Low-orbit multi-satellite distributed cooperative beam forming method and system based on high-orbit and low-orbit inter-satellite interference avoidance

Abstract

The invention relates to the technical field of wireless communication, in particular to a low-orbit multi-satellite distributed cooperative beam forming method and system based on high-orbit and low-orbit inter-satellite interference avoidance. The method comprises the following steps: establishing a high-orbit and low-orbit heterogeneous multi-satellite multi-beam cooperative transmission system; establishing an equivalent signal to interference plus noise ratio expression and a rate evaluation expression of the low-orbit user; constructing a beam forming optimization model, establishing a spectrum efficiency maximization model under a multi-satellite transmitting power constraint and a high-orbit and low-orbit inter-satellite interference avoidance constraint, and equivalently converting the spectrum efficiency maximization model into an independent sub-problem superposition form related to a pre-coding vector; solving a global variable, defining a feedback variable of each low earth orbit satellite, and representing an iterative update formula of the global variable as a function of the feedback variable; and solving a local precoding vector according to the global variable and the local channel state information, and repeating iteration until the problem converges. According to the method, parallel distributed calculation of low-orbit multi-satellite cooperative beam forming is realized, and interference to high-orbit users is avoided while spectrum efficiency is optimized.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and in particular to a low-Earth orbit multi-satellite distributed cooperative beamforming method and system based on high and low orbit inter-satellite interference avoidance. Background Technology

[0002] The next generation of mobile communication systems will integrate satellite and terrestrial mobile communication systems to achieve the vision of seamless global coverage of mobile broadband services. Ultra-dense low-Earth orbit (LEO) satellite constellations will form the infrastructure of future mobile communication networks, and LEO satellite networks will become an important component of the space-ground integrated network.

[0003] However, due to limited spectrum resources, the rapid increase in the number of low-Earth orbit (LEO) satellites has brought challenges to spectrum management. The ITU has stipulated requirements for interference coordination and mitigation between geostationary and non-geostationary satellite networks: firstly, NGSO (non-geostationary orbit) systems must not cause unacceptable interference to GSO (geostationary orbit) networks; secondly, unless otherwise specified, NGSO systems should not require protection against interference caused by GSO networks. To achieve interference avoidance and complete transmission with high frequency reuse, LEO satellites need to employ precoding techniques to achieve frequency reuse while avoiding interference with high-Earth orbit (HEO) satellites. Because LEO satellites have limited computing resources and, unlike terrestrial base stations with fixed fiber optic connections, the inter-satellite link topology is constantly changing, limiting backhaul capacity. This makes the application of traditional centralized computing models more difficult for large-scale precoding computation problems involving multiple LEO satellites. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, this invention provides a low-Earth orbit multi-satellite distributed cooperative beamforming method and system based on high-low orbit inter-satellite interference avoidance. It can avoid interfering with the normal communication of users of high-Earth orbit satellite systems through interference avoidance mechanisms. At the same time, this invention has a low-complexity semi-closed structure suitable for parallel distributed execution, which optimizes computational efficiency while ensuring system performance.

[0005] In a first aspect, the present invention provides a low-Earth orbit multi-satellite distributed cooperative beamforming method based on high and low orbit inter-satellite interference avoidance, comprising the following steps: S1. Establish a high- and low-Earth orbit heterogeneous multi-satellite multi-beam cooperative transmission system, including a high-Earth orbit single-satellite multi-beam subsystem and a low-Earth orbit multi-satellite multi-beam subsystem. The high-Earth orbit single-satellite multi-beam subsystem includes... One high-Earth orbit user, low-Earth orbit multi-satellite multi-beam subsystem including Adjacent low-orbit satellites and One low-orbit user; S2. Set up a transmission mechanism: high-orbit satellites and low-orbit satellites complete simple information exchange through ground gateway stations or central network controllers; multiple low-orbit satellites conduct incoherent cooperative transmission to jointly provide services to low-orbit users; low-orbit users receive and decode signals from low-orbit satellites and establish a signal reception model for low-orbit users. S3. Based on the received signal model of low-Earth orbit users, establish the equivalent signal-to-interference-plus-noise ratio (SINR) expression for low-Earth orbit users, and further obtain the sum rate evaluation expression for low-Earth orbit multi-satellite multi-beam subsystem based on the equivalent SINR expression. S4. Based on the sum rate evaluation expression of the low-orbit multi-satellite multi-beam subsystem, construct a beamforming optimization model and establish a spectral efficiency maximization model under the constraints of multi-satellite transmit power and the constraints of inter-satellite interference avoidance in high and low orbits. S5. Introduce the first auxiliary variable. Second auxiliary variable The spectral efficiency maximization model is equivalently transformed based on Lagrange duality and multidimensional fractional programming, and the problem after the equivalent transformation is expressed as a superposition of independent subproblems related to the precoding vector. S6. Define the first auxiliary variable. Second auxiliary variable The global variable is used as the global variable. For the problem after equivalent transformation, the optimal solution of the global variable is derived based on the first-order optimality condition and used as the iterative update formula. In each iteration, the global variable is calculated and broadcast to each low-Earth orbit satellite. The feedback variable of each low-Earth orbit satellite is defined, and the iterative update formula is expressed as a function of the feedback variable. S7. Each low-orbit satellite, based on the decoupled sub-problems, and using the global variables distributed by the central control node and the channel state information detected locally, completes the solution of the local precoding vector, compresses the local information, and uploads it to the central control node. This process is repeated iteratively until the problem converges.

[0006] Secondly, embodiments of the present invention also provide a low-Earth orbit multi-satellite distributed cooperative beamforming system based on high-low orbit inter-satellite interference avoidance, comprising the following modules: The high and low orbit satellite multi-satellite multi-beam system establishment module is used to establish a high and low orbit heterogeneous multi-satellite multi-beam cooperative transmission system, including a satellite cluster consisting of a high orbit satellite and ground users in the coverage area of ​​the satellite cluster; the transmission mechanism between low orbit multiple satellites and low orbit users is set to non-coherent cooperative transmission, so as to jointly provide services to low orbit users. The beamforming optimization model construction module is used to build a beamforming optimization model, establish a spectral efficiency maximization model under multi-satellite transmit power constraints and high- and low-orbit inter-satellite interference avoidance constraints, and perform equivalent transformation of the spectral efficiency optimization model based on Lagrange duality and multidimensional fractional programming methods. The central global variable calculation module is used to collect feedback information uploaded by each low-Earth orbit satellite, update the global variables based on the feedback information, and distribute the global variables and iterative convergence signals to each low-Earth orbit satellite to guide the distributed beamforming calculation process of the low-Earth orbit satellite. The onboard distributed precoding matrix calculation module is used to solve the local beamforming weights for each low-Earth orbit satellite. It combines global variables and locally detected channel state information, and solves the sub-problems based on the ADMM algorithm to obtain the beamforming weights for each low-Earth orbit satellite.

[0007] Compared with the prior art, the present invention has the following beneficial effects: Most existing low-Earth orbit (LEO) satellite beamforming algorithms employ centralized execution and fail to consider the real-world operating environment where LEO satellites coexist with high-Earth orbit (HEO) satellites, necessitating interference avoidance to ensure communication for HEO users. This invention's LEO multi-satellite distributed cooperative beamforming method employs an incoherent cooperative mode to avoid the high-precision synchronization requirements of multiple LEO satellites in terms of signal transmission. In terms of algorithm execution, through equivalent transformation and natural decoupling of the optimization problem, parallel distributed computation of multi-satellite multi-beamforming is achieved based on the derivation of first-order optimality conditions without introducing additional auxiliary consensus variables, ensuring the optimality of the solution. The technical solution adopted in this invention significantly improves computational efficiency while achieving high spectral efficiency and interference avoidance between LEO and HEO systems. Attached Figure Description

[0008] Figure 1 This is a flowchart illustrating the low-Earth orbit multi-satellite distributed cooperative beamforming method based on high-low orbit inter-satellite interference avoidance provided in this embodiment of the invention. Figure 2 This is a schematic diagram of the structure of the high-low orbit heterogeneous multi-satellite multi-beam transmission system established in an embodiment of the present invention; Figure 3 The figure shows the simulation results comparing the total transmission rate of a low-Earth orbit multi-satellite system with the performance of various algorithms, including centralized algorithms, interference-free avoidance algorithms, and inter-satellite cooperation-free algorithms, after adopting the low-Earth orbit multi-satellite distributed cooperative beamforming method provided in this embodiment of the invention. Figure 4 The figure shows the simulation results of the interference level of the low-Earth orbit system to different user groups of the high-Earth orbit system after adopting the low-Earth orbit multi-satellite distributed cooperative beamforming method provided in the embodiments of the present invention. Detailed Implementation

[0009] 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 some embodiments of the present invention, and not all embodiments. 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.

[0010] It should be noted that the step numbers in this document are only for the convenience of explaining the specific embodiments and are not intended to limit the order in which the steps are executed. The method provided in this embodiment can be executed by a relevant server, and the following description uses an edge server as the execution subject.

[0011] Example 1 like Figure 1 , Figure 2 As shown, this embodiment provides a low-Earth orbit multi-satellite distributed cooperative beamforming method based on high and low orbit inter-satellite interference avoidance, specifically including the following steps: S1. Establish a heterogeneous multi-satellite multi-beam cooperative transmission system for high and low orbits; the heterogeneous multi-satellite multi-beam cooperative transmission system for high and low orbits includes one high-orbit satellite and multiple high-orbit users, as well as multiple low-orbit satellites and multiple low-orbit users.

[0012] In this embodiment, the high-Earth orbit heterogeneous multi-satellite multi-beam cooperative transmission system includes a high-Earth orbit single-satellite multi-beam subsystem and a low-Earth orbit multi-satellite multi-beam subsystem; the high-Earth orbit single-satellite multi-beam subsystem includes One high-Earth orbit user, low-Earth orbit multi-satellite multi-beam subsystem including Two adjacent LEO satellites (i.e., low-Earth orbit satellites), and A single-antenna user terminal, namely Low Earth Orbit (LEO) users. LEO users are located within the service area of ​​LEO satellites and are provided with services jointly by these LEO satellites. High Earth Orbit (HEO) users are defined. subscript set The set of subscripts for low-Earth orbit satellites The set of subscripts for low-orbit users Each LEO satellite carries, including Uniform planar array antenna for the root radio frequency link.

[0013] In this embodiment, the high-orbit single-satellite multi-beam subsystem is equipped with 7 single-feed reflector antennas, which include a total of 35 high-orbit users; the low-orbit multi-satellite multi-beam subsystem includes four LEO satellites, and the satellite transmitter uses a phased array antenna with 36 radio frequency links as the transmitting antenna to provide access services for 36 ground satellite users.

[0014] Specifically, in the high-low orbit heterogeneous multi-satellite multi-beam system of this step, the transmitting antenna of the low-orbit multi-satellite multi-beam subsystem and the low-orbit user... The channel vector between the receiving antennas is denoted as ,Right now Indicates low-orbit satellites With low-orbit users Channel vectors between; Low Earth Orbit multi-satellite multi-beam subsystem for low Earth Orbit users The beamforming vector set is denoted as ,Right now Indicates low-orbit satellites For low-orbit users The beamforming vector is set; the transmission symbols for all LOR users are represented as follows: That is, the original signal. Indicates low-orbit satellites Send to low-orbit users The transmission symbols are received by every low-orbit user. Transmission symbols for a low-Earth orbit (LEO) satellite. The transmitting antenna of the LEO multi-satellite multi-beam subsystem and the high-Earth orbit user... The channel vector between the receiving antennas is denoted as ,Right now Indicates low-orbit satellites Transmitting antennas and high-orbit users The channel vector between the receiving antennas; the transmission symbols for all high-orbit users are represented as... In this context, the superscript H represents the conjugate transpose, the superscript T represents the transpose, the subscript LG of the channel vector represents the channel from the LEO satellite to the high-orbit user (i.e., the GEO user), the subscript LL of the channel vector represents the channel from the LEO satellite to the low-orbit user (i.e., the LEO user), the superscript L represents the information of the LEO user, and the superscript G represents the information of the GEO user.

[0015] S2. Set up a transmission mechanism: high-orbit satellites and low-orbit satellites complete simple information exchange through ground gateway stations or central network controllers; multiple low-orbit satellites conduct incoherent cooperative transmission to jointly provide services to low-orbit users. Low-orbit users receive and decode signals from low-orbit satellites and establish a signal reception model for low-orbit users.

[0016] In this embodiment, incoherent cooperative transmission is used among multiple low-Earth orbit (LEO) satellites to provide signal diversity for LEO users. LEO users employ omnidirectional antennas for reception and sequentially decode signals from each LEO satellite using a serial interference cancellation method. Among these, the LEO users... The received signal is represented as: ; in It is a high-orbit satellite to a low-orbit user Interference; For low-orbit users The receiver noise follows a zero-mean Gaussian distribution, i.e. ; Indicates low-orbit satellites With low-orbit users Channel vectors between; Indicates low-orbit satellites For low-orbit users The beamforming vector is set; This indicates that in a LEO system (i.e., a low-Earth orbit multi-satellite multi-beam subsystem), the system consists of low-Earth orbit satellites. Send to low-orbit users Transmission symbols.

[0017] Low-orbit users The receiver uses serial interference cancellation to decode information from various low-Earth orbit (LEO) satellites; therefore, LEO users Receive and decode from low-Earth orbit satellites The signal can be represented as: ; in Indicates low-orbit satellites With low-orbit users Channel vectors between; Indicates low-orbit satellites For low-orbit users The beamforming vector is set; Indicates low-orbit satellites Send to low-orbit users Transmission symbols; Indicates low-orbit satellites For low-orbit users The beamforming vector is set; Indicates low-orbit satellites Send to low-orbit users Transmission symbols; Indicates low-orbit satellites With low-orbit users Channel vectors between; Indicates low-orbit satellites For low-orbit users The beamforming vector is set; Indicates low-orbit satellites Send to low-orbit users Transmission symbols.

[0018] S3. Based on the received signal model of low-Earth orbit (LEO) users, establish the equivalent signal-to-interference-plus-noise ratio (SINR) expression for LEO users, and further obtain the sum rate evaluation expression for the LEO multi-satellite multi-beam subsystem based on the equivalent SINR expression.

[0019] This step calculates the signal-to-interference-plus-noise ratio (SIR) based on the received signal model established in step S2. This applies when a low-Earth orbit (LEO) user decodes signals from LEO satellites in any order. When receiving signals, the received signals The lower bound of the signal-to-interference-plus-noise ratio is expressed as: ; Where the equivalent noise variance , This represents the receiver noise variance for low-orbit users. Indicates low-orbit satellites Send to low-orbit users Signals in low-orbit users The square of the average signal amplitude received at that location; Indicates low-orbit satellites Send to low-orbit users Signal leakage to low-orbit users The average energy at that location.

[0020] Based on the lower bound of the signal-to-interference-plus-noise ratio of the received signal. Low-orbit users can be obtained The spectral efficiency is: ; In the formula Indicates low-orbit satellites Send to low-orbit users Signals in low-orbit users The square of the average signal amplitude received at that location; Indicates low-orbit satellites Send to low-orbit users Signals in low-orbit users The square of the average signal amplitude received at that location.

[0021] Therefore, low-orbit users can be obtained. The equivalent signal-to-interference-plus-noise ratio is: ; in Indicates low-orbit satellites To low-orbit users If the average channel is given, then the sum rate evaluation expression for the low-orbit multi-satellite multi-beam subsystem is: ; S4. Based on the sum rate evaluation expression of the low-orbit multi-satellite multi-beam subsystem, construct a beamforming optimization model and establish a spectral efficiency maximization model under the constraints of multi-satellite transmit power and the constraints of inter-satellite interference avoidance in high and low orbits.

[0022] This step models the beamforming optimization problem for low-Earth orbit (LEO) satellites. It is assumed that the transmit power of each LEO satellite does not exceed [a certain value]. The interference caused by the low-Earth orbit multi-satellite multi-beam subsystem to each high-Earth orbit user does not exceed the threshold. ;definition Then, we have the following optimization problem for the spectral efficiency maximization model: ; in, This represents the set of precoded vectors for all users. Indicates user The precoded vector, Indicates low-orbit satellites Transmitting antennas and high-orbit users The average channel vector between the receiving antennas, Indicates low-orbit satellites For low-orbit users The beamforming vector is set.

[0023] The above optimization problem The goal is to maximize the sum rate of the low-Earth orbit multi-satellite multi-beam subsystem, while the constraints are the transmission power of multiple satellites and the avoidance of interference from low-Earth orbit satellite beams to high-Earth orbit users.

[0024] S5. Introduce the first auxiliary variable. Second auxiliary variable Based on the Lagrange duality and multidimensional fractional programming method, the spectral efficiency maximization model is equivalently transformed, and the problem after the equivalent transformation is expressed as a superposition of independent subproblems related to the precoding vector.

[0025] In this embodiment, the equivalent transformation of the spectral efficiency maximization model first introduces a first auxiliary variable. Using Lagrange duality, we obtain the equivalent transformation problem. 1; Secondly, a second auxiliary variable is introduced. The equivalent transformation problem is obtained by using multidimensional fractional programming. 2. Equivalent transformation problem 3; Regarding the problem of equivalent transformation 3. Represent it as a superposition of independent subproblems related to the precoding vector. The specific steps are as follows: S51. Introduce the first auxiliary variable. Using Lagrange duality, we obtain the equivalent transformation problem. 1. The problem of equivalent transformation 1 is represented as: ; in, Indicates low-orbit users Signal-to-interference-to-noise ratio, Indicates low-orbit satellites To low-orbit users The conjugate transpose of the average channel.

[0026] S52, in the first auxiliary variable When the variable is fixed, a second auxiliary variable is introduced. The multidimensional fractional programming method is used to transform the equivalent transformation problem. 1. Equivalent transformation problem 2: ; in , This indicates the creation of a block diagonal matrix. This indicates the flow from each low-Earth orbit satellite to low-Earth orbit users. The block diagonal matrix composed of the average channels; Indicates the second auxiliary variable The List; This indicates the operation of taking the real part; , This indicates the intermediate processing result. Represents the identity matrix; Indicates low-orbit satellites Transmitting antennas and high-orbit users The conjugate transpose of the channel vector between the receiving antennas.

[0027] S53, Problem of Equivalent Transformation The vector form of 2 can be broken down and further equivalently transformed into a superposition of independent subproblems related to the pre-encoded vector, resulting in the equivalent transformation problem. 3: ; in Indicates low-orbit satellites Transmitting antennas and high-orbit users The conjugate transpose of the average channel vector between the receiving antennas; Indicates low-orbit satellites To low-orbit users The conjugate transpose of the channel vector.

[0028] Note the problem of equivalent transformation The objective function is When the second auxiliary variable When fixed, the objective function can be decomposed into a series of functions related to... Sub-functions: ; in: ; In the formula, Indicates low-orbit satellites Precoded vectors for all users.

[0029] S6. Define the first auxiliary variable. Second auxiliary variable The global variables are defined as follows: For problems after equivalent transformation, the optimal solution of the global variables is derived based on the first-order optimality condition, which is used as the iterative update formula; In each iteration, the central control node calculates the global variables and broadcasts them to each low-Earth orbit satellite; and defines the feedback variables of each low-Earth orbit satellite, expressing the iterative update formula as a function of the feedback variables.

[0030] In each iteration, the first auxiliary variable Second auxiliary variable These two global variables are calculated at the central control node and broadcast to each LEO satellite. This step is based on the equivalent transformation problem. 1. Export the first auxiliary variable The optimal solution, based on the equivalent transformation problem 2. Deriving the second auxiliary variable The optimal solution is found. Simultaneously, feedback variables for each low-Earth orbit satellite are defined, and the first auxiliary variable represented by the iterative update formula is used. Second auxiliary variable The optimal solution is expressed as a function of the feedback variable.

[0031] S61. Based on the problem of equivalent transformation 1. When the set When fixed, the first auxiliary variable is derived based on the first-order optimality condition. The optimal solution: ; S62. Based on the problem of equivalent transformation 2. When the set and the first auxiliary variable When fixed, the second auxiliary variable is derived column-wise based on the first-order optimality condition. The optimal solution: ; S63, Defining Low-Earth Orbit Satellites For low-orbit users The feedback variable is and .

[0032] S64. The first auxiliary variable in step S61 optimal solution and the second auxiliary variable derived column by column in step S62 optimal solution Represented as: ; ; in , This indicates that the central control node aggregates all low-Earth orbit satellites related to low-Earth orbit users. A vector consisting of feedback variables.

[0033] S7. Each low-orbit satellite, based on the decoupled sub-problems, and using the global variables distributed by the central control node and the channel state information detected locally, completes the solution of the local precoding vector, compresses the local information, and uploads it to the central control node. This process is repeated iteratively until the problem converges.

[0034] This step models a local subproblem based on the global variables distributed by the central control node and the channel state information detected locally. The local precoding vector is solved on each low-Earth orbit satellite node using the alternating direction multiplier method. Feedback information is generated based on the updated local precoding vector and uploaded to the central control node. Steps S6 and S7 are repeated until the problem converges.

[0035] This embodiment uses a low-Earth orbit satellite. The following are the specific steps to illustrate the solution process for the subproblem: S71, according to the... The global variables for this iteration are established for each low-Earth orbit satellite as follows. Subproblems concerning the precoding matrix : ; in , Indicates the second auxiliary variable In the The value of the next iteration. Represents the first auxiliary variable , Indicates low-orbit satellites To high-orbit users The conjugate transpose of the average channel; this subproblem can be further expressed in matrix form: ; in: ; ; ; In the formula, This represents the first-order statistical (average) channel deformation vector. This represents the second-order statistical channel deformation matrix. Indicates low-orbit satellites Regarding the precoded vectors of all users express The conjugate transpose of . Indicates low-orbit satellites With high-orbit users The second-order statistical channel deformation matrix, Indicates user In the Signal-to-interference-plus-noise ratio in the next iteration Representation matrix No. Line number The value of the column, Indicates low-orbit satellites To low-orbit users The conjugate transpose of the average channel, Indicates user In the Signal-to-interference-plus-noise ratio in the next iteration Representation matrix No. Line number The value of the column, Indicates low-orbit satellites To low-orbit users The conjugate transpose of the average channel.

[0036] S72, Sub-problems of the precoding matrix in step S71 The model is the following ADMM consensus optimization problem: ; in This represents the total number of constraints. ; Indicates the introduction of the first A consensus variable, Indicates low-orbit satellites With high-orbit users The second-order statistical channel deformation matrix, Indicates the introduction of the first Consensus variables.

[0037] S73. Based on the ADMM optimization framework, a penalty factor is introduced. Update according to the following formula : ; in It is the identity matrix; For the first The sum of the residuals from the next iteration is initially set to... ; For the first The iteration of the ... Consensus variables.

[0038] S74, Regarding the first Consensus variables Update according to the following formula: ; Among them, residual variables , It can be regarded as being caused by It is formed by concatenating sub-vectors of the same length, that is ; , Representing residual variables The Subvectors.

[0039] S75, Regarding the first Consensus variables Update according to the following formula: ; S76. Update the variables sequentially according to the following formula. : ; S77. Feedback variables defined in step S63 and Calculate low-orbit satellites Regarding all Feedback from low-orbit users and ,Will and Upload to the central control node.

[0040] S78, The central control node updates the following step according to S64. The first auxiliary variable in the next iteration Second auxiliary variable And compare it with the first auxiliary variable of the previous iteration. Determine whether convergence has been achieved; if convergence has been achieved, stop the iteration; otherwise, alternately execute steps S6 and S7 until the convergence condition is met.

[0041] In this embodiment, the Matlab 2024b Satellite Communication Toolbox was used to perform mathematical modeling and simulation of the system. Based on the channel model of a high-orbit satellite reflector antenna and a low-orbit satellite phased array antenna, numerical simulations were performed on the proposed beamforming method, such as... Figures 3-4 As shown.

[0042] from Figure 3The comparison shows that the distributed cooperative beamforming method proposed in this embodiment only reduces efficiency by about 6% compared to the centralized algorithm.

[0043] from Figure 4 The comparison shows that, based on the set threshold, the proposed low-orbit multi-satellite distributed beamforming method can effectively control the interference to high-orbit users within the threshold range.

[0044] Example 2 This embodiment, based on the same inventive concept as Embodiment 1, provides a low-Earth orbit multi-satellite distributed cooperative beamforming system for avoiding high and low orbit inter-satellite interference, including: The high and low orbit satellite multi-satellite multi-beam system establishment module is used to establish a high and low orbit heterogeneous multi-satellite multi-beam cooperative transmission system, including a satellite cluster consisting of a high orbit satellite and ground users in the coverage area of ​​the satellite cluster; the transmission mechanism between low orbit multiple satellites and low orbit users is set to non-coherent cooperative transmission, so as to jointly provide services to low orbit users. The beamforming optimization model construction module is used to build a beamforming optimization model, establish a spectral efficiency maximization model under multi-satellite transmit power constraints and high- and low-orbit inter-satellite interference avoidance constraints, and perform equivalent transformation of the spectral efficiency optimization model based on Lagrange duality and multidimensional fractional programming methods. The central global variable calculation module is used to collect feedback information uploaded by each low-Earth orbit satellite, update the global variables based on the feedback information, and distribute the global variables and iterative convergence signals to each low-Earth orbit satellite to guide the distributed beamforming calculation process of the low-Earth orbit satellite. The onboard distributed precoding matrix calculation module is used to solve the local beamforming weights for each low-Earth orbit satellite. It combines global variables and locally detected channel state information, and solves the sub-problems based on the ADMM algorithm to obtain the beamforming weights for each low-Earth orbit satellite.

[0045] In this embodiment, regarding the calculation of global variables, the optimal closed-form solution of the global variables is first derived based on the first-order optimality condition; then, this closed-form expression is expressed as a function of the feedback signals uploaded by each satellite. In subsequent iterative calculations, the central node first collects the feedback information from each satellite, updates the global variables based on this function, and broadcasts the updated global variables to each satellite node.

[0046] Furthermore, the satellite's solution to its local beamforming problem depends on global variables and locally detected channel state information; meanwhile, this subproblem can be expressed as a quadratic constraint quadratic programming problem, which can be solved using the alternating direction multiplier method.

[0047] Each module described in this embodiment is used to implement each step of Embodiment 1. For detailed implementation process, please refer to Embodiment 1, which will not be repeated here.

[0048] As can be seen from the detailed technical solutions described in the above embodiments, the technical solutions of the present invention have the following beneficial effects: This invention presents a low-Earth orbit (LEO) multi-satellite distributed cooperative beamforming technology that supports interference avoidance between LEO and EEO satellites. It avoids severe interference to EEO users while ensuring the overall performance of the LEO network and features a parallel computing structure, enabling distributed solution of local precoding vectors across multiple satellites. Most existing LEO satellite beamforming algorithms employ centralized execution and do not consider the coexistence with EEO satellites in the actual space environment, which can easily cause severe interference to EEO user communications. The LEO multi-satellite distributed cooperative beamforming method proposed in this invention controls the energy leaked to EEO users within an acceptable range and improves algorithm execution efficiency through high parallelization, thereby achieving spectrum sharing in heterogeneous multi-satellite coexistence systems in LEO and EEO orbits.

[0049] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications are also considered to be within the scope of protection of the present invention.

Claims

1. A low-Earth orbit multi-satellite distributed cooperative beamforming method based on high and low orbit inter-satellite interference avoidance, characterized in that, Includes the following steps: S1. Establish a high- and low-Earth orbit heterogeneous multi-satellite multi-beam cooperative transmission system, including a high-Earth orbit single-satellite multi-beam subsystem and a low-Earth orbit multi-satellite multi-beam subsystem. The high-Earth orbit single-satellite multi-beam subsystem includes... One high-Earth orbit user, low-Earth orbit multi-satellite multi-beam subsystem including Adjacent low-orbit satellites and One low-orbit user; S2. Set up a transmission mechanism so that high-orbit and low-orbit satellites can exchange simple information through ground gateways or a central network controller. Multiple low-Earth orbit (LEO) satellites engage in incoherent cooperative transmission to jointly provide services to LEO users. LEO users receive and decode signals from LEO satellites, and establish a received signal model for LEO users. S3. Based on the received signal model of low-Earth orbit users, establish the equivalent signal-to-interference-plus-noise ratio (SINR) expression for low-Earth orbit users, and further obtain the sum rate evaluation expression for low-Earth orbit multi-satellite multi-beam subsystem based on the equivalent SINR expression. S4. Based on the sum rate evaluation expression of the low-orbit multi-satellite multi-beam subsystem, construct a beamforming optimization model and establish a spectral efficiency maximization model under the constraints of multi-satellite transmit power and the constraints of inter-satellite interference avoidance in high and low orbits. S5. Introduce the first auxiliary variable. Second auxiliary variable The spectral efficiency maximization model is equivalently transformed based on Lagrange duality and multidimensional fractional programming, and the problem after equivalent transformation is expressed as a superposition of independent subproblems related to the precoding vector. S6. Define the first auxiliary variable. Second auxiliary variable The global variable is used as the global variable. For the problem after equivalent transformation, the optimal solution of the global variable is derived based on the first-order optimality condition and used as the iterative update formula. In each iteration, the global variable is calculated and broadcast to each low-Earth orbit satellite. The feedback variable of each low-Earth orbit satellite is defined, and the iterative update formula is expressed as a function of the feedback variable. S7. Each low-orbit satellite, based on the decoupled sub-problems, and using the global variables distributed by the central control node and the channel state information detected locally, completes the solution of the local precoding vector, compresses the local information, and uploads it to the central control node. This process is repeated iteratively until the problem converges.

2. The low-orbit multi-satellite distributed cooperative beamforming method as described in claim 1, characterized in that, Step S3 includes: The signal-to-interference-plus-noise ratio (SIR) of the signal received by a low-Earth orbit (LEO) user is calculated based on the received signal model, thus obtaining the signal-to-interference-plus-noise ratio when the LEO user decodes signals from LEO satellites in any order. When receiving a signal, the lower bound of the signal-to-interference-plus-noise ratio (SIR) of the received signal is expressed as: ； in Indicates low-orbit satellites With low-orbit users The channel vector between them, where H represents the conjugate transpose of the vector; Indicates low-orbit satellites For low-orbit users The beamforming vector is set; Indicates low-orbit satellites For low-orbit users Beamforming vector settings; equivalent noise variance , It is a high-orbit satellite to a low-orbit user Interference, This represents the receiver noise variance for low-orbit users. Indicates low-orbit satellites Send to low-orbit users Signals in low-orbit users The square of the average signal amplitude received at that location; Indicates low-orbit satellites Send to low-orbit users Signal leakage to low-orbit users The average energy at that location; Based on the lower bound of the signal-to-interference-plus-noise ratio (SIR) of the received signal, the low-Earth orbit (LEO) user is obtained. Spectral efficiency: ； In the formula Indicates low-orbit satellites With low-orbit users Channel vectors between; Indicates low-orbit satellites With low-orbit users Channel vectors between; Indicates low-orbit satellites For low-orbit users The beamforming vector is set; Indicates low-orbit satellites For low-orbit users The beamforming vector is set; Indicates low-orbit satellites Send to low-orbit users Signals in low-orbit users The square of the average signal amplitude received at that location; Indicates low-orbit satellites Send to low-orbit users Signals in low-orbit users The square of the average signal amplitude received at that location; Get low-orbit users The equivalent signal-to-interference-plus-noise ratio is: ； in Indicates low-orbit satellites To low-orbit users If the average channel is given, then the sum rate evaluation expression for the low-orbit multi-satellite multi-beam subsystem is: 。 3. The low-orbit multi-satellite distributed cooperative beamforming method as described in claim 1, characterized in that, In step S4, it is assumed that the transmission power of each low-Earth orbit satellite does not exceed The interference caused by the low-Earth orbit multi-satellite multi-beam subsystem to each high-Earth orbit user does not exceed the threshold. ;definition This paper proposes an optimization problem with the goal of maximizing the sum rate of a low-Earth orbit (LEO) multi-satellite multi-beam subsystem, constrained by the transmit power of multiple satellites and the avoidance of interference from LEO satellite beams to high-Earth orbit users. The problem involves establishing a spectral efficiency maximization model. Represents the set of precoded vectors for all users. Indicates user The precoded vector.

4. The low-orbit multi-satellite distributed cooperative beamforming method as described in claim 3, characterized in that, Set up high-speed rail users subscript set The set of subscripts for low-Earth orbit satellites The optimization problem of the established spectral efficiency maximization model is as follows: ； in For low-orbit users The equivalent signal-to-interference-plus-noise ratio. Indicates low-orbit satellites Transmitting antennas and high-orbit users The average channel vector between the receiving antennas, Indicates low-orbit satellites For low-orbit users The beamforming vector is set.

5. The low-orbit multi-satellite distributed cooperative beamforming method as described in claim 1, characterized in that, Step S5 includes: S51. Introduce the first auxiliary variable. Using Lagrange duality, we obtain the equivalent transformation problem. 1; S52, in the first auxiliary variable When the variable is fixed, a second auxiliary variable is introduced. The equivalent transformation problem is solved using a multidimensional fractional programming method.

1. Equivalent transformation problem 2; S53, Problem of Equivalent Transformation The vector form of 2 can be broken down and further equivalently transformed into a superposition of independent subproblems related to the pre-encoded vector, resulting in the equivalent transformation problem.

3.

6. The low-orbit multi-satellite distributed cooperative beamforming method as described in claim 5, characterized in that, Assuming the launch power of each low-Earth orbit satellite does not exceed The interference caused by the low-Earth orbit multi-satellite multi-beam subsystem to each high-Earth orbit user does not exceed the threshold. High-speed rail users subscript set The set of subscripts for low-Earth orbit satellites ,definition , Represents the set of precoded vectors for all users. Indicates user The precoded vector; Equivalent transformation problem 1 is represented as: ； in, Indicates low-orbit users Signal-to-interference-plus-noise ratio; Indicates low-orbit satellites With low-orbit users Channel vectors between; Indicates low-orbit satellites To low-orbit users The conjugate transpose of the average channel; Indicates low-orbit satellites For low-orbit users The beamforming vector is set; Indicates low-orbit satellites For low-orbit users The beamforming vector is set; This is the equivalent noise variance; Indicates low-orbit satellites Transmitting antennas and high-orbit users The conjugate transpose of the channel vectors between the receiving antennas; Equivalent transformation problem 2 is: ； in , This indicates the creation of a block diagonal matrix. This indicates the flow from each low-Earth orbit satellite to low-Earth orbit users. The block diagonal matrix composed of the average channels; Indicates the second auxiliary variable The List; This indicates the operation of taking the real part; , This indicates the intermediate processing result. Represents the identity matrix; Equivalent transformation problem 3 is: ； in Indicates low-orbit satellites Transmitting antennas and high-orbit users The conjugate transpose of the average channel vector between the receiving antennas; Indicates low-orbit satellites To low-orbit users The conjugate transpose of the channel vector; Note the problem of equivalent transformation The objective function is When the second auxiliary variable When fixed, the objective function is decomposed into a series of... Sub-functions: ； in: 。 7. The low-Earth orbit multi-satellite distributed cooperative beamforming method as described in claim 6, characterized in that, Step S6 includes: S61. Based on the problem of equivalent transformation 1. When the set When fixed, the first auxiliary variable is derived based on the first-order optimality condition. The optimal solution; S62. Based on the problem of equivalent transformation 2. When the set and the first auxiliary variable When fixed, the second auxiliary variable is derived column-wise based on the first-order optimality condition. The optimal solution; S63, Defining Low-Earth Orbit Satellites For low-orbit users The feedback variable is and , ; S64. Based on the summary of all low-Earth orbit satellites and information about low-Earth orbit users compiled by the central control node. The vector composed of feedback variables, and the first auxiliary variable in step S61 The optimal solution and the second auxiliary variable derived column by column in step S62 The optimal solution is then re-represented.

8. The low-orbit multi-satellite distributed cooperative beamforming method as described in claim 7, characterized in that, Step S7 models a local subproblem based on the global variables distributed by the central control node and the channel state information detected locally. The local precoding vector is solved on each low-Earth orbit satellite node using the alternating direction multiplier method. Feedback information is generated based on the updated local precoding vector and uploaded to the central control node. Steps S6 and S7 are repeated until the problem converges.

9. The low-Earth orbit multi-satellite distributed cooperative beamforming method as described in claim 8, characterized in that, Step S7 includes: S71, according to the... The global variables for this iteration are established for each low-Earth orbit satellite as follows. Subproblems concerning the precoding matrix ; S72, Sub-problems of the precoding matrix in step S71 Model it as an ADMM consensus optimization problem; S73. Based on the ADMM optimization framework, a penalty factor is introduced. Update low-orbit satellites Precoded vectors for all users ; S74, Update No. Consensus variables ; S75, Update No. Consensus variables ; S76, the sum of residuals from the update iteration; S77. Feedback variables defined in step S63 and Calculate low-orbit satellites Regarding all Feedback from low-orbit users and ,Will and Uploaded to the central control node; S78, The central control node updates the following step according to S64. The first auxiliary variable in the next iteration Second auxiliary variable And compare it with the first auxiliary variable of the previous iteration. Determine whether convergence has been achieved; if convergence has been achieved, stop the iteration; otherwise, alternately execute steps S6 and S7 until the convergence condition is met.

10. A low-Earth orbit multi-satellite distributed cooperative beamforming system based on high-low orbit inter-satellite interference avoidance, implemented using the beamforming method described in any one of claims 1-9, characterized in that, The beamforming system includes the following modules: The high and low orbit satellite multi-satellite multi-beam system establishment module is used to establish a high and low orbit heterogeneous multi-satellite multi-beam cooperative transmission system, including a satellite cluster consisting of a high orbit satellite and ground users in the coverage area of ​​the satellite cluster. The transmission mechanism between multiple low-Earth orbit satellites and low-Earth orbit users is set to be non-coherent cooperative transmission, so as to jointly provide services to low-Earth orbit users. The beamforming optimization model construction module is used to build a beamforming optimization model, establish a spectral efficiency maximization model under multi-satellite transmit power constraints and high- and low-orbit inter-satellite interference avoidance constraints, and perform equivalent transformation of the spectral efficiency optimization model based on Lagrange duality and multidimensional fractional programming methods. The central global variable calculation module is used to collect feedback information uploaded by each low-Earth orbit satellite, update the global variables based on the feedback information, and distribute the global variables and iterative convergence signals to each low-Earth orbit satellite to guide the distributed beamforming calculation process of the low-Earth orbit satellite. The onboard distributed precoding matrix calculation module is used to solve the local beamforming weights for each low-Earth orbit satellite. It combines global variables and locally detected channel state information, and solves the sub-problems based on the ADMM algorithm to obtain the beamforming weights for each low-Earth orbit satellite.

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