CN104698433A - Single-snapshot data-based coherent signal DOA (direction of arrival) estimating method - Google Patents

Abstract

The invention discloses a single-snapshot data-based coherent signal DOA estimating method and relates to the technical field of array antenna systems or methods capable of indicating different signal directions. The method comprises rearranging the single-snapshot received data of an array to obtain two pseudo-covariance matrixes, and then through two pseudo-covariance matrixes, expanding the covariance matrix of a subspace restructuring algorithm; performing singular value decomposition on the new pseudo-covariance matrixes to obtain a signal subspace and a noise subspace, and performing DOA estimation on incoming coherent wave signals through a MUSIC spectrum estimating method. The single-snapshot data-based coherent signal DOA estimating method can eliminate coherence among source signals under single-snapshot conditions and meanwhile further improve the DOA estimating precision. The single-snapshot data-based coherent signal DOA estimating method is mainly applied to rapid estimation of incoming directions of coherent signals under the single-snapshot conditions.

Description

Based on the DOA Estimation in Coherent Signal method of single fast beat of data

Technical field

The present invention relates to the array antenna system or method and technology field that can indicate unlike signal direction simultaneously, particularly relate to a kind of DOA Estimation in Coherent Signal method based on single fast beat of data.

Background technology

With multiple signal classification algorithm (MUSIC, multiple signal classification) and be an important research point of modern space Power estimation based on super-resolution direction of arrival (DOA) technology that the classic algorithm such as Signal parameter estimation algorithm (ESPRIT, estimation of signal parameter viarotational inviance techniques) of ESPRIT is representative.Its accuracy to signal space angle-of-arrival estimation, real-time and its widely application prospect cause the very big concern of people.In the DOA algorithm for estimating of classics, the realization of MUSIC algorithm and ESPRIT algorithm all depends on the covariance matrix receiving data, receive data covariance matrix and can only calculate approximate obtaining by the fast beat of data of limited number of time, and require that the order of this covariance matrix equals the number of signal source.In actual applications, when processing short-term burst data or Received signal strength only has single fast beat of data to use after coherent accumulation, the order of this covariance matrix reduces to 1, then classical MUSIC algorithm and ESPRIT algorithm lost efficacy.DOA under single snap condition estimates it is the practical problems that Estimation of Spatial Spectrum needs solution badly.

At present, the method estimated for the DOA under single snap condition comprises: direct data domain class methods, weighted sum method and based on the pretreated related algorithm of data cross-correlation etc.In immediate data class algorithm, this type of algorithm of great majority all only uses the reception data configuration pseudocovariance matrix of odd number array element, if element number of array is even number, then can cause the waste of receiving data information; Also have the constraint to signal source form that some these type of algorithms increase when constructing pseudocovariance matrix, when signal source form does not meet constraint condition, algorithm lost efficacy.Data configuration pseudocovariance matrix after weighted sum method utilizes part to receive data summation, the method obtains the lifting of signal to noise ratio (S/N ratio) by the signal number increasing summation, reduces the degree of freedom of pseudocovariance matrix simultaneously.Can obtain good DOA estimated performance based on the pretreated algorithm of data cross-correlation, but in data prediction, add extra calculated amount, and DOA estimated performance receives the impact of data by reference point.The pseudocovariance matrix constructed in DOA algorithm for estimating under current single snap condition is all square formation mostly, and other forms of pseudocovariance matrix is not yet fully applied.

Summary of the invention

Technical matters to be solved by this invention is to provide a kind of DOA Estimation in Coherent Signal method based on single fast beat of data, and described method make use of single all reception data taken soon, improves the accuracy that DOA estimates.

For solving the problems of the technologies described above, the technical solution used in the present invention is: a kind of DOA Estimation in Coherent Signal method based on single fast beat of data, is characterized in that said method comprising the steps of:

Step one: the array number of the uniform linear array of antenna is M, space has the far field narrow band signal of N number of correlativity the unknown to incide on described uniform linear array, then output data matrix X (t)=A (θ) S (the t)+N (t) of each array element of t be N × 1 complex matrix, wherein A (θ)=[a (θ ₁), a (θ ₂) ... a (θ _n)], be the array steering vector matrix of M × N, S (t) represents source signal vector matrix; N (t) represents that noise average that array exports be zero variance is σ ²additive white Gaussian noise, and uncorrelated with source signal;

Step 2: output data matrix X (t)=[x of each array element of t ₁(t), x ₂(t) ..., x _m(t)] ^t, utilize the output data configuration of each array element to go out pseudocovariance matrix R ₁and R ₂, wherein R ₁and R ₂be defined as follows:

When the array number M of uniform linear array is odd number, R ₁be expressed as

R ₂be expressed as

In formula, J _mfor the square formation that element on counter-diagonal is 1 entirely, dimension is [(M+1)/2] × [(M+1)/2];

When the array number M of uniform linear array is even number, R ₁be expressed as

R ₂be expressed as

Step 3: for the odd even situation of used antenna array elements, calculates the pseudocovariance matrix R that step 2 constructs ₁transposition, i.e. R ₁ ^t;

Step 4: the pseudocovariance matrix R=[R constructing the expansion made new advances ₁ ^tr ₂];

Step 5: carry out svd to R, under the condition of odd number bay, decompositing (M+1)/2 eigenwert is λ ₁>=λ ₂>=...>=λ _n>=λ _n+1=...=λ _(M+1)/2=σ ², under the condition of even number of antenna array element, decompositing (M+2)/2 eigenwert is λ ₁>=λ ₂>=...>=λ _n>=λ _n+1=...=λ _(M+2)/2=σ ², by judging that the number of large eigenwert carrys out estimated signal source number, and obtain signal subspace Us and noise subspace matrix U respectively according to corresponding proper vector _n;

Step 6: utilize MUSIC algorithm to build spatial spectrum function θ is the space angle of arrival of source signal, when M is odd number, represent rear (M+1)/2 row of a (θ), when M is even number, represent rear (M+2)/2 row of a (θ), make space angle of arrival θ change in (-90 °, 90 °) scope, find out spatial spectrum P _mUSIC(θ) angle corresponding to maximum point is the DOA of source signal.

The beneficial effect adopting technique scheme to produce is: described method obtains different pseudocovariance matrixes by resetting the reception data of aerial array under single snap condition, and obtain the pseudocovariance matrix of new expansion on this basis, the structure of this pseudocovariance matrix make use of all data of antenna array receiver, and its form is not limited to square formation, can remove the coherence between source signal, its order equals the number of antenna source signal.Svd is carried out to new correlation matrix and obtains signal subspace and noise subspace, recycling MUSIC Power estimation algorithm carries out DOA estimation to signal, further increases the accuracy of the estimation of DOA under single snap condition while removing the coherence of antenna source signal.

Accompanying drawing explanation

Fig. 1 is the structural representation of the uniform linear array of M array element;

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, be clearly and completely described the technical scheme in the embodiment of the present invention, obviously, described embodiment is only a part of embodiment of the present invention, instead of whole embodiments.Based on the embodiment in the present invention, those of ordinary skill in the art, not making the every other embodiment obtained under creative work prerequisite, belong to the scope of protection of the invention.

Set forth a lot of detail in the following description so that fully understand the present invention, but the present invention can also adopt other to be different from alternate manner described here to implement, those skilled in the art can when without prejudice to doing similar popularization when intension of the present invention, therefore the present invention is by the restriction of following public specific embodiment.

The invention discloses a kind of DOA Estimation in Coherent Signal method based on single fast beat of data, described method can be divided into three parts.

Part I is array received data modeling:

If space is incided on the uniform linear array that M omnidirectional's array element forms by the far field narrow band signal of individual N correlativity the unknown, if array pitch is d, Array Model as shown in Figure 1.If fast umber of beats is K, then Received signal strength model can be expressed as

X(t)＝A(θ)S(t)+N(t) (1)

The reception data matrix that in formula, X (t) ties up for M × K, A (θ)=[a (θ ₁), a (θ ₂) ... a (θ _n)], be the popular matrix of array of M × N dimension, the incoming signal matrix that S (t) is N × K, the noise signal matrix that N (t) ties up for M × K.Require K > > M > N under normal circumstances.The covariance matrix of array received data can be expressed as

$\begin{array}{c}{R}_X=E\left[X\left(t\right)X^H\left(t\right)\right]\\ =A\left(\mathrm{\θ}\right)E\left[S\left(t\right)S^H\left(t\right)\right]A^H\left(\mathrm{\θ}\right)+E\left[N\left(t\right)N^H\left(t\right)\right]\\ =A\left(\mathrm{\θ}\right)R_S{A}^H\left(\mathrm{\θ}\right)+R_N=A\left(\mathrm{\θ}\right)R_S{A}^H\left(\mathrm{\θ}\right)+{\mathrm{\σ}}^{2}I\end{array}---\left(2\right)$

Wherein, R _s=E [S (t) S ^h(t)], be the covariance matrix of incoming signal, R _n=E [N (t) N ^h(t)]=σ ²i is noise covariance matrix, σ ²for noise power, I is the unit matrix of M × M.Ideally, incoming signal is uncorrelated mutually, independent between signal and noise, and separate between noise, now R _sfor the diagonal matrix of full rank, be also Hermitian Toeplitz matrix, its diagonal element is the power of corresponding signal.In specific implementation, the correlation matrix of signal data asks correlation matrix after obtaining K fast beat of data by sampling replace:

$\hat{R}=\frac{1}{K}\underset{k=1}{\overset{K}{\mathrm{\Σ}}}{X}_k{X}_k^H---\left(3\right)$

Wherein, X _kbeing the data vector of kth time sampling snap output, needing the fast umber of beats of enough samplings to estimate to obtain signal correlation matrix comparatively accurately.The subspace class algorithm that DOA estimates all launches based on the correlation matrix of above formula, thus, when only having single fast beat of data to use, i.e. K=1, the order of sample covariance matrix will reduce to 1, will lose efficacy in subspace class algorithm (as: MUISC, ESPRIT etc.) based on this.

Part II is the structure based on the pseudocovariance matrix receiving data, comprise two parts content, first the pseudocovariance matrix of two different structures is constructed for the odd even situation of receiving array array element, next is the pseudocovariance matrix utilizing the pseudocovariance matrix construction obtained to make new advances, and new pseudocovariance matrix utilizing, the basis all receiving data reaches the object of decorrelation LMS.

Under single snap condition, the single fast beat of data received by pair array carries out rearrangement, and can to construct an order be signal number object matrix, claims this matrix to be pseudocovariance matrix.Structural matrix wherein, for by the capable submatrix formed of some continuous print in A (θ), if line number is J, then for the matrix of J × N; D is the non-singular matrix of N × N dimension.For ensureing that pseudocovariance rank of matrix equals number of source, require J > N, hypothesis D is a diagonal entry is simultaneously the diagonal matrix of source signal.As long as the diagonal element of D is not 0, the pseudocovariance rank of matrix of structure is just number of sources N, thus ensures the correct estimation of coherent signal DOA information.

The phase place of M array received signal is position arithmetic progression in scope, denotable phase range is wherein, value relevant with choosing of reference point, here it is structure pseudocovariance matrix time can information.Pseudocovariance matrix is J × J dimension, and the element of pseudocovariance matrix R can be expressed as

Wherein, d _nmfor the element of matrix D.When matrix D is diagonal matrix, formula (4) can be expressed as

In formula (5), the value of m-n is the integer of [1-J, J-1], and therefore the phase place of pseudocovariance is positioned at arithmetic progression in scope, phase range is order then there is J=(M+1)/2.It can thus be appreciated that when the whole array received signal utilized, the dimension of pseudocovariance matrix R is J _max=(M+1)/2.When array element quantity M is even number, J _max=M/2, now, will inevitably waste available single fast beat of data.

Suppose d _nn=s _n, with the even linear array of M omnidirectional's array element composition for receiving array, arranging first array element is reference array element, ignore the impact of noise, R=A (θ) DA ^h(θ) can be expressed as

When M is odd number, formula (6) can be expressed as:

Pseudocovariance matrix can be constructed as follows

Obviously, for R ₁have: R ₁=R ₁ ^t, contrast (7) can find, by R ₁the pseudocovariance matrix represented can be exchanged row sequence by the submatrix in formula (7) and obtain.Construct another pseudocovariance matrix R on this basis ₂, R ₂be expressed as follows

Contrast (8) formula (9) easily find, R ₂=R ₁ ^t× J _m.Wherein, J _mfor the square formation that element on counter-diagonal is 1 entirely, dimension is [(M+1)/2] × [(M+1)/2].Observation type (7) can find, R ₁a (θ) DA after exchanging row sequence ^h(θ) a submatrix, and R ₂inherently A (θ) DA ^h(θ) a submatrix.Structural matrix dimension be [(M+1)/2] × (M+1), claim herein for the pseudocovariance matrix of expansion reconstruct.By structure known, this expansion pseudocovariance matrix has reused signal message, R ₂the structure of self meets form, wherein, the popular matrix of even linear array array is met for [(M+1)/2] × N. the popular matrix of even linear array array is met for [(M+1)/2+1] × N.R ₁can by R ₂obtain through row-column transform, the matrix of their to be all order be M, has the ability of decorrelation LMS, therefore, by R ₁and R ₂the new extended matrix formed order be also M, also possess the ability of decorrelation LMS.

When M is even number, ignore the impact of noise equally, R=A (θ) DA ^h(θ) can be expressed as

Pseudocovariance matrix can be constructed as follows

Now R ₁for (M/2) × (M/2+1), then R ₁ ^tfor the matrix of (M/2+1) × (M/2).Construct another pseudocovariance matrix R ₂, R ₂be expressed as follows

Observation type (10) can find, R ₁exchange the matrix after row sequence and R ₂all A (θ) DA ^h(θ) submatrix, structural matrix dimension be (M/2+1) × M.Can obtain by deriving wherein, the popular matrix of even linear array array is met for (M/2+1) × N, the popular matrix of even linear array array is met for (M/2) × N.As long as diagonal element is non-vanishing, then the matrix constructed is the matrix that order is greater than N, can realize the decorrelation LMS of array.From the construction process of R, whole process does not retrain incoming signal, can not cause the waste receiving data while realizing decorrelation LMS.

Part III, mainly on the basis of expansion reconstruct correlation matrix, utilizes Subspace algorithm to carry out the process of DOA estimation.Theoretical analysis according to Part II can be known, for coherent source signal, the new relevant rank of matrix of reconstruct increases, information source coherence can be removed, on this basis, step 5 carries out svd to R, and under the condition of odd number bay, decompositing (M+1)/2 eigenwert is λ ₁>=λ ₂>=...>=λ _n>=λ _n+1=...=λ _(M+1)/2=σ ², under the condition of even number of antenna array element, decompositing (M+2)/2 eigenwert is λ ₁>=λ ₂>=...>=λ _n>=λ _n+1=...=λ _(M+2)/2=σ ², by judging that the number of large eigenwert carrys out estimated signal source number, and obtain signal subspace Us and noise subspace matrix U respectively according to corresponding proper vector _n.If large eigenwert characteristic of correspondence vector is e ₁, e ₂..., e _n, then Us=[e is defined ₁, e ₂..., e _p, e _p+1... e _n], little eigenwert characteristic of correspondence vector is U _n=[e _n+1..., e _(M+1)/2] (odd number array element) or U _n=[e _n+1..., e _m/2+1] (even number array element).Step 6 utilizes MUSIC algorithm to build spatial spectrum function, shown in (12)

$P_{\mathrm{MUSIC}}\left(\mathrm{\θ}\right)=\frac{1}{{\stackrel{\‾}{a}}^H\left(\mathrm{\θ}\right)U_N{U}_N^H\stackrel{\‾}{a}\left(\mathrm{\θ}\right)}---\left(12\right)$

Wherein, θ is the space angle of arrival of source signal, when M is odd number, represent rear (M+1)/2 row of a (θ), when M is even number, represent rear (M+2)/2 row of a (θ).Make space angle of arrival θ change in (-90 °, 90 °) scope, find out spatial spectrum P _mUSIC(θ) angle corresponding to maximum point is the DOA of source signal.

Described method obtains different pseudocovariance matrixes by resetting the reception data of aerial array under single snap condition, and obtain the pseudocovariance matrix of new expansion on this basis, the structure of this pseudocovariance matrix make use of all data of antenna array receiver, and its form is not limited to square formation, can remove the coherence between source signal, its order equals the number of antenna source signal.Svd is carried out to new correlation matrix and obtains signal subspace and noise subspace, recycling MUSIC Power estimation algorithm carries out DOA estimation to signal, further increases the accuracy of the estimation of DOA under single snap condition while removing the coherence of source signal.

Claims (1)

1., based on a DOA Estimation in Coherent Signal method for single fast beat of data, it is characterized in that said method comprising the steps of:

Step one: the array number of the uniform linear array of antenna is M, space has the far field narrow band signal of N number of correlativity the unknown to incide on described uniform linear array, then output data matrix X (t)=A (θ) S (the t)+N (t) of each array element of t be N × 1 complex matrix, wherein A (θ)=[a (θ ₁), a (θ ₂) ... a (θ _n)], be the array steering vector matrix of M × N, S (t) represents source signal vector matrix; N (t) represents that noise average that array exports be zero variance is σ ²additive white Gaussian noise, and uncorrelated with source signal;

Step 2: output data matrix X (t)=[x of each array element of t ₁(t), x ₂(t) ..., x _m(t)] ^t, utilize the output data configuration of each array element to go out pseudocovariance matrix R ₁and R ₂, wherein R ₁and R ₂be defined as follows:

When the array number M of uniform linear array is odd number, R ₁be expressed as

R ₂be expressed as

In formula, J _mfor the square formation that element on counter-diagonal is 1 entirely, dimension is [(M+1)/2] × [(M+1)/2];

When the array number M of uniform linear array is even number, R ₁be expressed as

R ₂be expressed as

Step 3: for the odd even situation of used antenna array elements, calculates the pseudocovariance matrix R that step 2 constructs ₁transposition, i.e. R ₁ ^t;

Step 4: the pseudocovariance matrix R=[R constructing the expansion made new advances ₁ ^tr ₂];

Step 5: carry out svd to R, under the condition of odd number bay, decompositing (M+1)/2 eigenwert is λ ₁>=λ ₂>=...>=λ _n>=λ _n+1=...=λ _(M+1)/2=σ ², under the condition of even number of antenna array element, decompositing (M+2)/2 eigenwert is λ ₁>=λ ₂>=...>=λ _n>=λ _n+1=...=λ _(M+2)/2=σ ², by judging that the number of large eigenwert carrys out estimated signal source number, and obtain signal subspace Us and noise subspace matrix U respectively according to corresponding proper vector _n;

Step 6: utilize MUSIC algorithm to build spatial spectrum function θ is the space angle of arrival of source signal, when M is odd number, represent rear (M+1)/2 row of a (θ), when M is even number, represent rear (M+2)/2 row of a (θ), make space angle of arrival θ change in (-90 °, 90 °) scope, find out spatial spectrum P _mUSIC(θ) angle corresponding to maximum point is the DOA of source signal.