CN104459606A - Sparse construction and reconstruction method of array space signals - Google Patents

Abstract

The invention discloses a sparse construction and reconstruction method of array space signals. Due to the fact that the angle of received incident signals changes constantly under the high dynamic condition, enough sampling signals can not be acquired to conduct traditional beam forming. According to the method, a gain test of the array space signals is conducted through the Capon beam forming method based on feature space decomposition, and establishment of a small-snapshot-number sparseness model and OPM reconstruction of the small-snapshot-number sparseness model are conducted based on the compressed sensing theory. The result shows that the method has the advantage of processing undersampled data and achieves estimation on the angle of arrival of the array signals. The method further shows that in the space signal processing field, sparsity makes extraction of related information faster and more effective, so that the signal acquisition cost and the signal processing cost are lowered. By means of the method, expected waveform gain can be obtained in the expected direction of arrival. Compared with a direct sampling method, the method can solve the small snapshot number problem occurring under the high dynamic condition and improve the robustness of a system.

Description

A kind of sparse structure of array manifold signal and method for reconstructing thereof

Technical field

The invention belongs to GNSS engineering safety technical field, be a kind of dynamic beam formation technology, belong to Array Signal Processing field, be specifically related to the method for the sparse structure of a kind of array manifold signal and reconstruction thereof.

Background technology

Array Signal Processing is at radar, communication, sonar, voice, medically all have a wide range of applications.An its important research direction is exactly Wave beam forming.Under static condition, Capon beam-forming schemes possesses good resolution and interference free performance.But under high dynamic environment, the snap quantity of the fast umber of beats obtained in the receiver unit interval under static and low-speed motion state, traditional Capon wave beam and improve one's methods and cannot form effective beam gain, so that wanted signal cannot normally receive.E.Candes, J.Romberg, T.Tao and Donoho etc. in 2006 demonstrate a signal with rarefaction representation and can compress measured value accurate reconstruction by its a small amount of linear non-self-adapting, formally propose compressive sensing theory.Mallat proposes to apply complete redundancy atom carries out Its Sparse Decomposition thought to signal, and introduces matched jamming (Matching Pursuit, MP) algorithm.J.A.Tropp and A.C.Gilbert proposes orthogonal matching pursuit (Orthogonal Matching Pursuit, OMP) algorithm.

Compressive sensing theory is pointed out, as long as signal is sparse or compressible under certain base, just can utilize random measurement matrix that the signal on higher dimensional space is embedded on lower dimensional space.The projection of signal on lower dimensional space contains the enough information required for reconstruction signal, can go out original signal with a small amount of sampled value Accurate Reconstruction on lower dimensional space.

The deficiencies in the prior art part is because the sampling rate of high dynamic receiver is far below Nyquist sampling frequency, adopt traditional spacing wave filtering method cannot recover few snap space sparse signal, and then the directive gain of wanted signal cannot be generated, this method first can be recovered low sampled signal, carry out Wave beam forming again, reach the effect of space wanted signal directive gain.

Summary of the invention

The present invention is directed to low Sampling, have studied the impact that sparse reconstruction property pair array direction of arrival (DOA) is estimated, the sparse structure of a kind of array manifold signal and method for reconstructing thereof are proposed, the openness of spacing wave refers to that the energy of most of spacing wave coefficient is less, and the comparatively large and distribution a kind of spacing wave distribution relatively far apart of the energy of several spacing wave.

The technical solution adopted in the present invention is: the method for the sparse structure of a kind of array manifold signal and reconstruction thereof, bends down Sampling for solving high dynamic condition; It is characterized in that: first carry out sparse sampling, set up the rarefaction model of spacing wave; Then signal reconstruction is carried out to rarefaction model OPM (orthogonal matching pursuit) method; Finally feature decomposition is carried out to the signal rebuild, and carry out Capon Wave beam forming.

As preferably, the process of establishing of the rarefaction model of described spacing wave is, supposes that X is R ⁿthe K rank sparse signal in space, is expressed as { x ₁..., x _n, L represents fast umber of beats, and wherein L>=K*log (N/K), Φ are M × N random observation matrix observation vector s is s=Φ X.

As preferably, described carries out signal reconstruction to rarefaction model OPM method, and its detailed process is, supposes discrete signal length be N, the size of random observation matrix Φ is M × N, and the observation equation of acquisition is

$y_d=\mathrm{\Φ}{x}_d^u---\left(1\right);$

Wherein, y _d=R ^{m × 1}represent observation vector, the rarefaction representation of to be substrate be Ψ, utilizes following optimization method to carry out sparse recovery:

$\min {\left|\right|{\tilde{x}}_d^u\left|\right|}_{l_1}s.t.y_d=\mathrm{\Φ}{\mathrm{\Ψ}}^{*}{\tilde{x}}_d^u---\left(2\right);$

Wherein, Ψ represents Fourier transform matrix;

Formula (2) meets following relation Ψ Ψ ^*=Ψ ^*Ψ=I, this is 1 norm problem, is realized by match tracing (OMP) algorithm, and the ultimate principle of OMP algorithm is from over-complete dictionary of atoms Θ (compressed sensing Θ=Φ Ψ with the method for greedy iteration ^*) in select to build sparse bayesian learning with the atom of signal optimum matching, first the atom selected is carried out Gram-Schmidt orthogonalization process, then just signal is projected to these orthogonalization atomic buildings spatially, and from signal, remove the projection section of signal on this atom, obtain residual signals, then continue to select the atom with residual signals optimum matching from over-complete dictionary of atoms; The continuous iteration of whole process, until the energy of residual signals is less than given threshold value or meets other given end conditions.

As preferably, described carries out feature decomposition to the signal rebuild, and carries out Capon Wave beam forming, and its specific implementation comprises the following steps:

Step 1, initialization: spacing wave surplus initial value is r ₀=s, expanding recovery matrix setup values is Λ ₀=φ, iterations initial value is t=1;

Step 2, take out important in maximal value be assigned to λ _t, optimization equation is

if maximal value initial value is repeated, do not perform;

Step 3, newly will be worth λ _tbe put into expand and recover in matrix, expression formula is Λ _t=Λ _t-1∪ { λ _t,

wherein Φ ₀for sky;

Step 4, separates minimum variance and obtains x _t=arg min _x|| s-Φ _tx|| ₂;

Step 5, calculates new observation vector and surplus is y _t=Φ _tx _t; r _t=s-y _t;

Step 6, count value t adds 1, until return step 2 during t<m, wherein m is iterations, m≤M;

Step 7, utilizes and recovers matrix Λ _min nonzero term estimate sampled signal estimated signal value x _tcorresponding to λ _ja jth element;

Step 8, estimates correlation matrix by sampled data

Step 9 is right do feature decomposition, the optimization method of structure Wave beam forming

Step 10, is constructed by the steering vector of supposition wanted signal

Step 11, the steering vector making wanted signal is estimated, obtains the optimal estimation of actual wanted signal steering vector

Step 12, calculates optimum power according to Capon method, namely

As preferably, calculate optimum power described in step 12 according to Capon method, its detailed process is:

Suppose have M narrow band signal to incide on N element array, M<N, then the model of array received signal is

$x\left(t_k\right)=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}a\left({\mathrm{\&theta;}}_m\right)s_m\left(t_k\right)+n\left(t_k\right),k=\mathrm{1,2},...m=\mathrm{0,1},...M-1---\left(3\right);$

A (θ in formula _m) represent the steering vector of array, s _m(t _k) represent the envelope of signal, n (t _k) be expressed as additive noise; Suppose that information source and noise are statistical iteration, wanted signal s ₀t () represents, other conduct interference and noise, work as s ₀t () and noise, when disturbing incoherent, the correlation matrix of data is:

$R={\mathrm{\&sigma;}}_0^{2}a\left({\mathrm{\&theta;}}_0\right)a^H\left({\mathrm{\&theta;}}_0\right)+\underset{k=1}{\overset{M-1}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_k^{2}a\left({\mathrm{\&theta;}}_k\right)a^H\left({\mathrm{\&theta;}}_k\right)+R_n---\left(4\right);$

In formula be expressed as the power of wanted signal and interference, R _nbe expressed as the correlation matrix of system noise; Wherein data correlation matrix is obtained by the snap data estimation of limited number of time, that is:

$\hat{R}=\frac{1}{L}\underset{n=1}{\overset{L}{\mathrm{\&Sigma;}}}{x}_n{x}_n^{*}---\left(5\right);$

The principle of Capon Wave beam forming is that constraint wanted signal is not suffered a loss, simultaneously the output power of minimized array, is expressed as follows:

$\left\{\begin{array}{cc}\min & w^H\mathrm{Rw}\\ s.t.& w^H\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right)=1\end{array}\right.---\left(6\right);$

In formula for the steering vector of wanted signal, array exports Signal to Interference plus Noise Ratio SINR and is:

$\mathrm{SINR}=\frac{{\left|w^{H}s\left(n\right)\right|}^2}{w^H{R}_{i+n}w}---\left(7\right);$

Formula (6) is substituted into formula (7), and abbreviation obtains:

$\mathrm{SINR}={\mathrm{SINR}}_0\&CenterDot;{\cos }^2(a\left({\mathrm{\&theta;}}_0\right),\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right),R_{i+n}^{-1})---\left(8\right);$

Wherein:

${\mathrm{SINR}}_0=N{\mathrm{\&sigma;}}_0^2{a}^H\left({\mathrm{\&theta;}}_0\right)R_{i+n}^{-1}a\left({\mathrm{\&theta;}}_0\right);$

${\cos }^2(a\left({\mathrm{\&theta;}}_0\right),\stackrel{\&OverBar;}{\mathrm{\&alpha;}}\left({\mathrm{\&theta;}}_0\right),R_{i+n}^{-1})=\frac{{\left|a^H\left({\mathrm{\&theta;}}_0\right)R_{i+n}^{-1}\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right)\right|}^2}{\left(a^H\left({\mathrm{\&theta;}}_0\right)R_{i+n}^{-1}a\left({\mathrm{\&theta;}}_0\right)\right)\left({\stackrel{\&OverBar;}{a}}^H\left({\mathrm{\&theta;}}_0\right)R_{i+n}^{-1}\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right)\right)};$

Due to so adaptive beam can form SLM Signal Label Mismatch, thus cause hydraulic performance decline, in order to overcome the impact of error, adopting MUSIC calculation ratio juris to improve the robustness of Wave beam forming, reducing signal cancellation phenomenon;

MUSIC algorithm utilizes subspace theory, carries out feature decomposition to signal, and show that the super-resolution of angle is estimated from the orthogonality of signal subspace and noise subspace, the optimization method of employing is:

$\left\{\begin{array}{c}\min a^H{U}_n{U}_n^{H}a\\ s.t.{\left|\right|(I-\frac{{\stackrel{\&OverBar;}{\mathrm{aa}}}^H}{{\stackrel{\&OverBar;}{a}}^H\stackrel{\&OverBar;}{a}})a\left|\right|}^2\&le;\mathrm{\&epsiv;}\end{array}\right.---\left(9\right)$

In formula, the steering vector of a representation signal, for supposition wanted signal steering vector, U _nu _n ^hrepresent noise subspace, ε is a little positive number; From then on optimization method obtains the optimal estimation of the steering vector of actual wanted signal then Capon Wave beam forming is utilized to obtain optimum power

Tool of the present invention has the following advantages: due under high dynamic condition, and the angle of received incoming signal is in constantly change, cannot obtain enough sampled signals to carry out traditional Wave beam forming.The present invention adopts the Capon beam-forming schemes of Feature Space Decomposing to carry out the gain experiment of space array signal.Utilize the principle of compressed sensing, the present invention establishes rarefaction model and the OPM reconstruction realization thereof of few snap.Result shows, this method has the advantage of process lack sampling data, solves the estimation problem of the array signal angle of arrival.The present invention further illustrates in Spatial signal processing field, and openness existence makes the extraction of relevant information become more fast effectively, thus reduces the cost in signal acquisition and processing procedure.The present invention can expect wave shape gain direction of arrival obtaining expection.Compared with Direct Sampling method, the few snap problem run under can solving high dynamic condition, improves the robustness of system.

Accompanying drawing explanation

Fig. 1: when the fast umber of beats for the embodiment of the present invention is 512, the Wave beam forming array pattern of Direct Sampling;

Fig. 2: when the fast umber of beats for the embodiment of the present invention is 12, the Wave beam forming array pattern of Direct Sampling;

Fig. 3: when the fast umber of beats for the embodiment of the present invention is 12, sparse sampling and rebuild after Wave beam forming array pattern.

Embodiment

Understand for the ease of those of ordinary skill in the art and implement the present invention, below in conjunction with drawings and Examples, the present invention is described in further detail, should be appreciated that exemplifying embodiment described herein is only for instruction and explanation of the present invention, is not intended to limit the present invention.

The present invention is directed to low Sampling, establish the rarefaction model of spacing wave, carry out signal reconstruction by OPM method, then feature decomposition is carried out to the signal rebuild, and carry out Capon Wave beam forming.

The flow process that the rarefaction model of spacing wave is set up is:

Suppose that X is R ⁿthe K rank sparse signal in space, is expressed as { x ₁..., x _n, L represents fast umber of beats, and wherein L>=K*log (N/K), Φ are M × N random observation matrix observation vector s is s=Φ X.

The flow process of the OMP reconstruction model of sparse signal is:

Talk about publicly known, nyquist sampling theorem is sampling rate when will double maximum sampling rate, and signal could undistorted recovery.And compressive sensing theory breaches this theory, it is according to the rarefaction feature of signal, can recover non-self-adapting signal far below in nyquist sampling situation.

The present invention supposes discrete signal length be N, the size of random observation matrix Φ is M × N, and the observation equation of acquisition is

$y_d=\mathrm{\&Phi;}{x}_d^u---\left(1\right);$

Wherein, y _d=R ^{m × 1}represent observation vector, the rarefaction representation of to be substrate be Ψ, utilizes following optimization method to carry out sparse recovery:

$\min {\left|\right|{\tilde{x}}_d^u\left|\right|}_{l_1}s.t.y_d=\mathrm{\&Phi;}{\mathrm{\&Psi;}}^{*}{\tilde{x}}_d^u---\left(2\right)$

Wherein, Ψ represents Fourier transform matrix;

It meets following relation Ψ Ψ ^*=Ψ ^*Ψ=I; This is 1 norm problem, is realized by match tracing (OMP) algorithm, and the ultimate principle of OMP algorithm is from over-complete dictionary of atoms Θ (compressed sensing Θ=Φ Ψ with the method for greedy iteration ^*) in select to build sparse bayesian learning with the atom of signal optimum matching, first the atom selected is carried out Gram-Schmidt orthogonalization process, then just signal is projected to these orthogonalization atomic buildings spatially, and from signal, remove the projection section of signal on this atom, obtain residual signals, then continue to select the atom with residual signals optimum matching from over-complete dictionary of atoms; The continuous iteration of whole process, until the energy of residual signals is less than given threshold value or meets other given end conditions.

Sparse sampling, the flow process of rebuilding Wave beam forming after recovering is:

(1) flow process of classic method (Direct Sampling Wave beam forming) is:

1) correlation matrix is estimated by sampled data

2) right feature decomposition, the optimization method of structure Wave beam forming

3) constructed by the steering vector of supposition wanted signal

4) steering vector making wanted signal is estimated, obtains the optimal estimation of actual wanted signal steering vector

5) optimum power is calculated according to Capon method, namely

(2) method flow of the present invention is:

1) initialization: surplus r ₀=s, Λ ₀=φ, t=1;

2) take out important in maximal value be assigned to λ _t, optimization equation is: if maximal value initial value is repeated, do not perform;

3) newly λ will be worth _tbe put into expand and recover in matrix, expression formula is Λ _t=Λ _t-1∪ { λ _t,

wherein Φ ₀for sky;

4) separate minimum variance and obtain x _t=arg min _x|| s-Φ _tx|| ₂;

5) new observation vector is calculated and surplus is y _t=Φ _tx _t; r _t=s-y _t;

6) count value t adds 1, until return step 2 during t<m, wherein m is iterations, m≤M;

7) recovery matrix Λ is utilized _min nonzero term estimate sampled signal estimated signal value x _tcorresponding to λ _ja jth element;

8) correlation matrix is estimated by sampled data

9) right do feature decomposition, the optimization method of structure Wave beam forming

10) constructed by the steering vector of supposition wanted signal

11) steering vector making wanted signal is estimated.Obtain the optimal estimation of actual wanted signal steering vector

12) optimum power is calculated according to Capon method, namely its detailed process is:

Suppose have M narrow band signal to incide on N element array, M<N, then the model of array received signal is

$x\left(t_k\right)=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}a\left({\mathrm{\&theta;}}_m\right)s_m\left(t_k\right)+n\left(t_k\right),k=\mathrm{1,2},...m=\mathrm{0,1},...M-1---\left(3\right);$

A (θ in formula _m) represent the steering vector of array, s _m(t _k) represent the envelope of signal, n (t _k) be expressed as additive noise; Suppose that information source and noise are statistical iteration, wanted signal s ₀t () represents, other conduct interference and noise, work as s ₀t () and noise, when disturbing incoherent, the correlation matrix of data is:

$R={\mathrm{\&sigma;}}_0^{2}a\left({\mathrm{\&theta;}}_0\right)a^H\left({\mathrm{\&theta;}}_0\right)+\underset{k=1}{\overset{M-1}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_k^{2}a\left({\mathrm{\&theta;}}_k\right)a^H\left({\mathrm{\&theta;}}_k\right)+R_n---\left(4\right);$

In formula be expressed as the power of wanted signal and interference, R _nbe expressed as the correlation matrix of system noise; Wherein data correlation matrix is obtained by the snap data estimation of limited number of time, that is:

$\hat{R}=\frac{1}{L}\underset{n=1}{\overset{L}{\mathrm{\&Sigma;}}}{x}_n{x}_n^{*}---\left(5\right);$

The principle of Capon Wave beam forming is that constraint wanted signal is not suffered a loss, simultaneously the output power of minimized array, is expressed as follows:

$\left\{\begin{array}{cc}\min & w^H\mathrm{Rw}\\ s.t.& w^H\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right)=1\end{array}\right.---\left(6\right);$

In formula for the steering vector of wanted signal, array exports Signal to Interference plus Noise Ratio SINR and is:

$\mathrm{SINR}=\frac{{\left|w^{H}s\left(n\right)\right|}^2}{w^H{R}_{i+n}w}---\left(7\right);$

Formula (6) is substituted into formula (7), and abbreviation obtains:

$\mathrm{SINR}={\mathrm{SINR}}_0\&CenterDot;{\cos }^2(a\left({\mathrm{\&theta;}}_0\right),\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right),R_{i+n}^{-1})---\left(8\right);$

Wherein:

${\mathrm{SINR}}_0=N{\mathrm{\&sigma;}}_0^2{a}^H\left({\mathrm{\&theta;}}_0\right)R_{i+n}^{-1}a\left({\mathrm{\&theta;}}_0\right);$

${\cos }^2(a\left({\mathrm{\&theta;}}_0\right),\stackrel{\&OverBar;}{\mathrm{\&alpha;}}\left({\mathrm{\&theta;}}_0\right),R_{i+n}^{-1})=\frac{{\left|a^H\left({\mathrm{\&theta;}}_0\right)R_{i+n}^{-1}\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right)\right|}^2}{\left(a^H\left({\mathrm{\&theta;}}_0\right)R_{i+n}^{-1}a\left({\mathrm{\&theta;}}_0\right)\right)\left({\stackrel{\&OverBar;}{a}}^H\left({\mathrm{\&theta;}}_0\right)R_{i+n}^{-1}\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right)\right)};$

Due to so adaptive beam can form SLM Signal Label Mismatch, thus cause hydraulic performance decline, in order to overcome the impact of error, adopting MUSIC calculation ratio juris to improve the robustness of Wave beam forming, reducing signal cancellation phenomenon;

MUSIC algorithm utilizes subspace theory, carries out feature decomposition to signal, and show that the super-resolution of angle is estimated from the orthogonality of signal subspace and noise subspace, the optimization method of employing is:

$\left\{\begin{array}{c}\min a^H{U}_n{U}_n^{H}a\\ s.t.{\left|\right|(I-\frac{{\stackrel{\&OverBar;}{\mathrm{aa}}}^H}{{\stackrel{\&OverBar;}{a}}^H\stackrel{\&OverBar;}{a}})a\left|\right|}^2\&le;\mathrm{\&epsiv;}\end{array}\right.---\left(9\right)$

In formula, the steering vector of a representation signal, for supposition wanted signal steering vector, U _nu _n ^hrepresent noise subspace, ε is a little positive number; From then on optimization method obtains the optimal estimation of the steering vector of actual wanted signal then Capon Wave beam forming is utilized to obtain optimum power

Below by way of concrete experiment, the present invention is further set forth;

Suppose that the array number M of antenna array is 20, array element distance is half wavelength.In addition suppose that white noise is uncorrelated white Gaussian noise, average power is zero.Signal to noise ratio (S/N ratio) is defined as for signal power, for noise power.The present invention only considers the elevation angle, expects that satellite direction is chosen for 0 degree, and consider that the array number M of antenna array is 20, the fast umber of beats L of stationary state is 512, and the fast umber of beats L under high dynamic condition is 12.

Fig. 1 is fast umber of beats when being 512, the Wave beam forming array pattern of Direct Sampling, and Fig. 2 is fast umber of beats when being 12, the Wave beam forming array pattern of Direct Sampling, and Fig. 3 is fast umber of beats when being 12, sparse sampling Wave beam forming array pattern after rebuilding.As apparent from this three width comparison diagram can fast umber of beats on the impact of beamforming algorithm, fast umber of beats is more, and the effect of beamforming algorithm is better.When few snap, the beamforming algorithm of Direct Sampling cannot reach the effect of wanted signal gain, and after adopting reconstruction algorithm, can address this problem, and achieves the effect of the wanted signal gain under few snap condition.

In sum, due under high dynamic condition, the angle of received incoming signal is in constantly change, and the present invention cannot obtain enough sampled signals to carry out traditional Wave beam forming.The present invention adopts the Capon beam-forming schemes of feature based spatial decomposition to carry out the gain experiment of space array signal.Utilize the principle of compressed sensing, the present invention establishes rarefaction model and the OPM reconstruction realization thereof of few snap.Result shows, the present invention has the advantage of process lack sampling data, solves the estimation problem of the array signal angle of arrival.The present invention further illustrates in Spatial signal processing field, and openness existence makes the extraction of relevant information become more fast effectively, thus reduces the cost in signal acquisition and processing procedure.

Should be understood that, the part that this instructions does not elaborate all belongs to prior art.

Should be understood that; the above-mentioned description for preferred embodiment is comparatively detailed; therefore the restriction to scope of patent protection of the present invention can not be thought; those of ordinary skill in the art is under enlightenment of the present invention; do not departing under the ambit that the claims in the present invention protect; can also make and replacing or distortion, all fall within protection scope of the present invention, request protection domain of the present invention should be as the criterion with claims.

Claims (5)

1. a method for the sparse structure of array manifold signal and reconstruction thereof, bends down Sampling for solving high dynamic condition; It is characterized in that: first carry out sparse sampling, set up the rarefaction model of spacing wave; Then signal reconstruction is carried out to rarefaction model OPM method; Finally feature decomposition is carried out to the signal rebuild, and carry out Capon Wave beam forming.

2. the method for the sparse structure of array manifold signal according to claim 1 and reconstruction thereof, is characterized in that: the process of establishing of the rarefaction model of described spacing wave is, supposes that X is R ⁿthe K rank sparse signal in space, is expressed as { x ₁..., x _n, L represents fast umber of beats, wherein L>=K*log (N/K) _,Φ is M × N random observation matrix observation vector s is s=Φ X.

3. the method for the sparse structure of array manifold signal according to claim 2 and reconstruction thereof, is characterized in that: described carries out signal reconstruction to rarefaction model OPM method, and its detailed process is, supposes discrete signal length be N, the size of random observation matrix Φ is M × N, and the observation equation of acquisition is

$y_d={\mathrm{\&Phi;x}}_d^u---\left(1\right);$

Wherein, y ₀=R ^{m × 1}represent observation vector, the rarefaction representation of to be substrate be Ψ, utilizes following optimization method to carry out sparse recovery:

$\min {\left|\right|{\tilde{x}}_d^u\left|\right|}_{l_1},s.t.y_d={\mathrm{\&Phi;\&Psi;}}^{*}{\tilde{x}}_d^u---\left(2\right);$

Wherein, Ψ represents Fourier transform matrix;

Formula (2) meets following relation Ψ Ψ ^*=Ψ ^*Ψ=I, this is 1 norm problem, is realized by match tracing (OMP) algorithm, and the ultimate principle of OMP algorithm is from over-complete dictionary of atoms Θ (compressed sensing Θ=Φ Ψ with the method for greedy iteration ^*) in select to build sparse bayesian learning with the atom of signal optimum matching, first the atom selected is carried out Gram-Schmidt orthogonalization process, then just signal is projected to these orthogonalization atomic buildings spatially, and from signal, remove the projection section of signal on this atom, obtain residual signals, then continue to select the atom with residual signals optimum matching from over-complete dictionary of atoms; The continuous iteration of whole process, until the energy of residual signals is less than given threshold value or meets other given end conditions.

4. the method for the sparse structure of array manifold signal according to claim 3 and reconstruction thereof, is characterized in that, described carries out feature decomposition to the signal rebuild, and carries out Capon Wave beam forming, and its specific implementation comprises the following steps:

Step 1, initialization: spacing wave surplus initial value is r ₀=s, expanding recovery matrix setup values is Λ ₀=φ, iterations initial value is t=1;

Step 2, take out important in maximal value be assigned to λ _t, optimization equation is

if maximal value initial value is repeated, do not perform;

Step 3, newly will be worth λ _tbe put into expand and recover in matrix, expression formula is Λ _t=Λ _t-1∪ { λ _t,

wherein Φ ₀for sky;

Step 4, separates minimum variance and obtains x _t=argmin _x|| s-Φ _tx|| ₂;

Step 5, calculates new observation vector and surplus is y _t=Φ _tx _t; r _t=s-y _t;

Step 6, count value t adds 1, until return step 2 during t < m, wherein m is iterations, m≤M;

Step 7, utilizes and recovers matrix Λ _min nonzero term estimate sampled signal estimated signal value x _tcorresponding to λ _ja jth element;

Step 8, estimates correlation matrix by sampled data

Step 9 is right do feature decomposition, the optimization method of structure Wave beam forming

Step 10, is constructed by the steering vector of supposition wanted signal

Step 11, the steering vector making wanted signal is estimated, obtains the optimal estimation of actual wanted signal steering vector

Step 12, calculates optimum power according to Capon method, namely

5. the method for the sparse structure of array manifold signal according to claim 4 and reconstruction thereof, is characterized in that, weighing according to the calculating of Capon method is optimum described in step 12, and its detailed process is:

Suppose have M narrow band signal to incide on N element array, M<N, then the model of array received signal is $x\left(t_k\right)=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}a\left({\mathrm{\&theta;}}_m\right)s_m\left(t_k\right)+n\left(t_k\right)$ k＝1,2…m＝0,1,…M-1(3)；

A (θ in formula _m) represent the steering vector of array, s _m(t _k) represent the envelope of signal, n (t _k) be expressed as additive noise; Suppose that information source and noise are statistical iteration, wanted signal s ₀t () represents, other conduct interference and noise, work as s ₀t () and noise, when disturbing incoherent, the correlation matrix of data is:

$R={\mathrm{\&sigma;}}_0^{2}a\left({\mathrm{\&theta;}}_0\right)a^H\left({\mathrm{\&theta;}}_0\right)+\underset{k=1}{\overset{M-1}{\mathrm{\&Sigma;}}}{\mathrm{\&sigma;}}_k^{2}a\left({\mathrm{\&theta;}}_k\right)a^H\left({\mathrm{\&theta;}}_k\right)+R_n---\left(4\right);$

In formula i=0 ..., M-1 is expressed as the power of wanted signal and interference, R _nbe expressed as the correlation matrix of system noise; Wherein data correlation matrix is obtained by the snap data estimation of limited number of time, namely

$\hat{R}=\frac{1}{L}\underset{n=1}{\overset{L}{\mathrm{\&Sigma;}}}{x}_n{x}_n^{*}---\left(5\right);$

The principle of Capon Wave beam forming is that constraint wanted signal is not suffered a loss, simultaneously the output power of minimized array, is expressed as follows:

$\left\{\begin{array}{cc}\min & w^H\mathrm{Rw}\\ s.t.& w^H\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right)=1\end{array}\right.---\left(6\right);$

In formula for the steering vector of wanted signal, array exports Signal to Interference plus Noise Ratio SINR and is:

$\mathrm{SINR}=\frac{|w^{H}s{\left(n\right)|}^2}{w^H+R_{i+n}w}---\left(7\right);$

Formula (6) is substituted into formula (7), and abbreviation obtains:

$\mathrm{SINR}={\mathrm{SINR}}_0\&CenterDot;{\cos }^2(a\left({\mathrm{\&theta;}}_0\right),\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right),R_{i+n}^{-1})---\left(8\right);$

Wherein:

${\mathrm{SINR}}_0={\mathrm{N\&sigma;}}_0^2{a}^H\left({\mathrm{\&theta;}}_0\right)R_{i+n}^{-1}a\left({\mathrm{\&theta;}}_0\right);$

${\cos }^2(a\left({\mathrm{\&theta;}}_0\right),\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right),R_{i+n}^{-1})=\frac{{\left|a^H\left({\mathrm{\&theta;}}_0\right)R_{i+n}^{-1}\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right)\right|}^2}{\left(a^H\left({\mathrm{\&theta;}}_0\right)R_{i+n}^{-1}a\left({\mathrm{\&theta;}}_0\right)\right)\left({\stackrel{\&OverBar;}{a}}^H\left({\mathrm{\&theta;}}_0\right)R_{i+n}^{-1}\stackrel{\&OverBar;}{a}\left({\mathrm{\&theta;}}_0\right)\right)};$

Due to so adaptive beam can form SLM Signal Label Mismatch, thus cause hydraulic performance decline, in order to overcome the impact of error, adopting MUSIC calculation ratio juris to improve the robustness of Wave beam forming, reducing signal cancellation phenomenon;

MUSIC algorithm utilizes subspace theory, carries out feature decomposition to signal, and show that the super-resolution of angle is estimated from the orthogonality of signal subspace and noise subspace, the optimization method of employing is:

$\left\{\begin{array}{c}\min a^H{U}_n{U}_n^{H}a\\ s.t.{\left|\right|(I-\frac{{\stackrel{\&OverBar;}{\mathrm{aa}}}^H}{{\stackrel{\&OverBar;}{a}}^H\stackrel{\&OverBar;}{a}})a\left|\right|}^2\&le;\mathrm{\&epsiv;}\end{array}\right.---\left(9\right)$

In formula, the steering vector of a representation signal, for supposition wanted signal steering vector, U _nu _n ^hrepresent noise subspace, ε is a little positive number; From then on optimization method obtains the optimal estimation of the steering vector of actual wanted signal then Capon Wave beam forming is utilized to obtain optimum power