CN102608602B - Ultralow sidelobe synthetic aperture radar imaging method based on complete complementary sequence - Google Patents

Abstract

The invention discloses an ultralow sidelobe synthetic aperture radar imaging method based on a complete complementary sequence. The ultralow sidelobe synthetic aperture radar imaging method includes steps of 1, dividing echo data based on signal waveforms of the complete complementary sequence into echo data which are obtained by means of utilizing two complementary sequences as radar transmitting signals independently; 2, compressing range pulses based on matched filtering; 3, performing azimuth Fourier transformation; 4, correcting range migratory motion; 5, performing azimuth data high-frequency zero fill; 6, shifting and adding the data after zero rill; and 7, performing azimuth compressing to obtain a final image. The ultralow sidelobe synthetic aperture radar imaging method has the advantages that radar signal waveforms are easy to be generated, pulse compressing is easy to be realized, azimuth ultralow sidelobe is realized, and azimuth resolution and image quality are high.

Description

A kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence

Technical field

The present invention relates to a kind of ULTRA-LOW SIDE LOBES based on fully-complementary sequence, high resolution synthetic aperture radar formation method, belong to the signal processing technology field.

Background technology

Synthetic aperture radar (SAR) has round-the-clock, round-the-clock earth observation ability, is the earth observation systems that receives much concern at present.Current, picture quality is one of restriction SAR key in application factor.Spatial resolution, secondary lobe ratio, blur level are to weigh the important indicator of SAR picture quality.The SAR system of traditional system adopts linear FM signal as the radar emission signal waveform, and under not weighting condition, it is about-13.2dB apart from the peak sidelobe ratio after compressing.In the actual imaging processing procedure, adopt the frequency domain weighting method to come suppressed sidelobes usually, its shortcoming is to have sacrificed spatial resolution.

In recent years, signal waveform that the scholar proposes to adopt other is arranged in succession as the radar emission signal, with improve distance to the secondary lobe ratio, and improve signal noise ratio (snr) of image.Wherein, phase-coded signal is one of present research focus.Because phase-coded signal is easy to generate and handle, therefore frequent pulse compression signal as radar.Yet common phase-coded signal still can't realize distance to the ULTRA-LOW SIDE LOBES performance, and for traditional linear FM signal, its advantage is also not obvious.

Fully-complementary sequence belongs to the phase encoding category, because its good related function has obtained to use widely in communication system.Research to complementary series starts from the sixties in 20th century, and it is right that Golay etc. have studied some scale-of-two complementary seriess, and the auto-correlation function value of these complementary pairs all is zero when all even number displacements.People such as Peter expand to two-dimentional two-phase, four phase quadrature complete complementary codes with the one dimension mutual-complementing code, the correlation properties of each dimensional signal are carried out the derivation of theoretical property.About mutual-complementing code as radar signal, also have pertinent literature to analyze: the mutual-complementing code of A.K.Ojha noise and object wave emotionally the performance under the condition study, the performance of complementary series and the performance of pseudo-random sequence are compared, and the robustness of the mutual-complementing code of quadrature sampling analyzed, draw the relation of resolution and sequence number and Baud Length.Z.Peter etc. have utilized Prometheus's orthogonal set technical construction one class complementary series is analyzed its fuzzy behaviour.Suehiro promotes the concept of mutual-complementing code, and having proposed auto-correlation function value all is zero in the non-zero displacement, and cross-correlation function value also all is zero fully-complementary sequence.

At present, the application in synthetic-aperture radar also rarely has the document introduction about fully-complementary sequence.Because fully-complementary sequence is made of two complementary phases bursts, needs at first carry out distance respectively to matched filtering to the radar echo signal of two complementary phases bursts, again they are sued for peace to finish distance to pulse compression, this pulse compression signal is approximately impulse function in theory, does not have secondary lobe.In order to take full advantage of this good characteristic of fully-complementary sequence, need two composition sequences are handled respectively.For fear of two composition sequence phases mutual interference of fully-complementary sequence, two sequences must be in the alternately emission of adjacent pulse repetition period.This means the difference of the residing orientation moment of pulse that two sequences form, cause its time-delay phase place difference, destroyed the no sidelobe performance of fully-complementary sequence pulse compression signal.This problem causes based on the imaging performance of fully-complementary sequence signal waveform even is worse than traditional linear FM signal, and its advantage does not embody fully, thereby has limited the application of fully-complementary sequence in synthetic-aperture radar.

Summary of the invention

The objective of the invention is in order to solve the bottleneck technical matters of fully-complementary sequence in the synthetic aperture radar image-forming system applies, a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence is proposed, take full advantage of orthogonality and the ULTRA-LOW SIDE LOBES performance of fully-complementary sequence, realize that synthetic-aperture radar high resolving power, distance are to ULTRA-LOW SIDE LOBES imaging New System.This method can improve the picture quality of synthetic-aperture radar, and then improves the interpretability of diameter radar image, the application of expansion synthetic-aperture radar in remote sensing science.

A kind of synthetic-aperture radar high resolving power based on fully-complementary sequence, ultralow distance comprise following step to the secondary lobe formation method:

Step 1: will be divided into the echo data that obtains as the radar emission signal with two complementary seriess separately based on the echo data of fully-complementary sequence signal waveform;

To be divided into the echo data that obtains as the radar emission signal with sequence A and sequence B separately based on the echo data C of fully-complementary sequence signal waveform, the echo data after the separation is respectively two-dimentional plural groups C ₁And C ₂, size is (X/2) * Y;

Step 2: the range pulse compression based on matched filtering is handled;

Utilize two mutual-complementing code sequence signals of fully-complementary sequence as the reference signal, respectively to the echo data C of sequence A and sequence B ₁And C ₂Carry out distance to matched filtering, finish apart from compression process, two signals after obtaining to compress are respectively D ₁And D ₂

Step 3: the orientation is to Fourier transform;

Data D after the distance compression that step 2 is obtained ₁And D ₂Carry out Fast Fourier Transform (FFT) (FFT) along each range gate (by row), obtain the orientation to frequency spectrum data D _1-FFTAnd D _2-FFT

Then with the orientation to frequency spectrum data D _1-FFTAnd D _2-FFTPreceding X/4 line data and back X/4 line data exchange, obtain orientation frequency spectrum data E ₁And E ₂

Step 4: range migration correction;

The orientation frequency spectrum data E that obtains for step 3 ₁And E ₂, utilize the sinc method of interpolation to carry out accurate correction distance migration, obtain carrying out the data F behind the range migration correction respectively ₁And F ₂

Step 5: the orientation is to the zero padding of data high frequency;

Data F behind the range migration correction that step 4 is obtained ₁And F ₂HFS in frequency domain carries out zero padding to be handled, and the zero padding number is Y/2; Data after the zero padding multiply by two times, obtain orientation data G after the high frequency zero padding ₁And G ₂

Step 6: data after the zero padding are carried out shifter-adder;

With the data G that obtains in the step 5 ₂Be shifted, then with G ₁Superpose; Obtain data H behind the shifter-adder;

Step 7: the orientation obtains final image to compression;

Data H behind the shifter-adder that obtains in the step 6 is carried out the orientation to compression, obtain final image I.

The advantage that the present invention has is:

(1) the present invention proposes a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence, has the advantages that the radar signal waveform is easy to generate.Owing to adopt the fully-complementary sequence that belongs to phase-coded signal, with respect to the employed linear FM signal of traditional system SAR, more easy-to-use digital device produces.

(2) the present invention proposes a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence, has the advantages that process of pulse-compression realizes easily.Because adopt the fully-complementary sequence that belongs to phase-coded signal, with respect to the employed linear FM signal of traditional system SAR, more easy-to-use digital device is finished process of pulse-compression.

(3) the present invention proposes a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence, has distance to the characteristics of ULTRA-LOW SIDE LOBES.Owing to adopt fully-complementary sequence, by process of pulse-compression, need not weighting, can so that final radar image in distance to realizing ULTRA-LOW SIDE LOBES.

(4) the present invention proposes a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence, has distance to the high characteristics of resolution.Because distance, makes that distance can be because of the weighting variation to resolution to need not being weighted, final radar image in distance to realizing high resolving power.

(5) the present invention proposes a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence, has the high characteristics of picture quality.Because after adopting fully-complementary sequence, the radar image distance is very low to secondary lobe, secondary lobe disturbs very little, and therefore, picture quality is higher, easier interpretation.

Description of drawings

Fig. 1 is a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method flow diagram based on fully-complementary sequence that the present invention proposes;

Fig. 2 is the single-point target imaging result in the embodiment of the invention;

Fig. 3 is based on the single-point target imaging result of linear FM signal;

Fig. 4 is that single-point target imaging distance in the embodiment of the invention is to sectional view;

Fig. 5 is based on the single-point target imaging distance of linear FM signal to sectional view;

Fig. 6 is that single-point target imaging orientation in the embodiment of the invention is to sectional view;

Fig. 7 is based on the single-point target imaging orientation of linear FM signal to sectional view.

Embodiment

The present invention is described in further detail below in conjunction with drawings and Examples.

The present invention proposes a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence, handle to as if with the echo data of fully-complementary sequence signal waveform as the radar emission signal, the result who obtains is that a panel height resolution, ultralow distance are to side lobe image.

Fully-complementary sequence is made of a pair of complementary series.The definition length be L fully-complementary sequence to A, B} is:

$\left\{\begin{array}{c}A=(a^0,a^1,...,a^{L-1})\\ B=(b^0,b^1,...,b^{L-1})\end{array}\right.---\left(1\right)$

Wherein, A and B are for constituting a pair of composition sequence of fully-complementary sequence.a ⁰, a ¹..., a ^L-1The code element of expression sequence A, b ⁰, b ¹..., b ^L-1The code element of expression sequence B.

Fully-complementary sequence constitutes a pair of train of impulses with these two composition sequences during as the radar emission signal, chronologically alternately emission.When each composition sequence was launched, each code element was launched after modulation successively continuously, and each element duration is T _c, be called the subpulse duration (or subpulse width).After whole transmission of symbols, the pulse battery has fired that this composition sequence (A or B) constitutes, the duration is t _p(t _p=LT _c), be called the duration of pulse (or pulse width).Its baseband signal form is:

$\left\{\begin{array}{c}{s}_A\left(t\right)=a^l,l\&CenterDot;T_c\&le;t<(l+1)\&CenterDot;T_c,l=\mathrm{0,1,2},...,L-1\\ s_B\left(t\right)=b^l,l\&CenterDot;T_c\&le;t<(l+1)\&CenterDot;T_c,l=\mathrm{0,1,2},...,L-1\end{array}\right.---\left(2\right)$

Wherein, t is apart to the fast time, is each pulse emission forward position with reference to starting point.s _A(t) and s _B(t) be respectively the baseband signal form of sequence A and B.

With the fully-complementary sequence signal waveform as the synthetic-aperture radar that transmits in when work, its antenna is with 1/f _pFor the cycle replaces transponder pulse signal s _A(t) and s _B(t), the duration of pulse is t _pF wherein _pThe pulse repetition rate of expression radar, 1/f _pThe pulse repetition time that is called radar.Each exomonental initial moment is called the orientation constantly, and adjacent two orientation time interval constantly is pulse repetition time 1/f _pAfter each pulse emission finished, antenna was opened the echo receiver window, receives the radar echo signal that the ground surface launching is returned, and closed the echo window before next pulse emission beginning.In echo receiver window opening time, with sample rate f _sEchoed signal to a pulse is sampled, and sampling number is Y, and saves as the delegation of echo data.Echo receiver window of every unlatching, storing one row data successively.After having launched X pulse, the radar power cut-off.

Be a two-dimentional plural groups (matrix) C with the fully-complementary sequence signal waveform as the synthetic-aperture radar echo data of radar emission signal, if its size is X * Y, one dimension be the orientation to, X sampled point arranged, the expression radar has obtained X orientation one dimension pulse echo data constantly, different orientation is to the corresponding different orientation moment of sampled point, and two adjacent orientation differ orientation 1/f constantly to sampled point _pAnother dimension be distance to, Y sampled point arranged, represent that each orientation opens the echo receiver window constantly one time, echoed signal is sampled (being called distance to sampling), one-time continuous is apart from having Y sampled point to sampling, sampling rate is f _s, different distances is to the corresponding different oblique distance of sampled point (the radar antenna phase center is to the distance of terrain object point), that is corresponding different range gate, and two neighbor distance differ oblique distance c/2f to sampled point (neighbor distance door) _s

The present invention proposes a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence, and flow process comprises following step as shown in Figure 1:

Step 1: will be divided into the echo data C that obtains as the radar emission signal with sequence A and sequence B separately based on the echo data C of fully-complementary sequence signal waveform ₁And C ₂

C ₁And C ₂Also be two-dimentional plural groups, size is (X/2) * Y.And satisfy

C ₁(m，n)＝C(2m-1，n)，m＝1，2，…，X/2；n＝1，2，…，Y (3)

C ₂(m，n)＝C(2m，n)，m＝1，2，…，X/2；n＝1，2，…，Y (4)

Wherein, C ₁(m, n) expression two-dimensional array C ₁N capable element of m, C ₂(m, n) expression two-dimensional array C ₂N capable element of m, ((2m n) represents n the capable element of 2m of two-dimensional array C to C to C for 2m-1, n) n the capable element of 2m-1 of expression two-dimensional array C.According to formula (3) and (4), just can obtain echo data C ₁And C ₂

Step 2: the range pulse compression based on matched filtering is handled;

Utilize two mutual-complementing code sequence signals of fully-complementary sequence as the reference signal, respectively to the echo data C of sequence A and sequence B ₁And C ₂Carry out distance to matched filtering, finish apart from compression process, two signals after obtaining to compress are respectively D ₁And D ₂, be specially:

(1) to the echo data C of the isolated two parts sequence A of step 1 and sequence B ₁And C ₂The edge distance is to doing Fast Fourier Transform (FFT) (FFT), namely to C ₁And C ₂Each orientation distance constantly do the one dimension Fast Fourier Transform (FFT) to data (by row), it is transformed to distance to frequency domain, obtain the distance of echo data of sequence A and sequence B to frequency domain data C _1-FFTAnd C _2-FFT

C _1-FFT(m，：)＝FFT(C ₁(m，：))，m＝1，2，…，X/2 (5)

C _2-FFT(m，：)＝FFT(C ₁(m，：))，m＝1，2，…，X/2 (6)

Wherein, C _1-FFT(m :) expression C _1-FFTM capable, C _2-FFT(m :) expression C _2-FFTM capable, C ₁(m :) expression C ₁M capable, C ₂(m :) expression C ₂M capable.FFT () expression is carried out Fast Fourier Transform (FFT) to one-dimension array.

(2) respectively with the baseband signal s of two mutual-complementing code sequences of fully-complementary sequence _A(t) and s _B(t) conduct is with reference to signal.To reference signal s _A(t) and s _B(t) sample, sampling number is n ₀(n ₀=t _pF _s), n ₀Less than echo distance to sampling number Y.Discrete-time signal after the sampling is respectively s _A(n) and s _B(n) (n=1,2 ..., n ₀).At discrete reference signal s _A(n) and s _B(n) back zero padding, zero padding number are Y-n ₀, make reference signal s _A(n) and s _B(n) sampling number also is Y.Reference signal after the zero padding is done Fast Fourier Transform (FFT), and Fourier transform is counted and is Y, and it is transformed to frequency domain, obtains reference signal frequency spectrum s _A-FFTAnd s _B-FFTs _A-FFTAnd s _B-FFTLength is Y.

(3) with the distance of two parts echo data to frequency domain data C _1-FFTAnd C _2-FFTBy row and corresponding reference signal frequency spectrum s _A-FFTAnd s _B-FFTConjugate multiplication, i.e. the echo data C of sequence A ₁Distance to frequency domain data C _1-FFTBy row and reference signal s _A(t) frequency spectrum s _A-FFTConjugate multiplication, the echo data C of sequence B ₂Distance to frequency domain data C _2-FFTBy row and reference signal s _B(t) frequency spectrum s _B-FFTConjugate multiplication.(by row) carries out inverse fast Fourier transform (IFFT) to the result that will obtain to constantly by each orientation respectively, obtains the data D after distance is compressed respectively ₁And D ₂, finish apart from compression process.

$D_1(m,:)=\mathrm{IFFT}(C_{1-\mathrm{FFT}}(m,:)\&CenterDot;s_{A-\mathrm{FFT}}^{*}),m=\mathrm{1,2},...,X/2---\left(7\right)$

$D_2(m,:)=\mathrm{IFFT}(C_{2-\mathrm{FFT}}(m,:)\&CenterDot;s_{B-\mathrm{FFT}}^{*}),m=\mathrm{1,2},...,X/2---\left(8\right)$

Wherein, D ₁(m :), D ₂(m :), C _1-FFT(m :), C _2-FFT(m :) represent apart from the data D after the compression respectively ₁, the data D after the distance compression ₂, the distance to frequency domain data C _1-FFT, the distance to frequency domain data C _2-FFTM capable, expression vector dot product.IFFT () expression is carried out inverse fast Fourier transform to one-dimension array, ^*The expression conjugation.

Step 3: the orientation is to Fourier transform;

Data D after the distance compression that step 2 is obtained ₁And D ₂Carry out Fast Fourier Transform (FFT) (FFT) along each range gate (by row), obtain the orientation to frequency spectrum data D _1-FFTAnd D _2-FFT

D _1-FFT(：，n)＝FFT(D ₁(：，n))，n＝1，2，…，Y (9)

D _1-FFT(：，n)＝FFT(D ₁(：，n))，n＝1，2，…，Y (10)

Wherein, D _1-FFT(:, n) expression D _1-FFTN row, D ₁(:, n) expression D ₁N row, D _2-FFT(:, n) expression D _2-FFTN row, D ₂(:, n) expression D ₂N row.FFT () expression is carried out Fast Fourier Transform (FFT) to one-dimension array.

Then with the orientation to frequency spectrum data D _1-FFTAnd D _2-FFTPreceding X/4 line data and back X/4 line data exchange, obtain orientation frequency spectrum data E ₁And E ₂

$E_1(m,n)=\left\{\begin{array}{c}{D}_{1-\mathrm{FFT}}(m+X/4,n),m=\mathrm{1,2}...,X/4;n=\mathrm{1,2}...,Y\\ D_{1-\mathrm{FFT}}(m-X/4,n),m=X/4+1,X/4+2,...,X/2;n=\mathrm{1,2}...,Y\end{array}\right.---\left(11\right)$

$E_2(m,n)=\left\{\begin{array}{c}{D}_{2-\mathrm{FFT}}(m+X/4,n),m=\mathrm{1,2}...,X/4;n=\mathrm{1,2}...,Y\\ D_{2-\mathrm{FFT}}(m-X/4,n),m=X/4+1,X/4+2,...,X/2;n=\mathrm{1,2}...,Y\end{array}\right.---\left(12\right)$

Wherein, E ₁(m, n) and E ₂(m n) represents E respectively ₁And E ₂N capable element of m, D _1-FFT(m+X/4, n) expression D _1-FFT(m+X/4) row n element, D _1-FFT(m-X/4, n) expression D _1-FFT(m-X/4) row n element, D _2-FFT(m+X/4, n) expression D _2-FFT(m+X/4) row n element, D _2-FFT(m-X/4, n) expression D _2-FFT(m-X/4) row n element.

Step 4: range migration correction;

The orientation frequency spectrum data E that obtains for step 3 ₁And E ₂, utilize the sinc method of interpolation to carry out accurate correction distance migration, obtain carrying out the data F behind the range migration correction respectively ₁And F ₂Be specially:

(1) the corresponding orientation frequency of every row of computer azimuth frequency spectrum data;

If the pulse repetition rate of radar is f _p, the orientation frequency of the capable correspondence of m of orientation frequency spectrum data is:

$f_{\mathrm{\&eta;}}^{\left(m\right)}=(m-X/4)\&CenterDot;f_p/X,m=\mathrm{1,2},...,X/2---\left(13\right)$

(2) calculate the corresponding oblique distance of each range gate (each row) according to the reference oblique distance;

If be R with reference to oblique distance ₀, distance is f to sampling rate _s, pulse width is t _p, the light velocity is c, the corresponding oblique distance of n range gate (n row) is R ⁽ⁿ⁾For:

R ⁽ⁿ⁾＝R ₀+(n-1-(Y-f _s·t _p)/2)·c/f _s/2，n＝1，2，…，Y (14)

(3) calculate the range migration amount of each range gate under each orientation frequency (each row);

If the wavelength that transmits is λ, the Texas tower velocity equivalent is v, under m the orientation frequency, the range migration amount Δ R of n range gate (n row) correspondence (m n) is:

$\mathrm{\&Delta;R}(m,n)=R^{\left(n\right)}(\frac{1}{\sqrt{1-\frac{{\mathrm{\&lambda;}}^2{\left(f_{\mathrm{\&eta;}}^{\left(m\right)}\right)}^2}{{4v}^2}}}-1),m=\mathrm{1,2},...,X/2;n=\mathrm{1,2},...,Y---\left(15\right)$

(4) utilize the sinc interpolation to E ₁And E ₂Carry out the accurate distance migration and proofread and correct, the data behind the range migration correction are respectively F ₁And F ₂

If sinc interpolation kernel length is N, the data F behind the range migration correction ₁And F ₂Calculated by following formula:

Wherein, n '=Δ R (m, n)+n, corresponding range unit (non-integer) before the n ' expression echo samples point range migration correction, n are represented the range unit (integer) of correspondence behind the echo samples point range migration correction,

Expression rounds downwards, and k represents the interpolated sample ordinal number, With

Represent E respectively ₁And E ₂M capable

Individual element, F ₁(m, n) and F ₂(m n) represents F respectively ₁And F ₂N capable element of m.

According to above two formulas, can obtain data F behind the range migration correction ₁And F ₂

Step 5: the orientation is to the zero padding of data high frequency;

Data F behind the range migration correction that step 4 is obtained ₁And F ₂HFS in frequency domain carries out zero padding to be handled, and the zero padding number is Y/2.Data after the zero padding multiply by two times, obtain orientation data G after the high frequency zero padding ₁And G ₂Be specially:

G ₁And G ₂Be two-dimentional plural groups, size is X * Y.And satisfy:

$G_1(m,n)=\left\{\begin{array}{c}{2F}_1(m,n),m=\mathrm{1,2},...,X/4;n=\mathrm{1,2},...,Y\\ {2F}_1(m-X/2,n),m=\frac{3}{4}X+1,\frac{3}{4}X+2,...,X;n=\mathrm{1,2},...,\mathrm{<figure-callout\; id="0"\; label="Y"\; filenames="HDA0000143028390000031.png,HDA0000143028390000032.png"\; state="\{\{state\}\}">Y</figure-callout>}\\ 0,m=X/4+1,X/4+2,...,\frac{3}{4}X;n=\mathrm{1,2},...,Y\end{array}\right.---\left(18\right)$

$G_2(m,n)=\left\{\begin{array}{c}{2F}_2(m,n),m=\mathrm{1,2},...,X/4;n=\mathrm{1,2},...,Y\\ {2F}_2(m-X/2,n),m=\frac{3}{4}X+1,\frac{3}{4}X+2,...,X;n=\mathrm{1,2},...,\mathrm{<figure-callout\; id="0"\; label="Y"\; filenames="HDA0000143028390000031.png,HDA0000143028390000032.png"\; state="\{\{state\}\}">Y</figure-callout>}\\ 0,m=X/4+1,X/4+2,...,\frac{3}{4}X;n=\mathrm{1,2},...,Y\end{array}\right.---\left(19\right)$

Wherein, G ₁(m, n), G ₂(m n) represents G respectively ₁, G ₂N capable element of m, F ₁(m, n), F ₂(m n) represents F respectively ₁, F ₂N capable element of m, F ₁(m-X/2, n), F ₂(m-X/2 n) represents F respectively ₁, F ₂(m-X/2) row n element.

Can calculate G by above two formulas ₁And G ₂

Step 6: data after the zero padding are carried out shifter-adder;

With the data G that obtains in the step 5 ₂Be shifted, then with G ₁Superpose.Obtain data H behind the shifter-adder.

Be specially:

(1) structure shifted divisor vector p;

Shifted divisor vector p is an one-dimension array, and array length is that the orientation is to sampling number X.Be calculated as follows each component of p:

$p\left(m\right)=\left\{\begin{array}{c}{e}^{-j2\mathrm{\&pi;}(m+X/2-1)/X},m=\mathrm{1,2},...,X/2\\ e^{-j2\mathrm{\&pi;}(m-X/2-1)/X},m=X/2+1,X/2+2,...,X\end{array}\right.---\left(20\right)$

In the formula, the j on the exponential term represents imaginary unit, m the component of p (m) expression shifted divisor vector p.

(2) multiply each other and superposition of data with shifted divisor.

With G ₂Multiply each other with shifted divisor vector p by row, and and G ₁Superimposed, obtain data H behind the shifter-adder:

H(：，n)＝G ₁(：，n)+G ₂(：，n)·p，n＝1，2，…，Y (21)

Wherein, H (:, n), G ₁(:, n), G ₂(:, n) represent H, G respectively ₁, G ₂N row, expression vector dot product.

Step 7: the orientation obtains final image to compression.

Data H behind the shifter-adder that obtains in the step 6 is carried out the orientation to compression, obtain final image I.Be specially:

(1) the corresponding orientation frequency of every row of data H behind the calculating shifter-adder;

If the pulse repetition rate of radar is f _p, the orientation frequency of the capable correspondence of m of H is

Then:

$f_{\mathrm{\&eta;}}^{\left(m\right)}=(m-X/2)\&CenterDot;f_p/X,m=\mathrm{1,2},...,X---\left(22\right)$

(2) calculate the corresponding oblique distance R of each range gate (each row) according to the reference oblique distance ⁽ⁿ⁾, n=1,2 ..., Y is identical with step 4 (2) method;

(3) at each row of data H, construct corresponding orientation compression filter and carry out filtering, obtain frequency spectrum data H ' after the azimuth filtering.

To the n row of data H, construct orientation compression filter h at frequency domain:

$h\left(m\right)=e^{j4\mathrm{\&pi;}/\mathrm{\&lambda;}{R}^{\left(n\right)}\sqrt{1-\frac{{\mathrm{\&lambda;}}^2{\left(f_{\mathrm{\&eta;}}^{\left(m\right)}\right)}^2}{{4v}^2}}},m=\mathrm{1,2},...,X---\left(23\right)$

Wherein, the j on the exponential term represents imaginary unit, and v represents the Texas tower velocity equivalent, and λ represents the wavelength that transmits.M the component of h (m) expression h.

N row with the data H of orientation compression filter h carry out filtering:

H′(：，n)＝H(：，n)·h，n＝1，2，…，Y (24)

Wherein, H ' (:, n), H (:, n) represent the n row of H ' and H respectively, expression vector dot product.

(4) the capable and back X/2 line data of the preceding X/2 of frequency spectrum data H ' after the azimuth filtering is exchanged the data H after obtaining exchanging ", to the exchange after data H " each row carry out inverse fast Fourier transform (IFFT), finally obtain view data I:

$H^{\&prime;\&prime;}(m,:)=\left\{\begin{array}{c}{H}^{\&prime;}(m+X/2,:),m=\mathrm{1,2},...,X/2\\ H^{\&prime;}(m-X/2,:),m=X/2+1,X/2+2,...,X\end{array}\right.---\left(25\right)$

I(：，n)＝IFFT(H″(：，n))，n＝1，2，…，Y (26)

The m of in the formula, H " (m :) expression H " is capable, H ' (m+X/2,) expression H ' (m+X/2) OK, (m-X/2) that H ' (m-X/2) represents H ' OK, I (:, n) the n row of, H " (:, n) represent I and H respectively ", IFFT () expression is carried out inverse fast Fourier transform to one-dimension array.

Embodiment

Present embodiment proposes a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence, and wherein the parameter that relates in the imaging process is as shown in table 1.

Table 1 embodiment parameter

Present embodiment specifically comprises following step:

Step 1: will be divided into the echo data C that obtains as the radar emission signal with sequence A and sequence B separately based on the echo data C of fully-complementary sequence signal waveform ₁And C ₂

C ₁And C ₂It also is two-dimentional plural groups.Can obtain C according to formula (3) and (4) ₁And C ₂

Step 2: the range pulse compression based on matched filtering is handled;

Utilize two mutual-complementing code sequence signals of fully-complementary sequence as the reference signal, respectively to the echo data C of sequence A and sequence B ₁And C ₂Carry out distance to matched filtering, finish apart from compression process, two signals after obtaining to compress are respectively D ₁And D ₂, be specially:

(1) to the echo data C of the isolated two parts sequence A of step 1 and sequence B ₁And C ₂The edge distance is to doing Fast Fourier Transform (FFT) (FFT), namely to C ₁And C ₂Each orientation distance constantly do the one dimension Fast Fourier Transform (FFT) to data (by row), it is transformed to distance to frequency domain, obtain the distance of echo data of sequence A and sequence B to frequency domain data C _1-FFTAnd C _2-FFTDetailed process is undertaken by formula (5) and (6).

(2) respectively with the baseband signal s of two mutual-complementing code sequences of fully-complementary sequence _A(t) and s _B(t) conduct is with reference to signal.To reference signal s _A(t) and s _B(t) sample, sampling number is 400, less than echo distance to sampling number 1024.Discrete-time signal after the sampling is respectively s _A(n) and s _B(n) (n=1,2 ..., 400).At discrete reference signal s _A(n) and s _B(n) back zero padding, the zero padding number is 1024-400=624, makes reference signal s _A(n) and s _B(n) sampling number also is 1024.Reference signal after the zero padding is done Fast Fourier Transform (FFT), and it is 1024 that Fourier transform is counted, and it is transformed to frequency domain, obtains reference signal frequency spectrum s _A-FFTAnd s _B-FFTs _A-FFTAnd s _B-FFTLength is 1024.

(3) with the distance of two parts echo data to frequency domain data C _1-FFTAnd C _2-FFTBy row and corresponding reference signal frequency spectrum s _A-FFTAnd s _B-FFTConjugate multiplication, i.e. the echo data C of sequence A ₁Distance to frequency domain data C _1-FFTBy row and reference signal s _A(t) frequency spectrum s _A-FFTConjugate multiplication, the echo data C of sequence B ₂Distance to frequency domain data C _2-FFTBy row and reference signal s _B(t) frequency spectrum s _B-FFTConjugate multiplication.(by row) carries out inverse fast Fourier transform (IFFT) to the result that will obtain to constantly by each orientation respectively, obtains the data D after distance is compressed respectively ₁And D ₂, finish apart from compression process.Detailed process is undertaken by formula (7) and (8).

Step 3: the orientation is to Fourier transform;

Data D after the distance compression that step 2 is obtained ₁And D ₂Carry out Fast Fourier Transform (FFT) (FFT) along each range gate (by row), obtain the orientation to frequency spectrum data D _1-FFTAnd D _2-FFTDetailed process is undertaken by formula (9) and (10).

Then with the orientation to frequency spectrum data D _1-FFTAnd D _2-FFTPreceding 256 line data and the back 256 line data exchange, obtain orientation frequency spectrum data E ₁And E ₂Detailed process is undertaken by formula (11) and (12).

Step 4: range migration correction;

The orientation frequency spectrum data E that obtains for step 3 ₁And E ₂, utilize the sinc method of interpolation to carry out accurate correction distance migration, obtain carrying out the data F behind the range migration correction respectively ₁And F ₂Be specially:

(1) the corresponding orientation frequency of every row of computer azimuth frequency spectrum data;

The orientation frequency of the capable correspondence of m of orientation frequency spectrum data is M=1,2 ..., 512, calculated by formula (13)

(2) calculate the corresponding oblique distance of each range gate (each row) according to the reference oblique distance;

The corresponding oblique distance of n range gate (n row) is R ⁽ⁿ⁾, n=1,2 ..., 1024, calculate R by formula (14) ⁽ⁿ⁾

(3) calculate the range migration amount of each range gate under each orientation frequency (each row);

Under m the orientation frequency, the corresponding range migration amount of n range gate (n row) be Δ R (m, n), m=1,2 ..., 512; N=1,2 ..., 1024, by formula (15) calculate Δ R (m, n).

(4) utilize the sinc interpolation to E ₁And E ₂Carry out the accurate distance migration and proofread and correct, the data behind the range migration correction are respectively F ₁And F ₂

If sinc interpolation kernel length is 16, the data F behind the range migration correction ₁And F ₂Calculated by formula (16) and (17).

Step 5: the orientation is to the zero padding of data high frequency;

Data F behind the range migration correction that step 4 is obtained ₁And F ₂HFS in frequency domain carries out zero padding to be handled, and the zero padding number is 512.Data after the zero padding multiply by two times, obtain orientation data G after the high frequency zero padding ₁And G ₂

G ₁And G ₂Be two-dimentional plural groups, size is 1024 * 1024.Can calculate G by formula (18) and (19) ₁And G ₂

Step 6: data after the zero padding are carried out shifter-adder;

With the data G that obtains in the step 5 ₂Be shifted, then with G ₁Superpose.Obtain data H behind the shifter-adder.

Be specially:

(1) structure shifted divisor vector p;

Shifted divisor vector p is an one-dimension array, and array length is that the orientation is to sampling number 1024.

Calculate each component of p by formula (20).

(2) multiply each other and superposition of data with shifted divisor.

Press formula (21) with G ₂Multiply each other with shifted divisor vector p by row, and and G ₁Superimposed, obtain data H behind the shifter-adder.

Step 7: the orientation obtains final image to compression.

Data H behind the shifter-adder that obtains in the step 6 is carried out the orientation to compression, obtain final image I.Be specially:

(1) the corresponding orientation frequency of every row of data H behind the calculating shifter-adder;

The orientation frequency of the capable correspondence of m of data H is designated as

M=1,2 ..., 1024, calculated by formula (22)

(2) calculate the corresponding oblique distance R of each range gate (each row) according to the reference oblique distance ⁽ⁿ⁾, n=1,2 ..., 1024, identical with step 4 (2) method;

(3) at each row of data H, construct corresponding orientation compression filter and carry out filtering, obtain frequency spectrum data H ' after the azimuth filtering.Specific implementation process is undertaken by formula (23), (24).

(4) with frequency spectrum data H ' after the azimuth filtering preceding 512 the row and the back 512 the row exchange the data H after obtaining exchanging ", to the exchange after data H " each row carry out inverse fast Fourier transform (IFFT), obtain final view data I.Specific implementation process is undertaken by formula (25), (26).

Through the imaging processing of above step, obtained the imaging results of a single point target, as shown in Figure 2.The image of the white point at this figure center for based on the synthetic-aperture radar of fully-complementary sequence the echoed signal of a single point target being obtained after this method is handled.The distance that Fig. 4 and Fig. 6 are respectively this point target to sectional view and orientation to sectional view.

Fig. 3 has provided under identical simulated conditions, based on the point target imaging results of the traditional system SAR of linear FM signal.By comparison diagram 2 and Fig. 3, illustrate that the step of utilizing this method to provide based on the synthetic-aperture radar of fully-complementary sequence can obtain the resulting similar result with traditional system SAR.Fig. 5 and Fig. 7 are respectively based on the resulting point target of the traditional system SAR of linear FM signal distance to sectional view and orientation to sectional view.

From Fig. 4-Fig. 7 as can be seen, in the SAR point target imaging results based on the fully-complementary sequence signal waveform, distance is 2.23m to resolution (slant range resolution), and the orientation is 1.95m to resolution, distance reaches-78.23dB to peak sidelobe ratio, and the orientation reaches-13.33dB to peak sidelobe ratio.And in the traditional system SAR point target imaging results based on linear FM signal, distance is 3.32m to resolution (slant range resolution), the orientation is 1.95m to resolution, and distance reaches-13.35dB to peak sidelobe ratio, and the orientation reaches-13.31dB to peak sidelobe ratio.Wherein, spatial resolution is defined as impulse response 3dB width.This illustrates that this formation method can suppress distance to secondary lobe effectively under the prerequisite that guarantees resolution.

Therefore, the synthetic aperture radar image-forming method based on fully-complementary sequence of the present invention's proposition can realize that high resolving power, ultralow distance are to the secondary lobe imaging.

Claims (9)

1. ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence is characterized in that concrete steps comprise:

Step 1: will be divided into the echo data C that obtains as the radar emission signal with sequence A and sequence B separately based on the echo data C of fully-complementary sequence signal waveform ₁And C ₂

C ₁And C ₂Be two-dimentional plural groups, size is (X/2) * Y;

Step 2: the range pulse compression based on matched filtering is handled;

Utilize two mutual-complementing code sequence signals of fully-complementary sequence as the reference signal, respectively to the echo data C of sequence A and sequence B ₁And C ₂Carry out distance to matched filtering, finish apart from compression process, two signals after obtaining to compress are respectively D ₁And D ₂

Step 3: the orientation is to Fourier transform;

Data D after the distance compression that step 2 is obtained ₁And D ₂Carry out Fast Fourier Transform (FFT) along each range gate, obtain the orientation to frequency spectrum data D _1-FFTAnd D _2-FFT

Then with the orientation to frequency spectrum data D _1-FFTAnd D _2-FFTPreceding X/4 line data and back X/4 line data exchange, obtain orientation frequency spectrum data E ₁And E ₂

Step 4: range migration correction;

The orientation frequency spectrum data E that obtains for step 3 ₁And E ₂, utilize the sinc method of interpolation to carry out accurate correction distance migration, obtain carrying out the data F behind the range migration correction respectively ₁And F ₂

Step 5: the orientation is to the zero padding of data high frequency;

Data F behind the range migration correction that step 4 is obtained ₁And F ₂HFS in frequency domain carries out zero padding to be handled, and the zero padding number is Y/2; Data after the zero padding multiply by two times, obtain orientation data G after the high frequency zero padding ₁And G ₂

Step 6: data after the zero padding are carried out shifter-adder;

With the data G that obtains in the step 5 ₂Be shifted, then with G ₁Superpose; Obtain data H behind the shifter-adder;

Step 7: the orientation obtains final image to compression;

Data H behind the shifter-adder that obtains in the step 6 is carried out the orientation to compression, obtain final image I.

2. a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence according to claim 1 is characterized in that, in the described step 1, and C ₁And C ₂For:

C ₁(m,n)＝C(2m-1,n)，m＝1,2,…,X/2;n＝1,2,…,Y (3)

C ₂(m,n)＝C(2m,n)，m＝1,2,…,X/2;n＝1,2,…,Y (4)

Wherein, C ₁(m, n) expression two-dimensional array C ₁N capable element of m, C ₂(m, n) expression two-dimensional array C ₂N capable element of m, ((2m n) represents n the capable element of 2m of two-dimensional array C to C to C for 2m-1, n) n the capable element of 2m-1 of expression two-dimensional array C; According to formula (3) and (4), obtain echo data C ₁And C ₂

3. a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence according to claim 1 is characterized in that described step 2 specifically comprises:

(1) to the echo data C of the isolated two parts sequence A of step 1 and sequence B ₁And C ₂The edge distance is to doing Fast Fourier Transform (FFT), namely to C ₁And C ₂Each orientation distance constantly do the one dimension Fast Fourier Transform (FFT) to data, it is transformed to distance to frequency domain, obtain the distance of echo data of sequence A and sequence B to frequency domain data C _1-FFTAnd C _2-FFT

C _1-FFT(m,:)＝FFT(C ₁(m,:))，m＝1,2,…,X/2 (5)

C _2-FFT(m,:)＝FFT(C ₁(m,:))，m＝1,2,…,X/2 (6)

Wherein, C _1-FFT(m :) expression C _1-FFTM capable, C _2-FFT(m :) expression C _2-FFTM capable, C ₁(m :) expression C ₁M capable, C ₂(m :) expression C ₂M capable; FFT () expression is carried out Fast Fourier Transform (FFT) to one-dimension array;

(2) respectively with the baseband signal s of two mutual-complementing code sequences of fully-complementary sequence _A(t) and s _B(t) conduct is with reference to signal; To reference signal s _A(t) and s _B(t) sample, sampling number is n ₀, n ₀=t _pF _s, t _pBe pulse width, f _sFor the distance to sample frequency, n ₀Less than echo distance to sampling number Y; Discrete-time signal after the sampling is respectively s _A(n) and s _B(n), n=1,2 ..., n ₀At discrete reference signal s _A(n) and s _B(n) back zero padding, zero padding number are Y-n ₀, make reference signal s _A(n) and s _B(n) sampling number also is Y; Reference signal after the zero padding is done Fast Fourier Transform (FFT), and Fourier transform is counted and is Y, and it is transformed to frequency domain, obtains reference signal frequency spectrum s _A-FFTAnd s _B-FFTs _A-FFTAnd s _B-FFTLength is Y;

(3) with the distance of two parts echo data to frequency domain data C _1-FFTAnd C _2-FFTBy row and corresponding reference signal frequency spectrum s _A-FFTAnd s _B-FFTConjugate multiplication, i.e. the echo data C of sequence A ₁Distance to frequency domain data C _1-FFTBy row and reference signal s _A(t) frequency spectrum s _A-FFTConjugate multiplication, the echo data C of sequence B ₂Distance to frequency domain data C _2-FFTBy row and reference signal s _B(t) frequency spectrum s _B-FFTConjugate multiplication; The result that will obtain carries out inverse fast Fourier transform by each orientation to the moment respectively, obtains the data D after the distance compression respectively ₁And D ₂, finish apart from compression process;

$D_1(m,:)=\mathrm{IFFT}(C_{1-\mathrm{FFT}}(m,:)\&CenterDot;s_{A-\mathrm{FFT}}^{*}),m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,X/2---\left(7\right)$

$D_2(m,:)=\mathrm{IFFT}(C_{2-\mathrm{FFT}}(m,:)\&CenterDot;s_{B-\mathrm{FFT}}^{*}),m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,X/2---\left(8\right)$

Wherein, D ₁(m :), D ₂(m :), C _1-FFT(m :), C _2-FFT(m :) represent apart from the data D after the compression respectively ₁, the data D after the distance compression ₂, the distance to frequency domain data C _1-FFT, the distance to frequency domain data C _2-FFTM capable, expression vector dot product; IFFT () expression is carried out inverse fast Fourier transform to one-dimension array, ^*The expression conjugation.

4. a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence according to claim 1 is characterized in that, in the described step 3:

The orientation is to frequency spectrum data D _1-FFTAnd D _2-FFTBe respectively:

D _1-FFT(:,n)＝FFT(D ₁(:,n)),n＝1,2,…,Y (9)

D _1-FFT(:,n)＝FFT(D ₁(:,n)),n＝1,2,…,Y (10)

Wherein, D _1-FFT(:, n) expression D _1-FFTN row, D ₁(:, n) expression D ₁N row, D _2-FFT(:, n) expression D _2-FFTN row, D ₂(:, n) expression D ₂N row; FFT () expression is carried out Fast Fourier Transform (FFT) to one-dimension array;

Orientation frequency spectrum data E ₁And E ₂Be respectively:

$E_1(m,n)=\left\{\begin{array}{c}{D}_{1-\mathrm{FFT}}(m+X/4,n),m=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;,X/4;n=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;,Y\\ D_{1-\mathrm{FFT}}(m-X/4,n),m=X/4+1,X/4+2,\&CenterDot;\&CenterDot;\&CenterDot;,X/2;n=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;,Y\end{array}\right.---\left(11\right)$

$E_2(m,n)=\left\{\begin{array}{c}{D}_{2-\mathrm{FFT}}(m+X/4,n),m=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;,X/4;n=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;,Y\\ D_{2-\mathrm{FFT}}(m-X/4,n),m=X/4+1,X/4+2,\&CenterDot;\&CenterDot;\&CenterDot;,X/2;n=\mathrm{1,2}\&CenterDot;\&CenterDot;\&CenterDot;,Y\end{array}\right.---\left(12\right)$

Wherein, E ₁(m, n) and E ₂(m n) represents E respectively ₁And E ₂N capable element of m, D _1-FFT(m+X/4, n) expression D _1-FFT(m+X/4) row n element, D _1-FFT(m-X/4, n) expression D _1-FFT(m-X/4) row n element, D _2-FFT(m+X/4, n) expression D _2-FFT(m+X/4) row n element, D _2-FFT(m-X/4, n) expression D _2-FFT(m-X/4) row n element.

5. a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence according to claim 1 is characterized in that described step 4 specifically comprises:

(1) obtains the corresponding orientation frequency of every row of orientation frequency spectrum data;

If the pulse repetition rate of radar is f _p, the orientation frequency of the capable correspondence of m of orientation frequency spectrum data is:

$f_{\mathrm{\&eta;}}^{\left(m\right)}=(m-X/4)\&CenterDot;f_p/X,m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,X/2---\left(13\right)$

(2) calculate the oblique distance of each range gate correspondence according to the reference oblique distance;

If be R with reference to oblique distance ₀, distance is f to sampling rate _s, pulse width is t _p, the light velocity is c, the oblique distance of n range gate correspondence is R ⁽ⁿ⁾For:

R ⁽ⁿ⁾＝R ₀+(n-1-(Y-f _s·t _p)/2)·c/f _s/2，n＝1,2,…,Y (14)

(3) obtain the range migration amount of each range gate under each orientation frequency;

If the wavelength that transmits is λ, the Texas tower velocity equivalent is v, under m the orientation frequency, the range migration amount Δ R of n range gate correspondence (m n) is:

$\mathrm{\&Delta;R}(m,n)=R^{\left(n\right)}(\frac{1}{\sqrt{1-\frac{{\mathrm{\&lambda;}}^2{\left(f_{\mathrm{\&eta;}}^{\left(m\right)}\right)}^2}{{4v}^2}}}-1),m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,X/2;n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,Y---\left(15\right)$

(4) utilize the sinc interpolation to E ₁And E ₂Carry out the accurate distance migration and proofread and correct, the data behind the range migration correction are respectively F ₁And F ₂

If sinc interpolation kernel length is N, the data F behind the range migration correction ₁And F ₂Obtained by following formula:

Wherein, n '=Δ R (m, n)+n, corresponding range unit before the n ' expression echo samples point range migration correction, n are represented the range unit of correspondence behind the echo samples point range migration correction,

Expression rounds downwards, and k represents the interpolated sample ordinal number, With

Represent E respectively ₁And E ₂M capable

Individual element, F ₁(m, n) and F ₂(m n) represents F respectively ₁And F ₂N capable element of m.

6. a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence according to claim 1 is characterized in that G in the described step 5 ₁And G ₂Be specially:

G ₁And G ₂Be two-dimentional plural groups, size is X * Y:

$G_1(m,n)=\left\{\begin{array}{c}{2F}_1(m,n),m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,X/4;n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,Y\\ {2F}_1(m-X/2,n),m=\frac{3}{4}X+1,\frac{3}{4}X+2,\&CenterDot;\&CenterDot;\&CenterDot;,X;n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,Y\\ 0,m=X/4+1,X/4+2,\&CenterDot;\&CenterDot;\&CenterDot;,\frac{3}{4}X;n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;Y\end{array}\right.---\left(18\right)$

$G_2(m,n)=\left\{\begin{array}{c}{2F}_2(m,n),m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,X/4;n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,Y\\ {2F}_2(m-X/2,n),m=\frac{3}{4}X+1,\frac{3}{4}X+2,\&CenterDot;\&CenterDot;\&CenterDot;,X;n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,Y\\ 0,m=X/4+1,X/4+2,\&CenterDot;\&CenterDot;\&CenterDot;,\frac{3}{4}X;n=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;Y\end{array}\right.---\left(19\right)$

Wherein, G ₁(m, n), G ₂(m n) represents G respectively ₁, G ₂N capable element of m, F ₁(m, n), F ₂(m n) represents F respectively ₁, F ₂N capable element of m, F ₁(m-X/2, n), F ₂(m-X/2 n) represents F respectively ₁, F ₂(m-X/2) row n element.

7. a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence according to claim 1 is characterized in that described step 6 specifically comprises:

(1) structure shifted divisor vector p;

Shifted divisor vector p is an one-dimension array, and array length is that the orientation is to sampling number X; Obtain each component of p by following formula:

$p\left(m\right)=\left\{\begin{array}{c}{e}^{-j2\mathrm{\&pi;}(m+X/2-1)/X},m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,X/2\\ e^{-j2\mathrm{\&pi;}(m-X/2-1)/X},m=X/2+1,X/2+2,\&CenterDot;\&CenterDot;\&CenterDot;,X\end{array}\right.---\left(20\right)$

In the formula, the j on the exponential term represents imaginary unit, m the component of p (m) expression shifted divisor vector p;

(2) multiply each other and superposition of data with shifted divisor;

With G ₂Multiply each other with shifted divisor vector p by row, and and G ₁Superimposed, obtain data H behind the shifter-adder:

H(:,n)＝G ₁(:,n)+G ₂(:,n)·p，n＝1,2,…,Y (21)

Wherein, H (:, n), G ₁(:, n), G ₂(:, n) represent H, G respectively ₁, G ₂N row, expression vector dot product.

8. a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence according to claim 1 is characterized in that described step 7 specifically comprises:

(1) obtains the corresponding orientation frequency of every row of data H behind the shifter-adder;

If the pulse repetition rate of radar is f _p, the orientation frequency of the capable correspondence of m of H is

Then:

(2) calculate the oblique distance R of each range gate correspondence according to the reference oblique distance ⁽ⁿ⁾, n=1,2 ..., Y;

If be R with reference to oblique distance ₀, distance is f to sampling rate _s, pulse width is t _p, the light velocity is c, the oblique distance of n range gate correspondence is R ⁽ⁿ⁾For:

R ⁽ⁿ⁾＝R ₀+(n-1-(Y-f _s·t _p)/2)·c/f _s/2，n＝1,2,…,Y (14)

(3) at each row of data H, construct corresponding orientation compression filter and carry out filtering, obtain frequency spectrum data H ' after the azimuth filtering;

To the n row of data H, construct orientation compression filter h at frequency domain:

$h\left(m\right)=e^{j4\mathrm{\&pi;}/\mathrm{\&lambda;}{R}^{\left(n\right)}\sqrt{1-\frac{{\mathrm{\&lambda;}}^2{\left(f_{\mathrm{\&eta;}}^{\left(m\right)}\right)}^2}{{4v}^2}}},m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,X---\left(23\right)$

Wherein, the j on the exponential term represents imaginary unit, and v represents the Texas tower velocity equivalent, and λ represents the wavelength that transmits; M the component of h (m) expression h;

N row with the data H of orientation compression filter h carry out filtering:

H′(:,n)＝H(:,n)·h,n＝1,2,…,Y (24)

Wherein, H ' (:, n), H (:, n) represent the n row of H ' and H respectively, expression vector dot product;

(4) the capable and back X/2 line data of the preceding X/2 of frequency spectrum data H ' after the azimuth filtering is exchanged, the data H ' ' after obtaining exchanging carries out inverse fast Fourier transform to respectively being listed as of the data H ' ' after the exchange, finally obtains view data I:

$H^{\&prime;\&prime;}(m,:)=\left\{\begin{array}{c}{H}^{\&prime;}(m+X/2,:),m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,X/2\\ H^{\&prime;}(m-X/2,:),m=X/2+1,X/2+2,\&CenterDot;\&CenterDot;\&CenterDot;,X\end{array}\right.---\left(25\right)$

I(:,n)＝IFFT(H′′(:,n)),n＝1,2,…,Y (26)

In the formula, H ' ' (m :) represent that the m of H ' ' is capable, H ' (m+X/2,): represent H ' (m+X/2) OK, H ' (m-X/2): represent H ' (m-X/2) OK, I (:, n), H ' ' (:, n) represent the n row of I and H ' ' respectively, IFFT () expression is carried out inverse fast Fourier transform to one-dimension array.

9. according to the described any described a kind of ULTRA-LOW SIDE LOBES synthetic aperture radar image-forming method based on fully-complementary sequence of claim 1-8, it is characterized in that, in the described formation method:

Fully-complementary sequence is made of a pair of complementary series, length be L fully-complementary sequence to A, B} is:

$\left\{\begin{array}{c}A=(a^0,a^1,\&CenterDot;\&CenterDot;\&CenterDot;,a^{L-1})\\ B=(b^0,b^1,\&CenterDot;\&CenterDot;\&CenterDot;,b^{L-1})\end{array}\right.$ (1)

Wherein, A and B are for constituting a pair of composition sequence of fully-complementary sequence; a ⁰, a ¹..., a ^L-1The code element of expression sequence A, b ⁰, b ¹..., b ^L-1The code element of expression sequence B;

Fully-complementary sequence is during as the radar emission signal, and two composition sequences constitute a pair of train of impulses, chronologically alternately emission; Each element duration is T in each composition sequence _c, after whole transmission of symbols, this composition sequence battery has fired, the duration is t _p, t _p=LT _c, be the duration of pulse, s _A(t) and s _B(t) the baseband signal form is:

$\left\{\begin{array}{c}{s}_A\left(t\right)=a^l,l\&CenterDot;T_c\&le;t<(l+1)\&CenterDot;T_c,l=\mathrm{0,1,2},\&CenterDot;\&CenterDot;\&CenterDot;,L-1\\ s_B\left(t\right)=b^l,l\&CenterDot;T_c\&le;t<(l+1)\&CenterDot;T_c,l=\mathrm{0,1,2},\&CenterDot;\&CenterDot;\&CenterDot;,L-1\end{array}\right.---\left(2\right)$

Wherein, t is apart to the fast time, is each pulse emission forward position with reference to starting point; s _A(t) and s _B(t) be respectively the baseband signal form of sequence A and B;

With the fully-complementary sequence signal waveform as the synthetic-aperture radar that transmits in when work, its antenna is with 1/f _pFor the cycle replaces transponder pulse signal s _A(t) and s _B(t), the duration of pulse is t _pF wherein _pThe pulse repetition rate of expression radar, 1/f _pThe pulse repetition time that is called radar; Each exomonental initial moment is called the orientation constantly, and adjacent two orientation time interval constantly is pulse repetition time 1/f _pAfter each pulse emission finished, antenna was opened the echo receiver window, receives the radar echo signal that the ground surface launching is returned, and closed the echo window before next pulse emission beginning; In echo receiver window opening time, with sample rate f _sEchoed signal to a pulse is sampled, and sampling number is Y, and saves as the delegation of echo data; Echo receiver window of every unlatching, storing one row data successively; After having launched X pulse, the radar power cut-off;

Be a two-dimentional plural groups C with the fully-complementary sequence signal waveform as the synthetic-aperture radar echo data of radar emission signal, its size is X * Y, one dimension be the orientation to, X sampled point arranged, the expression radar has obtained X orientation one dimension pulse echo data constantly, different orientation is to the corresponding different orientation moment of sampled point, and two adjacent orientation differ orientation 1/f constantly to sampled point _pAnother dimension be distance to, Y sampled point arranged, represent that each orientation opens the echo receiver window constantly one time, echoed signal is sampled, be called distance to sampling, one-time continuous is apart from having Y sampled point to sampling, sampling rate is f _s, different distances is to the corresponding different oblique distance of sampled point, and the radar antenna phase center is to the distance of terrain object point, that is corresponding different range gate, and two neighbor distance differ oblique distance c/2f to sampled point _s, c is the light velocity.

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