A resource sharing method for cognitive satellite-ground network based on double-layer game

Abstract

The embodiments of the present application relate to the technical field of cognitive satellite-ground network, and in particular to a resource sharing method of a cognitive satellite-ground network based on a double-layer game, including: establishing a system model of a cognitive satellite-ground network with multiple base stations on a single satellite; establishing a channel model of a satellite communication link and a channel model of a ground communication link; establishing a utility function of the satellite, a utility function of the base station, and an alliance value function of the alliance; gradually reducing the time slot division factor for iteration, using the alliance value function and an alliance formation algorithm based on merging rules and splitting rules to determine the highest alliance, and then based on the alliance value function, obtaining an optimal power allocation vector, and when the highest alliance under the optimal power allocation vector satisfies the safety rate constraint of the satellite, saving the time slot division factor, the optimal power allocation vector, and the highest alliance as candidate solutions in a candidate set; selecting a candidate solution that can maximize the utility function of the satellite from the candidate set as the optimal solution for resource sharing for resource sharing.

Description

Technical Field

[0001] Embodiments of the present application relate to the technical field of cognitive satellite-ground networks, and in particular to a resource sharing method of a cognitive satellite-ground network based on a double-layer game. Background Art

[0002] In order to realize resource sharing of satellite-to-ground networks and promote the integration of satellite networks and ground networks, cognitive radio technology has been applied to satellite-to-ground networks to form cognitive satellite-to-ground networks by virtue of its ability to intelligently perceive and learn the external environment. In the early research of cognitive satellite-to-ground networks, cognitive radio technology was only used as a spectrum reuse method to enable ground networks to access satellite spectrum to solve the problem of spectrum resource scarcity of ground networks, without considering the communication needs of satellite networks. Due to the broadcast characteristics of satellite-to-ground communications and the increasingly prominent security issues of satellite networks in the open electromagnetic environment, satellite-to-ground network collaboration based on resource sharing has begun to receive widespread attention in the research of cognitive satellite-to-ground networks.

[0003] Physical layer security can achieve secure transmission of wireless signals by utilizing the inherent random characteristics of wireless channels. It has been studied in depth. However, the characteristics of satellite communications have brought new challenges to physical layer security. Specifically, the resources available for physical layer security technology in satellite-to-ground communications, such as multiple antennas, computing, and power, are very limited. In addition, due to the high altitude of satellite orbits, the correlation between legitimate links and eavesdroppers is high, which makes it difficult for satellites to accurately distinguish between legitimate users and eavesdroppers (Eves). Therefore, cooperative interference technology has been widely studied as an effective method to enhance the security of satellite communications in cognitive satellite-to-ground networks. When cognitive satellite-to-ground networks share resources, satellites share spectrum resources with ground network base stations (BSs). At the same time, BSs will generate interference as a green interference source to enhance the secure transmission performance of satellite networks, thereby countering eavesdropping.

[0004] However, this resource sharing method of cognitive satellite-ground network based on collaborative interference technology ignores the fairness issue of satellite-ground collaboration in resource sharing research. In fact, the satellite network and ground network in the cognitive satellite-ground network generally belong to different operators. Both networks have their own interests. If their own interests are damaged, they will refuse to cooperate with each other, which will lead to the failure of resource sharing in the cognitive satellite-ground network. Summary of the invention

[0005] The embodiment of the present application proposes a resource sharing method for a cognitive satellite-to-ground network based on a two-layer game. From the perspective of fairness in resource sharing, a two-layer game is used to achieve simultaneous improvement in the security performance of the satellite network and the total utility of the ground network, thereby achieving a win-win performance between the satellite network and the ground network, thereby ensuring that the resource sharing of the cognitive satellite-to-ground network can proceed smoothly and normally.

[0006] To achieve the above-mentioned purpose, an embodiment of the present application provides a resource sharing method for a cognitive satellite-to-ground network based on a two-layer game, comprising the following steps: establishing a system model of a cognitive satellite-to-ground network in a single-satellite multi-base station scenario; wherein the system model includes a satellite as a primary transmitter and a number of base stations as secondary transmitters within the beam coverage of the satellite, and the system model allows base stations to be employed as collaborative interference sources for satellites in the form of an alliance; establishing a channel model for a satellite communication link, and establishing a channel model for a ground communication link; based on a time slot division factor of the satellite, dividing the satellite's transmission time slot into a first stage and a second stage, establishing a utility function of the satellite based on the first stage, the channel model of the satellite communication link, and the channel model of the ground communication link, establishing a utility function of the base station based on the second stage and the channel model of the ground communication link, and establishing an alliance value function of the alliance based on the utility function of the base station; wherein, in the first stage In the first stage, the satellite sends a signal to the primary user and employs the highest alliance. Each base station in the highest alliance acts as a collaborative interference source to send artificial noise to the eavesdropper. In the second stage, each base station in the highest alliance sends a signal to its corresponding secondary user. When resource sharing is required, the satellite gradually reduces the time slot division factor with a preset step size for iteration. In each iteration, the highest alliance is determined by using the alliance value function and the alliance formation algorithm based on the merging rule and the splitting rule. Then, based on the alliance value function, the optimal power allocation vector of the highest alliance is obtained. When the highest alliance under the optimal power allocation vector satisfies the safety rate constraint of the satellite, the time slot division factor, the optimal power allocation vector and the highest alliance in this iteration process are saved as candidate solutions in the candidate set. After the iteration process is completed, the candidate solution that can maximize the utility function of the satellite is selected from the candidate set as the optimal solution for resource sharing, and the resource sharing is performed with the optimal solution.

[0007] To achieve the above objectives, an embodiment of the present application further provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the above-mentioned resource sharing method of a cognitive satellite-ground network based on a two-layer game.

[0008] The embodiment of the present application proposes a resource sharing method for a cognitive satellite-to-ground network based on a double-layer game. First, a system model of the cognitive satellite-to-ground network in a single-satellite multi-base station scenario, a channel model of a satellite communication link, a channel model of a ground communication link, a utility function of a satellite, a utility function of a base station, and a coalition value function of an alliance are established. Based on these models and functions, from the perspective of fairness in resource sharing, a double-layer game is used to gradually reduce the time slot division factor with a preset step size for iteration. In each iteration, the alliance value function and an alliance formation algorithm based on merging rules and splitting rules are used to determine the highest alliance, and then the highest alliance is formed based on the alliance value function. number, and obtain the optimal power allocation vector of the highest alliance. When the highest alliance under the optimal power allocation vector satisfies the safety rate constraint of the satellite, the time slot division factor, the optimal power allocation vector and the highest alliance in this iteration are saved as candidate solutions in the candidate set. Finally, after the iteration, the candidate solution that can maximize the utility function of the satellite is selected from the candidate set as the optimal solution for resource sharing to carry out resource sharing, thereby achieving the simultaneous improvement of the safety performance of the satellite network and the total utility of the ground network, achieving a win-win performance of the satellite network and the ground network, and ensuring that the resource sharing of the cognitive satellite-ground network can be carried out smoothly and normally.

[0009] In some optional embodiments, the channel model of the satellite communication link is established by the following formula:

[0010]

[0011]

[0012] h aξ =Aexp(jψ aξ )+Zexp(jψ aξ )

[0013] ξ={p,e}

[0014] Among them, a represents the satellite, p represents the primary user corresponding to the satellite, e represents the eavesdropper, and L aξ represents the propagation loss model of the satellite communication link, h aξ represents the satellite channel fading model, C ap represents the path loss of the link from the satellite to the primary user, represents the satellite beam pattern of the primary user, C ae represents the path loss of the satellite-to-eavesdropper link, represents the satellite beam pattern of the eavesdropper, ψ aξ represents the uniformly distributed phase of the scattered component, φ aξrepresents the uniformly distributed phase of the line-of-sight component, A represents the amplitude of the scattered component that obeys the Rayleigh distribution, Z represents the amplitude of the line-of-sight component that obeys the Nakagami-m distribution, and g aξ A channel model representing an established satellite communication link;

[0015] The channel model of the ground communication link adopts the Nakagami-n channel model, and its formula is expressed as follows:

[0016]

[0017]

[0018] ζ={d i ,e}

[0019] Among them, s i represents the i-th base station in the system model, d i represents the secondary user corresponding to the i-th base station, represents the path loss of the link from the ith base station to the corresponding secondary user, represents the path loss of the link from the ith base station to the eavesdropper, represents the terrestrial channel fading model, represents the fading parameter, represents the average power, Represents the channel model of the established terrestrial communication link.

[0020] In some optional embodiments, the satellite utility function is established based on the first stage and the channel model of the satellite communication link, and is implemented by the following formula:

[0021]

[0022]

[0023]

[0024]

[0025] Where α represents the time slot division factor, T represents the satellite transmission time slot, S * represents the highest alliance, P J represents the interference power of the base stations in the highest alliance, represents the security rate of the primary user under the highest alliance collaboration, R P represents the information rate at the primary user, represents the information rate at the eavesdropper, [·] + =max{·,0},P a represents the satellite's transmission power, The conjugate transpose of the channel model for the satellite-to-primary user communication link, w a represents the satellite’s beamforming vector, represents the variance of the noise at the primary user, The conjugate transpose of the channel model representing the imperfect communication link from the satellite to the eavesdropper, represents the interference power of the ith base station in the highest alliance, represents the channel model of the imperfect communication link from the ith base station in the highest alliance to the eavesdropper, represents the distributed beamforming vector weight of the ith base station in the highest alliance, represents the variance of the noise at the eavesdropper, |S * | represents the total number of base stations in the highest alliance;

[0026] The utility function of the base station is established based on the second stage and the channel model of the ground communication link, which is implemented by the following formula:

[0027]

[0028]

[0029] in, represents the utility function of the ith base station in the highest alliance, represents the transmission rate of the secondary user corresponding to the i-th base station in the highest alliance, represents the transmission power of the ith base station in the highest alliance, represents the interference power of the ith base station in the highest alliance, C1 represents the unit interference energy consumption cost of the base station, C2 represents the unit transmission energy consumption cost of the base station, represents the channel model of the terrestrial communication link from the i-th base station in the highest alliance to the corresponding secondary user, represents the coordinated beamforming vector weight of the ith base station in the highest alliance, represents the variance of the noise at the secondary user.

[0030] In some optional embodiments, when resource sharing is required, a two-layer game model of Stackelberg and highest alliance formation is established based on the system model, the utility function of the satellite, the alliance value function, and the alliance formation algorithm based on merging rules and splitting rules; wherein the two-layer game model includes three optimization problems, namely, the optimization problem of time slot division factor, the optimization problem of alliance formation and the optimization problem of power allocation.

[0031] In some optional embodiments, for the optimization problem of alliance formation, the sum of the powers required for each base station in the alliance to broadcast information to the base station farthest from itself in the alliance is used as the cost of forming the alliance. The cost of forming the alliance is expressed by the formula:

[0032]

[0033]

[0034] in, represents the power required by the i-th base station in the alliance to send information to the base station farthest from it, represents the cost of forming the alliance, Λ0 is the minimum signal-to-noise ratio required for information exchange among potential alliance members, represents the variance of the noise at the base station farthest from the i-th base station in the alliance;

[0035] The alliance value function of the alliance is modeled as:

[0036]

[0037]

[0038] in, represents the income of alliance S, represents the preset maximum tolerable power cost, v(S) represents the alliance value function of alliance S;

[0039] The power allocation of base stations in the alliance is modeled as:

[0040]

[0041]

[0042]

[0043] in, represents the utility function of the ith base station in alliance S, represents the transmission power of the i-th base station in alliance S, represents the interference power of the i-th base station in alliance S, represents the maximum energy of the i-th base station in alliance S, represents the maximum power of the i-th base station in alliance S;

[0044] The satellite time slot allocation problem is modeled as:

[0045]

[0046] st0≤α≤1

[0047]

[0048] Among them, U a (α, P J |S) represents the utility function of the satellite under the collaboration of alliance S, It indicates the security rate of the primary user under the collaboration of alliance S. Indicates the safe rate of primary users without coordination.

[0049] In some optional embodiments, the method of determining the highest alliance by using a preset alliance value function and an alliance formation algorithm based on a merging rule and a splitting rule includes:

[0050] For the given two partitions and If there are the same game participants inside, the Max-Coalition order is defined as follows:

[0051]

[0052] Among them, max{·} represents the maximum value of the orientation amount, express s within i The utility function of

[0053] The merge rule is defined as follows: if compared to the alliance {S1,S2,…,S l}, the game participants prefer the merged alliance, so these alliances are merged, that is, when hour,

[0054] Define the split rule as: if compared to the alliance Game participants prefer the split alliances, so they split these alliances. hour,

[0055] Dividing the base stations in the system model into a number of non-cooperative alliances, that is, each base station forms a separate alliance, to obtain an initial division;

[0056] According to the alliance value function, an initial highest alliance is determined in the initial division, and an attempt is made to merge the initial highest alliance with the initial second highest alliance. Based on the Max-Coalition order, if the game participants prefer the merged alliance, the initial highest alliance is merged with the initial second highest alliance. Otherwise, an attempt is made to merge the initial highest alliance with the initial third highest alliance until all alliances in the initial division make a merger decision and there is no more alliance that can be merged, and then a final merged alliance is obtained;

[0057] Traverse each base station in the final merged alliance and split each base station in the final merged alliance. Based on the Max-Coalition order, if the game participants prefer the alliance obtained after the current base station is split from the final merged alliance, the current base station will be split from the final merged alliance. Otherwise, the current base station will be retained until the final merged alliance makes a split decision for each base station in the final merged alliance. When there are no base stations that can be split further, the highest alliance is obtained.

[0058] In some optional embodiments, obtaining the optimal power allocation vector of the highest alliance includes:

[0059] A Lagrangian function for modeling power allocation of base stations in the alliance is established. The Lagrangian function for modeling power allocation of base stations in the alliance is expressed by a formula:

[0060]

[0061] Where μ represents the Lagrange multiplier, λ=(λ1,λ2,λ3,λ4) T is a non-negative Lagrange multiplier vector;

[0062] The optimal power allocation vector satisfy:

[0063]

[0064] in,

[0065] In some optional embodiments, after each base station in the highest alliance determines the optimal power allocation vector, the satellite determines the optimal time slot division factor, and the satellite's time slot division problem is remodeled as:

[0066]

[0067]

[0068]

[0069] in, represents the maximum value of the time slot division factor under the optimal power allocation vector;

[0070] A remodeled Lagrangian function of the satellite time slot division is established, and the remodeled Lagrangian function of the satellite time slot division is expressed by the formula:

[0071]

[0072] in, represents the non-negative Lagrange multiplier vector;

[0073] The optimal time slot division factor α * satisfy:

[0074]

[0075] in,

[0076] The optimal time slot division factor α * It is expressed by the formula:

[0077]

[0078] in, α 2 Numerical solution via two-dimensional search get. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 It is a flowchart of a resource sharing method of a cognitive satellite-ground network based on a double-layer game provided in one embodiment of the present application;

[0080] Figure 2 is a schematic diagram of a system model of a cognitive satellite-to-ground network in a single-satellite multi-base station scenario provided in an embodiment of the present application;

[0081] Figure 3 It is a schematic diagram of the principle of a double-layer game model formed by Stackelberg and the highest alliance provided in an embodiment of the present application;

[0082] Figure 4 It is a schematic diagram of the principle of an alliance formation algorithm based on merging rules and splitting rules provided in an embodiment of the present application. DETAILED DESCRIPTION

[0083] To make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the embodiments of the present application will be described in detail below in conjunction with the accompanying drawings. However, it will be appreciated by those skilled in the art that in the present application, many technical details are proposed in order to enable the reader to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical scheme claimed in the present application can also be implemented. The division of the following embodiments is for the convenience of description, and the specific implementation of the present application should not be construed as any limitation, and the various embodiments can be combined and referenced with each other under the premise of no contradiction.

[0084] Physical layer security can achieve secure transmission of wireless signals by utilizing the inherent random characteristics of wireless channels, and has been studied in depth. However, the characteristics of satellite communications themselves bring new challenges to physical layer security. Specifically, the resources such as multiple antennas, computing, and power that can be used by physical layer security technology in satellite-to-ground communications are very limited. In addition, due to the high altitude of satellite orbits, the correlation between its legitimate links and eavesdropping links is high, making it difficult to accurately distinguish between legitimate users and eavesdroppers. Therefore, collaborative interference technology has been widely studied as an effective method to enhance the security of satellite communications in cognitive satellite-to-ground networks. Among them, base stations, while sharing satellite spectrum, cooperate with satellites as green interference sources to combat eavesdropping.

[0085] B.Li et al. proposed a robust BS beamforming scheme under imperfect channel state information (CSI) to enhance the security of satellite links. W.Lu et al. proposed a robust BS beamforming scheme for an integrated satellite-ground relay network, in which the BS acts as a relay to cooperate with satellites for secure transmission. In order to further improve security performance, many research teams have designed satellite-ground joint beamforming schemes for cognitive satellite-ground network systems. Specifically, M.Lin et al. proposed a joint beamforming scheme in a cognitive satellite-ground network with a software-defined architecture to minimize the total transmission power while ensuring the satellite safety rate and the quality of service of the ground network. J.Xiong et al. jointly optimized the beamforming vectors of the satellite and BS for a multicast cognitive satellite-ground network system to minimize the total transmission power. Considering the energy-limited characteristics of satellites, W.Lu et al. also studied a joint beamforming scheme to maximize the satellite safety and energy efficiency while meeting the transmission needs of satellite and ground users. In addition, Z.Lin et al. proposed a hybrid joint beamforming scheme, in which the BS adopts analog digital beamforming to reduce power consumption and implementation complexity. In order to further improve the security performance of satellite networks, B.Li et al. used artificial noise (AN) at the BS to counter eavesdroppers. Specifically, collaborative beamforming and AN are jointly optimized to minimize the transmission power of the effective signal under the constraints of satellite security rate and ground transmission rate. The above work only considers a single ground base station scenario, while W.Lu and J.Du et al. studied a more practical multi-ground base station scenario. Among them, W.Lu et al. designed a joint beamforming and AN scheme to minimize the total transmission power of the satellite and BS under the constraints of satellite security rate and ground user signal-to-interference-to-noise ratio. J.Du et al. proposed a joint beamforming and AN scheme to maximize the satellite's security rate while satisfying the satellite and ground user signal-to-interference-to-noise ratio constraints.

[0086] However, the above methods ignore the fairness issue of satellite-ground collaboration in resource sharing research. In fact, the satellite network and ground network in the cognitive satellite-ground network generally belong to different operators. Both networks have their own interests. If their own interests are damaged, they will refuse to cooperate with each other, resulting in the failure of resource sharing in the cognitive satellite-ground network.

[0087] In order to solve the technical problem that the resource sharing of the cognitive satellite-to-ground network fails because the satellite network and the ground network refuse to cooperate with each other due to their own interests being damaged, an embodiment of the present application proposes a resource sharing method of a cognitive satellite-to-ground network based on a two-layer game, which is applied to a processor, wherein the processor can be a processor inside a satellite or a processor capable of communicating with a satellite and each base station. This embodiment and the following embodiments do not limit this. The implementation details of the resource sharing method of a cognitive satellite-to-ground network based on a two-layer game proposed in this embodiment are specifically described below. The following content is only the implementation details provided for the convenience of understanding and is not necessary for the implementation of this solution.

[0088] The specific process of the resource sharing method of the cognitive satellite-ground network based on the double-layer game proposed in this embodiment can be as follows: Figure 1 As shown, including:

[0089] Step 101, establish a system model of a cognitive satellite-ground network in a single-satellite multi-base station scenario, wherein the system model includes a satellite as a primary transmitter and a plurality of base stations as secondary transmitters within the beam coverage of the satellite.

[0090] Specifically, the system model of the cognitive satellite-ground network in a single-satellite multi-base station scenario includes a satellite as a primary transmitter and several base stations as secondary transmitters within the satellite's beam coverage. The system model allows the base stations to be employed as collaborative interference sources for the satellite in the form of an alliance.

[0091] Step 102, establishing a channel model for a satellite communication link, and establishing a channel model for a terrestrial communication link.

[0092] Step 103, based on the satellite's time slot division factor, divide the satellite's transmission time slot into the first stage and the second stage, establish the satellite's utility function based on the first stage, the satellite communication link's channel model, and the ground communication link's channel model, establish the base station's utility function based on the second stage and the ground communication link's channel model, and establish the alliance value function of the alliance based on the base station's utility function.

[0093] Specifically, in the first stage, the satellite sends signals to the corresponding primary users, employing the highest alliance. Each base station in the highest alliance acts as a collaborative interference source to send artificial noise to the eavesdropper. In the second stage, each base station in the highest alliance sends signals to its corresponding secondary users.

[0094] Step 104, when resource sharing is required, the time slot division factor is gradually reduced with a preset step size for iteration. In each iteration, the highest alliance is determined by using the alliance value function and the alliance formation algorithm based on the merging rule and the splitting rule. Then, based on the alliance value function, the optimal power allocation vector of the highest alliance is obtained. When the highest alliance under the optimal power allocation vector satisfies the safety rate constraint of the satellite, the time slot division factor, the optimal power allocation vector and the highest alliance in this iteration are saved as candidate solutions in the candidate set.

[0095] Step 105: After the iteration process is finished, a candidate solution that can maximize the utility function of the satellite is selected from the candidate set as the optimal solution for resource sharing, and resources are shared with the optimal solution.

[0096] In this embodiment, a system model of a cognitive satellite-ground network in a single-satellite multi-base station scenario, a channel model of a satellite communication link, a channel model of a ground communication link, a satellite utility function, a base station utility function, and a coalition value function of the coalition are first established. Based on these models and functions, from the perspective of fairness of resource sharing, a double-layer game is used to gradually reduce the time slot division factor with a preset step size for iteration. In each iteration, the highest coalition is determined by using the coalition value function and the coalition formation algorithm based on the merging rule and the splitting rule. Then, based on the coalition value function, the optimal power allocation vector of the highest coalition is obtained. When the highest coalition under the optimal power allocation vector satisfies the safety rate constraint of the satellite, the time slot division factor, the optimal power allocation vector, and the highest coalition in this iteration are saved as candidate solutions in a candidate set. After the iteration, a candidate solution that can maximize the utility function of the satellite is selected from the candidate set as the optimal solution for resource sharing to perform resource sharing, thereby achieving the simultaneous improvement of the safety performance of the satellite network and the total utility of the ground network, achieving a win-win performance of the satellite network and the ground network, and ensuring that the resource sharing of the cognitive satellite-ground network can be carried out smoothly and normally.

[0097] The step division of the above methods is only for the purpose of clear description. When implemented, they can be combined into one step or some steps can be split and decomposed into multiple steps. As long as they include the same logical relationship, they are all within the scope of protection of this patent; adding insignificant modifications to the algorithm or process or introducing insignificant designs without changing the core design of the algorithm and process are all within the scope of protection of this patent.

[0098] The technical details of each step in this embodiment are described in detail below.

[0099] 1. System model.

[0100] A system model of cognitive satellite-ground network in a single-satellite multi-base station scenario can be described as follows: Figure 2 As shown in the figure, the satellite acts as a primary transmitter (PT) and communicates with the primary user (PU) when an eavesdropper eavesdrops on its signal. Due to the wide coverage of the satellite beam, there are multiple base stations within the coverage of the satellite beam. These base stations act as secondary transmitters (STs) and can be employed as collaborative interference sources to ensure satellite security communications. Here, the set of STs is represented by STs = {d i |i=1,2,…,N}, where N represents the number of base stations. In order to improve the transmission rate of the entire ground network and further improve the security rate of the satellite network, STs collaborate in the form of alliance S, where the highest alliance S * Collaborative satellite secure communications. The highest alliance here S * represents the alliance with the highest alliance value. Since too many STs will require more spectrum access time, resulting in a decrease in the safe rate of PU, it is assumed that PT allows at most one alliance to access the spectrum. In return, S * STs in the satellite spectrum obtain satellite spectrum access opportunities to achieve signal transmission to their corresponding secondary users (SUs). Assuming that PT is equipped with N a antennas, all other nodes in the network are equipped with a single antenna.

[0101] 2. Channel model.

[0102] Assume that the satellite communication link is g aξ , ξ={p,e}, using the shadow Rice channel model, the channel model of the satellite communication link can be expressed as:

[0103]

[0104] Among them, a represents the satellite, p represents the primary user corresponding to the satellite, e represents the eavesdropper, g aξ represents the channel model of the established satellite communication link, h aξ represents the satellite channel fading model, L aξ The propagation loss model of the satellite communication link, including the effects of path loss and satellite beam pattern, can be expressed as:

[0105]

[0106] Among them, C ap represents the path loss of the link from the satellite to the primary user, C ae represents the path loss of the satellite-to-eavesdropper link, represents the satellite beam pattern of the primary user, represents the satellite beam pattern of the eavesdropper, It can be expressed by the formula:

[0107]

[0108] Among them, b max represents the maximum antenna gain of the satellite, represents the angle between the beam center and the receiver ξ, represents the 3dB angle, J1(·) represents the first-order Bessel function of the first kind, and J3(·) represents the first-order Bessel function of the first kind.

[0109] In addition, the satellite channel fading model h aξ It can be expressed by the formula:

[0110] h aξ =Aexp(jψ aξ )+Zexp(jφ aξ )(1.4),

[0111] Among them, ψ aξ ∈[0,2π) represents the uniformly distributed phase of the scattered component, φ aξ ∈[0,2π) represents the uniformly distributed phase of the line-of-sight component, A represents the amplitude of the scattered component that obeys the Rayleigh distribution, and Z represents the amplitude of the line-of-sight component that obeys the Nakagami-m distribution. The shadow Rician fading distribution can be characterized by parameters (Ω, b, m), where Ω represents the average power of the line-of-sight component, 2b represents the average power of the multipath component, and m represents the Nakagami parameter.

[0112] Ground communication link ζ={d i ,e} adopts Nakagami-m channel model, and its formula is expressed as:

[0113]

[0114] Among them, s i represents the i-th base station in the system model, d i represents the secondary user corresponding to the i-th base station, represents the path loss of the link from the ith base station to the corresponding secondary user, represents the path loss of the link from the ith base station to the eavesdropper, represents the terrestrial channel fading model, represents the fading parameter, represents the average power, Represents the channel model of the established terrestrial communication link.

[0115] 3. Signal model.

[0116] In the system model, a PT will employ the highest alliance S in the transmission time slot αT it reserves for itself. * To improve the performance of secure communication, α is the time slot division factor, 0≤α≤1. As compensation, the remaining transmission time slots (1-α)T will be rented to the highest alliance S * Therefore, one transmission time slot of the satellite is divided into the first phase and the second phase.

[0117] In the first phase, αT, PT sends a signal to PU while Eve eavesdrops on PT's signal. * The STs in the PU will send ANs to Eve as cooperative interference sources to interfere with Eve. In order to eliminate the ANs received at the PU, it is assumed that the STs use distributed beamforming to send ANs in the orthogonal subspace of the channel between them and the PU, that is, Among them, |S * | indicates the highest alliance S * Therefore, the distributed beamforming scheme of STs can be expressed as w J =ψ J / ‖ψ J ‖Calculated, The superscript H indicates that the conjugate matrix is ​​taken, ‖·‖2 indicates that the L2 norm is taken, Represents the identity matrix. Based on this, the received signal of PU can be expressed as:

[0118]

[0119] in, represents the conjugate matrix of the channel parameters of the PT to PU link, represents the beamforming vector of PT, x a Indicates the signal sent by PT, P a represents the transmission power of PT, represents the noise at the PU that follows the complex Gaussian distribution, represents the variance of the noise at the PU.

[0120] Assuming that PT adopts the Maximum Ratio Transmission (MRT) beamforming scheme to reduce the computational complexity and achieve spatial diversity, the received signal of Eve is expressed as follows:

[0121]

[0122] in, represents the conjugate matrix of the channel parameters of the PT to Eve link, represents the channel parameter of the link from the ith base station in the highest alliance to Eve, represents the distributed beamforming vector weight of the ith base station in the highest alliance, z i represents the artificial noise sent by the ith base station in the highest alliance to Eve, represents the interference power of the ith base station in the highest alliance, represents the noise at Eve that obeys the complex Gaussian distribution, represents the variance of the noise at Eve.

[0123] In the second stage (1-α)T, under the premise of ensuring the safety of satellite communications, the highest alliance S * The STs in the second extreme receive a reward and perform their own transmissions, assuming that these STs use cooperative beamforming. cooperative transmission signal, then SU i (d i ) can be expressed as:

[0124]

[0125] in, represents the channel parameter of the link from the ith base station in the highest alliance to its corresponding secondary user, represents the channel parameter of the secondary user link corresponding to the j-th base station in the highest alliance to the i-th base station in the highest alliance, represents the coordinated beamforming vector weight of the ith base station in the highest alliance, The coordinated beamforming vector weight of the jth base station in the highest alliance, represents the signal sent by the i-th base station in the highest alliance, represents the signal sent by the jth base station in the highest alliance, represents the transmission power of the ith base station in the highest alliance, represents the transmission power of the jth base station in the highest alliance, represents the noise at the i-th secondary user that follows the complex Gaussian distribution.

[0126] In order to eliminate the secondary users from being subject to the highest alliance S * To avoid interference from other STs in the channel, STs can adopt a zero-forcing cooperative beamforming scheme, which can be calculated by multiplying the channel by its pseudo-inverse, that is, w C =H·(H H ·H) -1 ,here, Indicates the highest alliance S * The channels between STs and their corresponding secondary users in the channel, in particular, if |S * |=1, zero-forcing cooperative beamforming will degenerate into MRT beamforming.

[0127] Based on the above, the highest alliance S in the first phase of αT * The safety rate of PU under cooperation can be expressed as:

[0128] R p_sec (α,P J ,S * )=α·T·[R P -R E (P J ,S * )] + (1.9),

[0129] in,[·] + =max{·,0}, P J represents the interference power of the base station in the highest alliance, R p_sec (α,PJ,S * ) indicates that PU is in the highest alliance S * The safe rate under cooperation, R P represents the information rate at the PU, R E (P J ,S * ) represents the information rate at Eve, R p_sec (α,P J ,S * ) and R E (P J ,S * ) can be expressed by the formula:

[0130]

[0131] Among them, due to the uncertainty of Eve's location information, it is difficult for PT and STs to obtain Eve's accurate CSI in actual scenarios. Therefore, assuming that only the imperfect CSI of the PT to Eve and STs to Eve links can be obtained, the channel model of the imperfect communication link can be modeled as:

[0132]

[0133] The channel model representing the imperfect communication link from the satellite to the eavesdropper, represents the channel model of the imperfect communication link from the i-th base station in the highest alliance to the eavesdropper, Δh ae and represents the channel estimation uncertainty, ‖Δh ae ‖2≤ε a , ε a and is a non-negative upper bound. Substituting equation (1.11) into equation (1.10), the safe rate of PU can be rewritten as:

[0134] In addition, in the second phase, base station s i The transmission rate can be expressed as:

[0135]

[0136] in, Indicates the security rate of real master-level users under the highest alliance collaboration.

[0137] 4. Game structure.

[0138] In the cognitive satellite-ground network (system model), all network nodes, including PTs and STs, are regarded as rational and selfish independent decision-making individuals. In order to analyze the competitive and cooperative relationship between PTs and STs, this application proposes a two-layer game architecture consisting of Stackelberg game and alliance formation game. Specifically, PT, as the spectrum owner, always has the first priority, while STs try to maximize their own interests in the presence of PT. Stackelberg game provides a suitable framework to analyze the competitive interaction between PT and STs, in which PT acts as a leader and STs acts as a follower. In addition, in order to maximize the benefits of the ground network, STs will cooperate with each other to further improve the overall utility of the ground network. Therefore, the alliance formation game is integrated into the Stackelberg game to model the collaborative relationship between STs.

[0139] Under the proposed two-layer game framework, the utility function of PT is defined as the safety rate of PU under the assistance of the highest coalition cooperative interference, that is:

[0140]

[0141] It can be seen that in order to calculate this utility, PT only needs to measure the highest alliance S * The total interference power of the STs within the alliance without knowing the highest alliance S* Which STs are included?

[0142] In addition, i ∈S * The utility function of is defined as the difference between the benefits and costs, which is specifically modeled as the difference between the transmission rate of its own communication and the total transmission energy consumption cost, that is:

[0143]

[0144] in, represents the utility function of the ith base station in the highest alliance, represents the transmission rate of the secondary user corresponding to the i-th base station in the highest alliance, represents the transmission power of the ith base station in the highest alliance, represents the interference power of the ith base station in the highest alliance, C1 represents the unit interference energy cost of the base station, and C2 represents the unit transmission energy cost of the base station. The first half of formula (1.14) is the transmission rate of the base station, reflecting its satisfaction with the access to the satellite spectrum, while the second half reflects the energy consumption cost paid by the base station to obtain this satisfaction.

[0145] In summary, for the proposed two-layer game model, PT first adjusts the time slot division factor α to maximize its own utility, and under a given α, STs optimize the alliance structure S and power allocation method (P T ,P J ),in, represents the transmission power vector. Therefore, the proposed two-layer game model contains three optimization problems, namely, the optimization problem of time slot partitioning factor, the optimization problem of alliance formation and the optimization problem of power allocation. The relationship between these three optimization problems can be shown as follows: Figure 3 As shown, from Figure 3 It can be seen that the optimization problem of alliance formation and the optimization problem of power allocation are interrelated with the optimization problem of time slot partitioning factors.

[0146] 5. Optimization problem modeling.

[0147] like Figure 3 As shown in Figure 1, by observing the time slot division factor of the PT, STs determine their own response strategy, namely the alliance structure and power allocation method. Therefore, the modeling of STs alliance formation and power allocation is first given below. Then, the modeling of the PT time slot division problem is given.

[0148] 5.1. The problem of alliance formation among STs.

[0149] The collaboration among STs is modeled as a coalition game, where STs act as a group of game participants who seek the best partners to form a collaborative group. Specifically, STs within a coalition work together to achieve their own transmissions, while sending ANs together to ensure satellite secure communications. Therefore, the benefit (utility function) of the coalition S is defined as the sum of the utilities brought by its internal STs, that is:

[0150]

[0151] in, Denotes the utility function of alliance S.

[0152] In order to form an alliance, STs need to exchange each other's data and channel information. For this reason, this application uses the transmission power of information exchange as the cost of alliance formation. Due to the broadcast characteristics of the wireless channel, if the information broadcast by any ST in the alliance S can be received by the ST farthest from it in S, it can be received by any ST in S. Therefore, the cost of forming an alliance S is considered to be the sum of the power required for each ST in S to broadcast information to the ST farthest from it in S, that is:

[0153]

[0154] in, It represents the power required by the i-th base station in the alliance to send information to the base station farthest from it. The power is calculated as: Among them, Λ0 is the minimum signal-to-noise ratio required for potential alliance members to interact with each other. is the variance of the noise at the base station farthest from the i-th base station in the alliance.

[0155] Therefore, based on the benefits and power costs defined above, the alliance value of alliance S can be modeled as:

[0156]

[0157] in, Indicates the preset maximum tolerable power cost.

[0158] 5.2. Power allocation problem of STs.

[0159] In the proposed two-layer game framework, STs as followers optimize their power allocation method according to the time slot division factor determined by PT. For a given time slot division factor and alliance structure, STs in the alliance will find the optimal power allocation method to maximize their own utility.

[0160] Since STs adopt zero-forcing cooperative beamforming, s i The optimal power allocation strategies of are independent of each other, so λ i The power allocation problem can be modeled as:

[0161]

[0162]

[0163]

[0164] in, Represents λ i The maximum energy, Represents λ i Assuming that the selfish s i All energy will be used to increase its transmission rate, then the constraint (1.18b) can be rewritten as The constraint (1.18c) indicates that neither the cooperative interference nor the transmission power should exceed

[0165] 5.3. PT time slot division problem.

[0166] As the leader, PT will determine the optimal time slot division factor to maximize its own safety rate. Therefore, the time slot division problem of PT can be modeled as:

[0167]

[0168] St 0≤α≤1 (1.19b)

[0169]

[0170] Among them, constraint formula (1.19c) means that the PU safety rate under the cooperation of alliance S should not be worse than the safety rate without cooperation, that is, because so[·] + can be ignored, so It can be shortened to:

[0171] 6. Solve the two-layer game.

[0172] 6.1. Game solution for alliance formation.

[0173] In the process of alliance formation, not only are there opportunities for collaboration between STs, but since PT only selects one alliance, there is also a competitive relationship between STs. In order to maximize the sum utility of STs, it is assumed that PT will select the alliance with the highest alliance value, that is, the highest alliance. If the game participant is not in the highest alliance, he will get nothing when the alliance formation process ends. Therefore, under the premise of ensuring that the utility of each participant is non-negative, if two non-intersecting alliances can form an alliance with a higher alliance value, the two alliances are more inclined to cooperate with each other. In this way, the game participants within it will have a greater chance of winning spectrum access opportunities. Based on the above considerations, this application defines a new preference relationship for the proposed alliance formation game, which can be recorded as Max-Coalition order.

[0174] Given two partitions and If there are the same game participants inside, the definition of Max-Coalition order is as follows:

[0175]

[0176] Among them, max{·} represents the maximum value of the orientation amount, express s within i The utility function of

[0177] Using the alliance formation concept defined above, this application further proposes a distributed alliance formation algorithm based on merging rules and splitting rules. The principle of the algorithm is as follows: Figure 4 As shown, the following adjustments are allowed division.

[0178] Merger rule: If compared to the alliance {S1,S2,…,S l}, the game participants prefer the merged alliance, so these alliances are merged, that is, when When

[0179] The rules of division, compared to alliance The game participants prefer the split alliances, so they split these alliances. When

[0180] The following is an introduction to the coalition formation algorithm based on the merging rule and splitting rule. The algorithm can be divided into two stages: the initialization stage and the adaptive coalition formation stage. In the initialization stage, each ST is regarded as an independent and disjoint coalition, that is, Among them, S i ={si}, i = 1, 2, ..., N, in this partition, any alliance can start the merging process. Assume that the initial partition The highest league in Start the merging process and try to collaborate with the next highest coalition. If according to Max-Coalition order, the new coalition is preferred, then all members will enter into a merger agreement to form the new alliance, if If it is unable to merge with the second highest alliance, it will continue to try to merge with the third highest alliance, and then try to merge with all other alliances in turn. This search process will end with the final merged alliance, which is composed of and several other alliances (when no merger occurs, only The above merging process will be repeated in the remaining alliances until all alliances make a merger decision, resulting in the final division.

[0181] Similar to the merging process, for each coalition, if its internal coalition members can find a more preferred coalition after splitting according to the Max-Coalition order, the coalition splits. The continuous merging and splitting operations are iterated until termination. Assuming that the time slot partitioning factor α is given, the detailed coalition formation algorithm is shown in Algorithm 1.

[0182] Algorithm 1: Coalition formation algorithm based on merging rules and splitting rules.

[0183] Phase 1: Initialization.

[0184] The set of STs is divided into non-cooperative coalitions, i.e., the initial division

[0185] Phase 2: Adaptive alliance formation.

[0186] A coalition is formed based on the merging rule and the splitting rule, and the time index is set to: τ = 0.

[0187] Repeat:

[0188] 1) Alliances within a group make merger decisions based on merger rules.

[0189] 2) Alliances within a group make split decisions based on split rules.

[0190] 3) Update time index: τ=τ+1.

[0191] Until:

[0192] Merge and split operations to final partition termination.

[0193] 6.2. Solution of the optimal power allocation of Stackelberg game.

[0194] Assume that the highest alliance S is given * , and S * The time slot division factor α of the internal STs is known. Based on the reverse induction method, we first determine s by solving the optimization problem (1.18). i The optimal power allocation solution.

[0195] Since the Hessian matrix of the objective function in equation (1.18) is semi-negative definite, its is concave. In addition, the constraints in (1.18) are affine functions, so the feasible set is convex. In addition, the KKT condition is sufficient and necessary for the optimality of (1.18). Therefore, the Lagrangian function of (1.18) can be expressed as

[0196]

[0197] Where μ represents the Lagrange multiplier, λ=(λ1,λ2,λ3,λ4) T is a non-negative Lagrange multiplier vector.

[0198] At the optimal solution, we have:

[0199]

[0200] in,

[0201] From formula (1.22), we can deduce:

[0202]

[0203] Among them, max{β 1 ,β 2} means finding the variable β that can maximize the optimization problem (1.18).

[0204] Among them, if Then ΔC=C2-C1, otherwise, Similarly, if but otherwise,

[0205] Considering that the base station is a rational individual, the necessary condition for its willingness to cooperate with the PT is Therefore, substituting equation (1.23) into equation (1.18), we can obtain that only when α satisfies equation (1.24) can it be guaranteed that Right now:

[0206]

[0207] Among them,

[0208] 6.3. Solving the optimal time slot partitioning factors for the Stackelberg game.

[0209] After the optimal power allocation method of STs is known, the PT as the leader determines the optimal time slot division factor α * , to maximize its utility under the constraint of satisfying equation (1.19). Assume that there exists an α that satisfies the constraint in equation (1.19), Under the constraints of Substituting into equation (1.19), the optimization problem equation (1.19) can be remodeled as:

[0210]

[0211]

[0212]

[0213] The proof of the convexity of the objective function in equation (1.25a) is given below. Specifically, about The second-order derivative of can be derived as:

[0214]

[0215] in, and therefore, yes Convex function. In addition, considering that the constraints (1.25b) and (1.2, 5c) are affine functions, the problem (1.25) is a standard convex optimization problem. Therefore, it can be solved by the KKT condition. The Lagrangian function of formula (1.25) can be expressed as:

[0216]

[0217] in, is a non-negative Lagrange multiplier vector. The KKT condition of formula (1.27) can be written as:

[0218]

[0219] in, From formula (1.28), we can deduce:

[0220]

[0221] in, And α 2 It can be solved by numerical methods such as two-dimensional search Here, α * =1 means if PT is in the highest alliance S * If the PT cannot improve its safety rate under the cooperation of other players, the PT will refuse to cooperate.

[0222] Finally, we proposed a distributed two-layer game algorithm to achieve a stable alliance structure and Stackelberg equilibrium solution (SE solution), that is, the optimal power allocation vector of STs and the optimal time slot division factor of PT. The specific algorithm is shown in Algorithm 2. The core idea is that PT iteratively gradually reduces the time slot division factor, and in each iteration the highest alliance is determined by Algorithm 1, and then the optimal power allocation vector of STs in the highest alliance is obtained by formula (1.23). On this basis, PT will further confirm whether the highest alliance under the determined optimal power allocation vector meets its safety rate constraint. If satisfied, the time slot division factor, power allocation vector and highest alliance structure are saved to the candidate set At the end of the iteration, PT finally selects Determine the optimal solution that maximizes its own utility, that is:

[0223]

[0224] At this point, the optimal solution for resource sharing has been obtained, and the satellite and each base station in the highest alliance will share resources based on this optimal solution as a parameter.

[0225] Algorithm 2: Distributed algorithm for two-layer game.

[0226] definition:

[0227] At the tth iteration, let α(t) represent the time slot division factor, S * (t) indicates the highest alliance, Indicates S * (t) The optimal power allocation of STs within, Save PT and S * (t)α(t) when establishing collaboration, Save PT and S * (t)S when establishing collaboration * (t), Save PT and S * (t) When establishing collaboration

[0228] Initialization phase:

[0229] Let α(0)=1 and θ>0 be a small positive constant.

[0230] set up and

[0231] set up and

[0232] Assume time index: t=1.

[0233] Two-layer game stage:

[0234] 1) In the tth iteration, PT updates α(t) = (1-θ)α(t-1) and broadcasts α(t).

[0235] 2) After receiving α(t), each s i ∈S * (t) Make alliance formation decisions and determine the highest alliance S through Algorithm 1 * (t).

[0236] 3) If S * (t) = φ, set t = t + 1 and return to step 1).

[0237] 4) If S * (t)≠φ, each s i ∈S * (t) Determine the optimal power allocation through equation (1.23), if Update and Let t=t+1 and return to step 1).

[0238] Iteration termination:

[0239] The algorithm terminates when α(t) = 0, and the optimal solution Available via (1.30).

[0240] The proposed distributed two-level game algorithm can always converge to the SE solution of the Stackelberg game and the SE solution of the coalition formation game. -stable point, and the simulation results verify that the proposed two-layer game method can simultaneously improve the utility of satellite and ground networks. In order to verify the effectiveness of the proposed two-layer game algorithm, the main-level utility, alliance utility and number of STs in the alliance of the proposed two-layer game algorithm and the "minimum distance alliance and SE game strategy" algorithm are compared under different fading. Specifically, in the "minimum distance alliance and SE game strategy" comparison algorithm, STs form an alliance with the STs closest to themselves under the power cost constraint in formula (1.17), and under this alliance structure, STs and PTs adopt the SE game strategy.

[0241] The simulation results show that under mild and moderate shadow fading, When is smaller, the primary utility under the comparison algorithm is better than the two-layer game algorithm, but at this time, the alliance utility under the two-layer game algorithm is better than the comparison algorithm. Increase, the main-level utility under the two-layer game algorithm will be better than the comparison algorithm. Under severe shadow fading, both the main-level utility and the alliance utility under the two-layer game algorithm are better than the comparison algorithm, which verifies the effectiveness of the proposed algorithm.

[0242] Another embodiment of the present application relates to a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it can implement a resource sharing method of a cognitive satellite-ground network based on a double-layer game as described in the above method embodiment.

[0243] That is, those skilled in the art can understand that all or part of the steps in the above-mentioned embodiment method can be completed by instructing the relevant hardware through a program, and the program is stored in a storage medium, including a number of instructions to enable a device (which can be a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, referred to as: ROM), random access memory (Random Access Memory, referred to as: RAM), disk or optical disk and other media that can store program codes.

[0244] Those skilled in the art will appreciate that the above embodiments are specific embodiments for implementing the present application, and in actual applications, various changes may be made thereto in form and detail without departing from the spirit and scope of the present application.

Claims

1. A resource sharing method for a cognitive satellite-ground network based on a double-layer game, characterized in that: include: Establish a system model of a cognitive satellite-to-ground network in a single-satellite multi-base station scenario; wherein the system model includes a satellite as a primary transmitter and a number of base stations as secondary transmitters within the beam coverage of the satellite, and the system model allows the base stations to be employed as cooperative interference sources for the satellite in the form of an alliance; Establish a channel model for satellite communication links and establish a channel model for ground communication links; Based on the satellite's time slot division factor, the satellite's transmission time slot is divided into a first stage and a second stage, a satellite utility function is established based on the first stage and the channel model of the satellite communication link, a base station utility function is established based on the second stage and the channel model of the ground communication link, and an alliance value function of the alliance is established based on the base station utility function; wherein, in the first stage, the satellite sends a signal to a primary user, employs a highest alliance, and each base station in the highest alliance acts as a collaborative interference source to send artificial noise to the eavesdropper, and in the second stage, each base station in the highest alliance sends a signal to its corresponding secondary user; When resource sharing is required, the satellite gradually reduces the time slot division factor with a preset step size for iteration. In each iteration, the highest alliance is determined by using the alliance value function and the alliance formation algorithm based on the merging rule and the splitting rule. Then, based on the alliance value function, the optimal power allocation vector of the highest alliance is obtained. When the highest alliance under the optimal power allocation vector satisfies the safety rate constraint of the satellite, the time slot division factor, the optimal power allocation vector and the highest alliance in this iteration are saved as candidate solutions in the candidate set. After the iteration process is finished, a candidate solution that can maximize the utility function of the satellite is selected from the candidate set as the optimal solution for resource sharing, and resources are shared with the optimal solution; The channel model for establishing the satellite communication link is implemented by the following formula: h aξ =Aexp(jψ aξ )+Zexp(jφ aξ ) ξ={p,e} Among them, a represents the satellite, p represents the primary user corresponding to the satellite, e represents the eavesdropper, and L aξ represents the propagation loss model of the satellite communication link, h aξ represents the satellite channel fading model, C ap represents the path loss of the link from the satellite to the primary user, represents the satellite beam pattern of the primary user, C ae represents the path loss of the satellite-to-eavesdropper link, represents the satellite beam pattern of the eavesdropper, ψ aξ represents the uniformly distributed phase of the scattered component, φ aξ represents the uniformly distributed phase of the line-of-sight component, A represents the amplitude of the scattered component that obeys the Rayleigh distribution, Z represents the amplitude of the line-of-sight component that obeys the Nakagami-m distribution, and g aξ A channel model representing an established satellite communication link; The channel model of the ground communication link adopts the Nakagami-m channel model, and its formula is expressed as follows: ζ={d i ,e} Among them, s i represents the i-th base station in the system model, d i represents the secondary user corresponding to the i-th base station, represents the path loss of the link from the i-th base station to the corresponding secondary user, represents the path loss of the link from the i-th base station to the eavesdropper, represents the terrestrial channel fading model, represents the fading parameter, represents the average power, Represents the channel model of the established terrestrial communication link.

2. According to claim 1, a resource sharing method of a cognitive satellite-ground network based on a double-layer game is characterized in that: The utility function of the satellite is established based on the channel model of the first stage and the satellite communication link, and is implemented by the following formula: Where α represents the time slot division factor, T represents the satellite transmission time slot, S * represents the highest alliance, P J represents the interference power of the base stations in the highest alliance, represents the security rate of the primary user under the highest alliance collaboration, R P represents the information rate at the primary user, represents the information rate at the eavesdropper, [·] + =max{·,0},P a represents the satellite's transmission power, The conjugate transpose of the channel model for the satellite-to-primary user communication link, w a represents the satellite’s beamforming vector, represents the variance of the noise at the primary user, The conjugate transpose of the channel model representing the imperfect communication link from the satellite to the eavesdropper, represents the interference power of the ith base station in the highest alliance, represents the channel model of the imperfect communication link from the ith base station in the highest alliance to the eavesdropper, represents the distributed beamforming vector weight of the ith base station in the highest alliance, represents the variance of the noise at the eavesdropper, |S * | represents the total number of base stations in the highest alliance; The utility function of the base station is established based on the second stage and the channel model of the ground communication link, which is implemented by the following formula: in, represents the utility function of the ith base station in the highest alliance, represents the transmission rate of the secondary user corresponding to the i-th base station in the highest alliance, represents the transmission power of the ith base station in the highest alliance, represents the interference power of the ith base station in the highest alliance, C1 represents the unit interference energy consumption cost of the base station, C2 represents the unit transmission energy consumption cost of the base station, represents the channel model of the terrestrial communication link from the i-th base station in the highest alliance to the corresponding secondary user, represents the coordinated beamforming vector weight of the ith base station in the highest alliance, represents the variance of the noise at the secondary user.

3. A resource sharing method for a cognitive satellite-ground network based on a double-layer game according to claim 2, characterized in that: When resource sharing is required, a two-layer game model of Stackelberg and highest alliance formation is established based on the system model, the utility function of the satellite, the alliance value function, and the alliance formation algorithm based on merging rules and splitting rules; wherein the two-layer game model includes three optimization problems, namely, the optimization problem of time slot division factor, the optimization problem of alliance formation and the optimization problem of power allocation.

4. A resource sharing method for a cognitive satellite-ground network based on a double-layer game according to claim 3, characterized in that: For the optimization problem of alliance formation, the sum of the power required for each base station in the alliance to broadcast information to the base station farthest from itself in the alliance is taken as the cost of forming the alliance. The cost of forming the alliance is expressed by the formula: in, represents the power required by the i-th base station in the alliance to send information to the base station farthest from it, represents the cost of forming the alliance, Λ0 is the minimum signal-to-noise ratio required for information exchange among potential alliance members, represents the variance of the noise at the base station farthest from the i-th base station in the alliance, represents the distance between the ith base station and the base station farthest from the ith base station in the alliance; The alliance value function of the alliance is modeled as: in, represents the income of alliance S, represents the preset maximum tolerable power cost, v(S) represents the alliance value function of alliance S; The power allocation of base stations in the alliance is modeled as: in, represents the utility function of the ith base station in alliance S, represents the transmission power of the i-th base station in alliance S, represents the interference power of the i-th base station in alliance S, represents the maximum energy of the i-th base station in alliance S, represents the maximum power of the i-th base station in alliance S; The satellite time slot allocation problem is modeled as: Among them, U a (α, P J |S) represents the utility function of the satellite under the collaboration of alliance S, It indicates the security rate of the primary user under the collaboration of alliance S. Indicates the safe rate of primary users without coordination.

5. A resource sharing method for a cognitive satellite-ground network based on a double-layer game according to claim 4, characterized in that: The method of using the alliance value function and the alliance formation algorithm based on the merging rule and the splitting rule to determine the highest alliance includes: For the given two partitions and Representing different coalitions with the same game participants, the Max-Coalition order is defined as follows: Among them, max{·} represents the maximum value of the orientation amount, express s within i The utility function of Indicates belonging to a normal subgroup; The merge rule is defined as follows: if compared to the alliance {S1, S2, ..., S l }, the game participants prefer the merged alliance, so these alliances are merged, that is, when hour, Define the split rule as: if compared to the alliance The game participants prefer the split alliances, so they split these alliances. hour, Dividing the base stations in the system model into a number of non-cooperative alliances, that is, each base station forms a separate alliance, to obtain an initial division; According to the alliance value function, an initial highest alliance is determined in the initial division, and an attempt is made to merge the initial highest alliance with the initial second highest alliance. Based on the Max-Coalition order, if the game participants prefer the merged alliance, the initial highest alliance is merged with the initial second highest alliance. Otherwise, an attempt is made to merge the initial highest alliance with the initial third highest alliance until all alliances in the initial division make a merger decision and there is no more alliance that can be merged, and then a final merged alliance is obtained; Traverse each base station in the final merged alliance and split each base station in the final merged alliance. Based on the Max-Coalition order, if the game participants prefer the alliance obtained after the current base station is split from the final merged alliance, the current base station will be split from the final merged alliance. Otherwise, the current base station will be retained until the final merged alliance makes a split decision for each base station in the final merged alliance. When there are no base stations that can be split further, the highest alliance is obtained.

6. A resource sharing method for a cognitive satellite-ground network based on a double-layer game according to claim 5, characterized in that: The step of obtaining the optimal power allocation vector of the highest alliance includes: A Lagrangian function for modeling power allocation of base stations in the alliance is established. The Lagrangian function for modeling power allocation of base stations in the alliance is expressed by a formula: Where μ represents the Lagrange multiplier, λ = (λ1, λ2, λ3, λ4) T is a non-negative Lagrange multiplier vector; The optimal power allocation vector satisfy: in, 7. A resource sharing method for a cognitive satellite-ground network based on a double-layer game according to claim 6, characterized in that: After each base station in the highest alliance determines the optimal power allocation vector, the satellite determines the optimal time slot division factor. The satellite time slot division problem is remodeled as: in, represents the maximum value of the time slot division factor under the optimal power allocation vector, represents the optimal power allocation of the transmit power; A remodeled Lagrangian function of the satellite time slot division is established, and the remodeled Lagrangian function of the satellite time slot division is expressed by the formula: in, represents the non-negative Lagrange multiplier vector; The optimal time slot division factor α * satisfy: in, and w p represents the beamforming vector of the primary user; The optimal time slot division factor α * It is expressed by the formula: in, α 2 Numerical solution via two-dimensional search get.

8. The resource sharing method of a cognitive satellite-ground network based on a double-layer game according to claim 7 is characterized in that: The candidate solution that can maximize the utility function of the satellite is selected from the candidate set as the optimal solution for resource sharing, which is implemented by the following formula: in, represents the candidate set, Indicates the optimal solution determined.

9. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, a resource sharing method for a cognitive satellite-ground network based on a double-layer game as described in any one of claims 1 to 8 is implemented.

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