Multi-domain wireless communication anti-interference method and system based on master-slave game

Abstract

A multi-domain wireless communication anti-interference method and system based on master-slave game, the method includes: modeling the communication party as a leader, modeling the jammer as a follower, combining the power domain and the time domain, and establishing the utility function of the communication party and the jammer and the master-slave game model based on the weighted rate; modeling the jammer observation error model and the jammer finite rationality model for the observation error of the jammer on the communication party parameters; considering the jammer observation error model and the jammer finite rationality model, according to the utility function of the communication party and the jammer and the master-slave game model, the optimization problem of the transmitter and the jammer is obtained, and the reverse induction method is used to solve it, and the optimal time domain and power domain parameters of the communication party and the jammer are obtained, and the obtained parameters are used to control the wireless anti-interference communication process. The present invention comprehensively considers the joint optimization of the communication party and the jammer in the power domain and the time domain, and finds the optimal transmission strategy of the communication party according to the imprecise observation and finite rationality of the jammer.

Description

Technical Field

[0001] The present invention belongs to the field of wireless communication anti-interference, and specifically relates to a multi-domain wireless communication anti-interference method and system based on master-slave game. Background Art

[0002] In recent years, the application of wireless anti-interference technology has become more and more extensive. In the face of tracking interference, a direct way is to achieve anti-interference by increasing the frequency hopping rate. However, due to the limitations of RF devices and automatic gain controllers, there is a frequency switching time when the device state is unstable after the user switches the frequency, and the user cannot communicate during the frequency switching time. Under the condition of a certain time, if the hopping rate is too fast, the actual communication time will be reduced due to the existence of the frequency switching time; if the hopping rate is slow, the probability of being effectively perceived by the enemy and implementing tracking interference will increase. Therefore, the selection of the optimal hopping rate for frequency hopping communication is an important issue that needs to be solved. In order to obtain the best anti-interference effect, the communicating party needs to select a suitable hopping rate under the condition of considering the detection overhead and detection error of the interfering party, and compromise between the bit error caused by interference and the frequency hopping damage.

[0003] When the jammer can adaptively adjust the jamming strategy according to the communication environment, the researchers use game theory to model the confrontation between intelligent jamming and anti-jamming, and propose a variety of communication anti-jamming methods based on game theory. For example, the Markov game method is used to study the joint optimization problem of frequency modulation frequency and transmission rate under reactive sweeping interference conditions; the master-slave game method is used to study the allocation of optimal jamming power and optimal communication power under intelligent jamming; the optimal hopping speed problem of point-to-point frequency hopping communication systems with tracking interference is studied, and the communication interference and anti-jamming are modeled by using master-slave games; and some researchers have explored the application of master-slave game models with observation errors in communication interference and anti-jamming. Summary of the invention

[0004] The purpose of the present invention is to address the problems in the above-mentioned prior art and provide a multi-domain wireless communication anti-interference method and system based on master-slave game, which comprehensively considers the joint optimization of the communicating party and the interfering party in the power domain and the time domain, and finds the optimal transmission strategy of the communicating party based on the inaccurate observation and limited rationality of the interfering party, thereby achieving the purpose of anti-interference.

[0005] In order to achieve the above object, the present invention has the following technical solutions:

[0006] In a first aspect, a multi-domain wireless communication anti-interference method based on a master-slave game is provided, comprising the following steps:

[0007] The communication party is modeled as a leader and the jammer is modeled as a follower. The power domain and time domain are combined to establish the utility function of the communication party and the jammer and the master-slave game model based on the weighted rate.

[0008] Aiming at the observation error of the jammer on the communication party parameters, the jammer observation error model and the jammer finite rationality model are modeled;

[0009] Considering the jammer observation error model and the jammer finite rationality model, the optimization problem of the transmitter and the jammer is obtained according to the utility function of the communicator and the jammer and the master-slave game model. The reverse induction method is used to solve it, and the optimal time domain and power domain parameters of the communicator and the jammer are obtained. The obtained parameters are used to control the wireless anti-interference communication process.

[0010] Preferably, the observation error of the jammer on the communication party parameters includes the jammer's observation error on the transmitter transmission power P s The observation error of the frequency hopping period T is described by introducing the observation error factor ε, and the jammer observation error model is obtained as follows: In the formula, and are the observed values ​​of the jammer on the transmitter's transmit power and frequency hopping period respectively.

[0011] Preferably, when the finite rational model of the jammer is established, the transmission power P of the jammer is J Take the maximum value P Jmax , only for the detection time T E To model the bounded rationality, a zero-mean Gaussian perturbation T is introduced. E0 Modeling bounded rationality, we obtain The strategy adopted by the jammer under bounded rationality.

[0012] Preferably, the utility function of the communication party and the jammer is established based on the weighted rate by combining the power domain and the time domain, specifically including:

[0013] The probability of the jammer being in the detection state and the jamming state is analyzed, the utility function of the communication party is calculated according to the Shannon formula, and the utility function of the jammer is established according to the master-slave game;

[0014] The expression of the communication party's utility function is as follows:

[0015]

[0016] Among them, μ S Utility for the communication party; is the detection probability under bounded rationality; T0 is the transient process time of frequency hopping; T is the frequency hopping period; T E is the signal detection time; h sd ,h jd ,h sj are the channel gains between transmitter and receiver, jammer and receiver, and transmitter and jammer respectively; δ2 is the background noise power; P s and P J are the transmitter and receiver powers respectively; is the SINR when interference exists; is the SNR when there is no interference;

[0017] Detection probability under bounded rationality Calculate as follows:

[0018]

[0019] The expression of the utility function of the communication party is divided into three parts, among which the first part It indicates the channel capacity when the jammer detects the transmitting signal of the communication party and implements interference; the second part Indicates the channel capacity when the jammer is in the detection state. When in the detection state, the jammer does not send interference signals; the third part It indicates the channel capacity when the jammer does not detect the signal transmitted by the communication party, and the jammer does not send any interference signal at this time;

[0020] The utility function of the jammer is as follows:

[0021]

[0022] In the formula, is the detection probability of the jammer when there is an observation error, μ J is the jammer utility. In the master-slave game, both the communication party and the jammer want to maximize their utility values. Therefore, the jammer utility function is formally the negative of the communication party utility function.

[0023] Detection probability in the presence of observation errors Calculate as follows:

[0024]

[0025] Preferably, the optimization problem of the jammer is described as follows:

[0026] μ J (P J * ,T E * ,P S * ,T * )≥μ J (P J ,T E ,P S * ,T * )st0≤P J≤P Jmax ,0≤T E ≤T

[0027] The transmission power of the jammer P J Take the maximum value P Jmax In this optimization problem, the jammer determines the optimal detection time T E * ;

[0028] The optimization problem of the transmitter is described as follows:

[0029] μ S (P J * ,T E * ,P S * ,T * )≥μ S (P J * ,T E * ,P S ,T)st0≤P S ≤P Smax ,0≤T≤T max

[0030] In this optimization problem, the transmitter determines the optimal transmit power P S * and frequency hopping period T * .

[0031] Preferably, the reverse induction method is used to solve the optimal time domain and power domain parameters of the communication party and the jammer. The optimization problem of the jammer is solved first, and after the closed-form solution of the optimal strategy is found, it is substituted into the utility function of the communication party to solve the optimal action strategy of the communication party.

[0032] Preferably, the step of first solving the optimization problem of the jammer, finding a closed-form solution to the optimal strategy, and then introducing it into the utility function of the communicating party to solve the optimal action strategy of the communicating party is completed using a genetic algorithm.

[0033] In a second aspect, a multi-domain wireless communication anti-interference system based on master-slave game is provided, comprising:

[0034] The utility function and master-slave game model establishment module is used to model the communication party as a leader and the jammer as a follower, and to establish the utility function and the master-slave game model of the communication party and the jammer based on the weighted rate by combining the power domain and the time domain;

[0035] The jammer observation error and finite rationality model establishment module is used to build the jammer observation error model and the jammer finite rationality model according to the jammer's observation error of the communication party's parameters;

[0036] The optimization problem construction and solution module is used to consider the jammer observation error model and the jammer finite rationality model, obtain the optimization problem of the transmitter and the jammer according to the utility function of the communication party and the jammer and the master-slave game model, and use the reverse induction method to solve it, obtain the optimal time domain and power domain parameters of the communication party and the jammer, and use the obtained parameters to control the wireless anti-interference communication process.

[0037] As a preference, the jammer observation error and finite rationality model building module considers the jammer's observation error of the communication party parameters when building the model, including the jammer's observation error of the transmitter's transmission power P s The observation error of the frequency hopping period T is described by introducing the observation error factor ε, and the jammer observation error model is obtained as follows:

[0038] In the formula, and are respectively the observed values ​​of the jammer on the transmitter’s transmit power and frequency hopping period;

[0039] When the finite rational model of the jammer is established, the transmission power P of the jammer is J Take the maximum value P Jmax , only for the detection time T E To model the bounded rationality, a zero-mean Gaussian perturbation T is introduced. E0 Modeling bounded rationality, we obtain The strategy adopted by the jammer under bounded rationality.

[0040] Preferably, the utility function and master-slave game model establishment module combines the power domain and the time domain to establish the utility function of the communication party and the jammer based on the weighted rate, specifically including:

[0041] The probability of the jammer being in the detection state and the jamming state is analyzed, the utility function of the communication party is calculated according to the Shannon formula, and the utility function of the jammer is established according to the master-slave game;

[0042] The expression of the communication party's utility function is as follows:

[0043]

[0044] Among them, μ S Utility for the communication party; is the detection probability under bounded rationality; T0 is the transient process time of frequency hopping; T is the frequency hopping period; T E is the signal detection time; hsd ,h jd ,h sj are the channel gains between transmitter and receiver, jammer and receiver, and transmitter and jammer respectively; δ 2 is the background noise power; P s and P J are the transmitter and receiver powers respectively; is the SINR when interference exists; is the SNR when there is no interference;

[0045] Detection probability under bounded rationality Calculate as follows:

[0046]

[0047] The expression of the utility function of the communication party is divided into three parts, among which the first part It indicates the channel capacity when the jammer detects the transmitting signal of the communication party and implements interference; the second part Indicates the channel capacity when the jammer is in the detection state. When in the detection state, the jammer does not send interference signals; the third part It indicates the channel capacity when the jammer does not detect the signal transmitted by the communication party, and the jammer does not send any interference signal at this time;

[0048] The utility function of the jammer is as follows:

[0049]

[0050] In the formula, is the detection probability of the jammer when there is an observation error, μ J is the jammer utility. In the master-slave game, both the communication party and the jammer want to maximize their utility values. Therefore, the jammer utility function is formally the negative of the communication party utility function.

[0051] Detection probability in the presence of observation errors Calculate as follows:

[0052]

[0053] The optimization problem of the jammer to be solved by the optimization problem construction and solution module is described as follows:

[0054] μ J (P J * ,T E * ,P S * ,T * )≥μ J (PJ ,T E ,P S * ,T * )st0≤P J ≤P Jmax ,0≤T E ≤T

[0055] The transmission power of the jammer P J Take the maximum value P Jmax In this optimization problem, the jammer determines the optimal detection time T E * ;

[0056] The optimization problem of the transmitter to be solved by the optimization problem construction and solution module is described as follows:

[0057] μ S (P J * ,T E * ,P S * ,T * )≥μ S (P J * ,T E * ,P S ,T)st0≤P S ≤P Smax ,0≤T≤T max

[0058] In this optimization problem, the transmitter determines the optimal transmit power P S * and frequency hopping period T * .

[0059] Compared with the prior art, the present invention has at least the following beneficial effects:

[0060] The present invention is based on the master-slave game model, comprehensively considers the joint optimization problem of the communication party and the interference party in the power domain and the time domain, and considers the imprecise observation and limited rationality of the interference party. The communication party adjusts the transmission power and the frequency hopping period, and the interference party adjusts the interference power and the detection time to find the optimal transmission strategy of the communication party and the interference party. The simulation results show that the master-slave game between the communication party and the interference party will reach an equilibrium point, at which time both the communication party and the interference party will have the greatest benefit. No matter which party adopts a transmission strategy that deviates from the equilibrium point, it will not obtain greater benefits. Considering the imprecise observation of the interference party, the experiment shows that the larger the observation error, the lower the utility value of the interference party when the master-slave game equilibrium point is reached; considering the limited rationality of the interference party, the experiment shows that limited rationality does not have a significant impact on the utility value of both parties at the equilibrium point. By comparing with the single-domain game scheme and the multi-domain random scheme, the multi-domain game scheme of the present invention has a higher utility value and more stable performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0061] Figure 1 A schematic diagram of a wireless communication system model structure according to an embodiment of the present invention;

[0062] Figure 2 It is a structural schematic diagram of a frequency hopping signal;

[0063] Figure 3 A wireless communication simulation scene diagram according to an embodiment of the present invention;

[0064] Figure 4 It is a curve diagram showing the influence of the jammer's maximum transmission power on the utility value of the communication party;

[0065] Figure 5 It is a curve diagram showing the influence of the jammer's maximum transmission power on the frequency hopping period of the communication party;

[0066] Figure 6 It is a curve diagram of the utility value convergence effect of the communication party under ideal conditions;

[0067] Figure 7 This is a curve diagram showing the effect of observation error on the jammer effectiveness;

[0068] Figure 8 It is a curve diagram of the convergence of the utility value of the communication party under the condition of limited rationality;

[0069] Fig. 9 The utility value comparison curve diagram of the scheme proposed in the embodiment of the present invention and the comparative scheme is shown in FIG. DETAILED DESCRIPTION

[0070] The present invention is further described in detail below in conjunction with the accompanying drawings and embodiments.

[0071] See also Figure 1The wireless communication system model of the embodiment of the present invention consists of a user (transmitter S and receiver D) and a jammer J. There are independent links between each node. sd ,h jd ,h sj are the channel gains between each node, and the frequency hopping period of the communication system is defined as T. The jammer performs intelligent tracking and jamming on the communication system. Considering the application of this model in actual combat, the transmission cost of the communication party and the jammer is ignored, but both the communication party and the jammer have maximum transmission power limits, which are P and P, respectively. Smax and P Jmax .

[0072] Let the user's frequency hopping frequency set be F, F = [f1, f2, f3…f1], that is, the frequency hopping signal pseudo-randomly jumps in M ​​adjacent but non-intersecting sub-bands. The frequency hopping period satisfies T∈[0,T max ], T max is the maximum frequency hopping period, that is, the parameter that the frequency hopping user can track interference according to the guided method, in [0,T max ] range. Due to the limitations of devices and process levels, the frequency switching of the frequency hopping signal inevitably has an unstable transient process, during which the frequency hopping communication system neither transmits nor receives signals. Let the duration of this transient process be T0, which can be regarded as a fixed value during the operation of the frequency hopping communication system.

[0073] The jamming strategy of guided tracking jamming is: in each frequency hopping cycle, the jammer first detects the frequency hopping signal. If a frequency hopping communication signal is detected, the jammer is immediately guided to perform the jamming; otherwise, the jammer does not transmit the jamming signal. Figure 2 The structure diagram of the frequency hopping signal is shown. Figure 2 It can be seen that each frequency hopping cycle can be divided into two parts: signal detection time T E and interference time T J , and T = T E +T I Since the signal detection probability is often related to the detection time or the length of the detection signal: the longer the detection time, the higher the detection probability; conversely, the lower it is. The signal detection probability p is given below d The expression is:

[0074]

[0075] The present invention adopts the master-slave game model to find the optimal strategy. In the master-slave game model, the transmitter plays the role of the leader and the jammer plays the role of the follower. After the leader makes an action decision, the follower chooses its own behavior strategy according to the leader's action. In this process, the follower will have an inaccurate observation of the leader's action.

[0076] The present invention models this imprecise observation as the interference machine's transmission power P s and the frequency hopping period T, and introduces the observation error factor ε to describe this observation error, namely: and are the observed values ​​of the transmitter's transmission power and frequency hopping period by the jammer, respectively. Therefore, the utility function of the jammer is defined as:

[0077]

[0078] Here, in order to describe the utility of the communicating party and the interfering party more intuitively and accurately, the present invention uses the expected throughput of the communication channel to model the utility function.

[0079] After the jammer observes the transmitter's strategy, it will formulate its own jamming strategy accordingly. However, due to the existence of the previous observation error, the jammer's decision-making is irrational. Under perfect observation, the jammer will adopt the optimal jamming strategy, reflecting complete rationality. However, due to the existence of the jammer's observation error, the strategy inferred by the jammer may deviate from the optimal jamming strategy, making the jammer show limited rationality. Considering the actual application, since the jammer has decided to interfere, it will inevitably interfere at all costs. Therefore, in the game, the jammer's transmission power P J Will directly take P Jmax Therefore, the communication party needs to detect the jammer for a certain time T E To model the bounded rationality, a zero-mean Gaussian perturbation T is introduced here. E0 Modeling bounded rationality, i.e. is the strategy adopted by the jammer under limited rationality. Therefore, the utility function of the communication party is defined as:

[0080]

[0081] Since throughput is used as the utility function, the jammer and the transmitter have different goals in the optimization problem. The jammer hopes to interfere with the signal transmission of the communicator, so it hopes to minimize the expected communication throughput, while the communicator hopes to maximize the expected throughput, so both the communicator and the jammer hope to maximize their utility functions.

[0082] The optimization problem of the jammer as a follower is described as follows:

[0083] μ J (P J * ,T E * ,P S * ,T * )≥μ J (P J ,T E ,P S * ,T * )st 0≤P J ≤P Jmax ,0≤T E ≤T (4)

[0084] In the previous introduction, it has been determined that the jammer power is P Jmax , so in this optimization problem, the jammer needs to determine the optimal detection time T E * .

[0085] As a leader, the optimization problem of the transmitter is described as follows:

[0086] μ S (P J * ,T E * ,P S * ,T * )≥μ S (P J * ,T E * ,P S ,T)st 0≤P S ≤P Smax ,0≤T≤T max (5)

[0087] The transmitter determines the optimal transmit power P in this interference problem S * and frequency hopping period T * .

[0088] To solve the master-slave game model, the reverse induction method is used. First, the jammer parameter P J and T E In the previous discussion, it can be determined that the jammer power is P Jmax ,Right now:

[0089] P J* = P Jmax (6) For the convenience of calculation, first combine like terms and simplify μ J and let:

[0090]

[0091] It can be seen here that A < B. Substitute it into μ J to get:

[0092]

[0093] For the detection probability Perform Taylor expansion on it to get:

[0094]

[0095] Substitute P d into μ J and simplify to get:

[0096]

[0097] By observing the above formula, it can be found that μ j is a quadratic function of T E . Since A < B, it can be known that is less than 0. According to the properties of quadratic functions, it can be known that μ j has a unique maximum value. When and only when T E takes the value of the axis of symmetry, μ j takes the maximum value. According to the expression of the axis of symmetry of the quadratic function, we can get:

[0098]

[0099] When considering the observation error, the signal detection time of the jammer becomes:

[0100]

[0101] Next, discuss the parameter optimization problem of the communication party. In the master-slave game, the communication party plays the role of the leader. In this part, the optimal communication party parameters to be found are the transmitter power P S * and the hopping period T * . First, substitute the previously obtained T E * into the utility function μ S of the communication party and simplify to get:

[0102]

[0103] Let μ S Taking the first-order partial derivative of T, we get:

[0104]

[0105] Observing the expression of the first-order partial derivative, we can see that the graph of the expression is similar to the graph of a quadratic function with an opening downward. The graph has two intersections with the X-axis, which are the two zeros of the function. So we can determine μ S The trend of is to decrease first, then increase, and then decrease again, so it can be determined that the maximum value of the function is obtained at the zero point on the right side of the first-order derivative. Let Eliminate both sides of the equation Then simplify it to get:

[0106]

[0107] Observing the above expression, we can find that this is a typical quadratic equation. We can use the root-finding formula to find the solution of the equation. Here we should take the larger solution. Substitute the coefficients in equation (14) and let:

[0108]

[0109]

[0110] Solving equation (13) using the root-finding formula of a quadratic equation yields:

[0111]

[0112] Since a<0, we can get T * The expression is:

[0113]

[0114] When considering the limited rationality of the jammer, the jammer can use the signal detection time Instead of T E * , the estimated detection probability at the transmitter S becomes In this case, the transmitter's utility function becomes:

[0115]

[0116] In this case, μ′ s The third term of contains a zero-mean Gaussian random variable, which makes it possible to derive T and P s The closed-form solution of T is very difficult. E After expectation, it can be found that the average value of the optimal jump period in this case is the solution given in equation (19).

[0117] T * Substituting into formula (12), we get a s μ S Expression. Since μ S The expression is too complicated to obtain the optimal transmitter power P through mathematical derivation. S * Analytical expression of . A genetic algorithm (GA) is used to solve this optimization problem. The following is a brief introduction to the steps of GA;

[0118] 1. Initialize the population

[0119] The initial population is randomly generated in the solution space.

[0120] 2. Calculate population fitness

[0121] Establish a fitness function and calculate the fitness of each individual in the population.

[0122] 3. Select operation

[0123] Apply the selection operator to the population. The purpose of selection is to directly pass on the optimized individuals to the next generation or to generate new individuals through pairing and crossover and then pass on to the next generation. The selection operation is based on the fitness evaluation of individuals in the population. The roulette wheel selection method is used here.

[0124] 4. Coding

[0125] The selected individuals are encoded, and binary encoding is used here. Since the genetic algorithm cannot directly process the parameters of the problem space, the problem to be solved must be represented as a chromosome or individual in the genetic space through encoding.

[0126] 5. Cross

[0127] Apply the crossover operator to the population. The crossover operator plays a core role in the genetic algorithm. First, find the parent and parent generations of the crossover, then randomly generate the crossover position, and perform crossover according to the crossover rate to generate new individuals.

[0128] 6. Mutation

[0129] Apply the mutation operator to the group. That is, change the gene values ​​at certain loci of the individual strings in the group. After the mutation operation, the next generation of the group is finally generated.

[0130] 7. Decoding

[0131] Decode the binary code.

[0132] 8. Termination condition judgment

[0133] The algorithm terminates when the fitness of the best individual reaches a given threshold, or when the fitness of the best individual and the fitness of the group no longer increase, or when the number of iterations reaches a preset number of generations.

[0134] Simulation parameter setting: Maximum transmission power P of the communication party Smax =2W, the maximum power of the interference party P Jmax =5W, background noise power is -50dBm, maximum frequency hopping period of the communication party is T max =50ms, transient time T0 =1ms, number of channels M =32, all channels obey complex Gaussian distribution with 0 mean and unit variance. In the genetic algorithm, the initial population size is 100, the code length is 24, the selection rate is 0.5, the hybridization rate is 0.7, and the mutation rate is 0.001.

[0135] Figure 3 This is a simulation scenario diagram. The transmitter S is located on the midpoint of the line connecting the jammer J and the receiver D. Figure 4-7 The simulation result curves shown are all completed under the following scenarios: the transmitter is 4 km away from the jammer and the receiver, and the distance between the jammer and the receiver is 6 km.

[0136] In the present invention, it is considered that the jammer will interfere with the communication party with the maximum power, and the maximum transmission power of the jammer will affect the utility value of the communication party as follows: Figure 4 As shown in the figure, it can be seen that the utility value of the communication party is not sensitive to the maximum power of the jammer, and as the maximum power of the jammer gradually increases, the sensitivity gradually decreases. From the perspective of the utility function of the communication party, this is because if the power of the jammer is greater than or much greater than the transmit power of the transmitter, no matter how the transmitter increases its transmit power within the maximum power limit, it will not cause a significant change in the signal-to-interference-to-noise ratio, so it will not have a significant impact on the throughput, that is, it will not cause a significant change in the utility value. At this time, the transmitter will choose frequency hopping to deal with the jammer instead of blindly increasing its transmit power.

[0137] Figure 5 The effect of the maximum transmission power of the jammer on the frequency hopping period of the communication party is demonstrated. When the transmitter transmission power is 0.5W, as the maximum interference power of the jammer increases, the frequency hopping period of the communication party gradually decreases. This shows that when the jammer power is much greater than the transmitter power, the transmitter will counteract the interference of the jammer by reducing its own frequency hopping period.

[0138] In the ideal case without considering imprecise observation and bounded rationality, the convergence of the utility value of the communication party is as follows: Figure 6 As shown in the figure, after nearly 40 iterations, the utility value of the communication party is basically stable at around 4.44, and there is a small range of oscillation around it.

[0139] Figure 7 The influence of the observation error of the jammer on its utility value is given. Figure 7 It can be seen that the larger the observation error, the smaller the utility value of the jammer. This is because the error in the jammer's estimation of the transmitter's transmission parameters causes it to deviate from its optimal strategy when making decisions, thereby reducing its utility value. The existence of the jammer's observation error will reduce the jammer's utility value. Based on this, the jammer may not adopt the optimal strategy under the observation, but choose to deviate from the optimal strategy under the observation, showing irrationality.

[0140] Considering bounded rationality, the utility of the communication party is as follows: Figure 8 In this part of the simulation, the detection time T E A zero-mean Gaussian perturbation is added to model bounded rationality. Figure 8 It can be seen that after nearly 40 iterations, the utility value of the communication party is basically stable at around 4.44, and there is a small range of oscillation around it.

[0141] contrast Figure 6 and Figure 8 It can be found that the limited rationality does not affect the convergence of the utility value and the final convergence value, but considering the limited rationality, the utility value has a larger oscillation amplitude after convergence. The reason why limited rationality does not affect the final convergence value is that the modeling of limited rationality is to add a random deviation value to the optimal strategy. The mean of the limited rational strategy is still the optimal value in the center, so it will not affect the convergence value of the utility after multiple iterations.

[0142] Fig. 9 The utility value comparison of the multi-domain game scheme proposed in the present invention with the single-domain game scheme and the multi-domain random scheme. The single-domain game scheme includes the single-time domain game and the single-power domain game. In the single-time domain game scheme, the transmission power P is randomly selected. s , obtain the optimal frequency hopping period T by traversing, and finally use the closed-form solution obtained above to select the optimal signal detection period T E The single power domain solution randomly selects the frequency hopping period T and traverses to obtain the optimal transmission power P s , and then the optimal signal detection period T is obtained through the previous closed-form solution E The multi-domain random scheme randomly selects time domain and power domain parameters. In the simulation of the comparison scheme, the transmitter is moved on the midpoint of the line connecting the jammer and the receiver, starting from the midpoint of the line to a position 12 km away from the jammer and the receiver, and the performance of each scheme is observed.

[0143] observe Fig. 9It can be found that the multi-domain random scheme has the smallest communication party utility value, and the multi-domain game scheme proposed in the present invention has the largest communication party utility value. In the single-domain game scheme, as the distance from the transmitter to the jammer and the receiver increases, the utility values ​​of the single-time domain game scheme and the single-power domain game scheme both decrease, but the stability of the single-power domain game scheme is better than that of the single-time domain game scheme.

[0144] Another embodiment of the present invention further provides a multi-domain wireless communication anti-interference system based on master-slave game, including:

[0145] The utility function and master-slave game model establishment module is used to model the communication party as a leader and the jammer as a follower, and to establish the utility function and the master-slave game model of the communication party and the jammer based on the weighted rate by combining the power domain and the time domain;

[0146] The jammer observation error and finite rationality model establishment module is used to build the jammer observation error model and the jammer finite rationality model according to the jammer's observation error of the communication party's parameters;

[0147] The optimization problem construction and solution module is used to consider the jammer observation error model and the jammer finite rationality model, obtain the optimization problem of the transmitter and the jammer according to the utility function of the communication party and the jammer and the master-slave game model, and use the reverse induction method to solve it, obtain the optimal time domain and power domain parameters of the communication party and the jammer, and use the obtained parameters to control the wireless anti-interference communication process.

[0148] It should be noted that the information interaction, execution process and other contents between the above-mentioned module units are based on the same concept as the method embodiment. Their specific functions and technical effects can be found in the method embodiment part and will not be repeated here.

[0149] The technicians in the relevant field can clearly understand that for the convenience and simplicity of description, only the division of the above-mentioned functional units and modules is used as an example for illustration. In practical applications, the above-mentioned function allocation can be completed by different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiment can be integrated in a processing unit, or each unit can exist physically separately, or two or more units can be integrated in one unit. The above-mentioned integrated unit can be implemented in the form of hardware or in the form of software functional units. In addition, the specific names of the functional units and modules are only for the convenience of distinguishing each other, and are not used to limit the scope of protection of this application. The specific working process of the units and modules in the above-mentioned system can refer to the corresponding process in the aforementioned method embodiment, which will not be repeated here.

[0150] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the present application implements all or part of the processes in the above-mentioned embodiment method, which can be completed by instructing the relevant hardware through a computer program. The computer program can be stored in a computer-readable storage medium, and the computer program can implement the steps of the above-mentioned various method embodiments when executed by the processor. Among them, the computer program includes computer program code, and the computer program code can be in source code form, object code form, executable file or some intermediate form. The computer-readable medium may at least include: any entity or device that can carry the computer program code to the camera device / terminal device, recording medium, computer memory, read-only memory (ROM, Read-Only Memory), random access memory (RAM, Random Access Memory), electrical carrier signal, telecommunication signal and software distribution medium. For example, a USB flash drive, a mobile hard disk, a disk or an optical disk.

[0151] In the above embodiments, the description of each embodiment has its own emphasis. For parts that are not described or recorded in detail in a certain embodiment, reference can be made to the relevant descriptions of other embodiments.

[0152] The embodiments described above are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, a person skilled in the art should understand that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features may be replaced by equivalents. Such modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present application, and should all be included in the protection scope of the present application.

Claims

1. A multi-domain wireless communication anti-interference method based on master-slave game, characterized in that: The following steps are involved: The communication party is modeled as a leader and the jammer is modeled as a follower. The power domain and time domain are combined to establish the utility function of the communication party and the jammer and the master-slave game model based on the weighted rate. The utility function of the communication party and the jammer is established based on the weighted rate by combining the power domain and the time domain, specifically including: The probability of the jammer being in the detection state and the jamming state is analyzed, the utility function of the communication party is calculated according to the Shannon formula, and the utility function of the jammer is established according to the master-slave game; The expression of the communication party's utility function is as follows: Among them, μ S Utility for the communication party; is the detection probability under bounded rationality; T0 is the transient process time of frequency hopping; T is the frequency hopping period; T E is the signal detection time; h sd ,h jd ,h sj are the channel gains between transmitter and receiver, jammer and receiver, and transmitter and jammer respectively; δ 2 is the background noise power; P s and P J are the transmitter and receiver powers respectively; is the SINR when interference exists; is the SNR when there is no interference; Detection probability under bounded rationality Calculate as follows: The expression of the utility function of the communication party is divided into three parts, among which the first part It indicates the channel capacity when the jammer detects the transmitting signal of the communication party and implements interference; the second part Indicates the channel capacity when the jammer is in the detection state. When in the detection state, the jammer does not send interference signals; the third part It indicates the channel capacity when the jammer does not detect the signal transmitted by the communication party, and the jammer does not send any interference signal at this time; The utility function of the jammer is as follows: In the formula, is the detection probability of the jammer when there is an observation error, μ J is the jammer utility. In the master-slave game, both the communication party and the jammer want to maximize their utility values. Therefore, the jammer utility function is formally the negative of the communication party utility function. Detection probability in the presence of observation errors Calculate as follows: Aiming at the observation error of the jammer on the communication party parameters, the jammer observation error model and the jammer finite rationality model are modeled; The jammer's observation error of the communication party's parameters includes the jammer's observation error of the transmitter's transmission power P s The observation error of the frequency hopping period T is described by introducing the observation error factor ε, and the jammer observation error model is obtained as follows: In the formula, and are respectively the observed values ​​of the jammer on the transmitter’s transmit power and frequency hopping period; When the finite rational model of the jammer is established, the transmission power P of the jammer is J Take the maximum value P Jmax , only for the detection time T E To model the bounded rationality, a zero-mean Gaussian perturbation T is introduced. E0 Modeling bounded rationality, we obtain The strategies adopted by jammers under bounded rationality; Considering the jammer observation error model and the finite rationality model of the jammer, the optimization problem of the transmitter and the jammer is obtained according to the utility function of the communication party and the jammer and the master-slave game model, and the reverse induction method is used to solve it, and the optimal time domain and power domain parameters of the communication party and the jammer are obtained. The obtained parameters are used to control the wireless anti-interference communication process; The optimization problem of the jammer is described as follows: μ J (P J * ,T E * ,P S * ,T * )≥μ J (P J ,T E ,P S * ,T * )s.t.0≤P J ≤P Jmax ,0≤T E ≤T The transmission power of the jammer P J Take the maximum value P Jmax In this optimization problem, the jammer determines the optimal detection time T E * ; The optimization problem of the transmitter is described as follows: μ S (P J * ,T E * ,P S * ,T * )≥μ S (P J * ,T E * ,P S ,T)s.t.0≤P S ≤P Smax ,0≤T≤T max In this optimization problem, the transmitter determines the optimal transmit power P S * and frequency hopping period T * ; When using the reverse induction method to obtain the optimal time domain and power domain parameters of the communicator and the jammer, the optimization problem of the jammer is solved first. After finding the closed-form solution of the optimal strategy, it is substituted into the utility function of the communicator to solve the optimal action strategy of the communicator.

2. According to claim 1, the multi-domain wireless communication anti-interference method based on master-slave game is characterized in that: The steps of first solving the optimization problem of the jammer, finding the closed-form solution of the optimal strategy, and then bringing it into the utility function of the communication party to solve the optimal action strategy of the communication party are completed using a genetic algorithm.

3. A multi-domain wireless communication anti-interference system based on master-slave game, characterized in that: include: The utility function and master-slave game model establishment module is used to model the communication party as a leader and the jammer as a follower, and to establish the utility function and the master-slave game model of the communication party and the jammer based on the weighted rate by combining the power domain and the time domain; The utility function of the communication party and the jammer is established based on the weighted rate by combining the power domain and the time domain, specifically including: The probability of the jammer being in the detection state and the jamming state is analyzed, the utility function of the communication party is calculated according to the Shannon formula, and the utility function of the jammer is established according to the master-slave game; The expression of the communication party's utility function is as follows: Among them, μ S Utility for the communication party; is the detection probability under bounded rationality; T0 is the transient process time of frequency hopping; T is the frequency hopping period; T E is the signal detection time; h sd ,h jd ,h sj are the channel gains between transmitter and receiver, jammer and receiver, and transmitter and jammer respectively; δ 2 is the background noise power; P s and P J are the transmitter and receiver powers respectively; is the SINR when interference exists; is the SNR when there is no interference; Detection probability under bounded rationality Calculate as follows: The expression of the utility function of the communication party is divided into three parts, among which the first part It indicates the channel capacity when the jammer detects the transmitting signal of the communication party and implements interference; the second part Indicates the channel capacity when the jammer is in the detection state. When in the detection state, the jammer does not send interference signals; the third part It indicates the channel capacity when the jammer does not detect the signal transmitted by the communication party, and the jammer does not send any jamming signal at this time; The utility function of the jammer is as follows: In the formula, is the detection probability of the jammer when there is an observation error, μ J is the jammer utility. In the master-slave game, both the communication party and the jammer want to maximize their utility values. Therefore, the jammer utility function is formally the negative of the communication party utility function. Detection probability in the presence of observation errors Calculate as follows: The jammer observation error and finite rationality model establishment module is used to build the jammer observation error model and the jammer finite rationality model according to the jammer's observation error of the communication party's parameters; The jammer's observation error of the communication party's parameters includes the jammer's observation error of the transmitter's transmission power P s The observation error of the frequency hopping period T is described by introducing the observation error factor ε, and the jammer observation error model is obtained as follows: In the formula, and are respectively the observed values ​​of the jammer on the transmitter’s transmit power and frequency hopping period; When the finite rational model of the jammer is established, the transmission power P of the jammer is J Take the maximum value P Jmax , only for the detection time T E To model the bounded rationality, a zero-mean Gaussian perturbation T is introduced. E0 Modeling bounded rationality, we obtain The strategies adopted by jammers under bounded rationality; The optimization problem construction and solution module is used to consider the jammer observation error model and the jammer finite rationality model, obtain the optimization problem of the transmitter and the jammer according to the utility function of the communication party and the jammer and the master-slave game model, and solve it by reverse induction method to obtain the optimal time domain and power domain parameters of the communication party and the jammer, and use the obtained parameters to control the wireless anti-interference communication process; The optimization problem of the jammer is described as follows: μ J (P J * ,T E * ,P S * ,T * )≥μ J (P J ,T E ,P S * ,T * )s.t.0≤P J ≤P Jmax ,0≤T E ≤T The transmission power of the jammer P J Take the maximum value P Jmax In this optimization problem, the jammer determines the optimal detection time T E * ; The optimization problem of the transmitter is described as follows: μ S (P J * ,T E * ,P S * ,T * )≥μ S (P J * ,T E * ,P S ,T)s.t.0≤P S ≤P Smax ,0≤T≤T max In this optimization problem, the transmitter determines the optimal transmit power P S * and frequency hopping period T * ; When using the reverse induction method to obtain the optimal time domain and power domain parameters of the communicator and the jammer, the optimization problem of the jammer is solved first. After finding the closed-form solution of the optimal strategy, it is substituted into the utility function of the communicator to solve the optimal action strategy of the communicator.

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