CN113238184A - Two-dimensional DOA estimation method based on non-circular signals - Google Patents

Two-dimensional DOA estimation method based on non-circular signals Download PDF

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CN113238184A
CN113238184A CN202110533350.4A CN202110533350A CN113238184A CN 113238184 A CN113238184 A CN 113238184A CN 202110533350 A CN202110533350 A CN 202110533350A CN 113238184 A CN113238184 A CN 113238184A
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章泽昊
陈华
徐栋
周轶婷
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Abstract

The invention belongs to the technical field of array signal processing, relates to a direction of arrival (DOA) 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 of 1, expanding a received signal vector by utilizing the conjugation of an L array received signal to obtain an expanded signal vector; step 2, calculating a covariance matrix of the expanded signal vector and performing characteristic decomposition on the covariance matrix; step 3, expanding covariance matrix characteristic decomposition to obtain a signal subspace and a noise subspace; step 4, defining a new phase angle thetak(ii) a Step 5, constructing a one-dimensional spectrum peak search function by using the signal subspace, and obtaining a phase angle theta through the one-dimensional spectrum peak search; step 6, constructing a new spectrum peak search function according to the orthogonal relation of the signal subspace and the noise subspace, and passing through a phase angle thetakEstimating gammak(ii) a Step 7, passing through a phase angle thetakAnd gammakCalculating the pitch angle alphakAnd azimuth angle betak。

Description

Two-dimensional DOA estimation method based on non-circular signals
Technical Field
The invention belongs to the technical field of array signal processing, relates to a direction of arrival (DOA) estimation technology, and particularly relates to a two-dimensional DOA estimation method when an incident signal is a non-circular signal.
Background
Two-dimensional DOA estimation is always a research hotspot in the field of array signal processing and has wide application in the fields of radar, sonar, mobile communication and the like. The traditional DOA estimation method comprises a subspace decomposition-based multiple signal classification (MUSIC) algorithm and a rotation invariant subspace (ESPRIT) algorithm which are widely applied algorithms, but both algorithms are based on a one-dimensional uniform linear array, and if the two algorithms are directly expanded to a two-dimensional structure array, parameter pairing and complex calculation quantity problems (such as two-dimensional MUSIC search) can occur.
The two-dimensional structure of the array is various, and representatives are a plane array, a double parallel linear array, a circular array and an L array. As known from the document An L-shaped array for simulating 2-D directions of wave arrival published by Hua Y and the like, the L array has better direction-finding performance compared with arrays with other structures, and the research of a two-dimensional direction-finding algorithm based on the L array draws extensive attention. Tayem N et al, in the document L-shape 2-dimensional array estimation with predictor method, propose to use the cross-correlation matrix of L-matrix to construct a Toeplitz matrix to solve the two-bit angle matching problem, however, the problem of mismatching is easily generated when the signal-to-noise ratio is small. Liang J and other documents, Joint Elevation and Azimuth Direction pointing Using L-Shaped Array, put forward an automatically-paired two-dimensional Direction Finding algorithm based on the rank loss principle, and parameter separation is realized through rank loss, so that 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 characteristic of the non-circular signal, the number of distinguishable signals can be increased while improving the accuracy of DOA estimation. The document "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 twice of the original popularity and the resolvable signal number is also twice of the original number by simultaneously utilizing the covariance matrix and the elliptic covariance matrix of the non-circular signals, so the direction-finding precision is also improved. While Delmas J P and Abeida H documents "Stochastic Cramer-Rao bound for non-circular signals with application to DOA estimation" give a CRB for a non-circular signal DOA and indicate that the random CRB for a complex Gaussian non-circular signal is less than or equal to the random CRB for a complex Gaussian circular signal.
Therefore, it is feasible to further improve the direction-finding accuracy of the algorithm by using the non-circular characteristic of the signal on the basis of the L array, and the maximum distinguishable signal number of the algorithm and the improvement of the direction-finding accuracy can be improved on the basis of not increasing the array elements, so that the method has important research significance and value.
Disclosure of Invention
The invention aims to expand a received signal matrix by using the non-circular characteristic of a signal when an incident signal is a non-circular signal aiming at an L array, thereby improving the direction finding precision of an algorithm and avoiding parameter pairing.
In order to achieve the purpose, the invention provides the following technical scheme:
a two-dimensional DOA estimation method based on non-circular signals comprises the following steps,
step 1, expanding a received signal vector by utilizing the conjugate of an L array received signal to obtain an expanded signal vector;
step 2, calculating a covariance matrix of the expanded signal vector and performing characteristic decomposition on the covariance matrix;
step 3, expanding covariance matrix characteristic decomposition to obtain a signal subspace and a noise subspace;
step 4, defining a new phase angle thetak；
Step 5, constructing a one-dimensional spectral peak search function by utilizing the signal subspace, and obtaining a phase angle through the one-dimensional spectral peak search
Figure BDA0003068831340000021
Step 6, constructing a new spectrum peak search function according to the orthogonal relation of the signal subspace and the noise subspace, and passing through a phase angle thetakEstimating gammak；
Step 7, passing through a phase angle thetak and γkCalculating the pitch angle alphakAnd azimuth angle betak。
According to the technical scheme, the L array signal is further optimized, the L array signal is composed of 2M +1 array elements which are 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, narrow-band and non-relevant signals are incident, the wavelength is lambda, and the pitch angle and the azimuth angle of a K signal are respectively alphak and βkDefining two phase angles gammak＝-2πdsinαkcosβk/λ，φk＝-2πdcosαkAnd/lambda. Thus the steering vector can be recorded as
Figure BDA0003068831340000022
Let xm，n(t) represents the signal received by the (m, n) th array element at time t, then
X(t)＝[xM，0(t)xM-1，0(t)...x1，0(t)x0，M(t)x0，M-1(t)...x0，M(t)]T
Indicating that the array received the signal vector at time t.
In the further optimization of the technical solution, the extended reception vector in step 1 is y (t):
Y(t)＝[X(t) XH(t)]T。
in the further optimization of the technical scheme, the step 2 is to expand the covariance matrix into
Figure BDA0003068831340000031
wherein Rs＝E[s(t)sH(t)]Is a matrix of the autocorrelation of the signal,
Figure BDA0003068831340000032
is a diagonal matrix consisting of non-circular phases of the signal.
Further optimization of the technical scheme, step 3, feature decomposition of the extended covariance matrix:
Figure BDA0003068831340000033
wherein UsIs a signal subspace, UnIs a noise subspace and satisfies
Figure BDA0003068831340000034
And
Figure BDA0003068831340000035
in a further optimization of the present technical solution, step 4 defines a new phase angle:
Figure BDA0003068831340000036
rewriting the steering vector:
Figure BDA0003068831340000037
it can be known that the front M rows and the rear M rows of the steering vector satisfy the following relationship:
Figure BDA0003068831340000038
wherein ,
Figure BDA0003068831340000041
in a further optimization of the present technical solution, the step 5 specifically includes dividing the signal subspace into two equal parts U1 and U2Remember U1Front M behavior U of11Post M behavior U12，U2Front M behavior U of21Post M behavior U22Defining a matrix:
Figure BDA0003068831340000042
from the analysis in step 3, when θ ═ θkThen, the k-th column of the matrix Q will become 0, i.e. the matrix Q will decrease in rank; the spectral peak search function can thus be constructed:
Figure BDA0003068831340000043
k phase angles can be obtained through one-dimensional spectral peak search
Figure BDA0003068831340000044
In step 6, a new spectral peak search function can be constructed from the orthogonal relationship between the signal subspace and the noise subspace:
Figure BDA0003068831340000045
the estimated phase angle thetakThe corresponding phase angle gamma can be obtained by the substitutionkAnd automatically paired.
The technical scheme is further optimized, and the phase angle phi in the step 7k：
Figure BDA0003068831340000046
Pitch angle alphak：
Figure BDA0003068831340000047
Azimuth angle betak：
Figure BDA0003068831340000048
Different from 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 precision of angle estimation by utilizing the non-circular characteristics of the signals, realizes parameter separation by utilizing a rank loss principle, avoids two-bit search, greatly reduces the complexity of an algorithm, and simultaneously automatically pairs the parameters.
Drawings
FIG. 1 is a schematic diagram of root mean square error of pitch angle estimation versus signal-to-noise ratio;
FIG. 2 is a diagram illustrating the RMS error of azimuth angle estimation in relation to the SNR.
Detailed Description
To explain technical contents, structural features, and objects and effects of the technical solutions in detail, the following detailed description is given with reference to the accompanying drawings in conjunction with the embodiments.
Assuming that an L array consists of 2M +1 array elements which are uniformly distributed on an x axis and a z axis, the spacing between the array elements is d, a reference array element is positioned at the origin of coordinates, K far-field, narrow-band and non-relevant signals are incident, the wavelength is lambda, and the pitch angle and the azimuth angle of a kth signal are respectively alphak and βkDefining two phase angles gammak＝-2πdsinαkcosβk/λ，φk＝-2πdcosαkAnd/lambda. Thus the steering vector can be recorded as
Figure BDA0003068831340000051
Let xm，n(t) represents the signal received by the (m, n) th array element at time t, then
X(t)＝[xM，0(t)xM-1，0(t)...x1，0(t)x0，M(t)x0，M-1(t)...x0，M(t)]T
Indicating that the array received the signal vector at time t.
Step 1, expanding a received signal vector by utilizing the conjugate of an array received signal to obtain a new received signal vector;
defining a new extended receive vector as y (t):
Y(t)＝[X(t) XH(t)]T
step 2, calculating a covariance matrix of the expanded signal vector;
expanding a covariance matrix:
Figure BDA0003068831340000061
wherein Rs＝E[s(t)sH(t)]Is a matrix of the autocorrelation of the signal,
Figure BDA0003068831340000062
is a diagonal matrix consisting of non-circular phases of the signal. In practical application scenarios, the covariance matrix of the received signal is estimated from the measured data of L snapshot signals:
Figure BDA0003068831340000063
step 3, expanding covariance matrix characteristic decomposition to obtain a signal subspace and a noise subspace;
feature decomposition of the extended covariance matrix:
Figure BDA0003068831340000064
wherein UsIs a signal subspace, UnIs a noise subspace and satisfies
Figure BDA0003068831340000065
And
Figure BDA0003068831340000066
step 4, defining a new phase angle;
define a new phase angle:
Figure BDA0003068831340000067
rewriting the steering vector:
Figure BDA0003068831340000068
it can be known that the front M rows and the rear M rows of the steering vector satisfy the following relationship:
Figure BDA0003068831340000069
wherein ,
Figure BDA00030688313400000610
and 5, constructing a one-dimensional spectral peak search function.
Matlab generates a receiving signal, the receiving signal is processed to obtain an extended covariance matrix, and the characteristics of the extended covariance matrix are decomposed to obtain a signal subspace and a noise subspace.
Dividing the signal subspace into two equal parts U1 and U2Remember U1Front M behavior U of11Post M behavior U12，U2Front M behavior U of21Post M behavior U22Defining a matrix:
Figure BDA0003068831340000071
from the analysis in step 3, when θ ═ θkThen the k-th column of the matrix Q will become 0, i.e. the matrix Q will be rank reduced. The spectral peak search function can thus be constructed:
Figure BDA0003068831340000072
k phase angles can be obtained through one-dimensional spectral peak search
Figure BDA0003068831340000073
Step 6, passing through a phase angle thetakEstimating gammak；
From the orthogonal relationship of the signal subspace and the noise subspace, a new spectral peak search function can be constructed:
Figure BDA0003068831340000074
the estimated phase angle thetakThe corresponding phase angle gamma can be obtained by the substitutionkAnd automatically paired.
Step 7, passing through a phase angle thetak and γkCalculating the pitch angle alphakAnd azimuth angle betak；
Phase angle phik：
Figure BDA0003068831340000075
Pitch angle alphak：
Figure BDA0003068831340000076
Azimuth angle betak：
Figure BDA0003068831340000081
The invention is suitable for research of Direction-Finding algorithm of L-Shaped Array, in order to verify the performance advantage of the method in DOA estimation, the method is compared with the method of Joint Elevation and Azimuth Direction fixing Using L-Shaped Array proposed by Liang J and Liu D, and the conditions of simulation experiment are as follows: the number of the array elements is 13, the wavelength is 100, the spacing between the array elements is half of the wavelength, the snapshot is 200, the number of the information sources is 2, the azimuth angle is 60 degrees and 35 degrees, the pitch angle is 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 relation diagram of the root-mean-square error estimated for the pitch angle and the signal-to-noise ratio is shown in figure 1, and the relation diagram of the root-mean-square error estimated for the azimuth angle and the signal-to-noise ratio is shown in figure 2. It can be seen that the estimation accuracy of the method is better than that of the Liang J method whether the azimuth angle or the pitch angle is estimated.
It is noted that, herein, relational terms such as first and second, and the like may be 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. Also, 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 phrases "comprising … …" or "comprising … …" does not exclude the presence of additional elements in a process, method, article, or terminal that comprises the element. Further, herein, "greater than," "less than," "more than," and the like are understood to exclude the present numbers; the terms "above", "below", "within" and the like are to be understood as including the number.
Although the embodiments have been described, once the basic inventive concept is obtained, other variations and modifications of these embodiments can be made by those skilled in the art, so that the above embodiments are only examples of the present invention, and not intended to limit the scope of the present invention, and all equivalent structures or equivalent processes using the contents of the present specification and drawings, or any other related technical fields, which are directly or indirectly applied thereto, are included in the scope of the present invention.

Claims (9)

1. A two-dimensional DOA estimation method based on non-circular signals, characterized in that the method comprises the following steps,
step 1, expanding a received signal vector by utilizing the conjugate of an L array received signal to obtain an expanded signal vector;
step 2, calculating a covariance matrix of the expanded signal vector and performing characteristic decomposition on the covariance matrix;
step 3, expanding covariance matrix characteristic decomposition to obtain a signal subspace and a noise subspace;
step 4, defining a new phase angle thetak；
Step 5, constructing a one-dimensional spectral peak search function by utilizing the signal subspace, and obtaining a phase angle through the one-dimensional spectral peak search
Figure FDA0003068831330000012
Step 6, constructing a new spectrum peak search function according to the orthogonal relation of the signal subspace and the noise subspace, and passing through a phase angle thetakEstimating gammak；
Step 7, passing through a phase angle thetak and γkCalculating the pitch angle alphakAnd azimuth angle betak。
2. The non-circular signal based two-dimensional DOA estimation method according to claim 1, wherein the L-array signal is composed 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, narrow-band, non-correlated signal incidences, the wavelength is λ, the K-th signal has a pitch angle and an azimuth angle α respectivelyk and βkDefining two phase angles gammak＝-2πdsinαkcosβk/λ，φk＝-2πdcosαkAnd/lambda. Thus the steering vector can be recorded as
Figure FDA0003068831330000011
Let xm，n(t) represents the signal received by the (m, n) th array element at time t, then
X(t)＝[xM，0(t)xM-1，0(t)...x1，0(t)x0，M(t)x0，M-1(t)...x0，M(t)]T
Indicating that the array received the signal vector at time t.
3. A two-dimensional DOA estimation method based on non-circular signals according to claim 1, wherein the extended received vector in step 1 is y (t):
Y(t)＝[X(t) XH(t)]T。
4. the non-circular signal based two-dimensional DOA estimation method of claim 1 wherein said step 2 extends the covariance matrix to
Figure FDA0003068831330000021
wherein Rs＝E[s(t)sH(t)]Is a matrix of the autocorrelation of the signal,
Figure FDA0003068831330000022
is a diagonal matrix consisting of non-circular phases of the signal.
5. A two-dimensional DOA estimation method based on non-circular signals according to claim 1, characterized in that said step 3 extends the eigen decomposition of the covariance matrix:
Figure FDA0003068831330000023
wherein UsIs a signal subspace, UnIs a noise subspace and satisfies
Figure FDA0003068831330000024
And
Figure FDA0003068831330000025
6. a method of two-dimensional DOA estimation based on non-circular signals according to claim 1, characterized in that said step 4 defines a new phase angle:
Figure FDA0003068831330000026
rewriting the steering vector:
Figure FDA0003068831330000027
it can be known that the front M rows and the rear M rows of the steering vector satisfy the following relationship:
Figure FDA0003068831330000028
wherein ,
Figure FDA0003068831330000029
7. a two-dimensional DOA estimation method based on non-circular signals according to claim 1, characterized in that said step 5 specifically comprises dividing the signal subspace by two equal parts U1 and U2Remember U1Front M behavior U of11Post M behavior U12，U2Front M behavior U of21Post M behavior U22Defining a matrix:
Figure FDA0003068831330000031
from the analysis in step 3, when θ ═ θkWhen the k-th column of the matrix Q becomes 0, i.e., the matrix Q fallsRank; the spectral peak search function can thus be constructed:
Figure FDA0003068831330000032
k phase angles can be obtained through one-dimensional spectral peak search
Figure FDA0003068831330000033
8. A two-dimensional DOA estimation method based on non-circular signals according to claim 1, characterized in that said step 6 is to construct a new spectral peak search function from the orthogonal relationship of signal subspace and noise subspace:
Figure FDA0003068831330000034
the estimated phase angle thetakThe corresponding phase angle gamma can be obtained by the substitutionkAnd automatically paired.
9. The non-circular signal based two-dimensional DOA estimation method of claim 1 wherein the phase angle φ in step 7k：
Figure FDA0003068831330000035
Pitch angle alphak：
Figure FDA0003068831330000036
Azimuth angle betak：
Figure FDA0003068831330000037
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