A probabilistic jamming UAV-assisted wireless covert communication method and system

Abstract

The present invention discloses a probabilistic jamming UAV-assisted wireless covert communication method and system, comprising the following steps: constructing a transmission model and a communication process of the communication system; obtaining a signal received by a UAV, a forwarded signal of the UAV, and a forwarding amplification factor according to the transmission model and the communication process; during the signal forwarding process, a detector determines whether the UAV has signal forwarding by analyzing the transmitted signal of the UAV; the detector performs a binary hypothesis test based on the received signal, and obtains Willie's two detection error probability expressions according to the Neyman-Pearson optimal decision rule; constructing an optimization problem based on the effective concealment rate that can be obtained by the destination node under the condition that concealment constraints are met, and solving the optimization problem to obtain the maximized concealment rate; designing a source node function so that it sends probabilistic interference to confuse the detector's detection, thereby assisting the transmission of secret information, improving system performance through concealment performance constraints, and maximizing the final concealment rate that can be obtained.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communications, and in particular relates to a probabilistic jamming UAV-assisted wireless covert communication method and system. Background Art

[0002] With the rapid development of wireless network technology, modern communications, especially wireless communication systems, are experiencing rapid growth. Wireless communication encompasses the entire process from signal generation to reception, including modulation, transmission, propagation, reception, demodulation, and decoding, effectively meeting the needs of personal communication and information acquisition. However, due to the broadcast nature of wireless communication transmission and the complexity of the wireless communication environment, information in communications is vulnerable to security threats such as malicious eavesdropping, spoofing, and tampering, posing significant challenges in terms of communication confidentiality and reliability.

[0003] Existing solutions to wireless communication security primarily rely on application-layer encryption and encapsulation mechanisms, encrypting secret information to achieve security. However, these solutions face challenges in terms of concealing the communication itself and computational complexity. Therefore, as a complementary solution, physical-layer security technologies can achieve effective secure channels without encrypting data. Covert communication technologies, in particular, can prevent malicious third parties from eavesdropping on wireless transmissions.

[0004] Covert communication, also known as low-probability-of-detection communication, allows one party to transmit information to another without violating system security policies and preventing the communication signal from being detected by malicious eavesdroppers. The most common covert wireless communication system is the three-node model, which typically includes three roles: the source node, the destination node, and the detector. The relationship between them is shown in the following figure:

[0005] like Figure 1 As shown, the source node must transmit secret information to the destination node while preventing passive detection by the detector. The above model can be expanded to include roles such as relay nodes and jammers to assist in transmission. Existing research on covert communication technology focuses on direct transmission and collaborative transmission. Direct transmission, as in the model shown above, involves the source node directly sending secret information to the destination node. Collaborative transmission involves the source node indirectly sending secret information to the destination node with the assistance of one or more relay nodes. Different choices and the number of relay nodes used can lead to different performance results.

[0006] It's worth noting that to ensure a positive rate for covert communication, current research on covert communication leverages factors such as channel uncertainty, noise uncertainty, and interference signals to reduce the detector's detection performance, thereby significantly improving the stealth of the communication system. The use of interference signals not only impacts legitimate communication processes, but persistent interference also wastes resources. Summary of the Invention

[0007] In order to solve the problems existing in the prior art, the present invention provides a probabilistic interference drone-assisted wireless covert communication method. In view of the diversity of existing wireless covert communication scenarios, a probabilistic interference scheme is used, and friendly drone relays are used for covert communication, which not only reduces the interference to the legitimate communication process, but also reduces resource waste.

[0008] To achieve the above objectives, the present invention adopts a technical solution: a probabilistic jamming drone-assisted wireless covert communication method. The communication system includes a source node, a friendly drone repeater, a destination node, and a detector. The source node indirectly sends secret information to the destination node with the assistance of the drone repeater. The detector passively detects this communication process. The source node uses variable power to send variable noise to confuse the detector's detection, thereby achieving covert transmission. The method includes the following steps:

[0009] Constructing a transmission model and a communication process of the communication system;

[0010] Obtaining a signal received by the UAV, a forwarding signal of the UAV, and a forwarding amplification factor according to the transmission model and the communication process;

[0011] During the signal forwarding process, the detector analyzes the UAV's transmitted signal to determine whether the UAV has forwarded the signal. The detector performs a binary hypothesis test based on the received signal and obtains Willie's two detection error probability expressions based on the Neyman-Pearson optimal decision rule.

[0012] Based on the information transmission process, the detection error probability expression of the detector is obtained, and the effective concealment rate that the destination node can obtain under the concealment constraint condition is satisfied. An optimization problem is constructed and the optimization problem is solved to obtain the maximized concealment rate.

[0013] Furthermore, the signal received by the UAV is:

[0014]

[0015] The UAV's forwarding signal is:

[0016] x u (i) = G[y u (i)]

[0017] The forwarding amplification factor is:

[0018]

[0019] Where δ = 0 means Alice does not send the noise signal X j (i), while δ=1 is the opposite, and its probability is P(δ=1)=ρ, P(δ=0)=1-ρ.

[0020] Furthermore, the transmission power P of the noise signal sent by the source node j In the interval [0,P jmax ] follows a continuous uniform distribution, and the probability density function is as follows:

[0021]

[0022] Among them, f Pj (x) is the noise signal transmission power P of the source node j The probability density function, P jmax It's P j The maximum value of .

[0023] Furthermore, when the detector performs a binary hypothesis test based on the received signal, the detector has two optional hypotheses, H0 and H1, to obtain the detector's received signal. H0 is the null hypothesis, indicating that the detector believes that the source node did not send a signal. H1 is the alternative hypothesis, indicating that the detector believes that the source node sent a signal. Then Willie's received signal is as follows:

[0024]

[0025] Willie uses a ratio detector to judge Alice's transmission behavior. In each time period, Willie's average received power is:

[0026]

[0027] Get Willie's decision rule:

[0028]

[0029] Where τ is the detection threshold chosen by Willie, and D0 and D1 represent the decisions made by Willie under the assumptions H0 and H1, respectively.

[0030] Furthermore, Willie's total error probability is divided into two cases: when τ1>τ2, that is, |h aw | 2 ≥κ, where the value of k is Willie's total probability of error is as follows:

[0031]

[0032] Analyzing the above formula, we can see that the optimal detection threshold τ at Willie is * =τ2, the corresponding minimum test error probability is as follows:

[0033]

[0034] When τ1<τ2, that is, |h aw | 2 When <κ, the total probability of Willie's test error is as follows:

[0035]

[0036] By analyzing the above formula, we can see that the optimal detection threshold τ at Willie is * =τ2, the corresponding minimum detection error probability is 0.

[0037] Furthermore, the optimal detection threshold and minimum detection error probability expressions at Willie are as follows:

[0038]

[0039]

[0040] Then, the average minimum test error probability at Willie is as follows:

[0041]

[0042] in, refers to the average minimum detection error probability at Willie, ρ is the emission probability of the noise signal at Alice, and the value of κ is Among them, P u is the forwarding power of the UAV, β is the wireless channel gain value when the reference distance is 1m, Pjmax is the maximum transmission power of the noise signal transmitted by Alice, dw=||Lu-Lw|| represents the horizontal position difference between the UAV and Willie, H is the hovering height of the UAV, and f | haw | 2 (x) is the channel gain between Alice and Willie |h aw | 2 The probability density function it obeys.

[0043] Furthermore, the optimization problem of the system concealment rate is expressed as:

[0044] Maximize

[0045]

[0046] P s , P u , P j ∈(0, P jmax ),

[0047] ε∈(0,1),

[0048] O≤ρ≤1.

[0049] Among them, C b is the final stealth rate that can be obtained at Bob, Refers to the average minimum detection error probability at Willie, ε is the system concealment requirement, P s 、P j are the powers of Alice’s secret signal and interference signal, respectively, and P u is the forwarding power of the UAV, and ρ is the probability of interference signal transmission at Alice.

[0050] Furthermore, solving the optimization problem to obtain the maximized concealment rate includes:

[0051] Initialize each parameter and set the parameters for iterative calculation;

[0052] The specific iterative process includes two nested loops: the first outer loop adjusts the transmit power P s , each loop increases by 0.01W, the inner loop accumulates the number of iterations and calculates the minimum error rate, where the nested condition judgment: if the minimum error rate meets the covert transmission condition, then save the corresponding number of times and the transmission power P s(t) , that is, the optimal transmission power

[0053] The optimal concealed transmission rate is calculated by combining the concealed transmission rate and the optimal transmission power.

[0054] The present invention also provides a probabilistic interference drone-assisted wireless covert communication system, including a source node, a friendly drone repeater, a destination node and a detector. With the assistance of the drone repeater, the source node indirectly sends secret information to the destination node. At the same time, the source node sends variable artificial noise with varying power to confuse the detector's detection and achieve the concealment of communication; communication is carried out using the above-mentioned probabilistic interference drone-assisted wireless covert communication method.

[0055] Compared with the existing technology, the present invention has at least the following advantages: the present invention flexibly designs the function of the source node, allowing it to send probabilistic interference to confuse the detector to assist the transmission of secret information, thereby improving system performance by constraining the concealment performance and maximizing the ultimate concealment rate that can be achieved;

[0056] A new wireless covert communication scheme is proposed for a drone-assisted probabilistic jamming communication system. This scheme utilizes a probabilistic method to transmit variable-power artificial noise to counteract detection by the detector, effectively improving the overall performance of the system while ensuring stealth. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 It is the basic model for covert communication.

[0058] Figure 2 Schematic diagram of covert communication scenario.

[0059] Figure 3 The total average detection error probability at Willie varies with the probability of interference signal transmission under different UAV forwarding powers;

[0060] Figure 4 is the relationship curve between the total average detection error probability and the UAV transmission power;

[0061] Figure 5 The curve of the maximum concealment rate of the system changing with the probability of jamming signal transmission under three different UAV forwarding powers;

[0062] Figure 6 This is the relationship curve between the system's maximum concealment rate and the system's concealment requirement under different UAV forwarding powers. DETAILED DESCRIPTION

[0063] The present invention uses a probabilistic interference strategy and utilizes friendly drones to assist in covert communication to ensure the security of secret information. Applying the above transmission scheme, a theoretical model of a wireless communication system with four parts, namely, a source node, a friendly drone repeater, a destination node, and a detector, is constructed. Among them, the source node indirectly sends secret information to the destination node with the assistance of the drone repeater, and the detector passively detects this communication process, which is a behavior that the source node does not want. Therefore, the source node uses variable power to send variable noise to confuse the detector's detection, thereby ensuring concealment. For the transmission process, the expression of the detector's detection error probability and the average concealment rate under the given concealment requirements are derived, and the optimization problem is solved to maximize the concealment rate. Simulation data is used to verify that the design scheme of the present invention is feasible and effective.

[0064] Network Model

[0065] Reference for the covert communication scenario studied in this invention Figure 1 and Figure 2 ,There are four roles in the system, namely the source node (Alice), the destination node (Bob) and the detector (Willie) on the ground, and the UAV relay (UAV) hovering at a height H in the air.

[0066] Channel Model

[0067] The LOS link is used in the channel between the UAV and the ground equipment. Without loss of generality, the horizontal positions of the UAV and the ground equipment are defined as: L i =[x i ,y i ](i=a, b, w, u), therefore, the channel gain between the UAV and the ground equipment can be expressed as follows:

[0068]

[0069] Where β represents the wireless channel gain at a reference distance of 1 meter, and ||·|| represents the Euclidean norm. The quasi-static Rayleigh fading channel between ground devices follows a standard normal distribution. For example, the probability density function of the channel gain between Alice and Willie can be expressed as follows:

[0070]

[0071] In addition, the channel noise used is all subject to CN~(0,σ 2 ) with σ 2 Is the additive Gaussian white noise with variance, and the noise at each node also obeys i=u, w, b, with is the additive white Gaussian noise with the corresponding position variance. Alice, Bob, and Willie are equipped with different antennas. Assume that the UAV knows |h ua |、|h ub |、|h uw |, Bob only knows |h ub |, Willie only knows |h uw |,|h ua |、|h ub |、|h uw |represent the channel gains between Alice and UAV, between Bob and UAV, and between Willie and UAV, respectively.

[0072] Communication Process

[0073] First, Alice wants to send secret information to Bob via UAV. Alice’s transmission power is P a , the transmitted signal is X a (i), X a (i)~CN(0,1), the UAV is friendly, so the UAV's amplification and forwarding step can be trusted, where the signal forwarded by the UAV is a linearly scaled version of the received information with G as the scalar, and satisfies:

[0074]

[0075] The signal received by the UAV is:

[0076]

[0077] The UAV's forwarding signal is:

[0078] x u (i) = G[y u (i)]

[0079] The forwarding amplification factor is:

[0080]

[0081] Where δ = 0 means Alice does not send the noise signal X j (i), and δ = 1 is the opposite, and its probability is P(δ = 1) = ρ, P(δ = 0) = 1-ρ. In addition, the transmission power of the noise signal P j is variable, in the interval [0,P jmax ] follows a continuous uniform distribution, and the probability density function is as follows:

[0082]

[0083] Among them, f Pj (x) is the noise signal transmission power P of the source node j The probability density function, P jmax It's P j The maximum value of .

[0084] It is worth noting that this forwarding process will be detected by Willie. Willie determines whether the UAV is forwarding by analyzing the UAV's transmission signal. Of course, Alice hopes that the probability of the communication being detected is extremely small. To this end, Alice transmits artificial noise with variable transmission power while sending secret information to interfere with Willie's detection, which is a probabilistic interference strategy.

[0085] Willie's detection error probability, that is, the probability of Willie making an error in judging whether the UAV is performing the forwarding process.

[0086] (1) Concealment performance, that is, the ability of the system to transmit secret information under concealment constraints.

[0087] (2) Covert rate, that is, the optimal covert transmission that the system can ultimately achieve under the conditions of meeting a series of constraints and restrictions.

[0088] In order to determine whether Alice has sent secret information, Willie will perform a binary hypothesis test based on the received signal. Willie has two optional hypotheses, H0 and H1. H0 is the null hypothesis, indicating that Willie believes Alice did not send a signal, while H1 is the alternative hypothesis. Contrary to H0, H1 indicates that Willie believes Alice did send a signal. Based on these two hypotheses, Willie's received signal can be expressed as follows:

[0089]

[0090] In the present invention, the worst case is considered, that is, Willie knows the complete channel state information. Willie uses a ratio detector to judge Alice's transmission behavior. Therefore, in each time period, Willie's average received power is given by:

[0091]

[0092] According to the Nyman-Pearson optimal decision rule, Willie's total detection error probability can be minimized. Therefore, Willie's decision rule can be obtained:

[0093]

[0094] Where τ is the detection threshold chosen by Willie, and D0 and D1 represent the decisions made by Willie under the assumptions H0 and H1, respectively.

[0095] According to the above analysis, we can derive two expressions of Willie's detection error probability, the false alarm probability P FA = P(D1|H0) and probability of missed detection P MD =P(D0|H1) are:

[0096]

[0097]

[0098] in,

[0099] Since the sizes of τ1 and τ2 are uncertain, the present invention summarizes the total Willie error probability in two cases. When τ1>τ2, that is, |h aw | 2 ≥k, where the value of k is Willie's total probability of error is as follows:

[0100]

[0101] Analyzing the above formula, we can see that the optimal detection threshold τ at Willie is * =τ2, the corresponding minimum test error probability is as follows:

[0102]

[0103] When p1<τ2, that is, |h aw | 2 When <κ, the total probability of Willie's test error is as follows:

[0104]

[0105] By analyzing the above formula, we can see that the optimal detection threshold τ at Willie is * =τ2, the corresponding minimum detection error probability is 0. Based on this, the optimal detection threshold and minimum detection error probability expressions at Willie can be expressed as follows:

[0106]

[0107] Then, the average minimum test error probability at Willie is as follows:

[0108]

[0109] in, refers to the average minimum detection error probability at Willie, ρ is the emission probability of the noise signal at Alice, and the value of κ is Among them, P u is the forwarding power of the UAV, β is the wireless channel gain value when the reference distance is 1m, Pjmax is the maximum transmission power of the noise signal transmitted by Alice, dw=||Lu-Lw|| represents the horizontal position difference between the UAV and Willie, H is the hovering height of the UAV, and f |haw| 2 (x) is the channel gain between Alice and Willie |h aw | 2The probability density function it obeys.

[0110] The present invention uses the concealment requirement ε to measure the concealment of the system. The goal is to transmit secret information covertly, hoping that the average minimum detection error probability is always no less than a set threshold. The concealment constraint can be obtained as:

[0111]

[0112] According to the forwarded signal from the UAV, the received signal and received signal-to-noise ratio at Bob can be obtained as follows:

[0113]

[0114] in, d a =||L u -L a ||, d b =||L u -L b ||, based on which the final concealment rate of the system can be deduced as follows:

[0115]

[0116]

[0117] Since the purpose of communication is to maximize the available concealment rate of the system, the optimization problem of the system concealment rate is expressed as:

[0118] Maximize C b

[0119]

[0120] P s , P u , P j ∈(0, P jmax ),

[0121] ε∈(0,1),

[0122] 0≤ρ≤1.

[0123] Among them, C b is the final stealth rate that can be obtained at Bob, Refers to the average minimum detection error probability at Willie, ε is the system concealment requirement, P s 、P j are the powers of Alice’s secret signal and interference signal, respectively, and P u is the forwarding power of the UAV, and ρ is the probability of interference signal transmission at Alice.

[0124] Use an iterative algorithm to solve the above optimization problem, as shown in Algorithm 1 below.

[0125]

[0126]

[0127] First, initialize each parameter, and then set the relevant parameters for iterative calculation. The specific iterative process includes two nested loops. The first outer loop adjusts the transmit power P s , each loop increases by 0.01W, the inner loop accumulates the number of iterations and calculates the minimum error rate, where the nested condition judgment: if the minimum error rate meets the covert transmission condition, then save the corresponding number of times and the transmission power P s(t) , that is, the optimal transmission power Finally, substituting the optimal transmission power into the formula can obtain the optimal concealed transmission rate.

[0128] Figure 3 The variation of the total average detection error probability at Willie with the probability of interference signal transmission under different UAV forwarding powers is analyzed. Figure 3 It can be clearly seen that the total error detection probability at Willie increases with the increase of the interference signal transmission probability. Figure 4 is the relationship curve between the total average detection error probability and the UAV transmission power. Similarly, three different interference transmission probability values ​​are set. Figure 4 In the figure, it can be observed that when the probability of Alice's interference signal transmission is constant, when the forwarding power of the drone gradually increases, the total detection error probability at Willie gradually decreases. Figure 5 The curve of the maximum concealment rate of the system changes with the probability of interference signal transmission under three different UAV forwarding powers: Figure 5 From the analysis, we can know that the covert transmission rate of the system gradually decreases as the probability of interference signal transmission increases. Figure 6 This is the relationship curve between the maximum concealment rate of the system and the concealment requirement of the system under different UAV forwarding powers. Figure 6 The curve clearly shows that the system's confidentiality transmission rate decreases as the system's concealment requirements increase.

[0129] The above simulation results effectively verify the effectiveness of the scheme proposed in the present invention, verify the theoretical results, and show that the probabilistic interference scheme is one of the best options for maximizing system efficiency.

[0130] The above content is only for explaining the technical idea of ​​the present invention and cannot be used to limit the protection scope of the present invention. Any changes made on the basis of the technical solution in accordance with the technical idea proposed by the present invention shall fall within the protection scope of the claims of the present invention.

Claims

1. A probabilistic jamming UAV-assisted wireless covert communication method, characterized in that: The communication system consists of a source node, a friendly drone relay, a destination node, and a detector. The source node indirectly sends secret information to the destination node with the assistance of the drone relay. The detector passively detects this communication process. The source node uses variable power to send variable noise to confuse the detector, achieving covert transmission. The system includes the following steps: Constructing a transmission model and a communication process of the communication system; Obtaining a signal received by the UAV, a forwarding signal of the UAV, and a forwarding amplification factor according to the transmission model and the communication process; During the signal forwarding process, the detector analyzes the UAV's transmitted signal to determine whether the UAV has forwarded the signal. The detector performs a binary hypothesis test based on the received signal and obtains Willie's two detection error probability expressions based on the Neyman-Pearson optimal decision rule. Based on the information transmission process, the detection error probability expression of the detector is obtained. The effective concealment rate that the destination node can obtain under the concealment constraint is constructed, and the optimization problem is solved to obtain the maximized concealment rate. The optimal detection threshold and minimum detection error probability expressions at Willie are as follows: Then, the average minimum test error probability at Willie is as follows: in, Refers to the average minimum detection error probability at Willie, is the emission probability of the noise signal at Alice, The value of is ,in is the forwarding power of the drone, is the wireless channel gain value when the reference distance is 1m, Pjmax is the maximum transmission power of the noise signal transmitted by Alice, dw = ||Lu - Lw|| represents the difference in horizontal position between the drone and Willie, H is the hovering height of the drone, and f |haw| 2 (x) is the channel gain between Alice and Willie |h aw | 2 The probability density function it obeys.

2. The UAV-assisted wireless covert communication method with probabilistic jamming according to claim 1 is characterized in that: The signal received by the UAV is: The UAV's forwarding signal is: The forwarding amplification factor is: in, Indicates that Alice did not send a noise signal ,and On the contrary, the probability is 、 .

3. The UAV-assisted wireless covert communication method with probabilistic jamming according to claim 1 is characterized in that: The transmission power of the noise signal sent by the source node P j In the interval [0, P jmax ] follows a continuous uniform distribution, and the probability density function is as follows: Among them, f Pj (x) is the noise signal transmission power P of the source node j The probability density function, P jmax It's P j The maximum value of .

4. The UAV-assisted wireless covert communication method with probabilistic jamming according to claim 1 is characterized in that: When the detector performs a binary hypothesis test based on the received signal, the detector has two optional hypotheses, H0 and H1, to obtain the detector's received signal. H0 is the null hypothesis, indicating that the detector believes that the source node did not send a signal. H1 is the alternative hypothesis, indicating that the detector believes that the source node sent a signal. Then Willie's received signal is as follows: Willie uses a ratio detector to judge Alice's transmission behavior. In each time period, Willie's average received power is: Get Willie's decision rule: in, is the detection threshold chosen by Willie, and D0 and D1 represent the decisions made by Willie under the assumptions H0 and H1, respectively.

5. The UAV-assisted wireless covert communication method with probabilistic jamming according to claim 4 is characterized in that: Willie's total test error probability is divided into two cases: when ,Right now When the value of k is , Willie's total probability of error is as follows: Analyzing the above formula, we can see that the optimal detection threshold at Willie is , the corresponding minimum test error probability is as follows: when ,Right now When , Willie's total probability of error is as follows: By analyzing the above formula, we can see that the optimal detection threshold at Willie is , the corresponding minimum test error probability is 0.

6. The UAV-assisted wireless covert communication method with probabilistic jamming according to claim 1 is characterized in that: The optimization problem of the system concealment rate is expressed as: in, is the final stealth rate that can be obtained at Bob, Refers to the average minimum detection error probability at Willie, To conceal the system requirements, 、 are the powers of Alice’s secret signal and interference signal, respectively, and is the forwarding power of the drone, is the probability of interference signal transmission at Alice.

7. The UAV-assisted wireless covert communication method with probabilistic jamming according to claim 1 is characterized in that: Solving the optimization problem to maximize the concealment rate includes: Initialize each parameter and set the parameters for iterative calculation; The specific iterative process includes two nested loops: the first outer loop adjusts the transmit power , each loop increases by 0.01W, the inner loop accumulates the number of iterations and calculates the minimum error rate, where the nested condition judgment: if the minimum error rate meets the covert transmission condition, then the corresponding number of times and transmission power are saved , that is, the optimal transmission power ; The optimal concealed transmission rate is calculated by combining the concealed transmission rate and the optimal transmission power.

8. A probabilistic jamming UAV-assisted wireless covert communication system, characterized in that: The invention comprises a source node, a friendly UAV repeater, a destination node and a detector. With the assistance of the UAV repeater, the source node indirectly sends secret information to the destination node. At the same time, the source node sends variable artificial noise with varying power to confuse the detection of the detector and achieve the concealment of communication. The communication is carried out using the UAV-assisted wireless covert communication method with probabilistic interference as described in any one of claims 1 to 7.

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