Satellite-borne sar design method based on orthogonal coding and azimuth multichannel

Abstract

The application relates to a spaceborne SAR design method based on orthogonal coding and azimuth multi-channels, which comprises the following steps: deducing the relationship between the time resolution and the bandwidth of a bipolar equiprobable NRZ code; designing the sampling bandwidth based on the distance resolution requirement; designing the antenna azimuth direction sub-channel caliber based on the azimuth resolution requirement; designing the antenna distance direction caliber based on the mapping width requirement; designing the pulse repetition frequency (PRF) and the azimuth channel number; generating the bipolar equiprobable NRZ orthogonal code according to the orthogonal coding design criterion and combining a genetic algorithm; and calculating the performance indexes of the spaceborne SAR system, including the equivalent noise scattering coefficient (NESZ), the distance ambiguity and the azimuth ambiguity. The application can not only improve the distance resolution and the NESZ performance indexes of the SAR system, but also provide a wider optimization space for the design of the PRF, and can not only provide a solution for improving the performance of the spaceborne high-resolution wide-width SAR system, but also provide technical support for realizing higher resolution and larger width.

Description

Technical Field

[0001] This invention relates to the fields of aerospace technology and satellite payload technology, specifically to a spaceborne SAR design method based on orthogonal coding and azimuth multi-channel. Background Technology

[0002] Spaceborne SAR systems are radar systems mounted on a moving satellite platform that utilize range pulse compression and azimuth Doppler effects for imaging. Spaceborne SAR systems are characterized by all-weather, all-day operation and wide-area coverage, and have been widely applied in various fields such as ocean observation, forest monitoring, urban mapping, environmental disaster mitigation, and military reconnaissance, achieving significant results.

[0003] The United States launched its first SAR satellite in 1978, and in the past fifty years, hundreds of SAR satellites have been launched by various countries. Spaceborne SAR systems are progressing towards acquiring richer and more detailed information, with high-resolution and wide-swath SAR being one of the important directions in their development. However, traditional single-channel spaceborne SAR systems suffer from a contradiction between high resolution and large mapping swath width, making them unable to meet the urgent needs of both civilian and military applications.

[0004] Azimuth multi-channel technology is an important approach to achieving high-resolution and wide-swath satellite SAR. Recent research has mainly focused on imaging algorithms for azimuth multi-channel systems, scanning and TOPS mode optimization design, and phased array antenna design. However, it has the following main shortcomings:

[0005] 1) Existing technologies only mention that orthogonal coding has a certain suppressive effect on the range ambiguity of SAR systems, but research on the impact of orthogonal coding on other performance indicators of spaceborne high-resolution wide-swath SAR is relatively rare.

[0006] 2) In the existing technology, the use of bipolar equal probability NRZ orthogonal coding technology is rarely used to address the urgent need for high resolution and wide swath in spaceborne SAR systems.

[0007] 3) During the design of PRF values ​​for spaceborne SAR systems, various conditions and factors limit the range of PRF values ​​at certain positions, posing challenges to the optimal design of the SAR system. Existing technologies do not offer effective solutions to these PRF design problems. Summary of the Invention

[0008] In view of the above-mentioned technical problems, this invention proposes a spaceborne SAR design method based on orthogonal coding and azimuth multi-channel, which can improve the range resolution and NESZ performance of SAR system, and provide a wider optimization space for PRF design; it not only provides a solution for improving the performance of spaceborne high-resolution wide-swath SAR system, but also provides technical support for achieving higher resolution and wider swath.

[0009] The technical solution to the technical problem of this invention is: a spaceborne SAR design method based on orthogonal coding and azimuth multi-channel, comprising the following steps:

[0010] Step S1: Derive the relationship between the time resolution and bandwidth of bipolar equal probability NRZ codes;

[0011] Step S2: Design the sampling bandwidth based on the distance resolution requirements;

[0012] Step S3: Design the antenna azimuth sub-channel aperture based on the azimuth resolution requirements;

[0013] Step S4: Design the antenna range-direction aperture based on the required swath width;

[0014] Step S5: Design the pulse repetition frequency (PRF) and the number of azimuth channels;

[0015] Step S6: Generate bipolar equal probability NRZ orthogonal codes based on the orthogonal coding design criteria and combined with a genetic algorithm;

[0016] Step S7: Calculate the performance indicators of the spaceborne SAR system, including the equivalent noise scattering coefficient NESZ, range ambiguity, and azimuth ambiguity.

[0017] According to one technical solution of the present invention, step S1 includes:

[0018] Step S11: Derive the power spectral density of the bipolar NRZ code based on its spectrum:

[0019]

[0020] in, For the symbol period, Power spectral density;

[0021] Step S12: Calculate the 3dB bandwidth of the bipolar equal probability NRZ code based on the power spectral density: ;

[0022] Step S13: Derive the pulse compression function of the bipolar equal probability NRZ code. , is represented as:

[0023]

[0024] in, The code period;

[0025] Step S14: Determine the time resolution of the bipolar equiprobability NRZ code. Therefore, the relationship between 3dB bandwidth and time resolution is obtained as follows: .

[0026] According to one technical solution of the present invention, step S2 includes:

[0027] Step S21, with distance resolution and beam incident angle For input conditions;

[0028] Step S22: Calculate the sampling bandwidth based on the relationship between the time resolution and bandwidth of bipolar equiprobability NRZ codes. , is represented as:

[0029]

[0030] Where c is the speed of light.

[0031] According to one technical solution of the present invention, in step S3, based on the relationship between the azimuth resolution of the strip mode and the aperture of the antenna azimuth sub-channel, the azimuth resolution is... Design the antenna azimuth sub-channel aperture for input. The relational expression is:

[0032]

[0033] in, This is the azimuth signal processing broadening factor.

[0034] According to one technical solution of the present invention, step S4 includes:

[0035] Step S41: Calculate the downward viewing angle corresponding to the imaging center point based on satellite orbit parameters and radar wavelength. ;

[0036] Step S42: Calculate the initial aperture value based on the antenna distance. Calculate the 3dB beamwidth in the antenna range direction. ;

[0037] Step S43: The downward viewing angle corresponding to the imaging center point 3dB beamwidth in the direction of antenna distance Calculate the perihelion angle separately and the perspective from a distance Perimeter perspective and orbital height Calculate the angle of incidence at perigee and the geocentric angle From the perspective of the far point and orbital height Calculate the angle of incidence at the apogee and the geocentric angle ;

[0038] Step S44: Calculate the survey width based on the geocentric angles at perigee and apogee. And iteratively adjust the antenna range towards the aperture. Until the required survey width is met.

[0039] According to one technical solution of the present invention, step S5 includes:

[0040] Step S51: Based on the azimuth multi-channel system, determine whether the PRF and the number of azimuth channels meet the azimuth sampling bandwidth requirements.

[0041] in, For PRF, This represents the number of azimuth channels. For oversampling rate, The Doppler bandwidth corresponding to the 3dB azimuth beam is expressed as:

[0042]

[0043] in, For the satellite's flight speed;

[0044] Step S52: Based on orthogonal coding, when designing the PRF, the echo window does not avoid the nadir echo, but only satisfies that the echo within the mapping zone is within the echo window. The specific expression is:

[0045]

[0046] in, This is the slant distance from the perigee. The slant distance at the apogee. For the transmission pulse duration, The guard time between the transmitted pulse and the echo window. Let c be a positive integer, and c be the speed of light.

[0047] Step S53: Taking into account antenna size, performance indicators and timing relationships, determine the PRF and the number of azimuth channels.

[0048] According to one technical solution of the present invention, the design criteria for the number of orthogonal encoded signals in step S6 specifically include:

[0049] Step S61: Calculate the echo window number P of the first pulse's nadir point echo arrival and the echo window number Q of the first pulse echo arrival within the surveying zone, where Q>P.

[0050] Step S62: The initial value of the number of orthogonally encoded signals is at least 2.

[0051] when The remainder is 0, which means that within the Q-th echo window, the first pulse echo and the Q-P+1-th pulse echo in the mapping band use mutually orthogonal encoded signals and can be separated without increasing the number of signals.

[0052] when If the remainder is 1, it means that within the Q-th echo window, the 1st pulse echo and the (Q-P+1)th pulse echo within the mapping strip both use the same encoding method and cannot be separated. Therefore, one more signal is added to the two signal types to make... The remainder is not equal to 1; if The remainder is still equal to 1. Therefore, two more signal types need to be added to the base of the two signal types to make... The remainder is not equal to 1;

[0053] Step S63: The number of orthogonal coded signals is positively correlated with the distance ambiguity; the larger the number of signals, the better the distance ambiguity performance. An initial value for the number of orthogonal coded signals is typically used. ≥3:

[0054] when The remainder is not equal to 1. The number of signals can meet the requirements;

[0055] when The remainder is 1, and we need to... Add one more signal to the existing number of signals, making The remainder is not equal to 1;

[0056] In step S6, the process of generating bipolar equiprobable NRZ orthogonal codes based on genetic algorithms specifically includes:

[0057] Step S64: Generate the fitness function, the expression of which is:

[0058]

[0059] in, The optimal weights for autocorrelation and cross-correlation performance are used.

[0060] Step S65, Parameter Encoding: Map the positive integer sequence generated by the genetic algorithm to a "+1 / -1" sequence of bipolar equal probability NRZ codes;

[0061] Step S66: Initialize the population: According to the constraints of the above steps, randomly generate multiple L*N dimensional vectors as the initial individuals of the population.

[0062] Step S67: Calculate the fitness function of the current population: If the change in fitness function is less than the preset threshold, stop the iteration and convert the current population into a bipolar equiprobable NRZ orthogonal coding sequence; if not, perform selection, crossover, and mutation operations of the genetic algorithm to generate a new population, repeat the calculation of the fitness function of the new population and determine the iteration stopping condition until the requirements are met.

[0063] According to one technical solution of the present invention, step S7 includes:

[0064] Step S71: Based on the SAR system signal-to-noise ratio formula

[0065] in, For peak transmission power, For the effective gain of the antenna transmission, For the effective gain of the antenna reception, For wavelength, The normalized backscattering coefficient, Pulse repetition frequency, For distance-to-ground resolution, Slope distance For satellite speed, For system losses, Boltzmann's constant, For noise temperature, Noise figure For bandwidth,

[0066] Substituting the bandwidth and time resolution relationship into the bipolar equal-probability NRZ code:

[0067]

[0068] in, Average power;

[0069] Step S72: When the signal-to-noise ratio is 0dB, calculate the NESZ of a single channel, expressed as:

[0070]

[0071] The NESZ of a multi-channel bipolar equal-probability NRZ code is calculated as follows: ;

[0072] Step S73, the distance ambiguity of orthogonal coding is:

[0073] ;

[0074] As can be seen from the above formula for the distance ambiguity of orthogonal coding, the distance ambiguity power of orthogonal coding only needs to be calculated by the first... The power of the ambiguity zone is calculated, but the power of other ambiguity zones does not need to be calculated. As the number of coded signals increases, the distance ambiguity performance will be greatly improved.

[0075] Step S74, the expression for calculating the azimuth ambiguity is:

[0076]

[0077] in, This represents the total blur power resulting from aliasing after reconstruction. This is the radiation pattern of the transmitting antenna. The receiving antenna pattern for the j-th channel is shown below. The center of the Doppler frequency.

[0078] Compared with the prior art, the present invention has the following beneficial effects:

[0079] This invention discloses a spaceborne SAR design method based on orthogonal coding and azimuth multi-channel technology. By using bipolar equal-probability NRZ codes for orthogonal coding and combining them with azimuth multi-channel technology, this invention significantly improves the range resolution and equivalent noise scattering coefficient (NESZ) performance of the spaceborne SAR system, thereby enhancing key system performance indicators. Compared with traditional linear frequency modulated signals, bipolar equal-probability NRZ codes achieve higher range resolution within the same bandwidth, and reduce NESZ by approximately 2.86 dB, thus improving the signal-to-noise ratio and sensitivity of the image.

[0080] This invention utilizes the characteristics of orthogonal coding, enabling PRF design to avoid nadir echoes. Even if the nadir echo and the echo within the mapping zone are in the same echo window, signal separation can be achieved through pulse compression. This breaks through the limitations of traditional PRFs constrained by nadir echoes, providing a wider space for PRF optimization, enhancing the flexibility and adaptability of system design, and expanding the design space of pulse repetition frequency (PRF).

[0081] Through the collaborative design of azimuth multi-channel technology and orthogonal coding, this invention realizes an architecture for transmitting wide beams with a small aperture antenna and receiving echoes through multiple channels. Combined with the signal separation capability of orthogonal coding, it effectively suppresses range ambiguity and azimuth ambiguity, improves the performance of range ambiguity and azimuth ambiguity, meets the imaging requirements of high-resolution wide-swath SAR systems, and optimizes the performance of high-resolution wide-swath SAR systems.

[0082] This invention proposes a complete parameter design process for spaceborne SAR systems, providing a comprehensive and accurate system design method, including the derivation of the relationship between time resolution and bandwidth of bipolar equal probability NRZ codes, sampling bandwidth design, antenna azimuth and range aperture design, PRF and azimuth channel number design, orthogonal coding design, and performance index calculation methods. This process ensures the comprehensiveness and accuracy of system parameter design and reduces design complexity.

[0083] This invention employs a genetic algorithm for the optimized design of bipolar equal-probability NRZ orthogonal coding. By evaluating autocorrelation and cross-correlation performance through an adaptive degree function, it generates orthogonal coding sequences with low sidelobes and low cross-correlation. This method improves the efficiency and quality of coding design and further enhances the system's anti-interference capability and imaging reliability.

[0084] The method of this invention is applicable to various spaceborne SAR operating modes (such as strip mode, spotlight mode, etc.), and the parameters can be adjusted according to different mission requirements. Its modular and standardized design philosophy supports system upgrades and functional expansion, providing technical support for the widespread application of spaceborne SAR systems.

[0085] This invention organically combines orthogonal coding and azimuth multi-channel technology through an integrated design method, reducing the iterative process in system design and improving the development efficiency and engineering feasibility of spaceborne SAR systems. Attached Figure Description

[0086] Figure 1 This is a flowchart illustrating a spaceborne SAR design method based on orthogonal coding and azimuth multi-channel in one embodiment of the present invention.

[0087] Figure 2 This is a design flow for generating bipolar equiprobability NRZ orthogonal codes in one embodiment of the present invention;

[0088] Figure 3 This is an example of the optimization process of a genetic algorithm in one embodiment of the present invention;

[0089] Figure 4 The autocorrelation function of the encoded signal 1;

[0090] Figure 5 The autocorrelation function of the encoded signal 2;

[0091] Figure 6 The autocorrelation function of the encoded signal 3;

[0092] Figure 7 The autocorrelation function of the encoded signal;

[0093] Figure 8 Let be the cross-correlation function of coded signal 1 and coded signal 2;

[0094] Figure 9 This is the cross-correlation function of coded signal 1 and coded signal 3;

[0095] Figure 10 This is the cross-correlation function of coded signal 1 and coded signal 4;

[0096] Figure 11 The cross-correlation function of coded signal 2 and coded signal 3;

[0097] Figure 12 The cross-correlation function of coded signal 2 and coded signal 4;

[0098] Figure 13 This is the cross-correlation function of coded signal 3 and coded signal 4. Detailed Implementation

[0099] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments. The embodiments cannot be described in detail here, but the embodiments of the present invention are not limited to the following embodiments.

[0100] The SAR system design method flow of this invention is as follows: Figure 1 As shown. Spaceborne SAR system design involves numerous parameters that are closely related. This paper focuses on the design of SAR system parameters, starting with two key technologies that can improve SAR system performance: orthogonal coding and azimuth multi-channel.

[0101] First, the spectrum and pulse compression function of the bipolar equal-probability NRZ code are derived from the spectrum of the bipolar NRZ code. Furthermore, the relationship between the time resolution and bandwidth of the bipolar equal-probability NRZ code is derived. Based on this, the sampling bandwidth under different downward viewing angles is designed using range resolution as input. According to the design principles of azimuth multi-channel, the aperture of the antenna azimuth sub-channel is designed using azimuth resolution as input.

[0102] Secondly, given the known orbital parameters and radar center frequency, the satellite orbital altitude is derived from the satellite orbital parameters. Using the mapping swath width as a design constraint, the relationship between the four parameters—satellite orbital altitude, antenna range-direction aperture, mapping swath width, and downward viewing angle—is applied to design the antenna range-direction aperture under different downward viewing angles.

[0103] Next, the satellite's flight velocity is calculated from the satellite's orbital parameters. Taking into account the antenna range aperture, antenna azimuth aperture, NESZ, range ambiguity, azimuth ambiguity, and the timing relationship between transmission and reception, the PRF and the number of azimuth channels are designed. A bipolar equal-probability NRZ orthogonal code is designed using the MATLAB genetic algorithm toolbox.

[0104] Finally, the calculation method for the performance index parameters of SAR system design is given, and the calculation formulas for the two performance indices, NESZ and range ambiguity, are derived in detail. Figure 1 The gray boxes represent performance metrics.

[0105] The present invention provides a spaceborne SAR design method based on orthogonal coding and azimuth multi-channel, comprising the following steps:

[0106] Step S1: Derive the relationship between the time resolution and bandwidth of bipolar equal probability NRZ codes;

[0107] Bipolar NRZ code consists of multiple waveforms representing +1 and multiple waveforms representing -1, and the waveform representing +1... The waveform representing -1 The relationship between them is:

[0108]

[0109] The above The spectrum function is:

[0110]

[0111] The power spectrum of bipolar NRZ codes is derived from "Principles of Communication (5th Edition)" edited by Fan Changxin. for:

[0112]

[0113] in , Let P be the probability of the value +1, and 1-P be the probability of the value -1. Substituting these values, we get:

[0114]

[0115] For ease of calculation, the probabilities of +1 and -1 can be equalized during the design process, i.e., P=0.5. The power spectral density of the bipolar equal-probability NRZ code is then obtained as:

[0116]

[0117] Therefore, the 3dB bandwidth of the bipolar equal-probability NRZ code is... .

[0118] The inverse Fourier transform of the power spectrum is the autocorrelation function, which is also known as impulse compression. We have:

[0119]

[0120] Among the symbols This represents the Fourier transform and the inverse Fourier transform. Represents convolution. The pulse compression time-domain expression for bipolar equal-probability NRZ codes. That is, autocorrelation function for:

[0121]

[0122] From the above formula, we can see that:

[0123] 1) The pulse compression function of bipolar equal probability NRZ codes has only a main lobe and no side lobes. Compared with the pulse compression function of linear frequency modulated signals, which has a maximum side lobe of -13dB, bipolar equal probability NRZ codes have a significant advantage.

[0124] 2) The 3dB width of the square of the pulse compression function is the time resolution. The time resolution of bipolar equal probability NRZ codes is: .

[0125] As mentioned above, the 3dB bandwidth of a bipolar equiprobable NRZ code is... The relationship between bandwidth and time resolution for bipolar equal-probability NRZ codes is as follows: .

[0126] Step S2: Design the sampling bandwidth based on the distance resolution requirements;

[0127] Time resolution With range resolution The relationship is:

[0128]

[0129] in Let be the radar beam incident angle. The relationship between the bandwidth and time resolution of the bipolar equal-probability NRZ code in step S1 is then discussed. Substituting the values, the relationship between sampling bandwidth and range resolution is as follows:

[0130]

[0131] Therefore, the sampling bandwidth is designed with range resolution and beam incidence angle as input conditions.

[0132] Step S3: Design the antenna azimuth sub-channel aperture based on the azimuth resolution requirements;

[0133] Strip mode azimuth resolution Antenna azimuth sub-channel aperture The relationship is:

[0134]

[0135] in, This is the azimuth signal processing broadening factor. Therefore, the design of the antenna azimuth sub-channel aperture is based on azimuth resolution as an input condition.

[0136] Step S4: Design the antenna range-direction aperture based on the required swath width;

[0137] Given radar wavelength Given that satellite orbital parameters are the design inputs, the antenna range-direction aperture design must meet the requirements of the mapping swath width.

[0138] First, the downward angle corresponding to the imaging center point is calculated from the ground imaging center point and satellite orbit parameters. The initial value of the antenna distance to the aperture. Calculate the 3dB beamwidth in the antenna range direction. Secondly, the downward angle corresponding to the imaging center point. 3dB beamwidth in the direction of antenna distance Calculate the perihelion angle separately and the perspective from a distance Again, from a near-field perspective... and orbital height Calculate the angle of incidence at perigee and the geocentric angle Similarly, from the perspective of the far point and orbital height Calculate the angle of incidence at the apogee and the geocentric angle Finally, from the perigee's central angle... and the geocentric angle of the apogee Calculate the width of the survey sheet If the calculated survey width Smaller than the required survey width This will modify the antenna range towards the aperture. This continues until the required survey width is met. The specific calculation expression is as follows:

[0139]

[0140]

[0141]

[0142]

[0143]

[0144]

[0145]

[0146]

[0147]

[0148] in, This is the radius of Earth's orbit.

[0149] Step S5: Design the pulse repetition frequency (PRF) and the number of azimuth channels;

[0150] In an azimuth multi-channel SAR system, the PRF and the number of azimuth channels must meet the azimuth sampling bandwidth requirements, namely:

[0151]

[0152] in, For PRF, This represents the number of azimuth channels. For oversampling rate, The Doppler bandwidth corresponding to the 3dB azimuth beam is:

[0153]

[0154] in, The satellite's flight speed is given. The PRF design is similar to a single-channel design, but due to the use of orthogonal coding, it's possible to design code groups where the nadir echo and the echo within the mapping zone are orthogonal. Even if the nadir echo and the echo within the mapping zone are within the same echo window, the echo signal within the mapping zone can still be separated after pulse compression. Therefore, the echo window in the PRF design does not need to avoid the nadir echo; it only needs to ensure that the echo within the mapping zone is within the echo window. The specific expression is:

[0155]

[0156] in, This is the slant distance from the perigee. The slant distance at the apogee. For the transmission pulse duration, The guard time between the transmitted pulse and the echo window. is a positive integer, and c is the speed of light.

[0157] This design employs a multi-beam technique with an azimuth offset phase center. A small-aperture antenna transmits pulse signals to achieve wide-band coverage. During reception, multiple wide-beam channels with offset phase centers in the azimuth direction are used to receive the echoes. In this way, multiple azimuth sampling points can be obtained within a single azimuth sampling time. If the selected PRF (Positioning Resonance Filter) satisfies the requirement of spatially uniform distribution throughout the sampling process, a simple rearrangement of the multi-channel echoes can yield echo data equivalent to a traditional single-channel echo. A PRF that satisfies a spatially uniform sampling distribution is considered an ideal PRF. However, the selection of the PRF is also constrained by the aforementioned timing relationship, and ideal PRFs are typically not selected. When the actual PRF deviates from the ideal PRF, the azimuth sampling points exhibit a periodic, non-uniform distribution, requiring a multi-channel reconstruction algorithm to obtain azimuth echo information similar to that of a single channel.

[0158] Furthermore, the design of the PRF is also constrained by performance metrics such as NESZ, range ambiguity, and azimuth ambiguity. Therefore, the PRF is designed by comprehensively considering azimuth multi-channel design, performance metrics, antenna size, and transmit / receive timing relationships.

[0159] Step S6: Generate bipolar equal probability NRZ orthogonal codes based on the orthogonal coding design criteria and combined with a genetic algorithm;

[0160] Design principles of orthogonal coding

[0161] In a signal set There is One signal, namely Define the autocorrelation function The cross-correlation function is :

[0162]

[0163] If the above autocorrelation function and cross-correlation function satisfy:

[0164]

[0165] Such a signal set is called an ideal orthogonal signal set. In reality, it is difficult to obtain an ideal orthogonal signal set; most orthogonal signal sets are quasi-orthogonal signal sets. Quasi-orthogonal signal sets minimize the sidelobes of the autocorrelation function and the cross-correlation function, expressed as:

[0166]

[0167] The design principle for orthogonal coded signals is to apply the design principles for orthogonal continuous signals to discrete coding. That is, for a discrete signal set with a code length of N and L signals, When its autocorrelation function and cross-correlation function satisfy the following conditions:

[0168]

[0169] This discrete signal set is then called an orthogonal coded signal set. Let be the autocorrelation function of the discrete signal. Let be the cross-correlation function of the discrete signal. These are the optimized weights for autocorrelation and cross-correlation performance. and The expression is:

[0170]

[0171] Design criteria for orthogonal coded signal numbers

[0172] Given the aforementioned PRF design values, the nadir echo of the first pulse arrives in the P-th echo window, and the echo of the first pulse within the mapping zone arrives in the Q-th echo window, where Q > P. Within the Q-th echo window, there is not only the echo of the first pulse within the mapping zone but also the nadir echo of the (Q-P+1)-th pulse. To distinguish between the echoes, the first pulse and the (Q-P+1)-th pulse need to transmit orthogonal coded signals. Therefore, the number of orthogonally coded signals is at least 2.

[0173] When the initial number of signals for orthogonal coding is 2, there are two possible scenarios:

[0174] 1) When The remainder is 0, indicating that within the Q-th echo window, the 1st pulse echo and the (Q-P+1)th pulse echo within the mapping band use mutually orthogonal coded signals and can be separated. In this case, there is no need to increase the number of signals.

[0175] 2) When The remainder is 1, indicating that within the Q-th echo window, the 1st pulse echo and the (Q-P+1)th pulse echo within the mapping strip both use the same encoding method and cannot be separated. Therefore, one more signal type needs to be added to the existing two signal types to achieve this. The remainder is not equal to 1. If The remainder is still equal to 1. Therefore, two more signal types need to be added to the base of the two signal types to make... The remainder is not equal to 1.

[0176] The number of signals in orthogonal coding is related to the range ambiguity; the larger the number of signals, the better the range ambiguity performance. See step S7 for details. To obtain better SAR image performance, the initial value of the number of signals in orthogonal coding is usually greater than 2. When the initial value of the number of signals in orthogonal coding is... ( When ≥3), there are two possible scenarios:

[0177] 1) When The remainder is not equal to 1. The number of signals is sufficient to meet the requirements.

[0178] 2) When The remainder is 1, and we need to... Add one more signal to the existing number of signals, making The remainder is not equal to 1.

[0179] Design process of bipolar equal probability NRZ orthogonal coding based on genetic algorithm

[0180] Genetic algorithms are algorithms that simulate the inheritance of biological genes. After encoding an initial population, they apply certain operations to the individuals in the population according to their fitness to the environment, thereby achieving an evolutionary process of survival of the fittest. Genetic algorithms can optimize the solution to a problem generation by generation, approaching the optimal solution.

[0181] This design utilizes the MATLAB Genetic Algorithm Toolbox to generate bipolar equal-probability NRZ orthogonal codes. The design process is as follows: Figure 2 As shown, firstly, based on the design requirements of bipolar equal-probability NRZ orthogonal coding, a fitness function is generated. Then, the parameters in the fitness function calculation process are encoded to establish a mapping relationship with the genetic algorithm optimization criteria. Based on this, the population is initialized, and the fitness function of the existing population is calculated. If the fitness function or other parameters satisfy the algorithm's stopping condition, the algorithm terminates, and the existing population is transformed into an orthogonal coding sequence. If not, the genetic algorithm performs replication, crossover, and mutation operations according to the set state to generate a new population. Finally, the fitness function of the new population is calculated, and it is determined whether the algorithm's stopping condition is met; this process is iterated repeatedly. The main design flow is detailed below.

[0182] (1) Generate the fitness function. The optimization criterion of the MATLAB genetic algorithm is to find the minimum value of the fitness function. According to the design criteria of orthogonal coding, it is necessary to first generate the autocorrelation function and cross-correlation function of the coded signal, then find the maximum value of the sidelobe of the autocorrelation function and the maximum value of the cross-correlation function, and finally find the sum of these two as the fitness function. The autocorrelation function and cross-correlation function can be obtained by using the normalized cross-correlation function xcorr in MATLAB. The code length is N, the first... The autocorrelation function of a signal can be expressed as: Its largest side lobe is represented as The maximum value of the autocorrelation sidelobes in the L signals is: . No. The signal and the first The maximum value of the cross-correlation function of the signals can be expressed as: The maximum value of the cross-correlation function among the L signals is: Therefore, the fitness function is:

[0183]

[0184] in, The weights are used to optimize the autocorrelation and cross-correlation performance. Furthermore, the generated orthogonal codes must satisfy equal probabilities of +1 and -1.

[0185] (2) Parameter set encoding. Since the MATLAB genetic algorithm toolbox cannot directly generate encoded sequences consisting of +1 and -1, but can generate sequences consisting of positive integers, this design uses a sequence consisting of positive integers 1 and 2, and then maps the generated sequence to a sequence consisting of +1 and -1.

[0186] (3) Initialize the population. According to the constraints of the above steps, randomly generate multiple L*N dimensional vectors as the initial individuals of the population.

[0187] (4) Fitness function evaluation. The L*N dimensional individuals of the population are transformed one by one into L orthogonal coding sequences of length N represented by +1 and -1, and their fitness functions are calculated.

[0188] (5) Conditions for algorithm termination. In the Matlab Genetic Algorithm Toolbox, the conditions for algorithm termination include: exceeding the maximum number of iterations, running time exceeding the time limit, fitness function threshold being exceeded, fitness function showing no improvement for a certain number of consecutive generations, and fitness function change being less than the threshold, etc. This design chooses fitness function change being less than a certain threshold as the algorithm termination condition.

[0189] (6) Genetic Algorithm Operation: Selection. Selection algorithms include: elite individual selection algorithm and crossover ratio selection algorithm. The elite individual selection algorithm selects individuals with better fitness functions from the existing population without performing crossover or mutation operations. The crossover ratio selection algorithm determines the percentage of individuals in the existing population that will be the parents of the next generation. This design chooses the crossover ratio selection algorithm.

[0190] (7) Genetic Algorithm Operation: Crossover. Crossover algorithms include: dispersed crossover, single-point crossover, two-point crossover, intermediate crossover, heuristic crossover, and arithmetic crossover. This design chooses heuristic crossover.

[0191] (8) Genetic Algorithm Operation: Mutation. Mutation algorithms include: constraint-based automatic adjustment algorithm, Gaussian algorithm, uniform distribution algorithm, and adaptive feasible solution generation algorithm. This design selects the Gaussian algorithm.

[0192] Step S7: Calculate the performance indicators of the spaceborne SAR system, including the equivalent noise scattering coefficient NESZ, range ambiguity, and azimuth ambiguity.

[0193] The performance indicators analysis of the SAR system design includes: range resolution, azimuth resolution, swath width, NESZ, range ambiguity, and azimuth ambiguity. Range resolution has been explained in step S2, azimuth resolution in step S3, and swath width in step S4, and will not be repeated here.

[0194] I. NESZ

[0195] As shown in step S1, the bandwidth and time resolution of bipolar equal probability NRZ codes are significantly different from those of linear frequency modulated signals. Therefore, the NESZ of bipolar equal probability NRZ codes are also significantly different. The derivation process is as follows.

[0196] From "Synthetic Aperture Radar Design Technology", the signal-to-noise ratio of a SAR system is:

[0197]

[0198] in For peak transmission power, For the effective gain of the antenna transmission, For the effective gain of the antenna reception, For wavelength, The normalized backscattering coefficient, Pulse repetition frequency, For distance-to-ground resolution, Slope distance For satellite speed, For system losses, Boltzmann's constant, For noise temperature, Noise figure For bandwidth.

[0199] Based on step S1, the relationship between the bandwidth and temporal resolution of bipolar equiprobable NRZ symbols is as follows:

[0200]

[0201] in For the average power, substituting the above formula into the SNR formula yields:

[0202]

[0203] When the signal-to-noise ratio is 0dB, the NESZ is:

[0204]

[0205] The NESZ of a linear frequency modulated signal is:

[0206]

[0207] Comparing the NESZ of bipolar equal-probability NRZ codes and linear frequency modulated (LFM) signals, it can be seen that the NESZ of bipolar equal-probability NRZ codes has an additional coefficient of 1.9375 in the denominator, meaning that the NESZ of bipolar equal-probability NRZ codes is reduced by 2.86 dB. With other parameters remaining the same, using bipolar equal-probability NRZ codes improves the NESZ performance by 2.86 dB compared to using LFM signals.

[0208] The above discussion covered the NESZ of single-channel bipolar equal-probability NRZ codes. Applying the NESZ results of multi-channel linear frequency modulated (LFM) signal azimuth, the NESZ of multi-channel bipolar equal-probability NRZ codes is given as follows:

[0209]

[0210] Compared to single-channel NESZ, multi-channel NESZ increases the signal-to-noise ratio loss factor due to multi-channel signal reconstruction at the molecular level. The number of channels was increased in the denominator. If an ideal PRF is used, the signal-to-noise ratio loss factor is... The expression is: 1.

[0211]

[0212] These represent the coefficients of the reconstruction filter. Indicates the Doppler bandwidth. This indicates calculating the average value.

[0213] II. Distance Ambiguity

[0214] The range ambiguity function for a SAR system using linear frequency modulated signals is:

[0215]

[0216] in Let be the power of the j-th blurred region at the i-th (i=1,...,K) sampling point, where j typically ranges from -10 to 10. Let be the useful echo power at the i-th sampling point.

[0217] When sampling orthogonal coding is used, the j-th ( The power of each ambiguity region is orthogonal to the useful echo of the main lobe, and can be separated during pulse compression without causing ambiguity in the main lobe echo. Therefore, the distance ambiguity of orthogonal coding is:

[0218]

[0219] As can be seen from the above formula for the distance ambiguity of orthogonal coding, the distance ambiguity power of orthogonal coding only needs to be calculated in the first... The power of the ambiguity region is calculated, but the power of other ambiguity regions does not need to be calculated. As the number of coded signals increases, the distance ambiguity performance will be greatly improved.

[0220] III. Orientation Ambiguity

[0221] The azimuth multi-channel signal needs to undergo signal reconstruction processing before imaging, so the azimuth blur energy is also affected by the reconstruction algorithm. The expression for calculating the azimuth blur is:

[0222]

[0223] in This represents the total blur power resulting from aliasing after reconstruction. This is the radiation pattern of the transmitting antenna. The receiving antenna pattern for the j-th channel is shown below. The center of the Doppler frequency.

[0224] According to the design method of this invention, a spaceborne SAR system with a strip mode resolution of 1 meter and a swath width of 100 km is designed using a bipolar equal probability NRZ orthogonal code, with an orbital altitude of 450 km and a radar center frequency of 10 GHz. The design parameters and performance parameters are given for center downward viewing angles of 20 degrees, 30 degrees, 40 degrees and 50 degrees respectively.

[0225] Based on the relationship between sampling bandwidth, range resolution, and incident angle given in step S2, the sampling bandwidth and range resolution for center-downward viewing angles of 20 degrees, 30 degrees, 40 degrees, and 50 degrees are calculated, as shown in Table 1. Table 1 also lists the range resolution of linear frequency modulated (LFM) signals under the same bandwidth and incident angle. It can be seen from Table 1 that, when using the same bandwidth and incident angle, the bipolar equal-probability NRZ orthogonal code achieves a higher range resolution than the LFM signal.

[0226]

[0227] Table 1 Distance resolution and bandwidth

[0228] According to the relationship between the strip mode azimuth resolution and the antenna azimuth sub-channel aperture given in step S3, the antenna azimuth sub-channel aperture is 1.9m to achieve a strip mode resolution of 1m.

[0229] Based on the relationship between antenna range-direction aperture and swath width given in step S4, the antenna range-direction aperture, perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee perigee, and swath width are calculated for 20°, 30°, 40°, and 50°, as well as the swath width, as shown in Table 2. Table 2 shows that to meet the requirement of a 100km swath width for different perigee perigee perigee, the antenna range-direction aperture varies. In practical engineering, the largest range-direction antenna aperture is used as the design value, and other range-direction antenna apertures can be achieved using beamforming technology.

[0230]

[0231] Table 2 Antenna Range Aperture and Mapping Width

[0232] According to the PRF design criteria given in step S5, and taking into account the multi-beam technology based on the azimuth offset phase center and the azimuth ambiguity, the number of channels is designed to be 5. The PRF design values ​​at center down-angles of 20 degrees, 30 degrees, 40 degrees and 50 degrees are shown in Table 3.

[0233]

[0234] Table 3 PRF Design Values

[0235] Following the design process of the bipolar equal-probability NRZ orthogonal coding given in step S6, a MATLAB-based genetic algorithm is used, taking into account distance ambiguity, to design a signal count of 4 and a code length of 2000. The iterative optimization process of the genetic algorithm is as follows: Figure 3 As shown in the figure, after more than 300 generations of iterative calculations, the fitness function no longer changes and tends to stabilize, at which point the iterative algorithm stops. The autocorrelation function and cross-correlation function of the designed bipolar equal-probability NRZ orthogonal code are as follows: Figures 4-13 As shown in Table 4, the maximum sidelobes of the autocorrelation of the encoded signals 1 to 4 range from -26.74 dB to -26.56 dB. The maximum cross-correlation values ​​of the encoded signals range from -25.11 dB to -25.05 dB, as shown in Table 5.

[0236]

[0237] Table 4. Maximum sidelobe values ​​of the autocorrelation function

[0238]

[0239] Table 5. Maximum values ​​of cross-correlation function (dB)

[0240] Table 6 lists the design parameters and performance requirements of the SAR system in this design example. Following the method for calculating the NESZ, range ambiguity, and azimuth ambiguity given in step S7, the NESZ of the imaging center point and the NESZ at the perigee and apogee are calculated for center-downward viewing angles of 20°, 30°, 40°, and 50°, as shown in Table 7. Table 7 also lists the antenna transmit gain, receive gain, and average transmit power. Table 7 shows that the optimal NESZ is -27.02dB, and the worst NESZ is -20.07dB, meeting the NESZ design requirements. Table 8 presents the calculation results for range ambiguity and azimuth ambiguity. It shows that the range ambiguity ranges from -61.98dB to -53.75dB, meeting the performance requirements. Compared to the range ambiguity of approximately -30dB obtained using linear frequency modulated signals in related literature, orthogonal coding significantly improves this performance indicator. The azimuth ambiguity ranges from -25.35dB to -24.49dB, meeting the performance requirements.

[0241]

[0242] Table 6 SAR System Design Parameters

[0243]

[0244] Table 7 NESZ

[0245]

[0246] Table 8 Distance Ambiguity and Orientation Ambiguity

[0247] According to one aspect of the present invention, a spaceborne SAR system is proposed, designed using a spaceborne SAR design method based on orthogonal coding and azimuth multi-channel as described in any of the above technical solutions, comprising:

[0248] The orthogonal coding module is used to generate bipolar equal-probability NRZ orthogonal codes;

[0249] Azimuth multi-channel module, used to realize azimuth multi-beam reception;

[0250] The parameter design module is used to perform the design of sampling bandwidth, antenna aperture, PRF, and number of channels;

[0251] The performance evaluation module is used to calculate NESZ and distance ambiguity.

[0252] In summary, the design method of this invention derives the relationship between the time resolution and bandwidth of bipolar NRZ codes based on the spectrum of bipolar NRZ codes, providing theoretical support for the performance evaluation of SAR systems using this coding method.

[0253] Based on the derivation of the relationship between the time resolution and bandwidth of the bipolar equal probability NRZ code, the design method of this invention further derives the analytical expression for the improvement of the range resolution and NESZ performance of the SAR system by this coding method.

[0254] In existing technologies, azimuth multi-channel is an important approach to achieving high resolution and wide swath width. However, in the specific PRF design process, it is subject to timing constraints such as azimuth ambiguity, antenna aperture, NESZ, and avoiding nadir echoes. This results in a narrow PRF value space at some positions, which also brings difficulties to subsequent multi-channel reconstruction algorithms. To address these issues, this invention adopts orthogonal coding, which frees the PRF design from the constraint of avoiding nadir echoes. This not only provides a solution for optimal PRF design but also provides technical support for achieving higher resolution and wider swath width.

[0255] It should also be noted that, in this document, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0256] Finally, it should be noted that the above description represents a preferred embodiment of the present invention. It should be pointed out that although preferred embodiments have been described, those skilled in the art, once they understand the basic inventive concept of the present invention, can make various improvements and modifications without departing from the principles described herein. These improvements and modifications should also be considered within the scope of protection of the present invention. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the embodiments of the present invention.

Claims

1. A spaceborne SAR design method based on orthogonal coding and azimuth multi-channel, characterized in that, Includes the following steps: Step S1: Derive the relationship between the time resolution and bandwidth of bipolar equal probability NRZ codes; Step S2: Design the sampling bandwidth based on the distance resolution requirements; Step S3: Design the antenna azimuth sub-channel aperture based on the azimuth resolution requirements; Step S4: Design the antenna range-direction aperture based on the required swath width; Step S5: Design the pulse repetition frequency (PRF) and the number of azimuth channels; Step S6: Generate bipolar equal probability NRZ orthogonal codes based on the orthogonal coding design criteria and combined with a genetic algorithm; Step S7: Calculate the performance indicators of the spaceborne SAR system, including the equivalent noise scattering coefficient NESZ, range ambiguity, and azimuth ambiguity.

2. The method according to claim 1, characterized in that, Step S1 includes: Step S11: Derive the power spectral density of the bipolar NRZ code based on its spectrum: ， in, For the symbol period, Power spectral density; Step S12: Calculate the 3dB bandwidth of the bipolar equal probability NRZ code based on the power spectral density: ; Step S13: Derive the pulse compression function of the bipolar equal probability NRZ code. , is represented as: ， in, The code period; Step S14: Determine the time resolution of the bipolar equiprobability NRZ code. Therefore, the relationship between 3dB bandwidth and time resolution is obtained as follows: .

3. The method according to claim 1, characterized in that, Step S2 includes: Step S21, with distance resolution and beam incident angle For input conditions; Step S22: Calculate the sampling bandwidth based on the relationship between the time resolution and bandwidth of bipolar equiprobability NRZ codes. , is represented as: ， Where c is the speed of light.

4. The method according to claim 1, characterized in that, In step S3, based on the relationship between the azimuth resolution of the strip mode and the aperture of the antenna azimuth sub-channel, the azimuth resolution is... Design the antenna azimuth sub-channel aperture for input. The relational expression is: ， in, This is the azimuth signal processing broadening factor.

5. The method according to claim 1, characterized in that, Step S4 includes: Step S41: Calculate the downward viewing angle corresponding to the imaging center point based on satellite orbit parameters and radar wavelength. ; Step S42: Based on the antenna distance to the initial aperture value Calculate the 3dB beamwidth in the antenna range direction. ; Step S43: The downward viewing angle corresponding to the imaging center point 3dB beamwidth in the direction of antenna distance Calculate the perigee angle separately and the perspective from a distance Perimeter perspective and orbital height Calculate the angle of incidence at perigee and the geocentric angle From the perspective of the far point and orbital height Calculate the angle of incidence at the apogee and the geocentric angle ; Step S44: Calculate the survey width based on the geocentric angles at perigee and apogee. And iteratively adjust the antenna range towards the aperture. Until the required survey width is met.

6. The method according to claim 1, characterized in that, Step S5 includes: Step S51: Based on the azimuth multi-channel system, determine whether the PRF and the number of azimuth channels meet the azimuth sampling bandwidth requirements. in, For PRF, This represents the number of azimuth channels. For oversampling rate, The Doppler bandwidth corresponding to the 3dB azimuth beam is expressed as: ， in, The satellite's flight speed; Step S52: Based on orthogonal coding, when designing the PRF, the echo window does not avoid the nadir echo, but only satisfies that the echo within the surveying band is within the echo window. The specific expression is: ， in, This is the slant distance to perigee. The slant distance at the apogee. For the transmission pulse duration, The guard time between the transmitted pulse and the echo window. Let c be a positive integer, and c be the speed of light. Step S53: Taking into account antenna size, performance indicators and timing relationships, determine the PRF and the number of azimuth channels.

7. The method according to claim 1, characterized in that, The design criteria for the number of orthogonal encoded signals in step S6 specifically include: Step S61: Calculate the echo window number P of the first pulse's nadir point echo arrival and the echo window number Q of the first pulse echo arrival within the surveying zone, where Q>P. Step S62: The initial value of the number of orthogonally encoded signals is at least 2. when The remainder is 0, which means that within the Q-th echo window, the first pulse echo and the Q-P+1-th pulse echo in the mapping band use mutually orthogonal encoded signals and can be separated without increasing the number of signals. when If the remainder is 1, it means that within the Q-th echo window, the 1st pulse echo and the (Q-P+1)th pulse echo within the mapping strip both use the same encoding method and cannot be separated. Therefore, one more signal is added to the two signal types to make... The remainder is not equal to 1; if The remainder is still equal to 1. Therefore, two more signal types need to be added to the base of the two signal types to make... The remainder is not equal to 1; Step S63: The number of orthogonal coded signals is positively correlated with the distance ambiguity; the larger the number of signals, the better the distance ambiguity performance. An initial value for the number of orthogonal coded signals is typically used. ≥3: when The remainder is not equal to 1. The number of signals can meet the requirements; when The remainder is 1, and we need to... Add one more signal to the existing number of signals, making The remainder is not equal to 1; In step S6, the process of generating bipolar equiprobable NRZ orthogonal codes based on a genetic algorithm specifically includes: Step S64: Generate the fitness function, the expression of which is: ， in, The optimal weights for autocorrelation and cross-correlation performance are used. Step S65, Parameter Encoding: Map the positive integer sequence generated by the genetic algorithm to a "+1 / -1" sequence of bipolar equal probability NRZ codes; Step S66: Initialize the population: According to the constraints of the above steps, randomly generate multiple L*N dimensional vectors as the initial individuals of the population. Step S67: Calculate the fitness function of the current population: If the change in fitness function is less than the preset threshold, stop the iteration and convert the current population into a bipolar equiprobable NRZ orthogonal coding sequence; if not, perform selection, crossover, and mutation operations of the genetic algorithm to generate a new population, repeat the calculation of the fitness function of the new population and determine the iteration stopping condition until the requirements are met.

8. The method according to claim 1, characterized in that, Step S7 includes: Step S71: Based on the SAR system signal-to-noise ratio formula , in, For peak transmission power, For the effective gain of the antenna transmission, For the effective gain of the antenna reception, For wavelength, The normalized backscattering coefficient, Pulse repetition frequency, For distance-to-ground resolution, Slope distance For satellite speed, For system losses, Boltzmann's constant, For noise temperature, Noise figure For bandwidth, Substituting the bandwidth and time resolution relationship into the bipolar equal-probability NRZ code: ， in, Average power; Step S72: When the signal-to-noise ratio is 0dB, calculate the NESZ of a single channel, expressed as: ， The NESZ of a multi-channel bipolar equal-probability NRZ code is calculated as follows: , Step S73, the distance ambiguity of orthogonal coding is: ； As can be seen from the above formula for the distance ambiguity of orthogonal coding, the distance ambiguity power of orthogonal coding only needs to be calculated by the first... The power of the ambiguity zone is calculated, but the power of other ambiguity zones does not need to be calculated. As the number of coded signals increases, the distance ambiguity performance will be greatly improved. Step S74, the expression for calculating the azimuth ambiguity is: ， in, This represents the total blur power resulting from aliasing after reconstruction. This is the radiation pattern of the transmitting antenna. The receiving antenna pattern for the j-th channel is shown below. The center of the Doppler frequency.

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