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

Abstract

The invention belongs to the technical field of array signal processing, and relates to a direction of arrival (DOA) estimation technology, in particular to a two-dimensional DOA estimation method when an incident signal is a non-circular signal. The method includes the following steps: Step 1, using the conjugate of the L array received signal to expand the received signal vector to obtain an expanded signal vector; Step 2, calculating a covariance matrix of the expanded signal vector and performing eigendecomposition on the covariance matrix ; Step 3, the extended covariance matrix eigendecomposition obtains the signal subspace and the noise subspace; Step 4, defines a new phase angle θ _k ; Step 5, utilizes the signal subspace to construct a one-dimensional spectral peak search function, through the one-dimensional spectral peak The phase angle θ can be obtained by searching; Step 6, construct a new spectral peak search function from the orthogonal relationship between the signal subspace and the noise subspace, and estimate γ _{k through the phase angle θ k ;} Step 7, pass the phase angles θ _k and γ _k Elevation angle α _k and azimuth angle β _k are calculated.

Description

A Two-Dimensional DOA Estimation Method Based on Noncircular Signals

technical field

The invention belongs to the technical field of array signal processing, and relates to a direction of arrival (DOA) estimation technology, in particular to a two-dimensional DOA estimation method when an incident signal is a non-circular signal.

Background technique

Two-dimensional DOA estimation has always been a research hotspot in the field of array signal processing, and has been widely used in radar, sonar, mobile communications and other fields. Traditional DOA estimation methods include Multiple Signal Classification Based on Subspace Decomposition (MUSIC) and Rotation Invariant Subspace (ESPRIT) algorithms are widely used algorithms, but both algorithms are based on one-dimensional uniform linear arrays. If it is directly extended to two-dimensional structure arrays, there will be parameter pairing and tedious computational problems (such as two-dimensional MUSIC search) and so on.

The two-dimensional structure of the array is various, and the representative ones are the planar array, the double parallel linear array, the circular array and the L array. From the literature "An L-shaped array for estimating 2-D directions of wave arrival" published by Hua Y et al., it can be seen that compared with arrays of other structures, L array has better direction finding performance. The research on the algorithm has attracted widespread attention. In the literature "L-shape 2-dimensional arrival angle estimation with propagator method", Tayem N et al. proposed to use the cross-correlation matrix of the L matrix to construct a Toeplitz matrix to solve the two-bit angle pairing problem, but it is easy to generate when the signal-to-noise ratio is small. Mismatch problem. Liang J et al. "JointElevation and Azimuth Direction Finding Using L-Shaped Array" proposed an automatic pairing two-dimensional direction finding algorithm based on the principle of rank loss, and achieved parameter separation through rank loss, avoiding two-dimensional search and reducing the algorithm The complexity achieved good results.

However, the above algorithm does not consider the situation when the incident signal is a non-circular signal. The research shows that by using the non-circular characteristics of the non-circular signal, the number of distinguishable signals can be increased and the estimation accuracy of DOA can be improved. The paper "MUSIC-like estimation of direction of arrival for non-circular sources" by Abeida H and Delmas J P proposes the NC-MUSIC algorithm to realize DOA estimation. By using the covariance matrix and ellipse covariance matrix of non-circular signals at the same time, the array is popularized. The expansion is twice as large and the number of resolvable signals is also doubled, so the direction finding accuracy is also improved. At the same time, Delmas J P and Abeida H's literature "Stochastic Cramer-Rao boundfor non-circular signals with application to DOA estimation" gives the CRB of the non-circular signal DOA, and points out that the random CRB of the complex Gaussian non-circular signal is less than or equal to the complex Gaussian circular signal. Random CRB.

Therefore, it is feasible to further improve the direction finding accuracy of the algorithm by using the non-circular characteristics of the signal on the basis of the L array, and it can increase the maximum number of distinguishable signals of the algorithm and improve the direction finding accuracy without adding array elements. important research significance and value.

SUMMARY OF THE INVENTION

The purpose of the present invention is to expand the received signal matrix by using the non-circular characteristic of the signal when the L-array and the incident signal is a non-circular signal, thereby improving the direction finding accuracy of the algorithm, while avoiding parameter pairing.

For achieving the above object, the present invention provides the following technical solutions:

A two-dimensional DOA estimation method based on a non-circular signal, the method comprises the following steps,

Step 1. Extend the received signal vector by using the conjugate of the L array received signal to obtain the extended signal vector;

Step 2. Calculate the covariance matrix of the extended signal vector and perform eigendecomposition on the covariance matrix;

Step 3. Expand the covariance matrix eigendecomposition to obtain the signal subspace and the noise subspace;

Step 4, define a new phase angle θ _k ;

Step 5. Use the signal subspace to construct a one-dimensional spectral peak search function, and the phase angle can be obtained through the one-dimensional spectral peak search

Step 6. Construct a new spectral peak search function from the orthogonal relationship between the signal subspace and the noise subspace, and estimate _γk through the phase angle _θk ;

Step 7. Calculate the pitch angle α _k and the azimuth angle β _k through the phase angles θ _k and γ _k .

This technical solution is further optimized, the L array signal is composed of a total of 2M+1 array elements evenly distributed on the x-axis and the z-axis, the array element spacing is d, the reference array element is located at the coordinate origin, and there are K far-field, Narrowband, uncorrelated signal incident, wavelength is λ, the pitch angle and azimuth angle of the kth signal are α _k and β _k respectively, define two phase angles γ _k =-2πdsinα _k cosβ _k /λ, φ _k =-2πdcosα _k /λ. So the steering vector can be written as

Let x _{m, n} (t) denote the signal received by the (m, n)th array element at time t, then

X(t)=[x _M,0 (t)x _M-1,0 (t)... _x1,0 (t)x0 _,M (t)x0 _,M-1 (t).. .x _{0, M} (t)] ^T

Indicates that the array receives the signal vector at time t.

This technical solution is further optimized, and the extended receiving vector in the step 1 is Y(t):

Y(t)=[X(t) X ^H (t)] ^T .

This technical solution is further optimized, and the expanded covariance matrix in step 2 is:

是由信号的非圆相位组成的对角矩阵。where R _s =E[s(t)s ^H (t)] is the autocorrelation matrix of the signal,

is a diagonal matrix consisting of the non-circular phases of the signal.

This technical solution is further optimized, the step 3 expands the eigendecomposition of the covariance matrix:

和

where U _s is the signal subspace, U _n is the noise subspace, and satisfies

and

This technical solution is further optimized, and the step 4 defines a new phase angle:

Rewrite the steering vector:

It can be known that the first M lines and the last M lines of the steering vector satisfy the following relationship:

in,

This technical solution is further optimized. The step 5 specifically includes dividing the signal subspace into two equal parts U ₁ and U ₂ , denoting the first M of U ₁ as U ₁₁ , the last M as U ₁₂ , and the first M of U ₂ as U ₂₁ , after M row U ₂₂ , define the matrix:

From the analysis of step 3, it can be seen that when θ=θ _k , the kth column of matrix Q will become 0, that is, the rank of matrix Q will be reduced; therefore, the spectral peak search function can be constructed:

K phase angles can be obtained by one-dimensional spectral peak search

This technical solution is further optimized. In step 6, a new spectral peak search function can be constructed from the orthogonal relationship between the signal subspace and the noise subspace:

The corresponding phase angle γ _k can be obtained by bringing the estimated phase angle θ _k into it, and pairing is performed automatically.

This technical solution is further optimized. In the step 7, the phase angle φ _k is:

Pitch angle α _k :

Azimuth angle β _k :

Different from the prior art, the above-mentioned technical scheme has the following beneficial effects:

The present invention proposes a two-dimensional DOA estimation method based on a non-circular signal. By utilizing the non-circular characteristics of the signal, the accuracy of angle estimation is improved, and the rank loss principle is used to separate the parameters, thereby avoiding the two-digit search and greatly reducing the algorithm cost. complexity, while parameters are automatically paired.

Description of drawings

Figure 1 is a schematic diagram of the relationship between the root mean square error of pitch angle estimation and the signal-to-noise ratio;

FIG. 2 is a schematic diagram showing the relationship between the root mean square error of the azimuth angle estimation and the signal-to-noise ratio.

Detailed ways

In order to describe in detail the technical content, structural features, achieved objectives and effects of the technical solution, the following detailed description is given in conjunction with specific embodiments and accompanying drawings.

Assume that the L array is composed of a total of 2M+1 array elements evenly distributed on the x-axis and z-axis, the array element spacing is d, the reference array element is located at the origin of the coordinates, there are K far-field, narrow-band, non-correlated signals incident, and the wavelength is λ, the pitch angle and azimuth angle of the k-th signal are α _k and β _k respectively, define two phase angles γ _k =-2πdsinα _k cosβ _k /λ, φ _k =-2πdcosα _k /λ. So the steering vector can be written as

Let x _{m, n} (t) denote the signal received by the (m, n)th array element at time t, then

X(t)=[x _M,0 (t)x _M-1,0 (t)... _x1,0 (t)x0 _,M (t)x0 _,M-1 (t).. .x _{0, M} (t)] ^T

Indicates that the array receives the signal vector at time t.

Step 1. Expand the received signal vector by using the conjugate of the array received signal to obtain a new received signal vector;

Define a new extended receive vector as Y(t):

Y(t)=[X(t) X ^H (t)] ^T

Step 2, calculating the covariance matrix of the extended signal vector;

Extended covariance matrix:

是由信号的非圆相位组成的对角矩阵。实际应用场景下，接收信号的协方差矩阵是由L个快拍信号的测量数据估计出来：where R _s =E[s(t)s ^H (t)] is the autocorrelation matrix of the signal,

is a diagonal matrix consisting of the non-circular phases of the signal. In practical application scenarios, the covariance matrix of the received signal is estimated from the measurement data of L snapshot signals:

Step 3. Expand the covariance matrix eigendecomposition to obtain the signal subspace and the noise subspace;

Eigen decomposition of the extended covariance matrix:

和

where U _s is the signal subspace, U _n is the noise subspace, and satisfies

and

Step 4. Define a new phase angle;

Define a new phase angle:

Rewrite the steering vector:

It can be known that the first M lines and the last M lines of the steering vector satisfy the following relationship:

in,

Step 5. Build a one-dimensional spectral peak search function.

Matlab generates the received signal, processes the received signal to obtain the extended covariance matrix, and decomposes the extended covariance matrix to obtain the signal subspace and the noise subspace.

Divide the signal subspace into two equal parts U ₁ and U ₂ , record the first M row of U ₁ as U ₁₁ , the last M row as U ₁₂ , the first M row of U ₂ as U ₂₁ , and the last M row as U ₂₂ , define the matrix:

It can be known from the analysis in step 3 that when θ=θ _k , the k-th column of the matrix Q will become 0, that is, the rank of the matrix Q will be reduced. Therefore, the spectral peak search function can be constructed:

K phase angles can be obtained by one-dimensional spectral peak search

Step 6, estimating γ _{k through the phase angle θ k ;}

A new spectral peak search function can be constructed from the orthogonal relationship between the signal subspace and the noise subspace:

The corresponding phase angle γ _k can be obtained by bringing the estimated phase angle θ _k into it, and pairing is performed automatically.

Step 7. Calculate the pitch angle α _k and the azimuth angle β _k through the phase angles θ _k and γ _k ;

Phase angle φ _k :

Pitch angle α _k :

Azimuth angle β _k :

The present invention is suitable for the research of direction finding algorithm of L-shaped array. In order to verify the performance advantage of this method in terms of DOA estimation, this method is combined with the method of "Joint Elevation and Azimuth Direction Finding Using L-Shaped Array" proposed by Liang J and Liu D. For comparison, the conditions of the simulation experiment are as follows: the number of array elements is 13, the wavelength is 100, the distance between the array elements is 1/2 wavelength, the snapshot is 200, the number of sources is 2, the azimuth angle is 60° and 35°, the pitch is 60° and 35°. The angles are 40° and 55°, and the number of Monte Carlo simulations is 500. The two algorithms are compared under different signal-to-noise ratios, and the root mean square error of the angle is used as a measure of performance. See Figure 1 for the pitch angle. A schematic diagram of the relationship between the estimated root mean square error and the signal-to-noise ratio is shown in FIG. 2 , which is a schematic diagram of the relationship between the estimated root-mean-square error of the azimuth angle and the signal-to-noise ratio. It can be seen that the estimation accuracy of the method in this paper is better than that of Liang J, whether it is to estimate the azimuth angle or the pitch angle.

It should be noted that, in this document, relational terms such as first and second are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any relationship between these entities or operations. any such actual relationship or sequence exists. Moreover, the terms "comprising", "comprising" or any other variation thereof are intended to encompass non-exclusive inclusion, such that a process, method, article or terminal device comprising a list of elements includes not only those elements, but also a non-exclusive list of elements. other elements, or also include elements inherent to such a process, method, article or terminal equipment. Without further limitation, an element defined by the phrase "comprises..." or "comprises..." does not preclude the presence of additional elements in the process, method, article, or terminal device that includes the element. In addition, in this text, "greater than", "less than", "exceeds" and the like are understood as not including the number; "above", "below", "within" and the like are understood as including the number.

Although the above embodiments have been described, those skilled in the art can make additional changes and modifications to these embodiments once they know the basic inventive concept, so the above is only the implementation of the present invention For example, it does not limit the scope of patent protection of the present invention. Any equivalent structure or equivalent process transformation made by using the contents of the description and drawings of the present invention, or directly or indirectly used in other related technical fields, are similarly included in this document. The invention is within the scope of patent protection.

Claims (9)

1. a two-dimensional DOA estimation method based on a non-circular signal, is characterized in that, the method comprises the following steps, Step 1. Extend the received signal vector by using the conjugate of the L array received signal to obtain the extended signal vector; Step 2. Calculate the covariance matrix of the extended signal vector and perform eigendecomposition on the covariance matrix; Step 3. Expand the covariance matrix eigendecomposition to obtain the signal subspace and the noise subspace; Step 4, define a new phase angle θ _k ; Step 5. Use the signal subspace to construct a one-dimensional spectral peak search function, and the phase angle can be obtained through the one-dimensional spectral peak search

Step 6. Construct a new spectral peak search function from the orthogonal relationship between the signal subspace and the noise subspace, and estimate _γk through the phase angle _θk ; Step 7. Calculate the pitch angle α _k and the azimuth angle β _k through the phase angles θ _k and γ _k . 2. The two-dimensional DOA estimation method based on a non-circular signal as claimed in claim 1, wherein the L array signal is composed of a total of 2M+1 array elements evenly distributed on the x-axis and the z-axis, and the array element is composed of 2M+1 array elements. The spacing is d, the reference array element is located at the coordinate origin, there are K far-field, narrow-band, non-correlated signals incident, the wavelength is λ, the pitch angle and azimuth angle of the kth signal are α _k and β _k respectively, and two phases are defined. Angle γ _k = -2πdsinα _k cosβ _k /λ, φ _k = -2πdcosα _k /λ. So the steering vector can be written as

Let x _{m, n} (t) denote the signal received by the (m, n)th array element at time t, then X(t)=[x _M,0 (t)x _M-1,0 (t)... _x1,0 (t)x0 _,M (t)x0 _,M-1 (t).. .x _{0, M} (t)] ^T Indicates that the array receives the signal vector at time t. 3. The two-dimensional DOA estimation method based on non-circular signal as claimed in claim 1, is characterized in that, the extension receiving vector in described step 1 is Y(t): Y(t)=[X(t) X ^H (t)] ^T . 4. the two-dimensional DOA estimation method based on non-circular signal as claimed in claim 1, is characterized in that, described step 2 expanded covariance matrix is

where R _s =E[s(t)s ^H (t)] is the autocorrelation matrix of the signal,

is a diagonal matrix consisting of the non-circular phases of the signal. 5. the two-dimensional DOA estimation method based on non-circular signal as claimed in claim 1, is characterized in that, described step 3 expands the eigendecomposition of covariance matrix:

where U _s is the signal subspace, U _n is the noise subspace, and satisfies

and

6. The two-dimensional DOA estimation method based on non-circular signal as claimed in claim 1, is characterized in that, described step 4 defines new phase angle:

Rewrite the steering vector:

It can be known that the first M lines and the last M lines of the steering vector satisfy the following relationship:

in,

7. The two-dimensional DOA estimation method based on a non-circular signal as claimed in claim 1, wherein the step 5 specifically comprises dividing the signal subspace into two equal parts U ₁ and U ₂ , and denoting the first M behaviors of U ₁ U ₁₁ , the last M row is U ₁₂ , the first M row of U ₂ is U ₂₁ , the last M row is U ₂₂ , and the matrix is defined:

From the analysis of step 3, it can be seen that when θ=θ _k , the kth column of matrix Q will become 0, that is, the rank of matrix Q will be reduced; therefore, the spectral peak search function can be constructed:

K phase angles can be obtained by one-dimensional spectral peak search

8. the two-dimensional DOA estimation method based on non-circular signal as claimed in claim 1, is characterized in that, described step 6 can construct new spectral peak search function by the orthogonal relation of signal subspace and noise subspace:

The corresponding phase angle γ _k can be obtained by bringing the estimated phase angle θ _k into it, and pairing is performed automatically. 9. the two-dimensional DOA estimation method based on non-circular signal as claimed in claim 1, is characterized in that, in described step 7, phase angle φ _k :

Pitch angle α _k :

Azimuth angle β _k :

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