阅读说明：本技术 一种基于贝叶斯Stackelberg博弈的同时干扰与窃听方法 (Simultaneous interference and eavesdropping method based on Bayesian Stackelberg game ) 是由 王伟 刘一甲 戚楠 黄叶婷 王可为 苏悦悦 黄赞奇 于 2021-09-09 设计创作，主要内容包括：本发明公开了一种基于贝叶斯Stackelberg博弈的同时干扰与窃听方法,包括：场景建模：建立基于我方智能干扰机与敌方通信用户对的对抗场景模型；博弈建模：利用全双工技术,将敌我双方用户在不完全信息条件下通信对抗建模为贝叶斯Stackelberg博弈模型,将同时实施干扰与窃听的问题转化为博弈优化问题；优化求解：采用连续凸近似SCA转化领导者与跟随者的非凸优化问题,并通过KKT条件求解贝叶斯Stackelberg博弈均衡解。与半双工,单独干扰以及单独窃听方案相比,本发明提出的同时干扰与窃听仿真说明本发明方法具有很好的准确性与收敛性,优于其他方案。(The invention discloses a simultaneous interference and eavesdropping method based on a Bayesian Stackelberg game, which comprises the following steps: scene modeling: establishing an confrontation scene model based on the intelligent jammer of the party and the communication user pair of the enemy; game modeling: by utilizing a full-duplex technology, the communication countermeasure of the users of the enemy and the my parties under the incomplete information condition is modeled into a Bayesian Stackelberg game model, and the problem of simultaneously implementing interference and eavesdropping is converted into a game optimization problem; and (3) optimizing and solving: and transforming a non-convex optimization problem of the leader and the follower by adopting a continuous convex approximation SCA, and solving a Bayesian Stackelberg game equilibrium solution by using a KKT condition. Compared with half-duplex, single interference and single interception schemes, the simultaneous interference and interception simulation provided by the invention shows that the method has good accuracy and convergence and is superior to other schemes.)

1. A simultaneous interference and eavesdropping method based on a Bayesian Stackelberg game is characterized by comprising the following steps:

step 1: scene modeling: establishing an confrontation scene model based on the intelligent jammer of the party and the communication user pair of the enemy;

step 2: game modeling: based on the confrontation scene model in the step 1, by utilizing a full-duplex technology, the communication confrontation of the users of the two enemies and the two parties under the incomplete information condition is modeled into a Bayesian Stackelberg game model, a leader and a follower are determined, the problem of simultaneously implementing interference and eavesdropping is converted into a game optimization problem, and the game optimization problem is a non-convex optimization problem of the leader and the follower;

and step 3: and (3) optimizing and solving: and transforming a non-convex optimization problem of the leader and the follower by adopting a continuous convex approximation SCA, and solving a Bayesian Stackelberg game equilibrium solution by using a KKT condition.

2. The simultaneous interference and eavesdropping method based on the Bayesian Stackelberg game as claimed in claim 1, wherein in the confrontation scene model of step 1, the game parties are pairs of the intelligent jammer of my party and the communication user of the enemy party, wherein the working mode of the intelligent jammer of my party is full duplex, and the eavesdropping is performed on the communication user of the enemy party while the interference is released, and the communication user of the enemy party has a pair of communication transceiving pairs to transmit information in real time, specifically:

r represents the number of the intelligent jammer of our party, S-D represents the number of the enemy communication transceiving pair, in the countermeasure scene, the signal transmission between any two nodes has path loss and small-scale fading at the same time, the two users hardly know the exact channel state information of the opposite party, and the two users have incomplete cognition on the small-channel fading;

for the same channel, two different probabilities are needed to represent the uncertainty of the channel power gain, b and e respectively represent the R and the S-D communication pair of the enemy, and a belongs to the group of b and e;

a is the cognitive set of small-scale fading gains from node x to node y:

the small-scale fading gain value of the Z th under a certain probability is represented, Z belongs to {1,2, …, Z } and represents a set index number, and x belongs to { s, d, r };the nodes S, d and R respectively represent a transmitter S, a receiver R and a full-duplex node R; "-" is an exclude operator;

therefore, based on the knowledge of a, the channel gains from node x to node y are:

wherein the content of the first and second substances,for free space path loss, α is the path loss coefficient, d_x，yIs the distance from node x to node y;

because intelligent jammer R adopts full-duplex communication mode, can have certain self-interference, and the cognitive set of a to R's self-interference channel gain is:

where N ∈ {1, 2., N } represents a set index number,taking the value of the nth self-interference fading gain;

thus, based on the knowledge of a, the self-interference channel gain is defined as:

wherein k is₀Is a self-interference cancellation factor.

3. The Bayesian Stackelberg game-based simultaneous interference and interception method according to claim 2, wherein the confrontation scenario model in step 1 further defines a cognition-based SINR in the confrontation scenario where interference and interception exist, specifically:

in the S-D tactical communication process, the node D can be interfered and intercepted by a full-duplex jammer R, and based on the cognition of a, the signals received by the node D are as follows:

whereinIs the signal received from S;is an interference signal of node R; i belongs to {1,2, …, I }, I is a discrete sample of the small fading gain between S and D, J belongs to {1,2, …, J }, and J is a discrete sample of the small fading gain between R and D; p is a radical of_sAnd p_rRespectively, the transmission power of the node S and the interference power of the node R; x is the number of_sAnd x_rTransmit signals of S and R, respectively; n is₁Is additive white gaussian noise;

thus, a 'S knowledge of the received SINR at node D is a two-dimensional random variable, depending on a' S knowledge of the S-D and R-D channel gains, respectively denoted asAnd

therefore, a considers the received signal-to-interference-and-noise ratio at node D to be:

wherein the content of the first and second substances,N₁is the unilateral power spectral density of the gaussian noise at node D; b is_sIs the S-D channel bandwidth;

to monitor what tactical data is sent by S to its target recipient D, the full-duplex node R eavesdrops on the S-D transmission signal, so the signal received at R consists of an eavesdropping signal and a self-interference signal, and the knowledge of a on the signal received at R is expressed as:

whereinIs an eavesdropping signal;is a self-interference signal; m belongs to {1,2, …, M }, and M is a discrete sample of the S-R channel gain; n is₂Is additive white gaussian noise;

since the knowledge of a on S-R and self-interference channel gains are respectivelyAndthus, the eavesdropping signal-to-interference-and-noise ratio of node R is:

in the formulaN₂A single-sided power spectral density that is gaussian noise;

assuming that the R-D channel bandwidth is the same as the S-D channel, denoted B_sIn addition, withIn a similar manner to that described above,is a two-dimensional random variable that depends on the knowledge of a on the S-R and self-interference channel gains.

4. The Bayesian Stackelberg game-based simultaneous jamming and eavesdropping method according to claim 3, wherein the step 2 of communication countermeasure of the friend or foe user under incomplete information condition is a hierarchical countermeasure process of the following power domain:

the behavior of S-D is taken as a leader, action is taken firstly, and the intelligent jammer R of the client is a follower, and action is taken after S-D, specifically:

the leader S executes tactical communications and adjusts its power policy, with the goal of ensuring secure communications by reducing the data rate overheard by jammers, and facing interference threats by increasing tactical communications capacity;

after observing the power policy of the leader S, the follower R releases the interfering signal to force S to increase its transmit power, allowing R to eavesdrop on the S-D transmission and also force D to receive its intended signal at a lower rate;

the intelligent jammer R learns the transmitting power of the S and adaptively adjusts the interference power of the intelligent jammer R so as to maximize the utility;

in addition, both enemy and my parties have only incomplete channel condition information, including interference and eavesdropping on the link.

5. The Bayesian Stackelberg game-based simultaneous interference and eavesdropping method according to claim 4, wherein in the step 2, based on channel cognition of the user and the opponent, a communication countermeasure process of the user of the two sides of the enemy and the me under the incomplete information condition is described through the Bayesian Stackelberg game, and a Bayesian Stackelberg game model is constructed, specifically:

the goal of node S is to increase the S-D tactical communication rate while reducing the data rate eavesdropped by R at a lower data transmission power cost, so the utility of transmitting node S is related to the S-D tactical communication rate, the data transmission power and the data rate eavesdropped by R;

the utility of S is defined as:

wherein D is_sIs a normal number, guaranteed U_sIf the S value is positive, the S value can be independently and autonomously determined;expected S-D channel capacity for an adversary;is the expected S-R eavesdropping channel rate of enemy e; theta_sIs an interception factor which represents the attention degree of an enemy to the data rate intercepted by the R; eta_sp_sIs the power cost at S; eta_sIs the cost per unit power at S;

compared with S, the full-duplex node R aims to realize higher S-R eavesdropping rate and reduce S-D transmission with lower power cost;

the utility of the interfering node R is defined as:

wherein D is_rIs a normal number to ensure U_rIs positive;is the expected eavesdropping rate of R;is the expected channel capacity of R versus S-D; theta_rIs a rate suppression factor for R concerned about the extent to which the communication quality of its opponent is reduced, larger theta_rIt is stated that R focuses more on suppressing S-D communication; eta_rp_rIs the power cost of R; eta_rA cost per unit power of R;

based on Bayes formula, givesAndthe specific definition of (1):

is provided withDenotes the cognitive acquisition of a for the received signal to interference and noise ratio at ROf value of (a), wherein

Thus, definition a forThe expected values of (c) are:

wherein the content of the first and second substances,andfractional S-D and R-D small channel fading gain acquisitionAndthe probability of (d);

suppose thatAndis independent, therefore

According toDefining eavesdropping rateComprises the following steps:

wherein the content of the first and second substances,for eavesdropping signal-to-interference-and-noise ratio acquisitionProbability of value, and

suppose thatAndis independent, therefore Andrespectively S-R and self-interference channel gain takingAndthe probability of (c).

6. The Bayesian Stackelberg-based simultaneous jamming and eavesdropping method according to claim 1,

the step 3 specifically comprises the following steps:

step 3-1: constructing an optimization problem model: respectively establishing an optimization problem model of a follower intelligent jammer R and an optimization problem model of a leader S based on the interference power of the R and the data transmission power of the S;

step 3-2: establishing a Stackelberg balance based on an optimization problem model, and proving the existence of the Stackelberg balance;

step 3-3: transforming a non-convex problem of the optimization problem model by using continuous convex approximation, decomposing the non-convex problem into a series of sub-convex functions, and solving the sub-convex functions through a KKT condition;

step 3-4: and solving the Stackelberg balance by adopting an inverse induction method based on the solution of the sub-convex function.

7. The Bayesian Stackelberg game-based simultaneous jamming and eavesdropping method according to claim 6, wherein the step 3-1 is to construct an optimization problem model: respectively establishing an optimization problem model of a follower intelligent jammer R and an optimization problem model of a leader S based on the interference power of the follower intelligent jammer R and the data transmission power of the leader S, and specifically comprising the following steps of:

for the follower my intelligent jammer R, the optimization problem is defined as follows:

P1：

s.t.0＜p_r≤p_r，max

wherein p is_r，maxIs the maximum interference power;

optimizing problem for leader S due to channel expected capacity of enemy communication userRequiring more than a threshold value gamma₀Namely:

due to the fact thatRelative to p_sIs monotonically increasing, so that p is present_s，minWhen p is_s≥p_s，minWhen the temperature of the water is higher than the set temperature,

furthermore, p_sLess than maximum transmission power p_s，max；

Thus, the optimization problem defining the leader S is:

P2：s.t.p_s，min＜p_s≤p_s，max。

8. the Bayesian Stackelberg game-based simultaneous jamming and eavesdropping method according to claim 6, wherein the step 3-2 of constructing the Stackelberg balance based on the optimization problem model and proving the existence of the Stackelberg balance specifically comprises:

by usingAndrepresent the solutions of the optimization problems P1 and P2, respectivelyAndsatisfies the following conditions:

forming a Stackelberg balance;

thus, the existence of the above Stackelberg game balance is demonstrated as follows:

the follower optimization problem can be approximated by continuous convex to convex form, so it has an asymptotic optimal solution, which is recorded asThus, given any S-strategy p_sThe following is true:

by usingSubstituting to obtain

Similarly, the leader optimization problem can be approximated to be convex by continuous convex, and the progressive optimal solution of the leader optimization problem is recorded asThus, for any given R-policy p_rExistence ofBy usingIs substituted to obtain

9. The Bayesian Stackelberg game-based simultaneous jamming and eavesdropping method according to claim 6, wherein the non-convex problem of the optimization problem model is transformed by using continuous convex approximation in step 3-3, and is decomposed into a series of sub-convex functions, and the sub-convex functions are solved by KKT conditions, specifically:

1) and (3) problem decomposition: and (3) performing first-order Taylor expansion on the utility function of P1 to iteratively approximate a convex function of the utility function:

in each iteration, U_r(p_r，p_s) The approximate value of (d) is expressed as:

wherein, theta_rIs thatIn thatThe first-order Taylor expansion form is as follows:

wherein phi₁Is thatIn thatFunction value of (phi)₂Is thatIn thatA first derivative value of (d);

therefore, one further approximation problem to get P1 is:

SCP1:

s.t.p_r≤p_r,max

by solving for SCP1, the newly obtainedTaking the point as the next Taylor expansion point, and starting new iteration until the maximum iteration number is reached, or keeping the point unchanged;

when iteration stops, p of the last iteration round_rIs assigned to

2) Solving the sub-convex problem: the spread of any concave function at any point is the global upper bound, hence, U'_r(p_r，p_s) As an original objective function U_r(p_r，p_s) By iteratively solving SCP1, the original objective function in P1 is approximated, thereby approximating P1:

for the convex optimization problem SCP1, the lagrange function is introduced as follows:

L_r(p_r，p_s)＝U′_r(p_r，p_s)+λ_r(p_r，max-p_r)-μ_rp_r

wherein λ_rAnd mu_rIs the Lagrangian multiplier;

due to L_r(p_r，p_s) Is a concave function, so the dual gap between the lagrange dual problem and the original problem is zero;

then, under KKT conditions, a solution of SCP1 is obtained

Likewise, the same steps are taken to solve for P2.

10. The Bayesian Stackelberg game-based simultaneous interference and eavesdropping method according to claim 6, wherein the solution based on the sub-convex function in steps 3-4 is solved for Stackelberg equalization by an inverse induction method, and specifically the solution is subjected to an iterative process according to the following steps:

a) setting S initial iteration power, an initial Taylor expansion point of S and an initial Taylor expansion point of R;

b) solving a follower sub-convex function according to the S initial iteration power and the R initial Taylor expansion point to obtain a solution of the follower sub-convex function of the current round;

c) taking the solution of the previous follower sub-convex function as a new Taylor expansion point, and iteratively solving the follower sub-convex function until convergence;

d) taking the solution of the follower sub-convex function of the last round as input, and solving the leader sub-convex function through combining the initial Taylor expansion point of the sum S to obtain the solution of the leader sub-convex function of the round;

e) taking the solution of the previous leader sub-convex function as a new round of Taylor expansion point, iteratively solving the leader sub-convex function until convergence, and replacing the S initial iteration power with the solution of the leader sub-convex function of the last round;

f) repeating the steps b) and e) until convergence, and obtaining a Stackelberg equilibrium solution

Technical Field

The invention belongs to the technical field of electronic battlefield wireless communication countermeasure, and particularly relates to a simultaneous interference and eavesdropping method based on a Bayesian Stackelberg game.

Background

In recent years, in the field of military wireless communication, there is an urgent need to monitor tactical information sent by an enemy transmitter to a target receiver in time and immediately interrupt transmission when necessary. The information acquisition advantage is an important factor for determining the battlefield advantage, and in the face of an opponent with intelligent anti-interference capability, the simple electromagnetic interference is not enough to exert effective lethality, and meanwhile, the effective information of the opposite user is difficult to acquire by simple eavesdropping.

Full duplex technology is of great advantage in meeting the above requirements because it facilitates simultaneous jamming and eavesdropping. Therefore, the development of power strategies for simultaneous interference and eavesdropping is also a current research hotspot. Based on the full-duplex simultaneous interference and eavesdropping technology, as an emerging hot problem, the method still has an insufficiently explored research direction at present. Some existing studies can be divided into two study directions, namely theoretical and experimental.

In theory, t.riihonen introduced the aggressive application of simultaneous transmit and receive capabilities in 2017, and this capability enabled joint interference and perception in hostile situations. Mietzner, in 2012, studied responsive attack applications to protect vehicles from radio controlled explosives. L.kong studied in 2016 the physical security problem in the presence of an active eavesdropper that could eavesdrop on user data transmissions while releasing interfering signals, and derived therein the privacy disruption probability of the victim node.

Experimentally, several laboratory experimental works were performed on a generic software radio defined radio, which verified the feasibility of full duplex simultaneous jamming and eavesdropping techniques. However, the currently published works focus on eavesdropping on the signal to interference and noise ratio on the link, i.e. the listening effect, ignoring the interference effect and the fact that the opposite user may be intelligent. Yang innovatively modeled the power control problem as the Stackelberg game in 2013. Firstly, the optimal response strategy of the jammer (as a follower) is estimated, and the optimal strategy of the leader is determined on the basis of the optimal response strategy. In 2017, tang studies the problem that energy-saving transmission with security has a full-duplex active eavesdropper under the Stackelberg game framework, which improves the defense against simultaneous eavesdropping and interference, but none of these works stands on the ground of an attacker to study the formulation of simultaneous interference and eavesdropping strategies.

In electronic countermeasures, electromagnetic interference alone is not sufficient to exert an effective killing force. Meanwhile, it is difficult to obtain effective information of the opposite user by simple eavesdropping. The traditional electromagnetic countermeasure technology is difficult to meet the requirements of communication battlefields. In summary, the existing wireless communication countermeasure model and angle mainly have the following problems: 1) incompleteness of channel information in a hostile environment is not considered. 2) Without considering the intelligence of the user, the intelligent user can change own policy dynamically according to the policy of the other party. 3) And the method considers how efficiently the simultaneous interference and interception strategies are formulated from the perspective of an attacker.

Disclosure of Invention

The invention aims to solve the technical problem of providing a simultaneous interference and interception method based on a Bayesian Stackelberg game, which utilizes a full duplex technology to model the communication countermeasure of the users of both the enemy and the my into the Bayesian Stackelberg game under the incomplete information condition, realizes simultaneous interference and interception, converts the non-convex optimization problem of a leader and a follower through continuous convex approximation, and solves the Stackelberg game balance through the KKT condition.

In order to achieve the technical purpose, the technical scheme adopted by the invention is as follows:

a simultaneous interference and eavesdropping method based on a Bayesian Stackelberg game comprises the following steps:

step 1: scene modeling: establishing an confrontation scene model based on the intelligent jammer of the party and the communication user pair of the enemy;

step 2: game modeling: based on the confrontation scene model in the step 1, by utilizing a full-duplex technology, the communication confrontation of the users of the two enemies and the two parties under the incomplete information condition is modeled into a Bayesian Stackelberg game model, a leader and a follower are determined, the problem of simultaneously implementing interference and eavesdropping is converted into a game optimization problem, and the game optimization problem is a non-convex optimization problem of the leader and the follower;

and step 3: and (3) optimizing and solving: and transforming a non-convex optimization problem of the leader and the follower by adopting a continuous convex approximation SCA, and solving a Bayesian Stackelberg game equilibrium solution by using a KKT condition.

In order to optimize the technical scheme, the specific measures adopted further comprise:

in the confrontation scene model in step 1, the two game parties are a pair of the intelligent jammer of my party and the communication user of the enemy party, wherein the working mode of the intelligent jammer of my party is full duplex, the interference is released, the eavesdropping is carried out on the communication user of the enemy party, the communication user of the enemy party has a pair of communication transceiving pairs, and the information is transmitted in real time, specifically:

r represents the number of the intelligent jammer of our party, S-D represents the number of the enemy communication transceiving pair, in the countermeasure scene, the signal transmission between any two nodes has path loss and small-scale fading at the same time, the two users hardly know the exact channel state information of the opposite party, and the two users have incomplete cognition on the small-channel fading;

for the same channel, two different probabilities are needed to represent the uncertainty of the channel power gain, b and e respectively represent the R and the S-D communication pair of the enemy, and a belongs to the group of b and e;

a is the cognitive set of small-scale fading gains from node x to node y:

the Z small scale fading gain value under certain probability is shown, Z belongs to {1,2, …, Z } represents the index number of the set,the nodes S, d and R respectively represent a transmitter S, a receiver R and a full-duplex node R; "-" is an exclude operator;

therefore, based on the knowledge of a, the channel gains from node x to node y are:

wherein the content of the first and second substances,for free space path loss, α is the path loss coefficient, d_x，yIs the distance from node x to node y;

because intelligent jammer R adopts full-duplex communication mode, can have certain self-interference, and the cognitive set of a to R's self-interference channel gain is:

where N ∈ {1, 2., N } represents a set index number,taking the value of the nth self-interference fading gain;

thus, based on the knowledge of a, the self-interference channel gain is defined as:

wherein k is₀Is a self-interference cancellation factor.

In the countermeasure scene model in step 1, a cognitive signal-to-interference-and-noise ratio in the countermeasure scene where interference and eavesdropping exist is further defined, specifically:

in the S-D tactical communication process, the node D can be interfered and intercepted by a full-duplex jammer R, and based on the cognition of a, the signals received by the node D are as follows:

whereinIs the signal received from S;is an interference signal of node R; i belongs to {1,2, …, I }, I is a discrete sample of the small fading gain between S and D, J belongs to {1,2, …, J }, and J is a discrete sample of the small fading gain between R and D; p is a radical of_sAnd p_rRespectively, the transmission power of the node S and the interference power of the node R; x is the number of_sAnd x_rTransmit signals of S and R, respectively; n is₁Is additive white gaussian noise;

thus, a 'S knowledge of the received SINR at node D is a two-dimensional random variable, depending on a' S knowledge of the S-D and R-D channel gains, respectively denoted asAnd

therefore, a considers the received signal-to-interference-and-noise ratio at node D to be:

wherein the content of the first and second substances,N₁is the unilateral power spectral density of the gaussian noise at node D; b is_sIs the S-D channel bandwidth;

to monitor what tactical data is sent by S to its target recipient D, the full-duplex node R eavesdrops on the S-D transmission signal, so the signal received at R consists of an eavesdropping signal and a self-interference signal, and the knowledge of a on the signal received at R is expressed as:

whereinIs an eavesdropping signal;is a self-interference signal; m is belonged to {1,2, …, M }, and M is

The S-R channel gains one discrete sample; n is₂Is additive white gaussian noise;

since the knowledge of a on S-R and self-interference channel gains are respectivelyAndthus, the eavesdropping signal-to-interference-and-noise ratio of node R is:

in the formulaN₂A single-sided power spectral density that is gaussian noise;

assuming that the R-D channel bandwidth is the same as the S-D channel, denoted B_sIn addition, withIn a similar manner to that described above,is a two-dimensional random variable that depends on the knowledge of a on the S-R and self-interference channel gains.

The communication countermeasure of the users of the two enemies and the me under the incomplete information condition is a layered countermeasure process of the following power domain:

the behavior of S-D is taken as a leader, action is taken firstly, and the intelligent jammer R of the client is a follower, and action is taken after S-D, specifically:

the leader S executes tactical communications and adjusts its power policy, with the goal of ensuring secure communications by reducing the data rate overheard by jammers, and facing interference threats by increasing tactical communications capacity;

after observing the power policy of the leader S, the follower R releases the interfering signal to force S to increase its transmit power, allowing R to eavesdrop on the S-D transmission and also force D to receive its intended signal at a lower rate;

the intelligent jammer R learns the transmitting power of the S and adaptively adjusts the interference power of the intelligent jammer R so as to maximize the utility;

in addition, both enemy and my parties have only incomplete channel condition information, including interference and eavesdropping on the link.

In the step 2, based on channel cognition of the user and the opponent, a communication countermeasure process of the users of the two enemies and the me under the incomplete information condition is described through a Bayesian Stackelberg game, and a Bayesian Stackelberg game model is constructed, specifically:

the goal of node S is to increase the S-D tactical communication rate while reducing the data rate eavesdropped by R at a lower data transmission power cost, so the utility of transmitting node S is related to the S-D tactical communication rate, the data transmission power and the data rate eavesdropped by R;

the utility of S is defined as:

wherein D is_sIs a normal number, guaranteed U_sIs positive, can be independently and autonomously determined by STaking a value;expected S-D channel capacity for an adversary;is the expected S-R eavesdropping channel rate of enemy e; theta_sIs an interception factor which represents the attention degree of an enemy to the data rate intercepted by the R; eta_sp_sIs the power cost at S; eta_sIs the cost per unit power at S;

compared with S, the full-duplex node R aims to realize higher S-R eavesdropping rate and reduce S-D transmission with lower power cost;

the utility of the interfering node R is defined as:

wherein D is_rIs a normal number to ensure U_rIs positive;is the expected eavesdropping rate of R;is the expected channel capacity of R versus S-D; theta_rIs a rate suppression factor for R concerned about the extent to which the communication quality of its opponent is reduced, larger theta_rIt is stated that R focuses more on suppressing S-D communication; eta_rp_rIs the power cost of R; eta_rA cost per unit power of R;

based on Bayes formula, givesAndthe specific definition of (1):

is provided withDenotes the cognitive acquisition of a for the received signal to interference and noise ratio at ROf value of (a), wherein

Thus, definition a forThe expected values of (c) are:

wherein the content of the first and second substances,andfractional S-D and R-D small channel fading gain acquisitionAndthe probability of (d);

suppose thatAndis independent, therefore

According toDefining eavesdropping rateComprises the following steps:

wherein the content of the first and second substances,for eavesdropping signal-to-interference-and-noise ratio acquisitionProbability of value, and

suppose thatAndis independent, thereforeAndrespectively S-R and self-interference channel gain takingAndthe probability of (c).

The step 3 specifically includes the following steps:

step 3-1: constructing an optimization problem model: respectively establishing an optimization problem model of a follower intelligent jammer R and an optimization problem model of a leader S based on the interference power of the R and the data transmission power of the S;

step 3-2: establishing a Stackelberg balance based on an optimization problem model, and proving the existence of the Stackelberg balance;

step 3-3: transforming a non-convex problem of the optimization problem model by using continuous convex approximation, decomposing the non-convex problem into a series of sub-convex functions, and solving the sub-convex functions through a KKT condition;

step 3-4: and solving the Stackelberg balance by adopting an inverse induction method based on the solution of the sub-convex function.

Constructing an optimization problem model in the step 3-1: respectively establishing an optimization problem model of a follower intelligent jammer R and an optimization problem model of a leader S based on the interference power of the follower intelligent jammer R and the data transmission power of the leader S, and specifically comprising the following steps of:

for the follower my intelligent jammer R, the optimization problem is defined as follows:

P1：

s.t.0＜p_r≤p_r，max

wherein p is_r，maxIs the maximum interference power;

optimizing problem for leader S due to channel expected capacity of enemy communication userRequiring more than a threshold value gamma₀Namely:

due to the fact thatRelative to p_sIs monotonically increasing, so that p is present_s，minWhen p is_s≥p_s，minWhen the temperature of the water is higher than the set temperature,

furthermore, p_sLess than maximum transmission power p_s，max；

Thus, the optimization problem defining the leader S is:

P2：s.t.p_s，min＜p_s≤p_s，max。

the step 3-2 of constructing a Stackelberg balance based on the optimization problem model, and proving the existence of the Stackelberg balance specifically includes:

by usingAndrepresent the solutions of the optimization problems P1 and P2, respectivelyAndsatisfies the following conditions:

forming a Stackelberg balance;

thus, the existence of the above Stackelberg game balance is demonstrated as follows:

the follower optimization problem can be approximated by continuous convexity to convex form, thusIt has an asymptotic optimal solution, denoted asThus, given any S-strategy p_sThe following is true:

by usingSubstituting to obtain

Similarly, the leader optimization problem can be approximated to be convex by continuous convex, and the progressive optimal solution of the leader optimization problem is recorded asThus, for any given R-policy p_rExistence ofBy usingIs substituted to obtain

The non-convex problem of the optimization problem model is transformed by using the continuous convex approximation in the step 3-3, the non-convex problem is decomposed into a series of sub-convex functions, and the sub-convex functions are solved through the KKT condition, which specifically comprises the following steps:

1) and (3) problem decomposition: and (3) performing first-order Taylor expansion on the utility function of P1 to iteratively approximate a convex function of the utility function:

in each iteration, U_r(p_r，p_s) The approximate value of (d) is expressed as:

wherein, theta_rIs thatIn thatThe first-order Taylor expansion form is as follows:

wherein phi₁Is thatIn thatFunction value of (phi)₂Is thatIn thatA first derivative value of (d);

therefore, one further approximation problem to get P1 is:

SCP1:

s.t.p_r≤p_r,max

by solving for SCP1, the newly obtainedTaking the point as the next Taylor expansion point, and starting new iteration until the maximum iteration number is reached, or keeping the point unchanged;

when iteration stops, p of the last iteration round_rIs assigned to

2) Solving the sub-convex problem: the spread of any concave function at any point is the global upper bound, hence, U'_r(p_r，p_s) As an original objective function U_r(p_r，p_s) By iteratively solving SCP1, the original objective function in P1 is approximated, thereby approximating P1:

for the convex optimization problem SCP1, the lagrange function is introduced as follows:

L_r(p_r，p_s)＝U′_r(p_r，p_s)+λ_r(p_r，max-p_r)-μ_rp_r

wherein λ_rAnd mu_rIs the Lagrangian multiplier;

due to L_r(p_r，p_s) Is a concave function, so the dual gap between the lagrange dual problem and the original problem is zero;

then, under KKT conditions, a solution of SCP1 is obtained

Likewise, the same steps are taken to solve for P2.

The solution based on the sub-convex function in the step 3-4 is solved by adopting an inverse induction method to solve the Stackelberg equilibrium, and the specific solution is carried out in an iterative process according to the following steps:

a) setting S initial iteration power, an initial Taylor expansion point of S and an initial Taylor expansion point of R;

b) solving a follower sub-convex function according to the S initial iteration power and the R initial Taylor expansion point to obtain a solution of the follower sub-convex function of the current round;

c) taking the solution of the previous follower sub-convex function as a new Taylor expansion point, and iteratively solving the follower sub-convex function until convergence;

d) taking the solution of the follower sub-convex function of the last round as input, and solving the leader sub-convex function through combining the initial Taylor expansion point of the sum S to obtain the solution of the leader sub-convex function of the round;

e) taking the solution of the previous leader sub-convex function as a new round of Taylor expansion point, iteratively solving the leader sub-convex function until convergence, and replacing the S initial iteration power with the solution of the leader sub-convex function of the last round;

f) repeating the steps b) and e) until convergence, and obtaining a Stackelberg equilibrium solution

The invention has the following beneficial effects:

the invention researches an anti-game between an intelligent jammer with full duplex technology and an opposite user, and the specific form of the simultaneous interference and eavesdropping strategy of the invention is as follows: the intelligent jammer releases interference to reduce user data transmission of an enemy and eavesdrop data transmission of the other party. In order to describe the confrontation relationship of two parties under the incomplete information condition, the invention provides a Bayesian Stackelberg game frame model of a power domain, a Stackelberg game equilibrium solution is solved by adopting a continuous convex approximation SCA (successive convex approximation) to convert a non-convex problem and a KKT (Karush-Kuhn-Tucker) condition, namely how to utilize a full duplex technology in communication confrontation, the problem of efficiently and simultaneously implementing interference and eavesdropping is constructed into a Bayesian Stackelberg game model, the Bayesian Stackelberg game model is further converted into a game optimization problem, the non-convex optimization problem of a leader and a follower is converted by continuous convex approximation, and the Stackelberg game equilibrium is solved by the KKT condition.

Meanwhile, the invention proves that the game equilibrium solution is superior to Nash equilibrium, and the invention researches the influence of the rate suppression weight and the power cost coefficient of the full-duplex jammer on the power strategy and the utility. Compared with half-duplex, single interference and single interception schemes, the simultaneous interference and interception simulation provided by the invention shows that the method has good accuracy and convergence and is superior to other schemes.

Drawings

FIG. 1 is a schematic diagram of the present invention;

FIG. 2 is a diagram of a communication scenario between two parties;

FIG. 3 is a continuous convex approximation method convergence diagram;

FIG. 4 is a diagram of Stackelberg equalization iteration convergence;

FIG. 5 is a graph of performance analysis;

figure 6 is a graph comparing the utility of several reference protocols.

Detailed Description

Embodiments of the present invention are described in further detail below with reference to the accompanying drawings.

The embodiment of the invention is established under the condition of the communication countermeasure distribution of the users of the two enemies and the my people as shown in figure 2.

Fig. 1 is a flowchart showing the present invention, and the present invention provides a simultaneous jamming and eavesdropping method based on a bayesian Stackelberg game, which includes the following steps:

step 1: scene modeling: establishing an confrontation scene model based on the intelligent jammer of the party and the communication user pair of the enemy;

step 2: game modeling: based on the confrontation scene model in the step 1, by utilizing a full-duplex technology, the communication confrontation of the users of the two enemies and the two parties under the incomplete information condition is modeled into a Bayesian Stackelberg game model, a leader and a follower are determined, the problem of simultaneously implementing interference and eavesdropping is converted into a game optimization problem, and the game optimization problem is a non-convex optimization problem of the leader and the follower;

and step 3: and (3) optimizing and solving: and transforming a non-convex optimization problem of the leader and the follower by adopting a continuous convex approximation SCA, and solving a Bayesian Stackelberg game equilibrium solution by using a KKT condition.

In the embodiment, in the confrontation scene model described in step 1, the two game parties are a pair of an intelligent jammer of my party and a communication user of an enemy party, where the working mode of the intelligent jammer of my party is full duplex, so that the interference can be released and the communication user of the enemy party can be intercepted, the communication user of the enemy party has a pair of communication transceiver pairs to transmit information in real time, specifically:

r represents the number of the intelligent jammer of our party, S-D represents the number of the enemy communication transceiving pair, in the countermeasure scene, the signal transmission between any two nodes has path loss and small-scale fading at the same time, the two users hardly know the exact channel state information of the opposite party, and the two users have incomplete cognition on the small-channel fading;

for the same channel, two different probabilities are needed to represent the uncertainty of the channel power gain, b, e represent my full-duplex jammer R and enemy S-D communication pair, respectively, let a e (b, e),

wherein the cognitive set of the small-scale fading gains from node x to node y of a is:

the Z small scale fading gain value under certain probability is shown, Z belongs to {1,2, …, Z } represents the index number of the set,the nodes S, d and R respectively represent a transmitter S, a receiver R and a full-duplex node R; "-" is an exclude operator;

therefore, based on the knowledge of a, the channel gains from node x to node y are:

wherein the content of the first and second substances,for free space path loss, alpha is path loss coefficient, and the invention is set as 2, d_x，yIs the distance from node x to node y;

because intelligent jammer R adopts full-duplex communication mode, can have certain self-interference, and the cognitive set of a to R's self-interference channel gain is:

where N ∈ {1, 2., N } represents a set index number,taking the value of the nth self-interference fading gain;

thus, based on the knowledge of a, the self-interference channel gain is defined as:

wherein k is₀Is a self-interference cancellation factor.

In the embodiment, in the countermeasure scenario model in step 1, a cognitive signal to interference plus noise ratio in the presence of an interference and eavesdropping is further defined, specifically:

in the S-D tactical communication process, the node D can be interfered and intercepted by a full-duplex jammer R, and based on the cognition of a, the signals received by the node D are as follows:

whereinIs the signal received from S;is an interference signal of node R; i belongs to {1,2, …, I }, I is a discrete sample of the small fading gain between S and D, J belongs to {1,2, …, J }, and J is a discrete sample of the small fading gain between R and D; p is a radical of_sAnd p_rRespectively, the transmission power of the node S and the interference power of the node R; x is the number of_sAnd x_rTransmit signals of S and R, respectively; n is₁Is additive white gaussian noise;

thus, a 'S knowledge of the received SINR at node D is a two-dimensional random variable, depending on a' S knowledge of the S-D and R-D channel gains, respectively denoted asAnd

therefore, a considers the received signal-to-interference-and-noise ratio at node D to be:

wherein the content of the first and second substances,N₁is the unilateral power spectral density of the gaussian noise at node D; b is_sIs the S-D channel bandwidth;

in order to monitor what tactical data is sent by S to its target recipient D, the full-duplex node R eavesdrops on the S-D transmission signal, and therefore the signal received at R consists of an eavesdropping signal and a self-interference signal;

thus, the knowledge of a for the signal received at R is represented as:

whereinIs an eavesdropping signal;is a self-interference signal; m belongs to {1,2, …, M }, and M is a discrete sample of the S-R channel gain; n is₂Is additive white gaussian noise;

since the knowledge of a on S-R and self-interference channel gains are respectivelyAndthus, the eavesdropping signal-to-interference-and-noise ratio of node R is:

in the formulaN₂A single-sided power spectral density that is gaussian noise;

without loss of generality, the R-D channel bandwidth is assumed to be the same as the S-D channel, denoted as B_sIn addition, withIn a similar manner to that described above,and is also a two-dimensional random variable that depends on the knowledge of a on the S-R and self-interference channel gains.

In an embodiment, the communication countermeasure of the users of the two enemies and the my party under the incomplete information condition in the step 2 is a layered countermeasure process of the following power domain:

the behavior of S-D is taken as a leader, action is taken firstly, and the intelligent jammer R of the client is a follower, and action is taken after S-D, specifically:

the leader S executes tactical communications and adjusts its power policy, with the goal of ensuring secure communications by reducing the data rate overheard by jammers, and facing interference threats by increasing tactical communications capacity;

after observing the power policy of the leader S, the follower R releases the interfering signal to force S to increase its transmit power, which helps R eavesdrop on S-D transmissions, also forcing D to receive its intended signal at a lower rate;

the intelligent jammer R can rapidly learn the transmitting power of the S and adaptively adjust the interference power of the S, so that the utility is maximized;

the above process can be expressed as a hierarchical countermeasure process for one power domain.

In addition, both enemy and my parties have only incomplete channel condition information, including interference and eavesdropping on the link.

In the embodiment, in the step 2, based on channel cognition on the user and the opponent, the invention describes the communication countermeasure process of the users of the two enemies and the me under the incomplete information condition through the bayesian Stackelberg game, and constructs a bayesian Stackelberg game model, specifically:

the goal of node S is to increase the S-D tactical communication rate while reducing the data rate eavesdropped by R at a lower data transmission power cost, so the utility of transmitting node S is related to the S-D tactical communication rate, the data transmission power and the data rate eavesdropped by R;

the utility of S is defined as:

wherein D is_sIs a normal number, guaranteed U_sIf the S value is positive, the S value can be independently and autonomously determined;expected S-D channel capacity for an adversary;is the expected S-R eavesdropping channel rate of enemy e; theta_sIs an interception factor which represents the attention degree of an enemy to the data rate intercepted by the R; eta_sp_sIs the power cost at S; eta_sIs the cost per unit power at S;

compared with S, the full-duplex node R aims to realize higher S-R eavesdropping rate and reduce S-D transmission with lower power cost;

the utility of the interfering node R is defined as:

wherein D is_rIs a normal number to ensure U_rIs positive;is the expected eavesdropping rate of R;is the expected channel capacity of R versus S-D; theta_rIs a rate suppression factor for R concerned about the extent to which the communication quality of its opponent is reduced, larger theta_rIt is stated that R focuses more on suppressing S-D communication; eta_rp_rIs the power cost of R; eta_rIs the cost per unit power of R.

In the embodiment, based on Bayesian formula, the method is providedAndthe specific definition of (1):

is provided withDenotes the cognitive acquisition of a for the received signal to interference and noise ratio at RProbability of the value of (c). Note that, therein

Thus, definition a forThe expected values of (c) are:

wherein the content of the first and second substances,andfractional S-D and R-D small channel fading gain acquisitionAndthe probability of (d);

suppose thatAndis independent, therefore

According toDefining eavesdropping rateComprises the following steps:

wherein the content of the first and second substances,for eavesdropping signal-to-interference-and-noise ratio acquisitionOf valueProbability of, and

suppose thatAndis independent, thereforeAndrespectively S-R and self-interference channel gain takingAndthe probability of (c).

The step 3 specifically comprises the following steps:

step 3-1: constructing an optimization problem model: respectively establishing an optimization problem model of a follower intelligent jammer R and an optimization problem model of a leader S based on the interference power of the R and the data transmission power of the S;

specifically, the method comprises the following steps:

and constructing an optimization problem model. In the game, the interference power of R and the data transmission power of S need to be carefully designed. In particular, the present invention relates to a method for producing,

for R, blindly increasing the interference power may result in severe self-interference, resulting in a drop in the eavesdropping rate. Therefore, R needs to adjust its power to achieve maximum utility.

In addition, for S, to combat interference from R, blindly increasing the transmission power increases the risk of more data being overheard, increasing power costs.

Therefore, for the follower my intelligent jammer R, the optimization problem is defined as:

P1：s.t.0＜p_r≤p_r，max

wherein p is_r，maxIs the maximum interference power;

optimizing problem for leader S due to channel expected capacity of enemy communication userRequiring more than a threshold value gamma₀Namely:

due to the fact thatRelative to p_sIs monotonically increasing, so that p is present_s，minWhen p is_s≥p_s，minWhen the temperature of the water is higher than the set temperature,

furthermore, p_sLess than maximum transmission power p_s，max；

Thus, the optimization problem defining the leader S is:

P2：

s.t.p_s，min＜p_s≤p_s，max

step 3-2: constructing a Stackelberg balance based on an optimization problem model, and proving the existence of the Stackelberg balance:

in gaming, it is intelligent to both parties, and therefore both party power strategies are interacting.

R as a follower, can quickly observe opponent's strategy and adjust its power to maximize its utility using smart sensors and positioning devices.

And S is used as a leader, the power strategy of the follower R can be predicted, and a decision is made according to the prediction.

By usingAndrepresent the solutions of the optimization problems P1 and P2, respectivelyAndsatisfies the following conditions:

this means that R and S cannot unilaterally change their power, otherwise their utility will decrease, at which point,

forming a Stackelberg balance;

thus, the existence of the above Stackelberg game balance is demonstrated as follows:

the follower optimization problem can be approximated by continuous convex to convex form, so it has an asymptotic optimal solution, which is recorded asThus, given any S-strategy p_sThe following is true:

by usingSubstituting to obtain

Similarly, the leader optimization problem can be approximated to be convex by continuous convex, and the progressive optimal solution of the leader optimization problem is recorded asThus, for any given R-policy p_rExistence ofBy usingIs substituted to obtain

Step 3-3: and transforming the non-convex problem of the optimization problem model by using continuous convex approximation, decomposing the non-convex problem into a series of sub-convex functions, and solving the sub-convex functions through the KKT condition.

The objective function of P1 is non-convex, so solving for P1 is difficult. To effectively solve this problem, the present invention decomposes non-convex P1 into a series of sub-convex functions using a continuous convex approximation.

The basic idea is to approximate the original optimization problem P1 with a sub-convex function. To solve for P1, the following two steps are required:

1) the problem is resolved. By first order Taylor expansion of the utility function of P1, the present invention iteratively approximates the sub-convex function of the utility function. In each iteration, U_r(p_r，p_s) Can be expressed as

Wherein, theta_rIs thatIn thatIn the form of a first-order Taylor expansion, in particular

Wherein phi₁Is thatIn thatFunction value of (phi)₂Is thatIn thatThe first derivative value of (a). Therefore, one approximation problem to further derive P1 is

SCP1:

s.t.p_r≤p_r,max

By solving for SCP1, the newly obtainedAs the next taylor expansion point and start a new iteration until the maximum number of iterations is reached or remains unchanged. When iteration stops, p of the last iteration round_rIs assigned to

2) Solving the sub convex function. An expansion of any concave function at any point is a global upper bound. Therefore, U'_r(p_r，p_s) As an original objective function U_r(p_r，p_s) The upper bound of (c). By iteratively solving SCP1, the original objective function in P1 can be approximated, thereby approximating P1.

For the convex optimization problem SCP1, the lagrange function is introduced as follows:

L_r(p_r，p_s)＝U′_r(p_r，p_s)+λ_r(p_r，max-p_r)-μ_rp_r

wherein λ_rAnd mu_rIs the lagrange multiplier.

Due to L_r(p_r，p_s) Is a concave function, so the dual gap between the lagrange dual problem and the original problem is zero; then, under KKT conditions, a solution of SCP1 is obtained

Likewise, the same steps are taken to solve for P2.

Step 3-4: and solving the Stackelberg balance by adopting an inverse induction method based on the solution of the sub-convex function.

Specifically, the solution is subjected to an iterative process according to the following steps:

a) setting S initial iteration power, an initial Taylor expansion point of S and an initial Taylor expansion point of R;

b) solving a follower sub-convex function according to the S initial iteration power and the R initial Taylor expansion point to obtain a solution of the follower sub-convex function of the current round;

c) taking the solution of the previous follower sub-convex function as a new Taylor expansion point, and iteratively solving the follower sub-convex function until convergence;

d) taking the solution of the follower sub-convex function of the last round as input, and solving the leader sub-convex function through combining the initial Taylor expansion point of the sum S to obtain the solution of the leader sub-convex function of the round;

e) taking the solution of the previous leader sub-convex function as a new round of Taylor expansion point, iteratively solving the leader sub-convex function until convergence, and replacing the S initial iteration power with the solution of the leader sub-convex function of the last round;

f) repeating the steps b) and e) until convergence, and obtaining a Stackelberg equilibrium solution

Simulation analysis was performed based on the values of table 1 and table 2:

TABLE 1

TABLE 2

FIG. 3 illustrates the convergence process of the successive convex approximations employed by the present invention. It can be seen that when the convergence reaches about 10 th time, the interference power of R and the transmitting power of S both reach convergence, which shows that the method adopted by the invention has good convergence and can accelerate the decision speed of the two parties.

FIG. 4 shows the iterative process of the present invention in solving Stackelberg equalization. It can be seen that in the process of solving in the Stackelberg equalization, when iteration is performed for the 7 th time, convergence is already finished by both sides, and at this time, both sides cannot easily change their own decisions, so that the utility reaches the maximum. Meanwhile, the convergence results of the two parties meet the power constraint set by the invention, which shows the effectiveness of the method adopted by the invention.

Fig. 5 shows the utility values obtained by the method of the present invention compared to utility values that are not approximated in practice, and nash equalization. It can be seen that no matter how the power throttling factor and the power cost are taken, the method adopted by the invention is very close to the actual utility value, which shows the approximate reliability and accuracy of the method adopted by the invention. Meanwhile, the utility values of both sides are superior to the utility value of Nash balance, which illustrates the superiority of Stackelberg balance.

Figure 6 shows a comparison of the simultaneous jamming and eavesdropping method employed by the invention with several other reference schemes. It can be seen that as the power factor is increased, the effectiveness of R decreases in either case. This is because as the power throttle factor increases, R will focus more on hostile interference throttling, increasing the own interfering power. Since the interference power increases, the self-interference and the power cost increase, which results in increased utility. In addition, no matter how the value of the power suppression factor is taken, the simultaneous interference and interception method adopted by the invention is superior to other reference schemes, and the necessity of the simultaneous interference and interception method is illustrated.

The above is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may be made by those skilled in the art without departing from the principle of the invention.