Frequency spectrum access-oriented Bayesian Stackelberg game relay joint anti-interference and anti-eavesdropping method

Abstract

The invention relates to the technical field of electronic battlefield wireless communication confrontation, and particularly discloses a Bayesian Stackelberg game relay joint anti-interference and anti-eavesdropping method for spectrum access, comprising: constructing a communication confrontation scene comprising a relay party and a full duplex attacker, the relay party at least comprising a source node, a relay node and a destination node; the method comprises the following steps: constructing a Steinberg game model by taking a relay party as a leader and a full duplex attacker as a follower based on a communication confrontation scene, and defining a utility function of the two parties under the condition of incomplete information based on a Bayesian theory; and carrying out iterative solution by adopting a dobby machine algorithm on the basis of the utility function until the Bayesian equilibrium of the Steinberg game is converged, and determining an optimal transmitting power strategy of the relay node according to the Bayesian equilibrium so as to realize joint anti-interference and anti-eavesdropping under the interference and eavesdropping attack of the full-duplex attacker.

Description

Technical Field

[0001] This invention relates to the field of electronic battlefield wireless communication countermeasures technology, specifically to a Bayesian Steinberg game relay joint anti-interference and anti-eavesdropping method for spectrum access. Background Technology

[0002] Traditional relay anti-jamming technologies primarily focus on detecting and avoiding interfering signals, ensuring link connectivity through power control, spectrum shifting, and beamforming. For example, Chinese patent application CN109982338A proposes a cognitive relay network anti-jamming power control method based on Steinberg game theory. This method treats the source node and relay node as alliance leaders and malicious jammers as followers, using an iterative algorithm to solve for the Steinberg equilibrium, thus improving energy efficiency under primary user interference constraints. However, this type of method only addresses single-interference attack scenarios, failing to consider the dual threat of attackers simultaneously possessing eavesdropping capabilities. Furthermore, it assumes that both sides in the game possess complete channel state information, making it difficult to adapt to the asymmetric information warfare requirements in complex electromagnetic environments.

[0003] On the other hand, relay physical layer security technologies are dedicated to preventing eavesdropping attacks, improving the confidentiality capacity of legitimate channels through methods such as cooperative jamming, beamforming, and artificial noise. The non-patent literature "Bayesian Stackelberg Game for Anti-Jamming Transmission in Relay Networks" (IEEE ICC, 2020) first introduced Bayesian Stackelberg game theory into the relay anti-jamming problem, considering the privacy of jammer types and improving the adaptability of relay nodes to unknown interference. However, this work still limits the attacker's function to jamming, does not model synchronous eavesdropping behavior, and does not include security indicators such as confidentiality rate in the utility function, making it difficult to cope with the dual threats of "dynamic interference suppression" and "enhanced covert eavesdropping" posed by full-duplex attack devices.

[0004] Notably, attack devices based on full-duplex communication mechanisms overcome the timing limitations of traditional half-duplex attacks through self-interference cancellation technology, enabling them to simultaneously execute jamming and eavesdropping attacks. On one hand, full-duplex attackers reduce the received signal-to-interference-plus-noise ratio (SNR) of the target node by emitting jamming signals, causing communication interruptions or a surge in the bit error rate. On the other hand, they utilize full-duplex capability to eavesdrop on signals relayed by relay nodes in the same frequency band, intercepting sensitive information undetected. This concurrent "jamming + eavesdropping" attack mode poses a severe challenge to the reliability and security of relay communication systems, and existing research has not yet formed an effective joint defense theoretical framework.

[0005] Furthermore, existing game-theoretic anti-jamming methods typically assume that both players possess complete information, meaning they have precise knowledge of channel states, policy spaces, and utility functions. However, in real-world battlefield environments or non-cooperative spectrum access scenarios, relays struggle to accurately determine the interference channel gain from the attacker to the target node, and attackers also find it difficult to accurately perceive the eavesdropping channel gain from themselves to the relay node. This incompleteness and asymmetry of information leads to problems such as inaccurate modeling and convergence difficulties in traditional Steinberg game equilibrium solutions.

[0006] In summary, how to establish a joint anti-interference and anti-eavesdropping decision framework for relay communication systems under conditions of incomplete information, in response to the dual threat scenarios of simultaneous interference and eavesdropping by full-duplex attackers, and to achieve dynamic optimization allocation of limited power resources between reliable and secure transmission, has become an urgent technical challenge to be solved in this field. Summary of the Invention

[0007] To achieve the objectives of this invention, this application provides a joint anti-interference and anti-eavesdropping method for Bayesian Steinberg game relays oriented towards spectrum access, comprising: Step S1: Construct a communication adversarial scenario involving a relay party and a full-duplex attacker, wherein the relay party includes at least a source node, a relay node, and a destination node; Step S2: Based on the communication confrontation scenario, the relay party is designated as the leader and the full-duplex attacker as the follower. A Steinberg game model is constructed, and the utility functions of both parties are defined under the condition of incomplete information based on Bayesian theory. Step S3: Based on the utility function, the multi-armed slot machine algorithm is used for iterative solution until it converges to the Bayesian equilibrium of the Steinberg game. The optimal transmission power strategy of the relay node is determined according to the Bayesian equilibrium to achieve joint anti-interference and anti-eavesdropping under the interference and eavesdropping attacks of the full-duplex attacker.

[0008] In some specific embodiments, in step S1, the relay node is used to forward the information of the source node to the destination node; the full-duplex attacker is used to interfere with the link from the relay node to the destination node and simultaneously eavesdrop on the relay node.

[0009] In some specific embodiments, the relay node selects a transmit power from a predetermined set of discrete transmit powers, and the full-duplex attacker selects a jamming power from a predetermined set of discrete jamming powers.

[0010] In some specific embodiments, step S1 further includes: defining the signal-to-noise ratio (SNR) of the signal received by the relay node in the first transmission phase, and the first signal-to-interference-plus-noise ratio (SNR) of the signal received by the destination node and the second SNR of the full-duplex attacker eavesdropping signal in the second transmission phase.

[0011] In some specific embodiments, in step S2, the information incompleteness condition characterized by Bayesian theory includes: The relay party has incomplete knowledge of the interference channel state caused by the full-duplex attacker. The full-duplex attacker has incomplete knowledge of the state of his own eavesdropping channel.

[0012] In some specific embodiments, the utility function of the relay is positively correlated with the first signal-to-interference-plus-noise ratio (SINNR), and the utility function of the full-duplex attacker is positively correlated with the second SINNR and negatively correlated with the first SINNR.

[0013] In some specific embodiments, the optimization objective of the utility functions of both parties is defined as: maximizing their respective expected utilities under the condition of incomplete information.

[0014] In some specific embodiments, step S3 includes: Step S31: The relay party and the full-duplex attacker each maintain historical profit statistics for their respective optional strategies; Step S32: In each iteration, both parties select the strategy for the current round based on the upper bound criterion of the confidence interval and historical statistical data. Step S33: Update the historical return statistics based on the strategy execution results and proceed to the next iteration.

[0015] In some specific embodiments, the upper bound criterion for the confidence interval is: to calculate an upper bound value for each optional strategy, wherein the upper bound value is the sum of the historical average return of each optional strategy and the exploration reward, and to select the strategy with the highest upper bound value.

[0016] In some specific embodiments, the relay node and the full-duplex attacker update their strategies for the next period according to the following formula: in, Indicates that the relay node is in The total number of times a certain transmission power is selected within a certain period. Indicates when this strategy is selected Statistical average return over a period of time This indicates that a full-duplex attacker is... The total number of times a certain interference power is selected within a certain period. Indicates when this strategy is selected The statistical average return over a period of time.

[0017] The beneficial effects of the above technical solution are as follows: Compared with the prior art, the present invention has the following beneficial effects: (i) For the first time, joint decision-making for anti-interference and anti-eavesdropping in relay scenarios was achieved. Existing relay anti-attack methods typically treat interference suppression and eavesdropping prevention as two separate problems, or focus only on a single attack form, making it difficult to cope with the dual threat of full-duplex attackers simultaneously implementing "dynamic interference suppression" and "covert eavesdropping enhancement." This invention constructs a unified utility function encompassing both interference and eavesdropping links, simultaneously applying the relay node's transmit power selection to both the destination node's received signal-to-interference-plus-noise ratio (SNR) and the attacker's eavesdropping SNR. For the first time, it achieves joint decision optimization for anti-interference and anti-eavesdropping within the same game theory framework. Compared to traditional methods, this invention, without increasing additional hardware overhead, synergistically enhances the reliability and confidentiality of legitimate links, effectively suppressing concurrent threats from full-duplex attackers.

[0018] (ii) Adapting to incomplete information warfare scenarios in complex electromagnetic environments Traditional Steinberg game-based anti-jamming methods generally assume that both sides possess complete channel state information. However, in real-world scenarios such as battlefield communications, emergency networking, and non-cooperative spectrum access, relays struggle to accurately determine the interference channel gain from the attacker to the target node, and attackers also struggle to accurately perceive the eavesdropping channel gain from themselves to the relay node. This invention introduces Bayesian theory to probabilistically model this incomplete information, treating the interference channel state and the eavesdropping channel state as random variables with prior distributions, making the game model closer to real-world adversarial environments. Based on this, relays and attackers can complete strategy interactions with only the other party's channel statistical characteristics rather than instantaneous precise values, significantly improving the engineering applicability and robustness of this invention under non-ideal channel awareness conditions.

[0019] (III) Achieving Fast Adaptive Convergence through Equilibrium Solving Based on Multi-Armed Slot Machine Algorithm To address the challenges of high computational complexity, strong reliance on prior information, and poor adaptability to dynamic environments in Bayesian Steinberg game equilibrium solutions, this invention, for the first time, introduces a multi-armed slot machine algorithm into the decision-making process of relay anti-interference and anti-eavesdropping games. Through dynamic equilibrium strategy "exploration" and "exploitation" using the upper bound criterion of confidence intervals, relay nodes and full-duplex attackers do not need prior knowledge of each other's utility functions and complete channel distribution; they can learn the optimal strategy online solely based on local historical interaction payoff statistics. Simulation results show that the strategy selection ratio of both parties tends to stabilize after approximately 150 iterations, and the growth rate of the relay node's regret value significantly slows down, demonstrating the outstanding advantages of this invention in convergence speed and online learning capability.

[0020] (iv) Enhance the survivability and spectrum access guarantee capability of relay communication systems in harsh electromagnetic environments. This invention transforms complex network security issues into a sequential game optimization problem involving both parties, enabling dynamic optimization of limited power resources in adversarial environments. Relay nodes can adaptively adjust their forwarding power based on real-time interactive feedback, minimizing attackers' eavesdropping gains while ensuring their own communication quality. This mechanism effectively enhances the adaptability and resilience of relay communication systems in harsh electromagnetic environments with strong interference and high eavesdropping risks, providing reliable assurance for secure spectrum access for subsequent service nodes. It can be widely applied in key areas such as military tactical communications, emergency field networking, and anti-jamming transmission for the Internet of Things.

[0021] (v) The method is highly versatile and easy to deploy in engineering projects. The method proposed in this invention relies solely on the discrete power sets selectable by the relay node and the attacker, as well as their respective observable local revenue signals. It requires no additional hardware, no modification to existing relay communication protocol stacks, and no reliance on dedicated sensing hardware. The algorithm is implemented based on the upper bound criterion of confidence intervals, exhibiting low computational complexity, fast convergence speed, and good scalability and plug-and-play characteristics. It can be easily integrated into existing relay node devices and spectrum management systems, demonstrating significant engineering application value. Attached Figure Description

[0022] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0023] Figure 1 A flowchart illustrating a method for joint anti-interference and anti-eavesdropping of Bayesian Steinberg game relays for spectrum access, provided as an embodiment of the present invention; Figure 2 This is a schematic diagram of a power game confrontation scenario between the relay and the full-duplex attacker designed in this invention; Figure 3 This is a schematic diagram of the Steinberg game model proposed in this invention; Figure 4 This is a flowchart of the multi-armed slot machine algorithm upon which this invention is based; Figure 5 , Figure 6 This is a graph showing the ratio of transmission power to interference power selection between relay nodes and full-duplex attackers; Figure 7 This is a schematic diagram showing how the regret value of a relay node changes with the number of iterations. Detailed Implementation

[0024] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0025] Examples of the embodiments are shown in the accompanying drawings, wherein the same or similar symbols denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the invention, and should not be construed as limiting the invention.

[0026] Example 1 One embodiment of the present invention provides a joint anti-interference and anti-eavesdropping method for Bayesian Steinberg game relays oriented towards spectrum access, referring to... Figure 1 As shown, it includes: Step S1: Construct a communication adversarial scenario involving a relay party and a full-duplex attacker, wherein the relay party includes at least a source node, a relay node, and a destination node; In a specific embodiment of the present invention, in step S1, the relay node is used to forward the information of the source node to the destination node; the full-duplex attacker is used to interfere with the link from the relay node to the destination node and simultaneously eavesdrop on the relay node.

[0027] In one specific embodiment of the present invention, the relay node selects a transmission power from a predetermined set of discrete transmission powers, and the full-duplex attacker selects an interference power from a predetermined set of discrete interference powers.

[0028] In a specific embodiment of the present invention, step S1 further includes: defining the signal-to-noise ratio (SNR) of the signal received by the relay node in the first transmission phase, and the first signal-to-interference-plus-noise ratio (SNR) of the signal received by the destination node and the second SNR of the full-duplex attacker eavesdropping signal in the second transmission phase.

[0029] Step S2: Based on the communication confrontation scenario, the relay party is designated as the leader and the full-duplex attacker as the follower. A Steinberg game model is constructed, and the utility functions of both parties are defined under the condition of incomplete information based on Bayesian theory. In a specific embodiment of the present invention, step S2, the information incompleteness condition characterized by Bayesian theory includes: The relay party has incomplete knowledge of the interference channel state caused by the full-duplex attacker. The full-duplex attacker has incomplete knowledge of the state of his own eavesdropping channel.

[0030] In one specific embodiment of the present invention, the utility function of the relay is positively correlated with the first signal-to-interference-plus-noise ratio (SINNR), and the utility function of the full-duplex attacker is positively correlated with the second SINNR and negatively correlated with the first SINNR.

[0031] In one specific embodiment of the present invention, the optimization objective of the utility functions of both parties is defined as: maximizing their respective expected utilities under the condition of incomplete information.

[0032] Step S3: Based on the utility function, the multi-armed slot machine algorithm is used for iterative solution until it converges to the Bayesian equilibrium of the Steinberg game. The optimal transmission power strategy of the relay node is determined according to the Bayesian equilibrium to achieve joint anti-interference and anti-eavesdropping under the interference and eavesdropping attacks of the full-duplex attacker.

[0033] In a specific embodiment of the present invention, step S3 includes: Step S31: The relay party and the full-duplex attacker each maintain historical profit statistics for their respective optional strategies; Step S32: In each iteration, both parties select the strategy for the current round based on the upper bound criterion of the confidence interval and historical statistical data. Step S33: Update the historical return statistics based on the strategy execution results and proceed to the next iteration.

[0034] In one specific embodiment of the present invention, the upper bound criterion for the confidence interval is as follows: an upper bound value is calculated for each optional strategy, wherein the upper bound value is the sum of the historical average return of each optional strategy and the exploration reward, and the strategy with the highest upper bound value is selected.

[0035] In one specific embodiment of the present invention, the relay node and the full-duplex attacker respectively update their strategies for the next period according to the following formula: in, Indicates that the relay node is in The total number of times a certain transmission power is selected within a certain period. Indicates when this strategy is selected Statistical average return over a period of time This indicates that a full-duplex attacker is... The total number of times a certain interference power is selected within a certain period. Indicates when this strategy is selected The statistical average return over a period of time.

[0036] Example 2 (1) Establish a communication confrontation scenario, including relay parties (source node, relay node, destination node) and a full-duplex attacker. The relay node forwards the source node information to the destination node, and the full-duplex attacker performs eavesdropping and interference attacks on the relay link composed of "source node-relay node-destination node". Further define the signal-to-interference-plus-noise ratio of the first stage and the second stage of relay transmission; (2) The adversarial relationship between the two sides in the game is modeled as a Steinberg game. In addition, considering that in real-world scenarios, it is difficult for the relay party and the attacker to obtain all the information about the other party, Bayesian theory is introduced to characterize the incompleteness of information acquisition, and the utility functions and optimization objectives of the two sides in the game are defined; (3) The multi-armed slot machine algorithm is used to converge the Bayesian Steinberg game equilibrium.

[0037] Furthermore, in (1), a communication adversarial scenario is established, including a source node (s), a relay node (r), a destination node (d), and a full-duplex attacker (e). The relay node transmit power set and the attacker jamming power set are defined as follows: , The source node sends information to the relay node. The relay node then selects an appropriate power from its transmit power set to forward the information to the destination node. A full-duplex attacker selects an appropriate jamming power to block the relay communication link, while simultaneously eavesdropping on the relay node's transmitted signals and attempting to decode and steal information.

[0038] Furthermore, in (1), during the first stage of relay transmission, the source node transmits information to the relay node, and the received signal-to-noise ratio is defined as follows: in, The source node transmit power, For channel background noise, This represents the transmission channel gain between the source node and the relay node.

[0039] Furthermore, in (1), during the second stage of relay transmission, the relay node forwards the information to the destination node, and the received signal-to-interference-plus-noise ratio is defined as follows: in, This refers to the transmission channel gain from the relay node to the destination node. This refers to the relay node's transmit power. For the interference channel gain between the full-duplex attacker and the target node, This represents the interference power for a full-duplex attacker.

[0040] Furthermore, in (1), during the second stage of relay transmission, a full-duplex attacker simultaneously eavesdrops on the relay node, defining the received signal-to-interference-plus-noise ratio as follows: , in, For the eavesdropping channel gain from the relay node to the full-duplex attacker, This is for the self-transmit / receive channel gain of a full-duplex attacker.

[0041] Furthermore, in (2), considering the non-cooperative adversarial relationship between the relay party and the full-duplex attacker, it is constructed as a Steinberg game, and the proposed game can be represented as a tuple: in, The participants in the game are the relay party and the full-duplex attacker. These represent the discrete power policy spaces for the relay node and the full-duplex attacker, respectively. These are the utility functions for the relay and the full-duplex attacker, respectively.

[0042] Furthermore, in (2), based on Bayesian theory, from the perspective of the relay node, it cannot fully know the interference channel gain information from the full-duplex attacker to the target node, therefore: Among them, setting Total A state is defined as follows: ,and The probabilities of each state are respectively as follows: And satisfy .

[0043] Furthermore, in (2), from the perspective of a full-duplex attacker, since they cannot fully obtain the eavesdropping channel information from the relay node to the full-duplex attacker, we have: Among them, setting the channel gain Total A state is defined as follows: ,and The probabilities of each state are respectively as follows: ,satisfy .

[0044] Furthermore, in (2), the goal of both the relayer and the full-duplex attacker is to improve their respective utility. Therefore, the optimization objectives for the relayer and the full-duplex attacker are defined as follows: Furthermore, in (3), the multi-armed slot machine algorithm is used to converge the Bayesian Steinberg game equilibrium. Considering that the upper bound of the confidence interval is a commonly used and effective method for policy optimization in the multi-armed slot machine problem, the relay node and the full-duplex attacker update their policies for the next period according to the following rules: in, Indicates that the relay node is in The total number of times a certain transmission power is selected within a given period. Indicates when this strategy is selected The statistical average return over a period of time. This indicates that a full-duplex attacker is... The total number of times a certain interference power is selected within a given period. Indicates when this strategy is selected The statistical average return over a given period. The simulation scenario parameters are set as follows: The technical effects of the present invention are further illustrated below through specific examples and relevant experimental parameters: Here is a specific application example: Figure 2 This is a schematic diagram illustrating a power game scenario between the relay node and a full-duplex attacker, as designed in this invention. In this scenario, the relay node forwards raw information from the source node to the destination node, while the full-duplex attacker interferes with the destination node and simultaneously eavesdrops on the relay node, attempting to decode the forwarded information. Figure 3 This is a schematic diagram of the Steinberg game model proposed in this invention. The game involves two participants: a relay node and a full-duplex attacker, acting as the leader and follower, respectively. After receiving the transmission information from the source node, the relay node first selects the transmission power to forward the information. Subsequently, after sensing the relay node's behavior, the full-duplex attacker selects the interference power to interfere with the target node while also achieving eavesdropping effects. Figure 4 This is a flowchart of the multi-armed slot machine algorithm upon which this invention is based. First, the initial random relay node transmission power is input. During the game, both sides successively choose the optimal strategy based on their own constructed utility, and iteratively converge to the Steinberg game equilibrium. Finally, the recorded game equilibrium solution is output. Figure 5 , Figure 6 This is a graph showing the transmission power and interference power selection ratios between the relay node and the full-duplex attacker. The selection ratio represents the proportion of each power selection strategy in the total number of decisions during the iteration process. As shown in the graph, the strategy selection ratios of the relay node and the full-duplex attacker gradually converge after 150 iterations. Figure 7This diagram illustrates how the regret value of a relay node changes with the number of iterations. This invention uses the regret value to describe the historical losses and gains resulting from the relay not selecting the optimal transmission strategy. As shown in the diagram, the growth rate of the curve gradually slows down with the increase in the number of iterations. This is because, in order to reduce its own revenue losses, the relay node gradually selects the optimal strategy more often, thus causing the curve's growth rate to slow down.

[0045] This invention provides a joint anti-interference and anti-eavesdropping method for Bayesian Steinberg game relays oriented towards spectrum access. Many methods and approaches exist for implementing this technical solution; the above description is merely a preferred embodiment of the invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention. All components not explicitly stated in this embodiment can be implemented using existing technologies.

[0046] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

[0047] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. The embodiments of the present invention are described with reference to flowchart illustrations and / or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing terminal device to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal device, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 The computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing terminal device to operate in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable data processing terminal equipment to cause a series of operational steps to be performed on the computer or other programmable terminal equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable terminal equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the functions specified in one or more boxes. Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments as well as all changes and modifications falling within the scope of the embodiments of the invention. Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0048] The methods and apparatus provided by the present invention have been described in detail above. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

[0049] In the description of this specification, references to terms such as "an embodiment," "some embodiments," "example," "specific example," or "a specific embodiment" or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0050] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A joint anti-interference and anti-eavesdropping method for Bayesian-Stenberg game relays oriented towards spectrum access, characterized in that, include: Step S1: Construct a communication adversarial scenario involving a relay party and a full-duplex attacker, wherein the relay party includes at least a source node, a relay node, and a destination node; Step S2: Based on the communication confrontation scenario, the relay party is designated as the leader and the full-duplex attacker as the follower. A Steinberg game model is constructed, and the utility functions of both parties are defined under the condition of incomplete information based on Bayesian theory. Step S3: Based on the utility function, the multi-armed slot machine algorithm is used for iterative solution until it converges to the Bayesian equilibrium of the Steinberg game. The optimal transmission power strategy of the relay node is determined according to the Bayesian equilibrium to achieve joint anti-interference and anti-eavesdropping under the interference and eavesdropping attacks of the full-duplex attacker.

2. The Bayesian Steinberg game relay joint anti-interference and anti-eavesdropping method for spectrum access according to claim 1, characterized in that, In step S1, the relay node is used to forward the information of the source node to the destination node; the full-duplex attacker is used to interfere with the link from the relay node to the destination node and simultaneously eavesdrop on the relay node.

3. The Bayesian Steinberg game relay joint anti-interference and anti-eavesdropping method for spectrum access according to claim 2, characterized in that, The relay node selects a transmission power from a predetermined set of discrete transmission powers, and the full-duplex attacker selects a jamming power from a predetermined set of discrete jamming powers.

4. The Bayesian Steinberg game relay joint anti-interference and anti-eavesdropping method for spectrum access according to claim 1, characterized in that, Step S1 further includes: defining the signal-to-noise ratio (SNR) of the signal received by the relay node in the first transmission phase, and the first signal-to-interference-plus-noise ratio (SNR) of the signal received by the destination node in the second transmission phase and the second SNR of the signal eavesdropped by the full-duplex attacker.

5. The Bayesian Steinberg game relay joint anti-interference and anti-eavesdropping method for spectrum access according to claim 1, characterized in that, In step S2, the information incompleteness conditions described based on Bayesian theory include: The relay party has incomplete knowledge of the interference channel state caused by the full-duplex attacker. The full-duplex attacker has incomplete knowledge of the state of his own eavesdropping channel.

6. The Bayesian Steinberg game relay joint anti-interference and anti-eavesdropping method for spectrum access according to claim 5, characterized in that, The utility function of the relay is positively correlated with the first signal-to-interference-plus-noise ratio (SINNR), while the utility function of the full-duplex attacker is positively correlated with the second SINNR and negatively correlated with the first SINNR.

7. The Bayesian Steinberg game relay joint anti-interference and anti-eavesdropping method for spectrum access according to claim 6, characterized in that, The optimization objective of the utility functions of both parties is defined as: maximizing their respective expected utilities under the condition of incomplete information.

8. The Bayesian Steinberg game relay joint anti-interference and anti-eavesdropping method for spectrum access according to claim 1, characterized in that, Step S3 includes: Step S31: The relay party and the full-duplex attacker each maintain historical profit statistics for their respective optional strategies; Step S32: In each iteration, both parties select the strategy for the current round based on the upper bound criterion of the confidence interval and historical statistical data. Step S33: Update the historical return statistics based on the strategy execution results and proceed to the next iteration.

9. The Bayesian Steinberg game relay joint anti-interference and anti-eavesdropping method for spectrum access according to claim 8, characterized in that, The upper bound criterion for the confidence interval is as follows: calculate an upper bound value for each optional strategy, the upper bound value being the sum of the historical average return of each optional strategy and the exploration reward, and select the strategy with the highest upper bound value.

10. The Bayesian Steinberg game relay joint anti-interference and anti-eavesdropping method for spectrum access according to claim 8, characterized in that, Both the relay node and the full-duplex attacker update their strategies for the next period according to the following formula: in, Indicates that the relay node is in The total number of times a certain transmission power is selected within a certain period. Indicates when this strategy is selected Statistical average return over a period of time This indicates that a full-duplex attacker is... The total number of times a certain interference power is selected within a certain period. Indicates when this strategy is selected The statistical average return over a period of time.

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