CN103439692B - STAP method based on wide symmetrical characteristic of covariance matrix - Google Patents

Abstract

The invention discloses an STAP method based on a wide symmetrical characteristic of a covariance matrix. The method comprises the steps that (1) space-time two-dimensional echo data are received; (2) Doppler filtering processing is carried out; (3) wide symmetrical training samples are acquired; (4) a wide symmetrical covariance matrix is estimated; (5) a self-adaption weight vector is calculated; (6) self-adaption filtering processing is carried out; (7) a result is output. The method mainly solves the problem that the covariance matrix is inaccurately estimated due to the fact that the training samples meeting independent identically distributed conditions are insufficient when an airborne radar is in a heterogeneous clutter environment. The method is based on the wide symmetrical characteristic of the covariance matrix and can effectively improve the use ratio of the echo data, the clutter covariance matrix is estimated more accurately under the condition of few independent identically distributed training samples, and the better clutter retraining and target detection effect is obtained, and the method has better application prospects in the actual extremely-heterogeneous clutter environment.

Description

Based on the STAP method of the wide symmetry characteristic of covariance matrix

Technical field

The invention belongs to communication technical field, self-adaptive processing (space-time adaptive processing, STAP) method when further relating to a kind of airborne radar space based on the wide symmetry characteristic of covariance matrix in Radar Technology field.The present invention is mainly used in solving airborne radar in non-homogeneous clutter environment, owing to meeting the lack of training samples of independent same distribution condition and the inaccurate problem of covariance matrix caused, effectively can increase training sample, improve the clutter recognition performance of Adaptive Signal Processing, improve the detection probability of target.

Background technology

The main task of airborne early warn ing radar is the detection of a target position tracking to it in complex clutter background, and carries out effectively suppressing being the core means improving early warning radar serviceability to clutter.Space-time adaptive treatment S TAP technology makes full use of spatial domain and time-domain information, while carrying out coherent accumulation to echo signal, by space-time adaptive process filtering ground clutter, realizes the effective detection of airborne radar to target.E2-D airborne early warn ing radar as the U.S. just adopts this technology.In actual applications, mainly there are following two aspect problems in STAP processor: first, in clutter environment heterogeneous, obtain the abundant independent same distribution for estimate covariance matrix (independent and identically distributed, IID) training sample very difficult; Secondly, even if the demand of training sample is met, the excessive problem of full space time processing calculated amount can cause real-time to be difficult to ensure.For solving the problem, promoting STAP technology more practical, there has been proposed many innovative approachs or method.

The patent of invention " space-time adaptive processing method under non-homogeneous clutter environment " (number of patent application 201010129723.3, publication No. CN101819269A) of Tsing-Hua University's application discloses a kind of overcomplete sparse representation method of super-resolution estimation clutter space-time two-dimensional spectrum in non-homogeneous clutter environment.The method achieve when independent same distribution sample number deficiency, utilize single frames training sample to estimate clutter covariance matrix, thus avoid strong non-homogeneous clutter environment on the impact of self-adaptive processing effect.But, the main deficiency that the method still exists is: super complete radix order clutter spectrum being carried out to rarefaction representation is uncertain, but much larger than degree of freedom in system, and degree of freedom in system is usually thousands of in reality, operand required in the covariance matrix restructuring procedure of each range unit sample is like this very large, be unfavorable for real-time process, thus have influence on its practical engineering application effect.

The patent of invention " a kind of dimensionality reduction space-time adaptive processing method based on Covariance Matrix Weighting " (number of patent application 201210251589.3, publication No. CN102778669A) of Beijing Institute of Technology's application discloses a kind of method utilizing Covariance Matrix Weighting technology to estimate clutter covariance matrix.The method achieve broadening clutter recess adaptively and, to adapt to the clutter ridge in actual environment, thus make to exist clutter when revealing, also by STAP method clutter reduction effectively, improve STAP robustness in actual applications.But, the deficiency that the method still exists is: the broadening degree of clutter recess is artificial setting, can not clutter ridge situation in perception real data adaptively, when broadening amount is excessive, Minimum detectable can be caused to become large, very unfavorable to the detection of low speed Small object.

Summary of the invention

The present invention is directed to the deficiency of above-mentioned existing STAP technology, a kind of self-adaptive processing (space-time adaptive processing, STAP) method when proposing airborne radar space based on the wide symmetry characteristic of covariance matrix.The present invention effectively increases independent same distribution training sample by improving data separate efficiency, thus obtains the true clutter situation in real data, improves the accuracy that clutter covariance matrix is estimated, improves clutter recognition performance, improve the detection probability of moving-target.

For achieving the above object, the concrete steps of the present invention's realization are as follows:

(1) space-time two-dimensional echo data is received:

Utilize multiple array elements of airborne radar antenna, within the coherent accumulation time, receive the space-time two-dimensional echo data of ground return.

(2) doppler filtering process:

According to the following formula, utilize the dimensionality reduction transition matrix in spreading factor algorithm EFA, by the space-time two-dimensional echo data that airborne radar receives, be transformed into array element-Doppler domain from array element-pulse domain, obtain the raw radar data of pending Doppler's passage:

$x=T_{\mathrm{EFA}}\tilde{x}$

Wherein, x represents the raw radar data of pending Doppler's passage, T _eFArepresent the dimensionality reduction transition matrix in spreading factor algorithm EFA, represent space-time two-dimensional echo data.

(3) wide symmetrical training sample is obtained:

3a) adopt spatial domain transition matrix, spatial domain conversion is carried out to the raw radar data of pending Doppler's passage, obtains spatial domain translation data;

3b) adopt time domain transition matrix, time domain conversion is carried out to the raw radar data of pending Doppler's passage, obtains time domain translation data;

3c) adopt Space-time domain transition matrix, Space-time domain conversion is carried out to the raw radar data of pending Doppler's passage, obtains Space-time domain translation data.

(4) wide symmetrical covariance matrix is estimated:

4a) utilize maximum likelihood method, estimate original covariance matrix, spatial domain covariance matrix, time domain covariance matrix and Space-time domain covariance matrix that the raw radar data of pending Doppler's passage, spatial domain translation data, time domain translation data and Space-time domain translation data are corresponding respectively;

4b) above-mentioned four covariance matrixes are averaged, the result after being averaged is defined as wide symmetrical covariance matrix.

(5) self-adaptation weight vector is obtained:

According to self-adaptation weight vector solution formula, replace the original covariance matrix in conventional Extension factorization algorithm EFA by wide symmetrical covariance matrix, obtain self-adaptation weight vector.

(6) auto adapted filtering process:

Utilize self-adaptation weight vector, successively the raw radar data of pending Doppler's passage is distinguished according to range unit, carry out space-time adaptive filtering.

(7) Output rusults:

Filter result later for auto adapted filtering process is exported.

Compared with prior art, the present invention has the following advantages:

First, the present invention is based on the wide symmetry characteristic of covariance matrix, respectively spatial transform is carried out to Doppler domain raw radar data, time domain converts, Space-time domain converts, effectively improve prior art STAP method, clutter covariance matrix caused by available independent same distribution number of training deficiency estimates inaccurate problem, the present invention can be excavated more fully and use the clutter information in limited training sample, improve the utilization factor of echo data, while acquisition clutter distribution statistics information, the sample heterogeneity that the distance dependencies that distributed by clutter brings can be alleviated again to a great extent, in clutter extremely environment heterogeneous, there is better application prospect.

The second, the present invention utilizes the dimensionality reduction transition matrix in spreading factor algorithm EFA, carries out dimension-reduction treatment while carrying out doppler filtering process to the space-time two-dimensional echo data of airborne radar reception; Estimate that wide symmetrical covariance matrix adopts original covariance matrix, spatial domain covariance matrix, time domain covariance matrix, Space-time domain covariance matrix to be averaged, effectively overcome the STAP method of prior art, the excessive problem increased with equipment cost of the calculated amount caused due to the large degree of freedom of radar system, make the present invention while effectively increasing training sample, also can not bring too much computational complexity and structure complexity.

Accompanying drawing explanation

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is the range Doppler figure after prior art PD process and process of the present invention;

Fig. 3 is the improvement factor comparison diagram after prior art EFA and process of the present invention;

Fig. 4 is the detection probability comparison diagram after prior art EFA and process of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the invention will be further described.

With reference to Fig. 1, specific embodiment of the invention step is as follows:

Step 1, receives space-time two-dimensional echo data.

Utilize multiple array elements of airborne radar antenna, within the coherent accumulation time, receive the space-time two-dimensional echo data of ground return .

Step 2, doppler filtering process.

According to the following formula, utilize the dimensionality reduction transition matrix in spreading factor algorithm EFA, by the space-time two-dimensional echo data that airborne radar receives, be transformed into array element-Doppler domain from array element-pulse domain, obtain the raw radar data of pending Doppler's passage:

$x=T_{\mathrm{EFA}}\tilde{x}$

Wherein, x represents the raw radar data of pending Doppler's passage, T _eFArepresent the dimensionality reduction transition matrix in spreading factor algorithm EFA, represent space-time two-dimensional echo data;

Dimensionality reduction transition matrix T in spreading factor algorithm EFA _eFAobtained by following formula:

$T_{\mathrm{EFA}}=F_{\mathrm{EFA}}\⊗I_N$

Wherein, T _eFArepresent EFA dimensionality reduction transition matrix, F _eFArepresent the EFA Fourier transform matrix EFA Fourier transform matrix of pending Doppler's passage, I _nrepresent that the N in dimensionality reduction transition matrix ties up unit matrix, N represents the element number of array of airborne radar antenna.

The EFA Fourier transform matrix F of pending Doppler's passage _eFAobtained by following formula:

$F_{\mathrm{EFA}}=\left[\begin{array}{cccc}1& e^{-j2\mathrm{\π}{f}_{-1}}& ...& e^{-j2\mathrm{\π}{f}_{-1}(M-1)}\\ 1& e^{-j2\mathrm{\π}{f}_0}& ...& e^{-j2\mathrm{\π}{f}_0(M-1)}\\ 1& e^{-j2\mathrm{\π}{f}_1}& ...& e^{-j2\mathrm{\π}{f}_1(M-1)}\end{array}\right]$

Wherein, F _eFArepresent Fourier transform matrix, EFA represents that this matrix is the Fourier transform matrix in EFA algorithm, f _-1, f ₀, f ₁represent with pending Doppler f ₀centered by three adjacent normalization Doppler frequencies, M represents airborne radar transponder pulse number.

Step 3, obtains wide symmetrical training sample.

Adopt spatial domain transition matrix, spatial domain conversion carried out to the raw radar data of pending Doppler's passage, obtains spatial domain translation data:

$x_s=(I_3\⊗J)\·{\left(x\right)}^{*}$

Wherein, x _srepresent spatial domain translation data, s represents spatial domain symbol, represent spatial domain transition matrix, I ₃represent 3 dimension unit matrixs in the transition matrix of spatial domain, represent that Kronecker amasss sign of operation, J represents that the N in the transition matrix of spatial domain ties up permutation matrix, and N represents the element number of array of airborne radar antenna, and the raw radar data of the pending Doppler's passage of x, * represents conjugate operation symbol.

Adopt time domain transition matrix, time domain conversion carried out to the raw radar data of pending Doppler's passage, obtains time domain translation data:

$x_t=\left(U{\⊗I}_N\right)\·x$

Wherein, x _trepresent time domain translation data, t represents time-domain symbol, represent time domain transition matrix, U represents 3 dimension diagonal matrix in time domain transition matrix, I _nrepresent that the N in time domain transition matrix ties up unit matrix, N represents the element number of array of airborne radar antenna, and x represents the raw radar data of pending Doppler's passage.

Adopt Space-time domain transition matrix, Space-time domain conversion carried out to the raw radar data of pending Doppler's passage, obtains Space-time domain translation data:

$x_{\mathrm{st}}=(V\⊗J)\·{\left(x\right)}^{*}$

Wherein, x _strepresent Space-time domain translation data, st represents Space-time domain symbol, represent Space-time domain transition matrix, V represents 3 dimension diagonal matrix in Space-time domain transition matrix, and J represents that the N in the transition matrix of spatial domain ties up permutation matrix, and N represents the element number of array of airborne radar antenna, and x represents the raw radar data of pending Doppler's passage.

Step 4, estimates wide symmetrical covariance matrix.

Utilize the raw radar data of pending Doppler's passage to make training sample, estimate to obtain original covariance matrix by maximum likelihood method:

$R=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{x}_i{x_i}^H$

Wherein, R represents original covariance matrix, and L represents the length of the raw radar data of pending Doppler's passage, x _irepresent the raw radar data of pending Doppler's passage, i represents data x _icall number, H represents conjugate transpose;

Utilize spatial domain translation data to make training sample, estimate to obtain spatial domain covariance matrix by maximum likelihood method:

$R_s=\frac{1}{L_s}\underset{i=1}{\overset{L_s}{\mathrm{\Σ}}}{x}_{s,t}{x_{s,i}}^H$

Wherein, R _srepresent spatial domain covariance matrix, L _srepresent the length of spatial domain translation data, x _s,irepresent spatial domain translation data, s, i represent spatial domain and data directory number respectively;

Utilize time domain translation data to make training sample, estimate to obtain time domain covariance matrix by maximum likelihood method:

$R_t=\frac{1}{L_t}\underset{i=1}{\overset{L_t}{\mathrm{\Σ}}}{x}_{t,i}{x_{t,i}}^H$

Wherein, R _trepresent time domain covariance matrix, L _trepresent the length of time domain translation data, x _t,irepresent time domain translation data, t, i represent time domain and data directory number respectively;

Utilize Space-time domain translation data to make training sample, estimate to obtain Space-time domain covariance matrix by maximum likelihood method:

$R_{\mathrm{st}}=\frac{1}{L_{\mathrm{st}}}\underset{i=1}{\overset{L_{\mathrm{st}}}{\mathrm{\Σ}}}{x}_{\mathrm{st},i}{x_{\mathrm{st},i}}^H$

Wherein, R _strepresent Space-time domain covariance matrix, L _strepresent the length of Space-time domain translation data, x _{st, i}represent Space-time domain translation data, st, i represent Space-time domain and data directory number respectively;

Arithmetic mean is got to above-mentioned four covariance matrixes, the result after being averaged is defined as wide symmetrical covariance matrix:

$R_{\mathrm{Per}}=\frac{1}{4}(R+R_s+R_t+R_{\mathrm{st}})$

Wherein, R _perrepresent wide symmetrical covariance matrix, Per represents wide symmetry.

Step 5, obtains self-adaptation weight vector.

$W=\mathrm{\μ}{R}_{\mathrm{Per}}^{-1}S$

Wherein, W represents self-adaptation weight vector, and μ represents the constant set by radar system parameters, and S represents the goal orientation vector after dimensionality reduction, and the expression formula of S is: t _eFArepresent the dimensionality reduction transition matrix in spreading factor algorithm EFA, s _trepresent the time domain steering vector of target, s _texpression formula be: represent the time domain steering vector of target, t represents time-domain symbol, s _srepresent the spatial domain steering vector of target, s _sexpression formula be: s represents spatial domain symbol, f _d0represent normalization Doppler frequency, d0 represents that Doppler frequency is numbered, f _srepresent normalization spatial frequency, N represents airborne radar antenna element number of array, and M represents radar transmitted pulse number, and T represents transpose operation symbol.

Step 6, auto adapted filtering process.

Utilize self-adaptation weight vector W, successively each range unit raw radar data x of pending Doppler's passage is distinguished according to range unit, carry out space-time adaptive filtering.

Step 7, Output rusults.

Filter result later for auto adapted filtering process is exported.

Below in conjunction with accompanying drawing, effect of the present invention is described further.

1, simulated conditions:

Emulation experiment of the present invention is carried out under MATLAB7.11 software.In emulation experiment of the present invention, in order to simulate the sight of lack of training samples in non-homogeneous clutter environment truly, airborne radar adopts non-working side array antenna, the linear array that the antenna of airborne radar adopts 10 array element evenly distributed, and array element distance is half wavelength.In emulation experiment of the present invention, the echo data of use is that the clutter model simulation proposed according to Lincoln laboratory J.Ward produces, and detailed systematic parameter is with reference to following table.

With reference to accompanying drawing 2, to the residue situation of clutter after the airborne radar data adopting the present invention and prior art PD process.

Accompanying drawing 2 is the range Doppler figure after prior art PD process and process of the present invention.Accompanying drawing 2(a) be the range Doppler figure after prior art PD process, accompanying drawing 2(b) be the range Doppler figure after process of the present invention.Accompanying drawing 2(a) and accompanying drawing 2(b) transverse axis represent Doppler's channel position, the longitudinal axis represents range gate sequence number, accompanying drawing 2(a) and accompanying drawing 2(b) in white portion be clutter afterpower distribution after prior art PD process, black region is that noise afterpower after prior art PD process distributes.From accompanying drawing 2(a) can find out that stronger residual spur occupies more distance-Doppler unit, the direct detection affecting target in these regions, from accompanying drawing 2(b) can find out that white portion greatly reduces, show that the clutter component in echo data obtains fine suppression.In sum, the clutter of the airborne radar data of process of the present invention compared with prior art PD process remains and obviously weakens, and performance obviously improves.

The radar clutter improvement factor situation after prior art EFA and process of the present invention is compared with reference to accompanying drawing 3.

Accompanying drawing 3 is prior art EFA and improvement factor comparison diagram of the present invention, selected by the data area that compares be 300-350 range gate, degree of freedom in system is 30.The transverse axis of accompanying drawing 3 represents Doppler's channel position, the longitudinal axis represents improvement factor, the optimal processing result that what black matrix solid line represented is as comparing reference, real astragal and empty astragal represent respectively prior art EFA algorithm use 64 and 32 training samples under average improvement factor curve, solid line, dotted line and dotted line represent respectively the present invention use 64,32 and 8 training samples under average improvement factor curve.As can be seen from accompanying drawing 3, when sample number is more, when being greater than twice degree of freedom in system, result of the present invention is better than EFA, closer to optimal processing result; Basic and the curve co-insides of EFA in twice number of degrees of freedom sample situation of the improvement factor curve of the present invention when use one times of number of degrees of freedom sample, and the clutter recognition effect that the present invention only uses 8 training samples can reach EFA to use 32 samples to reach.This simulation result can illustrate, the present invention can improve Sample utilization efficiency, increases effective IID training sample, thus it is more accurate that covariance is estimated, obtains better clutter recognition effect.

The radar clutter detection probability situation after prior art EFA and process of the present invention is compared with reference to accompanying drawing 4.

Accompanying drawing 4 is the detection probability comparison diagrams after prior art EFA and process of the present invention, selected by the data area that compares be 161-360 range gate, 40-64 Doppler passage, degree of freedom in system is 30, and false alarm rate is set to 1%.The transverse axis of accompanying drawing 4 represents Doppler's channel position, the longitudinal axis represents detection probability, real astragal and empty astragal represent respectively prior art EFA algorithm use 60 and 30 training samples under detection probability curve, in figure, solid line and dotted line represent detection probability curve of the present invention under use 60 and 30 training samples respectively.As can be seen from accompanying drawing 4, when training sample is sufficient, i.e. during the twice of degree of freedom in system, compared to EFA process, the inventive method is had an appointment the performance improvement of 2dB; And when sample number reduces to one times of degree of freedom in system, the present invention can be better than EFA and be about 15dB.This simulation result shows, the present invention in less available training sample situation, in such as extreme non-homogeneous environment, can obtain better target detection effect.

Claims (6)

1., based on a STAP method for the wide symmetry characteristic of covariance matrix, comprise the following steps:

(1) space-time two-dimensional echo data is received:

Utilize multiple array elements of airborne radar antenna, within the coherent accumulation time, receive the space-time two-dimensional echo data of ground return;

(2) doppler filtering process:

According to the following formula, utilize the dimensionality reduction transition matrix in spreading factor algorithm EFA, by the space-time two-dimensional echo data that airborne radar receives, be transformed into array element-Doppler domain from array element-pulse domain, obtain the raw radar data of pending Doppler's passage:

$x=T_{\mathrm{EFA}}\tilde{x}$

Wherein, x represents the raw radar data of pending Doppler's passage, T _eFArepresent the dimensionality reduction transition matrix in spreading factor algorithm EFA, represent space-time two-dimensional echo data;

(3) wide symmetrical training sample is obtained:

3a) adopt spatial domain transition matrix, spatial domain conversion is carried out to the raw radar data of pending Doppler's passage, obtains spatial domain translation data;

3b) adopt time domain transition matrix, time domain conversion is carried out to the raw radar data of pending Doppler's passage, obtains time domain translation data;

3c) adopt Space-time domain transition matrix, Space-time domain conversion is carried out to the raw radar data of pending Doppler's passage, obtains Space-time domain translation data;

(4) wide symmetrical covariance matrix is estimated:

4a) utilize maximum likelihood method, estimate original covariance matrix, spatial domain covariance matrix, time domain covariance matrix and Space-time domain covariance matrix that the raw radar data of pending Doppler's passage, spatial domain translation data, time domain translation data and Space-time domain translation data are corresponding respectively;

4b) above-mentioned four covariance matrixes are averaged, the result after being averaged is defined as wide symmetrical covariance matrix;

(5) self-adaptation weight vector is obtained:

According to self-adaptation weight vector solution formula, replace the original covariance matrix in conventional Extension factorization algorithm EFA by wide symmetrical covariance matrix, obtain self-adaptation weight vector;

(6) auto adapted filtering process:

Utilize self-adaptation weight vector, successively respectively space-time adaptive filtering is carried out according to range unit to the raw radar data of pending Doppler's passage;

(7) Output rusults:

Filter result later for auto adapted filtering process is exported.

2. the STAP method based on the wide symmetry characteristic of covariance matrix according to claim 1, is characterized in that, step 3a) described in spatial domain conversion carry out according to the following formula:

$x_s=(I_3\⊗J)\·{\left(x\right)}^{*}$

Wherein, x _srepresent spatial domain translation data, s represents spatial domain symbol, represent spatial domain transition matrix, I ₃represent 3 dimension unit matrixs in the transition matrix of spatial domain, represent that Kronecker amasss sign of operation, J represents that the N in the transition matrix of spatial domain ties up permutation matrix, N represents the element number of array of airborne radar antenna, in permutation matrix, back-diagonal element is 1, all the other elements are zero, x represents the raw radar data of pending Doppler's passage, and * represents conjugate operation symbol.

3. the STAP method based on the wide symmetry characteristic of covariance matrix according to claim 1, is characterized in that, step 3b) described in time domain conversion carry out according to the following formula:

$x_t=(U\⊗I_N)\·x$

Wherein, x _trepresent time domain translation data, t represents time-domain symbol, represent time domain transition matrix, U represents 3 dimension diagonal matrix in time domain transition matrix, I _nrepresent that the N in time domain transition matrix ties up unit matrix, N represents the element number of array of airborne radar antenna, and x represents the raw radar data of pending Doppler's passage.

4. the STAP method based on the wide symmetry characteristic of covariance matrix according to claim 1, is characterized in that, step 3c) described in Space-time domain conversion carry out according to the following formula:

$x_{\mathrm{st}}=(V\⊗J)\·{\left(x\right)}^{*}$

Wherein, x _strepresent Space-time domain translation data, st represents Space-time domain symbol, represent Space-time domain transition matrix, V represents 3 dimension diagonal matrix in Space-time domain transition matrix, and J represents that the N in Space-time domain transition matrix ties up permutation matrix, and N represents the element number of array of airborne radar antenna, and x represents the raw radar data of pending Doppler's passage.

5. the STAP method based on the wide symmetry characteristic of covariance matrix according to claim 1, it is characterized in that, the formula that described in step (4), original covariance matrix, spatial domain covariance matrix, time domain covariance matrix and Space-time domain covariance matrix adopt identical maximum likelihood method to carry out estimating is as follows:

$R=\frac{1}{L}\underset{i=1}{\overset{L}{\mathrm{\Σ}}}{x}_i{x_i}^H$

Wherein, R represents one of them of original covariance matrix, spatial domain covariance matrix, time domain covariance matrix and Space-time domain covariance matrix, x _irepresent one of them of the raw radar data of pending Doppler's passage, spatial domain translation data, time domain translation data and Space-time domain translation data, i represents data x _icall number, L represents data x _ilength, H represents conjugate transpose operation symbol.

6. the STAP method based on the wide symmetry characteristic of covariance matrix according to claim 1, is characterized in that, the self-adaptation weight vector solution formula described in step (5) is as follows:

$W={\mathrm{\μR}}_{\mathrm{Per}}^{-1}S$

Wherein, W represents self-adaptation weight vector, and μ represents the constant set by radar system parameters, R _perrepresent wide symmetrical covariance matrix, per represents wide symmetry, and S represents the goal orientation vector after dimensionality reduction, and its expression formula is t _eFArepresent the dimensionality reduction transition matrix in spreading factor algorithm EFA, s _trepresent target time domain steering vector, t represents time-domain symbol, s _srepresent target spatial domain steering vector, s represents spatial domain symbol, represent that Kronecker amasss sign of operation.