CN116165664A - Space-borne SAR distance ambiguity suppression method based on two-dimensional waveform coding - Google Patents

Space-borne SAR distance ambiguity suppression method based on two-dimensional waveform coding Download PDF

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CN116165664A
CN116165664A CN202310430285.1A CN202310430285A CN116165664A CN 116165664 A CN116165664 A CN 116165664A CN 202310430285 A CN202310430285 A CN 202310430285A CN 116165664 A CN116165664 A CN 116165664A
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frequency
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phase
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CN116165664B (en
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王宇豪
邓云凯
王伟
张永伟
赵鹏飞
张衡
贾小雪
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Aerospace Information Research Institute of CAS
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9004—SAR image acquisition techniques
    • G01S13/9011—SAR image acquisition techniques with frequency domain processing of the SAR signals in azimuth
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/88—Radar or analogous systems specially adapted for specific applications
    • G01S13/89—Radar or analogous systems specially adapted for specific applications for mapping or imaging
    • G01S13/90—Radar or analogous systems specially adapted for specific applications for mapping or imaging using synthetic aperture techniques, e.g. synthetic aperture radar [SAR] techniques
    • G01S13/9004—SAR image acquisition techniques
    • G01S13/9017—SAR image acquisition techniques with time domain processing of the SAR signals in azimuth

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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

Space-borne SAR distance ambiguity suppression method based on two-dimensional waveform coding
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 signal
Figure SMS_1
Uniformly divide into->
Figure SMS_2
Segments, each segment length is->
Figure SMS_3
Start point of nth segment->
Figure SMS_4
Expressed as: />
Figure SMS_5
；
Wherein n=1, 2, … …, N;
thereby obtaining a bandwidth vector
Figure SMS_6
The method comprises the following steps:
Figure SMS_7
；
corresponding pulse width vector
Figure SMS_8
The method comprises the following steps:
Figure SMS_9
；
according to pulse width vector
Figure SMS_10
And bandwidth vector->
Figure SMS_11
Calculating piecewise linear frequency functions of the piecewise linear frequency signals, and calculating the frequency modulation rate of each piece of linear frequency functions>
Figure SMS_12
The method comprises the following steps:
Figure SMS_13
；
obtaining piecewise linear frequency functions
Figure SMS_14
The method comprises the following steps:
Figure SMS_15
；
the time domain expression of the piecewise chirped signal is:
Figure SMS_16
；
wherein ,
Figure SMS_17
is a rectangular function>
Figure SMS_18
For distance to time, add>
Figure SMS_19
Pulse time width +.>
Figure SMS_20
As an exponential function +.>
Figure SMS_21
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:
Figure SMS_22
；
wherein ,
Figure SMS_26
is the instantaneous frequency, +.>
Figure SMS_29
and />
Figure SMS_32
Constraint values of Peak Side Lobe Ratio (PSLR) and Integral Side Lobe Ratio (ISLR) of waveform respectively, +.>
Figure SMS_24
Is a minimization function, +.>
Figure SMS_30
For cross-correlation function +.>
Figure SMS_34
and />
Figure SMS_35
Respectively is waveform +>
Figure SMS_23
and />
Figure SMS_27
Peak side lobe ratio,/>
Figure SMS_31
and />
Figure SMS_33
Respectively is waveform +>
Figure SMS_25
and />
Figure SMS_28
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:
Figure SMS_36
；
wherein ,
Figure SMS_39
is inertial weight, ++>
Figure SMS_41
Is particle velocity, +.>
Figure SMS_43
and />
Figure SMS_38
Is a learning factor, < >>
Figure SMS_42
and />
Figure SMS_44
Is a uniform random number, < >>
Figure SMS_45
Is the instantaneous frequency of the corresponding moment, < >>
Figure SMS_37
Is an extremum of individuals,/->
Figure SMS_40
Is a population extremum.
Further, the particle swarm optimization algorithm comprises the following steps:
step a, setting an iteration counter
Figure SMS_46
Maximum number of iterations->
Figure SMS_47
Particle swarm size, inertial weight +.>
Figure SMS_48
Learning factor->
Figure SMS_49
、/>
Figure SMS_50
Two groups of codes are used as instantaneous frequency +.>
Figure SMS_51
And particle speed->
Figure SMS_52
；
Step b, calculating the fitness of each particle according to the objective function;
step c, calculating individual extremum of each particle
Figure SMS_53
And population extremum->
Figure SMS_54
；
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 the
Figure SMS_55
If->
Figure SMS_56
Go to step b until +.>
Figure SMS_57
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 waveform
Figure SMS_58
Turning to step (1), fixing the waveform +.>
Figure SMS_59
Instantaneous frequency of corresponding time of waveform +.>
Figure SMS_60
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:
Figure SMS_61
；
wherein ,
Figure SMS_62
for the transmission waveform kmod2 denotes an alternating transmission waveform in the form of a period 2 of the transmission waveform, +.>
Figure SMS_63
For distance to time, add>
Figure SMS_64
For azimuth time, < >>
Figure SMS_65
For azimuth encoding phase, the expression is:
Figure SMS_66
；
assuming the presence of
Figure SMS_67
Order distance blur, in>
Figure SMS_68
The ∈received by the receiving window>
Figure SMS_69
The code phase of the order range ambiguity echo is:
Figure SMS_70
；
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:
Figure SMS_71
；
wherein, PRF is pulse repetition frequency,
Figure SMS_72
is in combination with->
Figure SMS_73
An irrelevant constant.
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:
Figure SMS_74
；
wherein ,
Figure SMS_76
for signal amplitude +.>
Figure SMS_79
For distance-time envelope>
Figure SMS_81
For instantaneous pitch, add>
Figure SMS_77
For azimuth envelope->
Figure SMS_80
For the beam center crossing time, < > and->
Figure SMS_82
For carrier frequency->
Figure SMS_83
Is the phase of the non-chirped signal, +.>
Figure SMS_75
For distance to time, add>
Figure SMS_78
Is the speed of light;
performing distance Fourier transform on the echo signals:
Figure SMS_84
；
wherein ,
Figure SMS_85
for the amplitude of the distance spectrum>
Figure SMS_86
For distance frequency, < >>
Figure SMS_87
For distance spectrum envelope>
Figure SMS_88
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:
Figure SMS_89
；
wherein ,
Figure SMS_90
representing a fourier transform;
after distance matching filtering, the spectrum phase of the nonlinear frequency modulation signal is filtered, and the spectrum echo expression is:
Figure SMS_91
；
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:
Figure SMS_92
；
wherein ,
Figure SMS_93
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:
Figure SMS_94
；
wherein ,
Figure SMS_95
to compress the distance envelope of the object +.>
Figure SMS_96
Is the instantaneous skew.
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 comprises
Figure SMS_97
The non-chirped waveform of the individual sample points can be regarded as +.>
Figure SMS_98
The segment chirped waveforms are spliced together end to end. Bandwidth of chirped signal +.>
Figure SMS_99
Uniformly divide into->
Figure SMS_100
Segments, each segment length is->
Figure SMS_101
First->
Figure SMS_102
Start of segment->
Figure SMS_103
Expressed as:
Figure SMS_104
；
thereby obtaining a bandwidth vector
Figure SMS_105
The method comprises the following steps:
Figure SMS_106
；
corresponding pulse width vector
Figure SMS_107
The method comprises the following steps:
Figure SMS_108
；
according to pulse width vector
Figure SMS_109
And bandwidth vector->
Figure SMS_110
Calculating piecewise linear frequency functions of the piecewise linear frequency signals, and calculating the frequency modulation rate of each piece of linear frequency functions>
Figure SMS_111
The method comprises the following steps:
Figure SMS_112
；
a piecewise linear frequency function can be obtained
Figure SMS_113
The method comprises the following steps:
Figure SMS_114
；
the time domain expression of the piecewise chirped signal is:
Figure SMS_115
；
wherein ,
Figure SMS_116
is a rectangular function>
Figure SMS_117
For distance to time, add>
Figure SMS_118
Pulse time width +.>
Figure SMS_119
Is an indexFunction (F)>
Figure SMS_120
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:
Figure SMS_121
；
wherein ,
Figure SMS_124
is the instantaneous frequency, +.>
Figure SMS_127
and />
Figure SMS_131
Constraint values of Peak Side Lobe Ratio (PSLR) and Integral Side Lobe Ratio (ISLR) of waveform respectively, +.>
Figure SMS_125
Is a minimization function, +.>
Figure SMS_129
For cross-correlation function +.>
Figure SMS_132
and />
Figure SMS_134
Respectively is waveform +>
Figure SMS_122
and />
Figure SMS_126
Peak side lobe ratio,/>
Figure SMS_130
and />
Figure SMS_133
Respectively is waveform +>
Figure SMS_123
and />
Figure SMS_128
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:
Figure SMS_135
；
wherein ,
Figure SMS_138
is inertial weight, ++>
Figure SMS_141
Is particle velocity, +.>
Figure SMS_143
and />
Figure SMS_137
Is a learning factor, < >>
Figure SMS_140
and />
Figure SMS_142
Is a uniform random number, < >>
Figure SMS_144
Is the instantaneous frequency of the corresponding moment, < >>
Figure SMS_136
Is an extremum of individuals,/->
Figure SMS_139
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 counter
Figure SMS_145
Maximum number of iterations->
Figure SMS_146
Particle swarm size, inertial weight
Figure SMS_147
Learning factor->
Figure SMS_148
、/>
Figure SMS_149
Two groups of codes are used as instantaneous frequency +.>
Figure SMS_150
And particle speed->
Figure SMS_151
。
(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 particle
Figure SMS_152
And population extremum->
Figure SMS_153
。
(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 the
Figure SMS_154
If->
Figure SMS_155
Go to step (2) until +.>
Figure SMS_156
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 waveform
Figure SMS_157
Turning to step (1), fixing the waveform +.>
Figure SMS_158
Instantaneous frequency of corresponding time of waveform +.>
Figure SMS_159
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:
Figure SMS_160
；
wherein ,
Figure SMS_161
for the transmit waveform kmod2 represents an alternate transmit waveform in the form of a period of 2,
Figure SMS_162
for distance to time, add>
Figure SMS_163
For azimuth time, < >>
Figure SMS_164
For azimuth encoding phase, the expression is:
Figure SMS_165
；
neglecting the arrival of echoes across pulse repetition intervals, the first
Figure SMS_166
The code phase of the desired target echo received by each receive window is the same as above. Suppose there is +.>
Figure SMS_167
Order distance blur, in>
Figure SMS_168
The ∈received by the receiving window>
Figure SMS_169
The code phase of the order range ambiguity echo is:
Figure SMS_170
；
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:
Figure SMS_171
；
wherein, PRF is pulse repetition frequency,
Figure SMS_172
is in combination with->
Figure SMS_173
Constant of nothing, rootBy the nature of the fourier transformation, the spectrum of the blurred echo is shifted +.>
Figure SMS_174
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:
Figure SMS_175
；
wherein ,
Figure SMS_177
for signal amplitude +.>
Figure SMS_179
For distance-time envelope>
Figure SMS_182
For instantaneous pitch, add>
Figure SMS_176
For azimuth envelope->
Figure SMS_181
For the beam center crossing time, < > and->
Figure SMS_183
For carrier frequency->
Figure SMS_184
Is the phase of the non-chirped signal, +.>
Figure SMS_178
For distance to time, add>
Figure SMS_180
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:
Figure SMS_185
；
wherein ,
Figure SMS_186
for the amplitude of the distance spectrum>
Figure SMS_187
For distance frequency, < >>
Figure SMS_188
For distance spectrum envelope>
Figure SMS_189
Is the spectral phase of the non-chirped signal. Analytic +.>
Figure SMS_190
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:
Figure SMS_191
；
wherein ,
Figure SMS_192
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:
Figure SMS_193
。
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:
Figure SMS_194
；
wherein ,
Figure SMS_195
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:
Figure SMS_196
；
wherein ,
Figure SMS_197
to compress the distance envelope of the object +.>
Figure SMS_198
Is the instantaneous skew.
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 signal
Figure QLYQS_1
Uniformly divide into->
Figure QLYQS_2
Segments, each segment length is->
Figure QLYQS_3
Start point of nth segment->
Figure QLYQS_4
Expressed as:
Figure QLYQS_5
；
wherein n=1, 2, … …, N;
thereby obtaining a bandwidth vector
Figure QLYQS_6
The method comprises the following steps:
Figure QLYQS_7
；
corresponding pulse width vector
Figure QLYQS_8
The method comprises the following steps:
Figure QLYQS_9
；
according to pulse width vector
Figure QLYQS_10
And bandwidth vector->
Figure QLYQS_11
Calculating piecewise linear frequency functions of the piecewise linear frequency signals, and calculating the frequency modulation rate of each piece of linear frequency functions>
Figure QLYQS_12
The method comprises the following steps:
Figure QLYQS_13
；
obtaining piecewise linear frequency functions
Figure QLYQS_14
The method comprises the following steps:
Figure QLYQS_15
；
the time domain expression of the piecewise chirped signal is:
Figure QLYQS_16
；
wherein ,
Figure QLYQS_17
is a rectangular function>
Figure QLYQS_18
For distance to time, add>
Figure QLYQS_19
Pulse time width +.>
Figure QLYQS_20
As an exponential function +.>
Figure QLYQS_21
Is a complex constant. />
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:
Figure QLYQS_22
；
wherein ,
Figure QLYQS_24
is the instantaneous frequency, +.>
Figure QLYQS_27
and />
Figure QLYQS_32
Constraint values of peak side lobe ratio and integral side lobe ratio of waveform respectively, < >>
Figure QLYQS_25
Is a minimization function, +.>
Figure QLYQS_29
For cross-correlation function +.>
Figure QLYQS_33
and />
Figure QLYQS_35
Respectively is waveform +>
Figure QLYQS_23
and />
Figure QLYQS_30
Peak side lobe ratio,/>
Figure QLYQS_31
and />
Figure QLYQS_34
Respectively is waveform +>
Figure QLYQS_26
and />
Figure QLYQS_28
Is a ratio of integral sidelobes;
wherein one waveform remains unchanged and the other waveform is updated according to the following equation:
Figure QLYQS_36
；
wherein ,
Figure QLYQS_39
is inertial weight, ++>
Figure QLYQS_40
Is particle velocity, +.>
Figure QLYQS_43
and />
Figure QLYQS_38
Is a learning factor, < >>
Figure QLYQS_41
and />
Figure QLYQS_44
Is a uniform random number, < >>
Figure QLYQS_45
Is the instantaneous frequency of the corresponding moment, < >>
Figure QLYQS_37
Is an extremum of individuals,/->
Figure QLYQS_42
Is a population extremum.
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 counter
Figure QLYQS_46
Maximum number of iterations->
Figure QLYQS_47
Particle swarm size, inertial weight +.>
Figure QLYQS_48
Learning factor->
Figure QLYQS_49
、
Figure QLYQS_50
Two groups of codes are used as instantaneous frequency +.>
Figure QLYQS_51
And particle velocity/>
Figure QLYQS_52
；
Step b, calculating the fitness of each particle according to the objective function;
step c, calculating individual extremum of each particle
Figure QLYQS_53
And population extremum->
Figure QLYQS_54
；
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 the
Figure QLYQS_55
If->
Figure QLYQS_56
Go to step b until +.>
Figure QLYQS_57
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 waveform
Figure QLYQS_58
Turning to step (1), fixing the waveform +.>
Figure QLYQS_59
Instantaneous frequency of corresponding time of waveform +.>
Figure QLYQS_60
Optimization is performed, and vice versa, until the orthogonality of the two waveforms meets the requirements.
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 first
Figure QLYQS_61
The individual transmit waveforms are represented as:
Figure QLYQS_62
；
wherein ,
Figure QLYQS_63
for the transmission waveform kmod2 denotes an alternating transmission waveform in the form of a period 2 of the transmission waveform, +.>
Figure QLYQS_64
For distance to time, add>
Figure QLYQS_65
For azimuth time, < >>
Figure QLYQS_66
For azimuth encoding phase, the expression is:
Figure QLYQS_67
；
assuming the presence of
Figure QLYQS_68
Order distance blur, in>
Figure QLYQS_69
The ∈received by the receiving window>
Figure QLYQS_70
The code phase of the order range ambiguity echo is: />
Figure QLYQS_71
；
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:
Figure QLYQS_72
；
wherein, PRF is pulse repetition frequency,
Figure QLYQS_73
is in combination with->
Figure QLYQS_74
An irrelevant constant.
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:
Figure QLYQS_75
；
wherein ,
Figure QLYQS_77
for signal amplitude +.>
Figure QLYQS_80
For distance-time envelope>
Figure QLYQS_82
For instantaneous pitch, add>
Figure QLYQS_78
For azimuth envelope->
Figure QLYQS_81
For the beam center crossing time, < > and->
Figure QLYQS_83
For carrier frequency->
Figure QLYQS_84
Is the phase of the non-chirped signal, +.>
Figure QLYQS_76
For distance to time, add>
Figure QLYQS_79
Is the speed of light;
performing distance Fourier transform on the echo signals:
Figure QLYQS_85
；
wherein ,
Figure QLYQS_86
for the amplitude of the distance spectrum>
Figure QLYQS_87
For distance frequency, < >>
Figure QLYQS_88
For distance spectrum envelope>
Figure QLYQS_89
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:
Figure QLYQS_90
；
wherein ,
Figure QLYQS_91
representing a fourier transform;
after distance matching filtering, the spectrum phase of the nonlinear frequency modulation signal is filtered, and the spectrum echo expression is:
Figure QLYQS_92
；
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:
Figure QLYQS_93
；
wherein ,
Figure QLYQS_94
the frequency is adjusted for the distance direction;
multiplying the frequency spectrum phase and then carrying out inverse Fourier transform to obtain an echo time domain expression as follows:
Figure QLYQS_95
；
wherein ,
Figure QLYQS_96
to compress the distance envelope of the object +.>
Figure QLYQS_97
Is the instantaneous skew. />
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