CN116502476A - SAR system design method based on nonlinear frequency scanning response - Google Patents
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Abstract
The invention provides a SAR system design method based on nonlinear frequency scanning response, and the SAR system design method is applied to a frequency scanning SAR system, so that more excellent system performance can be obtained. Unlike the linear frequency sweep method, the nonlinear frequency sweep method of the present invention requires that the sweep speed of the pencil beam is no longer fixed and that the bandwidth of the available transmit signal be allocated to targets at different angles of incidence according to a specific rule. The invention improves the near-end ground distance resolution, and the ground distance resolution distribution in the whole swath is more balanced, thus realizing an advantageous nonlinear frequency scanning response.
Description
Technical Field
The invention relates to the field of high-resolution wide-amplitude (High Resolution Wide Swath, HRWS) synthetic aperture radars (Synthetic Aperture Radar, SAR), in particular to a SAR system design method based on nonlinear frequency scanning response.
Background
The spaceborne SAR has the characteristics of all-day time, all weather, no pilot space limitation and the like, and plays an important role in the fields of topographic mapping, polarized interference height measurement, land vegetation, moving target monitoring and the like. Thus, in the last decades, the HRWS technology of on-board SAR has been a hotspot for research in the SAR field. So far, many scholars at home and abroad have conducted intensive researches on a HRWS imaging system of a satellite-borne SAR and proposed several common imaging modes, mainly including a beam focusing mode (Spotlight-SAR), a scanning mode (Scan-SAR), a TOPS mode (Terrain Observation by Progressive Scans SAR, TOPSAR) and the like based on a beam scanning technology, however, the modes only compromise between azimuth resolution and distance breadth, and cannot realize high-resolution breadth in a real sense; thus, multichannel-based SAR systems are proposed successively, e.gDPCM-DBF-SAR, SPCMAB-DBF-SAR, etc. Notably, these SAR systems require multiple independent receive channels in the range direction, combined with digital beamforming (Digital Beamforming, DBF) techniques to ensure good system sensitivity and range ambiguity performance over a large imaging range.
However, for DBF technology of on-board SAR, it is generally required to equip more than ten channels at a distance to meet the system requirements, but this brings about some problems and challenges: on the one hand, the multiple independent receiving channels require corresponding receiving links, including antennas, radio frequency modules, digital modules, etc., which lead to a drastic rise in complexity, cost, etc. of the SAR system; on the other hand, in order to reduce the data rate of the system, the satellite-borne SAR system has on-board real-time processing capability, but massive calculation has very high requirements on the calculation power of hardware; furthermore, accurate beam control requires no distortion of the signal transmission within each channel and uniformity of the frequency response of each element channel, however, the frequency response of multiple channels of an actual system is difficult to meet such demanding requirements. For these main reasons, it is very difficult to apply the DBF technology to the on-board HRWS-SAR imaging system, and no on-orbit SAR has a distance-to-DBF capability yet.
Recently, DLR scholars have proposed a SAR imaging mode (Frequency Scan SAR, F-SAR) that implements Echo Compression (Time-of-Echo Compression) using Frequency Scan (Frequency Scan) techniques. The F-SAR solves the problems of insufficient receiving gain and poor distance ambiguity performance in large-breadth imaging, and can realize the same or even better effect as the DBF technology only in the case of a distance to a single channel. As shown in fig. 1, at the transmitting end, the F-SAR fully utilizes the dispersion effect of the antenna, forms a pencil beam with a beam direction linearly corresponding to the signal frequency by the frequency scanning antenna, and realizes scanning irradiation on the swath within a pulse transmitting time. At the receiving end, echo signals from different view angles are received in a frequency scanning mode. In the latter data processing, the method of frequency domain filtering is used to realize effective separation of echo signals. In addition, through setting up the accent frequency and the pulse width of transmission signal, can realize that far-end echo and near-end echo arrive the effect of receiver simultaneously, namely echo window compression frequency scanning response is favorable to realizing the broad width. However, since the F-SAR irradiates targets by means of narrow beam scanning, the effective imaging bandwidth acquired by each target is only a part of the transmission signal bandwidth, which results in that the range resolution and the imaging breadth of the F-SAR are mutually restricted at the same antenna height. In addition, ground range resolution is also an indicator of interest to on-board SAR users, and it is worth mentioning that ground range resolution is no longer a simple linear transformation of imaging bandwidth, or is a function of angle of incidence, which results in uneven distribution of ground range resolution at near-wave positions and very severe degradation at small angles of incidenceHeavy. For example, as a core instrument for the SWOT observation task, the ground projection pixel size generated by a Ka-band radar interferometer (Ka-In) varies from about 70 meters at a near distance (0.6 °) to 10 meters at a far distance (3.9 °), resulting In a limitation In that the estimation accuracy of the interferometry phase at a near distance is deteriorated by the ground range resolution. For F-SAR systems, the imaging bandwidth acquired for each target is very limited due to the linear frequency sweep, which makes the above-described ground range resolution problem "fly-through" in F-SAR systems. In the context of figure 1 of the drawings,indicating the speed of the satellite, +.>Representing the pulse repetition frequency of the system.
Disclosure of Invention
In order to solve the problems of serious deterioration of near-end ground range resolution and unbalanced ground range resolution of the existing F-SAR system, the invention provides a SAR system design method based on nonlinear frequency scanning response, which can realize nonlinear frequency scanning response (Nonlinear Frequency Scan Response) so as to obtain more excellent system performance. Unlike the linear frequency sweep approach, the present invention requires that the sweep speed of the pencil beam is no longer fixed and the bandwidth of the available transmit signal is allocated to targets at different angles of incidence according to a specific rule. This results in improved near-end ground range resolution and a more uniform ground range resolution distribution throughout the swath, i.e., an advantageous nonlinear frequency scanning response is achieved.
In order to achieve the above purpose, the invention adopts the following technical scheme:
a SAR system design method based on nonlinear frequency scanning response comprises the following steps:
step 1, defining a ground range resolution variance as an index for evaluating ground range resolution;
step 2, deducing ground range resolution based on scanning speed;
step 3, designing a frequency scanning criterion for improving ground distance resolution;
and 4, designing a nonlinear frequency scanning response method.
Further, in the step 1, the ground range resolution variance is calculated as follows:
(2)，
wherein ,representing ground range resolution variance,/>For the number of samples in the whole swath, depending on imaging breadth and distance sampling rate, +.>For ground range resolution at each sample, +.>The minimum value of the ground range resolution is represented, and i is an index value.
Further, the step 2 includes:
the residence time is defined as:
(3)，
wherein ,time required for the beam to pass a target point, < >>For taking out the mould->Is a partial differential operator, ++>For beam width +.>Is the scanning speed; />As the amount of change in the angle of the beam,to change the angle +.>Substituted into->Is performed by the method;
for a spaceborne SAR system, the beam pointing angleIncident angle->Is one-to-one correspondence, assuming that the transmitted signal is a chirp signal, substituting equation (2) into ground range resolution +>Formula>Is obtained by:
(4)，
wherein ,for the frequency modulation rate of the chirp signal, +.>For the speed of light->For incident angle, ++>For the resident bandwidth.
Further, the frequency scanning criteria in step 3 include:
causing the beam to followIs passed through the target at the distance, saving the scanning time at the distance, wherein +.>For modulating the frequency of the transmitted signal, < >>For the angle of incidence at distance +.>For ground range resolution at distance, c is speed of light, < >>Representing the speed of a target passing through a distance; with oneIs passed through the target in the near distance to ensure that the target in the near distance acquires a sufficiently long residence time,/for>For the angle of incidence at short distance, +.>For ground resolution at near distance, +.>Representing the speed of the object passing near.
Further, the step 4 includes:
first, a general frequency sweep format is proposed:
(5)，
wherein ,becomes a scan coefficient vector, ">For the scan coefficient +.>Is a scan time vector; />Is the beam pointing angle;
the form of simplifying the general frequency sweep is as follows:
(6)，
second, given the design constraints of the nonlinear frequency sweep response, including:
(1) Scene constraints, including imaging breadth and corresponding angular range, are expressed as:
(7)，
wherein ,for the operating point of the system->For the pulse width of the transmitted signal +.>For the pointing at the beginning of the beam sweep,pointing at the end of beam scanning;
(2) Ground range resolution constraints, namely, satisfy:
(8)，
wherein ,，/>the incidence angles at near and far distances, respectively, the subscript "1" indicates that the beam front passes through the incidence angle +.>The relative time of the target at which the trailing edge of the beam passes, while the subscript "2" indicates the relative time of the trailing edge of the beam passing the target;
(3) Scanning constraints, including constraints of scanning direction and scanning speed, andthe following constraint is given by equation (9):
(9)，
wherein ,relative time for beam center to point to near end target, +.>Relative time for the beam center to point to the far end target; />Indicating the time when the beam front passes the far end target, +.>Indicating the time when the trailing edge of the beam passes the near-end target,/->Beam pointing angle for near end target, +.>Beam pointing angle for a remote target;
simultaneous equation (7) -equation (9), a frequency sweep response for equally spacing the resolution is achieved.
The beneficial effects are that:
(1) The invention has strong engineering realizability, and the SAR system based on nonlinear frequency scanning, namely NF-SAR, finishes irradiation of the swath through the pen-shaped wave beam related to frequency, and the receiving end also receives the echo by adopting the wave beam with high gain. Compared with the DBF technology, the NF-SAR adopts a narrow-emission narrow-reception working mode, has higher system sensitivity and better distance ambiguity performance, and the distance direction only adopts a single channel, so that the difficulty of engineering realization is greatly reduced. In addition, the frequency dispersion network can be realized by a phase shifter and a true delay line, and compared with the DBF technology, the cost of the system is greatly reduced.
(2) The invention realizes balanced ground range resolution response through nonlinear frequency scanning design. This means that with a certain transmission bandwidth, the beam irradiates the target at different viewing angles with a "dispense on demand" principle, so that the resolution of the near end target is improved. Furthermore, a more balanced ground range resolution has the additional advantage: on one hand, the balanced ground distance resolution allows the requirement of a user on the ground distance resolution to be met under a smaller transmission bandwidth, so that the transmission cost of the system is reduced; on the other hand, nonlinear frequency scanning response has certain advantages in interferometry applications, etc., because balanced ground range resolution facilitates obtaining more balanced phase estimation errors throughout the measurement scene. In summary, the NF-SAR system has stronger engineering value and realizability.
Drawings
FIG. 1 is an imaging geometry diagram of a high-resolution wide-amplitude spaceborne SAR using a frequency scanning technique;
FIG. 2 is a schematic diagram of frequency sweep;
FIG. 3 is a schematic diagram of ground range resolution geometry;
FIG. 4 is a wave position zebra diagram;
FIG. 5a, FIG. 5b, FIG. 5c, FIG. 5d is a graph of nonlinear frequency scanning response design results; wherein, fig. 5a is a curve of the beam pointing angle with the scanning time, fig. 5b is a curve of the scanning speed with the scanning time, fig. 5c is a curve of the residence time with the scanning time, and fig. 5d is a curve of the residence bandwidth with the scanning time;
FIG. 6 is a flow chart of a method of designing a SAR system based on nonlinear frequency scanning response in accordance with the present invention;
FIG. 7 is a graph of ground range resolution as a function of angle of incidence;
FIG. 8 is a graph of ground range resolution as a function of angle of incidence;
fig. 9 is a graph of ground range resolution as a function of angle of incidence.
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 SAR system design method based on nonlinear frequency scanning response comprises the following steps:
step 1, defining the ground range resolution variance as an index for evaluating the ground range resolution:
as shown in fig. 2, the SAR system employing the frequency scanning technique generates a waveform with a frequency variation at the transmitting end so that the beam is directed at an angleWith the frequency of the transmitted signal->Changing by variation, irradiating for the duration of the whole pulseThe whole swath. At the receiving end, the echo is also scanned and received by the beam. However, the scanning transceiving mode is adopted, so that the imaging bandwidth acquired by each target is not equivalent to the bandwidth of the transmitted signal, but a part of the latter is called resident bandwidth +.>Satisfy->, wherein />For retention factor, ++>Is the bandwidth of the transmitted signal. The size of the dwell bandwidth directly affects the range resolution of the system, i.e., the range resolution and the range resolution. In addition, since the image acquired by the SAR system is generally from the ground plane, the ground range resolution will also change with the incident angle, as shown in FIG. 3 +.>As a unit direction vector of the geocentric pointing radar, < >>As perpendicular +.>And points to the unit direction vector of the ground distance, when the slant distance +>The range of variation is a skew resolution +.>When the earth's geodetic model is true, the ground range resolution can be expressed as:
，
wherein ,for the speed of light->Is the angle of incidence. As can be seen from the formula (1), the ground range resolution is essentially the projection of the slant range resolution along the ground direction, the size of which is affected by the incident angle, and when the incident angle is small, the ground range resolution is seriously deteriorated. In addition, for a swath of selected wavelengths, its range resolution is non-uniform over the entire range of angles of incidence, with the range being optimal and the range being worst. In order to quantify the extent to which the ground range resolution deviates from its optimal value, a new evaluation index is defined, ground range resolution variance (Ground Range Resolution Variance, GRRV):
，
wherein ,for the number of samples in the whole swath, depending on imaging breadth and distance sampling rate, +.>Ground range resolution at each sample. />Take the minimum of ground range resolution. i is an index value. Clearly, the greater the value of GRRV, the greater the degree to which the ground range resolution deviates from the optimum, the non-uniform the ground range resolution distribution.
Step 2, deducing ground range resolution based on scanning speed;
for SAR systems employing frequency sweep techniques and specific transmit waveforms, the dwell bandwidth and antenna height are generally related to the sweep speed. Specifically, when the scanning speed is fixed, the smaller the antenna height, the wider the beam, the longer the residence time used when passing through the target, the smaller the effective bandwidth, however, the smaller the antenna height, the worse the system sensitivity; when the antenna height is fixed, the angular displacement generated when the beam sweeps each target is fixed, the residence bandwidth is related to the scanning speed, when the scanning speed is higher, the shorter the time of the beam irradiating the target is, the smaller the allocated effective bandwidth is, and otherwise, the larger the effective bandwidth is. It can be seen that whether it is antenna height or scan speed, the dwell bandwidth of the target is affected by directly changing the dwell time of the target. The residence time is defined as:
，
wherein ,time required for the beam to pass a target point, < >>For taking out the mould->Is a partial differential operator, ++>For beam width +.>Is the scanning speed. />Is the amount of change in angle.To change the angle +.>Substituted into->Is performed in the following manner.
For spaceborne SAR, the beam pointing angleIncident angle->Is one-to-one correspondence, assuming that the transmitted signal is a chirped (Linear Frequency Modulated, LFM) signal, substituting equation (2) into equation (1) yields:
，
wherein ,is the frequency of the LFM signal.
Step 3, designing a frequency scanning criterion for improving ground range resolution:
as can be seen from equation (4), for a spaceborne SAR system employing frequency scanning techniques, the ground range resolution is related not only to the angle of incidence, but also to the beam width and beam scanning speed. Generally, the antenna height of the space-borne SAR is related to a plurality of system parameters, such as system sensitivity, distance ambiguity, etc., so that the improvement of ground-range resolution by adjusting the beam width during the whole design of the system will result in other system performance degradation, so the antenna height should be regarded as a constant during the whole design process, i.e. the beam width is a constant.
Fortunately, the scan speed is a new degree of freedom introduced into the ground range resolution, which has the potential to counteract the ground range resolution degradation due to the angle of incidence. In other words, the time that the target is illuminated at different angles of incidence can be varied by adjusting the scan speed, thereby varying its dwell bandwidth. In order to realize the frequency scanning response of ground distance equalization, a new frequency scanning principle is designed, namely, a beam passes through a target at a long distance at a higher speed, so that the scanning time is saved; the target at close range is passed at a slow speed to ensure that the target can acquire a sufficiently long dwell time.
In particular, making the beamIs passed through the target at the distance, saving the scanning time at the distance, wherein +.>For modulating the frequency of the transmitted signal, < >>For a far-range angle of incidence,for ground range resolution at distance, c is speed of light, < >>Representing the speed of a target passing through a distance; with oneIs passed through the target at a close distance to ensure that the target at the close distance acquires a sufficiently long residence time,/for>For the angle of incidence at short distance, +.>For ground resolution at near distance, +.>Representing the order of passing close distanceTarget speed.
Step 4, designing a nonlinear frequency scanning response method:
the linear frequency scanning mode proposed at present obviously cannot adjust the scanning speed along with the incident angle, so the invention provides a nonlinear frequency scanning mode to achieve the purpose of ground-to-ground resolution balance.
First, a general frequency sweep format is proposed:
，
wherein ,becomes a scan coefficient vector, ">For the scan coefficient +.>For the scan time vector, n is the index value, +.>Is the beam pointing angle. For ease of analysis, the simplest form of nonlinear frequency sweep is as follows:
，
in addition, the frequency scan design is subject to some other constraints such as imaging swath, range of incidence angles (beam pointing angles), scan direction, operating point, etc. The design constraints for the nonlinear frequency sweep response are given below:
(1) Scene constraint: scene constraints include imaging breadth and corresponding angular range, which are generally dependent on SAR user requirements, and can be expressed as:
，
wherein ,for the operating point of the system->For the pulse width of the transmitted signal +.>For the pointing at the beginning of the beam sweep,is the pointing at the end of the beam sweep.
(2) Ground range resolution constraints: in order to achieve a more uniform ground range resolution, one of the most straightforward ways is to force the ground range resolution to be the same at certain angles of incidence in the swath, satisfying:
，
wherein ,，/>the incidence angles at the near and far positions of the swath, respectively, the subscript "1" indicates that the beam front passes through the incidence angle +.>Relative time of target atWhile subscript "2" indicates the relative time that the trailing edge of the beam passes the target.
(3) Scanning constraint: scanning constraints include constraints on scanning direction and scanning speed. The scanning direction determines the time characteristics of the SAR echo, and defines the positive scanning direction from the far end to the near end of the swath, and the negative scanning direction. When the scanning direction is positive, the method has the advantage of echo window compression, and is beneficial to realizing wide width; when the scanning direction is negative, the echoes satisfy the time characteristics of reception in sequence from near to far. To meet the frequency scanning criteria for improved ground range resolution, requirements. Furthermore, from the principle of an actual frequency dispersive network, the beam pointing, i.e. the beam pointing angle, is a bijective function of the scan time. To sum up, equation (9) gives the following constraint:
，
wherein ,relative time for beam center to point to near end target, +.>The relative time at which the beam center is directed to the far end target. />Indicating the time when the beam front passes the far end target, +.>Representing the time the trailing edge of the beam passes the near-end target. />Beam pointing angle for near end target, +.>Beam pointing angle for far end target, +.>For the pulse width of the transmitted signal.
The three equation sets of the simultaneous formula (7) -formula (9) can realize frequency scanning response for realizing ground range resolution balance, and the nonlinear frequency scanning technology is applied to a satellite-borne SAR system, so that the performance of the system is further improved.
In the experimental verification part, simulation experiments are mainly carried out by referring to system parameters of a certain satellite-borne SAR. The main verification content comprises: (1) Simulation verification is carried out on the nonlinear frequency scanning principle and the design method; (2) NF-SAR system design and system performance evaluation;
the system parameters used in this simulation are shown in table 1 below, and the selected wave positions are shown in fig. 4:
TABLE 1
，
(1) Simulation verification of nonlinear frequency sweep response design for balanced ground-to-resolution:
according to table 1 and formula (7), formula (8), formula (9) can design nonlinear frequency scanning response, i.e. the ground distance resolution for realizing equalization, and simulation results are shown in fig. 5a, 5b, 5c and 5 d. The result of the designed nonlinear frequency sweep can be seen in fig. 5 a; FIG. 5b shows that the scanning speed is high at the near end and low at the far end, so as to meet the design principle; fig. 5c and 5d reflect that the longer the near-end target is illuminated under a nonlinear scanning response, the greater the effective bandwidth obtained.
(2) System design and performance evaluation:
the design of the NF-SAR system is accomplished according to the flow chart shown in fig. 6, in combination with the nonlinear frequency sweep constraint (equation (7), equation (8), equation (9)). Firstly, determining system performance requirements including resolution, mapping breadth, NESZ requirements, fuzzy requirements, power supply capacity, volume and weight requirements according to a specific task requirement; then, according to the system performance requirement, carrying out system parameter design, including determining the transmission bandwidth, the upper limit and the lower limit of azimuth antenna, the upper limit and the lower limit of PRF and the antenna size of the system; then, based on the designed system, analyzing the system performance, including the ground distance resolution, the ambiguity, the system NESZ and the antenna gain, judging whether the performances meet the user requirements, and if not, adjusting the system design parameters or task requirements until the requirements are met; and finally, outputting the designed system parameters. In order to compare the advantages of the NF-SCAN mode, under the condition that the control user requires and certain system parameters are certain, the traditional stripe mode, the SCORE mode based on the DBF technology and the F-SCAN mode are respectively simulated.
The results of the simulation experiment show that: (1) As shown in fig. 7, the N-FSCAN mode can achieve an equalized ground range resolution, with a GRRV value of about 11.5 m; in addition, under the condition that the requirement of a user on the ground distance resolution is met, compared with an F-SCAN mode, the transmission bandwidth of the NF-SCAN mode is greatly reduced; (2) As shown in fig. 8, in NF-SCAN mode, the SAR system has better sensitivity than the other three modes; (3) As shown in fig. 9, in NF-SCAN mode, the SAR system inherits excellent distance ambiguity performance of F-SCAN mode and is superior to the SCORE mode. Table 2 shows the design results based on the SCAN coefficients in the NF-SCAN mode and the F-SCAN mode under the parameters of Table 1. Table 3 depicts Table 2 shows the results for the two-bit resolution based on the parameters of Table 1, NF-SCAN mode, F-SCAN mode, SOCRE mode, and conventional stripe mode.
TABLE 2
，
TABLE 3 Table 3
，
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 (5)
1. The SAR system design method based on the nonlinear frequency scanning response is characterized by comprising the following steps of:
step 1, defining a ground range resolution variance as an index for evaluating ground range resolution;
step 2, deducing ground range resolution based on scanning speed;
step 3, designing a frequency scanning criterion for improving ground distance resolution;
and 4, designing a nonlinear frequency scanning response method.
2. The SAR system design method based on nonlinear frequency scanning response according to claim 1, wherein in step 1, the ground range resolution variance is calculated as follows:
(2),
wherein ,representing ground range resolution variance,/>For the number of samples in the whole swath, depending on imaging breadth and distance sampling rate, +.>For ground range resolution at each sample, +.>The minimum value of the ground range resolution is represented, and i is an index value.
3. The SAR system design method based on nonlinear frequency scanning response according to claim 2, wherein said step 2 comprises:
the residence time is defined as:
(3),
wherein ,time required for the beam to pass a target point, < >>For taking out the mould->Is a partial differential operator, ++>For beam width +.>Is the scanning speed; />As the amount of change in the angle of the beam,to change the angle +.>Substituted into->Is performed by the method;
for a spaceborne SAR system, the beam pointing angleIncident angle->Is one-to-one correspondence, assuming that the transmitted signal is a chirp signal, substituting equation (2) into ground range resolution +>Formula>Is obtained by:
(4),
wherein ,for the frequency modulation rate of the chirp signal, +.>For the speed of light->For incident angle, ++>For the resident bandwidth.
4. The SAR system design method based on nonlinear frequency scanning response according to claim 3, wherein the frequency scanning criteria in step 3 comprises:
causing the beam to followIs passed through the target at the distance, saving the scanning time at the distance, wherein +.>For modulating the frequency of the transmitted signal, < >>For the angle of incidence at distance +.>For ground range resolution at distance, c is speed of light, < >>Representing the speed of a target passing through a distance; with oneIs passed through the target in the near distance to ensure that the target in the near distance acquires a sufficiently long residence time,/for>For the angle of incidence at short distance, +.>For ground resolution at near distance, +.>Representing the speed of the object passing near.
5. The SAR system design method based on nonlinear frequency scanning response according to claim 4, wherein said step 4 comprises:
first, a general frequency sweep format is proposed:
(5),
wherein ,becomes a scan coefficient vector, ">In order to scan the coefficients of the light,is a scan time vector; />Is the beam pointing angle;
the form of simplifying the general frequency sweep is as follows:
(6),
second, given the design constraints of the nonlinear frequency sweep response, including:
(1) Scene constraints, including imaging breadth and corresponding angular range, are expressed as:
(7),
wherein ,for the operating point of the system->For the pulse width of the transmitted signal +.>For the pointing at the beginning of the beam scan, +.>Pointing at the end of beam scanning;
(2) Ground range resolution constraints, namely, satisfy:
(8),
wherein ,，/>the incidence angles at near and far distances, respectively, the subscript "1" indicates that the beam front passes through the incidence angle +.>The relative time of the target at which the trailing edge of the beam passes, while the subscript "2" indicates the relative time of the trailing edge of the beam passing the target;
(3) Scanning constraints, including constraints of scanning direction and scanning speed, andthe following constraint is given by equation (9):
(9),
wherein ,relative time for beam center to point to near end target, +.>Relative time for the beam center to point to the far end target; />Indicating the time when the beam front passes the far end target, +.>Indicating the time when the trailing edge of the beam passes the near-end target,/->Beam pointing angle for near end target, +.>Beam pointing angle for a remote target;
simultaneous equation (7) -equation (9), a frequency sweep response for equally spacing the resolution is achieved.
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