CN116165664A - Space-borne SAR distance ambiguity suppression method based on two-dimensional waveform coding - Google Patents
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Abstract
The invention provides a space-borne SAR distance ambiguity suppression method based on two-dimensional waveform coding. While alternately transmitting two orthogonal nonlinear frequency modulation signals, adding a periodic coding phase to each transmission waveform, decoding the received echoes, performing imaging processing, and ensuring that the echoes of a desired scene can be normally imaged, wherein the range ambiguity energy of a plurality of continuous orders is suppressed to different degrees. The invention improves the distance fuzzy energy inhibition performance on the premise of not increasing the complexity of the system, and has engineering application value.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a satellite-borne SAR distance ambiguity suppression method based on two-dimensional waveform coding.
Background
Synthetic aperture radar (Synthetic Aperture Radar, SAR) is an imaging radar with active earth observation and high resolution capabilities, can provide more useful target information beyond ranging and speed measurement functions, is less affected by weather factors, and has all-weather observation capabilities throughout the world. However, the conventional single channel SAR system cannot obtain a high-resolution wide-width image due to the limitation of the minimum antenna area. High azimuth resolution requires that the corresponding system employ high pulse repetition frequencies (Pulse Repetition Frequency, PRF) to avoid doppler aliasing, but high PRF can cause distance ambiguity, thus limiting breadth. The wide range requires a low PRF to avoid distance ambiguity, which is difficult to meet the azimuth space sampling requirement of high azimuth resolution. This contradiction is exacerbated on satellite-borne platforms. Thus, suppression of distance blur is important for eliminating unwanted echoes and achieving high-resolution wide-range imaging.
In order to effectively solve the problem of distance ambiguity, multiple technologies such as a multi-channel technology, a phase center offset antenna, digital beam forming, multiple input multiple output and the like are proposed in the prior art. Most of the new technologies are based on the system level for suppression, the complexity of the system is high, and a series of problems still need to be solved. The waveform diversity and waveform coding technology does not need to increase the complexity of the system, has higher cost performance and can bring more other advantages, and has huge application potential.
The conventional common waveform diversity and coding method is to scatter the distance-blurred energy in the distance direction, and does not really eliminate the energy, or only inhibits the single specific distance-blurred order, so that the distance-blurred energy is not thoroughly inhibited.
Disclosure of Invention
In order to reduce the distance blur energy of a plurality of continuous orders, the invention provides a satellite-borne SAR distance blur suppression scheme based on two-dimensional waveform coding.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a satellite-borne SAR distance ambiguity suppression method based on two-dimensional waveform coding comprises the following steps:
step 1: constructing a piecewise chirped signal;
step 2: optimizing the instantaneous frequency of the linear frequency modulation signal to obtain a quadrature nonlinear frequency modulation waveform;
step 3: adding phase codes to the continuously transmitted pulses;
step 4: SAR imaging of the non-chirped signal is performed.
Further, the step 1 includes: bandwidth of chirped signalUniformly divide into->Segments, each segment length is->Start point of nth segment->Expressed as: />
Wherein n=1, 2, … …, N;
according to pulse width vectorAnd bandwidth vector->Calculating piecewise linear frequency functions of the piecewise linear frequency signals, and calculating the frequency modulation rate of each piece of linear frequency functions>The method comprises the following steps:
the time domain expression of the piecewise chirped signal is:
wherein ,is a rectangular function>For distance to time, add>Pulse time width +.>As an exponential function +.>Is a complex constant.
Further, the step 2 includes:
two mutually orthogonal nonlinear frequency modulation waveforms are designed based on a particle swarm optimization algorithm, and the two piecewise linear frequency modulation waveforms are alternately optimized to reduce the cross-correlation energy, and the optimization problem is expressed as follows:
wherein ,is the instantaneous frequency, +.> and />Constraint values of Peak Side Lobe Ratio (PSLR) and Integral Side Lobe Ratio (ISLR) of waveform respectively, +.>Is a minimization function, +.>For cross-correlation function +.> and />Respectively is waveform +> and />Peak side lobe ratio,/> and />Respectively is waveform +> and />Is a side lobe ratio of the integral of (a).
Wherein one waveform remains unchanged and the other waveform is updated according to the following equation:
wherein ,is inertial weight, ++>Is particle velocity, +.> and />Is a learning factor, < >> and />Is a uniform random number, < >>Is the instantaneous frequency of the corresponding moment, < >>Is an extremum of individuals,/->Is a population extremum.
Further, the particle swarm optimization algorithm comprises the following steps:
step a, setting an iteration counterMaximum number of iterations->Particle swarm size, inertial weight +.>Learning factor->、/>Two groups of codes are used as instantaneous frequency +.>And particle speed->;
Step b, calculating the fitness of each particle according to the objective function;
Step d, updating the speed and the position of the particles according to the individual extremum and the population extremum of the particles;
step e, judging whether the updated speed and position exceed the boundary value, and if yes, modifying the updated speed and position into the boundary value;
f, judging a stopping rule: order theIf->Go to step b until +.>The maximum iteration times are reached, the position corresponding to the particle with the maximum adaptability is output, and the calculation is finished;
step g, alternately optimizing waveforms: if the output result is waveformTurning to step (1), fixing the waveform +.>Instantaneous frequency of corresponding time of waveform +.>Optimization is performed, and vice versa, until the orthogonality of the two waveforms meets the requirements.
Further, the step 3 includes:
each transmit pulse is phase encoded along a slow time, the kth transmit waveform is represented as:
wherein ,for the transmission waveform kmod2 denotes an alternating transmission waveform in the form of a period 2 of the transmission waveform, +.>For distance to time, add>For azimuth time, < >>For azimuth encoding phase, the expression is:
assuming the presence ofOrder distance blur, in>The ∈received by the receiving window>The code phase of the order range ambiguity echo is:
demodulating the aliased echo by taking the code phase of the expected echo as a reference, wherein the residual phase code of the fuzzy echo is as follows:
Further, the step 4 includes:
the baseband signal of a single point target after demodulating the target echo signal corresponding to the signal transmitted by mixing the baseband radar signal with constant amplitude is expressed as:
wherein ,for signal amplitude +.>For distance-time envelope>For instantaneous pitch, add>For azimuth envelope->For the beam center crossing time, < > and->For carrier frequency->Is the phase of the non-chirped signal, +.>For distance to time, add>Is the speed of light;
performing distance Fourier transform on the echo signals:
wherein ,for the amplitude of the distance spectrum>For distance frequency, < >>For distance spectrum envelope>Is the spectral phase of the non-chirped signal;
constructing a one-dimensional nonlinear frequency modulation signal, carrying out Fourier transform on the one-dimensional nonlinear frequency modulation signal, and then taking complex conjugate to obtain a required matched filter:
after distance matching filtering, the spectrum phase of the nonlinear frequency modulation signal is filtered, and the spectrum echo expression is:
after the distance is matched and filtered on the frequency domain, multiplying the distance by a linear compensation phase to construct a frequency spectrum of a linear frequency modulation signal:
wherein ,the frequency is adjusted for distance direction. Multiplying the frequency spectrum phase and then carrying out inverse Fourier transform to obtain an echo time domain expression as follows:
The beneficial effects are that:
1. the method adopts a particle swarm optimization algorithm to obtain the orthogonal nonlinear frequency modulation signal with reduced cross-correlation energy, and alternately transmits the expected echo after the echo matched filtering to normally match, the odd-order distance fuzzy echo is mismatched, and the odd-order distance fuzzy energy is reduced instead of being scattered in the distance direction.
2. According to the invention, a periodic phase code is added to each transmitting signal, the expected echo is kept unchanged after decoding, the range ambiguity echoes of all orders are offset in the azimuth spectrum to different degrees, wherein partial even orders can reach the maximum effective offset, and the band-pass filter is constructed to inhibit the range ambiguity energy of even orders to the greatest extent.
3. The space-borne SAR distance ambiguity suppression model with the two-dimensional waveform codes is constructed by combining the two methods, and the space-borne SAR distance ambiguity suppression model has the effect of suppressing the distance ambiguity energy of continuous orders on the premise of not increasing the complexity of the system.
Drawings
FIG. 1 is a flow chart for optimizing quadrature non-chirped waveforms;
FIG. 2 is a schematic diagram illustrating the principle of distance blur suppression;
FIG. 3 is a flow chart of SAR imaging of a non-chirped signal;
fig. 4 is a graph of distance blur ratio (RASR) performance comparisons.
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention. In addition, the technical features of the embodiments of the present invention described below may be combined with each other as long as they do not collide with each other.
The invention discloses a satellite-borne SAR distance ambiguity suppression method based on two-dimensional waveform coding, which comprises the following steps: and segmenting the bandwidth of the linear frequency modulation signals, and alternately optimizing the two segmented linear frequency modulation signals by using a particle swarm optimization algorithm to obtain two orthogonal nonlinear frequency modulation signals with reduced cross-correlation energy, low peak side lobe ratio and low integral side lobe ratio. While alternately transmitting two orthogonal nonlinear frequency modulation signals, adding a periodic coding phase to each transmission waveform, decoding the received echoes, performing imaging processing, and ensuring that the echoes of a desired scene can be normally imaged, wherein the range ambiguity energy of a plurality of continuous orders is suppressed to different degrees. The method specifically comprises the following steps:
step 1: constructing a piecewise chirp signal:
the concept of describing the instantaneous frequency function of a nonlinear frequency modulation waveform according to a piecewise linear function comprisesThe non-chirped waveform of the individual sample points can be regarded as +.>The segment chirped waveforms are spliced together end to end. Bandwidth of chirped signal +.>Uniformly divide into->Segments, each segment length is->First->Start of segment->Expressed as:
according to pulse width vectorAnd bandwidth vector->Calculating piecewise linear frequency functions of the piecewise linear frequency signals, and calculating the frequency modulation rate of each piece of linear frequency functions>The method comprises the following steps:
the time domain expression of the piecewise chirped signal is:
wherein ,is a rectangular function>For distance to time, add>Pulse time width +.>Is an indexFunction (F)>Is a complex constant. />
Step 2: optimizing the instantaneous frequency of the chirp signal to obtain a quadrature non-chirp waveform:
the non-chirped waveform alters the energy distribution within the spectrum by altering the instantaneous frequency function of the waveform. The smaller the cross-correlation energy of the waveform, the better the orthogonality of the non-chirped transmission waveform. Therefore, two mutually orthogonal nonlinear frequency modulation waveforms are designed based on a particle swarm optimization algorithm, and the two piecewise linear frequency modulation waveforms are alternately optimized to reduce the cross-correlation energy, and the optimization problem is expressed as follows:
wherein ,is the instantaneous frequency, +.> and />Constraint values of Peak Side Lobe Ratio (PSLR) and Integral Side Lobe Ratio (ISLR) of waveform respectively, +.>Is a minimization function, +.>For cross-correlation function +.> and />Respectively is waveform +> and />Peak side lobe ratio,/> and />Respectively is waveform +> and />Is a side lobe ratio of the integral of (a).
One waveform remains unchanged, and the other waveforms are updated according to the following equation:
wherein ,is inertial weight, ++>Is particle velocity, +.> and />Is a learning factor, < >> and />Is a uniform random number, < >>Is the instantaneous frequency of the corresponding moment, < >>Is an extremum of individuals,/->Is a population extremum.
As shown in fig. 1, the basic workflow of the particle swarm optimization algorithm is as follows:
(1) Initializing: setting an iteration counterMaximum number of iterations->Particle swarm size, inertial weightLearning factor->、/>Two groups of codes are used as instantaneous frequency +.>And particle speed->。
(2) And (3) calculating particle fitness: the fitness of each particle is calculated from the objective function.
(3) Calculating individual and population extremum of the particles: calculating individual extrema for each particleAnd population extremum->。
(4) Updating particle velocity and position: and updating the speed and the position of the particles according to the individual extremum and the population extremum of the particles.
(5) Boundary condition processing: and judging whether the updated speed and position exceed the boundary value, and if so, modifying the updated speed and position into the boundary value.
(6) And (3) judging a stopping rule: order theIf->Go to step (2) until +.>And (3) the maximum iteration times are reached, the position corresponding to the maximum fitness particle is output, and the calculation is finished.
(7) Alternately optimizing waveforms: if the output result is waveformTurning to step (1), fixing the waveform +.>Instantaneous frequency of corresponding time of waveform +.>Optimization is performed, and vice versa, until the orthogonality of the two waveforms meets the requirements.
Step 3: adding phase encoding to the continuously transmitted pulses:
as shown in fig. 2, each transmit pulse is phase encoded along a slow time, and the kth transmit waveform can be expressed as:
wherein ,for the transmit waveform kmod2 represents an alternate transmit waveform in the form of a period of 2,for distance to time, add>For azimuth time, < >>For azimuth encoding phase, the expression is:
neglecting the arrival of echoes across pulse repetition intervals, the firstThe code phase of the desired target echo received by each receive window is the same as above. Suppose there is +.>Order distance blur, in>The ∈received by the receiving window>The code phase of the order range ambiguity echo is:
demodulating the aliased echo by taking the code phase of the expected echo as a reference, wherein the residual phase code of the fuzzy echo is as follows:
wherein, PRF is pulse repetition frequency,is in combination with->Constant of nothing, rootBy the nature of the fourier transformation, the spectrum of the blurred echo is shifted +.>The actual PRF selection is typically greater than the doppler bandwidth, so that the ambiguous echo, after shifting, constructs a bandpass filter to filter out portions that lie outside the doppler bandwidth.
Step 4: SAR imaging of non-chirped signals:
as shown in fig. 3, a baseband signal of a single point target after demodulating a target echo signal corresponding to a signal transmitted by mixing a baseband radar signal with a constant amplitude may be expressed as:
wherein ,for signal amplitude +.>For distance-time envelope>For instantaneous pitch, add>For azimuth envelope->For the beam center crossing time, < > and->For carrier frequency->Is the phase of the non-chirped signal, +.>For distance to time, add>Is the speed of light.
Because the nonlinear frequency modulation signal has different performance from the linear frequency modulation signal, the direct adoption of the traditional imaging algorithm can lead to target defocusing, and the traditional algorithm needs to be improved and is applicable to the nonlinear frequency modulation signal. Performing distance Fourier transform on the echo signals:
wherein ,for the amplitude of the distance spectrum>For distance frequency, < >>For distance spectrum envelope>Is the spectral phase of the non-chirped signal. Analytic +.>Is not directly available, and therefore the spectral phase of the non-chirped signal needs to be filtered out by matched filtering. Constructing a one-dimensional nonlinear frequency modulation signal, carrying out Fourier transform on the one-dimensional nonlinear frequency modulation signal, and then taking complex conjugate to obtain a required matched filter:
wherein ,representing the fourier transform. After distance matching filtering, the spectrum phase of the nonlinear frequency modulation signal is filtered, and the spectrum echo expression is:
since the scaling operation in the CS algorithm needs to be based on a chirp model, further corrections are needed. After the distance is matched and filtered on the frequency domain, a linear compensation phase is multiplied to construct a frequency spectrum of a linear frequency modulation signal:
wherein ,the frequency is adjusted for distance direction. Multiplying the frequency spectrum phase and then carrying out inverse Fourier transform to obtain an echo time domain expression as follows:
At the moment, the echo model meets the echo model of the linear frequency modulation signal, and the traditional CS algorithm can be adopted for focusing and imaging the target. A window function is added to filter out the blurred energy of the azimuth offset after the distance-wise inverse Fourier transform and before azimuth compression.
Fig. 4 shows the distance blur suppression level of the present invention, and the distance blur is effectively suppressed, and the above results prove that the two-dimensional coding design scheme can effectively suppress the distance blur energy.
It will be readily appreciated by those skilled in the art that the foregoing description is merely a preferred embodiment of the invention and is not intended to limit the invention, but any modifications, equivalents, improvements or alternatives falling within the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (6)
1. The space-borne SAR distance ambiguity suppression method based on two-dimensional waveform coding is characterized by comprising the following steps of:
step 1: constructing a piecewise chirped signal;
step 2: optimizing the instantaneous frequency of the linear frequency modulation signal to obtain a quadrature nonlinear frequency modulation waveform;
step 3: adding phase codes to the continuously transmitted pulses;
step 4: SAR imaging of the non-chirped signal is performed.
2. The method for space-borne SAR distance ambiguity suppression based on two-dimensional waveform coding according to claim 1, wherein said step 1 comprises: bandwidth of chirped signalUniformly divide into->Segments, each segment length is->Start point of nth segment->Expressed as:
wherein n=1, 2, … …, N;
according to pulse width vectorAnd bandwidth vector->Calculating piecewise linear frequency functions of the piecewise linear frequency signals, and calculating the frequency modulation rate of each piece of linear frequency functions>The method comprises the following steps:
the time domain expression of the piecewise chirped signal is:
3. The method for space-borne SAR distance ambiguity suppression based on two-dimensional waveform coding according to claim 2, wherein said step 2 comprises:
two mutually orthogonal nonlinear frequency modulation waveforms are designed based on a particle swarm optimization algorithm, and the two piecewise linear frequency modulation waveforms are alternately optimized to reduce the cross-correlation energy, and the optimization problem is expressed as follows:
wherein ,is the instantaneous frequency, +.> and />Constraint values of peak side lobe ratio and integral side lobe ratio of waveform respectively, < >>Is a minimization function, +.>For cross-correlation function +.> and />Respectively is waveform +> and />Peak side lobe ratio,/> and />Respectively is waveform +> and />Is a ratio of integral sidelobes;
wherein one waveform remains unchanged and the other waveform is updated according to the following equation:
4. The method for space-borne SAR range ambiguity suppression based on two-dimensional waveform encoding as set forth in claim 3, wherein said particle swarm optimization algorithm comprises the steps of:
step a, setting an iteration counterMaximum number of iterations->Particle swarm size, inertial weight +.>Learning factor->、Two groups of codes are used as instantaneous frequency +.>And particle velocity/>;
Step b, calculating the fitness of each particle according to the objective function;
Step d, updating the speed and the position of the particles according to the individual extremum and the population extremum of the particles;
step e, judging whether the updated speed and position exceed the boundary value, and if yes, modifying the updated speed and position into the boundary value;
f, judging a stopping rule: order theIf->Go to step b until +.>The maximum iteration times are reached, the position corresponding to the particle with the maximum adaptability is output, and the calculation is finished;
5. The method for space-borne SAR distance ambiguity suppression based on two-dimensional waveform coding according to claim 3 or 4, wherein said step 3 comprises:
phase encoding each transmitted pulse along a slow time, the firstThe individual transmit waveforms are represented as:
wherein ,for the transmission waveform kmod2 denotes an alternating transmission waveform in the form of a period 2 of the transmission waveform, +.>For distance to time, add>For azimuth time, < >>For azimuth encoding phase, the expression is:
assuming the presence ofOrder distance blur, in>The ∈received by the receiving window>The code phase of the order range ambiguity echo is: />
Demodulating the aliased echo by taking the code phase of the expected echo as a reference, wherein the residual phase code of the fuzzy echo is as follows:
6. The method for space-borne SAR distance blur suppression based on two-dimensional waveform coding according to claim 5, wherein said step 4 comprises:
the baseband signal of a single point target after demodulating the target echo signal corresponding to the signal transmitted by mixing the baseband radar signal with constant amplitude is expressed as:
wherein ,for signal amplitude +.>For distance-time envelope>For instantaneous pitch, add>For azimuth envelope->For the beam center crossing time, < > and->For carrier frequency->Is the phase of the non-chirped signal, +.>For distance to time, add>Is the speed of light;
performing distance Fourier transform on the echo signals:
wherein ,for the amplitude of the distance spectrum>For distance frequency, < >>For distance spectrum envelope>Is the spectral phase of the non-chirped signal;
constructing a one-dimensional nonlinear frequency modulation signal, carrying out Fourier transform on the one-dimensional nonlinear frequency modulation signal, and then taking complex conjugate to obtain a required matched filter:
after distance matching filtering, the spectrum phase of the nonlinear frequency modulation signal is filtered, and the spectrum echo expression is:
after the distance is matched and filtered on the frequency domain, multiplying the distance by a linear compensation phase to construct a frequency spectrum of a linear frequency modulation signal:
multiplying the frequency spectrum phase and then carrying out inverse Fourier transform to obtain an echo time domain expression as follows:
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