of attention. Tayem N et al in the document L-shape 2-dimensional arrival angle estimation with propagator method propose to construct a Toeplitz matrix by using the cross correlation matrix of the L matrix to solve the two-position angle pairing problem, however, the problem of mispairing is easy to generate under the condition of small signal-to-noise ratio. The Liang J et al document Joint Elevation and Azimuth Direction Finding Using L-Shaped Array proposes an automatic pairing two-dimensional direction finding algorithm based on the principle of rank loss, parameter separation is realized through rank loss, two-dimensional search is avoided, and complexity of the algorithm is reduced to obtain good effect.
However, the above algorithm does not consider the case when the incident signal is a non-circular signal, and studies have shown that by using the non-circular characteristics of the non-circular signal, the number of resolvable signals can be increased while improving the estimation accuracy of the DOA. The literature MUSIC-like estimation of direction of arrival for non-circular sources of Abeida H and Delmas J P proposes that the NC-MUSIC algorithm realizes DOA estimation, and the array popularity is expanded to be twice as much as the original number of resolvable signals by utilizing the covariance matrix and the elliptic covariance matrix of non-circular signals at the same time, so that the direction finding precision is improved. Meanwhile, delmas J P and Abeida H document Stochastic Cramer-Rao bound for non-circular signals with application to DOA estimation give CRB of a non-circular signal DOA and indicate that the random CRB of a complex Gaussian non-circular signal is smaller than or equal to the random CRB of a complex Gaussian circular signal.
Therefore, it is feasible to further improve the direction-finding precision of the algorithm by utilizing the non-circular characteristic of the signals on the basis of the L array, and the maximum resolvable signal number of the algorithm and the direction-finding precision can be improved on the basis of not increasing array elements, so that the method has important research significance and value.
Disclosure of Invention
The invention aims at the L array and expands the receiving signal matrix by utilizing the non-circular characteristic of the signal when the incident signal is a non-circular signal, thereby improving the direction-finding precision of the algorithm and avoiding the pairing of parameters.
In order to achieve the above purpose, the present invention provides the following technical solutions:
a two-dimensional DOA estimation method based on non-circular signals, the method comprising the steps of,
step 1, utilizing conjugation of L array received signals to expand received signal vectors to obtain expanded signal vectors;
step 2, calculating a covariance matrix of the spread signal vector and carrying out feature decomposition on the covariance matrix;
step 3, expanding covariance matrix feature decomposition to obtain a signal subspace and a noise subspace;
step 4, defining a new phase angle theta k ；
Step 5, constructing a one-dimensional spectrum peak search function by utilizing the signal subspace, and obtaining a phase angle through one-dimensional spectrum peak search
Step 6, constructing a new spectral peak search function by the orthogonal relation between the signal subspace and the noise subspace, and passing the phase angle theta k Estimating gamma k ；
Step 7, passing the phase angle theta k and γk Calculating pitch angle alpha k And azimuth angle beta k 。
According to the technical scheme, the L-array signal is further optimized, the L-array signal consists of total 2M+1 array elements uniformly distributed on an x axis and a z axis, the distance between the array elements is d, a reference array element is positioned at a coordinate origin, K far-field, narrowband and uncorrelated signal incidence is realized, the wavelength is lambda, and the pitch angle and the azimuth angle of a kth signal are respectively alpha k and βk Defining two phase angles gamma k ＝-2πdsinα k cosβ k /λ，φ k ＝-2πdcosα k λ. Such that the steering vector can be written as
Let x m，n (t) represents the signal received by the (m, n) th array element at time t
X(t)＝[x M，0 (t)x M-1，0 (t)...x 1，0 (t)x 0，M (t)x 0，M-1 (t)...x 0，M (t)] T
Indicating that the array receives a signal vector at time t.
According to further optimization of the technical scheme, the expansion receiving vector in the step 1 is Y (t):
Y(t)＝[X(t) X H (t)] T 。
further optimizing the technical scheme, wherein the step 2 expansion covariance matrix is that
wherein Rs ＝E[s(t)s H (t)]Is an autocorrelation matrix of the signal,is a diagonal matrix consisting of non-circular phases of the signal.
The technical scheme is further optimized, and the step 3 expands characteristic decomposition of the covariance matrix:
wherein Us For signal subspace, U n Is a noise subspace and satisfiesAnd
the technical scheme is further optimized, and the new phase angle is defined in the step 4:
rewriting a guide vector:
the first M rows and the last M rows of the steering vector can be known to satisfy the following relationship:
wherein ,
further optimizing the technical scheme, the step 5 specifically comprises two equally dividing the signal subspace into U 1 and U2 Record U 1 Before M behavior U 11 Post M behavior U 12 ，U 2 Before M behavior U 21 Post M behavior U 22 Defining a matrix:
from the analysis of step 3, it can be seen that when θ=θ k When the kth column of matrix Q will become 0, i.e., matrix Q will decrease rank; thus, a spectral peak search function can be constructed:
k phase angles can be obtained through one-dimensional spectrum peak search
According to the technical scheme, the step 6 is further optimized, and a new spectral peak search function can be constructed according to the orthogonal relation between the signal subspace and the noise subspace:
to estimate the phase angle theta k Can be brought into a corresponding phase angle gamma k And automatically paired.
Further optimizing the technical scheme, wherein the phase angle phi in the step 7 k ：
Pitch angle alpha k ：
Azimuth angle beta k ：
Compared with the prior art, the technical scheme has the following beneficial effects:
the invention provides a two-dimensional DOA estimation method based on non-circular signals, which improves the accuracy of angle estimation by utilizing the non-circular characteristics of the signals, realizes parameter separation by utilizing the rank loss principle, avoids two-bit search, greatly reduces the complexity of an algorithm, and simultaneously carries out automatic parameter pairing.
Drawings
FIG. 1 is a graph of root mean square error versus signal to noise ratio for pitch angle estimation;
fig. 2 is a diagram illustrating the relation between the root mean square error and the signal to noise ratio of the azimuth estimation.
Detailed Description
In order to describe the technical content, constructional features, achieved objects and effects of the technical solution in detail, the following description is made in connection with the specific embodiments in conjunction with the accompanying drawings.
Assuming that the L array consists of total 2M+1 array elements uniformly distributed on the x axis and the z axis, the array element distance is d, the reference array element is positioned at the origin of coordinates, K far field, narrow band and uncorrelated signals are incident, the wavelength is lambda, and the pitch angle and the azimuth angle of the kth signal are alpha respectively k and βk Defining two phase angles gamma k ＝-2πdsinα k cosβ k /λ，φ k ＝-2πdcosα k λ. Such that the steering vector can be written as
Let x m，n (t) represents the signal received by the (m, n) th array element at time t
X(t)＝[x M，0 (t)x M-1，0 (t)...x 1，0 (t)x 0，M (t)x 0，M-1 (t)...x 0，M (t)] T
Indicating that the array receives a signal vector at time t.
Step 1, utilizing conjugation of array received signals to expand received signal vectors to obtain new received signal vectors;
defining a new extended receive vector as Y (t):
Y(t)＝[X(t) X H (t)] T
step 2, calculating a covariance matrix of the extended signal vector;
expanding covariance matrix:
wherein Rs ＝E[s(t)s H (t)]Is an autocorrelation matrix of the signal,is a diagonal matrix consisting of non-circular phases of the signal. In the practical application scenario, the covariance matrix of the received signal is estimated by the measurement data of the L snapshot signals:
step 3, expanding covariance matrix feature decomposition to obtain a signal subspace and a noise subspace;
feature decomposition of the extended covariance matrix:
wherein Us For signal subspace, U n Is a noise subspace and satisfiesAnd
step 4, defining a new phase angle;
defining a new phase angle:
rewriting a guide vector:
the first M rows and the last M rows of the steering vector can be known to satisfy the following relationship:
wherein ,
and 5, constructing a one-dimensional spectrum peak search function.
Matlab generates a received signal, processes the received signal to obtain an extended covariance matrix, and decomposes the characteristics of the extended covariance matrix to obtain a signal subspace and a noise subspace.
Dividing the signal subspace into two equal parts U 1 and U2 Record U 1 Before M behavior U 11 Post M behavior U 12 ，U 2 Before M behavior U 21 Post M behavior U 22 Defining a matrix:
from the analysis of step 3, it can be seen that when θ=θ k At this time, the kth column of matrix Q will become 0, i.e., matrix Q will decrease rank. Thus, a spectral peak search function can be constructed:
k phase angles can be obtained through one-dimensional spectrum peak search
Step 6, passing the phase angle theta k Estimating gamma k ；
A new spectral peak search function can be constructed from the orthogonal relationship of the signal subspace and the noise subspace:
to estimate the phase angle theta k Can be brought into a corresponding phase angle gamma k And automatically paired.
Step 7, passing the phase angle theta k and γk Calculating pitch angle alpha k And azimuth angle beta k ；
Phase angle phi k ：
Pitch angle alpha k ：
Azimuth angle beta k ：
The method is suitable for the research of a direction finding algorithm of an L-Shaped Array, and for verifying the performance advantage of the method in DOA estimation, the method is compared with a method of Joint Elevation and Azimuth Direction Finding Using L-Shaped Array proposed by Liang J and Liu D, and the simulation experiment conditions are as follows: the number of array elements is 13, the wavelength is 100, the distance between array elements is one half wavelength, the snapshot is 200, the number of information sources is 2, the azimuth angles are 60 degrees and 35 degrees, the pitch angles are 40 degrees and 55 degrees, the Monte Carlo simulation times are 500, the two algorithms are compared under different signal-to-noise ratios, the root mean square error of the angle is used as a measurement index of performance, the graph is shown in the figure 1, the relation diagram of the root mean square error of pitch angle estimation and the signal-to-noise ratio is shown in the figure 2, and the relation diagram of the root mean square error of azimuth angle estimation and the signal-to-noise ratio is shown in the figure 2. It can be seen that the estimation accuracy of the method herein is better than the method of Liang J, both in estimating azimuth and pitch.
It is noted that relational terms such as first and second, and the like are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Moreover, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or terminal. Without further limitation, an element defined by the statement "comprising … …" or "comprising … …" does not exclude the presence of additional elements in a process, method, article or terminal device comprising the element. Further, herein, "greater than," "less than," "exceeding," and the like are understood to not include the present number; "above", "below", "within" and the like are understood to include this number.
While the embodiments have been described above, other variations and modifications will occur to those skilled in the art once the basic inventive concepts are known, and it is therefore intended that the foregoing description and drawings illustrate only embodiments of the invention and not limit the scope of the invention, and it is therefore intended that the invention not be limited to the specific embodiments described, but that the invention may be practiced with their equivalent structures or with their equivalent processes or with their use directly or indirectly in other related fields.
Claims (8)
1. A two-dimensional DOA estimation method based on non-circular signals is characterized in that the method comprises the following steps,
step 1, utilizing conjugation of L array received signals to expand received signal vectors to obtain expanded signal vectors;
step 2, calculating a covariance matrix of the spread signal vector and carrying out feature decomposition on the covariance matrix;
step 3, expanding covariance matrix feature decomposition to obtain a signal subspace and a noise subspace;
step 4, defining a new phase angle theta k ；
Said step 4 defines a new phase angle:
rewriting a guide vector:
the first M rows and the last M rows of the steering vector can be known to satisfy the following relationship:
wherein ,
step 5, constructing a one-dimensional spectrum peak search function by utilizing the signal subspace, and obtaining a phase angle through one-dimensional spectrum peak search
Step 6, constructing a new spectral peak search function by the orthogonal relation between the signal subspace and the noise subspace, and passing the phase angle theta k Estimating gamma k ；
Step 7, passing the phase angle theta k and γk Calculating pitch angle alpha k And azimuth angle beta k 。
2. The two-dimensional DOA estimation method based on non-circular signals as in claim 1, wherein the L-array signal consists of a total of 2M+1 array elements uniformly distributed in the x-axis and the z-axis, the array element spacing is d, the reference array element is located at the origin of coordinates, there are K far-field, narrowband, non-correlated signal incidence, the wavelength is λ, the pitch angle and azimuth angle of the kth signal are α respectively k and βk Defining two phase anglesγ k ＝-2πdsinα k cosβ k /λ，φ k ＝-2πdcosα k Lambda; such that the steering vector can be written as
Let x m，n (t) represents the signal received by the (m, n) th array element at time t
X(t)＝[x M，0 (t)x M-1，0 (t)...x 1,0 (t)x 0，M (t)x 0，M-1 (t)...x 0，M (t)] T
Indicating that the array receives a signal vector at time t.
3. The two-dimensional DOA estimating method based on non-circular signals as recited in claim 1, wherein the extended receiving vector in step 1 is Y (t):
Y(t)＝[X(t) x H (t)] T 。
4. the two-dimensional DOA estimation method based on non-circular signals of claim 1, wherein the step 2 spread covariance matrix is
wherein Rs ＝E[s(t)s H (t)]Is an autocorrelation matrix of the signal,is a diagonal matrix consisting of non-circular phases of the signal.
5. The two-dimensional DOA estimation method based on non-circular signals as recited in claim 1, wherein step 3 expands the eigen decomposition of the covariance matrix:
wherein Us For signal subspace, U n Is a noise subspace and is full ofAnd
6. the method of two-dimensional DOA estimation based on non-circular signals as defined in claim 1, wherein the step 5 includes dividing the signal subspace into two equal halves U 1 and U2 Record U 1 Before M behavior U 11 Post M behavior U 12 ，U 2 Before M behavior U 21 Post M behavior U 22 Defining a matrix:
from the analysis of step 3, it can be seen that when θ=θ k When the kth column of matrix Q will become 0, i.e., matrix Q will decrease rank; thus, a spectral peak search function can be constructed:
k phase angles can be obtained through one-dimensional spectrum peak search
7. The two-dimensional DOA estimating method based on non-circular signals as recited in claim 1, wherein step 6 constructs a new spectral peak search function from the orthogonal relation of the signal subspace and the noise subspace:
to estimate the phase angleCan be brought into a corresponding phase angle gamma k And automatically paired.
8. The two-dimensional DOA estimation method based on non-circular signals according to claim 2, wherein the phase angle φ in step 7 k ：
Pitch angle alpha k ：
Azimuth angle beta k ：
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