A beam forming method for low earth orbit satellite to achieve equal power coverage of service area

Abstract

The application discloses a beam forming method for realizing equal-power coverage of a low-orbit satellite on a service area, and the method obtains a target direction diagram through the relationship between the gain of a low-orbit satellite array antenna and the communication distance, which is obtained by the equal power, position information of input terminals in the service area of the low-orbit satellite and the motion track of the low-orbit satellite; the excitation amplitude and phase of each unit of the low-orbit satellite array antenna are optimized through a genetic algorithm, and a fitness function is combined to obtain the target direction diagram; and then the equal power received by the service area of the low-orbit satellite in the moving process of the low-orbit satellite is calculated to determine the position of the low-orbit satellite for switching the target direction diagram of the low-orbit satellite array antenna on the motion track, so that the obvious disadvantage that the power of the input terminal is obviously different at different positions in the service area of the low-orbit satellite is overcome, and the design difficulty and cost of the input terminal are reduced.

Description

Technical Field

[0001] This invention belongs to the field of low-Earth orbit satellite communication and array antenna beamforming, and particularly relates to a beamforming method for low-Earth orbit satellites to achieve equal power coverage of the service area. Background Technology

[0002] Satellite mobile communication features wide coverage, large communication capacity, high transmission quality, and no terrain limitations. It has advantages that terrestrial communication methods cannot match in addressing the communication needs of remote and underdeveloped areas, and is an important component in realizing global integrated communication services.

[0003] Compared to satellite communication systems in other orbits, low Earth orbit (LEO) satellite communication systems have advantages such as low orbital altitude, short transmission delay, low launch cost, low space loss, and mass production capability, and are considered to be the satellite communication system with the greatest development potential.

[0004] However, due to the low orbital altitude and low communication angle with the ground of low-Earth orbit (LEO) satellites, the beam coverage of their array antennas is limited, resulting in significant differences in the radiated power received by terminal devices at different locations within the LEO satellite's service area. This places higher demands on the design of terminal devices, greatly increasing their design complexity. Therefore, if the beam of the LEO satellite array antenna could provide equal power coverage across the service area, the design complexity and cost of the terminal devices could be reduced.

[0005] Currently, there are three ways to achieve equal power coverage:

[0006] (1) By adjusting the antenna structure, its radiation pattern can be made to have an equal power coverage pattern. For example, adjusting the structural parameters of a quad-helical antenna can create a quad-helical antenna with an equal power radiation pattern for use in S-band satellite ground stations. However, this antenna is large in size and has a high profile, requiring modification of the antenna structure. The resulting radiation pattern is monotonous, and the adjusted structure can only be used in specific situations, which is not conducive to integration for low-Earth orbit satellite communications.

[0007] (2) A cosecting square beam is formed on the satellite array antenna to achieve equal power coverage of the ground, so that the received power of the ground terminal remains stable. However, the cosecting square beam requires the satellite to be offset from the direction of the service area by a certain angle. Since the positional relationship between the low-Earth orbit satellite and the service area is arbitrary during the movement, it is not suitable for low-Earth orbit satellite communication. This method can only form a fixed-shape radiation pattern and is mostly used for the synthesis of one-dimensional radiation patterns. It cannot meet the beam shape requirements of service areas with irregular boundaries.

[0008] (3) By compensating for the differences in path propagation loss from the satellite antenna to each beam, an ideal spherical beam shape is obtained, which is then divided into multiple beams to obtain beam shapes corresponding to different scanning angles. Finally, a genetic algorithm is used to optimize the amplitude and phase of the hexagonal array antenna elements. Simultaneously, the subarray division needs to be optimized to obtain the phase weight coefficients of the array antenna. Although this method overcomes the problem of received signal differences caused by different scanning distances when the phased array antenna of a low-Earth orbit satellite scans at large angles, the use of a "subarray" segmentation technique during the genetic algorithm synthesis process—that is, dividing the hexagonal array into a fixed number of arrays with identical amplitude and phase of the antenna elements in the divided arrays—may reduce the number of variables while potentially affecting the beam's ability to accurately conform to the ideal requirements, resulting in some areas not being covered. Furthermore, this method does not consider the motion of low-Earth orbit satellites and still has shortcomings in practical applications.

[0009] In conclusion, low-Earth orbit (LEO) satellite communication systems are considered to have the greatest development potential due to their unique advantages. Furthermore, phased array antennas are widely used in satellite communication systems, which will improve signal strength and the anti-interference performance of the system. However, current equal-power coverage methods are not suitable for LEO satellite communication. Summary of the Invention

[0010] To address the aforementioned problems in existing technologies, this invention proposes a beamforming method for achieving equal power coverage of the service area by low-orbit satellites.

[0011] The specific technical solution of this invention is as follows: a beamforming method for achieving equal power coverage of a service area by a low-Earth orbit (LEO) satellite, specifically as follows: The target radiation pattern of the LEO satellite array antenna is obtained by using the equal power and location information of the input terminal in the LEO satellite service area and the motion trajectory of the LEO satellite to obtain the relationship between the gain and communication distance of the LEO satellite array antenna; wherein, the excitation amplitude and phase of each element of the LEO satellite array antenna are optimized using a genetic algorithm and combined with a fitness function to obtain the target radiation pattern; the position where the LEO satellite needs to switch the target radiation pattern of the LEO satellite array antenna on its motion trajectory is determined by calculating the equal power received in the LEO satellite service area during the movement of the LEO satellite.

[0012] Furthermore, the step of obtaining the target radiation pattern by using the equal power and location information of the input terminal in the low-Earth orbit satellite service area and the motion trajectory of the low-Earth orbit satellite to obtain the relationship between the gain of the low-Earth orbit satellite array antenna and the communication distance is as follows:

[0013] S1. Input the motion trajectory of the low-Earth orbit satellite, the location information of the low-Earth orbit satellite service area m, and the equal-power reception range of the input terminal for the low-Earth orbit satellite service area m. , where P el P represents the minimum power received by the input terminal. eh This indicates the maximum power received by the input terminal;

[0014] S2. Randomly select a position on the trajectory of the low-Earth orbit satellite as the starting point of the low-Earth orbit satellite, denoted as... Determine the low-orbit satellite in The number of low-Earth orbit satellite service areas m is M, and the low-Earth orbit satellite service area m=1;

[0015] S21. Take a certain number of position coordinates at the boundary and inside the low-Earth orbit satellite service area m, and record the elevation angle of each position coordinate relative to the low-Earth orbit satellite array antenna. and azimuth ;

[0016] S22, using the position coordinates and the corresponding pitch angle and the azimuth angle To calculate the communication distance from the said location coordinates to the low-Earth orbit satellite array antenna. ;

[0017] S23, via the communication distance The transmit power of the low-orbit satellite array antenna Receiver gain Emit gain Gt and operating wavelength To calculate the received power at the receiver. And the transmission power The receiving gain and the operating wavelength If it remains unchanged, then the received power at each point in the low-orbit satellite service area m is a constant;

[0018] S24, By order To obtain the minimum power P received by the input terminal el At that time, the transmit gain of the low-orbit satellite array antenna required for the low-orbit satellite to achieve the equal power coverage is... The relationship between azimuth and elevation angles is established by setting...

[0019] ,

[0020] The maximum power P received by the input terminal is obtained. ehAt that time, the transmit gain of the low-orbit satellite array antenna required for the low-orbit satellite to achieve the equal power coverage is... With azimuth Pitch angle Relationship;

[0021] S25, by the and stated The upper and lower limits of the constraint range of the target radiation pattern within the main lobe are used to constrain the values ​​of the target radiation pattern in the region outside the main lobe, and the values ​​of the target radiation pattern in the region outside the main lobe are obtained by the low-orbit satellite. The target radiation pattern when the low-orbit satellite service area m is covered by the equal power coverage. The conditions that need to be met.

[0022] Furthermore, the step of optimizing the excitation amplitude and phase of each element of the low-Earth orbit satellite array antenna using a genetic algorithm and combining it with a fitness function to obtain the target radiation pattern includes:

[0023] S3. A genetic algorithm is used to optimize the excitation amplitude and phase of each element of the low-orbit satellite array antenna. The following steps are then taken to synthesize the target radiation pattern that satisfies the constraints. ;

[0024] S31. Encode the excitation amplitude and phase of each element of the low-orbit satellite array antenna to obtain an initial population, set the sidelobe level of the target pattern to SLL, set the number of iterations of the genetic algorithm to I, and calculate the low-orbit satellite array antenna pattern f based on the initial population;

[0025] S32. Sample the signal within the main lobe region of the radiation pattern f of the low-Earth orbit satellite array antenna, calculate the average difference between the value of the sampled point and the upper and lower limits of the constraints. If the value of the sampled point is within the constraint range, then that point is not included in the calculation, and the main lobe portion of the fitness function is obtained. ;

[0026] S33. Sample the sidelobe region of the radiation pattern f of the low-orbit satellite array antenna, calculate the maximum difference between the value of the sampled point and the sidelobe level SLL, if the value of a sampled point is less than the sidelobe level SLL, then that point is not included in the calculation, and the sidelobe part of the fitness function is obtained. ;

[0027] S34, Based on the main lobe portion and the sidelobe portion The fitness function is obtained as follows: ,in, , , Q and R are the number of sampling points;

[0028] S35. Calculate the value of the fitness function and determine whether the genetic algorithm meets the termination condition of the number of iterations I. If not, perform selection, crossover and mutation, calculate the radiation pattern of the low-orbit satellite array antenna corresponding to the new population, and return to step S32 to continue execution. If the termination condition of the number of iterations I is met, proceed to S4.

[0029] S4, Output the location of the low-orbit satellite in the... The optimal excitation amplitude and phase distribution of the low-Earth orbit satellite array antenna that achieves equal power coverage over the low-Earth orbit satellite service area m are used to obtain the optimal target radiation pattern. And calculate the target orientation pattern. The main lobe satisfies the width of equal power coverage;

[0030] S5. Maintain the target orientation pattern as follows: The received power at each point in the service area m of the low-Earth orbit satellite is calculated during the satellite's movement along its trajectory. ;

[0031] S6, if If, then return to S5, if Then record the first position that does not satisfy equal power coverage, denoted as . ;

[0032] S7. Let m = m + 1. If m ≤ M, return to step S21 and continue execution. If m > M, select the distance. Recent As the next starting point for low-Earth orbit satellites;

[0033] S8. If the calculation of one cycle of the low-orbit satellite's movement is completed, then each calculated starting point is used as the position for switching the low-orbit satellite and outputting the target radiation pattern. That is, the movement trajectory of the low-orbit satellite is discretized, and each position of the low-orbit satellite on the movement trajectory is output to achieve the optimal excitation amplitude and the optimal phase distribution of the low-orbit satellite array antenna with equal power coverage for different low-orbit satellite service areas m. If the calculation of one cycle of the low-orbit satellite's movement is not completed, then return to step S2 to continue execution.

[0034] The beneficial effects of this invention are as follows: Combining the background of low-Earth orbit (LEO) satellite communication, this invention utilizes the beamforming capabilities of LEO satellite array antennas to propose a beamforming method for achieving equal power coverage of the service area by LEO satellites. First, based on the communication equations and the received power range required for equal power coverage, the relationship between the array antenna path loss compensation and the communication elevation angle is obtained, thus yielding an ideal beam shape. Then, a genetic algorithm is used to optimize the element excitation amplitude and phase of the satellite array antenna to obtain a target radiation pattern that satisfies equal power coverage, ensuring that the received power of the terminal equipment remains within an effective range. Finally, the motion trajectory of the LEO satellite is discretized to determine the locations where beamforming is required, thereby reducing the number of times the satellite switches array antenna beams. This invention can form beams of arbitrary shapes while ensuring that the received power of the terminal equipment remains within an effective range, solving the problem of equal power coverage for terminal equipment under specific requirements. When the received power requirements differ, only the power value needs to be modified to calculate a new array antenna target radiation pattern. The synthesis process only requires optimization of the excitation amplitude and phase of the array antenna elements, without altering the antenna element structure or imposing special requirements on the array antenna shape. This reduces the integration difficulty of the array antenna on low-Earth orbit (LEO) satellites and eliminates the need for array partitioning, thus avoiding any additional impact on the accuracy of the synthesis results. Furthermore, the beamforming method proposed in this invention uses a single beam to cover a specific area, ensuring complete coverage. Finally, this invention discretizes the trajectory of the LEO satellite based on its high-speed movement to determine the locations where beamforming is required during its motion, reducing the number of beamforming operations and allowing the LEO satellite to anticipate the required beamforming locations and corresponding beam shapes during high-speed movement. Attached Figure Description

[0035] Figure 1 This is a schematic diagram illustrating the communication between a low-Earth orbit satellite and its service area as described in an embodiment of the present invention.

[0036] Figure 2 This is a flowchart illustrating the design of an equal-power beamforming method for low-Earth orbit satellite communication according to an embodiment of the present invention. Detailed Implementation

[0037] This invention aims to propose a beamforming method for achieving equal-power coverage of a service area by a low-Earth orbit (LEO) satellite, thereby realizing equal-power coverage of each service area by the LEO satellite. The target radiation pattern of the LEO satellite array antenna is obtained by using the equal-power and location information of the input terminal in the LEO satellite service area and the motion trajectory of the LEO satellite to determine the relationship between the gain and communication distance. Specifically, a genetic algorithm is used to optimize the excitation amplitude and phase of each element of the LEO satellite array antenna, combined with a fitness function, to obtain the target radiation pattern. The location where the LEO satellite needs to switch the target radiation pattern of the LEO satellite array antenna is determined by calculating the equal-power received in the service area during the LEO satellite's movement. This involves discretizing the LEO satellite's motion trajectory to determine the location requiring beamforming, thereby reducing the number of times the satellite switches the array antenna beam. This invention can form beams of arbitrary shapes while ensuring that the received power of the terminal equipment remains within an effective range, solving the problem of equal-power coverage of terminal equipment under specific requirements. When the received power requirements differ, only the power value needs to be modified to calculate a new array antenna target radiation pattern. The synthesis process only requires optimization of the excitation amplitude and phase of the array antenna elements, without altering the antenna element structure or imposing special requirements on the array antenna shape. This reduces the integration difficulty of the array antenna on low-Earth orbit (LEO) satellites and eliminates the need for array partitioning, thus avoiding any additional impact on the accuracy of the synthesis results. Furthermore, the beamforming method proposed in this invention uses a single beam to cover a specific area, ensuring complete coverage. Finally, this invention discretizes the trajectory of the LEO satellite based on its high-speed movement to determine the locations where beamforming is required during its motion, reducing the number of beamforming operations and allowing the LEO satellite to anticipate the required beamforming locations and corresponding beam shapes during high-speed movement.

[0038] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0039] Figure 1 The elevation angle involved in beamforming methods Azimuth and communication distance Representation of the spatial relationship between low-Earth orbit satellites and their service areas.

[0040] like Figure 2 As shown, the specific implementation steps of the present invention are as follows:

[0041] S1. Input the motion trajectory of the low-Earth orbit satellite, input the location information of the low-Earth orbit satellite service area, and input the equal power reception range of the input terminal in the low-Earth orbit satellite service area [5W, 10W], where W is the power unit watt;

[0042] S2. Take any position on the low-Earth orbit satellite's trajectory as the satellite's starting point, denoted as... To determine the satellite's location Given a service area of ​​5, and setting m=1, obtain the target orientation pattern of the low-orbit satellite in the service area m according to the following steps;

[0043] S21. Take a certain number of position coordinates at the boundary and inside the region m, and record the elevation angle of each position coordinate relative to the low-orbit satellite array antenna. and azimuth ;

[0044] S22. Based on the position coordinates and the corresponding pitch angle and azimuth Calculate the communication distance from this location to the low-Earth orbit satellite array antenna. ;

[0045] S23, Based on communication distance and the transmit power of low-Earth orbit satellite array antennas Receiver gain Operating wavelength Calculate the received power at the receiver. Assuming the transmission power Receiver gain The low-orbit satellite array antenna operates in the Ka band, with its trajectory 300km above the ground;

[0046] S24, Order This yields the relationship between the array antenna transmit gain and the azimuth and elevation angles required for a low-orbit satellite to achieve equal-power coverage when the receiver receives the minimum power. Let... The relationship between the array antenna transmit gain and the azimuth and elevation angles required for a low-orbit satellite to achieve equal power coverage when the receiver receives the maximum power is obtained.

[0047] S25, will and The upper and lower limits of the target radiation pattern of a low-Earth orbit (LEO) satellite array antenna are constrained within the main lobe, and the values ​​of the radiation pattern outside the main lobe are also constrained. The results are expressed in dB to obtain the LEO satellite's radiation pattern within the main lobe. Time required to achieve equal power coverage of region m (target radiation pattern) The conditions that need to be met;

[0048] S3. A genetic algorithm is used to optimize the excitation amplitude and phase of each element of the low-orbit satellite array antenna, and a target radiation pattern that satisfies the constraints is generated. ;

[0049] S31. Encode the excitation amplitude and phase of each element of the low-orbit satellite array antenna to obtain an initial population. Set the sidelobe level of the target pattern to -40dB and the number of iterations of the genetic algorithm to 150. Calculate the array antenna pattern f based on the initial population.

[0050] S32. Sample data within the main lobe region of the radiation pattern f of the low-Earth orbit satellite array antenna, taking 10,000 sampled values. Calculate the average difference between the sampled values ​​and the upper and lower limits. If the value of a sampled point is within the constraint range, that point is not included in the calculation. The main lobe portion of the fitness function is obtained.

[0051] S33. Sample the radiation pattern f of the low-Earth orbit satellite array antenna within its sidelobe region, taking 1000 sampled values. Calculate the maximum difference between the sampled values ​​and -40dB. If the value of a sampled point is less than -40dB, that point is not included in the calculation. This yields the sidelobe portion of the fitness function;

[0052] S34, according to and Obtain the fitness function.

[0053] ,in, Sampled values ​​from the main lobe or side lobe region;

[0054] S35. Calculate the value of the fitness function and determine whether the genetic algorithm meets the termination condition of the number of iterations of the genetic algorithm I. If not, perform selection, crossover and mutation, calculate the radiation pattern of the low-orbit satellite array antenna corresponding to the new population, and return to step S32 to continue execution; if the termination condition of the number of iterations of the genetic algorithm I is met, proceed to step S4.

[0055] S4, output low-orbit satellite is in The optimal amplitude and phase distribution of the array antenna to achieve equal power coverage over region m is used to obtain the optimal target radiation pattern. ,calculate The main lobe satisfies the width of equal power coverage, that is, the received power of the service area is calculated based on the obtained target pattern, and the synthesized target pattern can satisfy the main lobe beamwidth of the received power within the equal power reception range.

[0056] S5. Maintain the target orientation map as follows The satellite moves along its trajectory, and the received power at each point in region m is calculated during the movement. ;

[0057] S6, if If so, return to step S5; Then record the first position that does not satisfy equal power coverage, denoted as . ;

[0058] S7. Let m = m + 1. If m ≤ 5, return to step S21 and continue execution. If m > 5, select distance. Recent As the next starting point for low-Earth orbit satellites;

[0059] S8. If the calculation of one revolution of the low-Earth orbit satellite is completed, the trajectory of the low-Earth orbit satellite is discretized by using each calculated starting point as the position for switching the low-Earth orbit satellite and outputting the target radiation pattern. At the same time, the optimal excitation amplitude and phase distribution of the array antenna with equal power coverage in different areas is achieved by outputting each position of the satellite on the trajectory. If the calculation of one revolution of the low-Earth orbit satellite is not completed, return to step S2 to continue execution.

[0060] In summary, the beamforming method proposed in this invention for achieving equal power coverage of a service area by a low-Earth orbit (LEO) satellite can achieve equal power coverage of each service area by the LEO satellite. The target radiation pattern of the LEO satellite array antenna is obtained by using the equal power and location information of the input terminal in the LEO satellite service area and the motion trajectory of the LEO satellite to determine the relationship between the gain and communication distance. Specifically, a genetic algorithm is used to optimize the excitation amplitude and phase of each element of the LEO satellite array antenna and a fitness function is combined to obtain the target radiation pattern. The location where the LEO satellite needs to switch the target radiation pattern of the LEO satellite array antenna on its motion trajectory is determined by calculating the equal power received in the LEO satellite service area during the LEO satellite's movement, i.e., the motion trajectory of the LEO satellite is discretized. The method of this invention, combined with the background of LEO satellite communication and the condition of equal power coverage, derives the array antenna beam shape at different positions on the LEO satellite's motion trajectory, resulting in a beam shape that better matches the actual application scenarios of LEO satellite communication. After beam synthesis is completed, the motion trajectory of the low-Earth orbit satellite is discretized to determine the positions where different radiation patterns need to be calculated, thereby reducing the number of beamforming operations on the low-Earth orbit satellite's motion trajectory.

[0061] The principles of this invention should be understood to mean that the scope of protection of this invention is not limited to such specific statements and embodiments. Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand that various other specific modifications and combinations can be made based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A beamforming method for achieving equal power coverage of a service area by a low-orbit satellite, characterized in that, The process includes the following steps: obtaining the target radiation pattern of the low-Earth orbit (LEO) satellite array antenna by using the equal power and location information of the input terminal in the LEO satellite service area and the motion trajectory of the LEO satellite; wherein, the excitation amplitude and phase of each element of the LEO satellite array antenna are optimized by a genetic algorithm and combined with a fitness function to obtain the target radiation pattern; and determining the position where the LEO satellite needs to switch the target radiation pattern of the LEO satellite array antenna on its motion trajectory by calculating the equal power received in the LEO satellite service area during the movement of the LEO satellite. The step of obtaining the target radiation pattern by using the relationship between the gain of the low-Earth orbit satellite array antenna and the communication distance obtained from the equal power and location information of the input terminal in the low-Earth orbit satellite service area and the motion trajectory of the low-Earth orbit satellite includes: S1. Input the motion trajectory of the low-Earth orbit satellite, the location information of the low-Earth orbit satellite service area m, and the equal-power reception range of the input terminal for the low-Earth orbit satellite service area m. P el Indicates the minimum power received by the input terminal. ， P eh This indicates the maximum power received by the input terminal; S2. Randomly select a position on the trajectory of the low-Earth orbit satellite as the starting point of the low-Earth orbit satellite, denoted as... Determine the low-orbit satellite in The number of low-Earth orbit satellite service areas m is M, and the low-Earth orbit satellite service area m=1; S21. Take a certain number of position coordinates at the boundary and inside the low-Earth orbit satellite service area m, and record the elevation angle of each position coordinate relative to the low-Earth orbit satellite array antenna. and azimuth ; S22, using the position coordinates and the corresponding pitch angle and the azimuth angle To calculate the communication distance from the said location coordinates to the low-Earth orbit satellite array antenna. ; S23. Communication distance from the location coordinates to the low-Earth orbit satellite array antenna The transmit power of the low-orbit satellite array antenna Receiver gain Transmit gain G t and operating wavelength To calculate the received power at the receiver. And the transmission power The receiving gain and the operating wavelength If it remains unchanged, then the received power at each point in the low-orbit satellite service area m is a constant; S24, By order To obtain the minimum power P received by the input terminal el At that time, the transmit gain of the low-orbit satellite array antenna required for the low-orbit satellite to achieve the equal power coverage is... The relationship between azimuth and elevation angles is established by setting... ， The maximum power P received by the input terminal is obtained. eh At that time, the transmit gain of the low-orbit satellite array antenna required for the low-orbit satellite to achieve the equal power coverage is... With azimuth Pitch angle Relationship; S25, by the and stated The upper and lower limits of the constraint range of the target radiation pattern within the main lobe are used to constrain the values ​​of the target radiation pattern in the region outside the main lobe, and the values ​​of the target radiation pattern in the region outside the main lobe are obtained by the low-orbit satellite. The target radiation pattern when the low-orbit satellite service area m is covered by the equal power coverage. The conditions that need to be met.

2. The beamforming method for achieving equal power coverage of a service area by a low-orbit satellite according to claim 1, characterized in that, The steps of optimizing the excitation amplitude and phase of each element of the low-orbit satellite array antenna using a genetic algorithm and combining it with a fitness function to obtain the target radiation pattern include: S3. A genetic algorithm is used to optimize the excitation amplitude and phase of each element of the low-orbit satellite array antenna. The following steps are then taken to synthesize the target radiation pattern that satisfies the constraints. ; S31. Encode the excitation amplitude and phase of each element of the low-orbit satellite array antenna to obtain an initial population, set the sidelobe level of the target pattern to SLL, set the number of iterations of the genetic algorithm to I, and calculate the low-orbit satellite array antenna pattern f based on the initial population; S32. Sample the signal within the main lobe region of the radiation pattern f of the low-Earth orbit satellite array antenna, calculate the average difference between the value of the sampled point and the upper and lower limits of the constraints. If the value of the sampled point is within the constraint range, then that point is not included in the calculation, and the main lobe portion of the fitness function is obtained. ; S33. Sample the sidelobe region of the radiation pattern f of the low-orbit satellite array antenna, calculate the maximum difference between the value of the sampled point and the sidelobe level SLL, if the value of a sampled point is less than the sidelobe level SLL, then that point is not included in the calculation, and the sidelobe part of the fitness function is obtained. ; S34, Based on the main lobe portion and the sidelobe portion The fitness function is obtained as follows: ,in, , , Q and R are the number of sampling points; S35. Calculate the value of the fitness function and determine whether the genetic algorithm meets the termination condition of the number of iterations I. If not, perform selection, crossover and mutation, calculate the radiation pattern of the low-orbit satellite array antenna corresponding to the new population, and return to step S32 to continue execution. If the termination condition of the number of iterations I is met, proceed to S4. S4, Output the location of the low-orbit satellite in the... The optimal excitation amplitude and phase distribution of the low-Earth orbit satellite array antenna that achieves equal power coverage over the low-Earth orbit satellite service area m are used to obtain the optimal target radiation pattern. And calculate the target orientation pattern. The main lobe satisfies the width of equal power coverage; S5. Maintain the optimal target orientation pattern as follows: And calculate the received power at each point in the service area m of the low-Earth orbit satellite during the satellite's movement along its trajectory. ; S6, if If, then return to S5, if Then record the first position that does not satisfy equal power coverage, denoted as . ; S7. Let m = m + 1. If m ≤ M, return to S21 and continue execution. If m > M, select the distance. Recent As the next starting point for low-Earth orbit satellites; S8. If the calculation of the low-orbit satellite's movement around one orbit is completed, then each calculated starting point is used as the position for the low-orbit satellite to switch and output the target radiation pattern. At the same time, each position of the low-orbit satellite on the trajectory is output to achieve the optimal excitation amplitude and the optimal phase distribution of the low-orbit satellite array antenna with equal power coverage for different low-orbit satellite service areas m. If the calculation of the low-orbit satellite's movement around one orbit is not completed, then return to S2 to continue execution.

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