A method for selecting jammers and optimizing transmission power in a covert communication network

Abstract

The present invention proposes a covert communication network jammer selection strategy and a transmission power optimization method. In a jammer-assisted covert communication network, in order to simultaneously ensure the concealment and throughput of transmission, the jammer selection and transmission power control strategies adopted are particularly important. The time cost in the channel information perception process under the Rayleigh fading channel is used to maximize the throughput of covert information transmission under the concealment constraint. When the channel state information is unknown, the process of exploring the jammer is modeled as an optimal stopping problem, a jammer selection algorithm is proposed, and the optimal strategy is obtained. The present invention better solves the jammer selection and transmission power control problems in a covert communication network when the channel information is unknown. At the same time, it takes into account the trade-offs between concealment and throughput as well as exploration time and the optimal jammer, and effectively improves the performance of covert transmission compared with other strategies.

Description

Technical Field

[0001] The invention belongs to the field of covert communication resource optimization, and in particular relates to a covert communication network jammer selection strategy and a transmission power optimization method based on channel perception. Background Art

[0002] The serious problem of information leakage has received considerable attention recently, especially in the field of wireless communication. Due to the inherent openness of the communication medium, the signal can be received by any node in the network. Traditional encryption technology and physical layer security technology can only guarantee the security of information. However, due to the development of signal analysis and positioning technology, once the signal is discovered, the consequences will be disastrous. Covert communication is a technology with high security. It hides the signal to make it less likely to be discovered.

[0003] In recent years, achieving positive rate covert communication has been a very important research direction. Many studies have shown that creating uncertainty about the signal in malicious monitoring nodes helps improve the performance of covert communication. Many works have proven that introducing a friendly jammer to create artificial noise is effective in achieving a positive covert rate. The interference signal generated by the jammer makes it difficult for malicious monitoring nodes to distinguish whether the received signal is from the transmitter or the jammer, which is conducive to improving the covert performance. However, the interference signal will also cause interference to the receiver, and the signal-to-interference-to-noise ratio of the receiver will be seriously reduced. Therefore, in the scenario of jammer-assisted covert communication, how to select the jammer to minimize the negative impact of interference on communication performance while ensuring the concealment constraint is a problem worth studying.

[0004] There are few jammer selection strategies in existing covert communication networks, and there are three problems: one is that most strategies are heuristic and have no optimality guarantee; the second is that channel reciprocity is assumed in fading channels. However, when channel reciprocity is not perfect, that is, when the uplink CSI is not completely equal to the downlink CSI, each jammer cannot evaluate its actual interference to the receiver based on the channel state information from the receiver to the jammer; third, the design of the jammer selection strategy does not consider the optimization of the transmission power. Through the joint design of the jammer selection strategy and the information transmitter power, the covert communication system can achieve better concealment performance. Therefore, in view of the above three problems, the jammer selection problem under incomplete channel information needs to be solved urgently. Summary of the invention

[0005] Aiming at the problem of ensuring both concealment and transmission throughput in a jammer-assisted covert communication scenario, the present invention proposes a covert communication network jammer selection strategy and a transmission power optimization method based on channel perception. The method obtains channel state information through jammer exploration to maximize the concealment rate.

[0006] A covert communication network jammer selection strategy and transmission power optimization method, the specific steps are as follows:

[0007] Step 1, describe the jammer selection strategy and transmission power optimization problem in the jammer-assisted covert communication network;

[0008] Step 2: Establish a mathematical model for joint optimization of jammer selection strategy and transmit power when channel state information is known. This problem includes optimization objectives, optimization variables, and constraints.

[0009] Step 3: Solve the optimization problem in step 2. By deriving the mathematical relationship between the optimization variables, this mixed integer nonlinear programming problem is decomposed into two sub-problems, and finally the optimal solution is obtained;

[0010] Step 4: When the channel state information is unknown, the optimal strategy obtained in step 3 when the information is known is used to model the jammer exploration process as an optimal stopping problem.

[0011] Step five, design a jammer selection algorithm under jammer channel exploration, including selection criteria and exploration order, and use the algorithm to obtain the optimal strategy.

[0012] Compared with the prior art, the present invention has the following advantages:

[0013] 1. The present invention can better solve the trade-off between concealment and throughput in a jammer-assisted covert communication network, and solve the jammer selection strategy considering the channel state information acquisition time;

[0014] 2. Through the joint design of jammer selection strategy and information transmitter power, the covert communication system can achieve better concealment performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a scene schematic diagram and patent flow chart in the present invention. DETAILED DESCRIPTION

[0016] like Figure 1 As shown, a covert communication network jammer selection strategy and a transmission power optimization method of the present invention include the following steps:

[0017] Step 1, describe the jammer selection strategy and transmission power optimization problem in the jammer-assisted covert communication network;

[0018] In a covert communication network, the sending node wants to communicate with the receiving node without being detected by the malicious monitoring node. At the same time, there are K friendly jammers that can emit noise signals to help the sending node confuse the malicious monitoring node. The set of friendly jammers is Assume that all nodes have only one antenna and work in half-duplex mode. We consider the channel to be a Rayleigh fading channel, the transmitting node and the receiving node, the transmitting node and the malicious monitoring node, and the selected jammer J k and the receiving node and the selected jammer J k The channel gains between and malicious monitoring nodes are expressed as as well as Where h represents the channel fading coefficient, which obeys the standard complex Gaussian distribution, d represents the distance between nodes, and α is the large-scale path loss coefficient.

[0019] Assume that a transmission time slot consists of a codeword length n, and the time slots of all nodes are completely synchronized. The sending node and the selected jammer use independent Gaussian codebooks with the same distribution, which are composed of standard complex Gaussian random variables. In order to successfully decode, the sending node and the receiving node share a secret codebook that the malicious monitoring node does not know. The sending node transmits information to the receiving node with a certain probability. If the sending node needs to transmit, it will transmit with a power of P a The information is mapped to a symbol sequence x = [x[1], x[2], ..., x[n]].

[0020] The selected jammer is always P J The power of the interference signal sequence v = [v[1], v[2], ..., v[n]]. The noise at the malicious monitoring node and the receiving node is additive Gaussian white noise, which is represented by a set of zero-mean complex Gaussian random variable sequences, which are respectively n w =[n w [1],n w [2],...,n w [n]] and the power is n b =[n b [1],n b [2],...,n b [n]]. Therefore, the signal vector y observed at the malicious monitoring node w =[y w [1],y w [2],...,y w [n]] is

[0021]

[0022] Where H1 represents the transmitting node transmitting a signal at this time slot, and H0 represents the transmitting node not transmitting a signal at this time slot. Similarly, the signal vector y observed at the receiving node is b =[y b [1],y b [2],...,yb [n]] is

[0023]

[0024] Malicious monitoring nodes receive signal vector y w The judgment of whether the transmitting node transmits is a binary hypothesis test. We use and Denotes the probability of H0 and H1. There are two types of detection errors of malicious monitoring nodes: false alarm and missed detection. False alarm is when the malicious monitoring node mistakenly determines that there is a transmission under H0, and missed detection is when the malicious monitoring node mistakenly determines that there is no transmission under H1. Define P FA is the false alarm probability, P MD is the missed detection probability. Therefore, the detection error probability of a malicious monitoring node is The goal of the malicious monitoring node is to construct an optimal detector to minimize P E Following the common assumption, the malicious monitoring node has a full understanding of the network topology, including the location of the nodes and the distance between them, the transmission power P a , P J , Noise Variance and the statistical model of the codebook used by the sending node. In order to ensure the concealment of transmission in any case, we consider the worst case that the malicious monitoring node can always use the optimal detector. We assume that the prior probabilities of H1 and H0 are equal. Therefore, for a given ε, when ξ=P FA +P MD When >1-ε, the implicit degree constraint can be guaranteed to be satisfied.

[0025] In addition to the concealment of transmission, another important performance is the transmission rate. According to Shannon's theorem, the transmission rate is no greater than the channel capacity C = log(1 + γ b ), where γ b is the signal to noise ratio at the receiving node. We assume that the channel capacity is reachable, so the transmission rate is the channel capacity C. Here, we maximize the transmission rate C under the concealment constraint, which is called the concealment rate. In addition to the interference selection strategy, the transmission power P of the transmitting node is also a We consider a centralized strategy where the receiving node selects the jammer and notifies the sending node. Therefore, the sending node can adjust the transmit power according to the jammer selection strategy. The optimization problem of the combined jammer selection strategy and transmit power can be expressed as

[0026]

[0027] This is a mixed integer nonlinear programming problem with 2 feasible solutions. K When K is very large, it is difficult to solve it using an exhaustive search.

[0028] Step 2: Establish a mathematical model for joint optimization of jammer selection strategy and transmit power when channel state information is known. This problem includes the optimization objectives, optimization variables, and constraints as follows:

[0029] In a Rayleigh fading channel, it is assumed that the channel fading coefficient remains constant within a time slot, but changes independently between time slots. In order for the receiving node to adopt the best strategy to maximize the concealment rate, it needs to know the channel state information. and However, in general covert communication scenarios, malicious monitoring nodes do not send signals, and receiving nodes cannot obtain However, for friendly interference, the pilot sequence can be sent to the receiving node in sequence to help it estimate the channel state information. To select the best jammer. Here, we assume is perfect to get the optimal criterion for selecting the jammer.

[0030] Assume that the jammer J k is selected. Since the transmitted signals all obey the complex Gaussian distribution, the signals received by the malicious monitoring node also obey the complex Gaussian distribution:

[0031]

[0032] In general, malicious monitoring nodes know the channel state h aw But only know the instantaneous value of According to the Neyman-Pearson criterion, the optimal test to minimize the error probability of malicious monitoring nodes is the likelihood ratio test:

[0033]

[0034] in, y under H0 w The probability density function of For H1, y w The probability density function of . Using random sequence theory, it can be proved that the likelihood ratio test is equivalent to energy detection. That is, the average received power P w Compared with the threshold λ,

[0035] When the number of codewords in a time slot approaches infinity, that is, n→∞, χ 2n / n approaches 1, then the average received power P w for

[0036]

[0037] Then, the detection error probability at the malicious monitoring node can be derived as

[0038]

[0039]

[0040] Therefore, ξ=P FA +P MD for

[0041]

[0042] From the above formula, we can get that when When ξ is a monotonically decreasing function of λ. ξ is a monotonically increasing function of λ. Therefore, when When ξ is the smallest, it can be expressed as

[0043] Since the malicious monitoring node knows the channel state h aw The instantaneous value of h, but the sending node only knows h aw The distribution information of ξ * is the error probability of the malicious monitoring node. When considering the concealment of transmission from the perspective of the sending node, we need to consider the probability of h aw The average * :

[0044]

[0045] Then the hidden constraint can be expressed as

[0046] The signal-to-interference-to-noise ratio of the receiving node in a time slot is

[0047]

[0048] Among them, h ab and is a random variable, but the receiving node can obtain each time slot h through the pilot sequence ab and The instantaneous value of. Since the transmission rate C is γ b is a monotonically increasing function, so the optimization objective can be transformed into maximizing γ b .

[0049] In summary, the joint optimization mathematical model of jammer selection strategy and transmission power when the channel state information is known is:

[0050]

[0051] Step 3: Solve the optimization problem in step 2. By deriving the mathematical relationship between the optimization variables, this mixed integer nonlinear programming problem is decomposed into two sub-problems. The process of finally obtaining the optimal solution is as follows:

[0052] In formula (12), the optimization target γ b and hidden constraints It's all about jammer selection strategyJ k and the transmission power P a We can derive J k With P a The functional relationship between them decouples this optimization problem into two sub-problems. One is given the jammer selection strategy J k , satisfying the constraints and making γ b The largest P a , and the other is to optimize the jammer selection strategy J k To maximize γ b .

[0053] Substituting formula (10) into the hidden constraint (12), we can get P a The constraint is

[0054]

[0055] Due to γ b YesP a An increasing function, when P a The value is the maximum value that satisfies the hidden constraint γ b Maximum. Bringing it into the optimization problem can eliminate the constraints and turn it into an unconstrained optimization problem:

[0056]

[0057] in definition Considering that the noise power is very small compared to the interference power, we take Approximate value of The optimal jammer selection strategy can be expressed as

[0058]

[0059] This means that the optimal strategy is to select the jammer with the largest ratio between the average interference power to the monitoring node and the instantaneous interference power to the receiving node under appropriate power control.

[0060] Step 4: When the channel state information is unknown, the optimal strategy obtained in step 3 is used to model the jammer exploration process as an optimal stopping problem as follows:

[0061] Considering the time cost of acquiring channel state information, we divide a time slot into two phases: jammer detection phase and transmission phase. In the jammer detection phase, the jammer sends pilot signals to the receiving node in turn, and the receiving node estimates the To evaluate the current jammer. In the transmission phase, the sending node starts to send a signal, and the selected jammer sends a jamming signal to cover the sending node. The unit time for obtaining the channel state information of a jammer is defined as τ. If m (m≤K) jammers are explored, the receiving node can obtain the channel state information sequence The total exploration time is mτ, and the remaining transmission time is 1-mτ. We can observe that the more jammers to explore, the better the jammer can be selected, but the more time it takes. In addition, the jammer is selected among the explored jammers. Therefore, in order to maximize the covert throughput of the transmission phase, we first optimize the number of jammers to explore. Here it is assumed that the already explored jammers cannot be selected again.

[0062] After exploring a jammer, we can decide whether to stop by comparing the throughput of stopping exploration and continuing exploration. Therefore, optimizing the number of jammers to explore can be formulated as an optimal stopping problem. When m (m ≤ K) jammers are explored, the maximum throughput that can be obtained is:

[0063]

[0064] where η m is the throughput obtained by stopping exploration, and we can get:

[0065]

[0066] is the average throughput obtained by exploring the next jammer, and they all depend on the choice of the jammer and the transmit power. Therefore, the optimal number of jammers to be explored is

[0067]

[0068] Since the number of distractors that can be explored is upper bounded by K, the selection of distractors is a finite optimal stopping problem. is the expected throughput from m+1 to K, which can be calculated by reverse induction. Specifically, since we must stop at the last jammer, we can first deduce J K expectations, that is based on We can also calculate J K-1 expectations, that is And so on back to the first jammer. Specifically,

[0069]

[0070] in, Ei(x) is the exponential integral function. The equation transformation (*) is because Equivalent to But m=1,2,...,K-1. The special value of ω K =∞.

[0071] Step 5: Design a jammer selection algorithm under jammer channel exploration, including selection criteria and exploration order. The process of using the algorithm to obtain the optimal strategy is as follows:

[0072] Based on the optimal solution obtained in step 3, we can use As the selection criterion of the jammer, it can be obtained after obtaining the pilot signal. k The concealed throughput is In order to make the throughput V m To maximize, we should first find Higher jammers. Due to the unknown The probability density function is the same as Bigger jammers are more likely to get bigger Therefore, the order in which we explore the jammers is Based on this, the specific algorithm steps are designed as follows:

[0073] 5.1: Input: jammer set J, noise power of receiving node, unit time τ to obtain channel state information of a jammer, signal-to-interference-to-noise ratio coefficient γ * .

[0074] 5.2: Initialization: Calculate the jammer's And according to this, the jammers are arranged in descending order. Set m=0.

[0075] 5.3: (a) Update m=m+1,

[0076] (b) Receive J m After the pilot sequence, it is estimated

[0077] (c) Based on the channel state information sequence of the explored jammer and the jammer selection rule to calculate η m ,

[0078] (d) Calculation

[0079] 5.4: Determine the stop condition Or whether m=K is satisfied. If so, the algorithm stops; otherwise, execute step 5.3.

[0080] 5.5: Output: Optimal jammer selection strategy J * =J m .

[0081] The above embodiments are only preferred implementation modes of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and equivalent substitutions without departing from the principles of the present invention. These technical solutions after improvements and equivalent substitutions to the claims of the present invention all fall within the protection scope of the present invention.

Claims

1. A covert communication network jammer selection strategy and transmission power optimization method, characterized in that: The following steps are involved: Step 1, describe the jammer selection strategy and transmission power optimization problem in the jammer-assisted covert communication network; The specific process is as follows: In a covert communication network, if the sending node wants to communicate with the receiving node without being detected by the malicious monitoring node, there needs to be K friendly jammers that can emit noise signals to help the sending node confuse the malicious monitoring node. The set of friendly jammers is Assume that all nodes have only one antenna and work in half-duplex mode; consider the channel is Rayleigh fading channel, the transmitting node and the receiving node, the transmitting node and the malicious monitoring node, the selected friendly jammer J k and the receiving node and the selected friendly jammer J k The channel gains between and malicious monitoring nodes are expressed as as well as Where h represents the channel fading coefficient, which obeys the standard complex Gaussian distribution, d represents the distance between nodes, and α is the large-scale path loss coefficient; Assume that a transmission time slot consists of a codeword length n, and the time slots of all nodes are completely synchronized; the sending node and the selected jammer use independent Gaussian codebooks with the same distribution, which are composed of standard complex Gaussian random variables; in order to successfully decode, the sending node and the receiving node share a secret codebook that the malicious monitoring node does not know; the sending node transmits information to the receiving node with a certain probability, and if the sending node needs to transmit, it will transmit with a power of P a Map the information to the symbol sequence x = [x[1], x[2], ..., x[n]]; the selected jammer is always P J The power of the interference signal sequence v = [v[1], v[2], ..., v[n]] is sent; the noise at the malicious monitoring node and the receiving node is additive Gaussian white noise, which is represented by a set of zero-mean complex Gaussian random variable sequences, which are respectively n w =[n w [1],n w [2],…,n w [n]] and the power is n b =[n b [1],n b [2],...,n b [n]]; Therefore, the signal vector y observed at the malicious monitoring node w =[y w [1],y w [2],...,y w [n]] is Where H1 represents the transmitting node transmitting a signal at this time slot, and H0 represents the transmitting node not transmitting a signal at this time slot; similarly, the signal vector y observed at the receiving node is b =[y b [1],y b [2],...,y b [n]] is Malicious monitoring nodes receive signal vector y w The judgment of whether the transmitting node transmits is a binary hypothesis test; and represents the probability of H0 and H1; there are two types of detection errors of malicious monitoring nodes: false alarm and missed detection. False alarm means that the malicious monitoring node mistakenly determines that there is transmission under H0, and missed detection means that the malicious monitoring node mistakenly determines that there is no transmission under H1; define P FA is the false alarm probability, P MD is the missed detection probability; the detection error probability of a malicious monitoring node is The goal of the malicious monitoring node is to construct an optimal detector to minimize P E ; Following the common assumption, the malicious monitoring node has a full understanding of the network topology, including the location of the nodes and the distance between them, the transmission power P a , P J , Noise Variance As well as the statistical model of the codebook used by the sending node; Assuming that the prior probabilities of H1 and H0 are equal, for a given ε, when ξ=P FA +P MD >1-ε, the implicit degree constraint is guaranteed to be satisfied; According to Shannon's theorem, the transmission rate is no greater than the channel capacity C = log(1 + γ b ), where γ b is the signal-to-interference-to-noise ratio at the receiving node; assuming that the channel capacity is reachable, the transmission rate is the channel capacity C, and the transmission rate C is maximized under the concealment constraint, which is called the concealment rate; In addition to the interference selection strategy, the transmit power P of the transmitting node is also a The optimization was carried out and a centralized strategy was established. The receiving node selects the jammer and notifies the sending node. The sending node adjusts the transmission power according to the jammer selection strategy. The optimization problem of the joint jammer selection strategy and transmission power is expressed as We get a mixed integer nonlinear programming problem with 2 feasible solutions. K indivual; Step 2: Establish a mathematical model for joint optimization of jammer selection strategy and transmit power when channel state information is known. This problem includes optimization objectives, optimization variables, and constraints. The specific process is: In a Rayleigh fading channel, it is assumed that the channel fading coefficient remains constant within a time slot, but changes independently between time slots; in order for the receiving node to adopt the best strategy to maximize the concealment rate, it needs to know the channel state information and In general covert communication scenarios, malicious monitoring nodes do not send signals, and receiving nodes cannot obtain However, for friendly interference, the pilot sequence is sent to the receiving node in sequence to help the friendly jammer estimate the channel state information. To select the best friendly jammer; first assume is perfect, to get the optimal criterion for selecting friendly jammers; Assume friendly jammer J k is selected. Since the transmitted signals all obey the complex Gaussian distribution, the signals received by the malicious monitoring node also obey the complex Gaussian distribution: In general, malicious monitoring nodes know the channel state h aw But only know the instantaneous value of distribution; According to the Neyman-Pearson criterion, the optimal test to minimize the error probability of malicious monitoring nodes is the likelihood ratio test: in, y under H0 w The probability density function of For H1, y w The probability density function of the average received power P is obtained by using the random sequence theory to prove that the likelihood ratio test is equivalent to energy detection. w Compared with the threshold λ, When the number of codewords in a time slot approaches infinity, that is, n→∞, χ 2n / n approaches 1, then the average received power P w for Then, the detection error probability at the malicious monitoring node is derived as Therefore, ξ=P FA +P MD for From the above formula, we get that when When ξ is a monotonically decreasing function of λ; when ξ is a monotonically increasing function of λ; therefore, when When ξ is the smallest, it can be expressed as Since the malicious monitoring node knows the channel state h aw The instantaneous value of h, but the sending node only knows h aw The distribution information of ξ * is the error probability of the malicious monitoring node. When considering the concealment of transmission from the perspective of the sending node, it is necessary to consider the probability of h aw The average * : Then the hidden constraint is expressed as The signal-to-interference-to-noise ratio of the receiving node in a time slot is Among them, h ab and is a random variable, but the receiving node obtains each time slot h through the pilot sequence ab and The instantaneous value of b is a monotonically increasing function, so the optimization objective is transformed into maximizing γ b ; The joint optimization mathematical model of jammer selection strategy and transmission power is obtained when the channel state information is known; Step 3: Solve the optimization problem in step 2 by deducing the mathematical relationship between the optimization variables, decompose the mixed integer nonlinear programming problem into two sub-problems, and finally obtain the optimal solution; The specific process is: In formula (12), the optimization target γ b and hidden constraints It's all about jammer selection strategyJ k and the transmission power P a By deriving the function of J k With P a The functional relationship between them decouples this optimization problem into two sub-problems: one is given the jammer selection strategy J k , satisfying the constraints and making γ b The largest P a , and the other is to optimize the jammer selection strategy J k To maximize γ b ; Substituting formula (10) into the hidden constraint formula (12), we get P a The constraint is Due to γ b YesP a An increasing function, when P a The value is the maximum value that satisfies the hidden constraint γ b Maximum; bring it into the optimization problem, eliminate the constraints, and turn it into an unconstrained optimization problem: in definition Considering that the noise power is very small compared to the interference power; Approximate value of The optimal jammer selection strategy is expressed as This means that the optimal strategy is to select the jammer with the largest ratio between the average interference power to the monitoring nodes and the instantaneous interference power to the receiving nodes under appropriate power control; Step 4: When the channel state information is unknown, the optimal strategy obtained in step 3 when the information is known is used to model the jammer exploration process as an optimal stopping problem. The modeling is as follows: Considering the time cost of acquiring channel state information, a time slot is divided into two stages: jammer detection stage and transmission stage. In the jammer detection stage, the jammer sends pilot signals to the receiving node in turn, and the receiving node estimates the to evaluate the current jammer; in the transmission phase, the sending node starts to send a signal, and the selected jammer sends a jamming signal to cover the sending node; the unit time for obtaining the channel state information of a jammer is defined as τ, if m jammers are explored, where m≤K, the receiving node obtains the channel state information sequence The total exploration time is mτ, and the remaining transmission time is 1-mτ. It is observed that the more jammers to be explored, the better the jammer can be selected, but the more time is required. In addition, the jammer is selected from the explored jammers. Therefore, in order to maximize the covert throughput of the transmission phase, it is necessary to optimize the number of jammers to be explored first. It is assumed here that the jammers that have been explored cannot be selected again. After exploring a jammer, the decision to stop is made by comparing the throughput of stopping exploration and continuing exploration; therefore, optimizing the number of jammers to explore is formulated as an optimal stopping problem, where the maximum throughput obtained when m jammers are explored is: where η m The throughput obtained by stopping exploration is: in is the average throughput obtained by exploring the next jammer, which depends on the choice of jammer and the transmit power; therefore, the optimal number of jammers to explore is Since the number of distractors that can be explored is bounded by K, the selection of distractors is a finite optimal stopping problem, is the expected throughput from m+1 to K, calculated by reverse induction. Specifically, since we must stop at the last jammer, we first derive J K expectations, that is based on We can also calculate J K-1 expectations, that is And so on back to the first disruptor; specifically, in, Ei(x) is the exponential integral function. The equation transformation (*) is because Equivalent to But m=1,2,...,K-1, because The special value of ω K =∞; Step 5, design a jammer selection algorithm under jammer channel exploration, including selection criteria and exploration order, and use the algorithm to obtain the optimal strategy; The specific process is as follows: Based on the optimal solution obtained in step 3, As the selection criterion of the jammer, it can be obtained after obtaining the pilot signal. Since a jammer J is selected k The concealed throughput is In order to make the throughput V m To maximize, we should first find Higher jammers; due to the unknown of all jammers The probability density function is the same as Bigger jammers are more likely to get bigger So the order of exploring jammers is Based on this, the specific algorithm steps are designed as follows: 5.1: Input: jammer set J, noise power of receiving node, unit time τ to obtain channel state information of a jammer, signal-to-interference-to-noise ratio coefficient γ * ; 5.2: Initialization: Calculate the jammer's And according to this, the jammers are arranged in descending order, and m=0 is set; 5.3: (a) Update m = m + 1; (b) Receive J m After the pilot sequence, it is estimated (c) Based on the channel state information sequence of the explored jammer and the jammer selection rule to calculate η m ; (d) Calculation 5.4: Determine the stop condition Or whether m=K is satisfied, if so, the algorithm stops; otherwise, execute step 5.3; 5.5: Output: Optimal jammer selection strategy J * =J m .

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