CN109471080B - High-speed platform radar echo signal simulation system based on simulink - Google Patents
High-speed platform radar echo signal simulation system based on simulink Download PDFInfo
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- 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
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Abstract
The invention discloses a simulink-based high-speed platform radar echo signal simulation system, which mainly solves the problems of low simulation precision and echo efficiency in the prior art. The scheme is as follows: different functional modules are designed in simulink, wherein a PRT synchronization module generates a pulse trigger signal to control time sequence synchronization; the radar pulse transmitting module simulates and transmits radar pulse baseband signals; the radar track import module outputs radar real-time position and motion information; the beam center calculation module calculates and outputs real-time beam center coordinates; the sub-scene intercepting module intercepts the imaging sub-scene according to the beam center; the antenna directional diagram module calculates and updates the antenna gain of each point in the sub-scene; the system function calculation module calculates and updates the system function of the echo in real time; the echo generating module convolutes to generate an original echo signal. The invention improves the efficiency and the precision of echo simulation and is used for simulating radar echo signals under different radar working modes, environments and target scenes.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a radar echo signal simulation system which can be used for designing a radar system and verifying and evaluating the performance of an SAR system.
Background
The synthetic aperture radar SAR is a modern high-resolution microwave imaging radar and is widely applied to various fields, and in the research and development process of the SAR system, radar echo data plays an extremely important role in the research and development of an imaging algorithm, the design of radar system parameters and the verification and evaluation of the performance of the SAR system. However, the SAR system is very complex, and in practical application, various known, complex, even unknown, extreme situations and external conditions will be encountered, so that in the development and development stages of the whole system, a large amount of echo data needs to be combined to design and correct parameters of each system, and an algorithm is optimized and improved. If the huge echo data volume is obtained only by mounting the SAR on an actual flight device, such as an airplane and a satellite, actual measurement is carried out, the cost and the safety are both very big problems, and errors are easy to occur. The appearance and the development of the SAR echo simulation technology bring great convenience to the research and development of the SAR system.
The application of the echo simulation technology greatly reduces the research and development cost of the SAR system, and in the research and development process of the SAR, each module can be tested and debugged at any time without waiting for the mounting test after the complete machine is manufactured.
At present, SAR echo simulation at home and abroad has achieved a lot of achievements, and the SAR echo simulation system comprises a pure theoretical model, a semi-physical simulation system, computer software simulation and a pure hardware platform for realizing FPGA and DPS. However, different models and systems have disadvantages, or the calculated amount is too large, especially for a large scene, or the hardware system is too large, and the echo simulation support for a natural scene is poor.
In 1978, v.h.kaupp and j.c.holtaman et al, the university of kansas, developed a Ku radar simulator named RIS, which is based on a point scattering model and can simulate a variety of different types of scenes, but is not widely used due to limited backscattering coefficient data.
In 2004, mori et al proposed a multi-working-mode SAR echo simulator based on a time domain algorithm, which can simulate original echo signals under various non-ideal conditions, but has a large calculation amount under the condition of an excessively large scene.
In 2006, the university of qinghua provided an SAR original echo signal simulation method based on an inverse wave number domain algorithm, the method obtains a scene backscattering coefficient by processing an optical image, and then obtains an original echo signal by inversion of the wave number domain algorithm.
In 2010, a new SAR echo simulator RTS-RF is developed by Mistral of American company, the system has various functions, the man-machine interaction is convenient, but the hardware system is too large, and the echo simulation support for a natural scene is poor.
Disclosure of Invention
The invention aims to provide a high-speed platform radar echo signal simulation system based on simulink aiming at the defects of the radar echo simulation technology, so as to simulate radar echo signals under different radar working modes, different external environments and different target scenes, get rid of a huge hardware system on the premise of ensuring the precision, reduce the calculated amount and improve the echo simulation efficiency.
In order to achieve the above object, the technical solution of the present invention is to generate different modules by simulink, wherein the generated modules include:
the PRT synchronization module is used for finishing the generation of synchronization pulses, outputting the synchronization pulses to each module and synchronizing the clock of the whole system;
the radar pulse signal transmitting module is used for receiving the PRT synchronous pulse input, generating a radar pulse transmitting signal and outputting the radar pulse transmitting signal to the echo generating module;
the radar track importing module is used for reading radar track file information under the control of PRT synchronous pulse and respectively outputting the read radar track information to the beam center computing module, the sub-scene intercepting module, the antenna directional diagram computing module and the system function computing module;
the beam center calculation module is used for updating pixel point coordinate information of a beam center in a scene graph according to the input radar and the current mode marking bit under the control of the PRT synchronous pulse, and respectively outputting the beam center coordinate information to the sub-scene interception module, the antenna directional diagram calculation module and the system function calculation module;
the sub-scene intercepting module is used for intercepting an imaged sub-scene from a guided large scene according to different beam irradiation modes of different modes of the radar, input beam center coordinates and radar track information under the control of the PRT synchronous pulse, and respectively outputting data of the sub-scene to the antenna directional diagram calculating module and the system function calculating module;
the antenna directional pattern calculation module is used for calculating the antenna gain of each point in the sub-scene according to the input radar track information, the beam center coordinate information, the sub-scene size, the receiving beam offset angle, the distance direction and azimuth direction resolution ratio and the antenna beam width under the control of the PRT synchronous pulse, and outputting the result to the system function calculation module;
the system function calculation module is used for calculating a system function of an echo by utilizing a concentric circle algorithm according to an input radar position, a beam center coordinate, sub-scene data, an antenna directional diagram and initial range gate information of the echo under the control of a PRT synchronous pulse, and outputting the system function to the echo generation module;
the echo generating module is used for convolving the radar pulse transmitting signal with a system function, generating an original echo signal under the control of a PRT synchronous pulse, and outputting a result to the delay and range gate gating module;
and the time delay and range gate gating module is used for outputting echo data in a 'streaming' mode under the control of the PRT synchronous pulse, so that the radar echo signal stream is better simulated.
The invention has the following advantages:
1. because the invention is based on simulink to carry out modularization and hierarchical design, the system is relatively simple in construction and huge in function, namely radar echo signals under different radar working modes, different external environments and different target scenes can be conveniently and flexibly simulated according to the input SAR mode identifier, the imported radar track information file and the target scene;
2. the invention adopts the concentric circle algorithm to calculate the system function of the echo, so that a huge hardware system can be got rid of on the premise of ensuring the precision, the calculation amount is reduced, and the echo simulation efficiency is higher.
Drawings
FIG. 1 is a block diagram of a radar echo signal simulation system;
FIG. 2 is a flow diagram of a simulation system for generating radar return signals in simulink;
FIG. 3 is a flow chart for simulating a radar echo signal using the system of the present invention;
FIG. 4 is a schematic illustration of point target imaging using an imaging algorithm from a front side view;
FIG. 5 is a geometric model of the echo system function generated by the system function calculating module according to the present invention by using a concentric circle algorithm.
Detailed Description
The invention is described in further detail below with reference to the attached drawing figures:
at present, SAR echo simulation at home and abroad has achieved a lot of achievements, and the SAR echo simulation system comprises a pure theoretical model, a semi-physical simulation system, computer software simulation and a pure hardware platform for realizing FPGA and DPS. The invention utilizes simulink to carry out modular design on a radar echo signal simulation system.
The simulink is used as a visual simulation tool in MATLAB, provides an integrated environment of dynamic system modeling, simulation and comprehensive analysis, does not need to write a lengthy program, can construct a complex system through simple and intuitive interface operation, and is widely used for complex simulation and design of control theory and digital signal processing.
The process of the invention for system construction using simulink is shown in fig. 2. Firstly, defining basic parameters required by a seeker system through an M script, then constructing a model of each module in a simulink, setting input and output ports to realize functions of each module, calling an S function to package each module, generating a parameter setting interface, and finally connecting corresponding input and output ports in each module to generate a radar echo signal simulation system, wherein the system is shown in figure 1.
Referring to fig. 1, the system for simulating a radar echo signal generated by simulink of the present invention includes a PRT synchronization module 1, a radar pulse signal emission module 2, a radar track introduction module 3, a beam center calculation module 4, a sub-scene interception module 5, an antenna directional pattern calculation module 6, a system function calculation module 7, an echo generation module 8, and a delay and range gate gating module 9, wherein:
the PRT synchronization module 1 is used for finishing the generation of synchronization pulse, outputting the synchronization pulse to each module and synchronizing the clock of the whole system;
the radar pulse signal transmitting module 2 is used for receiving PRT synchronous pulse input, generating a radar pulse transmitting signal and outputting the radar pulse transmitting signal to the echo generating module 8;
the radar track importing module 3 is used for reading radar track file information under the control of PRT synchronous pulses and respectively outputting the read radar track information to the beam center calculating module 4, the sub-scene intercepting module 5, the antenna directional diagram calculating module 6 and the system function calculating module 7;
the beam center calculation module 4 is used for updating the pixel point coordinate information of the beam center in the scene graph according to the input radar and the current mode marking bit under the control of the PRT synchronous pulse, and outputting the beam center coordinate information to the sub-scene interception module 5, the antenna directional pattern calculation module 6 and the system function calculation module 7;
the sub-scene intercepting module 5 is used for intercepting an imaged sub-scene from a guided large scene according to different beam irradiation modes of different modes of the radar, input beam center coordinates and radar track information under the control of a PRT synchronous pulse, and outputting data of the sub-scene to the antenna directional diagram calculating module 6 and the system function calculating module 7;
an antenna directional pattern calculation module 6, configured to calculate antenna gains of each point in a sub-scene according to input radar track information, beam center coordinate information, sub-scene size, received beam offset angle, distance direction and azimuth direction resolution, and antenna beam width under control of the PRT synchronization pulse, and output a result to a system function calculation module 7;
the system function calculation module 7 is configured to calculate a system function of an echo by using a concentric circle algorithm according to an input radar position, a beam center coordinate, sub-scene data, an antenna directional diagram, and initial range gate information of the echo under the control of a PRT synchronization pulse, and output the system function to the echo generation module 8;
the echo generating module 8 is used for convolving the radar pulse transmitting signal with a system function, generating an original echo signal under the control of a PRT synchronous pulse, and outputting a result to the delay and range gate gating module 9;
and the time delay and range gate gating module 9 is used for outputting echo data in a 'streaming' mode under the control of the PRT synchronous pulse, so that the radar echo signal stream is better simulated.
Referring to fig. 3, the process of simulating a radar echo signal using the system of the present invention is as follows:
in the process 1, the PRT synchronization module 1 reads radar working frequency, sampling frequency, emission signal pulse width, emission signal bandwidth, pulse repetition time and emission pulse number in various modes from the simulation interactive interface, outputs PRT synchronization signals PRTTrigger to each module, and outputs a marker FrameTrigger of the radar working mode to the beam center calculation module.
And 2, receiving PRT synchronous pulse input by the radar pulse signal transmitting module 2, detecting a rising edge, generating a baseband linear frequency modulation signal LFM when the rising edge comes, and outputting N according to a pulse repetition period PRT a Sending the LFM pulse signals to an echo generating module 8;
the expression for generating the baseband chirp signal LFM is as follows:
wherein the content of the first and second substances,t is the fast time, t m Is a slow time, T p For the pulse width of the LFM signal, f c Is the carrier frequency, k r Frequency is adjusted linearly;
and 3, receiving PRT synchronous pulse input trigger by the radar track leading-in module 3, detecting a rising edge, reading track file information when the rising edge comes, updating a radar position, a speed, an acceleration, an incidence angle, a speed vector, a beam projection included angle on the ground and radar position information with errors, and outputting a result to the beam center calculating module 4, the sub-scene intercepting module 5, the antenna directional diagram calculating module 6 and the system function calculating module 7.
And 4, receiving PRT synchronous pulse input trigger by the beam center calculation module 4, detecting a rising edge, inputting the position, the speed, the target position coordinate and the current mode marking bit of the radar when the rising edge comes, calculating the pixel point coordinate information of the beam center in the scene graph, and outputting the result to the sub-scene interception module 5, the antenna directional diagram calculation module 6 and the system function calculation module 7.
And 5, inputting a beam center coordinate and a radar position coordinate by the sub-scene intercepting module 5 according to different beam irradiation modes of different radar modes, synchronously triggering by the PRT, intercepting an imaged sub-scene from a guided large scene, and outputting data to the antenna directional diagram calculating module 6 and the system function calculating module 7.
And 6, inputting radar position information, pixel point coordinate information of a beam center in a large scene, sub-scene size, receiving beam bias angle, distance direction and azimuth direction resolution and antenna beam width by the antenna directional pattern calculation module 6, receiving PRT synchronous pulse input trigger, detecting a rising edge, calculating antenna gain of each point in the sub-scene when the rising edge comes, and outputting a result to the system function calculation module 7.
The calculation of the antenna gain of each point in the sub-scene has two modes:
the first method is to use the directional diagram of a single antenna and the bias angle of the receiving antenna to be 0 for calculation in an SAR imaging mode, namely, firstly, the azimuth angle alpha of the beam center is obtained according to the input radar position information and the coordinates of the beam center on the central pixel point of the scene c And a pitch angle beta c Azimuth angle alpha of target relative to radar RT And a pitch angle beta RT (ii) a Then calculating the antenna gain rcs modulated by the directional diagram of the transmitting antenna 1 :
rcs 1 =abs((sinc(α RT -α c ))*(sinc(β RT -β c ))) <2>
the second is that under the single-pulse mode, four single antennas are used, and corresponding receiving offset angles are set to form a four-antenna directional diagram for calculation,firstly, obtaining an azimuth angle alpha of a beam center according to input radar position information, coordinates of the beam center at a pixel point at the scene center, an azimuth deviation angle +/-Delta alpha of a sub-beam relative sum beam and a pitching deviation angle +/-Delta beta c And a pitch angle beta c Azimuth angle alpha of target relative to radar RT And a pitch angle β RT (ii) a Respectively calculating the antenna gain rcs modulated by the directional diagrams of the transmitting antennas with different offsets 21 、rcs 22 、rcs 23 、rcs 24 :
rcs 21 =abs((sinc(α RT +Δα-α c ))*(sinc(β RT +Δβ-β c ))) <3>
rcs 22 =abs((sinc(α RT +Δα-α c ))*(sinc(β RT -Δβ-β c ))) <4>
rcs 23 =abs((sinc(α RT -Δα-α c ))*(sinc(β RT +Δβ-β c ))) <5>
rcs 24 =abs((sinc(α RT -Δα-α c ))*(sinc(β RT -Δβ-β c ))) <6>
Total antenna gain rcs 2 Comprises the following steps:
rcs 2 =rcs 21 *rcs 22 *rcs 23 *rcs 24 <7>
wherein, rcs 21 The antenna gain, rcs, is the azimuth deviation angle of the sub-beam relative to the sum beam, Δ α, and the elevation deviation angle, Δ β 22 The antenna gain with the sub-beams having an azimuth deviation angle of delta alpha and a pitch deviation angle of-delta beta with respect to the sum beam, rcs 23 The antenna gain with the sub-beams having an azimuth deviation angle of- Δ α and a pitch deviation angle of Δ β with respect to the sum beam, rcs 24 The antenna gain is obtained by the antenna with the sub-beam relative to the beam and the azimuth deviation angle of-delta alpha and the pitching deviation angle of-delta beta.
A process 7, inputting the position of the radar, the beam center coordinate, the sub-scene data, the antenna directional diagram and the initial distance gate information of the echo by the system function calculation module 7, receiving the input trigger of the PRT synchronous pulse, detecting the rising edge, calculating the system function of the echo by using a concentric circle algorithm when the rising edge comes, and outputting the result to the echo generation module 8;
the principle of the concentric circle algorithm is as follows:
without considering the wavefront curvature, taking the positive side as an example, the distribution of echoes of point targets on a two-dimensional plane like a rectangular array shown in the first graph of fig. 4 will become the result of the second graph after compressing the distance to the pulse, which is caused by the curvature generated by the radar motion. After correcting the overbending, the energy distribution of the point target will be in the same range unit, as shown in the third graph in fig. 4, and then the target can be subjected to azimuth imaging along the azimuth direction, and the imaging result of the point target is obtained, as shown in the last graph in fig. 4.
It can be seen that different point targets, which are located at different distances from the radar, are distributed in different range units, because the distances from different target points to the radar platform are different, which results in different delay times, and the distance sampling frequency f is used s Sampling the distance delay of the target point, wherein the interval of the sampling units is c/2f s C is the light speed, and the echo distribution of each target point is distributed according to the integral multiple relation of the interval of the sampling units; for reaching target points with the same radar range in a scene at different azimuth moments, the integral multiple relation of the sampling units is the same, so that the complex echoes of the target points are accumulated in the same range unit.
Therefore, in order to quickly obtain an echo system function so as to meet the requirement of real-time echo signal generation and maintain the calculation accuracy of the echo signal, points with the same length from a radar are considered to be located on the same distance unit, the points in a scene are accumulated along a concentric circle with the radar as the center of a circle to obtain a one-dimensional range profile of the radar, and then the FFT is used for quickly realizing the generation of the echo system function in a frequency domain, so that multiple points can be simultaneously processed, and the calculation amount is reduced.
According to the above thought, the specific method for calculating the echo system function is as follows:
at each azimuth moment, firstly, the distances R (k) from all point targets in the scene to the radar are calculated, and the distances are compared with the distance sampling unit to obtain the distribution situation of the points on all concentric circles, namely the distribution situation of the points on all concentric circles
Formula (II)<8>In, n k Indicating the position of the distance elements, i.e. the points are distributed on several concentric circles, delta r Is the size of a distance unit, and
as shown in fig. 5, after the concentric circles are distributed, P point targets are shared on a certain concentric circle within the beam irradiation range, according to the formula<9>It can be known that the P scattering points should be distributed in the same range unit, and they can uniformly generate echo signals, and because the azimuth phase information of the echo signals is more sensitive than the range envelope information, the integrity of the azimuth phase information is ensured, i.e. the P scattering points cannot be used as the range envelope<9>The distance approximation calculation is performed so that the azimuth phase signal s (mT; R) of each point B ) Independent calculation is required:
where σ is the gray value of the point target, mT is t m In discrete form of (A), R B Is the closest distance of the radar to the target, λ is the radar operating wavelength, R (mT; R) is the distance of the radar to the scattering point at mT, exp represents an exponential function.
Then, the pair formula<10>Summing to obtain the same concentric circleUpper point target azimuth phase signal s 2 :
Wherein σ i The gray value of the ith point target on the same concentric circle.
In pair type<11>Summing to obtain all the distance unit data s at the whole moment 3 :
Formula (II)<12>Where δ is the impulse response function, k denotes the distance falling within the several distance units, P n Indicating the number of point targets in the nth range bin. The number of ground scattering points in different distance units is different, and the difficulty of the accumulation process is different. In pair type<12>Fourier transform FFT is carried out to transform the frequency domain to a frequency modulation item of multiplying the frequency domain by the distance direction, and then inverse Fourier transform IFFT is utilized to transform the frequency domain back to the time domain, so that a system function s of an echo can be obtained 4 (k,mT;R B ):
Wherein f is r Indicating the range-wise frequency.
And 8, inputting a system function and a baseband linear frequency modulation signal LFM by the echo generating module 8, performing convolution operation to generate an original echo signal, receiving PRT synchronous pulse input trigger, detecting a rising edge, and outputting a result to the delay and range gate gating module 9 when the rising edge comes.
In the process 9, the delay and range gate gating module 9 outputs the input original echo signal in a 'stream' manner under the control of the PRT synchronization pulse.
In summary, the simulink-based high-speed platform radar echo signal simulation system has the advantages of being modular and hierarchical in design, being capable of conveniently and flexibly simulating radar echo signals under different radar working modes, different external environments and different target scenes, helping scientific researchers get rid of the limitation of radar equipment conditions, not needing to rely on expensive radar equipment to obtain relevant radar echo data, and being more efficient and convenient than the traditional actual measurement data mode.
While the invention has been described in connection with what is presently considered to be the most practical and preferred embodiment, it is to be understood that the invention is not to be limited to the disclosed embodiment, but on the contrary, is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
Claims (4)
1. High-speed platform radar return signal analog system based on simulink generates different modules through simulink, its characterized in that, the module that generates includes:
the PRT synchronization module (1) is used for finishing the generation of synchronization pulses, outputting the synchronization pulses to each module and synchronizing the clock of the whole system;
the radar pulse signal transmitting module (2) is used for receiving PRT synchronous pulse input, generating a radar pulse transmitting signal and outputting the radar pulse transmitting signal to the echo generating module (8);
the radar track importing module (3) is used for reading radar track file information under the control of PRT synchronous pulse, and respectively outputting the read radar track information to the beam center computing module (4), the sub-scene intercepting module (5), the antenna directional diagram computing module (6) and the system function computing module (7);
the beam center calculating module (4) is used for updating pixel point coordinate information of a beam center in a scene graph according to the input radar and the current mode marking bit under the control of a PRT synchronous pulse, and outputting the beam center coordinate information to the sub-scene intercepting module (5), the antenna directional diagram calculating module (6) and the system function calculating module (7);
the sub-scene intercepting module (5) is used for intercepting an imaged sub-scene from a guided large scene according to different beam irradiation modes of different modes of the radar, input beam center coordinates and radar track information under the control of the PRT synchronous pulse, and outputting data of the sub-scene to the antenna directional diagram calculating module (6) and the system function calculating module (7);
an antenna directional pattern calculation module (6) for calculating the antenna gain of each point in the sub-scene according to the input radar track information, the beam center coordinate information, the sub-scene size, the receiving beam bias angle, the distance direction and azimuth direction resolution and the antenna beam width under the control of the PRT synchronous pulse, and outputting the result to a system function calculation module (7);
the system function calculation module (7) is used for calculating a system function of an echo by utilizing a concentric circle algorithm according to an input radar position, a beam center coordinate, sub-scene data, an antenna directional diagram and initial range gate information of the echo under the control of a PRT synchronous pulse, and outputting the system function to the echo generation module (8);
the echo generating module (8) is used for convolving the radar pulse transmitting signal with a system function, generating an original echo signal under the control of a PRT synchronous pulse, and outputting a result to the delay and range gate gating module (9);
and the time delay and range gate gating module (9) is used for outputting echo data in a 'streaming' mode under the control of the PRT synchronous pulse, so that the radar echo signal stream is better simulated.
2. The system of claim 1, wherein different modules are generated by simulink, which is implemented as follows:
defining basic parameters required by a seeker system through an M script, constructing a model of each module in a simulink, and setting input and output ports to realize the functions of each module;
calling an S function to package each module and generating a parameter setting interface;
and connecting corresponding input and output ports in each module.
3. The system according to claim 1, characterized in that the antenna pattern calculation module (6) calculates the antenna gain for each point in the sub-scene, which is implemented as follows:
firstly, according to the input radar position information, the beam center coordinate information, the receiving beam offset angle and the antenna beam width, the azimuth angle alpha of the beam center is obtained c And a pitch angle β c Azimuth angle alpha of target relative to radar RT And a pitch angle β RT ;
And then calculating the antenna gain rcs after the directional diagram modulation of the transmitting antenna:
rcs=abs((sinc(α RT -α c ))*(sinc(β RT -β c ))), <1>
4. the system according to claim 1, characterized in that the system function calculation module (7) calculates the system function of the echo using a concentric circle algorithm, which is implemented as follows:
calculating the distances R (k) from all point targets to the radar in the scene, and comparing the distances with a distance sampling unit to obtain the distribution condition of points of all concentric circles, namely obtaining P point targets on a certain concentric circle in total in the beam irradiation range;
distributing the P scattering points in the same range unit, and calculating azimuth phase signal s of each point 1 (mT;R B ):
Wherein σ is the gray value of the point target; mT is the slow time t m Of discrete form of (A), R B Is the closest distance of the radar to the scattering point, λ is the radar operating wavelength, R (mT; R) B ) Is the distance of the radar to the scattering point at time mT;
by adding point targets on the same concentric circle, i.e. pair<2>Summing to obtain a distance sheetData s of elements containing azimuth phase 2 :
In pair type<3>Summing to obtain all the distance unit data s at the whole moment 3 :
Wherein, δ is an impact response function, and k is within a few distance units;
in pair type<4>Fourier transform FFT is carried out, the FFT is converted into a frequency domain multiplied by a frequency modulation item in the distance direction, and then inverse Fourier transform IFFT is utilized to convert the frequency domain back into a time domain, so that a system function s of an echo can be obtained 4 (k,mT;R B ):
Wherein k is r Indicating the range chirp, f r Indicating the range-wise frequency.
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