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

Abstract

The invention discloses a compressed sensing LASAR sparse linear array optimization method based on low coherence. The method is characterized in that coherence characteristic of a measurement matrix in the compressed sensing theory is utilized as a reference basis for compressed sensing LASAR sparse linear array optimization; and on the basis of minimum of coherence of the compressed sensing measurement matrix in a LASAR system, and by means of a Fourier transform iterative search method, compressed sensing LASAR sparse linear array antenna array element distribution optimization design is realized, more reasonable sparse linear array optimization is realized, and imaging performance of the compressed sensing LASAR system is improved favorably. The method provided in the invention is also suitable for other sparse linear array antenna optimization technical fields based on compressed sensing.

Description

Based on the compressed sensing LASAR bare cloth linear array optimization method of Low coherence

Technical field:

This technological invention belongs to Radar Technology field, and it is in particular to synthetic-aperture radar (SAR) imaging technique and array antenna design technical field.

Background technology:

Owing to having the advantages such as round-the-clock, round-the-clock and large scene observation, synthetic-aperture radar (SAR) has become an important remote sensing technology of current large-scale terrain mapping, plays a greater and greater role in fields such as topographic mapping, Natural calamity monitoring and survey of natural resources.Linear array SAR (LASAR) is the expansion of conventional two-dimensional SAR imaging technique target dimension space resolution characteristic, the three-dimensional radar imaging of observed object scene can be obtained, geometry and the scattering signatures of target in observation scene can be described more subtly, target's feature-extraction and the target recognition capability of radar system is improve compared with conventional two-dimensional SAR, the hot research problem becoming SAR imaging technique in recent years (refers to list of references " Zhang Qingjuan, Li Daojing, Li Liechen. the thinned array SAR side-looking three-dimensional imaging research of scene continuously. electronics and information journal, 2013, (5): 1097-1102. ").The ultimate principle of LASAR imaging system synthesizes a large virtual two-dimensional planar array by the motion of linear array antenna, two-dimentional high-resolution in the battle array plane of acquisition face, obtain radar line of sight direction high resolving power in conjunction with pulse compression technique again, thus realize the three-dimensional imaging to observed object scene.

The sparse reconstruct of compressed sensing is as a kind of new signal processing theory proposed in recent years, breach the constraint of traditional Nyquist sampling thheorem, can utilize far below Nyquist sampling rate Accurate Reconstruction original sparse signal (referring to list of references " D.L.Donoho.Compressedsensing.IEEETransactionsonInformati onTheory; 2006; 52 (4): 1289-1306 "), in reduction radar system sampling rate, raising image quality etc., have huge application potential.Because in LASAR imaging scene, the most of number of target is all space sparse distribution, therefore compressive sensing theory can organically combine with LASAR system, create the linear array three-dimensional SAR sparse imaging system based on compressed sensing, realize the raising (referring to list of references " S-J.WeiS; X-L.Zhang; J.Shi.LineararraySARimagingviacompressedsensing; ProgressInElectromagneticsResearch; 2011,117 (8): 299-319. ") of the down-sampled and three-dimensional imaging precision of the sparse signal of LASAR imaging system.

Linear array antenna is the key components of LASAR imaging system, for linear array three-dimensional SAR imaging system provides the imaging resolution characteristic of the third dimension.But for single antenna in traditional SAR system, the many array element of LASAR system neutral array antenna also considerably increases the difficulty and cost that hardware system realizes, cause that LASAR echo data amount is excessive, data transmission, to store and the problem such as difficult in imaging.In order to reduce the cost of LASAR hardware system and data processing, in LASAR system, usually adopt bare cloth linear array antenna to realize down-sampled echo data collection, but the array number of bare cloth linear array antenna does not meet the Nyquist sampling rate of conventional radar systems, cause traditional SAR formation method precision and Quality Down.But, for compressed sensing formation method, even if adopt Sparse array antenna, the sparse imaging system of LASAR still can ensure precision and the quality of imaging, realize high accuracy three-dimensional SAR imaging (refer to list of references " Li Xueshi, Sun Guangcai, Xu Gang etc. based on looking D S AR imaging new method under compressed sensing. electronics and information journal; 2012,34 (5): 1017-1023. ").Because the array element number of LASAR bare cloth linear array antenna and distribution mode directly determine the performance of compressed sensing formation method, distribution optimization need be carried out to the array element of bare cloth linear array antenna.But because compressed sensing and traditional imaging theory exist this qualitative difference, for the sparse imaging system of LASAR based on compressed sensing, traditional linear array antenna array element optimization method cannot be applicable to the array element optimization of bare cloth linear array antenna in its system.

For the sparse imaging system of LASAR based on compressed sensing, array number does not need to meet Nyquist sampling rate and only relevant with target sparse degree, if calculation matrix meets equidistant constraint character (RIP), bare cloth linear array antenna can realize the high-resolution imaging of sparse target.But, in linear array three-dimensional SAR system, the RIP of compressed sensing calculation matrix calculates is nondeterministic polynomial (NP) problem, therefore be difficult to utilize the RIP of calculation matrix in compressive sensing theory as weigh index that LASAR bare cloth linear array antenna optimizes (refer to list of references " Li little Bo. the calculation matrix based on compressed sensing is studied. Beijing Jiaotong University's PhD dissertation, 2010. ").Compressive sensing theory is pointed out, if the coherence of calculation matrix is less mean that the probability of compressed sensing algorithm accurate reconstruction target scattering coefficient is higher, therefore under calculation matrix RIP is difficult to calculated case, coherence can be utilized as the standard weighing LASAR Sparse array distribution optimization, and in LASAR system, the array element distribution design of bare cloth linear array antenna will make the coherence of compressed sensing calculation matrix in its system minimum as far as possible.

Summary of the invention:

The invention provides a kind of compressed sensing LASAR bare cloth linear array optimization method based on Low coherence, the method minimizes based on compressed sensing calculation matrix coherence's in LASAR system, by Fourier transform iterative search method, achieve the array element distribution optimization design of compressed sensing LASAR bare cloth linear array antenna, more reasonable to Sparse array optimization, be conducive to the imaging performance improving compressed sensing LASAR system.The method that the present invention proposes also is applicable to other bare cloth linear array antenna optimisation technique field based on compressed sensing.

Content of the present invention for convenience of description, first make following term definition:

Definition 1, norm

If X is number field linear Space, represent complex field, if it meets following character: || X||>=0, and || X||=0 only has X=0, || aX||=|a|||X||, a are arbitrary constant, || X ₁+ X ₂||≤|| X ₁||+|| X ₂||, then claiming || X|| is X norm spatially, || || represent norm sign, wherein X ₁and X ₂for X any two values spatially.Discrete signal vector X=[x is tieed up for N × 1 in definition 1 ₁, x ₂..., x _n] ^t, the LP norm expression formula of vectorial X is wherein x _ifor i-th element of vectorial X, || represent absolute value sign, Σ || represent absolute value summation symbol, the L1 norm expression formula of vectorial X is the L2 norm expression formula of vector X is the L0 norm expression formula of vector X is and x _i≠ 0.Refer to document " external electronics and communication teaching material series: Signals & Systems (second edition) ", AlanV.Oppenheim etc. write, and Liu Shutang translates, and Electronic Industry Press publishes.

Definition 2, nyquist sampling rate

In the transfer process of carrying out analog/digital signal, for limited bandwidth signal, when sample frequency is greater than 2 times of signal highest frequency, after sampling, digital signal intactly can retain and recover the information in original signal, and this sampling rate is called nyquist sampling rate.Sampling thheorem is also known as Nyquist's theorem (Nyquist theorem) or Shannon's theorems, and refer to document " matrix theory ", Huang Tingzhu etc. write, and Higher Education Publishing House publishes.

Definition 3, full front's array antenna and bare cloth linear array antenna

When utilizing linear array antenna to carry out target detection in radar system, if when the distribution of linear array antenna array element meets title Nyquist's theorem, then this linear array antenna is called full front array antenna, and the spacing between the adjacent array element of usual radar Zhong Man front battle array is 0.5 times of radar operation wavelength; If when the distribution of linear array antenna array element does not meet title Nyquist's theorem, then this linear array antenna is called bare cloth linear array antenna.

Definition 4, compressed sensing

Higher-dimension original signal is mainly carried out non-self-adapting linear projection to lower dimensional space with the structural information of holding signal by compressed sensing, reconstruct the theory of original signal again by solving linear optimal solution, this theory mainly comprises sparse signal representation, sparseness measuring and sparse reconstruct three aspects.The basic thought of the sparse reconstructing method of compressed sensing is solve optimum solution under particular constraints condition or near-optimal solution, and main method has greedy tracing algorithm and convex relaxed algorithm etc.Detailed content can list of references " DonohoDL.Compressedsensing.IEEETransactionsonInformation Theory, 2006,52 (4): 1289-1306. ".

The coherence of definition 5, compressed sensing calculation matrix

In perception theory, for certain measuring system, the coherence of compressed sensing observing matrix is defined as: wherein μ is the coefficient of coherence of measuring system observing matrix, χ _irepresent the i-th row of calculation matrix, χ _jrepresent the jth row of calculation matrix, <> represents that vectorial auto-correlation computation accords with, || be the sign of operation that takes absolute value, || || ₂for L2 norm sign of operation, max is function maximizing sign of operation.

Definition 6, linear array synthetic-aperture radar (LinearArraySAR is called for short LASAR)

Linear array synthetic-aperture radar linear array antenna to be fixed on loading movement platform and with Platform movement direction with vertical, motion in conjunction with motion platform realizes array plane dimension two-dimensional imaging to synthesize two-dimensional planar array, recycling radar beam realizes distance one-dimensional image to echo time delay, thus realizes a kind of Synthetic Aperture Radar Technique of observed object three-dimensional imaging.

Definition 7, linear array synthetic-aperture radar cut course made good

In online array synthetic-aperture radar observation process, the direction that linear array synthetic-aperture radar Platform movement trajectory direction is vertical and parallel with linear array antenna array element arranged direction, what be called linear array synthetic-aperture radar cuts course made good.

The linear array antenna observation space of definition 8, linear array synthetic-aperture radar

In online array synthetic-aperture radar observation process, by the two dimensional surface cut course made good and earth's surface vertical direction and form, be called the linear array antenna observation space of linear array synthetic-aperture radar.

The excitation vector of sparse array element in definition 9, linear array antenna

In linear array antenna, sparse array element excitation vector is the vector characterizing sparse array element position distribution in linear array antenna.Suppose that the array element can settled in linear array antenna adds up to N, sparse array element excitation vector is β=[β ₁..., β _n], the dimension of vectorial β is N, wherein β ₁table is vectorial β the 1st element value, β _ntable is the N number of element value of vectorial β, β _ktable is a vectorial β kth element value, the β when the array element of kth in linear array antenna is selected _k=1, in linear array antenna, a kth array element is not by β during selection _k=0.

The angular resolution of linear array antenna in definition 10, linear array synthetic-aperture radar

The minimum angles that in linear array synthetic-aperture radar, linear array antenna can effectively be distinguished at observation space, be called the angular resolution of linear array antenna in linear array polarization sensitive synthetic aperture radar system, angular resolution is relevant with linear array antenna length with radar operation wavelength, refer to document " double-base SAR and linear array SAR principle and imaging technique are studied ", Shi Jun, University of Electronic Science and Technology's PhD dissertation, 2012.

A kind of compressed sensing LASAR bare cloth linear array optimization method based on Low coherence provided by the invention, it comprises the following steps:

Step 1, initialization LASAR systematic parameter:

Initialization LASAR systematic parameter comprises: Texas tower height, is denoted as H; Radar operating center frequency, is denoted as f _c; Radar carrier frequency wavelength, is denoted as λ; The signal bandwidth of radar emission baseband signal, is denoted as B _r; Radar emission signal pulse width, is denoted as T _p; The chirp rate of radar emission signal, is denoted as f _dr; Radar receives ripple door and continues width, is denoted as T _o; The sample frequency of Radar Receiver System, is denoted as f _s; The pulse repetition rate of radar emission system, is denoted as PRF; The pulse-recurrence time of radar system, be designated as PRI; Antenna in orientation to effective aperture length, be denoted as D _a; Above-mentioned parameter is LASAR system standard parameter, wherein Texas tower height H, radar center frequency f _c, radar carrier frequency wavelength X, the signal bandwidth B of radar emission baseband signal _r, radar emission signal pulse width T _p, radar emission signal chirp rate f _dr, radar receives ripple door and continues width T _o, the sample frequency f of Radar Receiver System _s, the pulse repetition rate PRF of radar system, PRI pulse-recurrence time of radar system, antenna in orientation to effective aperture length D _adetermine in LASAR system and observation process; According to LASAR imaging system scheme and observation program, the initializes system parameters that LASAR bare cloth linear array antenna optimization method needs is known.

The parameter of step 2, initialization LASAR bare cloth linear array antenna:

The parameter of initialization LASAR bare cloth linear array antenna comprises: the array element sum of full front array antenna is designated as N _a; The spacing of adjacent array element in full front array antenna, be designated as d, in LASAR system, the value of d is the half of system carrier frequency wavelength, is wherein λ is the radar carrier frequency wavelength that in step 1, initialization obtains; The array length of full front array antenna, be designated as L, and the value of L is L=(N _a-1) d; Array element sum in bare cloth linear array antenna, is designated as N _s, and N _s< N _a; The subset of bare cloth linear array antenna array element Shi Man front array antenna array element, namely bare cloth linear array antenna array element is the N from full front array antenna _an is chosen in individual array element _sindividual array element composition; In full front array antenna, the 1st array element is cutting the position in flight path-elevation plane, is designated as p ₁; In full front array antenna, the 2nd array element is cutting the position in flight path-elevation plane, is designated as p ₂; N in full front array antenna _aindividual array element, cutting the position in flight path-elevation plane, is designated as in full front array antenna, the n-th array element is cutting the position in flight path-elevation plane, is designated as p _n, wherein subscript n is the sequence number of the n-th array element in full front array antenna, and n is natural number, n=1,2 ..., N _a, and p _n=[(n-1) d, H] ^t, wherein H is the Texas tower height that in step 1, initialization obtains; In full front array antenna, all array element is cutting the location sets in flight path-elevation plane, is denoted as P, and wherein gathering P is a 2 × N _athe matrix of dimension, and $P=\&lsqb;p_1,p_2,\mathrm{...},p_{N_A}\&rsqb;.$

Step 3, initialization LASAR linear array antenna observation space parameter:

Initialization linear array SAR linear array antenna observation space parameter, comprising: with the 1st of full front array antenna the element position for reference array element, and linear array antenna, cutting the interval size of the observation angle in flight path-elevation plane, is designated as θ ₀; LASAR linear array antenna, to cut the observation angle in flight path-elevation plane always interval, is designated as lASAR linear array antenna, cutting the total interval discretize cell sum of observation angle in flight path-elevation plane, is designated as M; With the reference array element of full front array antenna for the center of circle, LASAR linear array antenna is evenly divided into equal-sized angle-unit lattice cutting the total interval of observation angle in flight path-elevation plane, and angle value corresponding to each angle-unit lattice is less than LASAR linear array antenna is cutting the angular resolution of course made good; Adopt formula calculate m the position of cell on ground level in LASAR observation angle interval, be designated as q _m, m=1,2 ..., M, wherein m represents m angle-unit lattice in LASAR observation angle interval, and m is natural number, and m=1,2 ..., M; H is the Texas tower height that in step 1, initialization obtains, and upper right corner symbol T represents transpose operation symbol.

The correlation parameter of step 4, initialization LASAR bare cloth linear array antenna optimization method:

The correlation parameter of initialization LASAR bare cloth linear array antenna optimization method comprises: the maximum iteration time of algorithm iteration estimation procedure, is denoted as MaxIter; K is designated as the kth time iteration of iterative estimation procedure, and k is natural number, and k initial value is set to k=0, and the span of k is k=0, and 1,2 ..., MaxIter; Correlation coefficient threshold in iterative algorithm, is designated as T; Stopping criterion for iteration threshold value in iterative algorithm, is designated as ε; In kth time iteration, the excitation vector of LASAR bare cloth linear array antenna array element, is designated as β ^(k), k=0,1,2 ..., MaxIter, wherein β ^(k)a N _athe vector of dimension size, N _ait is the array element sum of the full front array antenna that in step 2, initialization obtains; Random generation N _athe vector of dimension, be designated as α, wherein in α, each element value is only 1 or 0, and the element number that value is 1 is N _s, N _sfor the array element sum of the bare cloth linear array antenna that initialization in step 2 obtains; Vectorial α assignment is given the excitation vector β of LASAR bare cloth linear array antenna array element in all iterative process ^(k), k=0,1,2 ..., MaxIter, as bare cloth linear array antenna array element excitation vector β ^(k)initial value; Excitation vector β in kth time iteration ^(k)middle element value is the sequence number set of the element position composition of 1, is designated as Ω ^(k), k=0,1,2 ..., MaxIter, wherein sequence number set omega ^(k)be a N _sthe vector of dimension size; Sequence number set omega ^(k)in element value be the array element sequence number that in kth time iteration, bare cloth linear array excitation array element is corresponding in full front array antenna;

Step 5, employing iterative algorithm carry out LASAR bare cloth linear array optimal design, and this iterative algorithm mainly comprises step 5.1 to step 5.5, and concrete steps realize as follows:

Step 5.1, in kth time iteration, calculate the position of LASAR bare cloth linear array antenna excitation array element

In kth time iterative process, if during iterations k=0, according to set omega ⁽⁰⁾in element, in full front array antenna, choose corresponding array element, obtain the location sets of LASAR bare cloth linear array excitation array element in the 0th iteration, be designated as S ⁽⁰⁾, wherein Ω ⁽⁰⁾for excitation vector β in the 0th iteration that step 4 initialization obtains ⁽⁰⁾middle element value is the sequence number set of the element position composition of 1, β ⁽⁰⁾it is the excitation vector of LASAR bare cloth linear array antenna array element in the 0th iteration; S ⁽⁰⁾be expressed as in location sets P and choose that to meet element numbers be Ω ⁽⁰⁾element value composition location sets, S ⁽⁰⁾be a 2 × N _sthe matrix of dimension, wherein P is that in the full front array antenna that in step 2, initialization obtains, each array element is cutting the location sets of course made good; Order matrix S ⁽⁰⁾column vector composition expression-form be wherein for matrix S ⁽⁰⁾the 1st row and physical significance be in the 0th iteration in bare cloth linear array antenna the 1st excitation element position, for matrix S ⁽⁰⁾the 2nd row and physical significance be in the 0th iteration in bare cloth linear array antenna the 2nd excitation element position, for matrix S ⁽⁰⁾n _srow and physical significance is N in bare cloth linear array antenna in the 0th iteration _sindividual excitation element position; Matrix S ⁽⁰⁾l row be designated as and physical significance be in the 0th iteration in bare cloth linear array antenna l excitation element position, l is natural number, and the span of l is l=1,2 ..., N _s, N _sfor the bare cloth linear array antenna array element sum that step 2 initialization obtains;

In algorithm kth time iteration, if during iterations k > 0, in full front array antenna, choose array element sequence number is set omega ^(k-1)corresponding to middle element array element, obtain the element position set of LASAR bare cloth linear array excitation array element in kth time iteration, be designated as S ^(k), wherein Ω ^(k-1)for the excitation vector β obtained in iterative algorithm kth-1 iteration ^(k-1)middle element value is the sequence number set of 1 element position composition, β ^(k-1)for the excitation vector of LASAR bare cloth linear array antenna array element in kth-1 iteration; S ^(k)be expressed as in location sets P and choose that to meet element numbers be Ω ^(k)element value composition location sets, S ^(k)be a 2 × N _sthe matrix of dimension; Definition matrix S ^(k)column vector composition expression-form be wherein for matrix S ^(k)the 1st row and physical significance is the 1st excitation element position in bare cloth linear array antenna in kth time iteration, for matrix S ^(k)the 2nd row and physical significance is the 2nd excitation element position in bare cloth linear array antenna in kth time iteration, for matrix S ^(k)n _srow and physical significance are N in bare cloth linear array antenna in kth time iteration _sindividual excitation element position, matrix S ^(k)l row be designated as and physical significance be in kth time iteration in bare cloth linear array antenna l encourage element position, l is natural number, and l=1,2 ..., N _s.

Related coefficient in step 5.2, calculating LASAR linear array antenna observation space between different units lattice

In algorithm kth time iteration, LASAR is cut to any two the different units lattice in course made good observation angle interval, sequence number is designated as i and j respectively, i and j is natural number, and the span of i and j is respectively i=1,2 ..., M and j=1,2,, M and i ≠ j, wherein M is that the total interval discretize cell sum of observation angle in flight path-elevation plane cut by the LASAR linear array antenna that in step 3, initialization obtains; M the position of cell on ground level in the LASAR observation angle interval utilizing initialization in step 3 to obtain $q_m={\&lsqb;m\&CenterDot;H\&CenterDot;\frac{{\mathrm{\&theta;}}_0}{M}-H\&CenterDot;\frac{{\mathrm{\&theta;}}_0}{2},0\&rsqb;}^T,m=1,2,\mathrm{...},M,$ M=i the unit obtaining sequence number i value corresponding cuts course made good position, is designated as q _i, and q _ivalue be m=j the unit obtaining sequence number j value corresponding cuts course made good position, is designated as q _j, and q _jvalue be

Adopt formula l=1,2 ..., N _s, i=1,2 ..., M, calculates the oblique distance of l excitation array element in interval i-th cell to bare cloth linear array antenna of LASAR observation angle in algorithm kth iteration, is designated as R ^(k)(l, i), wherein for the location sets S that step 5.2 obtains ^(k)l row, || || ₂represent the L2 norm sign of operation of vector; Adopt formula $R^{\left(k\right)}(l,j)=\left|\right|s_l^{\left(k\right)}-q_j|{|}_2,l=1,2,\mathrm{...},N_S,j=1,2,\mathrm{...},M,$ Calculate the oblique distance to l excitation array element in the interval jth cell to bare cloth linear array antenna of LASAR observation angle in k iteration, be designated as R ^(k)(l, j); Adopt computing formula Δ R ^(k)(l, i, j)=R ^(k)(l, j)-R ^(k)(l, i), to calculate in kth iteration LASAR observation angle interval i-th with a jth cell to bare cloth linear array antenna in l encourage the oblique distance of array element poor, be designated as Δ R ^(k)(l, i, j);

Adopt formula ${\mathrm{\&rho;}}^{\left(k\right)}(i,j)=\frac{1}{N_S}\left|\underset{l=1}{\overset{N_S}{\&Sigma;}}\exp (-1i\&CenterDot;K_0\&CenterDot;{\mathrm{\&Delta;R}}^{\left(k\right)}(l,i,j\left)\right)\right|,i=1,2,\mathrm{...},M,j=1,2,\mathrm{...},M$ And i ≠ j, calculate i-th, LASAR observation angle interval and the related coefficient of a jth cell under Sparse array antenna conditions in kth iteration, be designated as ρ ^(k)(i, j), wherein N _sfor the array element sum in the bare cloth linear array antenna that step 2 initialization obtains, for element l value is from 1 to N _sin scope function summation symbol, exp () for natural constant e be the exponent arithmetic symbol at the end, || be the sign of operation that takes absolute value, 1i represents imaginary symbols, K ₀for radar system wave number and π is circular constant, and λ is the radar carrier frequency wavelength that step 1 initialization obtains;

Adopt formula g=|j-i|, i=1,2 ..., M, j=1,2 ..., M, i ≠ j calculates interval i-th absolute value poor with the sequence number of a jth cell of LASAR observation angle, and be designated as g, the span of natural number g is g=1, and 2 ..., M-1; By meet corresponding to g value all i-th with the correlation coefficient ρ of a jth cell under Sparse array antenna conditions ^(k)(i, j) summation is averaged, and obtains related coefficient result and is designated as g=1,2 ..., M-1; By all to sort from small to large composition of vector according to subscript sequence number, obtain the related coefficient vector in kth time iteration in LASAR linear array antenna observation space between different units lattice, be designated as wherein element value corresponding when being expressed as g=1 element value corresponding when being expressed as g=2 element value corresponding when being expressed as g=M-1

Step 5.3, utilize the value of threshold value constraint related coefficient vector

In kth time iteration, if vectorial X ^(k)in g element value be less than threshold value T, then keep this element value constant, if vectorial X ^(k)in g element value value be greater than threshold value T, then element value be set to threshold value T, obtain the related coefficient after threshold value constraint vector, be designated as Y ^(k), wherein X ^(k)for the related coefficient vector that step 5.2 obtains, T is the iterative algorithm correlation coefficient threshold that in step 4, initialization obtains.

The excitation vector of step 5.4, estimation LASAR bare cloth linear array antenna array element

In kth time iteration, adopt expression Z ^(k)=| IFFT (Y ^(k)) | calculate the vector after inverse Fourier transform, be designated as Z ^(k), wherein Y ^(k)for the related coefficient vector after the threshold value constraint that time iteration of kth in step 5.3 obtains, IFFT () is inverse Fourier transform sign of operation, || be the sign of operation that takes absolute value; By vector Z ^(k)in before N _sthe value of individual maximal value element is set to 1, and the value of other position element is set to 0, and the vector obtained is designated as C ^(k), wherein N _sfor the array element sum of the bare cloth linear array antenna that step 2 obtains; Adopt β ^(k)=C ^(k)obtain the excitation vector of LASAR bare cloth linear array antenna array element in kth time iteration.

Step 5.5, iterative criterion

If and k < MaxIter, then the value of k is updated to k+1, performs step 5.1 to step 5.5, otherwise termination algorithm iteration, this moment the β that obtains of kth time iteration ^(k)be the excitation vector that LASAR bare cloth linear array antenna array element is final, wherein be expressed as the function maximizing symbol in i and j variation range, k represents the kth iterations in iterative estimation procedure, and MaxIter is the maximum iteration time of the algorithm reconstruction processing that in step 4, initialization obtains, ρ ^(k)related coefficient in the kth time iteration LASAR linear array antenna observation space that (i, j) obtains for step 5.2 between different units lattice, ε is the stopping criterion for iteration threshold value in the iterative algorithm that in step 4, initialization obtains.

Step 6, obtain final bare cloth linear array antenna array element optimum results:

The LASAR bare cloth linear array antenna array element excitation vector β utilizing alternative manner step 5.5 finally to obtain ^(k), the location sets S of middle LASAR bare cloth linear array excitation array element is obtained according to step 5.1 ^(k); By the location sets S of LASAR bare cloth linear array excitation array element ^(k)give bare cloth linear array antenna array element, obtain the array element optimum results that LASAR Sparse array antenna is final.

Innovative point of the present invention is to utilize coherence's characteristic of calculation matrix in compressive sensing theory, provide a kind of compressed sensing LASAR bare cloth linear array optimization method based on Low coherence, the method minimizes based on compressed sensing calculation matrix coherence's in LASAR system, by Fourier transform iterative search method, achieve the array element distribution optimization design of compressed sensing LASAR bare cloth linear array antenna.

The invention has the advantages that the reference frame utilizing coherence's characteristic of calculation matrix in compressive sensing theory to optimize as compressed sensing LASAR Sparse array, more reasonable to Sparse array optimization, be conducive to the imaging performance improving compressed sensing LASAR system.The method that the present invention proposes also is applicable to other bare cloth linear array antenna optimisation technique field based on compressed sensing.

Accompanying drawing illustrates:

Fig. 1 is the compressed sensing LASAR bare cloth linear array optimization method treatment scheme schematic diagram based on Low coherence provided by the present invention.

Fig. 2 is the system emulation parameter list that the specific embodiment of the invention adopts.

Embodiment

The present invention mainly adopts the method for emulation experiment to verify, institute all verifies correct with conclusion in steps on MATLABR2012b software.Concrete implementation step is as follows:

Step 1, initialization LASAR systematic parameter:

Initialization LASAR systematic parameter comprises: Texas tower height H=1000m; Radar operating center frequency f _c=35 × 10 ⁹hz; Radar carrier frequency wavelength X=0.00857m; The signal bandwidth B of radar emission baseband signal _r=1.5 × 10 ⁸hz; Radar emission signal pulse width T _p=5 × 10 ^-6s; The chirp rate f of radar emission signal _dr=3 × 10 ¹³hz/s; Radar receives ripple door and continues width T _o=6 × 10 ^-4s; The sample frequency f of Radar Receiver System _s=3 × 10 ⁸hz; The pulse repetition rate PRF=600Hz of radar emission system; PRI=1 × 10 pulse-recurrence time of radar system ^-3s; Antenna in orientation to effective aperture length D _a=1.06m; Above-mentioned parameter is LASAR system standard parameter, determines in LASAR system and observation process; According to LASAR imaging system scheme and observation program, the initializes system parameters that LASAR bare cloth linear array antenna optimization method needs is known.

The parameter of step 2, initialization LASAR bare cloth linear array antenna:

The parameter of initialization LASAR bare cloth linear array antenna comprises: the array element sum N of full front array antenna _a=1000; In full front array antenna, the spacing d of adjacent array element is the half of LASAR system carrier frequency wavelength, namely wherein λ is radar carrier frequency wavelength X=0.00857m that in step 1, initialization obtains; The array length L value of full front array antenna is L=(N _a-1) d; Array element sum N in bare cloth linear array antenna _s=500; The subset of bare cloth linear array antenna array element Shi Man front array antenna array element, namely bare cloth linear array antenna array element is from full front array antenna 1000 array elements, choose 500 array element compositions; In full front array antenna, the 1st array element is p cutting the position in flight path-elevation plane ₁=[0, H] ^t, wherein H is Texas tower height H=1000m that in step 1, initialization obtains; In full front array antenna, the 2nd array element is p cutting the position in flight path-elevation plane ₂=[d, H] ^t; N in full front array antenna _aindividual array element cutting the position in flight path-elevation plane is in full front array antenna, the n-th array element is set to p cutting flight path-elevation plane meta _n, wherein subscript n is the sequence number of the n-th array element in full front array antenna, and n is natural number, n=1,2 ..., N _a, N _a=1000, and p _n=[(n-1) d, H] ^t; In full front array antenna, all array element is cutting the location sets P in flight path-elevation plane, and wherein gathering P is a 2 × N _athe matrix of dimension, and $P=\&lsqb;p_1,p_2,\mathrm{...},p_{N_A}\&rsqb;.$

Step 3, initialization LASAR linear array antenna observation space parameter:

Initialization LASAR linear array antenna observation space parameter, comprising: with the 1st of full front array antenna the element position for reference array element, and the interval size θ of the observation angle in flight path-elevation plane cut by linear array antenna ₀=10 °; LASAR linear array antenna is [-5 °, 5 °] cutting the total interval of the observation angle in flight path-elevation plane; Total interval discretize cell sum M=1000 of observation angle in flight path-elevation plane cut by LASAR linear array antenna; With the reference array element of full front array antenna for the center of circle, LASAR linear array antenna is evenly divided into equal-sized angle-unit lattice cutting the total interval of observation angle in flight path-elevation plane; Adopt formula calculate m the position q of cell on ground level in LASAR observation angle interval _m, wherein m represents m angle-unit lattice in LASAR observation angle interval, and m is natural number, m=1,2 ..., M; H is Texas tower height H=1000m that in step 1, initialization obtains, upper right corner symbol T representing matrix transpose operation symbol.

The correlation parameter of step 4, initialization LASAR bare cloth linear array antenna optimization method:

The correlation parameter of initialization LASAR bare cloth linear array antenna optimization method comprises: the maximum iteration time MaxIter=100 of algorithm iteration estimation procedure; K is the kth time iteration of iterative estimation procedure, and k is natural number, and k initial value is set to k=0, and k span is k=0,1,2 ..., MaxIter; Correlation coefficient threshold T=0.3 in iterative algorithm; Stopping criterion for iteration threshold value in iterative algorithm is ε=0.1; The excitation vector β of LASAR bare cloth linear array antenna array element in kth time iteration ^(k), k=0,1,2 ..., MaxIter, MaxIter=100, β ^(k)a N _athe vector of dimension size; Random generation N _athe vectorial α of dimension, wherein in α, each element value is only 1 or 0, and the element number that value is 1 is N _s, wherein, N _afor array element sum N in the full front array antenna that step 2 initialization obtains _a=1000, N _sfor array element sum N in the bare cloth linear array antenna that step 2 initialization obtains _s=500; Vectorial α assignment is given the excitation vector β of LASAR bare cloth linear array antenna array element in all iterative process ^(k), k=0,1,2 ..., MaxIter, MaxIter=100, as bare cloth linear array antenna array element excitation vector β ^(k)initial value; Excitation vector β in kth time iteration ^(k)middle element value is the sequence number set of the element position composition of 1 is Ω ^(k), k=0,1,2 ..., MaxIter, MaxIter=100, sequence number set omega ^(k)be a N _sthe vector of dimension size, sequence number set omega ^(k)in element value be the array element sequence number that in kth time iteration, bare cloth linear array excitation array element is corresponding in full front array antenna.

Step 5, employing iterative algorithm carry out LASAR bare cloth linear array optimal design, and this iterative algorithm mainly comprises step 5.1 to step 5.5, and concrete steps realize as follows:

Step 5.1, in kth time iteration, calculate the position of LASAR bare cloth linear array antenna excitation array element

In kth time iterative process, if during iterations k=0, according to set omega ⁽⁰⁾in element, in full front array antenna, choose corresponding array element, obtain the location sets S of LASAR bare cloth linear array excitation array element in the 0th iteration ⁽⁰⁾; S ⁽⁰⁾be expressed as in location sets P and choose that to meet element numbers be Ω ⁽⁰⁾element value composition location sets, S ⁽⁰⁾a 2 × N _sthe matrix of dimension; Matrix S ⁽⁰⁾column vector composition expression-form be wherein for matrix S ⁽⁰⁾the 1st row and physical significance be in the 0th iteration in bare cloth linear array antenna the 1st excitation element position, for matrix S ⁽⁰⁾the 2nd row and physical significance be in the 0th iteration in bare cloth linear array antenna the 2nd excitation element position, for matrix S ⁽⁰⁾n _srow and physical significance is N in bare cloth linear array antenna in the 0th iteration _sindividual excitation element position; Matrix S ⁽⁰⁾l row be designated as and physical significance be in the 0th iteration in bare cloth linear array antenna l excitation element position, l is natural number, and the span of l is l=1,2 ..., N _s, wherein k=0,1,2 ..., MaxIter, MaxIter=100, Ω ⁽⁰⁾for excitation vector β in the 0th iteration that step 4 initialization obtains ⁽⁰⁾middle element value is the sequence number set of the element position composition of 1, β ⁽⁰⁾for the excitation vector of LASAR bare cloth linear array antenna array element in the 0th iteration in step 4, P is that in the full front array antenna that in step 2, initialization obtains, each array element is cutting the location sets of course made good, N _sfor the bare cloth linear array antenna array element sum N that step 2 initialization obtains _s=500;

In algorithm kth time iteration, if during iterations k > 0, in full front array antenna, choose array element sequence number is set omega ^(k-1)corresponding to middle element array element, obtain the element position S set of bare cloth linear array excitation array element in kth time iteration ^(k), k=0,1,2 ..., MaxIter, MaxIter=100; S ^(k)in location sets P, choose that to meet element numbers be Ω ^(k)element value composition location sets, S ^(k)a 2 × N _sthe matrix of dimension; Matrix S ^(k)column vector composition expression-form be $S^{\left(k\right)}=[s_1^{\left(k\right)},s_2^{\left(k\right)},...,s_{N_S}^{\left(k\right)}],k=\mathrm{0,1,2},...,\mathrm{MaxIter},$ MaxIter=100, for matrix S ^(k)the 1st row and physical significance is the 1st excitation element position in bare cloth linear array antenna in kth time iteration, for matrix S ^(k)the 2nd row and physical significance is the 2nd excitation element position in bare cloth linear array antenna in kth time iteration, for matrix S ^(k)n _srow and physical significance are N in bare cloth linear array antenna in kth time iteration _sindividual excitation element position, matrix S ^(k)l row be designated as and physical significance be in kth time iteration in bare cloth linear array antenna l encourage element position, l is natural number, l=1,2 ..., N _s, wherein MaxIter is the maximum iteration time MaxIter=100 of algorithm iteration estimation procedure in step 4, Ω ^(k-1)for the excitation vector β obtained in iterative algorithm kth-1 iteration in step 4 ^(k-1)middle element value is the sequence number set of 1 element position composition, β ^(k-1)for the excitation vector of LASAR bare cloth linear array antenna array element in-1 iteration of kth in step 4.

Related coefficient in step 5.2, calculating LASAR linear array antenna observation space between different units lattice

In algorithm kth time iteration, LASAR is cut to any two the different units lattice in course made good observation angle interval, sequence number is designated as i and j respectively, i and j is natural number, and the span of i and j is respectively i=1,2 ..., M and j=1,2,, M and i ≠ j, wherein M is that in step 3, total interval discretize cell sum M=1000 of observation angle in flight path-elevation plane cut by LASAR linear array antenna; M the position of cell on ground level in the LASAR observation angle interval utilizing initialization in step 3 to obtain $q_m={\&lsqb;m\&CenterDot;H\&CenterDot;\frac{{\mathrm{\&theta;}}_0}{M}-H\&CenterDot;\frac{{\mathrm{\&theta;}}_0}{2},0\&rsqb;}^T,m=1,2,\mathrm{...},M,M=1000,$ M=i the unit obtaining sequence number i value corresponding cuts course made good position q _i, and q _ivalue be m=j the unit obtaining sequence number j value corresponding cuts course made good position q _j, and q _jvalue be wherein H is Texas tower height H that in step 1, initialization obtains=1000m, θ ₀for the interval size θ of the observation angle in flight path-elevation plane cut by step 3 linear array antenna ₀=10 °, upper right corner symbol T representing matrix transpose operation symbol;

Adopt formula $R^{\left(k\right)}(l,i)=\left|\right|s_l^{\left(k\right)}-q_i|{|}_2,k=0,1,2,\mathrm{...},MaxIter,l=1,2,\mathrm{...},N_S,i=1,2,\mathrm{...},M,$ Calculate the oblique distance R of l excitation array element in interval i-th cell to bare cloth linear array antenna of LASAR observation angle in algorithm kth iteration ^(k)(l, i), wherein MaxIter is the maximum iteration time MaxIter=100 of algorithm iteration estimation procedure in step 4, N _sfor the bare cloth linear array antenna array element sum N that step 2 initialization obtains _s=500, M is that total interval discretize cell sum M=1000 of observation angle in flight path-elevation plane cut by the LASAR linear array antenna that in step 3, initialization obtains, for the location sets S that step 5.2 obtains ^(k)l row, || || ₂represent the L2 norm sign of operation of vector; Adopt formula $R^{\left(k\right)}(l,j)=\left|\right|s_l^{\left(k\right)}-q_j|{|}_2,l=1,2,\mathrm{...},N_S,j=1,2,\mathrm{...},M,$ Calculate the oblique distance R to l excitation array element in the interval jth cell to bare cloth linear array antenna of LASAR observation angle in k iteration ^(k)(l, j); Adopt formula Δ R ^(k)(l, i, j)=R ^(k)(l, j)-R ^(k)(l, i) calculate LASAR observation angle in kth iteration interval i-th with a jth cell to bare cloth linear array antenna in l encourage the poor Δ R of the oblique distance of array element ^(k)(l, i, j), k=0,1,2 ..., MaxIter, l=1,2 ..., N _s, i=1,2 ..., M, j=1,2 ..., M, MaxIter=100, N _s=500, M=1000;

Adopt formula ${\mathrm{\&rho;}}^{\left(k\right)}(i,j)=\frac{1}{N_S}\left|\underset{l=1}{\overset{N_S}{\&Sigma;}}\exp (-1i\&CenterDot;K_0\&CenterDot;{\mathrm{\&Delta;R}}^{\left(k\right)}(l,i,j\left)\right)\right|,k=0,1,2,\mathrm{...},MaxIter,i=1,2,\mathrm{...},M,$ $j=1,2,\mathrm{...},M$ And i ≠ j, calculate i-th, LASAR observation angle interval and the correlation coefficient ρ of a jth cell under Sparse array antenna conditions in kth iteration ^(k)(i, j), for element l value is from 1 to N _sin scope function summation symbol, exp () for natural constant e be the exponent arithmetic symbol at the end, || be the sign of operation that takes absolute value, 1i represents imaginary symbols, K ₀for radar system wave number and π is pi=3.1415, and λ is radar carrier frequency wavelength X=0.00857m that step 1 initialization obtains;

Adopt formula g=|j-i|, i=1,2 ..., M, j=1,2 ..., M, i ≠ j, M=1000, calculate interval i-th the absolute value g poor with the sequence number of a jth cell of LASAR observation angle, the span of natural number g is g=1,2 ..., M-1; By meet corresponding to g value all i-th with the correlation coefficient ρ of a jth cell under Sparse array antenna conditions ^(k)(i, j) summation is averaged, and obtains related coefficient result g=1,2 ..., M-1; By all to sort from small to large composition of vector according to subscript sequence number, obtain the related coefficient vector in kth time iteration in LASAR linear array antenna observation space between different units lattice wherein element value corresponding when being expressed as g=1 element value corresponding when being expressed as g=2 element value corresponding when being expressed as g=M-1 k=0,1,2 ..., MaxIter, MaxIter=100.

Step 5.3, utilize the value of threshold value constraint related coefficient vector

In kth time iteration, if vectorial X ^(k)in g element value be less than threshold value T, then keep this element value constant, if vectorial X ^(k)in g element value value be greater than threshold value T, then element value be set to threshold value T, obtain the related coefficient after threshold value constraint vector Y ^(k), wherein X ^(k)for the related coefficient vector in LASAR linear array antenna observation space in the kth time iteration that step 5.2 obtains between different units lattice, k=0,1,2, MaxIter, wherein MaxIter is the maximum iteration time MaxIter=100 of algorithm iteration estimation procedure in step 4, T is the iterative algorithm correlation coefficient threshold T=0.3 that in step 4, initialization obtains.

The excitation vector of step 5.4, estimation LASAR bare cloth linear array antenna array element

In kth time iteration, adopt expression Z ^(k)=| IFFT (Y ^(k)) | calculate the vector Z after inverse Fourier transform ^(k), by vector Z ^(k)in before N _sthe value of individual maximal value element is set to 1, and the value of other position element is set to 0, obtains vectorial C ^(k), adopt β ^(k)=C ^(k)obtain the excitation vector of LASAR bare cloth linear array antenna array element in kth time iteration, k=0,1,2 ..., MaxIter; Wherein Y ^(k)for the related coefficient vector after the threshold value constraint that time iteration of kth in step 5.3 obtains, MaxIter is the maximum iteration time of algorithm iteration estimation procedure in step 4 is MaxIter=100, IFFT () is inverse Fourier transform sign of operation, || be the sign of operation that takes absolute value, N _sfor the array element sum N of the bare cloth linear array antenna that step 2 obtains _s=500.

Step 5.5, iterative criterion

If and k < MaxIter, then the value of k is updated to k+1, performs step 5.1 to step 5.5, otherwise termination algorithm iteration, this moment the β that obtains of kth time iteration ^(k)be the excitation vector that LASAR bare cloth linear array antenna array element is final, wherein be expressed as the function maximizing symbol in i and j variation range, k represents the kth iterations in iterative estimation procedure, k=0,1,2 ... MaxIter, MaxIter are the maximum iteration time MaxIter=100 of the algorithm iteration estimation procedure obtained in step 4, ρ ^(k)related coefficient in the kth time iteration LASAR linear array antenna observation space that (i, j) obtains for step 5.2 between different units lattice, ε is stopping criterion for iteration threshold epsilon=0.1 in the iterative algorithm that in step 4, initialization obtains.

Step 6, obtain final bare cloth linear array antenna array element optimum results:

The LASAR bare cloth linear array antenna array element excitation vector β utilizing alternative manner step 5.5 finally to obtain ^(k), the location sets S of middle LASAR bare cloth linear array excitation array element is obtained according to step 5.1 ^(k), by the location sets S of LASAR bare cloth linear array excitation array element ^(k)give bare cloth linear array antenna array element, obtain the final array element of LASAR Sparse array antenna and optimize position.

Claims (1)

1., based on a compressed sensing LASAR bare cloth linear array optimization method for Low coherence, it is characterized in that it comprises the following steps:

Step 1, initialization LASAR systematic parameter:

Initialization LASAR systematic parameter comprises: Texas tower height, is denoted as H; Radar operating center frequency, is denoted as f _c; Radar carrier frequency wavelength, is denoted as λ; The signal bandwidth of radar emission baseband signal, is denoted as B _r; Radar emission signal pulse width, is denoted as T _p; The chirp rate of radar emission signal, is denoted as f _dr; Radar receives ripple door and continues width, is denoted as T _o; The sample frequency of Radar Receiver System, is denoted as f _s; The pulse repetition rate of radar emission system, is denoted as PRF; The pulse-recurrence time of radar system, be designated as PRI; Antenna in orientation to effective aperture length, be denoted as D _a; Above-mentioned parameter is LASAR system standard parameter, wherein Texas tower height H, radar center frequency f _c, radar carrier frequency wavelength X, the signal bandwidth B of radar emission baseband signal _r, radar emission signal pulse width T _p, radar emission signal chirp rate f _dr, radar receives ripple door and continues width T _o, the sample frequency f of Radar Receiver System _s, the pulse repetition rate PRF of radar system, PRI pulse-recurrence time of radar system, antenna in orientation to effective aperture length D _adetermine in LASAR system and observation process; According to LASAR imaging system scheme and observation program, the initializes system parameters that LASAR bare cloth linear array antenna optimization method needs is known;

The parameter of step 2, initialization LASAR bare cloth linear array antenna:

The parameter of initialization LASAR bare cloth linear array antenna comprises: the array element sum of full front array antenna is designated as N _a; The spacing of adjacent array element in full front array antenna, be designated as d, in LASAR system, the value of d is the half of system carrier frequency wavelength, is wherein λ is the radar carrier frequency wavelength that in step 1, initialization obtains; The array length of full front array antenna, be designated as L, and the value of L is L=(N _a-1) d; Array element sum in bare cloth linear array antenna, is designated as N _s, and N _s< N _a; The subset of bare cloth linear array antenna array element Shi Man front array antenna array element, namely bare cloth linear array antenna array element is the N from full front array antenna _an is chosen in individual array element _sindividual array element composition; In full front array antenna, the 1st array element is cutting the position in flight path-elevation plane, is designated as p ₁; In full front array antenna, the 2nd array element is cutting the position in flight path-elevation plane, is designated as p ₂; N in full front array antenna _aindividual array element, cutting the position in flight path-elevation plane, is designated as in full front array antenna, the n-th array element is cutting the position in flight path-elevation plane, is designated as p _n, wherein subscript n is the sequence number of the n-th array element in full front array antenna, and n is natural number, n=1,2 ..., N _a, and p _n=[(n-1) d, H] ^t, wherein H is the Texas tower height that in step 1, initialization obtains; In full front array antenna, all array element is cutting the location sets in flight path-elevation plane, is denoted as P, and wherein gathering P is a 2 × N _athe matrix of dimension, and $P=\&lsqb;p_1,p_2,...,p_{N_A}\&rsqb;;$

Step 3, initialization LASAR linear array antenna observation space parameter:

Initialization linear array SAR linear array antenna observation space parameter, comprising: with the 1st of full front array antenna the element position for reference array element, and linear array antenna, cutting the interval size of the observation angle in flight path-elevation plane, is designated as θ ₀; LASAR linear array antenna, to cut the observation angle in flight path-elevation plane always interval, is designated as $\&lsqb;-\frac{{\mathrm{\&theta;}}_0}{2},\frac{{\mathrm{\&theta;}}_0}{2}\&rsqb;;$ LASAR linear array antenna, cutting the total interval discretize cell sum of observation angle in flight path-elevation plane, is designated as M; With the reference array element of full front array antenna for the center of circle, LASAR linear array antenna is evenly divided into equal-sized angle-unit lattice cutting the total interval of observation angle in flight path-elevation plane, and angle value corresponding to each angle-unit lattice is less than LASAR linear array antenna is cutting the angular resolution of course made good; Adopt formula $q_m={\&lsqb;m\&CenterDot;H\&CenterDot;\frac{{\mathrm{\&theta;}}_0}{M}-H\&CenterDot;\frac{{\mathrm{\&theta;}}_0}{2},0\&rsqb;}^T,$ M=1,2 ..., M, calculates m the position of cell on ground level in LASAR observation angle interval, is designated as q _m, m=1,2 ..., M, wherein m represents m angle-unit lattice in LASAR observation angle interval, and m is natural number, and m=1,2 ..., M; H is the Texas tower height that in step 1, initialization obtains, and upper right corner symbol T represents transpose operation symbol;

The correlation parameter of step 4, initialization LASAR bare cloth linear array antenna optimization method:

The correlation parameter of initialization LASAR bare cloth linear array antenna optimization method comprises: the maximum iteration time of algorithm iteration estimation procedure, is denoted as MaxIter; K is designated as the kth time iteration of iterative estimation procedure, and k is natural number, and k initial value is set to k=0, and the span of k is k=0, and 1,2 ..., MaxIter; Correlation coefficient threshold in iterative algorithm, is designated as T; Stopping criterion for iteration threshold value in iterative algorithm, is designated as ε; In kth time iteration, the excitation vector of LASAR bare cloth linear array antenna array element, is designated as β ^(k), k=0,1,2 ..., MaxIter, wherein β ^(k)a N _athe vector of dimension size, N _ait is the array element sum of the full front array antenna that in step 2, initialization obtains; Random generation N _athe vector of dimension, be designated as α, wherein in α, each element value is only 1 or 0, and the element number that value is 1 is N _s, N _sfor the array element sum of the bare cloth linear array antenna that initialization in step 2 obtains; Vectorial α assignment is given the excitation vector β of LASAR bare cloth linear array antenna array element in all iterative process ^(k), k=0,1,2 ..., MaxIter, as bare cloth linear array antenna array element excitation vector β ^(k)initial value; Excitation vector β in kth time iteration ^(k)middle element value is the sequence number set of the element position composition of 1, is designated as Ω ^(k), k=0,1,2 ..., MaxIter, wherein sequence number set omega ^(k)be a N _sthe vector of dimension size; Sequence number set omega ^(k)in element value be the array element sequence number that in kth time iteration, bare cloth linear array excitation array element is corresponding in full front array antenna;

Step 5, employing iterative algorithm carry out LASAR bare cloth linear array optimal design, and this iterative algorithm mainly comprises step 5.1 to step 5.5, and concrete steps realize as follows:

Step 5.1, in kth time iteration, calculate the position of LASAR bare cloth linear array antenna excitation array element

In kth time iterative process, if during iterations k=0, according to set omega ⁽⁰⁾in element, in full front array antenna, choose corresponding array element, obtain the location sets of LASAR bare cloth linear array excitation array element in the 0th iteration, be designated as S ⁽⁰⁾, wherein Ω ⁽⁰⁾for excitation vector β in the 0th iteration that step 4 initialization obtains ⁽⁰⁾middle element value is the sequence number set of the element position composition of 1, β ⁽⁰⁾it is the excitation vector of LASAR bare cloth linear array antenna array element in the 0th iteration; S ⁽⁰⁾be expressed as in location sets P and choose that to meet element numbers be Ω ⁽⁰⁾element value composition location sets, S ⁽⁰⁾be a 2 × N _sthe matrix of dimension, wherein P is that in the full front array antenna that in step 2, initialization obtains, each array element is cutting the location sets of course made good; Order matrix S ⁽⁰⁾column vector composition expression-form be wherein for matrix S ⁽⁰⁾the 1st row and physical significance be in the 0th iteration in bare cloth linear array antenna the 1st excitation element position, for matrix S ⁽⁰⁾the 2nd row and physical significance be in the 0th iteration in bare cloth linear array antenna the 2nd excitation element position, for matrix S ⁽⁰⁾n _srow and physical significance is N in bare cloth linear array antenna in the 0th iteration _sindividual excitation element position; Matrix S ⁽⁰⁾l row be designated as and physical significance be in the 0th iteration in bare cloth linear array antenna l excitation element position, l is natural number, and the span of l is l=1,2 ..., N _s, N _sfor the bare cloth linear array antenna array element sum that step 2 initialization obtains;

In algorithm kth time iteration, if during iterations k > 0, in full front array antenna, choose array element sequence number is set omega ^(k-1)corresponding to middle element array element, obtain the element position set of LASAR bare cloth linear array excitation array element in kth time iteration, be designated as S ^(k), wherein Ω ^(k-1)for the excitation vector β obtained in iterative algorithm kth-1 iteration ^(k-1)middle element value is the sequence number set of 1 element position composition, β ^(k-1)for the excitation vector of LASAR bare cloth linear array antenna array element in kth-1 iteration; S ^(k)be expressed as in location sets P and choose that to meet element numbers be Ω ^(k)element value composition location sets, S ^(k)be a 2 × N _sthe matrix of dimension; Definition matrix S ^(k)column vector composition expression-form be wherein for matrix S ^(k)the 1st row and physical significance is the 1st excitation element position in bare cloth linear array antenna in kth time iteration, for matrix S ^(k)the 2nd row and physical significance is the 2nd excitation element position in bare cloth linear array antenna in kth time iteration, for matrix S ^(k)n _srow and physical significance are N in bare cloth linear array antenna in kth time iteration _sindividual excitation element position, matrix S ^(k)l row be designated as and physical significance be in kth time iteration in bare cloth linear array antenna l encourage element position, l is natural number, and l=1,2 ..., N _s;

Related coefficient in step 5.2, calculating LASAR linear array antenna observation space between different units lattice

In algorithm kth time iteration, LASAR is cut to any two the different units lattice in course made good observation angle interval, sequence number is designated as i and j respectively, i and j is natural number, and the span of i and j is respectively i=1,2 ..., M and j=1,2,, M and i ≠ j, wherein M is that the total interval discretize cell sum of observation angle in flight path-elevation plane cut by the LASAR linear array antenna that in step 3, initialization obtains; M the position of cell on ground level in the LASAR observation angle interval utilizing initialization in step 3 to obtain m=1,2 ..., M, m=i the unit obtaining sequence number i value corresponding cuts course made good position, is designated as q _i, and q _ivalue be m=j the unit obtaining sequence number j value corresponding cuts course made good position, is designated as q _j, and q _jvalue be

Adopt formula l=1,2 ..., N _s, i=1,2 ..., M, calculates the oblique distance of l excitation array element in interval i-th cell to bare cloth linear array antenna of LASAR observation angle in algorithm kth iteration, is designated as R ^(k)(l, i), wherein for the location sets S that step 5.2 obtains ^(k)l row, || || ₂represent the L2 norm sign of operation of vector; Adopt formula l=1,2 ..., N _s, j=1,2 ..., M, calculates the oblique distance to l excitation array element in the interval jth cell to bare cloth linear array antenna of LASAR observation angle in k iteration, is designated as R ^(k)(l, j); Adopt formula Δ R ^(k)(l, i, j)=R ^(k)(l, j)-R ^(k)(l, i) to calculate in kth iteration LASAR observation angle interval i-th with a jth cell to bare cloth linear array antenna in l encourage the oblique distance of array element poor, be designated as Δ R ^(k)(l, i, j);

Adopt formula ${\mathrm{\&rho;}}^{\left(k\right)}(i,j)=\frac{1}{N_S}\left|\underset{l=1}{\overset{N_S}{\&Sigma;}}\exp (-1i\&CenterDot;K_0\&CenterDot;{\mathrm{\&Delta;R}}^{\left(k\right)}(l,i,j\left)\right)\right|,$ I=1,2 ..., M, j=1,2 ..., M and i ≠ j, calculate LASAR observation angle in kth iteration interval i-th and the related coefficient of a jth cell under Sparse array antenna conditions, be designated as ρ ^(k)(i, j), wherein N _sfor the array element sum in the bare cloth linear array antenna that step 2 initialization obtains, for element l value is from 1 to N _sin scope function summation symbol, exp () for natural constant e be the exponent arithmetic symbol at the end, || be the sign of operation that takes absolute value, 1i represents imaginary symbols, K ₀for radar system wave number and π is circular constant, and λ is the radar carrier frequency wavelength that step 1 initialization obtains;

Adopt formula g=|j-i|, i=1,2 ..., M, j=1,2 ..., M, i ≠ j calculates interval i-th absolute value poor with the sequence number of a jth cell of LASAR observation angle, and be designated as g, the span of natural number g is g=1, and 2 ..., M-1; By meet corresponding to g value all i-th with the correlation coefficient ρ of a jth cell under Sparse array antenna conditions ^(k)(i, j) summation is averaged, and obtains related coefficient result and is designated as g=1,2 ..., M-1; By all to sort from small to large composition of vector according to subscript sequence number, obtain the related coefficient vector in kth time iteration in LASAR linear array antenna observation space between different units lattice, be designated as wherein element value corresponding when being expressed as g=1 element value corresponding when being expressed as g=2 element value corresponding when being expressed as g=M-1

Step 5.3, utilize the value of threshold value constraint related coefficient vector

In kth time iteration, if vectorial X ^(k)in g element value be less than threshold value T, then keep this element value constant, if vectorial X ^(k)in g element value value be greater than threshold value T, then element value be set to threshold value T, obtain the related coefficient after threshold value constraint vector, be designated as Y ^(k), wherein X ^(k)for the related coefficient vector that step 5.2 obtains, T is the iterative algorithm correlation coefficient threshold that in step 4, initialization obtains;

The excitation vector of step 5.4, estimation LASAR bare cloth linear array antenna array element

In kth time iteration, adopt expression Z ^(k)=| IFFT (Y ^(k)) | calculate the vector after inverse Fourier transform, be designated as Z ^(k), wherein Y ^(k)for the related coefficient vector after the threshold value constraint that time iteration of kth in step 5.3 obtains, IFFT () is inverse Fourier transform sign of operation, || be the sign of operation that takes absolute value; By vector Z ^(k)in before N _sthe value of individual maximal value element is set to 1, and the value of other position element is set to 0, and the vector obtained is designated as C ^(k), wherein N _sfor the array element sum of the bare cloth linear array antenna that step 2 obtains; Adopt β ^(k)=C ^(k)obtain the excitation vector of LASAR bare cloth linear array antenna array element in kth time iteration;

Step 5.5, iterative criterion

If and k < MaxIter, then the value of k is updated to k+1, performs step 5.1 to step 5.5, otherwise termination algorithm iteration, this moment the β that obtains of kth time iteration ^(k)be the excitation vector that LASAR bare cloth linear array antenna array element is final, wherein be expressed as the function maximizing symbol in i and j variation range, k represents the kth iterations in iterative estimation procedure, and MaxIter is the maximum iteration time of the algorithm reconstruction processing that in step 4, initialization obtains, ρ ^(k)related coefficient in the kth time iteration LASAR linear array antenna observation space that (i, j) obtains for step 5.2 between different units lattice, ε is the stopping criterion for iteration threshold value in the iterative algorithm that in step 4, initialization obtains;

Step 6, obtain final bare cloth linear array antenna array element optimum results:

The LASAR bare cloth linear array antenna array element excitation vector β utilizing alternative manner step 5.5 finally to obtain ^(k), the location sets S of middle LASAR bare cloth linear array excitation array element is obtained according to step 5.1 ^(k); By the location sets S of LASAR bare cloth linear array excitation array element ^(k)give bare cloth linear array antenna array element, obtain the array element optimum results that LASAR Sparse array antenna is final.