CN103760527A - Method for direction of arrival estimation of coherent source of single-base MIMO radar - Google Patents

Abstract

The invention belongs to the technical field of radars and discloses a method for direction of arrival estimation of a coherent source of a single-base MIMO radar. The method can be used for goal orientation and tracking of the single-base MIMO radar with any array manifold. The method is implemented in the following steps: step 1, a guiding vector of the single-base MIMO radar is written according to the array manifold; step 2, an M-dimension Vandermonde vector is set, and a transfer matrix G is obtained; step 3, a transformed guiding vector is obtained through a smooth transformation matrix F; step 4, matched filtering is conducted on received data of the MIMO radar, the received data obtained after matched filtering are recorded as X(k), transformed data Y(k)=FGX(k) are obtained through the transfer matrix G and the smooth transformation matrix F, and then an autocorrelation matrix is formed; step 5, eigen-decomposition is conducted on the autocorrelation matrix, and then a noise subspace is formed; step 6, a space zero spectral function is formed through the noise subspace; step 7, the polynomial rooting method is adopted to obtain a target azimuth angle.

Description

Single base MIMO radar coherent source Wave arrival direction estimating method

Technical field

The invention belongs to Radar Technology field, be specifically related to any single base MIMO radar coherent source Wave arrival direction estimating method, can be used for goal orientation and the tracking of single base MIMO radar of any array manifold.

Background technology

MIMO radar (being MIMO radar) makes full use of its spatial resolution of waveform diversity improving gain, and improving Parameter Estimation Precision and increase system maximum can localizing objects quantity.In recent years, the development of MIMO radar is very fast, and wherein direction of arrival estimates that (being DOA) method is the Important Problems of MIMO radar research.In various array structures, even linear array because it is simple in structure, realize easily, and can adopt various quick DOA algorithms and become the basis of current MIMO radar DOA algorithm research.But, one dimension even linear array can only provide 180 degree without fuzzy azimuth information, and identical in the resolution of different directions, the array that need to yet make of particular system may not be even linear array sometimes yet.For MIMO radar, during transmitting, do not form spatial beams, its array element directional diagram covers whole spatial domain, is used for surveying the whole spatial information of 360 degree, at this moment adopts linear array to there will be within the scope of 360 degree fuzzy, can not satisfy the demand.Therefore, for the direction of arrival of any array manifold, estimate it is the problem of a needs research.

At present, the most basic angle super-resolution method of estimation is to adopt Multiple Signal Classification MUSIC method, although this method can need angle to carry out full volume-search coverage working under array manifold arbitrarily, operand is very large.In addition, the subspace class high resolution DOA estimation algorithm that the MUSIC algorithm of take is representative has good resolution performance and higher estimated accuracy for noncoherent space information source, but its resolution performance runs down with the increase of degree of correlation between the information source of space.

Traditional array manifold smoothing algorithm is a kind of preprocess method of conventional processing coherent source, subsequently on the basis of front-rear space smooth technology, submatrix covariance arithmetic and weighted space smoothing algorithm have been there is again, these improved algorithms have reduced the aperture loss of array to a certain extent, improve the resolution characteristic of coherent source, but also brought larger calculated amount.The above-mentioned various solution coherent approach based on smoothing technique of mentioning are all based on uniform linear array structure, cannot process any array manifold; And these algorithms are all to obtain its decoherence ability by sacrificing the effective aperture of array, after decoherence, the resolution characteristic of coherent source is also had to decline by a relatively large margin.

Summary of the invention

Deficiency for above-mentioned prior art, the object of the invention is to propose a kind of single base MIMO radar coherent source Wave arrival direction estimating method, not only can be for the relevant processing of coherent source solution of the MIMO radar array of array manifold arbitrarily, and adopt polynomial rooting algorithm to replace spectrum peak search algorithm, when reducing calculated amount, realize single base MIMO radar coherent source DOA of any array manifold is estimated.

Realizing technical thought of the present invention is: the structure of first utilizing Array interpolation technology that MIMO radar vectoring resolution of vectors is multiplied each other for matrix and Fan Demeng vector; Then use for reference the thought of space smoothing, to coherent source decoherence; Finally adopt polynomial rooting method to replace 4 use spectrum peak search modes in classic method and obtain angle on target information, realize direction of arrival and estimate fast.

Technical scheme of the present invention is a kind of single base MIMO radar coherent source Wave arrival direction estimating method, it is characterized in that comprising the following steps:

Step 1, according to the array manifold of single base MIMO radar, obtains this array steering vector A (θ), and wherein, this array has N array element, and the polar coordinates of each array element are (r _n, β _n), n=1,2 ... N; N is array number;

Step 2, arranges M Wei Fandemeng vector B (θ), according to formula G=B (θ) A ^h(θ) [A (θ) A ^h(θ)] ^-1try to achieve transition matrix G; Wherein, order select model moral mentor to the dimension M ≈ 4kR of vector B (θ), k=2 π/λ, λ is the wavelength that transmits;

Step 3, carries out similar spaces smoothing processing to model moral mentor to vector B (θ), and F is smooth transformation matrix, steering vector C (the θ)=FB (θ) after level and smooth;

Step 4, reception data to MIMO radar are carried out matched filtering, reception data after matched filtering are designated as X (k), by transition matrix G and level and smooth transformation matrix F, data matrix Y (k)=FGX (k) after being converted, recycling data matrix Y (k) forms autocorrelation matrix R _y;

Step 5, to autocorrelation matrix R _ycarry out feature decomposition, obtain noise subspace

Step 6, utilizes noise subspace

form MUSIC space zero spectral function:

$f\left(\mathrm{\θ}\right)={\left|\right|{{\hat{E}}_n}^{H}C\left(\mathrm{\θ}\right)\left|\right|}^2=C^H\left(\mathrm{\θ}\right){\hat{E}}_n{{\hat{E}}_n}^{H}C\left(\mathrm{\θ}\right)$

Wherein || || ²represent 2-norm,

representing matrix

conjugate transpose;

Step 7, makes z=e ^{j θ}, f (θ) can be converted into:

$f\left(z\right)=C^H\left(z\right){\hat{E}}_n{{\hat{E}}_n}^{H}C\left(z\right)$

Make f (z)=0, P the azimuthal complex exponential form z that adopts the method for polynomial rooting to try to achieve to approach most unit circle and amplitude to be less than 1 _p(p=1,2 ... P); Wherein P is same range gate internal object number, θ _pit is the position angle of p target;

Step 8, utilizes the complex exponential form z of acceptance angle _p, try to achieve p and receive azimuth angle theta _p:

θ _p=angle(z _p)

Wherein, angle () represents to ask phasing degree;

p=1,2…P。

Obtain the position angle of P target, complete the estimation of the direction of arrival of MIMO radar coherent source.

The present invention compared with prior art has the following advantages: (1) existing DOA method of estimation that does not rely on array manifold is MUSIC spectrum method of estimation, but the method cannot be processed coherent source signal, the requirement to some extent of the equal pair array stream shape of quasi-coherent source, existing subspace disposal route, requiring array is linear uniform array or two dimensional linear uniform arrays, to irregular array stream shape, cannot process; (2) method that can process at present coherent source signal is maximum likelihood method, but the method needs multi-dimensional search, and operand is very large, and especially, in the situation that having a plurality of source, operand exponentially level increases, and is difficult to Project Realization.The present invention can become Fan Demeng form MIMO radar vectoring vector, and DOA estimates to adopt polynomial rooting form, greatly reduces operand.

Accompanying drawing explanation

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.

Fig. 1 is the realization flow figure of single base of the present invention MIMO radar coherent source Wave arrival direction estimating method;

Fig. 2 utilizes the simulation result figure of the present invention to 100 independent experiment gained of target;

Fig. 3 is that angle on target square error while utilizing the present invention to target 1 location is with signal to noise ratio snr variation diagram;

Fig. 4 is that angle on target square error while utilizing the present invention to target 2 location is with signal to noise ratio snr variation diagram.

Embodiment

With reference to Fig. 1, single base MIMO radar coherent source Wave arrival direction estimating method specific implementation step of invention is as follows:

Step 1, according to the array manifold of single base MIMO radar, obtains this array steering vector A (θ).

If single base MIMO radar array has N array element (this N of transmit-receive sharing array element), according to the array element polar coordinates can obtain each array element that distribute be (r _n, β _n), n=1,2 ... N, N is array number;

According to the polar coordinates (r of each array element _n, β _n), obtain the transmitting steering vector a of MIMO radar array _t(θ) with reception steering vector a _r(θ) be respectively:

$a_t\left(\mathrm{\&theta;}\right)={[e^{\mathrm{<figure-callout\; id="1"\; label="jk\; r"\; filenames="HDA0000460663590000031.png"\; state="\{\{state\}\}">jk</figure-callout>}{r}_{}{}_1\cos ({\mathrm{\&beta;}}_1-\mathrm{\&theta;})}\&CenterDot;\&CenterDot;\&CenterDot;e^{{\mathrm{jkr}}_n\cos ({\mathrm{\&beta;}}_n-\mathrm{\&theta;})}\&CenterDot;\&CenterDot;\&CenterDot;e^{j{\mathrm{kr}}_N\cos ({\mathrm{\&beta;}}_N-\mathrm{\&theta;})}]}^T$

$a_r\left(\mathrm{\&theta;}\right)={[e^{\mathrm{<figure-callout\; id="1"\; label="jk\; r"\; filenames="HDA0000460663590000031.png"\; state="\{\{state\}\}">jk</figure-callout>}{r}_{}{}_1\cos ({\mathrm{\&beta;}}_1-\mathrm{\&theta;})}\&CenterDot;\&CenterDot;\&CenterDot;e^{{\mathrm{jkr}}_n\cos ({\mathrm{\&beta;}}_n-\mathrm{\&theta;})}\&CenterDot;\&CenterDot;\&CenterDot;e^{j{\mathrm{kr}}_N\cos ({\mathrm{\&beta;}}_N-\mathrm{\&theta;})}]}^T$

Wherein, k=2 π/λ, λ is the wavelength that transmits, r _nand β _nbe respectively n array element apart from the distance of true origin the angle position with relative x axle in polar coordinates, θ is position angle, [] ^trepresenting matrix transposition;

According to transmitting steering vector a _t(θ) with reception steering vector a _r(θ) the steering vector A (θ) of acquisition MIMO radar array is:

$A\left(\mathrm{\&theta;}\right)=a_t\left(\mathrm{\&theta;}\right)\&CircleTimes;a_r\left(\mathrm{\&theta;}\right)$

In formula,

represent the long-pending computing of Kronecker;

Step 2, arranges M Wei Fandemeng vector B (θ), according to formula G=B (θ) A ^h(θ) [A (θ) A ^h(θ)] ^-1try to achieve transition matrix G.

2a) obtain the dimension M of Fan Demeng vector B (θ)

Order n=1,2 ... N, N is element number of array, selects model moral mentor to the dimension M ≈ 4kR of vector B (θ), k=2 π/λ, λ is the wavelength that transmits;

Ignore truncation error, model moral mentor to vector B (θ) is:

$B\left(\mathrm{\&theta;}\right)={[e^{\frac{-j(M-1)\mathrm{\&theta;}}{2}},\&CenterDot;\&CenterDot;\&CenterDot;,e^{\frac{j(M-1)\mathrm{\&theta;}}{2}}]}^T$

Wherein, [] ^trepresenting matrix transposition, j represents imaginary number.

2b) obtain transition matrix G

Equally spacedly in observation scope get J angle, that is: θ ₁, θ ₂..., θ _j;

According to θ ₁, θ ₂..., θ _j, form respectively steering vector matrix with Fan Demeng matrix

$\tilde{A}=[A\left({\mathrm{\&theta;}}_1\right),A\left({\mathrm{\&theta;}}_2\right),\&CenterDot;\&CenterDot;\&CenterDot;,A\left({\mathrm{\&theta;}}_J\right)]$

$\tilde{B}=[B\left({\mathrm{\&theta;}}_1\right),B\left({\mathrm{\&theta;}}_2\right),\&CenterDot;\&CenterDot;\&CenterDot;,B\left({\mathrm{\&theta;}}_J\right)]$

According to steering vector matrix

with Fan Demeng matrix

utilize least square method to obtain transition matrix G:

$G=\tilde{A}{\tilde{B}}^H{\left(\tilde{B}{\tilde{B}}^H\right)}^{-1}$

Wherein,

representing matrix conjugate transpose, () ^-1representing matrix is inverted.

Step 3, carries out similar spaces smoothing processing to model moral mentor to vector B (θ), and F is smooth transformation matrix, and the steering vector after level and smooth is expressed as C (θ)=FB (θ).

Model moral mentor is divided into an overlapped L submatrix to vector B (θ) (being equivalent to even linear array), and each submatrix dimension is Q=M-L+1; Wherein, M is the dimension of B (θ);

According to Q structure smooth transformation matrix: F _l=[0 _{q * (l-1)}| I _q| 0 _{q * (L-l)}], wherein, l=1,2 ... L, 0 _{q * (l-1)}represent rank zero battle array of Q * (l-1), I _qrepresent Q rank unit matrix, 0 _{q * (L-l)}represent rank zero battle array of Q * (L-l);

Smooth transformation matrix F can be obtained by following formula:

$F=\frac{1}{L}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{F}_l$

After conversion, steering vector C (θ) can be obtained by following formula:

C(θ)=FB(θ)

Step 4, reception data to MIMO radar are carried out matched filtering, reception data after matched filtering are designated as X (k), by transition matrix G and level and smooth transformation matrix F, data matrix Y (k)=FGX (k) after being converted, recycling data matrix Y (k) forms autocorrelation matrix R _y;

4a) the reception data of radar are carried out to matched filtering

The radar cross section RCS that supposes each target is identical, receives signal to be:

$X_r=\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}A\left({\mathrm{\&theta;}}_p\right){\mathrm{<figure-callout\; id="2"\; label="Se\; j"\; filenames="HDA0000460663590000022.png,HDA0000460663590000031.png"\; state="\{\{state\}\}">Se</figure-callout>}}^j+V$

Wherein, P is same range gate internal object number, θ _pbe the position angle of p target, f _dpbe p target Doppler frequency (p=1,2 ... P), V is the reception noise matrix of MIMO radar array.

Reception data to MIMO radar array are carried out matched filtering, and the reception data after matched filtering are designated as X (k).

X(k)=E(SX _r)

Wherein, E () represents mathematical expectation, S=[s ₁ ^t... s _i ^t, s _n ^t] ^texpression is by N matrix that transmits and form, s _irepresent that i transmits,

represent s _itransposition (i=1 ... N);

4b) the data matrix Y (k) after being converted by transition matrix G and level and smooth transformation matrix F

Y(k)=FGX(k)

4c) the data matrix Y (k) after recycling conversion forms autocorrelation matrix R _y

$R_y=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}Y\left(k\right)Y^H\left(k\right)$

Wherein K is sampling number, Y ^h(k) represent the conjugate transpose of Y (k).

Step 5, to autocorrelation matrix R _ycarry out feature decomposition, obtain noise subspace

To autocorrelation matrix R _ycarry out feature decomposition, obtain series of features value λ _mand characteristic of correspondence vector e _m(m=1,2 ..., Q), by eigenvalue λ _mλ from big to small sorts ₁>=λ ₂>=...>=λ _q, e ₁..., e _qfor character pair vector, choose P large eigenvalue λ ₁..., λ _p, P is target number, gets these eigenwert characteristic of correspondence vectors e ₁, e ₂..., e _pform signal subspace

${\hat{E}}_s=[{\mathrm{<figure-callout\; id="1"\; label="e"\; filenames="HDA0000460663590000031.png"\; state="\{\{state\}\}">e</figure-callout>}}_1,{\mathrm{<figure-callout\; id="2"\; label="e"\; filenames="HDA0000460663590000022.png,HDA0000460663590000031.png"\; state="\{\{state\}\}">e</figure-callout>}}_2\&CenterDot;\&CenterDot;\&CenterDot;,e_P]$

Noise subspace

meet:

${\hat{E}}_n{\hat{E}}_n^H=I-{\hat{E}}_s{\hat{E}}_s^H$

Wherein, I is that dimension is the unit matrix of Q.

Step 6, utilizes noise subspace

form MUSIC space zero spectral function:

$f\left(\mathrm{\&theta;}\right)={\left|\right|{{\hat{E}}_n}^{H}C\left(\mathrm{\&theta;}\right)\left|\right|}^2=C^H\left(\mathrm{\&theta;}\right){\hat{E}}_n{{\hat{E}}_n}^{H}C\left(\mathrm{\&theta;}\right)$

Wherein || || ²represent 2-norm,

representing matrix

conjugate transpose.

Step 7, makes z=e ^{j θ}, f (θ) can be converted into:

$f\left(z\right)=C^H\left(z\right){\hat{E}}_n{{\hat{E}}_n}^{H}C\left(z\right)$

Make f (z)=0, P the azimuthal complex exponential form z that adopts the method for polynomial rooting to try to achieve to approach most unit circle and amplitude to be less than 1 _p(p=1,2 ... P).

Step 8, utilizes the complex exponential form z of acceptance angle _p, try to achieve the azimuth angle theta of p target _p;

θ _p=angle(z _p)

Wherein, angle () represents to ask phasing degree;

p=1,2…P

Obtain the position angle of P target, complete the estimation of the direction of arrival of MIMO radar coherent source.

Effect of the present invention further illustrates by following l-G simulation test.

(1) simulated conditions:

Derivation step according to the present invention can find out, this method does not have the restriction of array manifold, is applicable to any array manifold.Without loss of generality, suppose that MIMO radar array is Homogeneous Circular array, the wavelength that transmits is 0.75m, array number is 10, array radius is 0.45m, the form that transmits is the phase-coded signal with carrier frequency quadrature, if there are two coherent signal sources, the position angle of signal source 1 is 22 °, and the position angle of signal source 2 is 45 °, received pulse repetition period number is 100, signal to noise ratio snr=20dB, Fan Demeng steering vector dimension M=11, space smoothing submatrix length is Q=9, carry out 100 independently Monte Carlo experiments, the square error of signal source p is calculated and is adopted formula

wherein

for the azimuthal estimated value of signal source p, θ _pposition angle for signal source p.

(2) emulation content:

Emulation 1, adopts the present invention to carry out target localization emulation to target azimuth angle, to 100 independent the simulation experiment result of target as shown in Figure 2.As can be seen from Figure 2, adopting the present invention to realize estimates the quick direction of arrival of single base MIMO radar of any array manifold.

Emulation 2, while adopting the present invention to signal source 1 location, the simulation result that angle on target square error changes with signal to noise ratio snr is as shown in Figure 3;

Emulation 3, while adopting the present invention to signal source 2 location, the simulation result that angle on target square error changes with signal to noise ratio snr as shown in Figure 4.

From Fig. 3 and Fig. 4, can find out, the square error that angle on target is estimated increases and reduces with signal to noise ratio snr, and the signal to noise ratio (S/N ratio) square error that angle on target is estimated while being 5dB just can reach below 0.1 °, and positioning precision is high, shows that the present invention is practicable.

In sum, the present invention can realize the estimation to single base multiple-input and multiple-output (MIMO) radar coherent source direction of arrival of any array manifold, and positioning precision is high.

Obviously, those skilled in the art can carry out various changes and modification and not depart from the spirit and scope of the present invention the present invention.Like this, if within modification of the present invention and modification are belonged to the scope of the claims in the present invention and equivalent technologies thereof, the present invention be also intended to comprise these change and modification interior.

Claims (4)

1. single base MIMO radar coherent source Wave arrival direction estimating method, is characterized in that, comprises the following steps:

Step 1, according to the array manifold of single base MIMO radar, obtains this array steering vector A (θ), and wherein, this array has N array element, and the polar coordinates of each array element are (r _n, β _n), n=1,2 ... N, N is array number;

Step 2, arranges M Wei Fandemeng vector B (θ), according to formula G=B (θ) A ^h(θ) [A (θ) A ^h(θ)] ^-1try to achieve transition matrix G; Wherein, order

select model moral mentor to the dimension M ≈ 4kR of vector B (θ), k=2 π/λ, λ is the wavelength that transmits;

Step 3, carries out similar spaces smoothing processing to model moral mentor to vector B (θ), and wherein F is smooth transformation matrix, steering vector C (the θ)=FB (θ) after level and smooth;

Step 4, reception data to MIMO radar are carried out matched filtering, reception data after matched filtering are designated as X (k), by transition matrix G and level and smooth transformation matrix F, data matrix Y (k)=FGX (k) after must converting, recycling data matrix Y (k) forms autocorrelation matrix R _y;

Step 5, to autocorrelation matrix R _ycarry out feature decomposition, obtain noise subspace

Step 6, utilizes noise subspace

form MUSIC space zero spectral function:

$f\left(\mathrm{\&theta;}\right)={\left|\right|{{\hat{E}}_n}^{H}C\left(\mathrm{\&theta;}\right)\left|\right|}^2=C^H\left(\mathrm{\&theta;}\right){\hat{E}}_n{{\hat{E}}_n}^{H}C\left(\mathrm{\&theta;}\right)$

Wherein || || ²represent 2-norm,

representing matrix

conjugate transpose;

Step 7, makes z=e ^{j θ}, f (θ) can be converted into:

$f\left(z\right)=C^H\left(z\right){\hat{E}}_n{{\hat{E}}_n}^{H}C\left(z\right)$

Make f (z)=0, P the azimuthal complex exponential form z that adopts the method for polynomial rooting to try to achieve to approach most unit circle and amplitude to be less than 1 _p(p=1,2 ... P); Wherein, P is the target number in same range gate, θ _pit is the position angle of p target;

Step 8, utilizes the complex exponential form z of acceptance angle _p, try to achieve the azimuth angle theta of p target _p:

θ _p=angle(z _p)

Wherein, angle () represents to ask phasing degree;

p=1,2…P

Obtain the position angle of P target, complete the estimation of the direction of arrival of MIMO radar coherent source.

2. single base according to claim 1 MIMO radar coherent source Wave arrival direction estimating method, is characterized in that,

M Wei Fandemeng vector B (θ) and transformation matrix G in step 2 try to achieve as follows:

First, order

r _nbe n array element apart from the distance of true origin, n=1,2 ... N (N is element number of array), the dimension M ≈ 4kR of selection Fan Demeng vector B (θ), k=2 π/λ, λ is the wavelength that transmits;

Ignore truncation error, Fan Demeng vector B (θ) is:

$B\left(\mathrm{\&theta;}\right)={[e^{\frac{-j(M-1)\mathrm{\&theta;}}{2}},\&CenterDot;\&CenterDot;\&CenterDot;,e^{\frac{j(M-1)\mathrm{\&theta;}}{2}}]}^T$

Wherein, [] ^trepresenting matrix transposition, j represents imaginary number.

Secondly, equally spacedly in observation scope get J angle, that is: θ ₁, θ ₂..., θ _j; According to θ ₁, θ ₂..., θ _j, form respectively guiding matrix

with Fan Demeng matrix

$\tilde{A}=[A\left({\mathrm{\&theta;}}_1\right),A\left({\mathrm{\&theta;}}_2\right),\&CenterDot;\&CenterDot;\&CenterDot;,A\left({\mathrm{\&theta;}}_J\right)]$

$\tilde{B}=[B\left({\mathrm{\&theta;}}_1\right),B\left({\mathrm{\&theta;}}_2\right),\&CenterDot;\&CenterDot;\&CenterDot;,B\left({\mathrm{\&theta;}}_J\right)]$

According to guiding matrix

with Fan Demeng matrix utilize least square method to obtain transition matrix G:

$G=\tilde{A}{\tilde{B}}^H{\left(\tilde{B}{\tilde{B}}^H\right)}^{-1}$

Wherein,

representing matrix conjugate transpose, () ^-1representing matrix is inverted.

3. single base according to claim 1 MIMO radar coherent source Wave arrival direction estimating method, is characterized in that, in step 3, smooth transformation matrix F is tried to achieve as follows:

First, model moral mentor is divided into an overlapped L submatrix to vector B (θ) (being equivalent to even linear array), each submatrix dimension is Q=M-L+1; Wherein, M is the dimension of B (θ);

Secondly, according to Q structure smooth transformation matrix: F _l=[0 _{q * (l-1)}| I _q| 0 _{q * (L-l)}], wherein, l=1,2 ... L, 0 _{q * (l-1)}represent rank zero battle array of Q * (l-1), I _qrepresent Q rank unit matrix, 0 _{q * (L-l)}represent rank zero battle array of Q * (L-l);

Finally, smooth transformation matrix F can be obtained by following formula:

$F=\frac{1}{L}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}{F}_l$

4. single base according to claim 1 MIMO radar coherent source Wave arrival direction estimating method, is characterized in that, the concrete sub-step of step 4 is as follows:

4a) the reception data of radar are carried out to matched filtering

The radar cross section RCS that supposes each target is identical, receives signal to be:

$X_r=\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}A\left({\mathrm{\&theta;}}_p\right){\mathrm{Se}}^{j2\mathrm{\&pi;}{f}_{\mathrm{dp}}t}+V$

Wherein, P is the target number in same range gate, θ _pbe the position angle of p target, f _dpbe p target Doppler frequency (p=1,2 ... P), V is the reception noise matrix of MIMO radar array.

Reception data to MIMO radar array are carried out matched filtering, and the reception data after matched filtering are designated as X (k);

X(k)=E(SX _r)

Wherein, E () represents mathematical expectation, S=[s ₁ ^t... s _i ^t, s _n ^t] ^texpression is by N matrix that transmits and form, s _irepresent that i transmits,

represent s _itransposition (i=1 ... N);

4b) the data matrix Y (k) after being converted by transition matrix G and level and smooth transformation matrix F

Y(k)=FGX(k)

4c) the data matrix Y (k) after recycling conversion forms autocorrelation matrix R _y

$R_y=\underset{k=1}{\overset{K}{\mathrm{\&Sigma;}}}Y\left(k\right)Y^H\left(k\right)$

Wherein K is sampling number, Y ^h(k) represent the conjugate transpose of Y (k).

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