Low-orbit super-dense constellation satellite beam forming method based on sparse array and two-dimensional Gaussian weighting

Abstract

The invention discloses a low-orbit ultra-dense constellation satellite beam forming method based on a sparse array and two-dimensional Gaussian weighting, and belongs to the field of satellite communication. According to the invention, the problems of interference between transmitting beams and high antenna structure complexity in networking satellites of the low-orbit ultra-dense constellation network are solved. The method comprises the following steps: firstly, designing a sparse array antenna model of a genetic algorithm based on 120-degree symmetric constraint; secondly, according to the characteristics of a planar phased array model antenna, setting a target function by constructing an optimization model of antenna array element arrangement, and regulating and controlling the arrangement of antenna array elements in a phased array model; and finally, a two-dimensional Gaussian function is adopted to weight the array element amplitude to optimize the amplitude of the antenna array element, so that the parameters of the transmitted beams are optimized, beam forming is performed through the optimized array element arrangement and the array element amplitude, the sidelobe level of the satellite transmitted beams can be suppressed, interference between the transmitted beams is avoided, and the antenna structure is simplified. The method can be applied to low-orbit super-dense constellation satellite beam forming.

Description

Technical Field

[0001] The invention belongs to the field of satellite communications, and in particular relates to a low-orbit ultra-dense constellation satellite beam forming method based on a sparse array and two-dimensional Gaussian weighting. Background Art

[0002] With the rapid development of information and communication technology, users have an increasing demand for high-speed, large-capacity, and diversified data communications, especially in remote areas such as mountains, oceans, and deserts, as well as in high-speed mobile scenarios. Traditional ground communication networks can no longer meet user needs. Therefore, seeking new communication solutions has become a hot research direction for scholars at home and abroad. As an emerging satellite communication system, the low-orbit ultra-dense constellation network has the advantages of wide coverage, low transmission delay, strong anti-destruction and low cost, and is considered to be an important part of the future global communication network.

[0003] The characteristics of low-orbit ultra-dense constellation networks are: first, there are many networking satellites. For example, typical low-orbit constellation networks such as OneWeb, StarLink, and Qianfan are committed to providing broadband communication services to billions of users and tens of billions of terminal devices around the world, and the number of networking satellites reaches thousands to tens of thousands. The onboard phased array antennas carried by low-orbit satellites need to face a complex and changeable interference environment. The interference links may come from the working links of other satellites in the same constellation, or from the working links of other satellite communication systems; second, the constellation network cost is high, but the budget allocated to a single networking satellite is limited. Therefore, the onboard phased array antenna needs to meet the requirements of miniaturization and lightweight structure, while meeting the working requirements of low-orbit ultra-dense constellation networks, such as suppressing the sidelobe level of the transmit beam.

[0004] In order to achieve rapid networking and long-term operation of low-orbit ultra-dense constellation networks, the phased array antennas of networking satellites need to be as simple and lightweight as possible, while meeting all the needs of onboard work and effectively avoiding interference between satellite-to-ground communication links. Although relevant research on simplifying antenna structures and suppressing interference has been carried out at home and abroad, the existing methods are still relatively limited in the effect of antenna structure simplification and interference suppression. It is very necessary to propose a new antenna structure simplification and interference suppression method to solve the problems of severe interference between transmit beams and high antenna structure complexity in low-orbit ultra-dense constellation network satellites. Summary of the invention

[0005] The purpose of the present invention is to solve the problems of interference between transmitting beams and high complexity of antenna structure in low-orbit ultra-dense constellation network satellites, and propose a low-orbit ultra-dense constellation satellite beamforming method based on sparse array and two-dimensional Gaussian weighting.

[0006] The technical solution adopted by the present invention to solve the above technical problems is: a low-orbit ultra-dense constellation satellite beamforming method based on sparse array and two-dimensional Gaussian weighting, the method specifically comprising the following steps:

[0007] Step 1: construct an interference scenario model for the satellite transmitter of the low-orbit ultra-dense constellation network, wherein the interference scenario model includes a gateway, a ground user terminal, and a LEO satellite, and establish a normalized ideal transmission beam model of the LEO satellite radiating antenna in the interference scenario model;

[0008] Step 2: Establish an objective function of the normalized ideal transmission beam model, and then establish a fitness function of the genetic algorithm based on the objective function, and use the genetic algorithm to optimize the arrangement of antenna array elements, that is, obtain the position of each antenna array element;

[0009] Step 3: Optimize the amplitude of the antenna array element at each position based on the two-dimensional Gaussian function to obtain the amplitude of each antenna element;

[0010] Step 4: Design a phased array antenna model according to the position and amplitude of each antenna element, and use the designed phased array antenna model to perform beam forming.

[0011] The beneficial effects of the present invention are:

[0012] The present invention designs a beamforming technology for optimizing the arrangement and amplitude of array elements of a phased array antenna model. Firstly, in order to simplify the structure of the phased array antenna and save satellite payload, a sparse array antenna model based on a genetic algorithm with a 120° symmetry constraint is designed, which reduces the number of antenna elements by 20%; secondly, according to the characteristics of the planar phased array model antenna, an optimization model of the antenna element arrangement is constructed to set an objective function, and the arrangement of the antenna elements in the phased array model is regulated; finally, a two-dimensional Gaussian function weighted element amplitude is used to optimize the amplitude of the antenna element, and then the parameters of the transmit beam are optimized. Beamforming is performed by optimizing the element arrangement and element amplitude, which can suppress the sidelobe level of the satellite transmit beam, avoid interference between transmit beams and simplify the antenna structure, and effectively solve the problems of severe interference between transmit beams and high complexity of the antenna structure in low-orbit ultra-dense constellation network satellites. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 This is an interference scenario model diagram of the low-orbit ultra-dense constellation network satellite transmitter in the present invention;

[0014] Figure 2 It is the genetic algorithm flow chart of the present invention;

[0015] Figure 3 It is an array element arrangement diagram of the sparse array phased array antenna model of the present invention;

[0016] Figure 4 This is the sparse array transmit beam antenna pattern based on Gaussian weighting of the present invention. DETAILED DESCRIPTION

[0017] Specific implementation method 1: This implementation method is a low-orbit ultra-dense constellation satellite beamforming method based on sparse array and two-dimensional Gaussian weighting, where the low orbit refers to an artificial earth satellite orbit with an orbit altitude below 2000 kilometers, and the ultra-dense constellation refers to a constellation with thousands of satellites in the constellation. The method specifically includes the following steps:

[0018] Step 1: construct an interference scenario model for the satellite transmitter of the low-orbit ultra-dense constellation network, wherein the interference scenario model includes a gateway, a ground user terminal, and a LEO satellite, and establish a normalized ideal transmission beam model of the LEO satellite radiating antenna in the interference scenario model;

[0019] Step 2: Establish an objective function of the normalized ideal transmission beam model, and then establish a fitness function of the genetic algorithm based on the objective function, and use the genetic algorithm to optimize the arrangement of antenna array elements, that is, obtain the position of each antenna array element;

[0020] Step 3: Optimize the amplitude of the antenna array element at each position based on the two-dimensional Gaussian function to obtain the amplitude of each antenna element;

[0021] Step 4: Design a phased array antenna model according to the position and amplitude of each antenna element, and use the designed phased array antenna model to perform beam forming.

[0022] Specific implementation method 2: This implementation method is different from the specific implementation method 1 in that the interference scenario model also includes the working link and interference link of the LEO satellite, wherein the working link of the LEO satellite specifically includes:

[0023] LEO satellites have user links to ground user terminals and LEO satellites have feeder links to gateways.

[0024] The other steps and parameters are the same as those in the first embodiment.

[0025] Specific implementation method three: This implementation method is different from specific implementation method one or two in that the normalized ideal transmission beam model of the LEO satellite radiating antenna is:

[0026]

[0027] Among them, G(τ) is the normalized ideal transmit beam model, G max represents the maximum gain of the LEO satellite radiating antenna, τ represents the off-axis angle of the LEO satellite radiating antenna, τ bis an intermediate variable, PSLL represents the peak sidelobe level in the transmit beam antenna pattern, and Y and Z are both thresholds.

[0028] The other steps and parameters are the same as those in the first or second embodiment.

[0029] In this embodiment, the base of the logarithm is 10.

[0030] Specific implementation method 4: This implementation method is different from any one of the specific implementation methods 1 to 3 in that the intermediate variable τ b for:

[0031]

[0032] Where D is the aperture size of the LEO satellite radiating antenna, λ is the signal wavelength, τ b Numerically equal to half the beamwidth;

[0033] The thresholds Y and Z are:

[0034] Y=1.5τ b

[0035]

[0036] The other steps and parameters are the same as those in Specific Embodiments 1 to 3.

[0037] Specific implementation method 5: This implementation method is different from any one of specific implementation methods 1 to 4 in that the objective function of the normalized ideal transmit beam model is:

[0038]

[0039] Where |PSLL| is the objective function of the normalized ideal transmit beam model, θ is the elevation angle of the LEO satellite radiating antenna, is the azimuth of the LEO satellite radiating antenna, is the antenna pattern function, S is the angular coverage of the main lobe beam, and |·| represents the absolute value.

[0040] The other steps and parameters are the same as those in Specific Embodiments 1 to 4.

[0041] Specific implementation method six: Combination Figure 2 This embodiment is different from the first to fifth embodiments in that, in step 2, a fitness function of a genetic algorithm is established based on the objective function, and the genetic algorithm is used to optimize the arrangement of antenna elements, that is, to obtain the position of each antenna element; the specific process is as follows:

[0042] Step 21: Define that each antenna element in the phased array antenna model is located on the YOZ plane of the spatial rectangular coordinate system, and the position of each antenna element satisfies the 120° symmetry constraint. The total number of antenna elements in the phased array antenna model is N′. Then select all antenna elements located within the range of 0 to 120° in the circumferential direction from the phased array antenna model (i.e., select N′ / 3). The position of the selected antenna element is used as the quantity to be optimized, and continue to execute step 22;

[0043] Step 22: Initialize the number of individuals in the genetic algorithm to N, each individual includes the position of each antenna array element selected in step 21, initialize the number of iterations to K, and initialize the crossover probability to P. c , initialize the mutation probability to P m , initialize the sparsity rate to η0;

[0044] Step 23, initialize the number of iterations k = 1;

[0045] Step 24, respectively calculate the fitness function value of each individual obtained in the k-1th iteration (before the first iteration, it is necessary to initialize the position of each antenna array element in each individual, and then perform random sparse processing on the initial individuals based on the sparsity rate, that is, the state value of the antenna array element position of the proportion η0 in each individual is recorded as 1, and the fitness function value is calculated using the antenna array element position with a state value of 1 in the individual);

[0046] Step 25: performing a selection operation according to the fitness function value calculation result in step 24, performing a crossover operation on the selection operation result according to the crossover probability, and performing a mutation operation on the crossover operation result according to the mutation probability;

[0047] Step 26: Determine whether the current number of iterations is equal to K;

[0048] If k=K, the iteration is terminated, and the sparse rate of each individual in the mutation operation result obtained in the last iteration is corrected (so that the sparse rate of each individual is still η0), and then the fitness function values ​​of each individual after the sparse rate correction are compared, and the individual with the largest fitness function value is taken as the optimal individual, and the antenna array element with a state value of 1 and the position of the antenna array element with a state value of 1 after the sparse rate correction in the optimal individual are output (due to the sparse processing, only η0 proportion of the antenna array elements in each individual have a state value of 1); and the positions of the antenna array elements corresponding to the output antenna array elements in the range of 120° to 240° and the range of 240° to 360° in the circumferential direction are obtained;

[0049] If k≠K, execute step 27;

[0050] Step 27: According to the sparse rate η0, the sparse rate of each individual in the mutation operation result of step 25 is corrected so that the sparse rate of each individual in the mutation operation result is η0, and then k=k+1 is set, and the execution of step 24 is returned.

[0051] The other steps and parameters are the same as those in Specific Implementation Methods 1 to 5.

[0052] For a traditional phased array antenna model including N′ antenna elements, the N′ antenna elements are uniformly arranged with a spacing of λ in the traditional phased array antenna model. In this embodiment, the N′ antenna elements are first set to satisfy the 120° symmetry constraint. By introducing the 120° symmetry constraint, the algorithm can only consider the positions of 1 / 3 of the elements in the array to reduce the amount of calculation in the optimization process; then the antenna elements in the antenna array are sparsely processed by setting the sparse rate, and finally only the positions corresponding to the antenna elements with a state value of 1 in each area of ​​the circumference after the sparse processing are output (because the 120° symmetry constraint is satisfied, the entire circle is divided into three areas, and the antenna elements with a state value of 1 have a corresponding position in each of the three areas). Finally, only the antenna elements with a state value of 1 at the corresponding positions of the various areas of the circumference are retained in the phased array antenna model. Therefore, compared with the traditional phased array antenna model, the phased array antenna model of the present invention can reduce the number of antennas required in the antenna structure and optimize the transmit beam sidelobe level.

[0053] Specific implementation method 7: This implementation method is different from the specific implementation methods 1 to 6 in that the selection operation adopts a roulette method, that is, the specific process of the selection operation is:

[0054] The value of the individual fitness function determines whether it can be retained to the next generation, and the probability of being retained to the next generation is calculated based on the fitness function value of each individual:

[0055]

[0056] Among them, p j is the probability that the jth individual is retained to the next generation, η j is the fitness function value of the jth individual.

[0057] The other steps and parameters are the same as those in Specific Embodiments 1 to 6.

[0058] Specific implementation eight: This implementation differs from any one of specific implementations one to seven in that the fitness function is:

[0059]

[0060] in, is the fitness function, ω is the weighting matrix, the superscript H represents the conjugate transpose of the matrix, and a is the steering matrix;

[0061] The calculation method of the weighted matrix ω is:

[0062]

[0063] Among them, (α, β) is the direction of arrival, e is the base of the natural logarithm, j is the imaginary unit, (y i ,z i ) is the position coordinate of the i-th antenna with a state value of 1 in the individual in the YOZ plane, i = 1, 2, 3, ..., M, M is the total number of antennas with a state value of 1 in the individual,

[0064] The calculation method of the steering matrix a is:

[0065]

[0066] in, is the antenna radiation direction.

[0067] The other steps and parameters are the same as those in Specific Embodiments 1 to 7.

[0068] Since in the normalized antenna pattern, except for the main lobe peak, the other beam gains are all negative values, the present embodiment sets the fitness function to the absolute value of the peak sidelobe level of the transmit beam antenna pattern.

[0069] Specific implementation method 9: This implementation method is different from specific implementation methods 1 to 8 in that the specific process of step 3 is as follows:

[0070] Step 31: Calculate the weight of the antenna element at each position based on the two-dimensional Gaussian function:

[0071]

[0072] Among them, μ1, μ2, σ1, σ2 and ρ are all constants, G i is the position (y i ,z i )The weight of the antenna element on the

[0073] Step 32: multiply the amplitude of the antenna element at each position (in the traditional phased array antenna model, the amplitude of each antenna element is set equal, and the present invention multiplies the corresponding weights based on the equal initial element amplitude) by the corresponding weight to obtain the weighted amplitude of each antenna element, that is, to obtain the final amplitude of each antenna element.

[0074] The other steps and parameters are the same as those in Specific Embodiments 1 to 8.

[0075] This implementation manner can further optimize the sidelobe level of the transmission beam by optimizing the amplitude of the antenna element.

[0076] Specific implementation method ten: This implementation method is different from any one of specific implementation methods one to nine in that, in step four, a phased array antenna model is designed according to the position and amplitude of each antenna element, specifically:

[0077] Antennas are set at the positions of the antenna elements output in step 26, and the final amplitudes of the antenna elements obtained in step 3 are used as the amplitudes of the set antennas to complete the design of the phased array antenna model.

[0078] The other steps and parameters are the same as those in Specific Embodiments 1 to 9.

[0079] Since the present invention performs sparse processing on the antenna elements, the designed phased array antenna model is also called a sparse antenna array model. Compared with the traditional phased array antenna model in which the antenna elements are evenly arranged at equal intervals and the amplitudes of each antenna element are equal, the method of the present invention first optimizes the arrangement of the antenna elements and reduces some antenna elements, and then weights the amplitudes of each antenna element. The phased array antenna model after position arrangement optimization and amplitude weighting can still meet the actual application requirements well, which also illustrates the feasibility of the method of the present invention.

[0080] Example

[0081] This embodiment proposes a beamforming method for low-orbit ultra-dense constellation satellites based on a sparse array and two-dimensional Gaussian weighting. The specific implementation process is as follows:

[0082] Step 1: construct an interference scenario model of the satellite transmitter of the low-orbit ultra-dense constellation network, wherein the interference scenario model includes a gateway station, a ground user terminal and a LEO satellite, and also includes a working link and an interference link of the LEO satellite, wherein the working link of the LEO satellite specifically includes: a user link of the LEO satellite to the ground user terminal and a feeder link of the LEO satellite to the gateway station;

[0083] like Figure 1 As shown, when a satellite transmits information to a ground terminal through a downlink, it will be interfered by other links and other satellites, causing the transmission beams to overlap with each other, resulting in the formation of grating lobes in the antenna pattern or a significant increase in the sidelobe level. The present invention suppresses the sidelobe level of the transmission beam by optimizing the antenna position and antenna amplitude, thereby effectively avoiding interference.

[0084] The normalized ideal transmission beam model of the LEO satellite radiating antenna in the interference scenario model is established:

[0085]

[0086] Among them, G(τ) is the normalized ideal transmit beam model, G max represents the maximum gain of the LEO satellite radiating antenna, τ represents the off-axis angle of the LEO satellite radiating antenna, τ b is an intermediate variable, PSLL represents the peak sidelobe level in the transmit beam antenna pattern, and Y and Z are both thresholds;

[0087]

[0088] Where D is the aperture size of the LEO satellite radiating antenna. Assume that the antenna aperture size is 15.6λ, the array elements are evenly arranged, the interval d is 0.5λ, λ is the signal wavelength, and the transmitted signal frequency is 12GHz, which belongs to the Ku-band downlink. τ b Numerically equal to half the beamwidth.

[0089] Y=1.5τ b

[0090]

[0091] Step 2: Establish the objective function of the normalized ideal transmit beam model:

[0092]

[0093] Where θ is the elevation angle of the LEO satellite radiating antenna, is the azimuth of the LEO satellite radiating antenna, is the antenna pattern function, PSLL is the peak sidelobe level of the transmit beam antenna pattern, S is the angular coverage of the main lobe beam, and |·| represents the absolute value.

[0094] Then, the fitness function of the genetic algorithm is established based on the objective function, and the genetic algorithm is used to optimize the arrangement of antenna elements, that is, to obtain the position of each antenna; the specific process is:

[0095] Step 21: Define that each antenna element in the phased array antenna model is located on the YOZ plane of the spatial rectangular coordinate system, and the position of each antenna element satisfies the 120° symmetry constraint. The total number of antenna elements in the phased array antenna model is N′. Then select all antennas located within the range of 0 to 120° in the circumferential direction from the phased array antenna model (i.e., select N′ / 3). Use the position of the selected antenna as the quantity to be optimized, and continue to execute step 22;

[0096] The 120° symmetry constraint means that for any antenna within the circumferential direction of 0° to 120°, after the antenna is rotated 120° in the circumferential direction, there is also an antenna at the new position reached, and within the circumferential direction of 120° to 240°, except for the new position reached by the antenna, there is no antenna array element at any other position, and after the antenna is rotated 240° in the circumferential direction, there is also an antenna at the new position reached, and within the circumferential direction of 240° to 360°, except for the new position reached by the antenna, there is no antenna array element at any other position, that is, after the area within the circumferential direction of 0° to 120° is rotated 120°, it will completely overlap with the area within the circumferential direction of 120° to 240°, and after all antennas within the circumferential direction of 0° to 120° are rotated 240° in the circumferential direction, they will completely overlap with the area within the circumferential direction of 240° to 360°. Moreover, the present invention does not specifically limit the direction of rotation, as long as it rotates in one direction throughout the entire process, it can rotate in the clockwise direction or in the counterclockwise direction throughout the entire process.

[0097] Step 22: Initialize the number of individuals in the genetic algorithm to N, each individual includes the position of each antenna selected in step 21, initialize the number of iterations to K, and initialize the crossover probability to P. c , initialize the mutation probability to P m , initialize the sparsity rate to η0;

[0098] Step 23, initialize the number of iterations k = 1;

[0099] Step 24, respectively calculate the fitness function value of each individual obtained in the k-1th iteration (before the first iteration, it is necessary to initialize the position of each antenna array element in each individual, and then perform random sparse processing on the initial individuals based on the sparsity rate, that is, the state value of the antenna array element position of the proportion η0 in each individual is recorded as 1, and the fitness function value is calculated using the antenna array element position with a state value of 1 in the individual);

[0100] The fitness function is:

[0101]

[0102] in, is the fitness function, ω is the weighting matrix, the superscript H represents the conjugate transpose of the matrix, and a is the steering matrix;

[0103] The calculation method of the weighted matrix ω is:

[0104]

[0105] Among them, (α, β) is the direction of arrival, e is the base of the natural logarithm, j is the imaginary unit, (y i ,z i ) is the position coordinate of the i-th antenna with a state value of 1 in the individual in the YOZ plane, i = 1, 2, 3, ..., M, M is the total number of antennas with a state value of 1 in the individual,

[0106] The calculation method of the steering matrix a is:

[0107]

[0108] in, is the antenna radiation direction.

[0109] Step 25: performing a selection operation according to the fitness function value calculation result in step 24, performing a crossover operation on the selection operation result according to the crossover probability, and performing a mutation operation on the crossover operation result according to the mutation probability;

[0110] The selection operation adopts the roulette method, that is, the specific process of the selection operation is:

[0111] The value of the individual fitness function determines whether it can be retained to the next generation, and the probability of being retained to the next generation is calculated based on the fitness function value of each individual:

[0112]

[0113] Among them, p j is the probability that the jth individual is retained to the next generation, η j is the fitness function value of the jth individual.

[0114] In the crossover operation, if P>P c , then the state values ​​of some array elements between individuals are exchanged by random selection to change the array arrangement between individuals. In the mutation operation, a random function is used to judge each array element of the individual. When the mutation condition is met, the state value of the array element is reversed. When it is not met, the state value is retained. Since the selection, crossover, and mutation operations are all based on the change of the array element state value, the state value of some array elements is adjusted according to the predetermined sparse rate.

[0115] Step 26: Determine whether the current number of iterations is equal to K;

[0116] If k=K, the iteration is terminated, and the sparse rate correction is performed on each individual in the mutation operation result obtained in the last iteration, and the fitness function values ​​of each individual after the sparse rate correction are compared. The individual with the largest fitness function value is taken as the optimal individual, and the antenna array element with a state value of 1 and the position of the antenna array element with a state value of 1 after the sparse rate correction in the optimal individual are output (due to the sparse processing, only η0 proportion of the antenna array elements in each individual have a state value of 1); and the positions of the antenna array elements corresponding to the output antenna array elements in the range of 120° to 240° and the range of 240° to 360° in the circumferential direction are obtained;

[0117] If k≠K, execute step 27;

[0118] Step 27: According to the sparse rate η0, the sparse rate of each individual in the mutation operation result of step 25 is corrected so that the sparse rate of each individual in the mutation operation result is η0, and then k=k+1 is set, and the execution of step 24 is returned.

[0119] Table 1 is the pseudo code of the genetic algorithm with 120° symmetry constraint, which is used to select the sparse array phased array antenna model. N represents the number of individuals in the genetic population, K represents the number of iterations, Y and Z represent the position coordinates of the array elements in the plane distribution, the array elements satisfy the 120° symmetry constraint, η0 represents the sparse rate, and q represents the array element state quantity. The goal of the genetic algorithm is to select the sparse array antenna model with the minimum peak sidelobe level after the iteration.

[0120] Table 1

[0121]

[0122]

[0123] The array element arrangement diagram obtained by the genetic algorithm of the present invention is as follows: Figure 3 As shown, Figure 3 The horizontal and vertical coordinates in the figure are normalized to λ, the signal frequency f=12 GHz, the antenna aperture size is 15.6λ, the number of array elements is 730, and the sparseness rate is 80%.

[0124] Step 3: Optimize the amplitude of the antenna array element at each position based on the two-dimensional Gaussian function to obtain the amplitude of each antenna array element; the specific process is as follows:

[0125] Step 3. Calculate the weight G of the antenna element at each position based on the two-dimensional Gaussian function. i :

[0126]

[0127] Among them, μ1, μ2, σ1, σ2 and ρ are all constants, Gi is the position (y i ,z i )The weight of the antenna element on the

[0128] Step 32: Multiply the amplitude of the antenna element at each position by the corresponding weight to obtain the weighted amplitude of each antenna element, that is, to obtain the final amplitude of each antenna element.

[0129] Step 4: Design the phased array antenna model according to the position and amplitude of each antenna, specifically:

[0130] Antennas are set at the positions of the antenna elements output in step 26, and the final amplitudes of the antenna elements obtained in step 3 are used as the amplitudes of the set antennas to complete the design of the phased array antenna model.

[0131] The designed phased array antenna model is used to perform beamforming. The antenna pattern function of the beamforming technology of the present invention is for:

[0132]

[0133] Among them, g represents the weighting factor, which is G i The weighted matrix composed of .

[0134] The antenna pattern of the beam forming technology of the present invention is as follows: Figure 4 As shown, in Figure 4 In the sparse array phased array antenna model, after adopting the two-dimensional Gaussian weighted element amplitude, the beam width is controlled at 4.4° and the peak sidelobe level is -27.05dB, which meets the beam width and peak sidelobe level requirements of the ideal model. Moreover, compared with the full array element antenna model with the same antenna aperture, the number of array elements is reduced by 20%, and the beamforming effect is close to the requirements of the normalized ideal transmit beam. The planar phased array antenna model of the present invention solves the problems of severe interference between transmit beams and high antenna structure complexity in low-orbit ultra-dense constellation network satellites.

[0135] The above calculation examples of the present invention are only used to explain the calculation model and calculation process of the present invention in detail, and are not intended to limit the implementation methods of the present invention. For ordinary technicians in the relevant field, other different forms of changes or modifications can be made based on the above description. It is impossible to list all the implementation methods here. All obvious changes or modifications derived from the technical solution of the present invention are still within the scope of protection of the present invention.

Claims

1. A beamforming method for low-orbit ultra-dense constellation satellites based on sparse array and two-dimensional Gaussian weighting, characterized in that: The method specifically comprises the following steps: Step 1: construct an interference scenario model for the satellite transmitter of the low-orbit ultra-dense constellation network, wherein the interference scenario model includes a gateway, a ground user terminal, and a LEO satellite, and establish a normalized ideal transmission beam model of the LEO satellite radiating antenna in the interference scenario model; Step 2: Establish an objective function of the normalized ideal transmission beam model, and then establish a fitness function of the genetic algorithm based on the objective function, and use the genetic algorithm to optimize the arrangement of antenna array elements, that is, to obtain the position of each antenna array element; Step 3: Optimize the amplitude of the antenna array element at each position based on the two-dimensional Gaussian function to obtain the amplitude of each antenna element; Step 4: Design a phased array antenna model according to the position and amplitude of each antenna element, and use the designed phased array antenna model to perform beam forming.

2. The beamforming method for low-orbit ultra-dense constellation satellites based on sparse array and two-dimensional Gaussian weighting according to claim 1, characterized in that: The interference scenario model also includes a working link and an interference link of a LEO satellite, wherein the working link of the LEO satellite specifically includes: LEO satellites have user links to ground user terminals and LEO satellites have feeder links to gateways.

3. The beamforming method for low-orbit ultra-dense constellation satellites based on sparse array and two-dimensional Gaussian weighting according to claim 2, characterized in that: The normalized ideal transmission beam model of the LEO satellite radiating antenna is: Among them, G(τ) is the normalized ideal transmit beam model, G max represents the maximum gain of the LEO satellite radiating antenna, τ represents the off-axis angle of the LEO satellite radiating antenna, τ b is an intermediate variable, PSLL represents the peak sidelobe level in the transmit beam antenna pattern, and Y and Z are both thresholds.

4. The beamforming method for low-orbit ultra-dense constellation satellites based on sparse array and two-dimensional Gaussian weighting according to claim 3, characterized in that: The intermediate variable τ b for: Where D is the aperture size of the LEO satellite radiating antenna, and λ is the signal wavelength; The thresholds Y and Z are: Y=1.5τ b 5. The beamforming method for low-orbit ultra-dense constellation satellites based on sparse array and two-dimensional Gaussian weighting according to claim 4, characterized in that: The objective function of the normalized ideal transmit beam model is: Where |PSLL| is the objective function of the normalized ideal transmit beam model, θ is the elevation angle of the LEO satellite radiating antenna, is the azimuth of the LEO satellite radiating antenna, is the antenna pattern function, S is the angular coverage of the main lobe beam, and |·| represents the absolute value.

6. The beamforming method for low-orbit ultra-dense constellation satellites based on sparse array and two-dimensional Gaussian weighting according to claim 5, characterized in that: In the step 2, a fitness function of a genetic algorithm is established based on the objective function, and the genetic algorithm is used to optimize the arrangement of antenna elements, that is, to obtain the position of each antenna element; the specific process is as follows: Step 21: define that each antenna element in the phased array antenna model is located on the YOZ plane of the spatial rectangular coordinate system, and the position of each antenna element satisfies the 120° symmetry constraint. The total number of antenna elements in the phased array antenna model is N′. Then select all antenna elements located within the range of 0 to 120° in the circumferential direction from the phased array antenna model, use the position of the selected antenna element as the quantity to be optimized, and continue to execute step 22; Step 22: Initialize the number of individuals in the genetic algorithm to N, each individual includes the position of each antenna array element selected in step 21, initialize the number of iterations to K, and initialize the crossover probability to P. c , initialize the mutation probability to P m , initialize the sparsity rate to η0; Step 23, initialize the number of iterations k = 1; Step 24: Calculate the fitness function value of each individual obtained in the k-1th iteration; Step 25: performing a selection operation according to the fitness function value calculation result in step 24, performing a crossover operation on the selection operation result according to the crossover probability, and performing a mutation operation on the crossover operation result according to the mutation probability; Step 26: Determine whether the current number of iterations is equal to K; If k=K, the iteration is terminated, and the sparse rate of each individual in the mutation operation result obtained in the last iteration is corrected respectively, and then the fitness function values ​​of each individual after the sparse rate correction are compared, and the individual with the largest fitness function value is taken as the optimal individual, and the antenna array element with a state value of 1 and the position of the antenna array element with a state value of 1 after the sparse rate correction in the optimal individual are output; and the positions of the antenna array elements corresponding to the output antenna array elements in the range of 120° to 240° and the range of 240° to 360° in the circumferential direction are obtained; If k≠K, execute step 27; Step 27: According to the sparse rate η0, the sparse rate of each individual in the mutation operation result of step 25 is corrected, and then k=k+1 is set, and the execution of step 24 is returned.

7. The beamforming method for low-orbit ultra-dense constellation satellites based on sparse array and two-dimensional Gaussian weighting according to claim 6, characterized in that: The selection operation adopts a roulette method, that is, the specific process of the selection operation is: The probability of being retained to the next generation is calculated based on the fitness function value of each individual: Among them, p j is the probability that the jth individual is retained to the next generation, η j is the fitness function value of the jth individual.

8. The beamforming method for low-orbit ultra-dense constellation satellites based on sparse array and two-dimensional Gaussian weighting according to claim 7, characterized in that: The fitness function is: in, is the fitness function, ω is the weighting matrix, the superscript H represents the conjugate transpose of the matrix, and a is the steering matrix; The calculation method of the weighted matrix ω is: Among them, (α, β) is the direction of arrival, e is the base of the natural logarithm, j is the imaginary unit, (y i ,z i ) is the position coordinate of the i-th antenna with a state value of 1 in the individual in the YOZ plane, i = 1, 2, 3, ..., M, M is the total number of antennas with a state value of 1 in the individual; The calculation method of the steering matrix a is: in, is the antenna radiation direction.

9. The beamforming method for low-orbit ultra-dense constellation satellites based on sparse array and two-dimensional Gaussian weighting according to claim 8, characterized in that: The specific process of step three is: Step 31: Calculate the weight of the antenna element at each position based on the two-dimensional Gaussian function: Among them, μ1, μ2, σ1, σ2 and ρ are all constants, G i is the position (y i ,z i )The weight of the antenna element on the Step 32: Multiply the amplitude of the antenna element at each position by the corresponding weight to obtain the weighted amplitude of each antenna element, that is, the final amplitude of each antenna element.

10. The beamforming method for low-orbit ultra-dense constellation satellites based on sparse array and two-dimensional Gaussian weighting according to claim 9, characterized in that: In the step 4, the phased array antenna model is designed according to the position and amplitude of each antenna element, specifically: Antennas are set at the positions of the antenna elements output in step 26, and the final amplitudes of the antenna elements obtained in step 3 are used as the amplitudes of the set antennas to complete the design of the phased array antenna model.

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