CN104515969A - Hexagonal array-based coherent signal two-dimensional DOA (Direction of Arrival) estimation method - Google Patents

Abstract

The invention belongs to the array signal processing field and relates to a hexagonal array-based coherent signal two-dimensional DOA (Direction of Arrival) estimation method, in particular to a high-precision, de-coherence, two-dimensional signal DOA subspace estimation method. According to the estimation method of the invention, an array is virtualized and extended through performing conjugate matrix solution on array receiving data, so that a hexagonal array including three sub arrays are obtained, and then, a correlation matrix of a subspace algorithm is extended and reconstructed according to an autocorrelation matrix and a cross correlation matrix of the three sub arrays, and therefore, de-coherence can be realized; and singular value decomposition is performed on the new correlation matrix, so that a signal subspace and a noise subspace can be obtained, and then, DOA estimation is performed on coherent receiving signals through utilizing a two-dimensional MUSIC (Multiple Signal Classification) estimation method. With the estimation method of the invention adopted, coherence between source signals can be eliminated, and the estimation accuracy of two-dimensional DOA can be further improved. The estimation method is mainly applied to two-dimensional high-precision DOA estimation of coherent signals.

Description

A kind of coherent signal arrival direction estimation method based on hexagonal array

Technical field

The invention belongs to antenna array signals process field, it is in particular to the Subspace Estimation Method of a kind of high precision, decoherence, 2D signal arrival bearing (DOA).

Background technology

Super-resolution Mutual coupling (DOA) technology is an important research point of Estimation of Spatial Spectrum, is widely used in high-resolution array signal transacting.High precision and its application prospect of its angle estimation cause people to pay close attention to greatly.Multiple signal classification algorithm (MUSIC, multiple signal classification) and be two kinds of classical super-resolution subspace class algorithms based on the Signal parameter estimation algorithm (ESPRIT, estimation of signal parameter via rotational inviance techniques) of ESPRIT.Wherein, MUSIC algorithm can be applied to the array of arbitrary shape, and can estimate the source signal of multiple parameter.But in actual applications, when snap number is limited for noise, and therefore angle measurement accuracy and the resolving power of MUSIC algorithm are restricted, and array number can be less than by direction-finding signal number.In actual environment, the impact due to multipath effect makes the performance of classical super-resolution DOA algorithm for estimating decline rapidly, even complete failure.The Mutual coupling of coherent signal is the practical problems that Estimation of Spatial Spectrum needs solution badly.

At present, the method for coherent signal decorrelation LMS comprises: the frequency domain smoothing method in space smoothing class algorithm, matrix reconstruction algorithm and non-reducing dimension algorithm in reducing dimension algorithm and virtual array method of changing etc.There is the shortcoming of array aperture loss in reducing dimension algorithm, but not reducing dimension algorithm is often for specific environment.For the estimation problem in coherent signal source, propose the approach of many solutions.The MUSIC decorrelation LMS algorithm improved based on Search Space Smoothing has good performance, but need array to be divided into multiple submatrix, not only reduce array number and array aperture, also pair array structure has certain requirement, good decorrelation performance cannot be obtained in actual applications, for arbitrary shape array, as hexagonal array does not have the algorithm of good decoherence.

The present invention is under hexagonal array structural model, goes the arrival direction estimation problem solving coherent signal.Sexangle planar array antenna be by an antenna element being positioned at center and several concentric hexagonal rings battle arrays that are the center of circle with it (each containing element number of array for 6n, be the hexagonal rings battle array near the center of circle during n=1) composition, it also can be seen as the modified circle ring array that a center exists array element.It is narrower that this kind of array makes main lobe become, and secondary lobe is lower, is effectively suppressed the interference beyond main lobe.The present invention studies based on the simplest hexagonal array structure, and due to its array structure, the reducing dimension algorithm of decorrelation is no longer applicable.The present invention is according to the design feature of hexagonal battle array self, utilize the characteristic that actual array output signal is complex signal, the thought of conjugate matrices is utilized to carry out virtual extended array, and utilize based on merging the thought that extended matrix increases Correlation Moment rank of matrix in the algorithm of matrix decomposition, to realize decorrelation LMS object, the basis of not reducing array element number and array aperture proposes a kind of arrival direction estimation algorithm of the decoherence based on expansion reconstruct correlation matrix.

Summary of the invention

Technical matters to be solved by this invention is to provide a kind of under the prerequisite not reducing array element number and array aperture, utilize the arrival direction estimation method of expansion reconstruct correlation matrix decoherence, the method for non-uniform linear arrays, can be estimated the arrival bearing in coherent signal source accurately.

The thought that present invention utilizes conjugate matrices carrys out array extending, pair array receive data ask based on its conjugate matrices, expansion reconstruct correlation matrix, provide a kind of based on hexagonal array, decoherence, two dimension DOA estimate.The raw data matrix that snap receives and conjugate matrices thereof, being equivalent to available array length is original 2 times, takes full advantage of the auto-correlation between raw data matrix and Qi Xin matrix and cross-correlation information, improves the performance that DOA estimates.

Based on a coherent signal arrival direction estimation method for hexagonal array, comprise the steps:

Step one: sexangle antenna array elements number is N, exporting the fast umber of beats of data is K, then each array element exports the data matrix X complex matrix that (k)=AS (k)+N (k) is N × K, asks its conjugate matrices X ^*(k), and the correlation matrix obtaining former array output data is R _xX=E{X (k) X (k) ^h, H represents its conjugate transpose, and A is the steering vector matrix of array, and S (k) represents source signal vector matrix; N (k) represents that noise average that array exports be zero variance is σ ²additive white Gaussian noise, and uncorrelated with source signal;

Step 2: conjugation data matrix is for aerial array, the data being equivalent to the symmetrical virtual array of its conjugation export, for the array after conjugation virtual extended, three sub-hexagonal arrays can be divided into, first sub-hexagonal array is real hexagonal array, and second sub-hexagonal array is centered by reference array element, in submatrix array element wherein half belong to the part of true array, second half is the part of conjugation virtual array, and the 3rd sub-hexagonal array is classified as conjugate radical matroid row;

Step 3: according to the array element contained by every sub-hexagonal array of array after expansion, draw the output data matrix X of sub-hexagonal array ₁(k), X ₂(k), X ₃(k);

Step 4: autocorrelation matrix and the cross-correlation matrix of obtaining three sub-hexagonal arrays respectively: $R_{X_1{X}_1}=E\{X_1\left(k\right)\·X_1{\left(k\right)}^H\},$ $R_{X_2{X}_2}=E\{X_2\left(k\right)\·X_2{\left(k\right)}^H\},$ $R_{X_3{X}_3}=E\{X_3\left(k\right)\·X_3{\left(k\right)}^H\},$ $R_{X_2{X}_1}=E\{X_2\left(k\right)\·X_1{\left(k\right)}^H\},$ $R_{X_3{X}_1}=E\{X_3\left(k\right)\·X_1{\left(k\right)}^H\},$ $R_{X_3{X}_2}=E\{X_3\left(k\right)\·X_2{\left(k\right)}^H\};$

Step 5: construct the correlation matrix made new advances $R=\left[\begin{array}{cccccc}{R}_{X_1{X}_1}& R_{X_2{X}_2}& R_{X_3{X}_3}& R_{X_2{X}_1}& R_{X_3{X}_1}& R_{X_3{X}_2}\end{array}\right];$

Step 6: carry out svd to R, decompositing N number of eigenwert is λ ₁>=λ ₂>=...>=λ _p>=λ _p+1=...=λ _n=σ ², by judging that the number of large eigenwert carrys out estimated signal source number, and obtain signal subspace Es and noise subspace matrix En respectively according to corresponding proper vector;

Step 7: utilize two-dimentional MUSIC algorithm to build spatial spectrum function, θ and be respectively the angle of pitch and the position angle of source signal, be with θ and the array steering vector to received signal of change.Make pitching angle theta at (0 °, 90 °) and position angle in (0 °, 360 °) scope during change, find out spatial spectrum angle corresponding to maximum point is the DOA of source signal.

Good effect of the present invention: the present invention receives data by pair array and asks conjugation to carry out virtual extended array, obtain the hexagonal battle array of three subarrays, then expand the correlation matrix of reconstruct Subspace algorithm according to the autocorrelation matrix of three subarrays and cross-correlation matrix, achieve the object of decoherence.Svd is carried out to new correlation matrix and obtains signal subspace and noise subspace, recycle two-dimentional MUSIC Power estimation method and DOA estimation is carried out to relevant incoming wave signal.The present invention further increases the estimated accuracy performance of two-dimentional DOA while coherence between source signal removing.

Accompanying drawing explanation

Fig. 1 is two kinds of array structures of hexagonal array: the sexangle planar array structural drawing of 7 array elements and 19 array elements;

Fig. 2 is the figure carrying out wave method of the simplest hexagonal array Received signal strength;

Fig. 3 is for the array of the minimum array number of hexagonal array, the array after the Conjugate extended drawn, and draws the structural drawing being divided into 3 subarrays;

Embodiment

Just further describe the course of work of this invention below by reference to the accompanying drawings.The arrival direction estimation process of decoherence can be divided into three parts.

Part I mainly receives data modeling, the virtual array extending of conjugation for hexagonal array, is divided into subarray form according to array structure, is mainly step one and step 2.

Suppose have narrow band signal source, D (D≤N) individual far field to incide in sexangle planar array as shown in Figure 2, element number of array is N, and array element distance is r, and the angle of pitch and the position angle of incoming signal are respectively the noise that array exports is the additive white Gaussian noise of zero-mean, and variance is σ ², and uncorrelated with source signal.

For being that example is to study the output data model of array containing the hexagonal battle array of minimum array number.

Get the leftmost array element of accompanying drawing 2 midplane array as true origin and reference array element, then the Received signal strength of this array is:

X(t)=AS(t)+N(t) (1)

Wherein A represents array manifold matrix; S (t)=[s ₁(t), s ₂(t) ... s _d(t)] ^trepresent signal phasor matrix; N (t)=[n ₁(t), n ₂(t) ... n _n(t)] ^trepresent the noise vector matrix of array, the transpose operation of T representing matrix.

Wherein: c is the light velocity, c=3 × 10 ⁸m/s, d=1,2 ... D;

In practical application, the output signal of array is complex signal, asks its conjugate matrices, carrys out array extending, as shown in Figure 3.For the data X (k) that array snap receives, then the reception data of its conjugation array are X ^*(k), the output data of array can be expressed as:

X(k)=[x ₁(k),…x _n(k),…x _N(k)] ^T(3)

The correlation matrix of array is expressed as:

R _xX=E{X (k) X (k) ^h(4) wherein, the conjugate transpose operation of H representing matrix.

The then data X of conjugate matrices ^*(k) be:

X ^*(k)=[x ₁ ^*(k),…x _n ^*(k),…x _N ^*(k)] ^T(5)

Namely as shown in Figure 2, be 3 crossing hexagonal arrays the array partition after virtual extended, array element spacing distance is respectively r to step 2.

Part II is the process for array after expansion, mainly comprises step 3 to step 5, comprises two parts content, is first for the array element contained by every sub-hexagonal array of array after expansion, draws the output data matrix X of 3 sub-hexagonal arrays ₁(k), X ₂(k), X ₃k () is secondly autocorrelation matrix and the cross-correlation matrix of obtaining three sub-hexagonal arrays respectively, expansion reconstructs the correlation matrix made new advances, and reaches the object of decoherence.

(1) subarray exports the structure of data

The output data of each subarray can be expressed as:

$\begin{array}{c}{X}_1\left(k\right)={[x_1\left(k\right),\·\·\·x_k\left(k\right),\·\·\·x_7\left(k\right)]}^T\\ X_2\left(k\right)={[x_5\left(k\right),x_1\left(k\right),{x_4\left(k\right),x_4}^{*}\left(k\right),x_1^{*}\left(k\right),x_7^{*}\left(k\right),x_6\left(k\right)]}^T\\ X_3\left(k\right)={[{x_1}^{*}\left(k\right),{x_5}^{*}\left(k\right),{x_4}^{*}\left(k\right),{x_3}^{*}\left(k\right),x_2^{*}\left(k\right),x_7^{*}\left(k\right),x_6\left(k\right)]}^T\end{array}---\left(6\right)$

Find out from the Array Model after expansion, submatrix 2 and submatrix 3 can be obtained to the distance of left r along x-axis successively by real hexagonal array, and according to formula (3) and (5), above formula can be expressed as again:

X ₁(k)=AS(k)+N(k)

X ₂(k)=A·Φ ₀S(k)+N(k) (7)

X ₃(k)=A·Φ ₀ ²S(k)+N(k)

In formula, Φ ₀for diagonal matrix:

(2) structure of expansion reconstruct correlation matrix

According in (1), spatial autocorrelation matrix and the cross-correlation matrix of each subarray can be obtained:

$\begin{array}{c}{R}_{X_1{X}_1}=E\{X_1\left(k\right)\·X_1{\left(k\right)}^H\}={\mathrm{AR}}_S{A}^H+R_N\\ R_{X_2{X}_2}=E\{X_2\left(k\right)\·X_2{\left(k\right)}^H\}={\mathrm{A\Φ}}_0{R}_S{{\mathrm{\Φ}}_0}^H{A}^H+R_N\\ R_{X_3{X}_3}=E\{X_3\left(k\right)\·X_3{\left(k\right)}^H\}=A\left({{\mathrm{\Φ}}_0}^2\right)R_S{\left({{\mathrm{\Φ}}_0}^2\right)}^H{A}^H+R_N\\ R_{X_2{X}_1}=E\{X_2\left(k\right)\·X_1{\left(k\right)}^H\}=A{\mathrm{\Φ}}_0{R}_S{A}^H+R_N\\ R_{X_3{X}_1}=E\{X_3\left(k\right)\·X_1{\left(k\right)}^H\}=A\left({{\mathrm{\Φ}}_0}^2\right)R_S{A}^H+R_N\\ R_{X_3{X}_2}=E\{X_3\left(k\right)\·X_2{\left(k\right)}^H\}=A\left({{\mathrm{\Φ}}_0}^2\right)R_S{{\mathrm{\Φ}}_0}^H{A}^H+R_N\end{array}---\left(8\right)$

In formula: E{ } represent statistical expection; H represents conjugate transpose operation; R _s=E{S (k) S ^h(k) } represent signal covariance matrix;

R _n=σ ²i represents the covariance matrix of array noise, and I is unit matrix.

According to above-mentioned autocorrelation matrix and cross-correlation matrix, merging the correlation matrix be expanded is:

$R=\left[\begin{array}{cccccc}{R}_{X_1{X}_1}& R_{X_2{X}_1}& R_{X_2{X}_2}& R_{X_3{X}_1}& R_{X_3{X}_2}& R_{X_3{X}_3}\end{array}\right]---\left(9\right)$

Can be expressed as again according to formula (8) and (9):

R=A[R _SΦ ₀R _SΦ ₀R _SΦ ₀ ^H(Φ ₀ ²)R _S(Φ ₀ ²)R _SΦ ₀ ^H(Φ ₀ ²)R _S(Φ ₀ ²) ^H]A ^H(10)

+[R _NR _NR _NR _NR _NR _N]

Order

G=[R _SΦ ₀R _SΦ ₀R _SΦ ₀ ^H(Φ ₀ ²)R _S(Φ ₀ ²)R _SΦ ₀ ^H(Φ ₀ ²)R _S(Φ ₀ ²) ^H] ,

R _n=[R _nr _nr _nr _nr _nr _n], then:

R=AGA ^H+R _n(11)

Theorem 1: establish Q to be the matrix (L≤M) of L × M dimension without zero row vector, P is that L × L ties up diagonal matrix, and its diagonal element is unequal mutually, if rank (Q)=r<L, then rank [Q PQ]=r+1.

Theorem 2: establish H to be the matrix (L≤M) of M × L dimension without zero row vector, P is that L × L ties up diagonal matrix, and its diagonal element is unequal mutually, if rank (H)=r<L, then rank [H HP]=r+1.

Suppose that D (D≤N) the individual signal reaching array is all relevant, then rank (R _s)=1, because each signal angle is not identical, when the angle of pitch sum at the position angle He another information source that there is not Arbitrary Information Sources be 90 ° (namely ) equal with any two angles of pitch time their position angle sum be 360 ° of (θ _i=θ _j, ) and the position angle of information source be not 90 ° and 270 ° time, Φ ₀diagonal element be different, be non-singular matrix.Theory deduction from above: rank (R _s)+n≤rank (G)≤D, wherein n is the number of matrix in G.Then, can decomposite the signal subspace of D dimension according to formula (11) known R, recycling DOA algorithm for estimating, as MUSIC algorithm, obtains the angle information of D signal, namely achieves the object of decorrelation.The method is according to relevant rank of matrix new after its expansion reconstruct, and the maximum coherent signal number that can estimate is at least N-1, adds and can estimate the Number of Coherent Sources.

Part III, mainly on the basis of expansion reconstruct correlation matrix, utilizes Subspace algorithm to carry out the process of DOA estimation, comprises step 6 and step 7.Theoretical analysis according to Part II can be known, for coherent source signal, the new relevant rank of matrix increase of reconstruct can be removed relevant, and on this basis, step 6 make use of svd and decomposes matrix R, is σ because noise is zero-mean variance ²additive white Gaussian noise, matrix G is full rank, knownly can decomposite N number of eigenwert and is:

λ ₁≥λ ₂≥…≥λ _P≥λ _P+1=…=λ _N=σ ²(12)

According to above formula relation, can find out that the number of large eigenwert is signal source number.Its characteristic of correspondence vector is respectively e ₁, e ₂..., e _p, e _p+1... e _nthen

$R=\underset{i}{\overset{N}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{e}_i{e_i}^H=\mathrm{E\&Sigma;}{E}^H---\left(13\right)$

Wherein E=[e ₁, e ₂..., e _p, e _p+1... e _n], Σ=diag{ λ ₁, λ ₂..., λ _p, σ ²..., σ ².Definition signal subspace is E _s=[e ₁, e ₂..., e _p], noise subspace is E _n=[e _p+1..., e _n].Thus, signal subspace Es and noise subspace matrix En is obtained according to eigenwert characteristic of correspondence vector; Step 7 have selected the wherein a kind of MUSIC algorithm in the class algorithm of subspace, utilizes noise subspace matrix En and steering vector orthogonality, ask its two-dimensional space spectral function, shown in (14):

Wherein, θ and be respectively the angle of pitch and the position angle of source signal, be with θ and the array steering vector to received signal of change.Make θ and change, finds out spatial spectrum the angle corresponding to maximum point be the DOA of source signal.

Claims (2)

1., based on a method for hexagonal array coherent signal arrival direction estimation, its feature is provided by following steps:

Step one: sexangle antenna array elements number is N, exporting the fast umber of beats of data is K, then each array element exports the data matrix X complex matrix that (k)=AS (k)+N (k) is N × K, asks its conjugate matrices X ^*(k), and the correlation matrix obtaining former array output data is R _xX=E{X (k) X (k) ^h, H represents its conjugate transpose, and A is the steering vector matrix of array, and S (k) represents source signal vector matrix; N (k) represents that noise average that array exports be zero variance is σ ²additive white Gaussian noise, and uncorrelated with source signal;

Step 2: conjugation data matrix is for aerial array, the data being equivalent to the symmetrical virtual array of its conjugation export, for the array after conjugation virtual extended, three sub-hexagonal arrays can be divided into, first sub-hexagonal array is real hexagonal array, and second sub-hexagonal array is centered by reference array element, in submatrix array element wherein half belong to the part of true array, second half is the part of conjugation virtual array, and the 3rd sub-hexagonal array is classified as conjugate radical matroid row;

Step 3: according to the array element contained by every sub-hexagonal array of array after expansion, draw the output data matrix X of sub-hexagonal array ₁(k), X ₂(k), X ₃(k);

Step 4: autocorrelation matrix and the cross-correlation matrix of obtaining three sub-hexagonal arrays respectively: $R_{X_1{X}_1}=E\{X_1\left(k\right)\&CenterDot;X_1{\left(k\right)}^H\},$ $R_{X_2{X}_2}=E\{X_2\left(k\right)\&CenterDot;X_2{\left(k\right)}^H\},$ $R_{X_3{X}_3}=E\{X_3\left(k\right)\&CenterDot;X_3{\left(k\right)}^H\},$ $R_{X_2{X}_1}=E\{X_2\left(k\right)\&CenterDot;X_1{\left(k\right)}^H\},$ $R_{X_3{X}_1}=E\{X_3\left(k\right)\&CenterDot;X_1{\left(k\right)}^H\},$ $R_{X_3{X}_2}=E\{X_3\left(k\right)\&CenterDot;X_2{\left(k\right)}^H\};$

Step 5: construct the correlation matrix made new advances $R=\left[\begin{array}{cccccc}{R}_{X_1{X}_1}& R_{X_2{X}_2}& R_{X_3{X}_3}& R_{X_2{X}_1}& R_{X_3{X}_1}& R_{X_3{X}_2}\end{array}\right];$

Step 6: carry out svd to R, decompositing N number of eigenwert is λ ₁>=λ ₂>=...>=λ _p>=λ _p+1=...=λ _n=σ ², by judging that the number of large eigenwert carrys out estimated signal source number, and obtain signal subspace Es and noise subspace matrix En respectively according to corresponding proper vector;

Step 7: utilize two-dimentional MUSIC algorithm to build spatial spectrum function, θ and be respectively the angle of pitch and the position angle of source signal, be with θ and the array steering vector to received signal of change.Make pitching angle theta at (0 °, 90 °) and position angle in (0 °, 360 °) scope during change, find out spatial spectrum angle corresponding to maximum point is the DOA of source signal.

2., according to a kind of method based on hexagonal array coherent signal arrival direction estimation described in claim 1, it is characterized in that: in described step 4, for coherent signal source, its correlation matrix R _xXorder can be less than source signal number, correct signal subspace can not be obtained, and new correlation matrix R carries out expansion reconstruct on the basis of former correlation matrix, makes its order arrive source signal number, the coherence of releasing source signal.