CN103954963A - Step frequency SAR imaging method based on CS algorithm - Google Patents

Abstract

The invention discloses a step frequency SAR imaging method based on a CS algorithm. With the method, step frequency SAR high-resolution imaging can be conducted. A frequency domain broadband splicing method is improved, under the condition that the operand is not increased, time domain broadband chirp signals with narrow pulse widths can be generated, the operation efficiency is high, and imaging can be performed on the generated chirp signals with the CS algorithm. Due to broadband synthesis, the signal to noise ratio of the range resolution and a point target is improved, and therefore compared with an existing synthetic algorithm, the step frequency SAR imaging method is more suitable for high-resolution imaging.

Description

A kind of Step Frequency SAR formation method based on CS algorithm

Technical field

The present invention relates to synthetic-aperture radar SAR technical field of imaging, be specifically related to a kind of Step Frequency SAR formation method based on CS algorithm.

Background technology

Synthetic-aperture radar (SAR) is a kind of high-resolution microwave imaging radar of round-the-clock, round-the-clock.Along with the development of technology, the resolution of SAR improves gradually, and the highest resolution of SAR system has reached 0.1m at present.There are some special problems in high-resolution acquisition, such as, in order to obtain the resolution of 0.1m, require the bandwidth transmitting to surpass 1.5GHz.Produce and concerning this Sampling for Wide-Band Signal for actual treatment being all difficulty very.

Step Frequency technology is that a kind of conventional distance of obtaining is to high-resolution technology.Ultra-broadband signal is synthesized by aftertreatment by one group of narrow band signal.The major advantage of Step Frequency technology is that the instant bandwidth transmitting will be much smaller than the bandwidth of final synthesized wideband signal, therefore Step Frequency SAR when obtaining identical high-resolution than common SAR to system require much lower, therefore distance can realize easily to high-resolution.

In Step Frequency SAR imaging based on Chirp scaling (CS) algorithm, by narrow band signal, generate broadband signal and need to carry out broadband splicing.At present, more efficient broadband joining method is frequency domain broadband joining method.The result of frequency domain broadband joining method is one dimension High Range Resolution, also pass through the broadband chirp signal of pulse compression, therefore it can only just carry out the algorithm apart from pulse pressure for first steps such as Range-Doppler (RD) algorithm, SPECAN algorithms, and can not before apart from pulse pressure, need to carry out the algorithm that nonlinear phase multiplies each other for CS algorithm etc.

Summary of the invention

In view of this, the invention provides a kind of Step Frequency SAR formation method based on CS algorithm, frequency domain broadband joining method is improved, making to splice result can carry out Step Frequency SAR high-resolution imaging by enough CS algorithms.

Step Frequency SAR formation method based on CS algorithm of the present invention comprises the steps:

Step 1, carries out broadband signal frequency spectrum by subpulse signal and synthesizes;

Step 2, the broadband signal frequency spectrum that step 1 is obtained is multiplied by a quadratic phase, and described quadratic phase is

$H_{\mathrm{virt}}\left(f\right)=\exp \left[\mathrm{j\π}\frac{f_r^2}{K_{\mathrm{virt}}}\right]$

Wherein, f _rrepresent frequency of distance, K _virtfor frequency modulation rate,

$K_{\mathrm{virt}}=-\frac{\mathrm{N\Δf}}{T_p}$

Wherein, N represents stepped-frequency interval, and Δ f represents stepped-frequency interval, T _pindicating impulse width;

Step 3, the broadband signal frequency spectrum that step 2 is obtained carries out IFFT and transforms to apart from time domain, obtains the chirp signal of a narrow pulsewidth wide bandwidth;

Step 4, the chirp signal of the narrow pulsewidth wide bandwidth that step 3 is synthesized carries out imaging processing for CS algorithm, obtains SAR imaging results.

Wherein, described step 1 comprises the steps:

Step 1.1, transforms to subpulse signal apart from frequency domain through FFT;

Step 1.2, is carrying out pulse compression apart from frequency domain antithetical phrase pulse signal;

Step 1.3, carries out zero padding, windowing at frequency domain antithetical phrase pulse signal frequency spectrum;

Step 1.4, the signal that step 1.3 is obtained carries out IFFT and transforms to time domain;

Step 1.5, carries out frequency domain displacement;

Step 1.6, the signal that step 1.5 is obtained carries out distance and transforms to frequency domain to FFT;

Step 1.7, does coherence stack by subpulse signal spectrum, obtains broadband signal frequency spectrum.

Beneficial effect:

The inventive method, in the situation that not increasing operand, can generate the time domain broadband chirp signal of narrow pulsewidth, and operation efficiency is higher, and synthetic result can be carried out imaging processing by enough CS class algorithms.The synthetic signal to noise ratio (S/N ratio) that has improved range resolution and point target in broadband, is therefore more suitable for high-resolution imaging than existing composition algorithm.

Accompanying drawing explanation

Fig. 1 is this method process flow diagram.

Fig. 2 (a) is the broadband splicing result in time domain against pulse pressure by narrow band signal frequency modulation rate; Fig. 2 (b) is the broadband splicing result in time domain against pulse pressure by frequency modulation rate of the present invention.

Fig. 3 is Area Objects imaging results, (a) is former figure; (b) be coarse resolution figure; (c) be broadband splicing+CS imaging results.

Embodiment

Below in conjunction with the accompanying drawing embodiment that develops simultaneously, describe the present invention.

The invention provides a kind of Step Frequency SAR formation method based on CS algorithm, first frequency domain broadband joining method is improved, compare with existing frequency domain broadband joining method, step before synthesized wideband signal frequency spectrum is identical, after synthesized wideband signal frequency spectrum, existing frequency domain broadband joining method directly carries out inverse fast Fourier transform (IFFT) to broadband signal frequency spectrum and obtains one dimension High Range Resolution, and the present invention also needs broadband signal frequency spectrum to be multiplied by a quadratic phase, carry out again afterwards IFFT to obtain a narrow pulsewidth, the chirp signal of wide bandwidth, then the broadband chirp signal of narrow pulsewidth is used to CS algorithm and carries out imaging processing, obtain final SAR image.Specifically comprise the following steps:

Step 1, broadband signal frequency spectrum synthesize

Subpulse signal expression for broadband splicing is

$\begin{array}{c}s(t_r,n)=\mathrm{rect}\left[\frac{t_r-\frac{2(R-R_{\min })}{c}}{T_p}\right]\·\exp [-\mathrm{j\π}{K}_r{(t_r-\frac{2(R-R_{\min })}{c})}^2]\\ \·\exp [-j\frac{4\mathrm{\πR}}{c}(f_0+n\·\mathrm{\Δf})]\end{array}---\left(1\right)$

Wherein, t _rrepresent Distance Time, n represents frequency number, rect[] represent that gate function, R represent that radar and target distance are from, R _minrepresent initial sampled distance, c represents the light velocity, T _pindicating impulse width, K _rrepresent signal chirp rate, f ₀represent initial carrier frequency, N represents frequency modulation number of times, and Δ f represents stepped-frequency interval.

Through distance, to Fast Fourier Transform (FFT) (FFT), narrow band signal is transformed to apart from frequency domain, its expression formula is

$\begin{array}{c}S(f_r,n)=\mathrm{rect}\left[\frac{f_r}{B_{\mathrm{sub}}}\right]\·\exp [-\mathrm{j\π}\frac{f_r^2}{K_r}]\·\exp [-j2\mathrm{\π}{f}_r\frac{2(R-R_{\min })}{c}]\\ \·\exp [-j\frac{4\mathrm{\πR}}{c}(f_0+n\·\mathrm{\Δf})]\end{array}---\left(2\right)$

Wherein, f _rrepresent frequency of distance, B _subrepresent narrow band signal bandwidth.

Apart from frequency domain, narrow band signal is being carried out to pulse compression, the pulse compression factor is

$H_{\mathrm{MF}}\left(f_r\right)=\exp \left[\mathrm{j\π}\frac{f_r^2}{K_r}\right]---\left(3\right)$

Narrow band signal frequency spectrum after pulse compression is

$\begin{array}{c}{S}_{\mathrm{MF}}(f_r,n)=\mathrm{rect}\left[\frac{f_r}{B_{\mathrm{sub}}}\right]\·\exp [-j2\mathrm{\π}{f}_r\frac{2(R-R_{\min })}{c}]\\ \·\exp [-j\frac{4\mathrm{\πR}}{c}(f_0+n\·\mathrm{\Δf})]\end{array}---\left(4\right)$

Because narrow band signal bandwidth is less, therefore sampling rate is lower and much smaller than broadband signal bandwidth, therefore need to carry out rising sampling to narrow band signal, this can realize by narrow band signal frequency spectrum blank space being carried out to zero padding at frequency domain.In addition, because narrow band signal bandwidth is generally greater than stepped-frequency interval, narrow band signal frequency spectrum need to carry out windowing and remove the lap between narrow band signal frequency spectrum, and this step is carried out together with frequency domain zero padding.

In order to carry out accurate frequency displacement, need to be by the narrow band signal Spectrum Conversion after pulse compression to time domain, the narrow band signal time-domain expression after pulse compression is

$s_{\mathrm{MF}}(t_r,n)=\sin c\left[\mathrm{\Δf}(t_r-\frac{2(R-R_{\min })}{c})\right]\·\exp [-j\frac{4\mathrm{\πR}}{c}(f_0+n\·\mathrm{\Δf})]---\left(5\right)$

Sinc[wherein] represent sinc function.Frequency-shifting operator for frequency displacement is

${\mathrm{\φ}}_{\mathrm{fs}}(t_r,n)=\exp [-j2\mathrm{\π}(n-\frac{N-1}{2})\mathrm{\Δf}(t_r-\frac{2(R-R_{\min })}{c})]---\left(6\right)$

Narrow band signal after multiplying each other with frequency-shifting operator is transformed to frequency domain through FFT, can obtain the narrow band signal frequency spectrum after frequency displacement, this spectrum expression formula is

$\begin{array}{c}{S}_{\mathrm{fs}}(f_r,n)=\mathrm{rect}\left[\frac{f_r-(n-\frac{N-1}{2})\mathrm{\Δf}}{\mathrm{\Δf}}\right]\·\exp [-j2\mathrm{\π}{f}_r\frac{2(R-R_{\min })}{c}]\\ \·\exp [-j\frac{4\mathrm{\πR}}{c}(f_0+\frac{N-1}{2}\·\mathrm{\Δf})]\end{array}---\left(7\right)$

Narrow band signal spectral overlay after each frequency displacement is got up, can obtain the broadband signal frequency spectrum of needs, broadband signal spectrum expression formula is

$\begin{array}{c}{S}_{\mathrm{wide}}\left(f_r\right)=\mathrm{rect}\left[\frac{f_r}{\mathrm{N\Δf}}\right]\·\exp [-j2\mathrm{\π}{f}_r\frac{2(R-R_{\min })}{c}]\\ \·\exp [-j\frac{4\mathrm{\πR}}{c}(f_0+\frac{N-1}{2}\·\mathrm{\Δf})]\end{array}---\left(8\right)$

Step 2, narrow pulsewidth broadband chirp signal generate

In CS algorithm process, need to carry out CS processing to chirp signal, therefore need to not carry out the echo data apart from pulse pressure.Theoretically, only need to the broader frequency spectrum in formula (8), be multiplied by a quadratic phase at frequency domain, IFFT converts back time domain just can obtain a broadband chirp signal.But because the bandwidth of broadband signal is N times (wherein N represents stepped-frequency interval) of narrow band signal; if the frequency modulation rate of the quadratic phase multiplying each other is constant; the pulsewidth of broadband chirp signal can be also narrow band signal N doubly, this can cause data at time domain generation aliasing conventionally.Therefore it is infeasible, adopting the frequency modulation rate of narrow band signal to construct quadratic phase.According to existing conclusion, when bandwidth one timing, if frequency modulation rate increases, time domain pulsewidth reduces, therefore can consider to increase frequency modulation rate, constructs quadratic phase, the corresponding broadband chirp signal that can obtain a narrow pulsewidth.Its detailed process is as follows:

Broader frequency spectrum in formula (8) and a quadratic phase are multiplied each other, and this quadratic phase is

$H_{\mathrm{virt}}\left(f\right)=\exp \left[\mathrm{j\π}\frac{f_r^2}{K_{\mathrm{virt}}}\right]---\left(9\right)$

Wherein, K _virtfor the frequency modulation rate after adjusting.Broader frequency spectrum after multiplying each other with quadratic phase can be expressed as

$\begin{array}{c}{S}_{\mathrm{virt}}\left(f_r\right)=\mathrm{rect}\left[\frac{f_r}{\mathrm{N\Δf}}\right]\·\exp [-j2\mathrm{\π}{f}_r\frac{2(R-R_{\min })}{c}]\·\exp \left[\mathrm{j\π}\frac{f_r^2}{K_{\mathrm{virt}}}\right]\\ \·\exp [-j\frac{4\mathrm{\πR}}{c}(f_0+\frac{N-1}{2}\·\mathrm{\Δf})]\end{array}---\left(10\right)$

Through IFFT, convert back time domain, the broadband signal expression formula of time domain is

$\begin{array}{c}{s}_{\mathrm{virt}}\left(t_r\right)=\mathrm{rect}\left[\frac{t_r-\frac{2(R-R_{\min })}{c}}{\left|\frac{\mathrm{N\Δf}}{K_{\mathrm{virt}}}\right|}\right]\·\exp \left[j\mathrm{\π}{K}_{\mathrm{virt}}{(t_r-\frac{2(R-R_{\min })}{c})}^2\right]\\ \·\exp [-j\frac{4\mathrm{\πR}}{c}(f_0+\frac{N-1}{2}\·\mathrm{\Δf})]\end{array}---\left(11\right)$

From formula (11), the chirp signal that time domain forms, frequency modulation rate corresponding to quadratic phase that its frequency modulation rate is multiplied each other by frequency spectrum determine, pulsewidth is determined by the business of broadband signal bandwidth and frequency modulation rate.When frequency modulation rate is larger, the pulsewidth of time domain chirp signal is less.If get frequency modulation rate, be

$K_{\mathrm{virt}}=-\frac{\mathrm{N\Δf}}{T_p}---\left(12\right)$

Time domain broadband chirp signal expression is

$\begin{array}{c}{s}_{\mathrm{virt}2}\left(t_r\right)=\mathrm{rect}\left[\frac{t_r-\frac{2(R-R_{\min })}{c}}{T_p}\right]\·\exp \left[j\mathrm{\π}{(-\frac{\mathrm{N\Δf}}{T_p})(t_r-\frac{2(R-R_{\min })}{c})}^2\right]\\ \·\exp [-j\frac{4\mathrm{\πR}}{c}(f_0+\frac{N-1}{2}\·\mathrm{\Δf})]\end{array}---\left(13\right)$

Now chirp signal in broadband has and the identical pulsewidth of arrowband chirp signal, therefore can there is not time domain aliasing.Because processing is counted and is not increased, thus this synthetic method and traditional frequency domain broadband synthetic method to compare calculated amount basic identical.In addition, the result finally generating is chirp signal, and this synthetic method can be used in CS algorithm and carries out imaging processing.

Step 3, CS algorithm imaging processing

Broadband chirp signal through the synthetic narrow pulsewidth of step 2 will carry out imaging processing for CS algorithm, wherein the treatment scheme of CS algorithm is identical with the treatment scheme of classical CS algorithm: by the broadband chirp signal of narrow pulsewidth through orientation to FFT, the CS factor multiply each other, distance multiplies each other to FFT, distance to compensating factor, distance multiplies each other to IFFT, orientation to compensating factor and orientation to IFFT, obtain final SAR imaging results.

For the broadband synthetic method of verifying that the present invention provides, carried out relevant emulation, adopt narrow band signal frequency modulation rate against the broadband of pulse pressure acquisition, to splice result in time domain as shown in Figure 2 against the frequency modulation rate of pulse pressure and the present invention's employing, can find out, if the frequency modulation rate of using while not changing contrary pulse pressure, can there is time domain aliasing (Fig. 2 (a)), and change after the frequency modulation rate of contrary pulse pressure use, the pulsewidth of time domain chirp signal becomes very narrow (Fig. 2 (b)), therefore there will not be time domain aliasing.In order to verify the validity of the method, also carry out Area Objects emulation.Emulation former figure used and imaging results as shown in Figure 3, can find out, utilizes the method to use CS imaging to count in the situation that not increasing distance, and imaging results and former figure difference little, can meet the requirement of imaging.

In sum, these are only preferred embodiment of the present invention, be not intended to limit protection scope of the present invention.Within the spirit and principles in the present invention all, any modification of doing, be equal to replacement, improvement etc., within all should being included in protection scope of the present invention.

Claims (2)

1. the Step Frequency SAR formation method based on CS algorithm, is characterized in that, comprises the steps:

Step 1, carries out broadband signal frequency spectrum by subpulse signal and synthesizes;

Step 2, the broadband signal frequency spectrum that step 1 is obtained is multiplied by a quadratic phase, and described quadratic phase is

$H_{\mathrm{virt}}\left(f\right)=\exp \left[\mathrm{j\π}\frac{f_r^2}{K_{\mathrm{virt}}}\right]$

Wherein, f _rrepresent frequency of distance, K _virtfor frequency modulation rate,

$K_{\mathrm{virt}}=-\frac{\mathrm{N\Δf}}{T_p}$

Wherein, N represents stepped-frequency interval, and Δ f represents stepped-frequency interval, T _pindicating impulse width;

Step 3, the broadband signal frequency spectrum that step 2 is obtained carries out IFFT and transforms to apart from time domain, obtains the chirp signal of a narrow pulsewidth wide bandwidth;

Step 4, the chirp signal of the narrow pulsewidth wide bandwidth that step 3 is synthesized carries out imaging processing for CS algorithm, obtains SAR imaging results.

2. the Step Frequency SAR frequency domain broadband joining method for CS algorithm as claimed in claim 1, is characterized in that, described step 1 comprises the steps:

Step 1.1, transforms to subpulse signal apart from frequency domain through FFT;

Step 1.2, is carrying out pulse compression apart from frequency domain antithetical phrase pulse signal;

Step 1.3, carries out zero padding, windowing at frequency domain antithetical phrase pulse signal frequency spectrum;

Step 1.4, the signal that step 1.3 is obtained carries out IFFT and transforms to time domain;

Step 1.5, carries out frequency domain displacement;

Step 1.6, the signal that step 1.5 is obtained carries out distance and transforms to frequency domain to FFT;

Step 1.7, does coherence stack by subpulse signal spectrum, obtains broadband signal frequency spectrum.