A Game Theory-Based Distributed Downlink Spectrum Sharing Method for Large-Scale Hybrid Constellations

Abstract

This invention discloses a large-scale hybrid constellation distributed downlink spectrum sharing method based on game theory, comprising the following steps: establishing a link channel model in the hybrid constellation; using a perceived satisfaction function as an evaluation index of user performance; formulating a channel allocation game to capture the interaction and conflict between links, formalizing the channel allocation problem as a latent game; to solve the Nash equilibrium solution of the game model, dividing the system cycle into several equal topology cycles, with the topology of the ground-satellite link remaining unchanged within each topology cycle; dividing the topology cycle into a link establishment superframe and a data transmission superframe; and then using a distributed channel allocation algorithm based on stochastic learning for allocation. This application transforms a dynamic social problem into a static channel allocation problem; establishes a mathematical model based on game theory to represent user interaction; balances convergence speed and overall network satisfaction, and improves spectrum efficiency.

Description

Technical Field

[0001] This invention belongs to the field of satellite control technology, and in particular relates to a large-scale hybrid constellation distributed downlink spectrum sharing method based on game theory. Background Technology

[0002] Due to the enormous growth potential and wide range of applications of low-Earth orbit (LEO) constellations, large-scale satellite constellation communication systems are a key research area globally. The rapid expansion of these constellations has led to a severe shortage of global space spectrum resources. Currently, major frequency bands used for mobile services, such as the L / S band, are fully allocated, while frequency bands used for fixed broadband services, such as the Ku / Ka band, are nearing depletion, resulting in a scarcity of available spectrum resources.

[0003] However, despite the limited supply of spectrum resources, the average utilization rate of allocated frequency bands is typically below 15%, with the highest utilization rate reaching only around 85%. This indicates that allocated spectrum resources are not being fully utilized. In particular, geostationary orbit (GEO) satellites have extensive beam coverage areas, while GEO ground stations (GGS) are often dispersed, resulting in low spectrum utilization efficiency. With the rapid development of large-scale low Earth orbit (LEO) satellite constellations, spectrum resources are becoming increasingly scarce. Therefore, spectrum sharing between GEO and LEO satellites in large-scale hybrid satellite constellations has become a valuable research area.

[0004] Spectrum sharing between GEO and LEO satellites is based on application modes and can be categorized as follows: GEO satellite downlink and LEO satellite downlink, GEO satellite uplink and LEO satellite uplink, GEO satellite downlink and LEO satellite uplink, and GEO satellite uplink and LEO satellite downlink. This invention focuses on the first scenario. In this case, ground stations (GGS and LGS) in a hybrid satellite constellation share the downlink spectrum, such as... Figure 1 As shown.

[0005] Due to the random geographical distribution and dynamic rate requirements of LGS (Local Range Satellites), centralized control algorithms consume significant bandwidth and power to collect global network information. This problem is particularly prominent in special scenarios, such as military or complex communication environments, where obtaining global network information is often difficult or impractical. Centralized resource management for distributed LEO satellites and LGS nodes typically requires substantial computation, and even with centralized algorithms, a globally optimal solution cannot be guaranteed. Furthermore, relying on a single control node introduces significant vulnerabilities; if the central node fails or is damaged, the entire network's functionality is at risk.

[0006] LEO satellite communications are distributed. They are designed to autonomously and independently select their transmission channels. This presents several challenges compared to terrestrial wireless communication systems and traditional satellite constellations:

[0007] (1) The number of satellites in a large-scale hybrid satellite constellation is enormous, far exceeding that of a traditional satellite constellation. Therefore, effectively managing and scheduling so many satellites is a major challenge.

[0008] (2) Due to the frequent switching of the satellite-to-ground link, the channel strategy of LGS must be dynamically adjusted. As LEO satellites move at high speed, their visibility changes constantly. Therefore, after switching the satellite-to-ground link, the channel strategy of LGS must be readjusted.

[0009] (3) The large number of satellites and the scarcity of available spectrum resources lead to multiple satellite-to-ground links sharing the same channel. Therefore, avoiding channel conflicts and ensuring fair allocation of resources becomes a complex task.

[0010] (4) Due to the distance and high-speed movement of LEO satellites, the dynamic channel allocation problem requires a distributed, low-complexity learning algorithm. LEO satellites typically operate at altitudes of 500km-1000km, resulting in an information delay of approximately 15ms to 30ms for the LGS. The topology cycle typically switches between 5 and 10 minutes. However, traditional dynamic channel allocation algorithms require frequent negotiation of channel information between LEO satellites and the LGS. Therefore, these algorithms are not suitable for such short topology cycles because they cannot converge quickly. Thus, developing an efficient real-time dynamic channel allocation algorithm is necessary for large-scale hybrid satellite constellations.

[0011] The aforementioned studies primarily focus on spectrum sharing between geostationary orbit (GEO) satellites and terrestrial wireless communication systems, where their relative positions remain constant. Therefore, these methods may not be directly applicable to spectrum sharing scenarios in large-scale hybrid constellation systems. Summary of the Invention

[0012] In view of this, this invention is the first to propose research on the dynamic channel allocation problem in large-scale hybrid satellite constellations. This includes: proposing a time-segmentation model to protect against the impact of dynamic changes in satellite-to-ground links. The system cycle is divided into several equal topology cycles, further subdivided into connection establishment superframes and transmission superframes. The connection establishment superframes are ultimately divided into equal time slots. In each topology cycle, users update their channel policies slot by slot until a termination condition is met. A system model based on game theory is developed to capture mutual interference between links. The proposed game model is proven to be an exact potential game with at least one pure policy Nash equilibrium. A Dynamic Channel Allocation Algorithm (DCASLA) based on stochastic learning theory is proposed, which can asymptotically converge to the Nash equilibrium of the game model. The proposed algorithm dynamically adjusts the channel selection strategy based on the transmission rate sensed by the LGS, without requiring frequent interactions with other links. A general simulation scenario is constructed to verify the effectiveness of the proposed algorithm. The results show that the DCASLA algorithm has a good convergence speed and overall network satisfaction balance.

[0013] The game theory-based method for large-scale hybrid constellation distributed downlink spectrum sharing disclosed in this application includes the following steps:

[0014] Establish a link channel model in a hybrid constellation;

[0015] Using the perceived satisfaction function as an evaluation metric for user performance, we can capture the personalized network needs and preferences of different users.

[0016] During the topological period, each LGS is treated as an independent participant. In the optimization process, each LGS strives to maximize its perceived satisfaction while minimizing the interference to neighboring LGS.

[0017] We formulate a channel allocation game to capture the interactions and conflicts between links, and formalize the channel allocation problem into a potential game.

[0018] To solve the Nash equilibrium solution of the game model, the system cycle is divided into several equal topology cycles, and the topology of the ground-satellite link remains unchanged in each topology cycle; the topology cycle is further divided into a link establishment superframe and a data transmission superframe; and then a distributed channel allocation algorithm based on random learning is used for allocation.

[0019] Furthermore, the hybrid constellation comprises three GEO satellites and a low Earth orbit (LEO) satellite constellation configured according to the Walker pattern, the LEO satellite set... N L The total number of LEO satellites, and the LEO of the i-th LEO satellite. i The beam set is iN BLet be the total number of beams for the i-th satellite, and let be the set of LEO ground stations LGS. N G This is the total number of LGS, and the number of channels is N. M (N G >N M The set of available channels for LEO ground station LGS and geostationary satellite GGS is represented as follows:

[0020] Furthermore, the link channel model in the hybrid constellation is as follows:

[0021] According to Shannon's theorem, the b-th beam LEO of the i-th LEO satellite... ib And the nth ground station of the LEO constellation, LGS n Downlink established between Channel capacity is defined as:

[0022]

[0023] in, LGS n In channel a m The received signal-to-interference-plus-noise ratio, B M Represents channel bandwidth;

[0024] The link SINR model in the hybrid constellation is as follows:

[0025] LGS n via channel a m With Link Communication is affected by two types of potential interference:

[0026] i) Co-channel interference from downlinks of other low-Earth orbit satellites, denoted as I inter ;

[0027] ii) Co-channel interference from other beams of the same low-Earth orbit satellite in the downlink, denoted as I exter ,

[0028] LGS n The received SINR is represented as:

[0029]

[0030]

[0031]

[0032]

[0033]

[0034] in, Representation chain Channel noise of the path, P ib P kl P il These represent beam B. ib B kl B il Antenna transmit power, Indicates link Channel gain, Indicates that it comes from a link Gain from co-channel interference Indicates that it comes from a link Gain of co-frequency interference;

[0035] Channel gain Represented as:

[0036]

[0037] It's LEO i To LGS n Free space fading parameters, It is B ib Maximum transmit gain of the antenna It's LGS n Maximum receiving gain of the antenna.

[0038] Co-channel interference gain and Represented as:

[0039]

[0040]

[0041] yes against LGS n Interference gain, It's LGS n In LEO k Receiver gain in the direction of travel;

[0042] The transmit and receive gains of the antenna are calculated as follows:

[0043]

[0044]

[0045]

[0046]

[0047] Among them, G max Let θ represent the antenna's maximum gain, θ be the antenna's off-axis angle, and η represent the antenna's efficiency. and Here, A represents the first-order and third-order Bessel functions, c represents the speed of light, f is the center frequency of the channel, D is the diameter of the LEO satellite antenna, and λ represents the wavelength of the signal.

[0048] The formula for calculating the path loss of a link is:

[0049]

[0050] Where d represents the signal propagation distance.

[0051] Furthermore, the calculation method for perceived satisfaction level is as follows:

[0052]

[0053] Where r represents the resources allocated to the user, r req R is the transmission rate required by the user, while K is a parameter that adjusts the slope of the demand utility curve, reflecting the demand for r. req The degree of demand for resource r. Specifically, a lower K-slope indicates the user's demand for resource r. req Insensitive; on the contrary, a higher K-slope indicates that the user is sensitive to resource r. req The demand is strong;

[0054] The perceived satisfaction function is used to quantify the level of resources obtained by users. n The perceived satisfaction function is defined as follows:

[0055] q n (a n a -n )=s(r n ),

[0056] Among them, a -n Indicates excluding a n In addition to LGS's channel selection strategy, r n It's LGS n The normalized value of the obtained transmission rate;

[0057] r n The definition is as follows:

[0058]

[0059]

[0060] The optimization objective of the system is the overall perceived satisfaction of all LGS, defined as follows:

[0061]

[0062] Furthermore, the channel allocation game problem is represented as: in It is a collection of LGS. It is a set of available channels, u n This represents the utility function of LGS.

[0063] Furthermore, within the topology time period, for LGS n For example, the corresponding radiation beam B ix It's fixed, LGS n The obtained transmission rate is considered a link With the channel capacity, each LGS is treated as an independent participant. During the optimization process, each LGS strives to maximize its perceived satisfaction while minimizing interference to neighboring LGS.

[0064] LGS n Possibly with a radius of Other LGS within the range have potential co-channel interference; LGS with potential interference are considered as LGS. n The neighbor, and represented as:

[0065]

[0066] Where d(LGS) n LGS m ) represents LGS n and LGS m The distance between them Representing LGS n Interference protection radius.

[0067] Furthermore, LGS n The utility function is defined as:

[0068]

[0069] Where a -n In addition to LGS n Channel selection sequence for users other than those mentioned above. LGS n The channel selection sequence of neighboring users, LGS n The channel selection sequence of neighboring users;

[0070] The decision-making method is expressed as:

[0071]

[0072] The game theory model can be further expressed as:

[0073]

[0074] Furthermore, game theory models It is an exact potential energy game, if there exists a potential energy function. Satisfy the following formula:

[0075] The game model It is an exact potential game, in which there exists at least one pure policy NE, and the global or local optimal solution of the potential function constitutes the pure policy NE.

[0076] Furthermore, the distributed channel allocation algorithm based on random learning negotiates the channel strategy of LGS during the link establishment superframe to determine the optimal channel selection. After the channel is established, LGS transmits data during the data transmission superframe.

[0077] The link establishment superframe is further divided into several equal time slots. Each LGS updates its channel policy within one time slot, while the other LGSs remain unchanged. All LGSs update their channel policy once within one period, which consists of NG time slots. The update process continues until the distributed channel allocation algorithm based on random learning converges or reaches the maximum number of iterations. Attached Figure Description

[0078] Figure 1 This is a scenario diagram of spectrum sharing in a large-scale hybrid satellite constellation;

[0079] Figure 2 This is a spectrum sharing model diagram;

[0080] Figure 3 This is a time-segmentation model diagram;

[0081] Figure 4 This is the flowchart of the DCASLA algorithm;

[0082] Figure 5 This is a beam assignment diagram under LGS random distribution;

[0083] Figure 6 It is a channel selection probability curve;

[0084] Figure 7 This is a chart comparing online satisfaction levels. Detailed Implementation

[0085] The present invention will be further described below with reference to the accompanying drawings, but this is not intended to limit the present invention in any way. Any modifications or substitutions made based on the teachings of the present invention shall fall within the protection scope of the present invention.

[0086] The technical solutions provided in this application relate to satellite control technology, and are specifically described and illustrated through the following embodiments.

[0087] This invention focuses on downlink spectrum sharing scenarios in large-scale hybrid constellations. Neighboring satellites are interconnected via inter-satellite links, allowing all satellites to exchange important information such as ephemeris data, antenna patterns, spectrum usage, and the distribution of GGS and LGS. Both geostationary orbit (GEO) and low Earth orbit (LEO) satellites possess multi-beam capabilities and full-frequency reuse technology. LGS satellites are located outside the protection radius Rth and share the downlink spectrum with GGS. In this invention, the beam patterns of GEO satellites include Earth-pointing beams, whose transmission directions remain constant with satellite motion. In contrast, the beam patterns of LEO satellites include Earth-fixed beams, whose transmission directions change with satellite motion. The shared system operates in Frequency Division Duplex (FDD) mode. Due to the limitation of the GGS spectrum protection radius, it is assumed that the beam transmission directions of LEO and GEO satellites are different in the shared system. Assuming the transmit power of the LEO satellite's beam antenna is fixed, this study focuses on the dynamic spectrum allocation of the LGS.

[0088] System Model

[0089] like Figure 1 As shown, the hybrid constellation includes three GEO satellites and a LEO constellation configured according to the Walker pattern (the Walker pattern refers to a satellite orbit configuration in which multiple circular orbit satellites with the same orbital altitude and inclination are evenly distributed around the Earth. This pattern typically uses circular orbits with zero eccentricity, and the same number of satellites are evenly distributed within each orbital plane). Let the LEO satellite set... LEO i The beam set is The set of LGS is The number of channels is N M (N G >N M The set of available channels for LGS and GGS is represented as follows: Figure 1 Please refer to Table 1 for the parameter descriptions.

[0090] Table 1: Parameter Descriptions in the System Model

[0091]

[0092] In one embodiment, a link channel model is established to describe the cooperation and interference relationships between the links in the hybrid constellation.

[0093] 1) Link-channel model:

[0094] According to Shannon's theorem, Figure 2 middle The channel capacity of a link can be defined as:

[0095]

[0096] in, LGS n In channel a m The received signal-to-interference-plus-noise ratio (SINR), B M This represents the channel bandwidth.

[0097] 2) Link SINR model:

[0098] Assuming LGS n via channel a m With Link Communication can be affected by two types of potential interference:

[0099] i) Co-channel interference from downlinks of other low-Earth orbit satellites, denoted as I inter ;

[0100] ii) Co-channel interference from other beams of the same low-Earth orbit satellite in the downlink, denoted as I exter .

[0101] LGS n The received SINR can be represented as:

[0102]

[0103]

[0104]

[0105]

[0106]

[0107] in, Indicates link Channel noise, P ib P kl P il It is the antenna transmit power allocated to each beam. Indicates link Channel gain, Indicates that it comes from a link Gain from co-channel interference Indicates that it comes from a link Gain for co-channel interference.

[0108] Channel gain It can be represented as:

[0109]

[0110] Co-channel interference gain and It can be represented as:

[0111]

[0112]

[0113] The transmit gain and receive gain of the antenna can be calculated as follows:

[0114]

[0115]

[0116]

[0117]

[0118] Among them, G max Let θ represent the antenna's maximum gain, θ be the antenna's off-axis angle, and η represent the antenna's efficiency. and Let A and C be the first-order and third-order Bessel functions, respectively, where A represents the effective area of ​​the antenna, c represents the speed of light, f is the center frequency of the channel, D is the diameter of the LEO satellite antenna, and λ represents the wavelength of the signal.

[0119] The formula for calculating the path loss of a link is:

[0120]

[0121] Where d represents the signal propagation distance.

[0122] Problem formalization

[0123] 1) In wireless communication, a typical optimization objective for spectrum resource allocation is to maximize the total system throughput. However, this objective ignores the needs and preferences of different users, and maximum system throughput does not necessarily equate to the best user experience. Therefore, to overcome the limitations of the perceived satisfaction function, it is used as an evaluation metric for user performance, capturing the personalized network needs and preferences of different users. The perceived satisfaction function ranges from 0 to 1, representing the level of satisfaction. A higher satisfaction value indicates better optimization for the user. The perceived satisfaction level is calculated as follows:

[0124]

[0125] Where r represents the resources allocated to the user, r req R is the transmission rate required by the user, while K is a parameter that adjusts the slope of the demand utility curve, reflecting the demand for r. req The degree of demand for resource r. Specifically, a lower K-slope indicates the user's demand for resource r. req Insensitive; on the contrary, a higher K-slope indicates that the user is sensitive to resource r. req The demand is strong.

[0126] 2) System Optimization Objective: This application uses a perceived satisfaction function to quantify the level of resources obtained by users. LGS n The perceived satisfaction function is defined as follows:

[0127] q n (a n a -n )=s(r n (16)

[0128] Among them, a -n Indicates excluding a n In addition to LGS's channel selection strategy, r n It's LGS n The normalized value of the obtained transmission rate.

[0129] r n The definition is as follows:

[0130]

[0131]

[0132] Based on the above analysis, the optimization objective of the system is the overall perceived satisfaction of all LGS, defined as follows:

[0133]

[0134] Channel allocation game model

[0135] The channel allocation problem in large-scale hybrid constellations (LGS) faces four modeling challenges, which were described and addressed in Section 1. Therefore, this application proposes a channel allocation game to address these challenges, capturing the interactions and conflicts between links to gain a deeper understanding of the impact of channel allocation strategies. By analyzing the NE solution of the proposed game, the steady state of the system can be accurately predicted. This approach provides theoretical guidance for solving the LGS channel allocation problem.

[0136] Game Theory Model

[0137] The channel allocation problem mentioned above can be formalized as a latent game. This dynamic channel allocation game can be represented as follows: in It is a collection of LGS. It is a set of available channels, u n This represents the utility function of LGS.

[0138] During the topology period, for LGS n For example, the corresponding radiation beam B ix It's fixed, LGS n The obtained transmission rate can be considered as a link The channel capacity. In the game, each LGS is treated as an independent participant. During optimization, each LGS strives to maximize its perceived satisfaction while minimizing interference with neighboring LGS.

[0139] LGS n Possibly with a radius of Other LGS within the range exhibit potential co-channel interference. LGS exhibiting potential interference are considered as LGS. n The neighbor, and represented as:

[0140]

[0141] Where d(LGS) n LGS m ) represents LGS n and LGS m The distance between them Representing LGS n Interference protection radius.

[0142] Compared to terrestrial wireless communication systems, low Earth orbit (LEO) satellites have limited computing power and operate over much greater distances. Frequent data exchange between system participants can severely impact algorithm performance. Furthermore, due to the dynamic nature of satellite topology, convergence speed is also a critical factor affecting performance. By employing the concept of interference neighbor radius, we can dynamically adjust the number of interfering satellites. This adjustment helps balance interference accuracy and convergence speed, improving the overall efficiency of the algorithm.

[0143] Therefore, LGS n The utility function can be defined as:

[0144]

[0145] Where a -n In addition to LGS n Channel selection sequence for users other than those mentioned above. LGS nThe channel selection sequence of neighboring users, LGS k The channel selection sequence of neighboring users.

[0146] The decision-making method can be expressed as:

[0147]

[0148] The established game theory model can be expressed as:

[0149]

[0150] Equilibrium Analysis

[0151] Next, this application proves that the game is an exact latent game. Subsequently, the existence of the Nash equilibrium (NE) in the proposed game is confirmed.

[0152] Definition 1 (NE): A strategy configuration is valid if and only if no player can gain more profit through unilateral deviation. It is a pure strategy Nash equilibrium.

[0153]

[0154] Definition 2 (Exact Potential Game): Game Model It is an exact potential energy game, if there exists a potential energy function. Satisfy the following formula:

[0155]

[0156] Theorem 1: Defined Game Theory Model It is an exact potential energy game with at least one NE.

[0157] Proof: The potential function for constructing this game model is as follows:

[0158]

[0159] This potential function This corresponds to the system optimization objective. Assume any LGS n Both unilaterally changed the channel selection strategy from a n Change to This causes a change in the utility function, as shown below.

[0160]

[0161] The corresponding change in the potential energy function is:

[0162]

[0163] because,

[0164]

[0165] Therefore, combining formulas (27), (28) and (29), we get:

[0166] Based on the above analysis, it can be inferred that the change in utility function caused by unilaterally altering the channel strategy is equivalent to the change in potential energy function. (Game Theory Model) It is a precise potential game.

[0167] Exact potential games have several important characteristics, the two most important of which are as follows:

[0168] (1) There exists at least one pure strategy NE (Nash equilibrium).

[0169] (2) The global or local optimal solution of the potential energy function constitutes a pure policy NE.

[0170] The above conclusions indicate It is an exact potential game, and there exists at least one pure policy NE. The optimal solution that maximizes the overall system satisfaction corresponds to a pure policy NE.

[0171] To solve the Nash equilibrium solution of the game model, this application proposes a distributed channel allocation algorithm based on stochastic learning (DCASLA).

[0172] Time segmentation model

[0173] Considering the high-speed motion and periodicity of low Earth orbit (LEO) satellites, topological snapshot technology discretizes and stabilizes the dynamic ground-satellite connection. The system period is divided into several equal topological periods, such as... Figure 3 As shown. The topology of the ground-satellite link remains unchanged within each topology cycle.

[0174] The topology cycle is further divided into a link establishment superframe and a data transmission superframe. During the link establishment superframe, the algorithm negotiates the LGS channel strategy to determine the optimal channel selection. Once the channel is established, the LGS can transmit data during the data transmission superframe.

[0175] The link establishment superframe is further divided into several equal time slots. Each LGS updates its channel policy within one time slot, while other LGS remain unchanged. All LGS update their channel policy once within a period consisting of NG time slots. The update process continues until the algorithm converges or reaches the maximum number of iterations. This strategy effectively manages dynamic satellite-to-ground connections. Table 2 describes... Figure 3 The parameters presented in the text.

[0176] Table 2: Description of Time Segmentation Model Parameters

[0177] parameter describe T System cycle tq Topological periodicity Flink Link building superframe Fdata Data transmission superframe slott Time slice t epochk kth iteration

[0178] In the proposed algorithm, the game G is first extended to a mixed strategy form, LGS. n The mixing strategy in time slot t can be expressed as:

[0179]

[0180] LGS n The reward obtained at time slot t can be expressed as:

[0181]

[0182] Figure 4 The basic process of DCASLA is explained. The proposed algorithm eliminates the requirement for frequent interaction between the LGS and channel information. In each period, each LGS selects a channel through a hybrid strategy, while the channel strategies of other LGS remain unchanged. The hybrid strategy is then updated according to the transmission rate achieved by the LGS. The algorithm terminates when (indicating convergence) or when the maximum number of iterations is reached.

[0183] Step 1: k = 0, t = 0, initialize the mixing strategy Each LGS randomly selects a channel a based on a hybrid strategy. m (0);

[0184] Step 2: During time slice t of iteration period k, each LGS selects a channel based on the current hybrid strategy;

[0185] Step 3: LGS n By the rate of acquisition Calculate the utility function u n (k);

[0186] Step 4: According to formulas (32) and (33), LGS n Upgrade Hybrid Strategy

[0187] if a m (k+1)=a m (k)

[0188]

[0189] if a m (t+1)≠a m (t)

[0190]

[0191] Where λ∈(0,1) represents LGS n Learning step size It's LGS n Select channel a in time slot k m The probability of;

[0192] Step 5: Update k = k + 1, and return to step 2 until the algorithm terminates.

[0193] Convergence analysis

[0194] Assume that the channel selection strategy combination for all LGS in time slot t is as follows:

[0195] The combination of hybrid strategies is as follows:

[0196]

[0197]

[0198] Theorem 2: If λ→0 is satisfied, then the game model The DCASLA converges to the pure policy NE.

[0199] Prove that if λ→0, then the sequence It converges to the solution of the ordinary differential equation.

[0200]

[0201] These are the initial conditions, and (38), (39), and (40) represent the update rules.

[0202]

[0203]

[0204]

[0205] In addition, the function The definition is as follows:

[0206]

[0207] Therefore, combining (25), (31) and (41), we can conclude that:

[0208]

[0209] Theorem 2 is thus proved.

[0210] Next, experimental simulations will be conducted to analyze the convergence and performance evaluation of DCASLA in a dynamic environment. The simulation scenario and parameter configuration are as follows: It is assumed that the hybrid constellation consists of three geostationary orbit satellites and one low Earth orbit satellite constellation, and its Walker configuration is designed based on the Starlink satellite constellation. The parameters of the hybrid constellation are shown in Table 3.

[0211] Table 3: Constellation Orbit Parameters

[0212]

[0213] Because collinear interference between low Earth orbit (LEO) satellites and geostationary orbit (GEO) satellites is most pronounced near the equator, this application selects users in low-latitude regions for simulation experiments. The GGS (Geostationary Satellite System) is located in a certain sea area, and the LGS (Low Earth Orbit Satellites) are randomly distributed outside the spectrum protection radius around the GGS. It is assumed that all LGS and GGS are within the same beam of the GEO satellite, and that the LEO satellite's channel resources are limited to 12:00 to 14:00 per day. To ensure that the LGS can access the LEO satellite system, the LEO satellite shares the downlink spectrum with the GEO satellite without interfering with the normal communication of the GGS. The LEO satellite constellation completely covers all LEO satellites, and each LEO satellite beam can only serve one LEO satellite.

[0214] In the above experimental scenario, the system cycle is divided into 240 topology cycles, each lasting 5 minutes. The duration of the link establishment superframe is dynamic, typically ranging from 5 to 15 seconds. This application randomly selects one topology cycle for channel resource optimization simulation, and the optimization process is similar to that of other topology cycles.

[0215] The simulation implementation steps are as follows:

[0216] Step 1: Assume that each beam of a low Earth orbit (LEO) satellite can only serve one LEO satellite, and the center of the serving beam points towards the LEO satellite. Assign serving satellites and beams to each LEO satellite based on its coverage area (see...). Figure 5 );

[0217] Step 2: Based on the satellites and beams assigned to each LGS in LEO i and LGS n Establish a downlink L between them. LEO i and LGS n Establish a downlink L between them;

[0218] Step 3: Each LGS is an individual player in the game, establishing a channel allocation game model. In this model, N represents a set of LGS, M is a set of available channels, and u nThe utility function defined in formula (31);

[0219] Step 4: Solve for the optimal channel combination of LGS using DCASLA. Where a n LGS n The optimal channel strategy;

[0220] Step 5: Based on the optimal channel strategy LGS is connected to the LEO satellite system.

[0221] This section will verify the convergence of the proposed DCASLA through simulation experiments. The parameter configuration is as follows: the number of LGS is N. G =16, LGS distribution as follows Figure 5 As shown, the number of available channels is N. M =16.

[0222] In the simulation, a random LGS is selected to record the channel selection probability curve. For example... Figure 6 As shown, after approximately 120 iterations, the probability of LGS selecting channel q5 approaches 1. The simulation experiment was repeated 200 times, and statistical results show that the channel selection probability of LGS converges on average after 122 iterations.

[0223] The convergence performance of different algorithms was compared. The methods evaluated included DCASLA, Brute Force Computation (BFC), Best Response (BR) algorithm, and Trial and Error Learning (TE) algorithm.

[0224] The Quality of Experience (QoE) assessment is based on the overall network satisfaction across all LGS, where overall network satisfaction is defined as (43). The following simulation data are the average results of over 1000 independent experiments.

[0225]

[0226] Where, q n Indicates to LGS n The perceived satisfaction level is N, where N is the number of LGS.

[0227] The convergence time of the dynamic channel allocation algorithm in a satellite system consists of two parts:

[0228] i) The computation time of the optimization process.

[0229] ii) The timing of the dissemination of information.

[0230] Figure 7 The curves in the figure illustrate the convergence process of the three algorithms mentioned above. The experimental results yielded several important conclusions:

[0231] i) Processing time

[0232] The BR algorithm converges the fastest, requiring an average of only 35 iterations. DCASLA follows closely, converging in approximately 122 iterations. The TE learning algorithm converges in about 970 iterations, while BFC converges the slowest, requiring approximately 3800 iterations.

[0233] ii) Transmission time

[0234] To calculate the utility of an LGS, the BR algorithm must acquire channel selection information from all other links visited by the LGS. In other words, each LGS must interact with low Earth orbit satellites N=16 times to negotiate information. Therefore, despite having fewer iterations, the overall convergence time of the BR algorithm is longer than that of DCASLA. Furthermore, the BR algorithm is prone to getting trapped in local optima.

[0235] The BFC algorithm finds the optimal solution by traversing each channel strategy in the LGS. Although this algorithm can find the optimal solution, it takes the longest time and is therefore unsuitable for dynamic channel allocation schemes in satellite systems.

[0236] Both DCASLA and TE algorithms utilize sensing LGS. n Calculate LGS using the obtained transmission rate n The utility q n (a n a -n They update the LGS hybrid strategy based on utility as an environmental reward or penalty. Unlike the BR algorithm, they do not need to acquire channel selection information from other links. After updating the LGS hybrid strategy, they only need to transmit the hybrid strategy to the corresponding low-Earth orbit satellite, thus saving more path propagation time. The overall network satisfaction after convergence is comparable for both algorithms. However, the TE learning algorithm explores only one channel per iteration, resulting in slower convergence speed in later stages.

[0237] In the above scenario, the dynamic channel allocation problem involves an interaction time of approximately 15ms-20ms between the low Earth orbit satellite and the LGS for each round trip. Therefore, the frequency of information exchange between the satellite and the LGS is an important aspect to consider when evaluating the convergence of the algorithms. Table V reports the convergence times of the three algorithms, highlighting that the number of potential interfering neighbors can be controlled by adjusting the interfering neighbor distance radius, thus affecting the convergence performance of the algorithms.

[0238] C. Performance Evaluation

[0239] 1) Overall Network Satisfaction of Different Algorithms: The overall network satisfaction of the proposed DCASLA is compared with that of other algorithms, and the following parameters are set: LGS number is N. G=16, the distribution of LGS is as follows Figure 5 As shown, the number of available channels ranges from 2 to 10. The experiment compares DCASLA with other algorithms such as random selection, best NE, and worst NE.

[0240] Most existing literature focuses primarily on the overall optimization objective, often neglecting to ensure fair resource access for users. To better demonstrate the effectiveness of the algorithm proposed in this application, a network Quality of Experience (QoE) fairness index is introduced. Considering the current channel policy a, the QoE fairness index is expressed as follows:

[0241]

[0242] Where, N G t represents the number of LGS. n For LGS n The throughput. From this, we can conclude that J... QoE The closer it is to 1, the higher the fairness of the system.

[0243] Some important insights can be drawn from the experimental results of the QoS fairness index based on throughput and satisfaction optimization.

[0244] i) The total throughput of the two objectives is comparable, but the throughput of the overall network satisfaction optimization objective is slightly lower.

[0245] ii) Compared to system throughput optimization, overall network satisfaction optimization has a much higher QoE fairness index. This difference arises because overall network satisfaction optimization addresses the specific needs of the LGS, while system throughput optimization's sole objective is to maximize system throughput.

[0246] The impact of LGS and available channels on algorithm stability

[0247] The following experiments will investigate the impact of key parameters such as the number of LGS and the number of available channels on the stability of the algorithm.

[0248] The parameters are set as follows: the number of LGS is set to N. G =8, N G =12, N G =16, with the number of available channels set to 2, 4, 6, 8, 10, 12, 14, and 16 respectively. The required LGS rate for the experiment was randomly generated from 10 Mbps to 30 Mbps. The experimental results are the average of 1000 independent experiments. Two observations were observed in the experimental results:

[0249] i) The more channels available, the higher the overall satisfaction. This means that ample spectrum resources will lead to a better user browsing experience.

[0250] ii) The overall network satisfaction reaches its maximum when the number of available channels exceeds or equals the number of LGS, which means that each LGS can obtain a dedicated channel without interference.

[0251] The beneficial effects of this application are as follows:

[0252] This paper proposes a snapshot technique to transform the dynamic social problem into a static channel allocation problem. Furthermore, a game theory-based mathematical model is established to represent user interactions. It successfully proves the existence of at least one pure policy (NE) in the game and proposes a dynamic channel allocation algorithm based on stochastic learning. Simulation experiments demonstrate that DCASLA balances convergence speed and overall network satisfaction, outperforming other algorithms. This application provides valuable insights into dynamic channel allocation in hybrid constellations and offers possibilities for improving spectral efficiency.

Claims

1. A method for large scale hybrid constellation distributed downlink spectrum sharing based on game theory, characterized in that, The method comprises the following steps: a link channel model in the hybrid constellation is established; a perception satisfaction function is used as an evaluation index of user performance to capture the individualized network demand and preference of different users; in a topology period, each LGS is regarded as an independent participant, and each LGS strives to maximize its perception satisfaction and minimize the interference caused to neighboring LGSes in the optimization process; a frequency channel allocation game is formulated to capture the interaction and conflict between links, and the frequency channel allocation problem is formalized as a potential game; to solve the Nash equilibrium solution of the game model, the system cycle is divided into a plurality of equal topology cycles, the topology of the ground-satellite link remains unchanged in each topology cycle; the topology cycle is further divided into a link establishment superframe and a data transmission superframe; and a distributed channel allocation algorithm based on random learning is used for allocation.

2. The game theory based large scale hybrid constellation distributed downlink spectrum sharing method according to claim 1, characterized in that, The mixed constellation comprises three GEO satellites and a low earth orbit satellite LEO constellation configured in a Walker pattern, the set of LEO satellites N L is the total number of LEO satellites, the i-th LEO satellite LEO i is the set of beams of iN B is the total number of beams of the i-th satellite, the set of LEO ground stations LGS is N G is the total number of LGS, the number of channels is N M (N G > N M ), the set of available channels for a LEO ground station LGS and a geostationary satellite GGS is 3. The game theory based large scale hybrid constellation distributed downlink spectrum sharing method according to claim 2, characterized in that, The link channel model in the hybrid constellation is as follows: According to Shannon's theorem, the b-th beam LEO of the i-th LEO satellite... ib And the nth ground station of the LEO constellation, LGS n Downlink established between Channel capacity is defined as: wherein represents LGS n received on channel a m received on channel a M represents channel bandwidth; The link SINR model in the hybrid constellation is as follows: LGS n through channel a m with link communicating, it is affected by two types of potential interference: i) co-frequency interference from downlinks of other low earth orbit satellites, denoted I inter ; ii) co-frequency interference from downlinks of other beams of the same low earth orbit satellite, denoted as I exter , LGS n The received SINR is expressed as: wherein, denotes a chain denotes a channel noise, P ib denotes a channel noise, P kl denotes a channel noise, P il denotes a beam B ib denotes a beam B kl denotes a beam B il denotes an antenna transmit power of a beam B denotes a channel gain of a link denotes a channel gain of a link denotes an intra-frequency interference gain from a link denotes an intra-frequency interference gain from a link denotes an intra-frequency interference gain from a link denotes an intra-frequency interference gain from a link Channel gain is represented as: is LEO i to LGS n free space fading parameter, is B ib antenna maximum transmit gain, is LGS n antenna maximum receive gain; Co-channel interference gain and is represented as: is to LGS n interference gain, is LGS n in LEO k receive gain in the direction of The transmission gain and reception gain of the antenna are calculated as: where Gmax max represents the maximum gain of the antenna, θ is the off-boresight angle of the antenna, η represents the efficiency of the antenna, and are the first and third order Bessel functions, respectively, A represents the effective area of the antenna, c represents the speed of light, f is the center frequency of the channel, and D is the diameter of the LEO satellite antenna, λ represents the wavelength of the signal; The path loss of the link is calculated according to the following formula: Wherein, d represents the signal propagation distance.

4. The game theory based large scale hybrid constellation distributed downlink spectrum sharing method according to claim 3, characterized in that, The calculation method of the perception satisfaction degree is as follows: where r denotes the resource allocated to the user, r req is the transmission rate required by the user, and K is a parameter that adjusts the slope of the demand utility curve, reflecting the degree of demand for r req , in particular, a lower K slope indicates that the user is not sensitive to the resource r req , on the contrary, a higher K slope indicates that the user is strongly demanding of the resource r req ; The perceived satisfaction function quantifies the level of resources a user obtains, LGS n The perceived satisfaction function of LGS is defined as follows: q n (a n ,a -n )=s(r n ), where a -n represents the channel selection strategy of LGS other than a n r n is the normalized value of the transmission rate obtained by LGS n ​ r n are defined as follows: The optimization target of the system is the overall perception satisfaction of all LGSes, and is defined as:

5. The game theory based large scale hybrid constellation distributed downlink spectrum sharing method according to claim 4, characterized in that, The channel allocation game problem is represented as where is a set of LGSs, is a set of available channels, u n denotes a utility function of LGS.

6. The game theory based large scale hybrid constellation distributed downlink spectrum sharing method according to claim 5, characterized in that, Within a topology period, for LGS n , the corresponding radiation beam B ix is fixed, the transmission rate obtained by LGS n is regarded as the channel capacity of the link , each LGS is regarded as an independent participant, and in the optimization process, each LGS strives to maximize its perceived satisfaction while minimizing the interference caused to neighboring LGS; LGS n may potentially interfere with other LGS within a radius of LGS that potentially interfere are considered neighbors of the LGS n and are denoted as: where d(LGS n , LGS m ) represents the distance between LGS n and LGS m , represents the interference protection radius of LGS n .

7. The game theory based large scale hybrid constellation distributed downlink spectrum sharing method according to claim 6, characterized in that, LGS n The utility function of LGS is defined as: where a -n represents the channel selection sequence of other users than LGS n , represents the channel selection sequence of neighbor users of LGS n , represents the channel selection sequence of neighbor users of LGS k ; The decision method is represented as: The game model is further represented as:

8. The game theory based large scale hybrid constellation distributed downlink spectrum sharing method according to claim 7, characterized in that, Game model is a precise potential game, if there exists a potential function satisfying the following equation: The game model is a precise potential game, at least one pure strategy NE exists in the game model, and the global or local optimal solution of the potential function constitutes the pure strategy NE.

9. The game theory based large scale hybrid constellation distributed downlink spectrum sharing method according to claim 8, characterized in that, The distributed channel allocation algorithm based on random learning negotiates the channel strategy of the LGS during the link establishment superframe, determines the optimal channel selection, and transmits data during the data transmission superframe after the channel is established. The link establishment superframe is further divided into a plurality of equal time interval slots, each LGS updates the channel strategy in a time slot, and other LGSes remain unchanged, all LGSes update the channel strategy once in a cycle, the cycle is composed of NG time slots, and the updating process continues until the distributed channel allocation algorithm based on random learning converges or the maximum iteration number is reached.

10. The game theory based large scale hybrid constellation distributed downlink spectrum sharing method according to claim 9, characterized in that, In the random learning based distributed channel allocation algorithm, the game G is first extended to a mixed strategy form, LGS n The mixed strategy representation at time slot t is: N G is the total number of mixed strategies; LGS n The reward obtained at time slot t is represented as: Step 1: k = 0, t = 0, initialize mixed strategy vector Each LGS randomly selects a channel a based on the mixed strategy m (0); Step2: In the time slice t of the iteration cycle k, each LGS selects a channel based on the current hybrid strategy; Step 3: LGS n by the rate of acquisition computing the utility function u n (k), a m (k) is the mth channel at time k, is B xy to the LGS n link; Step 4: LGS is calculated by the following equation n Upgrading the hybrid policy vector if a m (k+1) = a m (k) if a m (k+1)≠a m (k) where λ ∈ (0, 1) represents the learning step size of the LGS n , is the utility function of the LGS n , is the probability that the LGS n selects channel a m at time slot k; Step5: Update k=k+1, and return to step Step2 until the algorithm termination condition is met.

Images