CN105487052A - Compressed sensing LASAR sparse linear array optimization method based on low coherence - Google Patents

Abstract

The invention discloses a low-coherence-based compression sensing LASAR sparse line array optimization method, which uses the coherence characteristics of the measurement matrix in the compressed sensing theory as a reference basis for compressive sensing LASAR sparse line array optimization, and is based on the compressed sensing method in the LASAR system. The minimization of the coherence of the perceptual measurement matrix, with the help of the Fourier transform iterative search method, realizes the optimal design of the array element distribution of the compressed sensing LASAR sparse wiring array antenna, which is more reasonable for the sparse linear array optimization and is conducive to improving the compressed sensing LASAR System imaging performance. The method proposed by the invention is also applicable to other technical fields of sparse wiring array antenna optimization based on compressed sensing.

Description

Optimization method of compressed sensing LASAR sparse array based on low coherence

Technical field:

The technical invention belongs to the technical field of radar, and in particular relates to the technical fields of synthetic aperture radar (SAR) imaging technology and array antenna design.

Background technique:

Due to its advantages of all-day, all-weather and large-scale scene observation, synthetic aperture radar (SAR) has become an important remote sensing technology for large-area topographic surveying and mapping. greater effect. Linear array SAR (LASAR) is an extension of the target dimension space resolution capability of traditional two-dimensional SAR imaging technology, which can obtain three-dimensional radar imaging of the observed target scene, and can more precisely describe the geometric and scattering characteristics of the target in the observed scene, compared with the traditional two-dimensional SAR imaging technology. Two-dimensional SAR has improved the target feature extraction and target recognition capabilities of radar systems, and has become a hot research topic in SAR imaging technology in recent years (see reference "Zhang Qingjuan, Li Daojing, Li Liechen. Sparse array SAR side-view 3D imaging research in continuous scenes. Journal of Electronics and Information, 2013, (5): 1097-1102.”). The basic principle of the LASAR imaging system is to synthesize a large virtual two-dimensional area array antenna through the motion of the linear array antenna to obtain two-dimensional high resolution in the plane of the area array, and then combine pulse compression technology to obtain high resolution in the direction of the radar line of sight, so as to realize Three-dimensional imaging of the observation target scene.

As a newly proposed signal processing theory in recent years, compressed sensing sparse reconstruction breaks through the constraints of the traditional Nyquist sampling theorem, and can accurately reconstruct the original sparse signal with a sampling rate much lower than that of Nyquist (see reference "D.L.Donoho.Compressedsensing .IEEE Transactions on Information Theory, 2006, 52 (4): 1289-1306"), which has great application potential in reducing the sampling rate of radar systems and improving imaging quality. Since most of the targets in the LASAR imaging scene are spatially sparsely distributed, the compressed sensing theory can be combined with the LASAR system to produce a linear array 3D SAR sparse imaging system based on compressed sensing, which realizes the sparse signal downsampling of the LASAR imaging system. and the improvement of three-dimensional imaging accuracy (see reference "S-J.WeiS, X-L.Zhang, J.Shi.LineararraySARimagingviacompressedsensing, ProgressInElectromagneticsResearch, 2011, 117(8):299-319.").

The linear array antenna is a key component of the LASAR imaging system, which provides the third-dimensional imaging resolution capability for the linear array 3D SAR imaging system. However, compared with the single antenna in the traditional SAR system, the multi-array elements of the linear array antenna in the LASAR system also greatly increase the difficulty and cost of hardware system implementation, resulting in excessive LASAR echo data volume, difficulties in data transmission, storage and imaging, etc. question. In order to reduce the cost of LASAR hardware system and data processing, sparse wiring array antennas are usually used in LASAR systems to achieve down-sampled echo data acquisition, but the number of array elements of sparse wiring array antennas does not meet the Nyquist sampling rate of traditional radar systems, resulting in The accuracy and quality of traditional SAR imaging methods have declined. However, for the compressed sensing imaging method, even if the sparse linear array antenna is used, the LASAR sparse imaging system can still guarantee the accuracy and quality of the imaging, and realize high-precision 3D SAR imaging (see reference "Li Xueshi, Sun Guangcai, Xu Gang et al. Based on compression A new method of perception-based three-dimensional SAR imaging. Journal of Electronics and Information Technology, 2012,34(5):1017-1023.”). Since the number and distribution of array elements of the LASAR sparse wiring array antenna directly determine the performance of the compressed sensing imaging method, it is necessary to optimize the distribution of the array elements of the sparse wiring array antenna. However, due to the essential difference between compressed sensing and traditional imaging theory, for the LASAR sparse imaging system based on compressed sensing, the traditional linear array antenna element optimization method cannot be applied to the array element optimization of the sparse wire array antenna in the system.

For the LASAR sparse imaging system based on compressed sensing, the number of array elements does not need to meet the Nyquist sampling rate but is only related to the target sparsity. If the measurement matrix satisfies the Equidistance Constraint Property (RIP), the sparse wiring array antenna can achieve a high accuracy of the sparse target. resolution imaging. However, the RIP calculation of the compressed sensing measurement matrix in the linear array 3D SAR system is a non-deterministic polynomial (NP) problem, so it is difficult to use the RIP of the measurement matrix in the compressed sensing theory as an index to measure the optimization of the LASAR sparse linear array antenna (see References "Li Xiaobo. Research on Measurement Matrix Based on Compressive Sensing. Doctoral Dissertation of Beijing Jiaotong University, 2010."). The compressed sensing theory points out that if the coherence of the measurement matrix is smaller, the probability of the compressed sensing algorithm to accurately reconstruct the target scattering coefficient is higher. Therefore, when the measurement matrix RIP is difficult to calculate, the coherence can be used as a measure of the sparse linear array distribution of LASAR. As an optimization standard, the element distribution design of the sparse wiring array antenna in the LASAR system should minimize the coherence of the compressed sensing measurement matrix in the system as much as possible.

Invention content:

The present invention provides a low-coherence-based optimization method for compressive sensing LASAR sparse array. The method is based on the minimization of the coherence of the compressed sensing measurement matrix in the LASAR system, and realizes the compressed sensing by means of the Fourier transform iterative search method. The optimal design of array element distribution for LASAR sparse line array antenna is more reasonable for sparse line array optimization, which is beneficial to improve the imaging performance of compressed sensing LASAR system. The method proposed by the invention is also applicable to other technical fields of sparse wiring array antenna optimization based on compressed sensing.

In order to describe content of the present invention conveniently, at first do following term definition:

Definition 1, norm

Let X be a number field on linear space, Represents a field of complex numbers, if it satisfies the following properties: ||X||≥0, and ||X||＝0 only X＝0, ||aX||＝|a|||X||, a is arbitrary Constant, ||X ₁ +X ₂ ||≤||X ₁ ||+||X ₂ ||, then ||X|| is called the norm on the X space, and |||| , where X ₁ and X ₂ are any two values in X space. For the N×1-dimensional discrete signal vector X=[x ₁ ,x ₂ ,…,x _N ] ^T in Definition 1, the LP norm expression of the vector X is Where x _i is the i-th element of the vector X, |·| represents the absolute value symbol, Σ|·| represents the absolute value summation symbol, and the expression of the L1 norm of the vector X is The L2 norm expression of vector X is The expression of L0 norm of vector X is And x _i ≠0. For details, see the document "Foreign Electronics and Communication Textbook Series: Signals and Systems (Second Edition)", edited by AlanV.Oppenheim et al., translated by Liu Shutang, and published by Electronic Industry Press.

Definition 2, Nyquist sampling rate

In the conversion process of analog/digital signals, for signals with limited bandwidth, when the sampling frequency is greater than twice the highest frequency of the signal, the digital signal can completely retain and restore the information in the original signal after sampling. This sampling rate is called Nyquist sampling rate. Sampling theorem is also called Nyquist theorem (Nyquist theorem) or Shannon theorem. For details, see the document "Matrix Theory", edited by Huang Tingzhu et al., published by Higher Education Press.

Definition 3. Full line array antenna and sparse line array antenna

When a linear array antenna is used for target detection in a radar system, if the distribution of elements of the linear array antenna satisfies the Nyquist theorem, the linear array antenna is called a full array antenna. The spacing between the elements is 0.5 times of the working wavelength of the radar; if the element distribution of the linear array antenna does not satisfy the Nyquist theorem, the linear array antenna is called a sparse wiring array antenna.

Definition 4. Compressed Sensing

Compressed sensing is mainly a theory of non-adaptive linear projection of high-dimensional original signals to low-dimensional space to maintain the structural information of the signal, and then reconstructing the original signal by solving the linear optimal solution. The theory mainly includes signal sparse representation, sparse measurement and There are three aspects to sparse reconstruction. The basic idea of the compressed sensing sparse reconstruction method is to solve the optimal or suboptimal solution under certain constraints. The main methods include greedy pursuit algorithm and convex relaxation algorithm. For details, please refer to the document "DonohoDL. Compressed sensing. IEEE Transactions on Information Theory, 2006, 52(4): 1289-1306.".

Definition 5. Coherence of compressed sensing measurement matrix

In perception theory, for a measurement system, the coherence of the compressed sensing observation matrix is defined as: Where μ is the coherence coefficient of the measurement system observation matrix, χ _i represents the i-th column of the measurement matrix, χ _j represents the j-th column of the measurement matrix, <·> represents the vector autocorrelation operator, and |·| is the operator symbol for taking the absolute value , ||·|| ₂ is the L2 norm operation symbol, and max is the maximum value operation symbol of the function.

Definition 6. Linear Array SAR (LASAR for short)

Linear array synthetic aperture radar is to fix the linear array antenna on the load motion platform and perpendicular to the motion direction of the platform, combine the motion of the motion platform to synthesize a two-dimensional planar array to realize the two-dimensional imaging of the array plane, and then use the radar beam to echo It is a synthetic aperture radar technology that realizes one-dimensional imaging of range and three-dimensional imaging of observation targets with time delay.

Definition 7. Tangent track direction of linear array synthetic aperture radar

During the line-array SAR observation process, the direction of the line-array SAR platform motion trajectory is perpendicular to and parallel to the arrangement direction of the line-array antenna elements, which is called the tangential direction of the line-array SAR.

Definition 8. Linear array antenna observation space of linear array synthetic aperture radar

During the observation process of linear array synthetic aperture radar, the two-dimensional plane composed of the tangential direction and the vertical direction of the ground surface is called the linear array antenna observation space of linear array synthetic aperture radar.

Definition 9. The excitation vector of the sparse array element in the linear array antenna

The sparse element excitation vector in the linear array antenna is a vector used to characterize the position distribution of the sparse element in the linear array antenna. Assuming that the total number of array elements that can be placed in the linear array antenna is N, the excitation vector of sparse array elements is β=[β ₁ ,…,β _N ], and the dimension of vector β is N, where β ₁ is the first element of vector β element value, β _N represents the value of the Nth element of vector β, and β _k represents the value of the kth element of vector β, when the kth array element in the linear array antenna is selected, β _k = 1, the linear array antenna β _k =0 when k array elements are not selected.

Definition 10. Angular resolution of linear array antenna in linear array synthetic aperture radar

The minimum angle that the linear array antenna can effectively distinguish in the observation space in the linear array synthetic aperture radar is called the angular resolution of the linear array antenna in the linear array synthetic aperture radar system. The angular resolution is related to the radar operating wavelength and the length of the linear array antenna. For details, see Document "Bistatic SAR and Linear Array SAR Principles and Imaging Technology Research", Shi Jun, Ph.D. thesis, University of Electronic Science and Technology of China, 2012.

A kind of compressed sensing LASAR sparse line array optimization method based on low coherence provided by the present invention, it comprises the following steps:

Step 1. Initialize the LASAR system parameters:

Initialize LASAR system parameters include: radar platform height, denoted as H; radar working center frequency, denoted as f _c ; radar carrier frequency wavelength, denoted as λ; radar transmitting baseband signal bandwidth, denoted as B _r ; radar transmitting signal pulse Width, denoted as T _P ; frequency modulation slope of radar transmitting signal, denoted as f _dr ; duration width of radar receiving gate, denoted as T _o ; sampling frequency of radar receiving system, denoted as f _s ; pulse repetition frequency of radar transmitting system , denoted as PRF; the pulse repetition time of the radar system, denoted as PRI; the effective aperture length of the antenna in the azimuth direction, denoted as D _a ; the above parameters are standard parameters of the LASAR system, where the radar platform height H, radar center frequency f _c , radar carrier frequency wavelength λ, radar transmitting baseband signal bandwidth B _r , radar transmitting signal pulse width T _P , radar transmitting signal FM slope f _dr , radar receiving wave gate duration T _o , radar receiving system sampling frequency f _s , the pulse repetition frequency PRF of the radar system, the pulse repetition time PRI of the radar system, and the effective aperture length D _a of the antenna in the azimuth direction have been determined during the LASAR system design and observation process; according to the LASAR imaging system scheme and observation scheme, the LASAR sparse wiring The initialization system parameters required by the array antenna optimization method are all known.

Step 2. Initialize the parameters of the LASAR sparse wiring array antenna:

The parameters for initializing the LASAR sparse wiring array antenna include: the total number of array elements of the full array antenna is denoted as N _A ; the distance between adjacent array elements in the full array antenna is denoted as d, and the value of d in the LASAR system is the system load half of the frequency wavelength, which is Where λ is the radar carrier frequency wavelength obtained by initialization in step 1; the array length of the full-array linear array antenna is denoted as L, and the value of L is L=(N _A -1)d; the array elements in the sparse-array array antenna The total number is denoted as N _S , and N _S <NA; the sparse wiring array antenna elements are _{a subset of the full array antenna elements, that is, the sparse wiring array antenna elements are N A array} elements from the full array antenna N _S array elements are selected in ; the position of the first array element in the full-array linear array antenna in the tangent track-altitude plane is denoted as p ₁ ; the second array element in the full-array linear array antenna is in the tangential track-altitude plane The position in the height plane is denoted as p ₂ ; the position of the N _Ath array element in the tangential track-height plane in the full-array linear array antenna is denoted as The position of the nth array element in the full array array antenna in the tangent track-height plane is denoted as p _n , where the subscript n is the serial number of the nth array element in the full array array antenna, n is a natural number, n= 1,2,...,NA , and p _{n ＝} [(n-1)d,H] ^T , where H is the height of the radar platform initialized in step 1; The set of positions in the track-altitude plane is denoted as P, where the set P is a 2×N _A -dimensional matrix, and $P=\&lsqb;p_1,p_2,\mathrm{...},p_{N_A}\&rsqb;.$

Step 3. Initialize the LASAR linear array antenna observation space parameters:

Initialize the observation space parameters of the linear array SAR array antenna, including: taking the position of the first array element of the full array array antenna as the reference array element, the size of the observation angle interval of the linear array antenna in the tangential track-height plane, denoted as θ ₀ ; the total interval of the observation angle of the LASAR linear array antenna in the tangential track-height plane, denoted as The total number of discretized cells in the total interval of the observation angle of the LASAR linear array antenna in the tangential track-height plane is denoted as M; taking the reference array element of the full-array linear array antenna as the center of the circle, the LASAR linear array antenna in the tangential track-height plane The total range of observation angles in the plane is evenly divided into angular cells of equal size, and the angle value corresponding to each angular cell is smaller than the angular resolution of the LASAR linear array antenna in the tangential track direction; the formula Calculate the position of the mth cell on the ground plane in the LASAR observation angle interval, denoted as q _m , m=1,2,...,M, where m represents the mth angle cell in the LASAR observation angle interval, m is a natural number, and m=1,2,...,M; H is the height of the radar platform initialized in step 1, and the symbol T in the upper right corner represents the transpose operation symbol.

Step 4. Initialize the relevant parameters of the LASAR sparse wiring array antenna optimization method:

Initialize the relevant parameters of the LASAR sparse wire array antenna optimization method include: the maximum number of iterations in the iterative estimation process of the algorithm, denoted as MaxIter; k is denoted as the kth iteration of the iterative estimation process, k is a natural number, and the initial value of k is set to k=0 , and the value range of k is k=0,1,2,...,MaxIter; the correlation coefficient threshold in the iterative algorithm is denoted as T; the iteration termination condition threshold in the iterative algorithm is denoted as ε; in the kth iteration The excitation vector of the LASAR sparse wiring array antenna element is denoted as β ^(k) , k=0,1,2,...,MaxIter, where β ^(k) is a N _A -dimensional vector, and N _A is the vector in step 2 The total number of array elements of the full-array linear array antenna obtained by initialization; randomly generate a N _A -dimensional vector, denoted as α, where the value of each element in α is only 1 or 0, and the number of elements with a value of 1 is N _S , N _S is the total number of elements of the sparse wiring array antenna initialized in step 2; assign the vector α to the excitation vector β ^(k) of the LASAR sparse wiring array antenna elements in all iterations, k=0,1,2, ..., MaxIter, as the initial value of the excitation vector β ^(k) of the sparse wiring array antenna element; in the kth iteration, the set of sequence numbers composed of the positions of the elements whose element value is 1 in the excitation vector β ^(k) is denoted as Ω ^{( k)} , k=0,1,2,…,MaxIter, where the serial number set Ω ^(k) is a vector of N _S dimension; the element value in the serial number set Ω ^(k) is the sparse wiring in the kth iteration Array element number corresponding to the array excitation element in the full-array linear array antenna;

Step 5. Use an iterative algorithm to optimize the design of the LASAR sparse wiring array. The iterative algorithm mainly includes steps 5.1 to 5.5. The specific steps are as follows:

Step 5.1. Calculate the position of the excitation element of the LASAR sparse wiring array antenna in the kth iteration

In the k-th iteration process, if the number of iterations k=0, according to the elements in the set Ω ⁽⁰⁾ , select the corresponding array elements in the full array antenna, and obtain the LASAR sparse wiring array excitation array in the 0th iteration The location set of elements, denoted as S ⁽⁰⁾ , where Ω ⁽⁰⁾ is the sequence number set composed of the positions of the elements whose element value is 1 in the excitation vector β ⁽⁰⁾ in the 0th iteration initialized in step 4, β ^{( 0)} is the excitation vector of the LASAR sparse wiring array antenna element in the 0th iteration; S ⁽⁰⁾ represents the position set composed of selected element values satisfying the element number Ω ⁽⁰⁾ in the position set P, S ⁽⁰⁾ is a 2×N _S -dimensional matrix, where P is the position set of each array element in the tangential track direction of the full-array linear array antenna initialized in step 2; the expression form of the column vector composition of the matrix S ⁽⁰⁾ is in is the first column of the matrix S ⁽⁰⁾ and its physical meaning is the position of the first excitation element in the sparse wiring array antenna in the 0th iteration, is the second column of the matrix S ⁽⁰⁾ and its physical meaning is the position of the second excitation element in the sparse wiring array antenna in the 0th iteration, is the N Sth column of the matrix _S ⁽⁰⁾ and its physical meaning is the position of the N _Sth excitation element in the sparse wiring array antenna in the 0th iteration; the lth column of the matrix S ⁽⁰⁾ is denoted as And the physical meaning is the position of the lth excitation element in the sparse wiring array antenna in the 0th iteration, l is a natural number, and the value range of l is l=1,2,..., _NS , _NS is initialized in step 2 The total number of antenna elements of the sparsely wired array obtained;

In the k-th iteration of the algorithm, if the number of iterations k>0, select the array element whose serial number is the element corresponding to the element in the set Ω ^(k-1) in the full-array linear array antenna, and obtain the LASAR sparse array in the k-th iteration The set of array element positions of the wiring array excitation element, denoted as S ^(k) , where Ω ^(k-1) is the value of the element in the excitation vector β ^(k-1) obtained in the k-1 iteration of the iterative algorithm is 1 The sequence number set composed of the position of the element, β ^{(k-1) is} the excitation vector of the LASAR sparse wiring array antenna element in the k ^- 1th iteration; The position collection that the element value of ^k) is formed, S ^(k) is a matrix of 2 * N _S dimensions; The column vector composition expression form of definition matrix S ^(k) is in is the first column of the matrix S ^(k) and its physical meaning is the position of the first excitation element in the sparse wiring array antenna in the k-th iteration, is the second column of the matrix S ^(k) and its physical meaning is the position of the second excitation element in the sparse wiring array antenna in the k-th iteration, is the N Sth column of the matrix _S ^(k) and its physical meaning is the position of the N _Sth excitation element in the sparse wiring array antenna in the kth iteration, and the lth column of the matrix S ^(k) is denoted as And the physical meaning is the position of the lth excitation element in the sparse wiring array antenna in the kth iteration, l is a natural number, and l=1,2,...,N _S .

Step 5.2. Calculate the correlation coefficient between different cells in the LASAR linear array antenna observation space

In the kth iteration of the algorithm, for any two different cells in the LASAR tangential track direction observation angle interval, the serial numbers are respectively recorded as i and j, i and j are both natural numbers, and the value ranges of i and j are respectively i=1,2,...,M and j=1,2,...,M and i≠j, where M is the total interval of the observation angle of the LASAR linear array antenna in the tangential track-height plane initialized in step 3 The total number of discretized cells; use the position of the mth cell on the ground plane in the LASAR observation angle interval initialized in step 3 $q_m={\&lsqb;m\&Center\; Dot;h\&Center\; Dot;\frac{{\mathrm{\&theta;}}_0}{m}-h\&CenterDot;\frac{{\mathrm{\&theta;}}_0}{2},0\&rsqb;}^T,m=1,2,\mathrm{...},m,$ Obtain the tangential position of the m=i unit corresponding to the value of serial number i, denoted as q _i , and the value of q _i is Obtain the tangential position of the m=jth unit corresponding to the serial number j value, denoted as q _j , and the value of q _j is

use the formula l=1,2,…,N _S , i=1,2,…,M, calculate the distance from the i-th unit cell in the LASAR observation angle interval to the l-th excitation element in the sparse wiring array antenna in the k-th iteration of the algorithm Slope distance, denoted as R ^(k) (l,i), where It is the lth column of the position set S ^(k) that step 5.2 obtains, and ||·|| ₂ represents the L2 norm operation symbol of the vector; $R^{\left(k\right)}(l,j)=\left|\right|{\mathrm{the\; s}}_l^{\left(k\right)}-q_j|{|}_2,l=1,2,\mathrm{...},N_S,j=1,2,\mathrm{...},m,$ Calculate the slant distance from the jth cell in the LASAR observation angle interval to the lth excitation element in the sparse wiring array antenna in k iterations, denoted as R ^(k) (l, j); use the calculation formula ΔR ^(k) (l,i,j)=R ^(k) (l,j)-R ^(k) (l,i), calculate the i-th and j-th cells of the LASAR observation angle interval in the k-th iteration to the sparse wiring The slant range difference of the lth excitation array element in the array antenna, denoted as ΔR ^(k) (l,i,j);

use the formula ${\mathrm{\&rho;}}^{\left(k\right)}(i,j)=\frac{1}{N_S}\left|\underset{l=1}{\overset{N_S}{\&Sigma;}}\exp (-1i\&Center\; Dot;K_0\&CenterDot;{\mathrm{\&Delta;R}}^{\left(k\right)}(l,i,j\left)\right)\right|,i=1,2,\mathrm{...},m,j=1,2,\mathrm{...},m$ And i≠j, calculate the correlation coefficient between the i-th and j-th cells in the LASAR observation angle interval in the k-th iteration under the condition of sparse linear array antenna, denoted as ρ ^(k) (i,j), where N _S is the total number of array elements in the sparse wiring array antenna obtained by initialization in step 2, is the summation symbol of the function whose value of element l ranges from 1 to _NS , exp( ) is the exponent operation symbol with the natural constant e as the base, |·| is the absolute value operation symbol, 1i represents the imaginary number symbol, and K ₀ is Radar system wavenumber and π is the circumference ratio, and λ is the radar carrier frequency wavelength obtained by initialization in step 1;

Use the formula g=|ji|, i=1,2,...,M,j=1,2,...,M,i≠j to calculate the absolute difference between the serial number of the i-th cell and the j-th cell in the LASAR observation angle interval Value, denoted as g, the value range of the natural number g is g=1,2,...,M-1; it will satisfy all the i-th and j-th cells corresponding to the g value under the sparse linear array antenna condition The correlation coefficient ρ ^(k) (i, j) is summed and averaged, and the result of the correlation coefficient is recorded as g=1,2,...,M-1; put all According to the subscript sequence numbers, the vectors are sorted from small to large, and the correlation coefficient vector between different cells in the LASAR linear array antenna observation space in the kth iteration is obtained, which is denoted as in Expressed as the corresponding element value when g=1 Expressed as the corresponding element value when g=2 Expressed as the corresponding element value when g=M-1

Step 5.3, use the threshold to constrain the value of the correlation coefficient vector

In the k-th iteration, if the g-th element in the vector X ^(k) If the value is less than the threshold T, keep the element The value of is unchanged, if the value of the gth element in the vector X ^(k) The value is greater than the threshold T, then the element The value of is set as the threshold T, and the correlation coefficient vector after the threshold constraint is obtained, denoted as Y ^(k) , where X ^(k) is the correlation coefficient vector obtained in step 5.2, and T is the iterative algorithm correlation coefficient threshold initialized in step 4 .

Step 5.4. Estimate the excitation vector of the LASAR sparse wiring array antenna element

In the kth iteration, use the expression Z ^(k) =|IFFT(Y ^(k) )| to calculate the vector after the inverse Fourier transform, denoted as Z ^(k) , where Y ^(k) is step 5.3 The correlation coefficient vector after the threshold constraint obtained in the kth iteration, IFFT (·) is the inverse Fourier transform operation symbol, |·| is the absolute value operation symbol; the first N _S largest in the vector Z ^(k) The value of the value element is set to 1, and the value of other position elements is set to 0, and the obtained vector is recorded as C ^(k) , where N _S is the total number of array elements of the sparse wiring array antenna obtained in step 2; using β ^(k) = C ^(k) obtains the excitation vector of the LASAR sparse wiring array antenna elements in the kth iteration.

Step 5.5, iterative judgment

if And k<MaxIter, then update the value of k to k+1, execute step 5.1 to step 5.5, otherwise the algorithm iteration is terminated, and the β ^(k) obtained in the kth iteration at this moment is the final excitation of the LASAR sparse wiring array antenna element vector, where Expressed as the symbol for finding the maximum value of the function within the range of i and j, k represents the kth iteration number in the iterative estimation process, MaxIter is the maximum number of iterations of the algorithm reconstruction process initialized in step 4, ρ ^(k) ( i, j) is the correlation coefficient between different cells in the observation space of the k-th iteration LASAR linear array antenna obtained in step 5.2, and ε is the iteration termination condition threshold in the iterative algorithm initialized in step 4.

Step 6. Obtain the final optimization result of the sparse wiring array antenna element:

Using the excitation vector β ^(k) of the LASAR sparse wiring array antenna element finally obtained in step 5.5 of the iterative method, the position set S ^(k) of the LASAR sparse wiring array excitation element in the medium is obtained according to step 5.1; the LASAR sparse wiring array excitation element The location set S ^(k) of the sparse wire array antenna is assigned to the array element, and the final array element optimization result of the LASAR sparse linear array antenna is obtained.

The innovation of the present invention is to use the coherence characteristics of the measurement matrix in the compressed sensing theory to provide a low-coherence based compressed sensing LASAR sparse wiring array optimization method, which is based on the minimum coherence of the compressed sensing measurement matrix in the LASAR system With the aid of the Fourier transform iterative search method, the optimal design of the array element distribution of the compressed sensing LASAR sparse wiring array antenna is realized.

The invention has the advantage of using the coherence characteristics of the measurement matrix in the compressed sensing theory as a reference basis for the optimization of the compressed sensing LASAR sparse line array, which is more reasonable for the optimization of the sparse line array, and is beneficial to improving the imaging performance of the compressed sensing LASAR system. The method proposed by the invention is also applicable to other technical fields of sparse wiring array antenna optimization based on compressed sensing.

Description of drawings:

FIG. 1 is a schematic diagram of the processing flow of the low-coherence-based compressed sensing LASAR sparse array optimization method provided by the present invention.

FIG. 2 is a table of system simulation parameters used in a specific embodiment of the present invention.

detailed description

The present invention mainly adopts the method of simulation experiment to verify, and all steps and conclusions are verified correct on MATLABR2012b software. The specific implementation steps are as follows:

Step 1. Initialize the LASAR system parameters:

Initialize LASAR system parameters include: radar platform height H = 1000m; radar operating center frequency f _c = 35×10 ⁹ Hz; radar carrier frequency wavelength λ = 0.00857m; radar baseband signal bandwidth B _r = 1.5×10 ⁸ Hz ; pulse width of radar transmitting signal T _P ＝5×10 ^-6 s; frequency modulation slope of radar transmitting signal f _dr ＝3×10 ¹³ Hz/s; duration width of radar receiving wave gate T _o ＝6×10 ^-4 s; The sampling frequency f _s of the receiving system = 3×10 ⁸ Hz; the pulse repetition frequency PRF of the radar transmitting system = 600 Hz; the pulse repetition time of the radar system PRI = 1×10 ^-3 s; the effective aperture length D _a of the antenna in the azimuth direction =1.06m; the above parameters are standard parameters of the LASAR system, which have been determined during the design and observation process of the LASAR system; according to the LASAR imaging system scheme and observation scheme, the initialization system parameters required by the LASAR sparse wiring array antenna optimization method are all known.

Step 2. Initialize the parameters of the LASAR sparse wiring array antenna:

The parameters for initializing the LASAR thin-wire array antenna include: the total number of array elements N _A =1000 in the full-array linear array antenna; the distance d between adjacent array elements in the full-array linear array antenna is half of the carrier frequency wavelength of the LASAR system, that is, Where λ is the radar carrier frequency wavelength λ=0.00857m obtained by initialization in step 1; the array length L of the full-array linear array antenna is taken as L ₌ (NA -1)d; the total number of array elements in the sparse-wire array antenna N _S = 500; the sparse wiring array antenna element is a subset of the full array antenna element, that is, the sparse wiring array antenna element is composed of 500 array elements selected from the 1000 array elements of the full array antenna; the first in the full array array antenna The position of one array element in the tangential track-height plane is p ₁ =[0,H] ^T , where H is the radar platform height H=1000m obtained by initialization in step 1; The position of the element in the tangential track-height plane is p ₂ =[d,H] ^T ; the position of the N Ath element in the full _- array linear array antenna in the tangential track-height plane is The position of the nth array element in the full array linear array antenna is p _n in the tangent track-altitude plane, where the subscript n is the serial number of the nth array element in the full array array antenna, n is a natural number, n=1,2 ,...,N _A , N _A ＝1000, and p _n ＝[(n-1)d,H] ^T ; the position set P of all elements in the full-array linear array antenna in the tangential track-height plane, where the set P is a 2×N _A -dimensional matrix, and $P=\&lsqb;p_1,p_2,\mathrm{...},p_{N_A}\&rsqb;.$

Step 3. Initialize the LASAR linear array antenna observation space parameters:

Initialize the observation space parameters of the LASAR linear array antenna, including: taking the position of the first array element of the full-array linear array antenna as the reference array element, the observation angle interval size of the linear array antenna in the tangent track-height plane is θ ₀ =10°; The total interval of the observation angle of the LASAR linear array antenna in the tangential track-altitude plane is [-5°, 5°]; the total number of discretized cells M =1000; taking the reference array element of the full-array linear array antenna as the center of the circle, the total range of observation angles of the LASAR linear array antenna in the tangent track-altitude plane is evenly divided into angular cells of equal size; using the formula Calculate the position q _m of the mth cell in the LASAR observation angle interval on the ground plane, where m represents the mth angle cell in the LASAR observation angle interval, m is a natural number, m=1,2,...,M; H is the radar platform height H=1000m obtained by initialization in step 1, and the symbol T in the upper right corner represents the matrix transposition operation symbol.

Step 4. Initialize the relevant parameters of the LASAR sparse wiring array antenna optimization method:

Initialize the relevant parameters of the LASAR sparse wire array antenna optimization method include: the maximum number of iterations of the algorithm iterative estimation process MaxIter = 100; k is the kth iteration of the iterative estimation process, k is a natural number, and the initial value of k is set to k = 0, k The value range is k=0,1,2,...,MaxIter; the correlation coefficient threshold in the iterative algorithm is T=0.3; the iteration termination condition threshold in the iterative algorithm is ε=0.1; the LASAR sparse wire array antenna in the kth iteration The excitation vector β ^(k) of the array element, k=0,1,2,..., MaxIter, MaxIter=100, β ^(k) is a vector of N _A dimension size; a vector α of N _A dimension is randomly generated, where The value of each element in α is only 1 or 0, and the number of elements with a value of 1 is N _S , where N _A is the total number of elements in the full-array linear array antenna obtained by the initialization in step 2 N _A =1000, and N _S is The total number of array elements N _S =500 in the sparse wiring array antenna obtained by initialization in step 2; assign the vector α to the excitation vector β ^(k) of the LASAR sparse wiring array antenna elements in all iterations, k=0,1,2, ..., MaxIter, MaxIter=100, as the initial value of the excitation vector β ^(k) of the sparse wiring array antenna element; in the kth iteration, the sequence number set composed of the elements with the element value 1 in the excitation vector β ^(k) is Ω ^(k) , k=0,1,2,..., MaxIter, MaxIter=100, the sequence number set Ω ^(k) is a vector of N _S dimension size, and the element value in the sequence number set Ω ^(k) is the kth In the second iteration, the array element number corresponding to the sparse wiring array excitation element in the full array antenna.

Step 5. Use an iterative algorithm to optimize the design of the LASAR sparse wiring array. The iterative algorithm mainly includes steps 5.1 to 5.5. The specific steps are as follows:

Step 5.1. Calculate the position of the excitation element of the LASAR sparse wiring array antenna in the kth iteration

In the k-th iteration process, if the number of iterations k=0, according to the elements in the set Ω ⁽⁰⁾ , select the corresponding array elements in the full array antenna, and obtain the LASAR sparse wiring array excitation array in the 0th iteration The position set S ⁽⁰⁾ of element; S ⁽⁰⁾ is expressed as the position set that is selected to satisfy the element sequence number in the position set P and is the element value that Ω ⁽⁰⁾ forms, and S ⁽⁰⁾ is a matrix of 2 * N _S dimensions; The expression form of column vector composition of matrix S ⁽⁰⁾ is in is the first column of the matrix S ⁽⁰⁾ and its physical meaning is the position of the first excitation element in the sparse wiring array antenna in the 0th iteration, is the second column of the matrix S ⁽⁰⁾ and its physical meaning is the position of the second excitation element in the sparse wiring array antenna in the 0th iteration, is the N Sth column of the matrix _S ⁽⁰⁾ and its physical meaning is the position of the N _Sth excitation element in the sparse wiring array antenna in the 0th iteration; the lth column of the matrix S ⁽⁰⁾ is denoted as And the physical meaning is the position of the lth excitation element in the sparse wiring array antenna in the 0th iteration, l is a natural number, and the value range of l is l=1,2,...,N _S , where k=0,1 ,2,...,MaxIter, MaxIter=100, Ω ⁽⁰⁾ is the sequence number set composed of the position of the element whose element value is 1 in the excitation vector β ⁽⁰⁾ in the 0th iteration initialized in step 4, β ⁽⁰⁾ is the excitation vector of the LASAR thin line array antenna element in the 0th iteration in step 4, P is the position set of each element in the full array linear array antenna initialized in step 2 in the tangential track direction, N _S is the step 2 The total number of antenna elements of the sparse wiring array N _S =500 obtained by initialization;

In the k-th iteration of the algorithm, if the number of iterations k>0, select the array element whose array element number corresponds to the element in the set Ω ^(k-1) in the full-array linear array antenna, and obtain the sparse wiring in the k-th iteration The array element position set S ^(k) of the array excitation element, k=0,1,2,...,MaxIter, MaxIter=100; S ^(k) is the element in the position set P that satisfies the element number Ω ^(k) The location set composed of values, S ^(k) is a 2×N _S -dimensional matrix; the expression form of the column vector of matrix S ^(k) is $S^{\left(k\right)}=[{\mathrm{the\; s}}_1^{\left(k\right)},{\mathrm{the\; s}}_2^{\left(k\right)},...,{\mathrm{the\; s}}_{N_S}^{\left(k\right)}],k=\mathrm{0,1,2},...,\mathrm{MaxIter},$ MaxIter=100, is the first column of the matrix S ^(k) and its physical meaning is the position of the first excitation element in the sparse wiring array antenna in the k-th iteration, is the second column of the matrix S ^(k) and its physical meaning is the position of the second excitation element in the sparse wiring array antenna in the k-th iteration, is the N Sth column of the matrix _S ^(k) and its physical meaning is the position of the N _Sth excitation element in the sparse wiring array antenna in the kth iteration, and the lth column of the matrix S ^(k) is denoted as And the physical meaning is the position of the lth excitation element in the sparse wiring array antenna in the kth iteration, l is a natural number, l=1,2,..., _NS , where MaxIter is the maximum iteration of the algorithm iterative estimation process in step 4 The number of times MaxIter=100, Ω ^(k-1) is the set of sequence numbers where the element value is 1 in the excitation vector β ^(k-1) obtained in the k-1 iteration of the iterative algorithm in step 4, and β ^{(k -1)} is the excitation vector of the LASAR sparse wiring array antenna element in the k-1th iteration in step 4.

Step 5.2. Calculate the correlation coefficient between different cells in the LASAR linear array antenna observation space

In the kth iteration of the algorithm, for any two different cells in the LASAR tangential track direction observation angle interval, the serial numbers are respectively recorded as i and j, i and j are both natural numbers, and the value ranges of i and j are respectively i=1,2,...,M and j=1,2,...,M and i≠j, where M is the discretization unit of the total range of observation angles of the LASAR linear array antenna in the tangential track-height plane in step 3 The total number of cells M = 1000; use the position of the mth cell on the ground plane in the LASAR observation angle interval initialized in step 3 $q_m={\&lsqb;m\&CenterDot;h\&CenterDot;\frac{{\mathrm{\&theta;}}_0}{m}-h\&Center\; Dot;\frac{{\mathrm{\&theta;}}_0}{2},0\&rsqb;}^T,m=1,2,\mathrm{...},m,m=1000,$ Obtain the position q _i of the m=i th unit corresponding to the value of serial number i, and the value of q _i is Obtain the position q _j of the m=j th unit corresponding to the value of serial number j, and the value of q _j is Among them, H is the radar platform height H=1000m obtained by initialization in step 1, θ ₀ is the observation angle interval size θ ₀ =10° of the linear array antenna in step 3 in the tangential track-height plane, and the symbol T in the upper right corner represents the matrix rotation Set operation symbols;

use the formula $R^{\left(k\right)}(l,i)=\left|\right|{\mathrm{the\; s}}_l^{\left(k\right)}-q_i|{|}_2,k=0,1,2,\mathrm{...},maxIter,l=1,2,\mathrm{...},N_S,i=1,2,\mathrm{...},m,$ Calculate the slant distance R ^(k) (l,i) from the i-th cell in the LASAR observation angle interval to the l-th excitation element in the sparse wiring array antenna in the k-th iteration of the algorithm, where MaxIter is the iterative estimation of the algorithm in step 4 The maximum number of iterations of the process is MaxIter=100, N _S is the total number of sparse wire array antenna elements N _S =500 obtained by initialization in step 2, and M is the LASAR linear array antenna obtained by initialization in step 3 observed in the tangential track-height plane The total number of discretized cells in the total interval of the angle M=1000, It is the lth column of the position set S ^(k) that step 5.2 obtains, and ||·|| ₂ represents the L2 norm operation symbol of the vector; $R^{\left(k\right)}(l,j)=\left|\right|{\mathrm{the\; s}}_l^{\left(k\right)}-q_j|{|}_2,l=1,2,\mathrm{...},N_S,j=1,2,\mathrm{...},m,$ Calculate the slant distance R ^(k) (l,j) from the jth cell in the LASAR observation angle interval to the lth excitation element in the sparse wiring array antenna in k iterations; use the formula ΔR ^(k) (l,i ,j)=R ^(k) (l,j)-R ^(k) (l,i) Calculate the i-th and j-th unit cells in the LASAR observation angle interval in the k-th iteration to the l-th cell in the sparse wiring array antenna The slant range difference ΔR ^(k) (l,i,j) of four exciting array elements, k=0,1,2,…,MaxIter, l=1,2,…, _NS ,i=1,2,… ,M, j=1,2,...,M, MaxIter=100, _NS =500, M=1000;

use the formula ${\mathrm{\&rho;}}^{\left(k\right)}(i,j)=\frac{1}{N_S}\left|\underset{l=1}{\overset{N_S}{\&Sigma;}}\exp (-1i\&CenterDot;K_0\&Center\; Dot;{\mathrm{\&Delta;R}}^{\left(k\right)}(l,i,j\left)\right)\right|,k=0,1,2,\mathrm{...},maxIter,i=1,2,\mathrm{...},m,$ $j=1,2,\mathrm{...},m$ And i≠j, calculate the correlation coefficient ρ ^(k) (i,j) between the i-th and j-th cells in the LASAR observation angle interval in the k-th iteration under the sparse linear array antenna condition, is the summation symbol of the function whose value of element l ranges from 1 to _NS , exp( ) is the exponent operation symbol with the natural constant e as the base, |·| is the absolute value operation symbol, 1i represents the imaginary number symbol, and K ₀ is Radar system wavenumber and π is the circular ratio π=3.1415, and λ is the radar carrier frequency wavelength λ=0.00857m obtained by initialization in step 1;

Using the formula g=|ji|, i=1,2,...,M,j=1,2,...,M,i≠j, M=1000, calculate the i-th and j-th units of the LASAR observation angle interval The absolute value of the serial number difference g of the cell, the value range of the natural number g is g=1,2,...,M-1; it will satisfy all the i-th and j-th cells corresponding to the g value in the sparse linear array antenna condition The correlation coefficient ρ ^(k) (i,j) under is summed and averaged to obtain the correlation coefficient result g=1,2,...,M-1; put all According to the subscript sequence number, sort the vectors from small to large, and get the correlation coefficient vector between different cells in the LASAR linear array antenna observation space in the kth iteration in Expressed as the corresponding element value when g=1 Expressed as the corresponding element value when g=2 Expressed as the corresponding element value when g=M-1 k=0, 1, 2, . . . , MaxIter, MaxIter=100.

Step 5.3, use the threshold to constrain the value of the correlation coefficient vector

In the k-th iteration, if the g-th element in the vector X ^(k) If the value is less than the threshold T, keep the element The value of is unchanged, if the value of the gth element in the vector X ^(k) The value is greater than the threshold T, then the element The value of is set as the threshold T, and the correlation coefficient vector Y ^(k) after the threshold constraint is obtained, where X ^(k) is the correlation coefficient between different cells in the LASAR linear array antenna observation space in the kth iteration obtained in step 5.2 Vector, k=0,1,2,...,MaxIter, where MaxIter is the maximum number of iterations MaxIter=100 in the algorithm iterative estimation process in step 4, and T is the iterative algorithm correlation coefficient threshold T=0.3 initialized in step 4.

Step 5.4. Estimate the excitation vector of the LASAR sparse wiring array antenna element

In the kth iteration, use the expression Z ^{( k) =} | _IFFT (Y ^(k) )| The value of the maximum value element is set to 1, and the values of other position elements are set to 0, and the vector C ^(k ) is obtained, and the excitation of the LASAR sparse wiring array antenna element in the k-th iteration is obtained by using β ^(k) = C ^(k) Vector, k=0,1,2,...,MaxIter; where Y ^(k) is the threshold-constrained correlation coefficient vector obtained by the kth iteration in step 5.3, and MaxIter is the maximum iteration number of the algorithm iterative estimation process in step 4 MaxIter=100, IFFT(·) is the operation symbol of inverse Fourier transform, |·| is the operation symbol of absolute value, N _S is the total number of array elements N _S =500 of the sparse wiring array antenna obtained in step 2.

Step 5.5, iterative judgment

if And k<MaxIter, then update the value of k to k+1, execute step 5.1 to step 5.5, otherwise the algorithm iteration is terminated, and the β ^(k) obtained in the kth iteration at this moment is the final excitation of the LASAR sparse wiring array antenna element vector, where Expressed as the symbol for finding the maximum value of the function within the range of i and j, k represents the kth iteration number in the iterative estimation process, k=0,1,2,...,MaxIter, MaxIter is the iterative estimation of the algorithm obtained in step 4 The maximum number of iterations of the process MaxIter=100, ρ ^(k) (i, j) is the correlation coefficient between different cells in the observation space of the k-th iteration LASAR linear array antenna obtained in step 5.2, and ε is the initialization obtained in step 4 The iteration termination condition threshold ε=0.1 in the iterative algorithm of .

Step 6. Obtain the final optimization result of the sparse wiring array antenna element:

Using the excitation vector β ^(k) of the LASAR sparse wiring array antenna element finally obtained in step 5.5 of the iterative method, the location set S ^(k) of the LASAR sparse wiring array excitation element is obtained according to step 5.1, and the LASAR sparse wiring array excitation element The location set S ^(k) of the sparse wire array antenna is assigned to the array element, and the final optimal location of the array element of the LASAR sparse linear array antenna is obtained.

Claims (1)

1. A low-coherence-based compressed sensing LASAR sparse line array optimization method is characterized in that it comprises the following steps: Step 1. Initialize the LASAR system parameters: Initialize LASAR system parameters include: radar platform height, denoted as H; radar working center frequency, denoted as f _c ; radar carrier frequency wavelength, denoted as λ; radar transmitting baseband signal bandwidth, denoted as B _r ; radar transmitting signal pulse Width, denoted as T _P ; frequency modulation slope of radar transmitting signal, denoted as f _dr ; duration width of radar receiving gate, denoted as T _o ; sampling frequency of radar receiving system, denoted as f _s ; pulse repetition frequency of radar transmitting system , denoted as PRF; the pulse repetition time of the radar system, denoted as PRI; the effective aperture length of the antenna in the azimuth direction, denoted as D _a ; the above parameters are standard parameters of the LASAR system, where the radar platform height H, radar center frequency f _c , radar carrier frequency wavelength λ, radar transmitting baseband signal bandwidth B _r , radar transmitting signal pulse width T _P , radar transmitting signal FM slope f _dr , radar receiving wave gate duration T _o , radar receiving system sampling frequency f _s , the pulse repetition frequency PRF of the radar system, the pulse repetition time PRI of the radar system, and the effective aperture length D _a of the antenna in the azimuth direction have been determined during the LASAR system design and observation process; according to the LASAR imaging system scheme and observation scheme, the LASAR sparse wiring The initialization system parameters required by the array antenna optimization method are all known; Step 2. Initialize the parameters of the LASAR sparse wiring array antenna: The parameters for initializing the LASAR sparse wiring array antenna include: the total number of array elements of the full array antenna is denoted as N _A ; the distance between adjacent array elements in the full array antenna is denoted as d, and the value of d in the LASAR system is the system load half of the frequency wavelength, which is Where λ is the radar carrier frequency wavelength obtained by initialization in step 1; the array length of the full-array linear array antenna is denoted as L, and the value of L is L=(N _A -1)d; the array elements in the sparse-array array antenna The total number is denoted as N _S , and N _S <NA; the sparse wiring array antenna elements are _{a subset of the full array antenna elements, that is, the sparse wiring array antenna elements are N A array} elements from the full array antenna N _S array elements are selected in ; the position of the first array element in the full-array linear array antenna in the tangent track-altitude plane is denoted as p ₁ ; the second array element in the full-array linear array antenna is in the tangential track-altitude plane The position in the height plane is denoted as p ₂ ; the position of the N _Ath array element in the tangential track-height plane in the full-array linear array antenna is denoted as The position of the nth array element in the full array array antenna in the tangent track-height plane is denoted as p _n , where the subscript n is the serial number of the nth array element in the full array array antenna, n is a natural number, n= 1,2,...,NA , and p _{n ＝} [(n-1)d,H] ^T , where H is the height of the radar platform initialized in step 1; The set of positions in the track-altitude plane is denoted as P, where the set P is a 2×N _A -dimensional matrix, and $P=\&lsqb;p_1,p_2,...,p_{N_A}\&rsqb;;$ Step 3. Initialize the LASAR linear array antenna observation space parameters: Initialize the observation space parameters of the linear array SAR array antenna, including: taking the position of the first array element of the full array array antenna as the reference array element, the size of the observation angle interval of the linear array antenna in the tangential track-height plane, denoted as θ ₀ ; the total interval of the observation angle of the LASAR linear array antenna in the tangential track-height plane, denoted as $\&lsqb;-\frac{{\mathrm{\&theta;}}_0}{2},\frac{{\mathrm{\&theta;}}_0}{2}\&rsqb;;$ The total number of discretized cells in the total interval of the observation angle of the LASAR linear array antenna in the tangential track-height plane is denoted as M; taking the reference array element of the full-array linear array antenna as the center of the circle, the LASAR linear array antenna in the tangential track-height plane The total range of observation angles in the plane is evenly divided into angular cells of equal size, and the angle value corresponding to each angular cell is smaller than the angular resolution of the LASAR linear array antenna in the tangential track direction; the formula $q_m={\&lsqb;m\&CenterDot;h\&Center\; Dot;\frac{{\mathrm{\&theta;}}_0}{m}-h\&CenterDot;\frac{{\mathrm{\&theta;}}_0}{2},0\&rsqb;}^T,$ m=1,2,...,M, calculate the position of the mth cell on the ground plane in the LASAR observation angle interval, denoted as q _m , m=1,2,...,M, where m represents the LASAR observation angle The mth angle cell in the interval, m is a natural number, and m=1,2,...,M; H is the height of the radar platform initialized in step 1, and the symbol T in the upper right corner represents the transpose operation symbol; Step 4. Initialize the relevant parameters of the LASAR sparse wiring array antenna optimization method: Initialize the relevant parameters of the LASAR sparse wire array antenna optimization method include: the maximum number of iterations in the iterative estimation process of the algorithm, denoted as MaxIter; k is denoted as the kth iteration of the iterative estimation process, k is a natural number, and the initial value of k is set to k=0 , and the value range of k is k=0,1,2,...,MaxIter; the correlation coefficient threshold in the iterative algorithm is denoted as T; the iteration termination condition threshold in the iterative algorithm is denoted as ε; in the kth iteration The excitation vector of the LASAR sparse wiring array antenna element is denoted as β ^(k) , k=0,1,2,...,MaxIter, where β ^(k) is a N _A -dimensional vector, and N _A is the vector in step 2 The total number of array elements of the full-array linear array antenna obtained by initialization; randomly generate a N _A -dimensional vector, denoted as α, where the value of each element in α is only 1 or 0, and the number of elements with a value of 1 is N _S , N _S is the total number of elements of the sparse wiring array antenna initialized in step 2; assign the vector α to the excitation vector β ^(k) of the LASAR sparse wiring array antenna elements in all iterations, k=0,1,2, ..., MaxIter, as the initial value of the excitation vector β ^(k) of the sparse wiring array antenna element; in the kth iteration, the set of sequence numbers composed of the positions of the elements whose element value is 1 in the excitation vector β ^(k) is denoted as Ω ^{( k)} , k=0,1,2,…,MaxIter, where the serial number set Ω ^(k) is a vector of N _S dimension; the element value in the serial number set Ω ^(k) is the sparse wiring in the kth iteration Array element number corresponding to the array excitation element in the full-array linear array antenna; Step 5. Use an iterative algorithm to optimize the design of the LASAR sparse wiring array. The iterative algorithm mainly includes steps 5.1 to 5.5. The specific steps are as follows: Step 5.1. Calculate the position of the excitation element of the LASAR sparse wiring array antenna in the kth iteration In the k-th iteration process, if the number of iterations k=0, according to the elements in the set Ω ⁽⁰⁾ , select the corresponding array elements in the full array antenna, and obtain the LASAR sparse wiring array excitation array in the 0th iteration The location set of elements, denoted as S ⁽⁰⁾ , where Ω ⁽⁰⁾ is the sequence number set composed of the positions of the elements whose element value is 1 in the excitation vector β ⁽⁰⁾ in the 0th iteration initialized in step 4, β ^{( 0)} is the excitation vector of the LASAR sparse wiring array antenna element in the 0th iteration; S ⁽⁰⁾ represents the position set composed of selected element values satisfying the element number Ω ⁽⁰⁾ in the position set P, S ⁽⁰⁾ is a 2×N _S -dimensional matrix, where P is the position set of each array element in the tangential track direction of the full-array linear array antenna initialized in step 2; the expression form of the column vector composition of the matrix S ⁽⁰⁾ is in is the first column of the matrix S ⁽⁰⁾ and its physical meaning is the position of the first excitation element in the sparse wiring array antenna in the 0th iteration, is the second column of the matrix S ⁽⁰⁾ and its physical meaning is the position of the second excitation element in the sparse wiring array antenna in the 0th iteration, is the N Sth column of the matrix _S ⁽⁰⁾ and its physical meaning is the position of the N _Sth excitation element in the sparse wiring array antenna in the 0th iteration; the lth column of the matrix S ⁽⁰⁾ is denoted as And the physical meaning is the position of the lth excitation element in the sparse wiring array antenna in the 0th iteration, l is a natural number, and the value range of l is l=1,2,..., _NS , _NS is initialized in step 2 The total number of antenna elements of the sparsely wired array obtained; In the k-th iteration of the algorithm, if the number of iterations k>0, select the array element whose serial number is the element corresponding to the element in the set Ω ^(k-1) in the full-array linear array antenna, and obtain the LASAR sparse array in the k-th iteration The set of array element positions of the wiring array excitation element, denoted as S ^(k) , where Ω ^(k-1) is the value of the element in the excitation vector β ^(k-1) obtained in the k-1 iteration of the iterative algorithm is 1 The sequence number set composed of the position of the element, β ^{(k-1) is} the excitation vector of the LASAR sparse wiring array antenna element in the k ^- 1th iteration; The position collection that the element value of ^k) is formed, S ^(k) is a matrix of 2 * N _S dimensions; The column vector composition expression form of definition matrix S ^(k) is in is the first column of the matrix S ^(k) and its physical meaning is the position of the first excitation element in the sparse wiring array antenna in the k-th iteration, is the second column of the matrix S ^(k) and its physical meaning is the position of the second excitation element in the sparse wiring array antenna in the k-th iteration, is the N Sth column of the matrix _S ^(k) and its physical meaning is the position of the N _Sth excitation element in the sparse wiring array antenna in the kth iteration, and the lth column of the matrix S ^(k) is denoted as And the physical meaning is the position of the lth excitation array element in the sparse wiring array antenna in the kth iteration, l is a natural number, and l=1,2,...,N _S ; Step 5.2. Calculate the correlation coefficient between different cells in the LASAR linear array antenna observation space In the kth iteration of the algorithm, for any two different cells in the LASAR tangential track direction observation angle interval, the serial numbers are respectively recorded as i and j, i and j are both natural numbers, and the value ranges of i and j are respectively i=1,2,...,M and j=1,2,...,M and i≠j, where M is the total interval of the observation angle of the LASAR linear array antenna in the tangential track-height plane initialized in step 3 The total number of discretized cells; use the position of the mth cell on the ground plane in the LASAR observation angle interval initialized in step 3 m=1,2,...,M, get the tangential position of the m=ith unit corresponding to the value of serial number i, denoted as q _i , and the value of q _i is Obtain the tangential position of the m=jth unit corresponding to the serial number j value, denoted as q _j , and the value of q _j is use the formula l=1,2,…,N _S , i=1,2,…,M, calculate the distance from the i-th unit cell in the LASAR observation angle interval to the l-th excitation element in the sparse wiring array antenna in the k-th iteration of the algorithm Slope distance, denoted as R ^(k) (l,i), where It is the lth column of the position set S ^(k) that step 5.2 obtains, and ||·|| ₂ represents the L2 norm operation symbol of the vector; l=1,2,…,N _S , j=1,2,…,M, calculate the slope from the jth unit cell in the LASAR observation angle interval in k iterations to the lth excitation element in the sparse wiring array antenna distance, denoted as R ^(k) (l,j); use the formula ΔR ^(k) (l,i,j)=R ^(k) (l,j)-R ^(k) (l,i) to calculate the first The slant distance difference between the i-th and j-th cells in the LASAR observation angle interval to the l-th excitation element in the sparse wiring array antenna in k iterations is denoted as ΔR ^(k) (l,i,j); use the formula ${\mathrm{\&rho;}}^{\left(k\right)}(i,j)=\frac{1}{N_S}\left|\underset{l=1}{\overset{N_S}{\&Sigma;}}\exp (-1i\&Center\; Dot;K_0\&CenterDot;{\mathrm{\&Delta;R}}^{\left(k\right)}(l,i,j\left)\right)\right|,$ i=1,2,…,M, j=1,2,…,M and i≠j, calculate the i-th and j-th cells in the LASAR observation angle interval in the k-th iteration under the condition of sparse linear array antenna The correlation coefficient of , denoted as ρ ^(k) (i,j), where N _S is the total number of array elements in the sparse wiring array antenna obtained by initialization in step 2, is the summation symbol of the function whose value of element l ranges from 1 to _NS , exp( ) is the exponent operation symbol with the natural constant e as the base, |·| is the absolute value operation symbol, 1i represents the imaginary number symbol, and K ₀ is Radar system wavenumber and π is the circumference ratio, and λ is the radar carrier frequency wavelength obtained by initialization in step 1; Use the formula g=|ji|, i=1,2,...,M,j=1,2,...,M,i≠j to calculate the absolute difference between the serial number of the i-th cell and the j-th cell in the LASAR observation angle interval Value, denoted as g, the value range of the natural number g is g=1,2,...,M-1; it will satisfy all the i-th and j-th cells corresponding to the g value under the sparse linear array antenna condition The correlation coefficient ρ ^(k) (i, j) is summed and averaged, and the result of the correlation coefficient is recorded as g=1,2,...,M-1; put all According to the subscript sequence numbers, the vectors are sorted from small to large, and the correlation coefficient vector between different cells in the LASAR linear array antenna observation space in the kth iteration is obtained, which is denoted as in Expressed as the corresponding element value when g=1 Expressed as the corresponding element value when g=2 Expressed as the corresponding element value when g=M-1 Step 5.3, use the threshold to constrain the value of the correlation coefficient vector In the k-th iteration, if the g-th element in the vector X ^(k) If the value is less than the threshold T, keep the element The value of is unchanged, if the value of the gth element in the vector X ^(k) The value is greater than the threshold T, then the element The value of is set as the threshold T, and the correlation coefficient vector after the threshold constraint is obtained, denoted as Y ^(k) , where X ^(k) is the correlation coefficient vector obtained in step 5.2, and T is the iterative algorithm correlation coefficient threshold initialized in step 4 ; Step 5.4. Estimate the excitation vector of the LASAR sparse wiring array antenna element In the kth iteration, use the expression Z ^(k) =|IFFT(Y ^(k) )| to calculate the vector after the inverse Fourier transform, denoted as Z ^(k) , where Y ^(k) is step 5.3 The correlation coefficient vector after the threshold constraint obtained in the kth iteration, IFFT (·) is the inverse Fourier transform operation symbol, |·| is the absolute value operation symbol; the first N _S largest in the vector Z ^(k) The value of the value element is set to 1, and the value of other position elements is set to 0, and the obtained vector is recorded as C ^(k) , where N _S is the total number of array elements of the sparse wiring array antenna obtained in step 2; using β ^(k) = C ^(k) obtains the excitation vector of the LASAR sparse wiring array antenna element in the kth iteration; Step 5.5, iterative judgment if And k<MaxIter, then update the value of k to k+1, execute step 5.1 to step 5.5, otherwise the algorithm iteration is terminated, and the β ^(k) obtained in the kth iteration at this moment is the final excitation of the LASAR sparse wiring array antenna element vector, where Expressed as the symbol for finding the maximum value of the function within the range of i and j, k represents the kth iteration number in the iterative estimation process, MaxIter is the maximum number of iterations of the algorithm reconstruction process initialized in step 4, ρ ^(k) ( i, j) is the correlation coefficient between different cells in the k-th iteration LASAR linear array antenna observation space obtained in step 5.2, and ε is the iteration termination condition threshold in the iterative algorithm initialized in step 4; Step 6. Obtain the final optimization result of the sparse wiring array antenna element: Using the excitation vector β ^(k) of the LASAR sparse wiring array antenna element finally obtained in step 5.5 of the iterative method, the position set S ^(k) of the LASAR sparse wiring array excitation element in the medium is obtained according to step 5.1; the LASAR sparse wiring array excitation element The location set S ^(k) of the sparse wire array antenna is assigned to the array element, and the final array element optimization result of the LASAR sparse linear array antenna is obtained.