A low-orbit satellite network joint beam hopping and resource allocation optimization method

Abstract

This invention claims protection for a joint beam hopping and resource allocation optimization method for low-Earth orbit satellite networks. Utilizing Lyapunov optimization theory, this invention transforms a long-term stochastic optimization problem lacking future prior information into a single-period deterministic subproblem. Under the premise of strictly ensuring the long-term queue stability of the system, it maximizes the long-term average capacity of the system and minimizes the ratio of system satellite load gaps to total satellite service time, ensuring long-term service continuity in complex environments. Regarding system optimization, this invention constructs a multi-dimensional joint resource optimization framework encompassing multi-user group preprocessing, satellite-to-ground condition correlation, beam hopping modes, and user-level resource block and transmit power allocation. It integrates an improved P-center algorithm, matching theory, weighted maximum independent sets, and non-convex generalized Benders decomposition and continuous convex approximation techniques, successfully achieving effective dimensionality reduction and decoupling of multi-dimensional continuous variables and discrete decision variables in high-dimensional, strongly coupled mixed-integer nonlinear problems.

Description

Technical Field

[0001] This invention relates to the field of satellite wireless communication technology, and in particular to a joint beam hopping and resource allocation optimization method for low-Earth orbit satellite networks based on non-fixed cell partitioning. This method maximizes the long-term average utility function under highly dynamic network topology and random service arrival environments, while ensuring long-term queue stability, by jointly optimizing dynamic cell partitioning, satellite-to-ground resource association based on service duration, beam hopping mechanisms, and user-level orthogonal subcarrier and transmit power allocation. Background Technology

[0002] In recent years, low Earth orbit (LEO) satellite communication networks have become a key infrastructure for achieving seamless air-space-ground connectivity due to their unique advantages such as low propagation delay, low path loss, and wide global coverage. To alleviate resource bottlenecks, beam hopping (BH) technology has been widely used. This technology allows satellites to dynamically allocate system bandwidth to active beams in different time slots, significantly improving resource utilization efficiency. However, existing technologies still face the following challenges: First, existing beam hopping research largely relies on traditional fixed geographic grid divisions, failing to deeply integrate with the uneven distribution of ground users and the highly dynamic coverage characteristics of satellites, easily leading to severe resource mismatches (such as idle resources in sparse areas and congestion in hotspot areas) and co-channel interference. Second, mainstream scheduling strategies are mostly limited to optimizing instantaneous performance (such as throughput or latency), lacking consideration for random service arrivals and the dynamic evolution of data queues, making it difficult to maintain long-term queue stability of the system. In addition, existing research often ignores the evolution of actual visible service duration and dynamic load of satellites, resulting in frequent inter-satellite handovers, high signaling overhead, and severe inter-satellite load imbalances. Finally, most existing multi-satellite collaborative scheduling methods remain at the macro level of cells or beams, neglecting resource competition within cells and lacking micro-level fine-grained resource allocation for complex multi-user scenarios. Therefore, it is urgent to break through the limitations of fixed network structures and explore the construction of a long-term joint optimization framework that takes into account both macro-level topology continuity and micro-level fine-grained user-level resource allocation.

[0003] A search revealed application publication number CN114665952B, entitled "A Beam-hopping Optimization Method for Low-Earth Orbit Satellite Networks Based on a Space-Ground Fusion Architecture," belonging to the field of satellite mobile communication technology. The method includes: S1: Establishing a stochastic optimization model that maximizes the fairness of satellite user service processing under a space-ground fusion architecture, and decomposing it into a beam-level resource allocation problem and a user-level resource allocation problem; S2: Transforming the beam-level resource allocation problem into a Markov game, and employing a centralized training and distributed execution mechanism based on a multi-agent architecture actor-judge algorithm, so that each agent only needs to observe its local state and execute local decisions; S3: Based on convex optimization theory, transforming the user-level resource allocation problem into a Lagrange problem for solution.

[0004] Existing technologies (such as CN114665952B) largely rely on fixed physical cell division and seek instantaneous fairness through black-box algorithms such as multi-agent reinforcement learning. This not only struggles to adapt to the real-world scenarios of high dynamics and non-uniform user distribution in low-Earth orbit satellites, but also fails to theoretically avoid frequent inter-satellite handovers and long-tail queue congestion. In contrast, this invention reconstructs spatial topology through non-fixed cell division, establishes long-term queue stability using Lyapunov theory, and innovatively integrates N-GBD with qualitative perturbation mechanisms to solve the high-dimensional resource coupling problem. It provides a cross-layer collaborative solution with strong robustness, rigorous interpretability, and significantly reduced signaling overhead. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing low-Earth orbit (LEO) satellite communication beam-hopping technologies, such as reliance on static grids leading to resource misallocation, lack of consideration for long-term data queue stability, frequent inter-satellite handovers, and coarse-grained micro-resource allocation. This invention proposes a multi-satellite collaborative LEO satellite network joint optimization method oriented towards non-static cell partitioning. Breaking away from the conventional fixed-cell model, this invention introduces Lyapunov optimization theory to transform the long-term stochastic optimization problem lacking future prior information into a single-slot deterministic subproblem. It employs a low-complexity online dimensionality reduction and decoupling algorithm architecture. Through joint optimization improvements to the P-center algorithm's multi-user grouping preprocessing, satellite-ground condition correlation based on continuous coverage time and matching theory, beam-hopping modes based on the weighted maximum independent set (WMIS) to construct conflict graphs, and user-level resource block and power allocation based on nonconvex generalized Benders decomposition (Nonconvex-GBD) and continuous convex approximation (SCA), this invention maximizes the long-term average capacity of the system and minimizes the ratio of system satellite load differences to total satellite service time while strictly ensuring the long-term stability of the system's user queues.

[0006] The technical solution of the present invention is as follows:

[0007] A method for optimizing joint beam hopping and resource allocation in low-Earth orbit satellite networks includes the following steps:

[0008] Step 1: Construct a system model, determine the low-orbit satellite multi-satellite cooperative communication model, non-fixed cell partitioning model, and dynamic data queue model, analyze the time-varying topology of satellite and ground and the uneven distribution of traffic, and form a joint optimization problem based on Lyapunov;

[0009] Step 2: Decompose the joint optimization problem in Step 1 into a multi-user grouping cell partitioning problem, a joint satellite-to-ground correlation and beam hopping mode optimization problem, and a joint resource block allocation and power optimization problem. Through cluster analysis of the macro-user geographical distribution, prioritize the use of the improved P-center algorithm to solve the dynamic cell partitioning and user grouping problems. The improvement of the improved P-center algorithm lies in defining a global bottleneck radius, iteratively unloading edge users of the bottleneck cell to neighboring cells based on a strict monotonically decreasing criterion, fixing the cell through recursive dimensionality reduction after reaching a local optimum, and combining continuous minimum enclosing circle updates and preset extreme value radius constraints for cell merging.

[0010] Step 3: For the joint satellite-to-ground correlation and beam hopping mode subproblem under non-fixed cell, the satellite-to-ground correlation is solved by introducing matching theory to achieve inter-satellite load balancing, and the micro-time slot beam hopping indicator variable is solved by combining the weighted maximum independent set (WMIS) conflict graph.

[0011] Step 4: For the joint resource block allocation and power optimization subproblem, the non-convex generalized Benders decomposition algorithm is used to decouple discrete and continuous variables, and the continuous convex approximation (SCA) is combined to solve the resource and power solutions.

[0012] Step 5: Under the premise of satisfying long-term queue stability, derive and iteratively execute the aforementioned multi-dimensional scheduling decisions, prove and obtain the joint optimal strategy to ensure the maximization of system utility and service continuity.

[0013] Furthermore, step 1 includes the following specific contents:

[0014] Construct a system model that includes: A low-Earth orbit satellite constellation, a resource management center (RMC), gateways, and multiple legitimate mobile users on the ground, in the process of multi-satellite coordinated beam coverage, assume that in each scheduling cycle, the satellites provide services to non-uniformly distributed ground users through beam hopping (BH) technology; each satellite in the system is equipped with A maximum of one phased array beam, activated in each time slot. One beam; to avoid co-channel interference, the system adopts a spatial isolation mechanism, so adjacent cells are not illuminated at the same time; the gateway aggregates network information through the feeder link and forwards it to the RMC, which executes user grouping and jointly optimizes beam switching and the allocation of time, space and frequency resources;

[0015] There are a total of There are 3 users, and the user set is denoted as _ . Users are categorized by RMC as A collection of independent communities, denoted as [a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8, a_9, a_1, a_1, a_2 ... In the current scheduling cycle, the system introduces a binary beam transition indicator variable. and resource allocation indicator variables The satellite's transmitting antenna gain and the user's receiving antenna gain are determined by radiation patterns conforming to ITU standards, which combine maximum antenna gain and off-axis angle parameters; mission timing is determined by a series of scheduling cycles. Composition, each cycle is divided into One time slot, of which This refers to the duration of each time slot; the satellite's orbital motion causes time-varying satellite-to-ground topology. The geocentric angle and elevation angle of the satellite relative to the cell are determined based on geometric relationships. When the elevation angle meets a minimum threshold... At the same time, the duration of continuous available service from the satellite to the cell was derived and calculated; channel fading was comprehensively considered in light of free space loss and antenna gain; satellite To users The channel power gain is expressed as It combines satellite launch gain, user reception gain, and free-space propagation loss;

[0016] In the In each time slot, the satellite transmits signals to the user, with an allocated transmission power of [missing information]. If the cell is illuminated and the user is allocated the corresponding resource block, the resource block bandwidth is... The target signal power received by the user will be affected by co-channel interference (CCI) caused by other users simultaneously occupying the same resource block, as well as additive white Gaussian noise. The impact; the signal-to-interference-plus-noise ratio (SINR) of communication users is in fractional form, and the transmission capacity from satellite to ground users. Calculated based on Shannon's formula;

[0017] During satellite communication, the transmit power constraint must be met. The system introduces binary variables. and This represents the satellite-to-ground association status and the cell-user dependency relationship; it defines the ratio of the total system load variance to the service duration within the scheduling period:

[0018]

[0019] The ratio of the total system load variance to the service duration within the defined scheduling period. System satellite load gap, Service time of satellite n associated with m Cell-satellite correlation variable, where n represents the nth satellite and m represents the mth cell.

[0020] Queue backlog for each user The average rate stability condition must be met. ;; , These represent the queue backlog and scheduling period for user u, respectively. The global system utility function is defined as follows: , , , , Let f represent the weighting factor, the total system capacity at time f, and different normalization factors, respectively. The problem is described as follows:

[0021]

[0022] These represent the cell-user correlation variables and cell-satellite correlation variables in period f, the beam hopping mode variable in time slot t in period f, the user-resource block allocation variable, and the power allocation variable, respectively. Indicates the scheduling period, For the global system utility function in period f, These represent the scheduling period, time slot, satellite index, cell index, beam index, user index, and resource block index, respectively. This indicates the total number of beams carried by a single satellite, U represents the total number of users, and K represents the total number of resource blocks. Indicates the maximum power of the resource block, Total system service time Minimum system service time Indicates the total number of communities, This indicates the queue backlog for user u during period f.

[0023] Among the constraints Represents the binary variable to be optimized; Each user belongs to only one ground unit; This means that a ground unit can only be served by one satellite at any given time. This indicates the maximum number of ground units that a satellite can be associated with at any given time. This means that one beam can only illuminate one ground cell; This indicates the number of beams activated by a satellite in the same time slot at any given time period; This indicates that the user can use the resource block that illuminates the spot beam, and the spot beam must belong to the satellite accessed by the ground unit to which the user is currently grouped; This means that a resource block can only be assigned to one user; This indicates the number of resource blocks allocated to a user within a beam. This indicates that the power allocated to the resource block user does not exceed the specified maximum power; Minimum requirements for the service time of the constraint system in the cell; The backlog length of the user data queue must not grow indefinitely;

[0024] To achieve long-term online optimization, a Lyapunov drift plus penalty function is introduced, transforming the original problem into minimizing the upper bound of the queue drift and network utility penalty term at each epoch. The problem, among which , , These represent the capacity and queue backlog of cell m in period f, respectively. These are control parameters.

[0025] Furthermore, step 2 includes the following specific details:

[0026] The joint optimization problem constructed in step 1 with the goal of maximizing long-term system utility and ensuring queue stability is a mixed integer nonlinear programming (MINLP) problem with highly coupled variables and NP-hard complexity. It is decomposed into three sub-problems using a decoupling strategy: cell partitioning problem for multi-user groups, joint satellite-to-ground correlation and beam hopping mode optimization problem, and joint resource block allocation and power optimization problem.

[0027] First, the ground segmentation is transformed into a non-fixed user clustering problem; then, an improved P-center algorithm is used to randomly select... Using each user as the initial group center, the minimum circle cover (MEC) method is used to iteratively update the group center and radius. Extreme value group migration tests are performed to eliminate cover overlap, ultimately generating groups that satisfy the radius constraint. Non-static cell partitioning set The MEC refers to: for any user cluster group generated in each iteration, based on the three-dimensional / two-dimensional spatial geographic coordinates of all users in the group, using a geometric optimization algorithm to find a circumcircle with the smallest radius that completely includes all users in the group; subsequently, the geometric center coordinates of this smallest circumcircle are updated as the new initial center of the group, and its radius is updated as the current coverage radius of the cell, thus providing a basis for subsequent radius extremum constraints (…). and The determination provides precise physical boundary parameters;

[0028] By utilizing an improved P-center algorithm, large-scale user distributions are handled to dynamically determine the optimal number of cells. The method randomly selects the initial group center and updates the center and radius of each group using the minimum circumcircle (MEC) method, thus forming a complete user partition; a global radius metric is defined. That is, the maximum distance from all users to their group center. The algorithm iteratively identifies the extreme group, i.e., the group with the largest radius, and performs objective function capacity testing and migration testing on users within its bound subset to continuously optimize the grouping structure; subsequently, it introduces the maximum coverage radius of the physical beam. and minimum radius A constrained iterative merging strategy is used to eliminate invalid cells.

[0029] Furthermore, step 3 includes the following specific details:

[0030] Given the updated user group topology from step 2, the given cell and available satellite status, optimize the macroscopic satellite-to-ground correlation matrix. Beam jump indicator variable with micro time slot First, a conditional handover mechanism is introduced. Using matching theory, the switching operation between the cell and the satellite is defined, accepting the target of load difference while satisfying satellite capacity constraints. The decreasing matching solution ultimately outputs the optimal association decision. ;

[0031] Secondly, after the satellite-to-ground relationship is determined, a weighted conflict diagram is constructed. Perform modeling; The graph represents vertices, where each vertex represents a potential beam hopping decision. Conflict edges are established based on system interference constraints. The weighted maximum independent set (WMIS) is solved by greedy search, and the optimal beam hopping mode that maximizes system utility while avoiding interference is output in time slots.

[0032] Furthermore, step 4 includes the following specific details:

[0033] Given the parameters from steps 2 and 3 above, we jointly optimize the discrete resource block allocation decision. With continuous transmission power In each time slot, a non-convex generalized Benders decomposition technique is introduced to alternately solve the primal problem and the master problem. The non-convex generalized Benders decomposition technique is an iterative framework that decouples discrete and continuous variables. It generates the optimal cut by solving the continuous variables in the primal problem with fixed discrete variables, or by introducing a feasibility problem to generate a feasible cut when the primal problem is infeasible. The generated cut constraints are then passed to the master problem to update the discrete resource block allocation decision. Through alternating iterations, the global upper and lower bounds are continuously tightened until convergence. In the primal problem, the discrete decision is fixed. For the non-convex Shannon rate function objective caused by co-frequency interference, a continuous convex approximation (SCA) technique is used to decompose the objective function into the difference of concave functions. , This represents the total capacity of cell m under a given power and resource block allocation during scheduling period f and time slot t. The power matrix of time slot t during scheduling period f. and This represents the concave decomposition term of the Shannon rate. And in the... In the next iteration, Perform a first-order Taylor expansion as Construct a concave approximation function using this linear lower bound. , , Let each represent a nonconvex term in the j-th iteration. The linear approximation function obtained after first-order Taylor expansion at local points, and the representation function V for continuous power variables. The gradient and the optimal solution of the transmit power obtained in the (j-1)th iteration are used. The non-convex primal problem is transformed into a convex programming problem for solution, and the Lagrange multiplier information is extracted. ; These represent the optimal Lagrange multipliers extracted after solving the subproblems of the original problem in the i-th GBD iteration, the optimal continuous variable solution obtained by solving the convexized subproblems after giving discrete variables in the i-th GBD iteration, and the resource block allocation variable, respectively. Subsequently, the main problem uses these Lagrange multipliers to construct the Benders optimal cut in mixed integer linear programming (MILP), narrowing the search range of discrete variables.

[0034] Furthermore, step 5 includes the following specific content: Based on the overall online Lyapunov alternating optimization algorithm framework, the system optimizes the algorithm in each scheduling cycle. The inner loop performs the aforementioned non-fixed cell division, satellite-to-ground correlation and beam hopping optimization, as well as time slot-level optimization. The Nonconvex-GBD resource and power joint allocation steps continuously update the system queue state equations without needing to know future prior information, until the long-term average rate stability condition is met, and finally output a joint optimal scheduling strategy that satisfies the robustness of multi-star cooperative systems, physical constraints, and user-level service continuity.

[0035] An electronic device includes a processor, a memory, an input device, and an output device, the processor, memory, input device, and output device being interconnected, the memory storing a computer program including program instructions, and the processor being configured to invoke the program instructions to execute any of the methods described above.

[0036] A computer-readable storage medium storing a computer program, the computer program including program instructions that, when executed by a processor, cause the processor to perform any of the methods described above.

[0037] The advantages and beneficial effects of this invention are as follows:

[0038] This invention constructs a long-term beam hopping and resource joint optimization framework for the forward link of multi-satellite collaborative low-Earth orbit satellite networks. Through joint optimization of non-fixed cell partitioning, satellite-to-ground condition correlation based on service duration and load balancing, beam hopping modes, and user-level resource and power allocation, it effectively maximizes the long-term average capacity of the system while minimizing the ratio of satellite load differences to total satellite service time, all while strictly ensuring the long-term queue stability of users. The introduction of non-static cell partitioning and conditional switching mechanisms enables the system to break through the limitations of traditional fixed geographical grid partitioning, dynamically adapting to the unevenness of user spatial distribution and the highly dynamic characteristics of satellite coverage. This avoids frequent inter-satellite handovers and high signaling overhead, and significantly improves the service continuity and inter-satellite load balancing capabilities of the network topology. This invention introduces Lyapunov optimization theory to model and derive upper bounds for the dynamic evolution of random service arrivals and data queues. It transforms a long-term stochastic optimization problem lacking future prior information into a single-slot deterministic subproblem, effectively ensuring the long-term stability of refined resource allocation in complex multi-user scenarios and enhancing the system's communication performance in the face of complex co-channel interference. Addressing the high-dimensional, strongly coupled, and NP-hard complex mixed-integer nonlinear programming (MINLP) problem, this invention integrates Weighted Maximum Independent Set (WMIS), Continuous Convex Approximation (SCA), and Nonconvex Generalized Benders Decomposition (Nonconvex-GBD) techniques to derive a low-complexity online dimensionality reduction and decoupling algorithm architecture. This successfully decouples discrete cell association and beam hopping decisions from continuous power allocation variables, providing a solution architecture for system parameter design that overcomes nonconvexity and possesses efficient iterative convergence capabilities. Experimental results demonstrate the high efficiency of the proposed scheme in improving long-term global system utility, suppressing local queue congestion, ensuring communication fairness for tail users, and improving resource utilization efficiency.

[0039] This invention constructs a long-term beam hopping and resource joint optimization framework for the forward link of multi-satellite collaborative LEO satellite networks. Its core innovation lies in (corresponding to the cross-dimensional collaboration in steps 1 to 5 of claims): through joint optimization of non-fixed cell partitioning, satellite-ground condition correlation based on service duration and load balancing, beam hopping modes, and user-level resource and power allocation, it effectively maximizes the long-term average capacity of the system and minimizes the ratio of system satellite load differences to total satellite service time, while strictly ensuring the long-term stability of the system's user queues. In existing technologies, spatial topology partitioning and underlying physical resource allocation are typically treated separately, and are often limited to instantaneous snapshot optimization, making it difficult to cope with highly dynamic LEO environments. This invention breaks through this conventional thinking by constructing a strongly coupled cross-layer mapping relationship across multiple time scales. Specifically (corresponding to steps 2 and 3), the introduction of non-static cell partitioning and condition switching mechanisms enables the system to break through the limitations of traditional fixed geographical grid partitioning. This invention does not employ conventional static clustering methods such as K-means, but innovatively designs an improved P-center algorithm based on a strict monotonically decreasing unloading criterion and extreme radius constraints. This collaborative mechanism is not easily associated with conventional technologies and more dynamically adapts to the unevenness of the real spatial distribution of users and the highly dynamic characteristics of satellite coverage. Furthermore, by introducing matching theory to deeply integrate dynamic load differences, it significantly improves the service continuity of the network topology and the inter-satellite load balancing capability, avoiding frequent inter-satellite handovers and high signaling overhead. In the time dimension (corresponding to steps 1 and 5), this invention introduces Lyapunov optimization theory to model and derive upper bounds for the random arrival of services and the dynamic evolution of data queues, transforming the long-term stochastic optimization problem lacking future prior information into a single-period deterministic subproblem, and then further into a single-time slot problem. The combination of this long-term theoretical framework and micro-level resource allocation clearly defines the strict orthogonality between different resource blocks (i.e., ensuring that co-channel interference is only calculated when using the same resource block, and that different resource blocks do not interfere with each other). This rigorous physical layer premise, in conjunction with the upper-level queue theory, effectively guarantees the long-term stability of refined resource allocation in complex multi-user scenarios and enhances the system's communication performance in dealing with complex co-channel interference. For the high-dimensional, strongly coupled, and NP-hard complex mixed-integer nonlinear programming (MINLP) problem, conventional heuristic algorithms or direct relaxation methods are prone to getting trapped in local optima, losing accuracy, or failing to guarantee convergence. This invention creatively integrates Weighted Maximum Independent Set (WMIS), Continuous Convex Approximation (SCA), and Nonconvex Generalized Benders Decomposition (Nonconvex-GBD) techniques to derive a mathematically solvable online dimensionality reduction and decoupling algorithm architecture. This successfully decouples discrete cell association and beam hopping decisions from continuous power allocation variables, providing a solution architecture for system parameter design that overcomes nonconvexity and has efficient iterative convergence capabilities. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the forward link system model of the multi-satellite collaborative low-Earth orbit satellite communication network proposed in this invention, provided by a preferred embodiment of the present invention.

[0041] Figure 2 This is a schematic diagram illustrating the geometric coverage relationship between the low-orbit satellite beam and the ground cell in this invention.

[0042] Figure 3 This invention provides an example of a low-Earth orbit satellite communication scenario and its corresponding conflict graph construction.

[0043] Figure 4 This is a comparison chart of the distribution of users in a residential community provided in an embodiment of the present invention.

[0044] Figure 5 A comparison diagram of network topology structures for different ground cell division methods provided in embodiments of the present invention.

[0045] Figure 6 A comparative diagram of the evolution of system queue backlog under different Lyapunov penalty factors provided for embodiments of the present invention.

[0046] Figure 7 This is a comparison chart of the network performance of different satellite-to-ground association algorithms provided in the embodiments of the present invention.

[0047] Figure 8 This is a performance comparison chart of different beam-hopping strategies provided in the embodiments of the present invention in terms of congestion control, fairness, and system utility.

[0048] Figure 9 This is a comparison chart of the overall performance of different resource allocation and power control algorithms provided in the embodiments of the present invention. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and thoroughly described below with reference to the accompanying drawings. The described embodiments are merely some embodiments of the present invention.

[0050] The technical solution of the present invention to solve the above-mentioned technical problems is:

[0051] Figure 1 This is a schematic diagram of the forward link system model for a multi-satellite collaborative low-Earth orbit satellite communication network proposed in this invention. It shows the composition structure of the Resource Management Center (RMC), ground gateway, low-Earth orbit satellite cluster, dynamically divided ground cells, and users, as well as their information interaction and data transmission relationships.

[0052] Figure 2This diagram illustrates the geometric coverage relationship between the low-Earth orbit satellite beam and the ground cell in this invention. The diagram shows the elevation angle change of the satellite beam projection onto the ground cell during its orbital operation, demonstrating that the system can accurately calculate the continuous service time of the satellite to the cell based on geometric relationships and minimum elevation angle constraints. This provides a geometric and theoretical basis for rationally scheduling transmission tasks and avoiding frequent inter-satellite handovers to reduce communication resource waste.

[0053] Figure 3 This invention provides an example of a low-Earth orbit satellite communication scenario and its corresponding conflict graph construction. The graph visually illustrates a specific multi-satellite, multi-cell network topology, where satellite 1 serves cells 1 and 2, and satellite 2 serves cells 3 and 4. Each satellite is configured with two beams, and each beam contains three resource blocks (RBs). In this specific scenario, the graph further illustrates how potential beam hopping decisions are mapped to vertices in the conflict graph. Based on system constraints (including two vertices belonging to the same cell, representing different cells served by the same beam, and the number of merged users in adjacent cells exceeding a resource threshold), a set of edges representing activated conflicts is established, thus providing model support for subsequent graph-based optimization of beam hopping patterns.

[0054] Figure 4 This is a comparison diagram of cell user distribution provided in an embodiment of the present invention. The diagram shows the number of users in each cell after the application of the cell division algorithm of the present invention, indicating that the present invention can effectively avoid the situation of extreme cell load concentration of users, and lay a robust traffic distribution foundation for subsequent satellite-to-ground correlation, beam switching and resource allocation.

[0055] Figure 5 This diagram compares the network topology of different ground cell partitioning methods provided in embodiments of the present invention. It illustrates the spatial layout differences between the cell partitioning algorithm proposed in this invention and various benchmark schemes under a specific user Poisson point distribution scenario. The diagram shows that the algorithm of this invention can generate a topology distribution with a more uniform layout, smoother scale changes, and a highly regular spatial structure, effectively reducing coverage overlap and co-layer interference while strictly satisfying geometric constraints.

[0056] Figure 6 This figure shows a comparison of the evolution of system queue backlog under different Lyapunov penalty factors, provided for embodiments of the present invention. The figure illustrates the changes in queue backlog under different penalty factors. The figure illustrates the convergence process of the system queue backlog under the given value. It verifies the balance between utility and latency. The trade-off relationship shows that the system architecture of the present invention has a high degree of adjustability, and can achieve a flexible performance trade-off between minimizing queue backlog and maximizing the overall system utility by adjusting the penalty factor.

[0057] Figure 7 This diagram compares the network performance of different satellite-to-ground association algorithms provided in this embodiment of the invention. It comprises four sub-graphs, respectively illustrating the average association duration, the cumulative distribution function (CDF) of traffic load distribution, the cumulative handover overhead, and the CDF of the number of active satellites. The results show that, compared to benchmark schemes based on maximum elevation angle or pure load balancing, the algorithm of this invention maintains low handover overhead while ensuring continuous and stable service, and effectively avoids the problems of excessive traffic concentration on a few satellites or excessive satellite activation, achieving an optimal trade-off between load balancing and space resource utilization.

[0058] Figure 8 This diagram compares the performance of different beam-hopping strategies provided in this invention in terms of congestion control, fairness, and system utility. Specifically, it includes four sub-diagrams: average queue length, cell queue backlog CDF, user queue backlog CDF, and cumulative system utility. The diagram shows that the algorithm of this invention can effectively suppress continuous queue surges, stabilize the average queue length at a low level (approximately 4 Gbit), and significantly eliminate the long-tail effect of queue backlog present in the baseline scheme. This effectively alleviates local congestion and user resource scarcity, thereby maximizing global system utility while ensuring queue stability.

[0059] Figure 9 This diagram compares the overall performance of different resource allocation and power control algorithms provided in this invention. Specifically, it includes four sub-graphs: average queue length, cell queue backlog CDF, user queue backlog CDF, and cumulative system utility. The results show that, when dealing with complex co-channel interference and high-dimensional discrete scheduling, this invention utilizes non-convex generalized Benders decomposition (GBD) for structured search, effectively overcoming the edge user tail congestion problem caused by greedy search and continuous relaxation methods. This invention not only maintains the system queue backlog at an extremely low level (approximately 4.2 Gbit), but also ensures the fairness of refined multi-user resource allocation and achieves significantly better long-term cumulative utility than benchmark schemes. Experimental results show that the multi-dimensional resource joint optimization architecture and conditional handover mechanism proposed in this invention can effectively reduce inter-satellite handover frequency and achieve load balancing, significantly alleviating the long-tail effect of queue backlog under highly dynamic network environments and random service arrivals. It significantly outperforms benchmark schemes in ensuring long-term system queue stability, improving long-term global utility, and ensuring the fairness of refined multi-user resource allocation.

[0060] This invention provides a method for optimizing joint beam hopping and resource allocation in low-Earth orbit satellite networks based on non-fixed cell partitioning. The method includes:

[0061] Step 1: Construct a multi-satellite collaborative network system model, analyze the dynamic evolution of the data queue, and establish a long-term optimization objective function:

[0062] In low Earth orbit (LEO) multi-satellite collaborative forward link communication systems, the Resource Management Center (RMC) needs to perform joint scheduling based on dynamically arriving user service demands, network topology changes, and load conditions. To strike a trade-off between system handover frequency and satellite load balancing, the ratio of total system load variance to service duration within the scheduling period is defined as follows:

[0063]

[0064] Simultaneously define the overall system during the scheduling period. The system utility function within is:

[0065]

[0066] in, Representative period The total system capacity of the entire network It represents the continuity and stability of the system network topology (i.e., the ratio of satellite load variation to total satellite service time). As a weighting factor, and is a dimensionless normalization constant.

[0067] Meanwhile, to ensure the long-term stability of the multi-user data queue across the entire network, the Lyapunov mean rate stability condition must be met, which means that all users must be constrained. The queue backlog satisfies Construct a joint optimization problem with the objective of maximizing the long-run average utility function of the system, and decompose it. The optimization problem is constructed as follows:

[0068]

[0069] Step 2: Decompose the original optimization problem according to the objective and corresponding constraints:

[0070] Based on the objective and corresponding constraints, the problem is first decomposed into two sub-problems: one is the cell partitioning problem for multi-user groups, and the other is the long-term stochastic optimization problem for multi-satellite cooperative resource allocation. Then, Lyapunov optimization theory is introduced to transform the long-term stochastic optimization problem into a single-period deterministic problem, which is decomposed into three sub-problems: the sub-problem of non-fixed cell dynamic partitioning (multi-user groups) based on the improved P-center algorithm, the sub-problem of constructing joint satellite-ground association and beam hopping mode optimization based on matching theory and graph theory, and the sub-problem of joint resource block allocation and power optimization.

[0071] Since the original optimization problem is a long-running stochastic mixed-integer nonlinear programming (MINLP) problem lacking future prior information and involving cross-time slot decision coupling, it is extremely difficult to solve directly. To address this mathematical challenge, this invention constructs a Lyapunov quadratic function. And introduce the Lyapunov drift-plus-penalty function:

[0072]

[0073] in, This is a control parameter used to balance queue stability and system utility. By deriving the theoretical upper bound of this drift plus penalty term, the original problem is decoupled and transformed into minimizing this upper bound independently for each individual period, while preserving the long-term stability constraint of the system. The problem of determinism:

[0074]

[0075] This transformation process successfully eliminates the dependence on future channel states and service arrivals, laying a solid mathematical foundation for subsequent low-complexity online resource optimization solutions.

[0076] Step 3: Dynamically partition non-fixed cells (multi-user grouping) based on the improved P-center algorithm:

[0077] To address the coverage resource mismatch problem caused by uneven distribution of multiple users, this invention utilizes an improved P-center algorithm to handle large-scale user distributions and dynamically determine the optimal number of cells. And boundaries. This method randomly selects the initial group centers and updates the center and radius of each group using the minimum circumcircle (MEC) method, thus forming a complete user-defined mesh. To eliminate dead zones caused by traditional static meshes, this method defines a global radius metric. That is, the maximum distance from all users to their group center. The algorithm iteratively identifies the extreme group (the group with the largest radius) and performs objective function capacity and migration tests on users within its bound subset, continuously optimizing the grouping structure. Subsequently, this invention introduces the maximum coverage radius of the physical beam. and minimum radius An iterative merging strategy based on constraints is used to eliminate invalid cells. This transformation process breaks the rigid constraints of fixed geographic grids, establishing a robust and load-balanced geometric topology foundation for subsequent dynamic resource allocation.

[0078] Step 4: Construct a joint satellite-to-ground correlation and beam hopping mode optimization model based on matching theory and graph theory:

[0079] To address the issues of frequent handovers and severe satellite load imbalances in dynamic networks, this method employs a conditional handover triggering mechanism based on Matching Theory: handover is only allowed when the serving satellite leaves the cell's line of sight or when the current load exceeds its maximum capacity. By defining two operations—unilateral transfer and pairwise exchange—the algorithm iteratively exchanges associated states under verified spatial geometric constraints, thereby improving the system's network stability indicators. Decrease the values ​​until convergence to obtain the optimal solution for the satellite-to-ground correlation matrix. To address the non-convexity constraint caused by co-channel interference (CCI) in microbeam hopping, this step utilizes graph theory techniques to construct a weighted conflict graph reflecting the spatiotemporal state in each time slot. In this graph, vertices represent candidate beam switching decisions, and edges represent conflict constraints arising from duplicate coverage within the same cell, violations of physical isolation between adjacent cells, or excessive co-channel interference. The dynamic vertex weights associated with the data queue backlog state are defined as follows:

[0080]

[0081] This step introduces a method that incorporates the current data queue backlog status. Dynamic vertex weights with transmission capacity The complex beam scheduling problem is cleverly transformed into a weighted maximum independent set (WMIS) problem in graph theory, and a heuristic greedy search algorithm is used to output conflict-free beam hopping strategy solutions in time slots.

[0082] Step 5: For the joint optimization subproblem of resource allocation and power control, a joint solution is achieved using non-convex generalized Benders decomposition and continuous convex approximation (SCA) algorithm:

[0083] Substituting the optimal satellite-to-ground correlation and beam hopping mode obtained in step 4, we can make decisions on the allocation of discrete resource blocks. With continuous transmission power The non-convex MINLP problem caused by deep coupling is addressed in this invention by introducing a variant GBD algorithm for alternating solutions:

[0084] (1) Primal Problem: Fixed current integer scheduling decision The optimal solution is sought for continuous power variables. Because the denominator of the signal-to-interference-plus-noise ratio (SIR) formula includes co-channel interference terms from other users, the objective function exhibits a highly non-convex logarithmic difference. This invention utilizes SCA technology to decompose the objective function into the difference of concave functions:

[0085]

[0086] In the Local points in the next iteration Perform a first-order Taylor expansion on the non-convex disturbance term:

[0087]

[0088] It is equivalently transformed into a standard convex programming problem, and the optimal power is solved to update the upper bound of the overall optimization objective of the system.

[0089] (2) Master Problem: Introduce continuous scalar auxiliary variables By utilizing the relaxed optimal value fed back from the original problem, a better resource allocation scheme is searched in the discrete variable space. Through constructing an optimality cut plane and feasibility cut plane constraints, new discrete decisions are sought under the accumulated cut plane constraints, and the lower bound is updated. The difference between the global upper and lower bounds is then considered. Less than the preset threshold At this point, the GBD algorithm converges and outputs the optimal user-level resource allocation matrix and power allocation strategy. Ultimately, it achieves joint optimal scheduling under the physical constraints of the entire system and the requirement for long-term queue stability.

[0090] The systems, devices, modules, or units described in the above embodiments can be implemented by computer chips or entities, or by products with certain functions.

[0091] Computer-readable media includes both permanent and non-permanent, removable and non-removable media that can store information using any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transferable medium that can be used to store information accessible by a computing device. As defined herein, computer-readable media does not include transient computer-readable media, such as modulated data signals and carrier waves.

[0092] It should also be noted that the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0093] The above embodiments should be understood as illustrative only and not as limiting the scope of protection of the present invention. After reading the description of the present invention, those skilled in the art can make various alterations or modifications to the present invention, and these equivalent changes and modifications also fall within the scope defined by the claims of the present invention.

Claims

1. A method for optimizing joint beam hopping and resource allocation in low-Earth orbit satellite networks, characterized in that, Includes the following steps: Step 1: Construct a system model, determine the low-orbit satellite multi-satellite cooperative communication model, non-fixed cell partitioning model, and dynamic data queue model, analyze the time-varying topology of satellite and ground and the uneven distribution of traffic, and form a joint optimization problem based on Lyapunov; Step 2: Decompose the joint optimization problem in Step 1 into a multi-user grouping cell partitioning problem, a joint satellite-to-ground correlation and beam hopping mode optimization problem, and a joint resource block allocation and power optimization problem. Through cluster analysis of the macro-user geographical distribution, prioritize the use of the improved P-center algorithm to solve the dynamic cell partitioning and user grouping problems. The improvement of the improved P-center algorithm lies in defining a global bottleneck radius, iteratively unloading edge users of the bottleneck cell to neighboring cells based on a strict monotonically decreasing criterion, fixing the cell through recursive dimensionality reduction after reaching a local optimum, and combining continuous minimum enclosing circle updates and preset extreme value radius constraints for cell merging. Step 3: For the joint satellite-to-ground correlation and beam hopping mode subproblem under non-fixed cell, the satellite-to-ground correlation is solved by introducing matching theory to achieve inter-satellite load balancing, and the micro-time slot beam hopping indicator variable is solved by combining the weighted maximum independent set (WMIS) conflict graph. Step 4: For the joint resource block allocation and power optimization subproblem, the non-convex generalized Benders decomposition algorithm is used to decouple discrete and continuous variables, and the continuous convex approximation (SCA) is combined to solve the resource and power solutions. Step 5: Under the premise of satisfying long-term queue stability, derive and iteratively execute the aforementioned multi-dimensional scheduling decisions, prove and obtain the joint optimal strategy to ensure the maximization of system utility and service continuity.

2. The method according to claim 1, characterized in that, Step 1 includes the following specific contents: Construct a system model that includes: A low-Earth orbit satellite constellation, a resource management center (RMC), gateways, and multiple legitimate mobile users on the ground, in the process of multi-satellite coordinated beam coverage, assume that in each scheduling cycle, the satellites provide services to non-uniformly distributed ground users through beam hopping (BH) technology; each satellite in the system is equipped with A maximum of one phased array beam, activated in each time slot. One beam; to avoid co-channel interference, the system adopts a spatial isolation mechanism, so adjacent cells are not illuminated at the same time; the gateway aggregates network information through the feeder link and forwards it to the RMC, which executes user grouping and jointly optimizes beam switching and the allocation of time, space and frequency resources; There are a total of There are 3 users, and the user set is denoted as _ . Users are categorized by RMC as A collection of independent communities, denoted as [a_1, a_2, a_3, a_4, a_5, a_6, a_7, a_8, a_9, a_1, a_1, a_2 ... In the current scheduling cycle, the system introduces a binary beam transition indicator variable. and resource allocation indicator variables The satellite's transmitting antenna gain and the user's receiving antenna gain are determined by radiation patterns conforming to ITU standards, which combine maximum antenna gain and off-axis angle parameters; mission timing is determined by a series of scheduling cycles. Composition, each cycle is divided into One time slot, of which It is the duration of each time slot; The satellite's orbital motion causes time-varying satellite-to-ground topology. Based on geometric relationships, the satellite's geocentric angle and elevation angle relative to the cell are determined. When the elevation angle meets a minimum threshold... Then, the duration of continuous available satellite service to the cell was derived and calculated; Channel fading takes into account both free space loss and antenna gain; satellite To users The channel power gain is expressed as It combines satellite launch gain, user reception gain, and free-space propagation loss; In the In each time slot, the satellite transmits signals to the user, with an allocated transmission power of [missing information]. If the cell is illuminated and the user is allocated the corresponding resource block, the resource block bandwidth is... The target signal power received by the user will be affected by co-channel interference (CCI) caused by other users simultaneously occupying the same resource block, as well as additive white Gaussian noise. The impact; the signal-to-interference-plus-noise ratio (SINR) of communication users is in fractional form, and the transmission capacity from satellite to ground users. Calculated based on Shannon's formula; During satellite communication, the transmit power constraint must be met. ; The system introduces binary variables. and This represents the satellite-to-ground association status and the cell-user dependency relationship; it defines the ratio of the total system load variance to the service duration within the scheduling period: The ratio of the total system load variance to the service duration within the defined scheduling period. System satellite load gap, Service time of satellite n associated with m Cell-satellite correlation variable, where n represents the nth satellite and m represents the mth cell; Queue backlog for each user The average rate stability condition must be met. ; , These represent the queue backlog and scheduling period for user u, respectively. The global system utility function is defined as follows: , , , , Let f represent the weighting factor, the total system capacity at time f, and different normalization factors, respectively; the problem is described as follows: These represent the cell-user correlation variables and cell-satellite correlation variables in period f, the beam hopping mode variable in time slot t in period f, the user-resource block allocation variable, and the power allocation variable, respectively. Indicates the scheduling period, For the global system utility function in period f, These represent the scheduling period, time slot, satellite index, cell index, beam index, user index, and resource block index, respectively. This indicates the total number of beams carried by a single satellite, U represents the total number of users, and K represents the total number of resource blocks. Indicates the maximum power of the resource block, Total system service time Minimum system service time Indicates the total number of communities, This indicates the queue backlog for user u in period f; Among the constraints Represents the binary variable to be optimized; Each user belongs to only one ground unit; This means that a ground unit can only be served by one satellite at any given time. This indicates the maximum number of ground units that a satellite can be associated with at any given time. This means that one beam can only illuminate one ground cell; This indicates the number of beams activated by a satellite in the same time slot at any given time period; This indicates that the user can use the resource block that illuminates the spot beam, and the spot beam must belong to the satellite accessed by the ground unit to which the user is currently grouped; This means that a resource block can only be allocated to one user; This indicates the number of resource blocks allocated to a user within a beam. This indicates that the power allocated to the resource block user does not exceed the specified maximum power; Minimum requirements for the service time of the constraint system in the cell; The backlog length of the user data queue must not grow indefinitely; To achieve long-term online optimization, a Lyapunov drift plus penalty function is introduced, transforming the original problem into minimizing the upper bound of the queue drift and network utility penalty term at each epoch. The problem, among which , , These represent the capacity and queue backlog of cell m in period f, respectively. These are control parameters.

3. The method according to claim 1 or 2, characterized in that, Step 2 includes the following specific contents: The joint optimization problem constructed in step 1 with the goal of maximizing long-term system utility and ensuring queue stability is a mixed integer nonlinear programming (MINLP) problem with highly coupled variables and NP-hard complexity. It is decomposed into three sub-problems using a decoupling strategy: cell partitioning problem for multi-user groups, joint satellite-to-ground correlation and beam hopping mode optimization problem, and joint resource block allocation and power optimization problem. First, the ground segmentation is transformed into a non-fixed user clustering problem; then, an improved P-center algorithm is used to randomly select... Using each user as the initial group center, the minimum circle cover (MEC) method is used to iteratively update the group center and radius. Extreme value group migration tests are performed to eliminate cover overlap, ultimately generating groups that satisfy the radius constraint. Non-static cell partitioning set The MEC refers to: for any user cluster group generated in each iteration, based on the three-dimensional / two-dimensional spatial geographic coordinates of all users in the group, using a geometric optimization algorithm to find a circumcircle with the smallest radius that can completely contain all users in the group. Subsequently, the geometric center coordinates of the minimum circumcircle are updated to the new initial center of the group, and its radius is updated to the current coverage radius of the cell, thus providing a basis for subsequent radius extremum constraints. and The determination provides precise physical boundary parameters; By utilizing an improved P-center algorithm, large-scale user distributions are handled to dynamically determine the optimal number of cells. The method randomly selects the initial group center and updates the center and radius of each group using the minimum circumcircle (MEC) method, thus forming a complete user partition; a global radius metric is defined. That is, the maximum distance from all users to their group center. The algorithm iteratively identifies the extreme group, i.e. the group with the largest radius, and performs objective function capacity testing and migration testing on users within its bound subset to continuously optimize the grouping structure. Subsequently, the maximum coverage radius of the physical beam is introduced. and minimum radius A constrained iterative merging strategy is used to eliminate invalid cells.

4. The method according to claim 1, characterized in that, Step 3 includes the following specific contents: Given the updated user group topology from step 2, the given cell and available satellite status, optimize the macroscopic satellite-to-ground correlation matrix. Beam jump indicator variable with micro time slot First, a conditional handover mechanism is introduced. Using matching theory, the switching operation between the cell and the satellite is defined, accepting the target of load difference while satisfying satellite capacity constraints. The decreasing matching solution ultimately outputs the optimal association decision. ; Secondly, after the satellite-to-ground relationship is determined, a weighted conflict diagram is constructed. Perform modeling; The graph represents vertices, where each vertex represents a potential beam hopping decision. Conflict edges are established based on system interference constraints. The weighted maximum independent set (WMIS) is solved by greedy search, and the optimal beam hopping mode that maximizes system utility while avoiding interference is output in time slots.

5. The method according to claim 1, characterized in that, Step 4 includes the following specific contents: Given the parameters from steps 2 and 3 above, we jointly optimize the discrete resource block allocation decision. With continuous transmission power In each time slot, a non-convex generalized Benders decomposition technique is introduced to alternately solve the original problem and the main problem. The non-convex generalized Benders decomposition technique is an iterative framework that decouples discrete and continuous variables. It generates the optimal cut by solving the continuous variables in the original problem with fixed discrete variables, or introduces a feasibility problem to generate a feasible cut when the original problem is infeasible. Then, the generated cut constraints are passed to the main problem to update the discrete resource block allocation decision. The global upper and lower bounds are continuously tightened through alternating iterations until convergence. In the original problem, with a fixed discrete decision, and considering the non-convex Shannon rate function objective caused by co-frequency interference, the Continuous Convex Approximation (SCA) technique is used to decompose the objective function into the difference of concave functions. , This represents the total capacity of cell m under a given power and resource block allocation during scheduling period f and time slot t. The power matrix of time slot t during scheduling period f. and The concave function decomposition term representing the Shannon rate; and in the th In the next iteration, Perform a first-order Taylor expansion as Construct a concave approximation function using this linear lower bound. , , Let each represent a nonconvex term in the j-th iteration. The linear approximation function obtained after first-order Taylor expansion at local points, and the representation function V for continuous power variables. The gradient and the optimal solution of the transmission power obtained in the (j-1)th iteration are used; the non-convex primal problem is transformed into a convex programming problem for solution, and the Lagrange multiplier information is extracted. ; These represent the optimal Lagrange multiplier extracted after solving the subproblem of the original problem in the i-th GBD iteration, the optimal continuous variable solution obtained by solving the convex subproblem after giving discrete variables in the i-th GBD iteration, and the resource block allocation variable, respectively. The main problem then utilizes these Lagrange multipliers to construct the Benders optimal cut in mixed integer linear programming (MILP), narrowing the search range for discrete variables.

6. The method according to claim 1, characterized in that, Step 5 includes the following specific content: Based on the overall online Lyapunov alternating optimization algorithm framework, the system optimizes the algorithm in each scheduling cycle. The inner loop performs the aforementioned non-fixed cell division, satellite-to-ground correlation and beam hopping optimization, as well as time slot-level optimization. The Nonconvex-GBD resource and power joint allocation steps continuously update the system queue state equations without needing to know future prior information, until the long-term average rate stability condition is met, and finally output a joint optimal scheduling strategy that satisfies the robustness of multi-star cooperative systems, physical constraints, and user-level service continuity.

7. An electronic device, characterized in that, The device includes a processor, a memory, an input device, and an output device, which are interconnected. The memory is used to store a computer program, which includes program instructions. The processor is configured to invoke the program instructions to execute the method according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program, the computer program including program instructions that, when executed by a processor, cause the processor to perform the method according to any one of claims 1 to 6.

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