IPB-SAR system parameter design method based on frequency division multi-dimensional waveform coding

Abstract

The application relates to an IPB-SAR system parameter design method based on frequency division multi-dimensional waveform coding. The method comprises the following steps: a linear and phase-synchronous frequency offset is configured for a transmitting array element by adopting a phase-correlated frequency diversity array configuration, and a transmitting beam which is continuously scanned in space-time within a single pulse is generated. The inherent beam scanning speed is calculated according to a SAR imaging geometry, the system scanning speed of the FDA is determined in combination with a preset beam scanning factor, and then a matching relationship between the frequency offset and the transmitting pulse width is established, so that the echo receiving timing is optimized. Based on the FDA beam characteristics and the echo time delay model, a timing constraint for avoiding the interference of transmitting pulses and the nadir point echoes is constructed, and then the available range and the optimal value of the pulse repetition frequency are determined. According to the distance direction resolution requirement and the dwell factor, the antenna height is determined, the array element spacing is designed in combination with the grating lobe suppression requirement, and the systematic IPB-SAR system parameter design is completed. By adopting the method, the accurate matching of the FDA beam scanning and the SAR imaging geometry and the signal processing requirement can be realized.

Description

Technical Field

[0001] This application relates to the field of radar signal technology, and in particular to a method for designing IPB-SAR system parameters based on frequency division multidimensional waveform coding. Background Technology

[0002] With the increasing demand for Earth observation, high-resolution wide-swath (HRWS) imaging is an important direction for the development of Synthetic Aperture Radar (SAR) technology. Traditional single-channel SAR is limited by the "minimum antenna area" constraint, making it difficult to achieve both high resolution and wide coverage. While multi-channel SAR and multiple-input multiple-output (MIMO) technology offer more degrees of freedom, their beam scanning modes are often discontinuous, leading to gain fluctuations within the mapping band that create a scallop effect, and also complicating system design and signal processing.

[0003] Frequency Diverse Arrays (FDAs) introduce small, controllable frequency offsets on the carrier frequencies of each element, giving their transmit patterns unique space-time coupling characteristics. This enables continuous, automatic beam pointing within a single transmit pulse cycle. Coherent FDAs further ensure phase synchronization between elements, laying the foundation for precise beamforming and fully coherent processing. Implementing Intrapulse Beam Scanning (IPB) SAR systems based on coherent FDAs is an effective way to overcome the shortcomings of traditional scanning modes.

[0004] However, applying FDA technology to practical IPB-SAR systems faces a series of parameter design challenges. Key parameters of the FDA, such as frequency offset, pulse parameters, antenna array geometry, and system timing, are interdependent and jointly determine the system's core performance characteristics, including beam scanning characteristics, imaging resolution, blur suppression capability, and signal-to-noise ratio. The lack of a systematic parameter design methodology will prevent the system from achieving its theoretical optimal performance, and may even lead to malfunction due to parameter mismatch. Existing research largely focuses on the signal model and processing algorithms of the FDA, lacking a complete parameter design guideline and process that covers key design dimensions from a system-level perspective. Summary of the Invention

[0005] Therefore, it is necessary to provide a parameter design method for IPB-SAR system based on frequency division multidimensional waveform coding that can achieve precise matching between FDA beam scanning and SAR imaging geometry and signal processing requirements, addressing the aforementioned technical problems.

[0006] A method for designing IPB-SAR system parameters based on frequency division multidimensional waveform coding, the method comprising:

[0007] In the transmitting array of the synthetic aperture radar system, a coherent frequency diversity array configuration is set up, and a linear and phase-synchronized frequency offset is configured for each element of the transmitting array to generate a transmitting beam that can perform spatiotemporal continuous scanning within one pulse period. The inherent beam scanning speed is calculated based on the imaging geometry of the synthetic aperture radar system. Based on the inherent beam scanning speed and the preset beam scanning factor, the system beam scanning speed required for the frequency diversity array to match the inherent beam scanning speed is determined. Based on the system beam scanning speed, the matching relationship between the frequency offset required by the frequency diversity array and the transmit pulse width is determined. The matching relationship is used to optimize the reception timing of the echo signal. Based on the transmit beam scanning characteristics of the frequency diversity array and the echo delay model of the synthetic aperture radar system, timing constraints are constructed to avoid transmit pulse interference and nadir echo interference. The available range and optimal value of the pulse repetition frequency of the synthetic aperture radar system are determined according to the timing constraints. Based on the range resolution requirements of the synthetic aperture radar system and the preset dwell factor, the physical height of the range antenna is determined; at the same time, based on the requirement to suppress grating lobes within the specified angular coverage range of the transmitting array, the spacing between adjacent array elements in the transmitting array is designed, thus completing the systematic IPB-SAR system parameter design process.

[0008] The above-mentioned IPB-SAR system parameter design method based on frequency division multidimensional waveform coding generates an intra-pulse space-time continuous scanning beam by combining the coherent FDA configuration with the linear phase synchronization frequency offset. This directly solves the scallop effect of beam scanning discreteness and gain fluctuation in the mapping zone in traditional mode. Compared with the segmented scanning of multi-channel SAR, continuous scanning can make the beam uniformly cover the mapping zone, eliminating the root cause of gain unevenness at the hardware level. By calculating the inherent scanning speed through imaging geometry and then correlating the FDA system scanning speed with the beam scanning factor, a matching relationship between frequency offset and pulse width is established. This process binds the originally independent parameters into an organic whole adapted to SAR geometry, avoiding the isolated decisions of setting frequency offset based on experience and considering pulse width only for resolution in traditional designs. This ensures the synchronization of beam scanning and SAR platform movement, and compresses the receiving window through timing optimization, logically resolving the contradiction between "high resolution and wide coverage." In the construction of timing constraints and the derivation of the optimal PRF value, quantization rules replace empirical trial and error. Interference constraints between transmitted pulses and nadir echoes transform the requirement to avoid echo overlap from a vague qualitative requirement into a set of inequalities in the PRF, ensuring no signal interference during system operation. Simultaneously, the range resolution and dwell factor are combined to determine... The antenna height and element spacing are designed with grating lobe suppression requirements in mind, moving away from the crude approach of relying solely on larger sizes for antenna and array parameters. The dwell factor balances antenna gain and scanning range, while grating lobe suppression controls hardware complexity while ensuring performance. This systematic process ensures that each parameter meets its own functional requirements and mutually supports overall performance, thereby improving signal-to-noise ratio and blur suppression capabilities while maintaining resolution. It also provides a clear and replicable guideline for the engineering implementation of high-resolution wide-bandgap SAR. Simulation results show that the SAR system based on the FDA-approved IPB mode configured in this application outperforms traditional modes in imaging uniformity, overall signal-to-noise ratio, and blur suppression performance. This provides a reliable and efficient design tool for the development of high-resolution wide-bandgap SAR systems and has significant engineering application value. Attached Figure Description

[0009] Figure 1 This is a flowchart illustrating a parameter design method for an IPB-SAR system based on frequency division multidimensional waveform coding in one embodiment. Figure 2 This is a schematic diagram of a coherent FDA transceiver model in one embodiment; Figure 3 This is a schematic diagram illustrating the relationship between echo arrival time and slant range under three typical beam scanning factor values ​​in one embodiment; (a) is when (a) is a schematic diagram showing the relationship between echo arrival time and slant range; (b) is... A schematic diagram illustrating the relationship between the arrival time of echoes deviating from the unit value and the slant range; (c) is... Another schematic diagram illustrating the relationship between the arrival time of echoes deviating from the unit value and the slant range; Figure 4 This is a graph showing the change of echo width and remaining time with respect to relative scanning speed in one embodiment; Figure 5 This is an example diagram of a time-series zebra diagram design in one embodiment; Figure 6 This is a graph showing the variation of RASR with ground distance for a different system in one embodiment; Figure 7 This is a graph showing the NESZ variation with ground distance for different systems under the same average transmit power in one embodiment. Figure 8 This is a graph showing the NESZ variation with ground distance for different systems with the same peak transmit power in one embodiment. Detailed Implementation

[0010] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0011] In one embodiment, such as Figure 1 As shown, a method for designing IPB-SAR system parameters based on frequency division multidimensional waveform coding is provided, including: Step 102: In the transmitting array of the synthetic aperture radar system, a coherent frequency diversity array configuration is set, and a linear and phase-synchronized frequency offset is configured for each element of the transmitting array to generate a transmitting beam that can perform spatiotemporal continuous scanning within one pulse period.

[0012] Coherent frequency diversity array (FDA) refers to an array where all elements transmit the same baseband waveform while introducing a defined frequency offset between their respective radio frequency carriers. This offset is applied in a phase-synchronized manner to maintain a stable and predictable phase relationship between the elements over time. This enables precise beamforming and fully coherent signal processing throughout the entire scanning cycle, transforming frequency progression into a controlled "space-time-range" coupled beam pattern. Ultimately, this achieves continuous beam scanning, providing the system with greater operational flexibility and new degrees of freedom for advanced SAR imaging.

[0013] Linear and phase-synchronized frequency offset means that the offset of the carrier frequency of each array element changes linearly, and the signal phase between each array element always remains synchronized. This is the key to forming a space-time continuous scanning transmission beam and ensures that the beam scanning process is stable and controllable.

[0014] Spatiotemporal continuous scanning transmit beams refer to beam pointing that can continuously change in both spatial angle and temporal dimensions within one transmit pulse cycle, rather than the discrete switching of traditional beams. This can cover a wider mapping range and avoid gain fluctuations within the mapping band.

[0015] In this step, the implementation of coherent frequency offset can follow two main architectures, such as Figure 2 As shown. One approach is to use a single transmit / receive module to generate a common baseband waveform, and then distribute this signal to all channels. Each channel applies its own independent static frequency bias to the common signal via a dedicated digital upconverter or mixer. This approach has a simpler hardware structure and lower cost. Another more flexible approach is to pre-synthesize the required frequency bias into a digital baseband waveform unique to each transmit channel before digital-to-analog conversion. Then, each channel uses dedicated hardware to directly generate and amplify its specific waveform. This architecture allows for time-varying or adaptive frequency bias, but the transmitter complexity and cost are higher. The choice between the two approaches depends on the trade-off between system flexibility and hardware resources, and should be guided by specific mission requirements.

[0016] Step 104: Calculate the inherent beam scanning speed based on the imaging geometry of the synthetic aperture radar system; determine the system beam scanning speed required for the frequency diversity array to match the inherent beam scanning speed based on the inherent beam scanning speed and the preset beam scanning factor; determine the matching relationship between the frequency offset required for the frequency diversity array and the transmit pulse width based on the system beam scanning speed; the matching relationship is used to optimize the reception timing of the echo signal.

[0017] SAR imaging geometry refers to the geometric configuration of a SAR system during side-looking observations, where the platform's azimuth movement causes continuous changes in elevation angle. Simultaneously, influenced by the Earth's curvature, the slant range and elevation angle exhibit a non-linear mapping. This configuration determines the inherent beam scanning characteristics of the SAR system. The inherent beam scanning velocity refers to the naturally occurring beam scanning velocity of the SAR system due to the imaging geometry, as the elevation angle changes with distance. Because of the Earth's curvature and the non-linear mapping between slant range and elevation angle, the instantaneous inherent beam scanning velocity is time-varying. To simplify system-level analysis, an average beam scanning velocity approximation is used, treating the mapping from slant range to elevation angle as locally linear within the imaging mapping zone. The beam scanning factor is a parameter describing the relative relationship between the beam scanning velocity of a frequency diversity array system and the inherent beam scanning velocity of the SAR. Adjusting this factor allows for flexible control of echo reception timing, enabling compression of the reception window and improving system signal reception efficiency. The matching relationship between frequency offset and transmitted pulse width refers to determining the correspondence between the carrier frequency offset of each element in the frequency diversity array and the duration of the transmitted pulse, based on the system beam scanning speed. This ensures that the beam scanning can be geometrically adapted to SAR imaging, optimizes echo reception timing, and avoids echo overlap interference. In spaceborne synthetic aperture radar systems, the geometry of side-looking observation causes continuous changes in the elevation angle as the platform moves along the azimuth direction. Therefore, the system has an inherent beam scanning speed as the elevation angle changes with distance. Due to the curvature geometry of the Earth and the nonlinear mapping relationship between slant range and elevation angle, the instantaneous beam scanning speed is time-varying, and the analysis process is relatively complex. To simplify and maintain the operability of system-level analysis, the average beam scanning speed is used as an approximation. This approximation treats the mapping from slant range to elevation angle as locally linear within the imaging mapping zone. The fundamental difference between the FDA-based IPB mode and the strip mode is that the IPB mode shifts the delay of the mapping strip from the receiving window to the transmitting pulse. This conversion significantly reduces the width of the receiving window and increases the transmitting duty cycle, thereby improving the signal-to-noise ratio performance while reducing the peak power requirement.

[0018] Specifically: The average beam scanning speed of the FDA is defined as the ratio of total angular displacement to pulse width, and its expression can be written as: (1) in, Indicates the width of the surveying strip. Indicates the pulse width. This represents the frequency bias. Indicates wavelength. Indicates the spacing between array elements.

[0019] For spaceborne synthetic aperture radar systems, the geometry of side-looking observation causes a continuous change in elevation angle as the platform moves along the azimuth. Therefore, the system possesses an inherent beam scanning velocity as the elevation angle changes with range. Due to the Earth's curvature geometry and the nonlinear mapping between slant range and elevation angle, the instantaneous beam scanning velocity is time-varying, and the analysis process is complex. To simplify and maintain the operability of system-level analysis, this application uses the average beam scanning velocity as an approximation. This approximation treats the mapping from slant range to elevation angle as locally linear within the imaging mapping zone. Therefore, the average beam scanning velocity can be expressed as: (2) in, Indicates the scan range. and These represent the slope distances at the far and near ends of the survey strip, respectively. This represents the speed of light. The beam scanning speed is determined by geometry and remains constant when the mapping strip width is fixed. The average beam scanning speed of the FDA system... With SAR beam scanning speed When the frequencies are equal, the echo signals from the far and near ends of the mapping strip will be received simultaneously. Under this condition, the required frequency increment is... Represented as (3) Substituting equation (3) into equation (1), the pulse width required to achieve the synchronous beam scanning process of the system can be expressed as: (4) in, The dwell factor is the ratio of the total coverage area of ​​the beam scan to the instantaneous beamwidth.

[0020] The fundamental difference between the FDA-based IPB mode and the strip mode lies in the shift of the mapping strip's delay from the receive window to the transmit pulse. This conversion significantly reduces the receive window width while increasing the transmit duty cycle, thereby improving signal-to-noise ratio performance while reducing the peak power requirement. To characterize this beam scanning mechanism, this application defines a parameter describing the relative beam scanning speed of the FDA system: (5) At the same time, we can obtain: (6) When beam scanning factor At that time, the beam scanning speed of the FDA system Greater than SAR beam scanning speed At this point, the echo from the near-surveyed zone arrives before the echo from the far-surveyed zone, which is consistent with the conventional echo timing observed in strip mode. Conversely, if , Less than This will cause an echo timing reversal, meaning that echoes from the far mapping zone arrive before those from the near mapping zone, thus forming the "far-first" characteristic unique to the FDA-based IPB mode. This timing reversal presents challenges for signal processing, but also provides the possibility for system adaptation.

[0021] Next, this application analyzes the temporal characteristics of the echo in the FDA-compliant IPB mode. The pulse is emitted at time... Beginning. Given the actual mapping strip width, if the Earth's curvature effect is negligible, the beam scanning process can be effectively modeled with a constant angular velocity. Therefore, at any given observation time... ,in, The instantaneous beam scanning angle can be expressed as the time elapsed since emission. (7) in, Indicates the central angle of incidence.

[0022] According to the SAR geometric model, the corresponding slant range can be expressed as: (8) in, Represents the Earth's radius. This indicates the height of the radar platform above the ground.

[0023] Therefore, the echo arrival time can be expressed as: (9) Figure 3 Demonstrates three typical beam scanning factors The relationship between echo arrival time and slant range under the given values. Figure 3 In (a), when At this time, the arrival time curves corresponding to the near and far ends of the mapping strip converge at their respective boundaries, indicating that the echoes from both ends are received simultaneously. However, due to the nonlinear mapping relationship between slant range and elevation angle in SAR geometry, this synchronicity does not extend to all points within the mapping strip. Instead, as... Figure 3 As shown in (b) and (c), Deviations from the unit value disrupt temporal alignment, causing echo time curves to separate and reversing the reception order of echoes from different distances. Theoretical analysis further predicts that even if echoes from both near and far ends arrive simultaneously, their arrival times will reach a minimum at a certain intermediate angle within the mapping zone. This extreme value can be calculated as: (10) in, This represents the minimum time elapsed since launch. Indicates the time of arrival of the echo. The pitch angle corresponding to reaching the minimum value. Therefore, this application defines the remaining time as the time-domain offset between the earliest arriving echo and the minimum arrival time of the mapping zone boundary, and its expression is: (11) in, and These are the echo arrival times at the far and near ends of the survey strip, respectively. Therefore, the total width of the echo window is: (12) in, This indicates the beam dwell time for each target.

[0024] Figure 4 The remaining time and echo time width are shown as a function of the beam scan factor. The changes in time. The results show that the remaining time only occurs in... Within the range, and in It reaches its peak at that time. It is worth noting that the echo time width is exactly at... The minimum value is reached at that time. These results indicate that setting... Optimal compression of the receive window width can be achieved in FDA-based IPB mode. However, the system offers operational flexibility. It can be adaptively adjusted according to specific radar requirements, and can even be set as time-varying parameters to adapt to different types of targets within the mapping zone.

[0025] Step 106: Based on the transmit beam scanning characteristics of the frequency diversity array and the echo delay model of the synthetic aperture radar system, construct timing constraints to avoid transmit pulse interference and nadir point echo interference; determine the available range and optimal value of the pulse repetition frequency of the synthetic aperture radar system according to the timing constraints.

[0026] The FDA transmit beam scanning characteristic refers to the space-time coupled beam scanning characteristics formed by the linear offset of the array element carrier frequencies of the frequency diversity array. This includes the changes in beam scanning speed, scanning range, and beamwidth over time, which determine the temporal distribution characteristics of the echo signal. The echo delay model is a mathematical model describing the relationship between the time delay of the echo signal reaching the receiver after the radar transmit signal is reflected by the target and parameters such as the target slant range, SAR platform height, and Earth curvature. It is the basis for deriving timing constraints. Transmit pulse interference refers to the phenomenon where, during the periodic transmission of pulses by the SAR system, the target echo of a subsequent transmitted pulse overlaps with the target echo of the preceding transmitted pulse in time, causing interference with the echo signal and making it impossible to accurately extract. Nadir echo interference refers to the phenomenon where the echo signal reflected from the nadir point (the ground point directly below the radar platform), due to its small incident angle and high reflection intensity, causes strong interference to the mapping zone echo signal if it overlaps with the mapping zone echo in time. Timing constraints refer to the constraints imposed on the relationship between the echo arrival time and parameters such as the transmitted pulse period and guard time to avoid transmitted pulse interference and nadir echo interference. These constraints are usually presented as inequalities and are used to determine a reasonable range for the pulse repetition frequency (PRF). The Pulse Repetition Frequency (PRF) refers to the number of pulses transmitted by the SAR system per unit time. Its value directly affects the echo timing distribution, and the optimal value must be determined while satisfying the timing constraints to balance system imaging performance, fuzziness suppression capability, and data processing complexity.

[0027] Timing design is a crucial step in ensuring the successful operation of a SAR system. Since the transmitted pulses are periodically emitted, interference between the radar echo and the transmitted pulses must be avoided. Typically, this interference can be categorized into two types: transmitted pulse interference and nadir echo interference.

[0028] (1) Transmit pulse interference Appropriate timing design should be adopted to avoid temporal overlap between the echo and the transmitted pulse. Assuming the echo transmitted at a certain moment needs to be processed... It arrives after one pulse cycle. To avoid overlapping with the transmitted pulse, the echo should be located within the time interval. Within, among them Indicates the pulse repetition interval. This indicates the protection time. Therefore, the echo arrival time must satisfy: (13) when Then, the timing constraint in equation (13) can be rewritten as: (14) when Then, equation (13) can be written as: (15) (2) Sub-satellite point echo interference Appropriate timing design should be adopted to avoid temporal overlap between the mapping zone echo and the nadir echo. The nadir echo, due to its smaller angle of incidence, has a higher amplitude and undergoes [further processing / processing]. It arrives after one pulse cycle. If it is not effectively suppressed by the array pattern, it will cause strong interference in the echo signal. Due to the periodic emission of the pulse, the arrival time interval of the nadir echo is... Therefore, the arrival time of the echo must not intersect with this interval, thus requiring the following condition to be met: (16) Similarly, when Then, equation (16) can be written as: (17) when At that time, the timing constraint can be written as: (18) Once the required mapping zone is determined, an appropriate pulse repetition frequency can be selected based on the aforementioned time constraints. Figure 5 An example of a timing stripe design is shown, which allows for a visual observation of the temporal distribution relationship between the echo, the transmitted pulse, and the nadir echo under different PRF values, thus helping to determine the optimal PRF value.

[0029] Step 108: Determine the physical height of the range antenna based on the range resolution requirements of the synthetic aperture radar system and the preset dwell factor; at the same time, design the spacing between adjacent elements in the transmission array based on the requirement to suppress grating lobes within the coverage range of the transmission array at a specified angle, thus completing the systematic IPB-SAR system parameter design process.

[0030] Range resolution requirement refers to the minimum distance at which a SAR system can distinguish two adjacent targets in the range direction (aligned with the radar line of sight). It is a key indicator for evaluating SAR imaging accuracy and directly determines the design of parameters such as antenna height and signal bandwidth. Dwell time factor is a parameter describing the characteristics of a beam's residence within the mapping zone. It is defined as the ratio of the angular coverage area of ​​the mapping zone to the instantaneous beamwidth, or the ratio of the transmitted pulse width to the beam dwell time. It is used to quantify the matching degree between beam scanning and target coverage, guiding antenna height design. Range antenna height refers to the physical dimensions of the SAR antenna in the range direction. Its size directly affects the instantaneous beamwidth, which in turn affects the dwell time factor and range resolution. It needs to be determined collaboratively based on resolution requirements and dwell time factor. Raster lobes refer to the extra beams that appear outside the specified scanning angle range of the array antenna. They can cause energy dispersion, decreased target detection accuracy, and even the generation of false targets. Therefore, grating lobes need to be suppressed through element spacing design. Specified angular coverage area refers to the spatial angular range corresponding to the mapping zone that the SAR system needs to image. Element spacing design must ensure that there are no grating lobes or that the grating lobes are in a low-gain region within this range.

[0031] In the FDA-based IPB mode, azimuth processing follows the same principles as in strip or SCORE modes, but the system introduces a unique elevation-dimensional beam scanning. This beam scanning mechanism directly determines the instantaneous beamwidth. Its height is determined by the antenna. The dwell factor is set. For a given survey strip width, the dwell factor can be derived as follows: (19) in, This represents the antenna height corresponding to the strip pattern covering the same mapping strip. Therefore, the antenna height based on the FDA's IPB pattern can be calculated as follows: (20) The design of the element spacing is primarily constrained by the need to suppress grating lobes within a specified angular coverage area. The optimal condition requires that no grating lobes appear within the specified angular coverage area during intra-pulse fast scanning. For a specific angle... The angle of the nearest neighbor grating lobe must satisfy: (twenty one) To ensure that the grating lobe remains outside the visible area at all times, its angle must meet the following requirements. This is equivalent to requiring Based on the above constraints, the element spacing can be derived. Required conditions: (twenty two) This constraint may be too stringent, potentially leading to an excessive number of receiving channels and a large data volume. In practical applications, this can be mitigated by allowing grating lobes to exist in the main lobe region of the array element pattern. This requirement can be relaxed from the outside. In this case, the constraint in equation (22) can be appropriately relaxed as follows: (twenty three) However, this condition is too lenient, leading to unacceptably high gate lobe levels. To mitigate this problem, this application proposes to reduce the element spacing from the theoretical value... Halved. This improved configuration achieves a dual key enhancement: it doubles the effective scanning range while still preventing grating lobes from appearing in the element radiation pattern. Within the main lobe region; and for the required working scan range, the motion of the nearest array grating lobe can be constrained to only be directed towards... The grating lobe is positioned halfway along the boundary, ensuring it remains within the null region of the element radiation pattern. Therefore, the grating lobe is significantly suppressed by the natural roll-off of the element radiation characteristics.

[0032] Under this constrained configuration, the antenna only affects the element pattern. Operating within half the width of the main lobe, the nearest array grating lobe is always affected by the natural roll-off characteristics of the element pattern during beam scanning. The suppression of [something]. Within this design framework, the value of the residency factor can be expressed as: (twenty four) Integrate the above parameters to form a systematic design process.

[0033] To address the aforementioned parameter design steps and achieve a systematic and processable derivation from system requirements to key parameters, this application further proposes a programmable parameter design algorithm, the specific process of which is shown in Algorithm 1:

[0034] The above-mentioned IPB-SAR system parameter design method based on frequency division multidimensional waveform coding generates an intra-pulse space-time continuous scanning beam by combining the coherent FDA configuration with the linear phase synchronization frequency offset. This directly solves the scallop effect of beam scanning discreteness and gain fluctuation in the mapping zone in traditional mode. Compared with the segmented scanning of multi-channel SAR, continuous scanning can make the beam uniformly cover the mapping zone, eliminating the root cause of gain unevenness at the hardware level. By calculating the inherent scanning speed through imaging geometry and then correlating the FDA system scanning speed with the beam scanning factor, a matching relationship between frequency offset and pulse width is established. This process binds the originally independent parameters into an organic whole adapted to SAR geometry, avoiding the isolated decisions of setting frequency offset based on experience and considering pulse width only for resolution in traditional designs. This ensures the synchronization of beam scanning and SAR platform movement, and compresses the receiving window through timing optimization, logically resolving the contradiction between "high resolution and wide coverage." In the construction of timing constraints and the derivation of the optimal PRF value, quantization rules replace empirical trial and error. Interference constraints between transmitted pulses and nadir echoes transform the requirement to avoid echo overlap from a vague qualitative requirement into a set of inequalities in the PRF, ensuring no signal interference during system operation. Simultaneously, the range resolution and dwell factor are combined to determine... The antenna height and element spacing are designed with grating lobe suppression requirements in mind, moving away from the crude approach of relying solely on larger sizes for antenna and array parameters. The dwell factor balances antenna gain and scanning range, while grating lobe suppression controls hardware complexity while ensuring performance. This systematic process ensures that each parameter meets its own functional requirements and mutually supports overall performance, thereby improving signal-to-noise ratio and blur suppression capabilities while maintaining resolution. It also provides a clear and replicable guideline for the engineering implementation of high-resolution wide-bandgap SAR. Simulation results show that the SAR system based on the FDA-approved IPB mode configured in this application outperforms traditional modes in imaging uniformity, overall signal-to-noise ratio, and blur suppression performance. This provides a reliable and efficient design tool for the development of high-resolution wide-bandgap SAR systems and has significant engineering application value.

[0035] In one embodiment, the beam scanning factor is defined as the ratio of the system beam scanning speed of the frequency diversity array to the inherent beam scanning speed of the synthetic aperture radar system; by adjusting the beam scanning factor, the reception timing of the echo signal is controlled to be either a conventional sequence from the near end to the far end of the mapping band, or a reverse sequence from the far end to the near end of the mapping band.

[0036] Specifically, the definition of the beam scan factor clarifies the relative relationship between the FDA system beam scan rate and the inherent SAR beam scan rate, and is a core parameter for achieving echo timing control. When the beam scan factor... At that time, the beam scanning speed of the FDA system Greater than SAR beam scanning speed At this point, the echo from the near-surveyed zone arrives before the echo from the far-surveyed zone, which is consistent with the conventional echo timing observed in strip mode. Conversely, if , Less than This will cause an echo timing reversal, meaning that echoes from the far mapping zone arrive before those from the near mapping zone, thus forming the "far-first" characteristic unique to the FDA-based IPB mode. This timing reversal presents challenges for signal processing but also provides the possibility for system adaptation. This timing can further optimize the receiver window configuration and reduce the probability of echo overlap. By flexibly adjusting the beam scanning factor, an appropriate echo timing can be selected according to the needs of different mapping tasks, effectively compressing the receiver window width, improving the system's reception efficiency and processing flexibility for echo signals, and laying the foundation for subsequent signal deblurring and signal-to-noise ratio improvement.

[0037] In one embodiment, the system beam scanning speed of the frequency diversity array is

[0038] in, Indicates the width of the surveying strip. Indicates the pulse width. This represents the frequency bias. Indicates wavelength. Indicates the spacing between array elements.

[0039] Specifically, this formula provides a clear basis for the quantitative design of beam scanning speed in the FDA system, ensuring that the beam scanning characteristics can be accurately matched with the geometric requirements of SAR imaging, avoiding problems such as incomplete coverage of the mapping zone or echo overlap caused by improper scanning speed, and is the key mathematical foundation for achieving the coordinated design of frequency offset and pulse width.

[0040] In one embodiment, the inherent beam scanning speed of the synthetic aperture radar system is:

[0041] in, Indicates the scan range. and These represent the slope distances at the far and near ends of the survey strip, respectively. It represents the speed of light.

[0042] Specifically, it provides a quantitative calculation method for the inherent scanning characteristics of SAR systems, enabling designers to accurately grasp the natural requirements of SAR imaging geometry for beam scanning, thereby guiding the design of beam scanning speed for FDA systems. By adjusting frequency offset, element spacing, etc., it achieves precise matching between FDA scanning characteristics and inherent SAR scanning characteristics, avoiding problems such as gain fluctuations and imaging blurring in the mapping band caused by mismatch between the two. This is an important prerequisite for subsequently determining the beam scanning factor and establishing the matching relationship between frequency offset and pulse width.

[0043] In one embodiment, determining the matching relationship between the frequency offset required for the frequency diversity array and the transmit pulse width includes: Let the beam scanning factor be , Based on the matching relationship, the required frequency offset is:

[0044] The transmit pulse width is

[0045] in, This represents the dwell factor, which is the ratio of the total coverage area of ​​the beam scan to the instantaneous beamwidth. and These represent the slope distances at the far and near ends of the survey strip, respectively. Represents the speed of light. Indicates wavelength. Indicates the spacing between array elements. Indicates the scan range. This represents the frequency bias.

[0046] Specifically, this embodiment breaks through the limitation of independent design of frequency offset and pulse width in traditional design, establishes a quantitative matching relationship between the two, makes the design process reversible, and incorporates dwell factor and beam scanning factor to ensure that the parameter design meets the imaging resolution requirements and adapts to the SAR geometric scanning characteristics. It effectively solves the problems of complex parameter coupling and reliance on experience trial and error in traditional design, and provides a clear mathematical basis for the systematic design of system parameters.

[0047] In one embodiment, the timing constraints specifically include: The first constraint is used to ensure that the arrival time of the echo at any point within the mapping strip does not overlap with any transmitted pulse in time; The second constraint is used to ensure that the arrival time of the echo from any point within the mapping zone does not overlap with the echo from the nadir point in time. Based on the echo delay model, the first and second constraints are expressed as a set of inequalities with respect to the pulse repetition frequency. Solving the set of inequalities yields the available range of the pulse repetition frequency, and the value that optimizes the system efficiency or performance is selected as the optimal value.

[0048] Specifically, the first constraint addresses transmitted pulse interference. Since the SAR system periodically transmits pulses, if the echo of a preceding pulse is not received before the subsequent pulse is transmitted, it will cause the echo to overlap with the transmitted pulse, resulting in signal distortion. This constraint ensures that the echo falls within the receiving window between two transmitted pulses by limiting the relationship between the echo arrival time, pulse repetition interval, and guard time, thus avoiding direct interference between the transmitted signal and the echo. The second constraint addresses nadir echo interference. Nadir echoes, due to their small incident angle and strong ground reflection, can mask weak target echoes if they overlap with the mapping zone echo. This constraint eliminates the impact of strong interference on imaging quality by isolating the time interval between the mapping zone echo and the nadir echo. Transforming these two constraints into a system of inequalities in PRF essentially controls the pulse repetition interval through the value of PRF, thereby adjusting the time distribution of the transmitted pulse and the echo—for example, when the mapping zone echo delay is large, the PRF needs to be reduced to increase the pulse repetition interval, preventing the echo from overlapping with subsequent transmitted pulses. Within the usable range of the obtained PRF, selecting the optimal value requires a comprehensive consideration of multiple factors: if high imaging efficiency is desired, a PRF close to the upper limit of the usable range can be selected (emitting more pulses per unit time, increasing the data rate); if low ambiguity and high signal-to-noise ratio are prioritized, a PRF value that minimizes the echo window redundancy time and is far from the nadir echo interval can be selected. This design process clarifies the PRF range through quantitative constraints and then determines the optimal value based on system performance requirements, avoiding the subjectivity of traditional PRF design and ensuring that the system timing design meets both interference-free requirements and maximizes imaging performance.

[0049] In one embodiment, the first constraint includes: when At that time, the first timing constraint is:

[0050] when At that time, the first timing constraint is:

[0051] in, Indicates the pulse repetition interval. Indicates the protection time. Indicates the beam scanning factor. Indicates the pulse width. Indicates the receive window redundancy time; The second constraint includes: when At that time, the second timing constraint is:

[0052] when At that time, the second timing constraint is:

[0053] in, This represents the dwell factor, which is the ratio of the total coverage area of ​​the beam scan to the instantaneous beamwidth. and These represent the slope distances at the far and near ends of the survey strip, respectively. Represents the speed of light. Indicates the radar platform altitude. Indicates the arrival time of the echo near the end point of the survey strip. Indicates the arrival time of the echo at the far end of the survey zone. This indicates the number of pulse cycles corresponding to the transmitted pulse. This indicates the number of pulse cycles corresponding to the sub-satellite point echo.

[0054] In one embodiment, the physical height of the range antenna is ,in, Resident factor, The antenna height required when using a strip pattern to cover the same mapping strip.

[0055] Specifically, this embodiment clarifies that the IPB mode improves antenna gain without sacrificing the coverage of the surveying strip by coordinating the design of antenna height and dwell factor, thus resolving the contradiction between wide coverage and high gain in the traditional strip mode and providing a hardware design basis for improving the system signal-to-noise ratio.

[0056] In one embodiment, the preset residence factor is:

[0057] in, This indicates the antenna height corresponding to the strip pattern covering the same mapping zone. Indicates the range-direction antenna height. Indicates the scan range. Indicates wavelength.

[0058] Transforming the dwell factor from an abstract concept into a quantifiable and designable parameter clarifies the dwell factor's requirements for the number of beam scans and links it to antenna height. This makes the dwell factor a bridge connecting the system's scanning characteristics and hardware parameters, ensuring the consistency and systematic nature of parameter design.

[0059] In one embodiment, the process of designing the spacing between adjacent elements in the transmission array includes: Based on satisfying the grating lobe suppression condition, the array element spacing is designed so that when the frequency diversity array performs intra-pulse beam scanning, no grating lobes appear in the array pattern within the specified angular coverage range, or the grating lobes that appear fall into the zero point or low-gain sidelobe region of the array element pattern.

[0060] Specifically, by suppressing grating lobes to ensure imaging quality, while avoiding problems such as increased hardware costs and excessive data volume caused by too small a spacing, a feasible solution is provided for the engineering implementation of array hardware.

[0061] In a specific embodiment, in order to verify the effectiveness of this application, the following simulation experiment was designed for illustration: The parameters of the FDA-based IPB system in this application are shown in Table 1 below.

[0062] Table 1

[0063] Based on the system parameters listed in Table 1, and using the parameter design method described in this application to optimize and determine key parameters for the FDA-based IPB mode, numerical simulations were performed to evaluate and compare its performance differences with the strip mode and the Scanon Receive (SCORE) mode in terms of Range Ambiguity-to-Signal Ratio (RASR) and Noise Equivalent Sigma Zero (NESZ). To ensure the systematicity and fairness of the comparison, all modes were configured under uniform system-level parameter constraints (including carrier frequency, signal bandwidth, platform height, and mapping strip coverage). The parameters for the strip mode and the SCORE mode were also set based on the same design principles and constraints to fairly reflect the performance improvement of the FDA-based IPB mode under the same physical conditions.

[0064] Each mode is configured with parameters according to its working principle and beamforming requirements: the strip mode requires wide beam coverage, and its range-direction antenna height is correspondingly shortened; the SCORE mode performs receiving digital beamforming based on the same transmitting antenna; while the FDA-based IPB mode, based on the aforementioned parameter design method, simultaneously optimizes frequency offset, pulse width, antenna size, and element spacing to achieve continuous beam scanning and a "narrow transmit, narrow receive" structure. Simulations are then conducted to compare the performance of the three modes under the same imaging geometry and scattering conditions, thus objectively verifying the significant advantages of the FDA-based IPB mode in terms of imaging signal-to-noise ratio and range ambiguity suppression.

[0065] The graphs showing the variation of RASR with ground distance for different systems are as follows: Figure 5As shown, the SCORE mode, due to its high-gain narrow beamforming via receiver-side deep beamforming (DBF), exhibits superior ambiguity suppression performance compared to the stripe mode. However, the IPB mode, based on the FDA (Front-Ended Beam), not only employs receiver-side DBF but also utilizes the FDA to achieve an equivalent transmitter-side DBF, thus forming a "narrow transmit, narrow receive" architecture. Compared to the SCORE mode, this architecture achieves even better range ambiguity suppression performance.

[0066] Figure 6 The diagram shows the NESZ variation with ground distance for different systems at the same average transmit power. Under the same average transmit power, the strip mode has the worst signal-to-noise ratio, and its performance deteriorates significantly at the edge of the mapping strip. This is mainly due to its use of a shorter antenna to achieve wide beam coverage, resulting in lower antenna gain and a performance gap of approximately 6 dB compared to the SCORE mode, which uses a longer antenna, and the FDA-based IPB mode. The SCORE mode shows improved performance due to its high-gain narrow-beam reception. The FDA-based IPB mode has a slight advantage over the SCORE mode at the edge of the mapping strip. This limited improvement stems from a fundamental trade-off: while the FDA-based IPB mode benefits from narrow-beam transmission, its shorter beam dwell time on any target limits the potential for improved signal-to-noise ratio, which largely offsets the pattern loss caused by the wide-beam transmission in the SCORE mode.

[0067] Figure 7 The diagram shows the NESZ variation with ground distance for different systems with the same peak transmit power. The strip mode remains the worst due to the inherent gain limitations of its shorter antenna structure. In contrast, the FDA-based IPB mode significantly outperforms the SCORE mode in signal-to-noise ratio. This significant improvement is directly related to the operating mechanism of the FDA-IPB mode. By utilizing a narrow scanning transmit beam, this mode achieves higher antenna gain to concentrate the available peak power. More importantly, compared to the wide-beam transmission of the SCORE mode, this approach supports a significantly higher transmit duty cycle. This allows the FDA-based IPB mode to deliver more total energy to the target within a given system peak power constraint. Figure 8 The diagram shows the NESZ variation with ground distance for different systems with the same peak transmit power. The strip mode remains the worst due to the inherent gain limitation of its shorter antenna structure. In contrast, the FDA-based IPB mode has a significantly better signal-to-noise ratio than the SCORE mode. This significant improvement is directly related to the operating mechanism of the FDA-IPB mode. By utilizing a narrow scanning transmit beam, this mode achieves higher antenna gain to concentrate the available peak power. More importantly, compared to the wide-beam transmission of the SCORE mode, this method supports a significantly higher transmit duty cycle. This allows the FDA-based IPB mode to deliver more total energy to the target under a given system peak power constraint. In summary, addressing the problems of discontinuous intra-pulse beam scanning, uneven gain within the mapping band, and lack of systematic theoretical guidance for system parameter design in traditional SAR imaging, this application proposes a complete IPB-SAR system parameter design method based on frequency division multidimensional waveform coding. This method achieves precise matching between FDA beam scanning characteristics and SAR imaging geometry by establishing a collaborative design criterion between frequency offset, pulse parameters, antenna size, and system timing. Fair comparative simulations of the FDA-based IPB mode optimized using this method with strip mode and SCORE mode effectively verify its significant advantages in improving range ambiguity suppression and system signal-to-noise ratio. This research provides crucial theoretical basis and feasible technical approaches for the systematic design of high-resolution wide-swathe SAR, and has significant engineering application value in remote sensing mapping, Earth observation, and other fields.

[0068] It should be understood that, although Figure 1 The steps in the flowchart are shown sequentially as indicated by the arrows, but these steps are not necessarily executed in the order indicated by the arrows. Unless explicitly stated in this application, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Furthermore, Figure 1 At least some of the steps in the process may include multiple sub-steps or multiple stages. These sub-steps or stages are not necessarily completed at the same time, but can be executed at different times. The execution order of these sub-steps or stages is not necessarily sequential, but can be executed in turn or alternately with other steps or at least some of the sub-steps or stages of other steps.

[0069] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0070] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of this application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these modifications and improvements all fall within the protection scope of this application. Therefore, the protection scope of this application should be determined by the appended claims.

Claims

1. A method for designing IPB-SAR system parameters based on frequency division multidimensional waveform coding, characterized in that, The method includes: In the transmitting array of the synthetic aperture radar system, a coherent frequency diversity array configuration is set, and a linear and phase-synchronized frequency offset is configured for each element of the transmitting array to generate a transmitting beam that can perform spatiotemporal continuous scanning within one pulse period. The inherent beam scanning speed is calculated based on the imaging geometry of the synthetic aperture radar system. Based on the inherent beam scanning speed and a preset beam scanning factor, the system beam scanning speed required for the frequency diversity array to match the inherent beam scanning speed is determined. Based on the system beam scanning speed, the matching relationship between the frequency offset required by the frequency diversity array and the transmit pulse width is determined. The matching relationship is used to optimize the reception timing of the echo signal. Based on the transmit beam scanning characteristics of the frequency diversity array and the echo delay model of the synthetic aperture radar system, timing constraints are constructed to avoid transmit pulse interference and nadir echo interference; the available range and optimal value of the pulse repetition frequency of the synthetic aperture radar system are determined according to the timing constraints. Based on the range resolution requirements of the synthetic aperture radar system and the preset dwell factor, the physical height of the range antenna is determined; at the same time, based on the requirement to suppress grating lobes within the specified angular coverage range of the transmitting array, the spacing between adjacent array elements in the transmitting array is designed, thus completing the systematic IPB-SAR system parameter design process.

2. The method according to claim 1, characterized in that, The beam scanning factor is defined as the ratio of the system beam scanning speed of the frequency diversity array to the inherent beam scanning speed of the synthetic aperture radar system. By adjusting the beam scanning factor, the reception sequence of the echo signal is controlled to be either a conventional sequence from the near end to the far end of the mapping band, or a reverse sequence from the far end to the near end of the mapping band.

3. The method according to claim 2, characterized in that, The system beam scanning speed of the frequency diversity array is in, Indicates the width of the surveying strip. Indicates the pulse width. This represents the frequency bias. Indicates wavelength. Indicates the spacing between array elements.

4. The method according to claim 2, characterized in that, The inherent beam scanning speed of the synthetic aperture radar system is: in, Indicates the scan range. and These represent the slope distances at the far and near ends of the survey strip, respectively. It represents the speed of light.

5. The method according to claim 1, characterized in that, Determining the matching relationship between the required frequency offset and the transmit pulse width for the frequency diversity array includes: Let the beam scanning factor be ， Based on the matching relationship, the required frequency offset is: The width of the transmitted pulse is in, This represents the dwell factor, which is the ratio of the total coverage area of ​​the beam scan to the instantaneous beamwidth. and These represent the slope distances at the far and near ends of the survey strip, respectively. Represents the speed of light. Indicates wavelength. Indicates the spacing between array elements. Indicates the scan range. This represents the frequency bias.

6. The method according to claim 1, characterized in that, The timing constraints specifically include: The first constraint is used to ensure that the arrival time of the echo at any point within the mapping strip does not overlap with any transmitted pulse in time; The second constraint is used to ensure that the arrival time of the echo from any point within the mapping zone does not overlap with the echo from the nadir point in time. Based on the echo delay model, the first and second constraints are expressed as a set of inequalities about the pulse repetition frequency. Solving the set of inequalities yields the available range of the pulse repetition frequency, and the value that optimizes the system efficiency or performance is selected as the optimal value.

7. The method according to claim 6, characterized in that, The first constraint includes: when At that time, the first timing constraint is: when At that time, the first timing constraint is: in, Indicates the pulse repetition interval. Indicates the protection time. Indicates the beam scanning factor. Indicates the pulse width. Indicates the receive window redundancy time; The second constraint includes: when At that time, the second timing constraint is: when At that time, the second timing constraint is: in, This represents the dwell factor, which is the ratio of the total coverage area of ​​the beam scan to the instantaneous beamwidth. and These represent the slope distances at the far and near ends of the survey strip, respectively. Represents the speed of light. Indicates the radar platform altitude. Indicates the arrival time of the echo near the end point of the survey strip. Indicates the arrival time of the echo at the far end of the survey zone. This indicates the number of pulse cycles corresponding to the transmitted pulse. This indicates the number of pulse cycles corresponding to the sub-satellite point echo.

8. The method according to claim 1, characterized in that, The physical height of the range antenna is ,in, The residency factor, The antenna height required when using a strip pattern to cover the same mapping strip.

9. The method according to claim 1, characterized in that, The preset residence factor is in, This indicates the antenna height corresponding to the strip pattern covering the same mapping zone. Indicates the range-direction antenna height. Indicates the scan range. Indicates wavelength.

10. The method according to claim 1, characterized in that, The process of designing the spacing between adjacent elements in the transmission array includes: Based on satisfying the grating lobe suppression condition, the array element spacing is designed so that when the frequency diversity array performs intra-pulse beam scanning, no grating lobes appear in the array pattern of the frequency diversity array within the specified angular coverage range, or the grating lobes that appear fall into the zero point or low gain sidelobe region of the array element pattern.

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