A method for optimizing dynamic beam coverage of satellite communication assisted by a rotatable antenna array

Abstract

The application discloses a kind of rotatable antenna array auxiliary satellite communication dynamic beam coverage optimization method, comprising: establishing the channel model under the communication scene of low-orbit satellite, specified coordinate system is constructed, satellite orbit parameter, coverage area, visible area and interference area are defined;Combined with the specified parameter of rotatable antenna array on satellite to establish specified calculation model;Satellite service time is time slot discretization, ground angular domain is grid discretization, constructs joint optimization problem, with minimum as target interference area average signal leakage power, and satisfies coverage gain constraint, antenna pitch angle constraint, rotation rate constraint and transmission power constraint;Using alternate optimization strategy, optimize transmission beam forming vector when fixed rotatable antenna deflection angle, optimize antenna deflection angle when fixed transmission beam forming vector, iteration is solved to obtain the optimal beam control parameter in target period.The application can better adapt to the coverage direction change caused by satellite high-speed movement.

Description

Technical Field

[0001] This invention relates to the field of satellite signal interference suppression technology, specifically to a method, device, and storage medium for dynamic beam coverage optimization of satellite communication assisted by a rotatable antenna array for low-Earth orbit satellites. It can be applied to coverage enhancement, interference suppression, beam control, and related intelligent resource optimization scenarios in low-Earth orbit satellite communication systems. Background Technology

[0002] The sixth-generation mobile communication system is designed to meet the application requirements of ubiquitous connectivity, wide-area coverage and large-scale access. Since it is difficult to provide continuous and reliable wireless services in deserts, oceans, mountains, forests and disaster-stricken areas by relying solely on terrestrial base stations, low-orbit satellite networks have become an important part of future wireless communication networks due to their advantages such as wide coverage, flexible deployment and strong disaster resistance.

[0003] In low-Earth orbit satellite communication scenarios, satellites move at high speeds along their orbits, and the directions of the ground coverage area and the interference area relative to the onboard antenna array change continuously over time. At the same time, with the increase in constellation density and the popularization of multi-beam concurrent transmission, the interference problem between adjacent beams and adjacent satellites is becoming increasingly prominent.

[0004] At this time, traditional fixed antenna arrays, due to their fixed array geometry and limited beam adjustment freedom, are difficult to dynamically adjust their pointing according to the satellite's motion state and changes in the service area, which can easily lead to insufficient gain in the coverage area and increased signal leakage in the interference area.

[0005] Furthermore, while existing technologies can improve the performance of satellite-to-ground links to some extent through digital beamforming, relying solely on the transmission weight adjustment of a fixed array makes it difficult to simultaneously meet the requirements of coverage enhancement and interference suppression. This is especially true in low-Earth orbit satellite scenarios, where the coverage area, visible area, and interference area all exhibit significant time-varying characteristics. Optimizing only the transmission beamforming vector makes it difficult to fully utilize the spatial freedom brought by the physical rotation of the antenna, resulting in limited overall system performance.

[0006] To address this, this application proposes a method for optimizing dynamic beam coverage of satellite communications using a rotatable antenna array. This method combines the structural degrees of freedom of the rotatable antenna array with the degrees of freedom of digital beamforming. It can effectively reduce signal leakage power in the interference area while satisfying coverage gain constraints, mechanical rotation constraints, and transmit power constraints, thereby improving coverage flexibility and interference suppression capabilities in low-Earth orbit satellite non-terrestrial networks and solving the aforementioned technical problems. Summary of the Invention

[0007] The main objective of this invention is to provide a method for optimizing dynamic beam coverage of satellite communication using a rotatable antenna array, in order to solve the technical problems mentioned in the background art, such as the difficulty of existing fixed antenna arrays in dynamically adapting to changes in satellite orbits, limited gain in coverage areas, and severe interference leakage.

[0008] The present invention solves the above-mentioned technical problems by adopting the following technical solutions:

[0009] A method for optimizing dynamic beam coverage in satellite communications using a rotatable antenna array, executed via computer equipment, includes the following steps:

[0010] Step S1. Establish a channel model for low-Earth orbit satellite communication scenarios, construct a geocentric spherical coordinate system, a geocentric rectangular coordinate system, and a satellite coordinate system with the center of the satellite antenna array as the origin, and define the satellite orbit parameters, ground coverage area, satellite visible area, and interference area accordingly.

[0011] Step S2. Determine the position of each element in the rotatable antenna array on the satellite, the deflection angle vector of each rotatable antenna, the corresponding pointing vector, and the transmit beamforming vector according to the channel model, and establish a calculation model for beamforming gain in the specified coverage area and signal leakage power in the interference area.

[0012] Step S3. By discretizing the continuous time interval, the satellite service time is divided into multiple specified number of time slots, and the ground corner domain is divided into multiple specified number of discrete grids, finally obtaining the coverage area sample and interference area sample under each time slot and each discrete grid.

[0013] Step S4. With the goal of minimizing the average signal leakage power within the interference area, and with constraints on the average beamforming gain within the coverage area, the elevation angle of the rotatable antenna, the rotation rate of the rotatable antenna, and the satellite transmit power, a joint optimization problem is constructed.

[0014] Step S5. Solve the joint optimization problem using an alternating optimization method, wherein the transmit beamforming vector is optimized when the rotatable antenna deflection angle is fixed, and the rotatable antenna deflection angle is optimized when the transmit beamforming vector is fixed.

[0015] Step S6. Iteratively update the control parameters using the solution results until the specified convergence condition is met. Finally, output the optimal beam control parameters and optimal antenna deflection angle control parameters for the target time period, including the satellite transmission beam and the deflection angle of each rotatable antenna, to achieve coverage enhancement and interference suppression.

[0016] Preferably, the satellite orbital parameters in step S1 include at least the Earth's radius. Satellite orbital inclination Satellite orbital altitude The orbital period, number of satellites in orbit, service time per satellite, and geocentric angle are used to calculate the geocentric latitude, geocentric longitude, and position coordinates of the satellite in the geocentric rectangular coordinate system at different times. Furthermore, the spatial vector and unit spatial vector of any point on the ground relative to the satellite, as well as the direction vector in the satellite coordinate system, are obtained to characterize the geometric relationship between the satellite and the ground point. The orbital period is defined as:

[0017] ;

[0018] in, It is the gravitational constant. It is the mass of the Earth;

[0019] At this point, regarding the number of satellites in orbit The single satellite service time is defined as follows: ;

[0020] Therefore, based on the orbital parameters, the geocentric longitude, geocentric latitude, and position coordinates of the satellite in the geocentric rectangular coordinate system at different times can be calculated in the channel model:

[0021] Geocentric latitude: ;

[0022] Earth's longitude: ;

[0023] in, Let be the satellite angular distance at time t. The inclination of the satellite orbit;

[0024] The satellite's position coordinates in the geocentric rectangular coordinate system:

[0025] ;in .

[0026] Furthermore, based on the satellite's position coordinates in the geocentric rectangular coordinate system, we can also obtain the spatial vector of any point on the ground relative to the satellite, as follows:

[0027] ;

[0028] The formulas for the unit space vector and the direction vector in the satellite coordinate system are as follows:

[0029] Unit space vector: ;

[0030] And the direction vector in the satellite coordinate system: ;

[0031] Among them, for and , representing the geocentric latitude and geocentric longitude of any point on the ground at time t, respectively;

[0032] , used to characterize the geometric relationship between the satellite and ground points;

[0033] Therefore, the ground target area is the coverage area. If the visible area is the area of ​​the ground that the satellite can observe at the current moment, then: ;

[0034] Finally, the difference between the visible area and the covered area is defined as the interference area, with the following: .

[0035] Preferably, in step S2, the rotatable antenna array is configured as a planar array antenna deployed on the satellite. , This represents the total number of antennas. This represents the number of antennas along the x-axis of the array. Let be the number of antennas along the y-axis of the array, then there exists a... A rotatable antenna The position is defined as:

[0036]

[0037] in, The preset spacing between adjacent antennas For the first The position of the rotatable antenna on the array's x-axis For the first The position of a rotatable antenna along the array's y-axis;

[0038] There exists the first The deflection angle vector of a rotatable antenna Defined as:

[0039]

[0040] in, This represents the total number of antennas. The pitch angle, Azimuth

[0041] At this time, in the satellite coordinate system, the first The pointing vector of the root antenna is defined as: ;

[0042] The transmit beamforming vector is defined as: ,in It is the transmitted beamforming vector at time t, represented as an N-dimensional complex vector, where each element... It is the complex weight (amplitude and phase) applied to the nth antenna.

[0043] Preferably, in step S2, if a transmit beamforming vector is defined, the downlink channel from the satellite to the ground point is represented as a combination of path loss, array response, and rotatable antenna directional gain. The transmit beamforming vector and the downlink channel together determine the channel gain at the ground point, and the average beamforming gain within the coverage area is calculated accordingly. The calculation model for beamforming gain includes the average signal leakage power within the interference area.

[0044] (1) Path loss term, which is defined as:

[0045] ;

[0046] ;

[0047] This represents the signal transmitted from the satellite to the ground point. The power attenuation, of which Represents the geocentric latitude and geocentric longitude of any point on the Earth's surface;

[0048] The path loss constant is the reference distance (1 meter). Represents the ground point at time t Relative to the satellite's spatial vector, It is the Earth's radius. It is the satellite's orbital altitude. The geocentric latitude of the satellite at time t. The geocentric longitude of the satellite at time t. It is the vector L2 norm, i.e., the ground point Relative to the distance of the satellite, The path loss exponent is typically greater than or equal to 2.

[0049] (2) Array response term, which is defined as:

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] in, It is an N-dimensional complex vector, and its nth element is Used to describe the different positions of the antenna array due to electromagnetic waves reaching the nth antenna element on the antenna array. The phase difference caused by the path difference of the wave It is the carrier wavelength, and j is the imaginary unit. This refers to the coordinate system in which the distance from the center of the satellite antenna array to the ground point is measured. The unit direction vector, The rotation matrix refers to the rotation from the geocentric rectangular coordinate system to the satellite coordinate system. It is the satellite orbital inclination angle (the angle between the satellite orbital plane and the Earth's equatorial plane). The geocentric latitude of the satellite at time t. The geocentric longitude of the satellite at time t. Represents the ground point at time t The unit spatial vector relative to the satellite;

[0055] (3) The directional gain term of the rotatable antenna is defined as follows:

[0056] ;

[0057] ;

[0058] in, Represents the antenna gain vector, which is an N-dimensional vector where each element... It is the square root of the gain of a single antenna, encompassing the effects of all antenna directivity on the signal amplitude. These are shape parameters that control the beamwidth of the antenna pattern. The larger the antenna, the narrower its main lobe and the steeper the gain change. The maximum gain of the antenna is calculated using the following formula: , Antenna pointing ground point direction The angle between them It refers to the deflection angle vector of the nth antenna at time t. Refers to the deflection angle of all antennas at time t. The set is a 2N-dimensional vector;

[0059] (4) The downlink channel table from satellite to ground point is defined as follows:

[0060] ;

[0061] in, As an N-dimensional complex channel vector, it is used to represent the interaction between N antenna elements and ground points. downlink channel, For path amplitude loss, This indicates a distance-dependent common phase, which represents the distance traveled by electromagnetic waves. The resulting absolute phase delay, which is the same for all antenna elements, is determined by the antenna directivity gain. and array response composition, The Hadamard product is the element-wise multiplication of vectors. Refers to the deflection angle of all antennas at time t. The set is a 2N-dimensional vector;

[0062] (5) Therefore, the antenna gain is:

[0063] , ;

[0064] (6) The transmit beamforming vector and the downlink channel together determine the channel gain at the ground point as follows:

[0065] ;

[0066] in Let be the path power loss at time t. For antenna directivity gain, For array response;

[0067] (7) The average beamforming gain within the coverage area is as follows:

[0068] ;

[0069] ;

[0070] Where the numerator is the channel gain. In the coverage area double integral, The target coverage area is a pre-defined constant region, and the denominator is the path power loss at time t. In the coverage area double integral, To combine antenna directivity gain and array response The composite channel steering vector.

[0071] Preferably, the formula for calculating the signal leakage power within the interference area in step S2 is:

[0072] ;

[0073] Where the numerator is the channel gain. In the interference area double integral, Defined as interference area (visible area) (Difference set with the covered area) The visible area is defined as the area of ​​the ground that the satellite can observe at the current moment:

[0074] ;

[0075] The denominator is the path power loss at time t. In the interference area double integral, This is a composite channel steering vector, incorporating the antenna directivity gain at time t. and array response at time t ; The service time for a single satellite is calculated using the following formula: , , The number of satellites in orbit. For orbital period, The gravitational constant is... For Earth mass, For the Earth's radius, The satellite's orbital altitude, This represents the average leakage power in the interference area during the service duration. refer to The set of all antenna deflection angles within a given time period. refer to The set of all transmitted beamforming vectors within a given time.

[0076] Preferably, in step S3, spatiotemporal discretization is used, wherein time discretization is: the satellite service time interval is divided into M time slots, and the average performance of the time slot is characterized by the midpoint of each time slot; spatial discretization is: the target angular domain is divided into multiple discrete grids, and a set of discrete grids in the coverage area and a set of discrete grids in the interference area are constructed with the center point of each discrete grid, so as to obtain the discretized average beamforming gain and average signal leakage power respectively.

[0077] The specific calculation process for obtaining the coverage area samples and interference area samples under each time slot and each discrete grid includes:

[0078] The satellite service time interval is divided into M equal time slots, and the midpoint of the m-th time slot is used as the starting point. Characterizing the average performance of this time slot, we have , For single satellite service time;

[0079] The target angular domain is divided into multiple discrete grids. Simultaneously, a set of discrete grids in the coverage area is constructed using the center points of each discrete grid. And the discrete grid set in the interference region, we have:

[0080] ;

[0081] ;

[0082] ;

[0083] in, This is the set of all grid center points after discretizing the entire corner domain. To encompass the entire Earth's angular region (latitude [ π / 2, π / 2], longitude ( When discretizing π,π), the number of grids divided in the latitude and longitude directions. For coverage area Discrete sets The intersection, i.e., the coverage area The set of all discrete grid points, number of which is ; For the m-th time slot, the interference region The set of all discrete grid points, number of which is ;

[0084] At this point, the discretized average beamforming gain can be obtained as follows:

[0085]

[0086] in, This represents the average beamforming gain after discretization of the m-th time slot. for The time, i.e., the time from the m-th time slot satellite to the ground point in the interference area. Path power loss, For the transmit shaping vector of the m-th time slot, Let M be the steering vector for the m-th time slot composite channel, where M is the total number of time slots.

[0087] Preferably, the constraints in the joint optimization problem of step S4 specifically include:

[0088] (a) The average beamforming gain in each time slot coverage area is not lower than a preset threshold. ,Right now:

[0089] ;

[0090] (b) The elevation angle of each rotatable antenna is within a preset angle range, that is:

[0091] ;

[0092] in, Let be the elevation angle of the nth antenna in the mth time slot. This represents the minimum elevation angle of the antenna, and is a constant.

[0093] (c) The pointing variation of the same rotatable antenna between adjacent time slots does not exceed a preset rotation rate limit, i.e.:

[0094] ;

[0095] in, This is represented as the pointing unit vector of the nth rotatable antenna. and Let represent the pointing vectors of the nth antenna at times m and m+1, respectively, which will be simplified as follows: The vector magnitude is 1; This represents the upper limit of the antenna's rotation speed. This represents the upper limit of the rotation angle of adjacent time slot antennas;

[0096] (d) The norm of the transmit beamforming vector in each time slot is not greater than the preset transmit power limit. ,Right now:

[0097] ;

[0098] in This is the satellite's maximum launch power.

[0099] Preferably, in step S5, when the deflection angle of the rotatable antenna is fixed, the transmit beamforming vector for each time slot is optimized, transforming the corresponding subproblem into an optimization problem with coverage gain and power constraints, and solving it using the Lagrange multiplier method. The optimization problem is as follows:

[0100]

[0101] in:

[0102] ;

[0103] At this time, due to The optimization is independent for each time slot, and the optimization objective can be equivalent to optimizing each time slot. , can be represented as:

[0104] ;

[0105] ;

[0106] at the same time It can be represented as:

[0107] ;

[0108] ;

[0109] In the above formula, It refers to the set of all transmitted beamforming vectors across all time slots. For the transmit shaping vector of the m-th time slot, The average signal leakage power over the interference region across all time slots. Let be the average signal leakage power in the interference region of the m-th time slot; Let m be the average beamforming gain in the coverage area of ​​the m-th time slot. It is the set of all antenna deflection angles obtained in the i-th iteration for the m-th time slot (the solution for optimizing the deflection angle of the rotatable antenna when the transmit beamforming vector is fixed in the i-th iteration), and is used as a constant when optimizing the transmit beamforming vector for each time slot with the rotatable antenna deflection angle fixed. The average beamforming gain threshold. This is the satellite's maximum transmission power;

[0110] During the solution process using the Lagrange multiplier method, when the coverage gain constraint is activated but the power constraint is not activated, i.e. In order to satisfy In the set, consider arbitrary directions (non-zero), then , This is the amplitude scaling factor. ,therefore The optimization objective can be expressed as: Equivalent to:

[0111] The minimum value is the solution to the generalized eigenvalue problem. The minimum generalized eigenvalue The optimal direction is the corresponding generalized eigenvector. ,have:

[0112] ,in Represents the optimal transmit shaping vector for the m-th time slot;

[0113] When both coverage gain constraint and power constraint are activated, i.e. The optimal solution that satisfies the constraints is obtained through a one-dimensional search. In the set, consider unit vectors in arbitrary directions. , Thus, the coverage constraint is obtained:

[0114] ;

[0115] ;

[0116] Simultaneously, the optimization objective is obtained:

[0117] ;

[0118] The existence of an optimization problem is equivalent to:

[0119]

[0120] Construct the Lagrangian function:

[0121] ;

[0122] get:

[0123] ;

[0124] ;

[0125] ;

[0126] One-dimensional search Solve for the eigenvectors under the current optimization. And check the constraints. Does it meet the requirements?

[0127] in, Let n be the pointing vector of the nth antenna in the mth time slot. For the transmit shaping vector of the m-th time slot, The average beamforming gain threshold. This is the satellite's maximum transmission power. It is a Lagrange multiplier.

[0128] Preferably, in step S5, when fixing the transmit beamforming vector, a pointing vector determined by the elevation angle and azimuth angle is introduced. The optimization problem of the rotatable antenna deflection angle is equivalently transformed into an optimization problem about the pointing vector. For the non-convex objective function and non-convex covering constraints, a continuously convex approximation method based on first-order Taylor expansion is used to construct a convex approximation subproblem that is updated round by round, and then solved using CVX tools. The rotatable antenna deflection angle optimization problem is as follows:

[0129] ;

[0130] in, The pointing vector of the nth antenna in the mth time slot is represented by... Pitch and azimuth Sure; This represents the set of all antenna pointing vectors in the m-th time slot; It represents the set of all antenna pointing vectors in all time slots; This represents the average signal leakage power in the interference region across all time slots. This represents the average beamforming gain in the coverage area over the m-th time slot; ; This represents the minimum antenna elevation angle; This represents the maximum antenna rotation speed;

[0131] For the non-convex objective function and non-convex covering constraints, a continuous convex approximation method based on first-order Taylor expansion is used to construct a round-by-round updated convex approximation subproblem, which is then solved using the CVX tool.

[0132] Furthermore, the original leak target is:

[0133] ;

[0134] ;

[0135] ;

[0136] For the m-th time slot Leakage function of the region;

[0137] The definitions are:

[0138] ;

[0139] ;

[0140] Then the first-order approximation (affine) of Z is:

[0141] ;

[0142] For the m-th time slot The area receives signals, For the m-th time slot The area receives affine signals;

[0143] SCA Round k As a convex approximation target for:

[0144] ;

[0145] To approximate the received signal, Based on the set of antenna pointing vectors A convex approximation of the objective function;

[0146] The original covering constraint is:

[0147] ;

[0148] ;

[0149] We obtain the k-th iteration, the m-th time slot, and the... Leakage function of the region Linear lower bound:

[0150] ;

[0151] For real number operations, the covering constraint linearization is as follows:

[0152] ;

[0153] During the optimization of the pointing vector, a unit modulus constraint relaxation condition is set: ;

[0154] Simultaneously, setting an iteration step size limit ensures that the first-order approximation holds: ;

[0155] set up: ;

[0156] During the optimization process of the pointing vector Approaching 1;

[0157] After each round of optimization, the obtained pointing vector is projected back onto the unit sphere; at the same time, combined with the pointing difference constraint between adjacent time slots, the rotatable antenna can achieve dynamic tracking of the coverage area and suppression of the interference area while satisfying the mechanical rotation continuity.

[0158] Preferably, the optimization problem of the pointing vector is:

[0159] ;

[0160] in, The number of discrete grid points in the interference area; , representing the distance from the m-th time slot satellite to the ground point in the interference area. Normalized weights for path power loss; Let represent the set of all antenna pointing vectors in the m-th time slot; for any discrete point, define:

[0161] ;

[0162] ;

[0163] The objective function is expressed as:

[0164] ;

[0165] in This represents the transmit shaping vector for the m-th time slot. This is the steering vector for the m-th time slot composite channel. This refers to the coordinate system in which the distance from the center of the satellite antenna array to the ground point is measured. The unit direction vector; This represents the position of the nth antenna element on the antenna array; This refers to the antenna's maximum gain;

[0166] make , , This represents the current iteration point, which is the antenna pointing vector of the m-th time slot obtained in the previous iteration;

[0167] At point At, for the function Perform a first-order Taylor expansion: Using a first-order approximation of the square As an optimization target;

[0168] The number of discrete grid points in the coverage area. Represents the distance from the m-th time slot satellite to the ground point in the coverage area. The normalized weights for path power loss, with the coverage constraint expressed as: ;

[0169] Using a first-order approximation replace You can get ,in Represents taking the lower bound. Representative of the real part, The conjugate constraint is represented as:

[0170] ;

[0171] This represents the minimum antenna elevation angle; This represents the maximum antenna rotation speed; This represents a parameter used in continuous convex approximation algorithms to limit the step size update in each iteration, ensuring that the first-order approximation is valid near the current iteration point. Used to ensure Approaching 1.

[0172] Preferably, the specific steps in step S5, which use an alternating optimization algorithm to alternately transmit the beamforming vector and the rotatable antenna pointing vector, include:

[0173] Step S51. Initialize the rotatable antenna pointing vector For all antennas, each time slot is perpendicular to the Earth's center; that is, the pointing vector of the nth antenna in the mth time slot. Fixed rotatable antenna pointing vector With optimized emission shaping vector ;

[0174] Step S52. In the i-th iteration, perform the following two steps in sequence:

[0175] a. Fixed emission shaping vector Optimize the pointing vector of the rotatable antenna ;

[0176] b. Fixed rotatable antenna pointing vector Optimize the emission shaping vector ;

[0177] Step S53. Execute the convergence criterion: If there are variables and If the update increment is less than the specified value, it is considered small enough, the iteration stops, and the result is returned.

[0178] In another aspect, the present invention also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method described above.

[0179] In another aspect, the present invention also discloses a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method described above.

[0180] As can be seen from the above technical solution, the present invention provides a method for optimizing dynamic beam coverage in satellite communication using a rotatable antenna array. Compared with the prior art, the present invention has the following advantages:

[0181] 1. This invention combines the structural degrees of freedom of a rotatable antenna array with the degrees of freedom of digital beamforming, which can effectively reduce signal leakage power in the interference area while satisfying coverage gain constraints, mechanical rotation constraints, and transmit power constraints, thereby improving coverage flexibility and interference suppression capabilities in low-Earth orbit satellite non-terrestrial networks.

[0182] 2. This invention fully utilizes the physical rotational degrees of freedom and digital beamforming degrees of freedom of the rotatable antenna array, enabling it to adjust the beam pointing in real time with satellite movement, so that the coverage area always obtains high beamforming gain.

[0183] 3. This invention uses the average signal leakage power within the interference area as the optimization target, which suppresses the leakage of ineffective energy while satisfying coverage constraints. It is applicable to low-orbit satellite non-terrestrial network scenarios with multiple beams and strong interference.

[0184] 4. This invention decomposes the original complex joint optimization problem into two sub-problems that are easy to solve by combining spatiotemporal discretization and alternating optimization, and has good engineering feasibility.

[0185] 5. This invention takes into account pitch angle constraints, rotation rate constraints, and transmit power constraints, ensuring that the optimization results meet the actual mechanical conditions and system power conditions of the spaceborne antenna, making it easy to deploy and apply in engineering systems.

[0186] It should be understood that the description in this section is not intended to identify key or essential features of embodiments of the invention, nor is it intended to limit the scope of the invention. Other features of the invention will become readily apparent from the following description. Of course, implementing any product of the invention does not necessarily require achieving all of the advantages described above simultaneously. Attached Figure Description

[0187] The accompanying drawings, which form part of this application, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention. In the drawings:

[0188] Figure 1 This is a schematic diagram of the overall calculation method of the present invention;

[0189] Figure 2 This is an illustration of the satellite orbital area coverage of the present invention;

[0190] Figure 3 This is a schematic diagram of the rotatable antenna array of the present invention;

[0191] Figure 4 This is a schematic diagram of the rotatable antenna pointing according to the present invention;

[0192] Figure 5 This is a comparison chart of the average leakage power of the schemes in the embodiments of the present invention;

[0193] Figure 6 This is a cloud map showing the leakage power / channel gain distribution of different schemes in time slot m=1 in the comparison of schemes of the embodiments of the present invention;

[0194] Figure 7 This is a cloud map showing the leakage power / channel gain distribution of different schemes in time slot m=15 during the comparison of schemes in the embodiments of the present invention. Detailed Implementation

[0195] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. Unless otherwise specified, the embodiments and features in the embodiments of this application can be combined with each other. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0196] For details in the embodiments, please refer to Figures 1 to 7 .

[0197] In this embodiment, the parameters are preferentially set as shown in Table 1 below:

[0198] Table 1. Parameter Comparison Table

[0199]

[0200] like Figure 1 As shown in the embodiment of the present invention, the method for optimizing dynamic beam coverage of satellite communication using a rotatable antenna array includes the following steps:

[0201] The first step is to establish a channel model for low-Earth orbit satellite communication scenarios, whose parameters include the Earth's radius. Satellite orbital inclination Satellite orbital altitude The orbital period is defined as:

[0202] ;

[0203] in It is the gravitational constant. It is the mass of the Earth. The number of satellites in orbit. The service time of a single satellite is defined as:

[0204] ;

[0205] Calculate the satellite's geocentric latitude at different times based on the orbital parameters:

[0206] ;

[0207] Earth's longitude:

[0208] ;

[0209] And the satellite's position coordinates in the geocentric rectangular coordinate system:

[0210] ;

[0211] in And further, the spatial vector of any point on the ground relative to the satellite is obtained:

[0212] ;

[0213] Unit space vector:

[0214] ;

[0215] And the direction vector in the satellite coordinate system:

[0216] ;

[0217] in:

[0218] Used to characterize the geometric relationship between satellites and ground points. The coverage area is the ground target region. The visible area is defined as the area of ​​the ground that the satellite can observe at the current moment.

[0219] ;

[0220] The difference between the visible area and the covered area is defined as the interference area:

[0221] ;

[0222] The above-mentioned areas cover as follows Figure 2 As shown.

[0223] The second step, as Figure 3 and Figure 4 As shown, based on the channel model, the positions of each element in the rotatable antenna array on the satellite, the deflection angle vector of each rotatable antenna, the corresponding pointing vector, and the transmit beamforming vector are determined. A calculation model is then established for the beamforming gain within the coverage area and the signal leakage power within the interference area. Figure 3 , Figure 4 As shown. Rotatable antenna arrays are planar array antennas deployed on satellites, with predetermined spacing between adjacent antennas. The position of the nth rotatable antenna is defined as follows:

[0224] ;

[0225] The deflection angle vector of the nth rotatable antenna is defined as:

[0226] ;

[0227] The pitch angle, Let be the azimuth angle. The pointing vector of the nth antenna in the satellite coordinate system is defined as:

[0228] ;

[0229] The transmit beamforming vector is defined as:

[0230] ;

[0231] The path loss term mentioned above:

[0232] ;

[0233] Array response terms:

[0234] ;

[0235] And the directional gain term for rotatable antennas:

[0236] ;

[0237] Downlink channel table from satellite to ground point:

[0238] ;

[0239] Antenna gain:

[0240] ;

[0241] in .

[0242] The transmit beamforming vector and the downlink channel together determine the channel gain at the ground point:

[0243] ;

[0244] And based on this, the average beamforming gain within the coverage area is calculated:

[0245] ;

[0246] in:

[0247] ;

[0248] Average signal leakage power within the interference area:

[0249] ;

[0250] The third step is to proceed with the algorithm description process, such as... Figure 5As shown. The continuous time interval is discretized, dividing the satellite service time into multiple time slots, and the ground corner domain into multiple discrete grids, obtaining coverage area samples and interference area samples for each time slot and each discrete grid. The time discretization involves dividing the satellite service time interval into M equal time slots, and using the midpoint time of each time slot as the basis for the discretization.

[0251] ;

[0252] Characterizing the average performance of this time slot; spatial discretization is achieved by dividing the target angular domain into multiple discrete grids:

[0253] ;

[0254] Construct a set of discrete grids within the coverage area using the center points of each discrete grid:

[0255] ;

[0256] And the discrete grid set in the interference region:

[0257] ;

[0258] Thus, the discretized average beamforming gain is obtained respectively:

[0259] ;

[0260] And average signal leakage power:

[0261] ;

[0262] The fourth step involves constructing a joint optimization problem with the goal of minimizing the average signal leakage power within the interference area, and constraints on the average beamforming gain, rotatable antenna elevation angle, rotatable antenna rotation rate, and satellite transmit power within the coverage area. This joint optimization problem is expressed as: minimizing the average signal leakage power over all time slots as the objective function. And simultaneously satisfy the following constraint: the average beamforming gain in the coverage area of ​​each time slot is not lower than a preset threshold:

[0263] ;

[0264] The elevation angles of each rotatable antenna are within a preset angle range:

[0265] ;

[0266] The pointing variation of the same rotatable antenna between adjacent time slots shall not exceed a preset rotation rate limit:

[0267] ;

[0268] The norm of the transmit beamforming vector in each time slot is no greater than the preset transmit power limit.

[0269] ;

[0270] The fifth step involves solving the joint optimization problem using an alternating optimization approach. With a fixed rotatable antenna deflection angle, the transmit beamforming vector for each time slot is optimized separately, transforming the corresponding subproblem into an optimization problem with coverage gain and power constraints.

[0271] ;

[0272] The Lagrange multiplier method is used to solve the problem; when the coverage gain constraint is activated and the power constraint is not activated, the optimal transmit beam direction is obtained through the generalized eigenvalue problem.

[0273] ;

[0274] When both coverage gain and power constraints are activated, the optimal solution that satisfies the constraints is obtained through a one-dimensional search.

[0275] When fixing the transmit beamforming vector, a pointing vector determined by the elevation and azimuth angles is introduced. The optimization problem of the deflection angle of a rotatable antenna can be equivalently transformed into an optimization problem about the pointing vector:

[0276] ;

[0277] For the non-convex objective function and non-convex covering constraints, a continuous convex approximation method based on first-order Taylor expansion is used to construct a round-by-round updated convex approximation subproblem, which is then solved using the CVX tool.

[0278] The original target of the leak was:

[0279] ;

[0280] ;

[0281] ;

[0282] definition:

[0283] ;

[0284] ;

[0285] The first-order approximation (affine) of Z is:

[0286] ;

[0287] SCA Round k As a convex approximation target:

[0288] ;

[0289] The original covering constraint is:

[0290] ;

[0291] ;

[0292] get Linear lower bound:

[0293] ;

[0294] The covering constraint is linearized as follows:

[0295] ;

[0296] During the optimization of the pointing vector, a unit modulus constraint relaxation condition is set:

[0297] ;

[0298] Simultaneously, setting an iteration step size limit ensures that the first-order approximation holds:

[0299] ;

[0300] set up:

[0301] ;

[0302] During the optimization process of the pointing vector Approximate 1. After each optimization round, the obtained pointing vector is projected back onto the unit sphere; simultaneously, combined with the pointing difference constraint between adjacent time slots, the rotatable antenna achieves dynamic tracking of the coverage area and suppression of interference areas while satisfying the continuity of mechanical rotation. Ultimately, the optimization problem is transformed into:

[0303] .

[0304] In a further embodiment, the above method is used to calculate the process, referring to... Figure 2 As shown, for the satellite service period of 0-463.2s, it is discretized into 15 time slots. When the time slot m=8, the satellite is located directly above the coverage area. At this time, the coverage area is a circle centered at (Θ, Φ)=(0, 0), and the geocentric angle between the coverage center and the boundary is 5°.

[0305] In a rectangular coordinate system with the Earth's center as the origin, a point on the ground With satellite points The space vector is:

[0306]

[0307] Combined with the reference at this time Figure 3 Satellite orbital angle The geocentric angle at time t is 75°: The satellite's geocentric latitude and longitude are respectively and .

[0308] You can also refer to Figure 4 As shown, the number of rotatable antennas is 5*5, and the spacing between adjacent antennas is... The antenna is 8.33mm in diameter and can be rotated for both elevation and azimuth.

[0309] In further experimental comparisons, the following schemes exist:

[0310] Option 1: Optimize the satellite launch beamforming vector using only the maximum ratio combining method to ensure the launch beam is pointed towards the coverage center;

[0311] Option 2: This option is used only for optimizing satellite launch beamforming vectors;

[0312] Option 3: Simultaneously use this option to optimize the satellite launch beamforming vector and the rotatable antenna;

[0313] The results of executing the same set of data using the above method are shown in the table below:

[0314] Table 2: Comparison of Average Leakage Power in Interference Area and Minimum Average Channel Gain in Coverage Area

[0315]

[0316] Based on the above data, combined with Figures 5 to 7 It is evident that Scheme 3 (this method) is significantly effective in suppressing leakage power and improving signal quality in the coverage area;

[0317] All three schemes achieved a minimum average channel gain of 10 in the coverage area, indicating that the service requirements of the coverage area were met. This demonstrates that the signal gain performance of the three schemes within the coverage area is basically equivalent, and all can meet the target coverage quality requirements. However, the core advantage of Scheme 3 (this scheme) is not reflected in the difference in coverage area performance, but mainly in the significant reduction of signal leakage in interference areas. It performs better in suppressing interference leakage in non-target areas, improving system spectrum utilization efficiency and electromagnetic compatibility performance, fully verifying the superior effect of the coordinated optimization of transmit beamforming vector and rotatable antenna. In summary, Scheme 3, which simultaneously optimizes transmit beamforming vector and rotatable antenna, achieves optimal control of leakage power while taking coverage quality into account, and has significant engineering advantages.

[0318] In another aspect, the present invention also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, causes the processor to perform the steps of the method described above.

[0319] In another aspect, the present invention also discloses a computer device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the method described above.

[0320] In another embodiment provided in this application, a computer program product containing instructions is also provided, which, when run on a computer, causes the computer to execute any of the rotatable antenna array-assisted satellite communication dynamic beam coverage optimization methods described in the above embodiments.

[0321] It is understood that the system provided in the embodiments of the present invention corresponds to the method provided in the embodiments of the present invention, and the explanation, examples and beneficial effects of the relevant content can be referred to the corresponding parts of the above methods.

[0322] This application also provides an electronic device, including a processor, a communication interface, a memory, and a communication bus, wherein the processor, communication interface, and memory communicate with each other via the communication bus.

[0323] Memory, used to store computer programs;

[0324] When the processor executes the program stored in the memory, it implements the above-mentioned method for optimizing dynamic beam coverage of satellite communication assisted by a rotatable antenna array.

[0325] The communication bus mentioned in the above-mentioned electronic devices can be a standard bus for interconnecting peripheral components or an extended industrial standard structure bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc.

[0326] The communication interface is used for communication between the aforementioned electronic devices and other devices.

[0327] The memory may include random access memory or non-volatile memory, such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.

[0328] The processors mentioned above can be general-purpose processors, including central processing units, network processors, etc.; they can also be digital signal processors, application-specific integrated circuits, field-programmable gate arrays or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0329] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The computer-readable storage medium can be any available medium accessible to a computer or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, an optical medium, or a semiconductor medium, etc.

[0330] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

[0331] Furthermore, it should be noted that if any directional indication (such as up, down, left, right, front, back, etc.) is involved in the embodiments of the present invention, the directional indication is only used to explain the relative positional relationship and movement of each component in a specific posture. If the specific posture changes, the directional indication will also change accordingly.

[0332] Furthermore, those skilled in the art should understand that in the actual use of the embodiments of this application, there may be preset thresholds used as the basis for judging the corresponding technical solutions. These thresholds are conventional technical means commonly used in the field to implement functions such as state judgment, condition recognition, and control logic switching. The specific values, setting basis, value selection methods, determination methods, and adjustment rules of the thresholds involved in this technical solution are all conventional technical choices that can be reasonably determined by those skilled in the art based on conventional technical factors such as actual application scenarios, system working states, characteristics of the detection object, hardware performance parameters, and functional requirements, through conventional experiments, calibrations, and debugging. The specific setting and adjustment of the aforementioned thresholds will not cause this technical solution to be unimplementable as a whole, nor will it affect the realization of the core concept and the achievement of the technical effects of this technical solution.

[0333] Furthermore, if the embodiments of this invention involve descriptions such as "first" or "second," these descriptions are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined with "first" or "second" may explicitly or implicitly include at least one of those features. Additionally, the meaning of "and / or" throughout the text includes three parallel solutions; for example, "A and / or B" includes solution A, solution B, or a solution where both A and B are satisfied simultaneously. Furthermore, in the embodiments of this invention, "multiple" refers to two or more. Moreover, the technical solutions of the various embodiments can be combined with each other, but this must be based on the ability of those skilled in the art to implement them. When the combination of technical solutions is contradictory or cannot be implemented, it should be considered that such a combination of technical solutions does not exist and is not within the scope of protection claimed by this invention.

Claims

1. A method for optimizing dynamic beam coverage in satellite communication using a rotatable antenna array, characterized in that, The specific operating steps include the following: Step S1. Establish a channel model for low-Earth orbit satellite communication scenarios, construct a geocentric spherical coordinate system, a geocentric rectangular coordinate system, and a satellite coordinate system with the center of the satellite antenna array as the origin, and define the satellite orbit parameters, ground coverage area, satellite visible area, and interference area accordingly. Step S2. Determine the position of each element in the rotatable antenna array on the satellite, the deflection angle vector of each rotatable antenna, the corresponding pointing vector, and the transmit beamforming vector according to the channel model, and establish a calculation model for beamforming gain and signal leakage power in the interference area. Step S3. Divide the satellite service time into a specified number of time slots and the ground corner domain into a specified number of discrete grids to obtain coverage area samples and interference area samples under each time slot and each discrete grid; Step S4. With the goal of minimizing the average signal leakage power within the interference area, and with constraints on the average beamforming gain within the coverage area, the elevation angle of the rotatable antenna, the rotation rate of the rotatable antenna, and the satellite transmit power, a joint optimization problem is constructed. Step S5. Solve the joint optimization problem using an alternating optimization method, wherein the transmit beamforming vector is optimized when the rotatable antenna deflection angle is fixed, and the rotatable antenna deflection angle is optimized when the transmit beamforming vector is fixed. Step S6. Iteratively update using the solution results, and finally output the optimal beam control parameters and optimal antenna deflection angle control parameters within the target time period; In the joint optimization problem of step S4, the objective function is to minimize the average signal leakage power over all time slots. The average signal leakage power is: in, Let m be the average signal leakage power in the interference region of the m-th time slot. for The time, i.e., the time from the m-th time slot satellite to the ground point in the interference area. Path power loss, For the transmit shaping vector of the m-th time slot, Let M be the steering vector for the composite channel in the m-th time slot, where M is the total number of time slots. The constraints in the joint optimization problem in step S4 specifically include: (a) The average beamforming gain in each time slot coverage area is not lower than a preset threshold. ,Right now: ； in, Let m be the average beamforming gain within the coverage area of ​​the m-th time slot. for The time, i.e., the time from the m-th time slot satellite to the ground point in the interference area. Path power loss, For the transmit shaping vector of the m-th time slot, This is the steering vector for the m-th time slot composite channel; (b) The elevation angle of each rotatable antenna is within a preset angle range, that is: ； in, Let be the elevation angle of the nth antenna in the mth time slot. The minimum elevation angle of the antenna is N, and the total number of antennas is N. (c) The pointing variation of the same rotatable antenna between adjacent time slots does not exceed a preset rotation rate limit, i.e.: ； in, and Let represent the pointing vectors of the nth antenna at times m and m+1, respectively, which can be simplified as follows: , This represents the upper limit of the antenna's rotation speed. For a single satellite service cycle, This represents the upper limit of the rotation angle of adjacent time slot antennas; (d) The norm of the transmit beamforming vector in each time slot is not greater than the preset transmit power limit. ,Right now: ,in This is the satellite's maximum launch power.

2. The method for optimizing dynamic beam coverage of satellite communication assisted by a rotatable antenna array as described in claim 1, characterized in that, In step S2, the rotatable antenna array is configured as a planar array antenna deployed on the satellite, and there exists a first... A rotatable antenna The position is defined as: in, The preset spacing between adjacent antennas For the first The position of the rotatable antenna on the array's x-axis For the first The position of a rotatable antenna along the array's y-axis; There exists the first The deflection angle vector of a rotatable antenna Defined as: in, This represents the total number of antennas. The pitch angle, Azimuth At this time, in the satellite coordinate system, the first The pointing vector of the root antenna is defined as: ; The transmit beamforming vector is defined as: ,in It is the transmitted beamforming vector at time t, represented as an N-dimensional complex vector, where each element... It is the complex weight applied to the nth antenna.

3. The method for optimizing dynamic beam coverage of satellite communication assisted by a rotatable antenna array as described in claim 2, characterized in that, The calculation models for beamforming gain and average signal leakage power in the interference region in step S2 include: (1) Path loss term, which is defined as: ； This represents the signal transmitted from the satellite to the ground. The power attenuation, of which Represents the geocentric latitude and geocentric longitude of any point on the Earth's surface. The path loss constant at the reference distance. Represents the ground point at time t Relative to the satellite's spatial vector, ground point Relative to the distance of the satellite, Path loss index; (2) Array response term, which is defined as: ； ； ； ； in, As a set of N-dimensional complex vectors, its nth element is This is used to describe the position of the nth antenna element on the antenna array when an electromagnetic wave arrives. The phase difference caused by the path difference It is the carrier wavelength, and j is the imaginary unit. This refers to the coordinate system from the center of the satellite antenna array to the ground point. The unit direction vector, The rotation matrix refers to the rotation from the geocentric rectangular coordinate system to the satellite coordinate system. For the satellite's orbital inclination, The geocentric latitude of the satellite at time t. The geocentric longitude of the satellite at time t. Represents the ground point at time t The unit spatial vector relative to the satellite; (3) The directional gain term of the rotatable antenna is defined as follows: ； ； ； ； in, Represents the antenna gain vector, which is an N-dimensional vector where each element... It is the square root of the gain of a single antenna, encompassing the effects of all antenna directivity on the signal amplitude. These are shape parameters that control the beamwidth of the antenna pattern. The maximum gain of the antenna is calculated using the following formula: , Antenna pointing and ground point direction The angle between them It refers to the deflection angle vector of the nth antenna at time t. Refers to the deflection angle of all antennas at time t. A set; (4) The downlink channel from the satellite to the ground point is defined as follows: ； in, As an N-dimensional complex channel vector, it is used to represent the interaction between N antenna elements and ground points. downlink channel, For path amplitude loss, Indicates the common phase related to distance. For Hadama accumulation, Refers to the deflection angle of all antennas at time t. A set; (5) Therefore, there exists an antenna gain of: ， ； (6) The transmit beamforming vector and the downlink channel together determine the channel gain at the ground point as follows: ； in Let be the path power loss at time t. For antenna directional gain, For array response; (7) The average beamforming gain within the coverage area is as follows: ； ； in, For the target coverage area, This represents the path power loss at time t. To combine antenna directivity gain and array response The composite channel steering vector; (8) The formula for calculating the average signal leakage power within the interference area is: ； in, Interference area This represents the average leakage power in the interference area during the service duration. refer to The set of all antenna deflection angles within a given time period. refer to The set of all transmitted beamforming vectors within a given time.

4. The method for optimizing dynamic beam coverage of satellite communication assisted by a rotatable antenna array as described in claim 1, characterized in that, The specific calculation process for obtaining the coverage area samples and interference area samples under each time slot and each discrete grid in step S3 includes: The satellite service time interval is divided into M equal time slots, and the midpoint of the m-th time slot is used as the starting point. , Characterizing the average performance of this time slot, For single satellite service time; The target angular domain is divided into multiple discrete grids. Simultaneously, a set of discrete grids in the coverage area is constructed using the center points of each discrete grid. and the discrete grid set in the interference region ,have: ； ； ； in, This is the set of all grid center points after discretizing the entire corner domain. and These represent the number of grids divided in the latitude and longitude directions when the entire Earth's angular domain is discretized. For coverage area The set of all discrete grid points, number of which is , For the m-th time slot in the interference region The set of all discrete grid points, number of which is .

5. The method for optimizing dynamic beam coverage of satellite communication assisted by a rotatable antenna array as described in claim 1, characterized in that, In step S5, when the deflection angle of the rotatable antenna is fixed, the transmit beamforming vector for each time slot is optimized, transforming the corresponding subproblem into an optimization problem with coverage gain and power constraints. The Lagrange multiplier method is then used to solve this problem, which is: in, It refers to the set of all transmitted beamforming vectors across all time slots. For the transmit shaping vector of the m-th time slot, The average signal leakage power over the interference region across all time slots. Let m be the average beamforming gain in the coverage area of ​​the m-th time slot. The average beamforming gain threshold; During the solution process using the Lagrange multiplier method, when the coverage gain constraint is activated and the power constraint is not activated, the optimal transmit beam direction is obtained through the generalized eigenvalue problem. When both coverage gain and power constraints are activated, the optimal solution that satisfies the constraints is obtained through a one-dimensional search.

6. The method for optimizing dynamic beam coverage of satellite communication assisted by a rotatable antenna array as described in claim 1, characterized in that, In step S5, when fixing the transmit beamforming vector, a pointing vector determined by the elevation angle and azimuth angle is introduced. The optimization problem of the deflection angle of a rotatable antenna can be equivalently transformed into an optimization problem about the pointing vector. Therefore, the optimization problem of the deflection angle of a rotatable antenna is as follows: in, The pointing vector of the nth antenna in the mth time slot is represented by... Pitch and azimuth Sure, This represents the set of all antenna pointing vectors in the m-th time slot. Represents the set of all antenna pointing vectors in all time slots. This represents the average signal leakage power in the interference region across all time slots. This represents the average beamforming gain over the coverage area in the m-th time slot. This represents the minimum antenna elevation angle. Represents the maximum antenna rotation speed. Represents the duration of service per satellite. Represents the number of time slots; For the non-convex objective function and non-convex covering constraints, a continuous convex approximation method based on first-order Taylor expansion is used to construct a round-by-round updated convex approximation subproblem, which is then solved using the CVX tool.

7. The method for optimizing dynamic beam coverage of satellite communication assisted by a rotatable antenna array as described in claim 6, characterized in that, The optimization problem of the pointing vector is: in, The number of discrete grid points in the interference area. For the m-th time slot The area receives signals, For the m-th time slot The area receives affine signals. Represents the distance from the m-th time slot satellite to the ground point in the interference area. The normalized weights of path power loss, This represents the set of all antenna pointing vectors in the m-th time slot. This is the pointing vector of the nth antenna in the mth time slot. The current iteration point represents the set of all antenna pointing vectors in the m-th time slot. This represents the current iteration point of the pointing vector of the nth antenna in the mth time slot. The number of discrete grid points in the coverage area. Represents the distance from the m-th time slot satellite to the ground point in the coverage area. The normalized weights of path power loss, The representative takes the conjugate. This represents the minimum antenna elevation angle. Represents the maximum antenna rotation speed. This represents the parameter used in continuous convex approximation algorithms to limit the step size for each iteration update.

8. The method for optimizing dynamic beam coverage of satellite communication assisted by a rotatable antenna array as described in claim 1, characterized in that, The specific steps in step S5, which use the alternating optimization algorithm to alternately transmit the beamforming vector and the rotatable antenna pointing vector, include: Step S51. Initialize the rotatable antenna pointing vector For all antennas, point vertically to the Earth's center in each time slot, and fix the pointing vector of the rotatable antennas. With optimized emission shaping vector ; Step S52. In the i-th iteration, perform the following two steps in sequence: a. Fixed emission shaping vector Optimize the pointing vector of the rotatable antenna ; b. Fixed rotatable antenna pointing vector Optimize the emission shaping vector ; Step S53. Execute the convergence criterion: If there are variables and If the update increment is less than the specified value, the iteration stops and the result is returned.

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