Buffer area-based auxiliary unmanned aerial vehicle relay covert communication method

Abstract

The invention discloses a hidden communication method for assisting unmanned aerial vehicle relay based on a buffer area, and the method achieves the maximization of the average throughput of a system through the introduction of the buffer area, and meets the hidden detection constraint of an eavesdropper. Aiming at the characteristics that the position of an eavesdropper is uncertain and the eavesdropper has mobility, the optimal detection threshold of the eavesdropper is deduced, and then a closed expression for detecting error probability is obtained. In the aspect of system optimization, the concealment constraint is converted into a new form, an optimal transmitting power distribution scheme of an unmanned aerial vehicle relay and a friendly unmanned aerial vehicle jammer is designed, and the balance between the communication concealment and throughput is ensured. Meanwhile, the existence of the optimal unmanned aerial vehicle track is proved by analyzing the upper and lower bounds of the throughput of the system, and the optimal receiving and transmitting strategy of the unmanned aerial vehicle relay is provided by combining the size constraint of the buffer area. Numerical simulation and theoretical analysis results show that the method has remarkable effects in improving the average throughput of the system and guaranteeing the communication concealment.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of wireless communication technology, in particular to a covert communication method based on buffer-aided unmanned aerial vehicle relay, which optimizes the transmission power, trajectory and buffer decision of the unmanned aerial vehicle to improve the concealment and system throughput. BACKGROUND

[0002] In recent years, unmanned aerial vehicle communication technology is widely regarded as a key technology to achieve covert communication due to its high mobility and flexible deployment capability. Covert communication effectively avoids eavesdropping risk by making the communication signal indistinguishable from the environmental noise. As a mobile relay, unmanned aerial vehicles can enhance communication coverage and meet the concealment requirement by dynamically adjusting the position and transmission parameters. However, existing technologies mainly rely on passive optimization strategies, which are difficult to balance concealment and system throughput in real time, especially when facing a position-uncertain mobile eavesdropper, there is a lack of optimization of sending and receiving decisions for buffer-aided unmanned aerial vehicle relay. In addition, the complex concealment constraints and multi-unmanned aerial vehicle cooperative optimization make it difficult to obtain the analytical optimal solution. Therefore, it is of great research value and application prospect to design a covert communication method that considers buffer management, mobile eavesdropper characteristics and multi-unmanned aerial vehicle cooperation to optimize the concealment performance and communication efficiency. SUMMARY

[0003] The present application aims to overcome the shortcomings of existing covert communication technology and proposes a covert communication method based on buffer-aided unmanned aerial vehicle relay, which uses analytical optimization and cooperative strategy to jointly optimize the transmission power, flight trajectory of the unmanned aerial vehicle relay and the transmission and receiving decisions of the buffer, to achieve concealment guarantee and system throughput maximization in the presence of a mobile eavesdropper.

[0004] Therefore, the technical scheme adopted by the present application is as follows: a covert communication method based on buffer-aided unmanned aerial vehicle relay, comprising the following steps:

[0005] Construct a system model to determine the network model, communication model and buffer model, and construct an optimization problem with the goal of maximizing the average system throughput; the system model includes the sender Alice, the receiver Bob, two unmanned aerial vehicles and the eavesdropper Willie whose position changes in real time;

[0006] The optimization problem is divided into three sub-problems, including the unmanned aerial vehicle transmission power optimization sub-problem, the unmanned aerial vehicle flight trajectory optimization sub-problem and the unmanned aerial vehicle relay transmission and receiving decision optimization sub-problem;

[0007] The optimal solution of the unmanned aerial vehicle relay and the interference unmanned aerial vehicle transmission power sub-problem is obtained by transforming the concealment constraint;

[0008] The optimal relative position of the UAV relay and the jamming UAV relative to the eavesdropper is solved by analyzing the upper and lower bounds of the system average throughput.

[0009] The optimal logical rule for the UAV relay to make transmission and reception decisions is solved under the premise of meeting the concealment constraint and the buffer capacity constraint.

[0010] Further, the optimization problem aiming to maximize the system average throughput is:

[0011]

[0012] where P = {P a [i], P r [i], P j [i]} is the transmission power of Alice, the UAV relay and the UAV jammer in the i-th time slot, q = {q r [i], q j [i]} is the coordinate of the UAV relay and the UAV jammer in the i-th time slot, H = {H a [i], H r [i]} and H a [i] ∈ {0, 1} indicates whether Alice transmits information to the UAV relay in the i-th time slot, H r [i] ∈ {0, 1} indicates whether the UAV relay transmits information to Bob in the i-th time slot, N represents the number of time slots, R rb [i] is the transmission rate of the UAV relay to Bob, represents the detection error probability of Willie about the transmission from Alice to the UAV relay, represents the detection error probability of Willie about the transmission from the UAV relay to Bob, ε represents the minimum concealment requirement, P a max , P r max , P j max respectively represent the maximum transmission power of Alice, the UAV relay and the UAV jammer, q r [i] represents the coordinate of the UAV relay in the i-th time slot, q j [i] represents the coordinate of the UAV jammer in the i-th time slot, δ represents the time length of each time slot, V max is the maximum moving speed of the UAV, H a [i] indicates whether Alice transmits information to the UAV relay in the i-th time slot, H r [i] indicates whether the UAV relay transmits information to Bob in the i-th time slot, Q r [i] represents the buffer size of the UAV relay in the i-th time slot, C rrepresents the maximum buffer size of the UAV relay;

[0013] Constraint C1 ensures the concealment requirement when Alice sends information to the UAV relay, constraint C2 guarantees the concealment requirement when the UAV relay sends information to Bob, constraints C3-C5 are the transmit power size constraints, constraints C6 and C7 are the movement constraints of the UAV relay and the UAV jammer respectively, constraint C8 is the transmit-receive decision constraint of the UAV relay, and constraint C9 is the buffer size constraint of the UAV relay.

[0014] The above optimization problem is a mixed integer nonlinear programming (MINLP) problem, which is decomposed into three sub-problems by the present application: a UAV transmit power optimization sub-problem (P2); a UAV flight trajectory optimization sub-problem (P3); and a UAV relay transmission and reception decision optimization sub-problem (P4). Given the current position of the UAV and the transmission and reception decision of the UAV relay, the sub-problem P2 aims to optimize the transmit power of each transmitting node. Firstly, the complex concealment constraints in the original optimization problem are transformed into mathematical inequalities about the transmit power, which are easier to handle. This transformation is based on the analysis of Willie's detection performance and introduces auxiliary constants related to the channel parameters and the preset concealment requirement. Based on these transformed concealment constraints and the maximum transmit power limit of each node itself, the structure of two possible optimal solutions of the transmit power of the UAV relay and the UAV jammer in different communication stages is derived. These optimal solution structures usually represent that the transmitting node uses its maximum allowed power, while the cooperative jamming node uses the minimum jamming power that just meets the concealment requirement, or vice versa, the jamming node uses the maximum power, while the transmitting node uses the maximum power under the premise of meeting the concealment. Finally, the power combination that maximizes the transmission rate in the current time slot is selected.

[0015] Given the transmit power allocation scheme obtained or optimized and the transmission and reception decision of the UAV relay, the sub-problem P3 aims to optimize the three-dimensional flight trajectories of the UAV relay and the UAV jammer. The optimization goal is to adjust the flight path of the UAV to maximize the long-term average system throughput after power optimization. To simplify the analysis, firstly, by considering the geometric upper and lower bounds of the distances of the key links and substituting the power optimization results obtained in the previous step, the complex trajectory optimization objective function related to the instantaneous rate is transformed into a mathematical expression that mainly depends on the relative distance between the UAV and the eavesdropper Willie. Based on this transformed objective function, the existence of the optimal UAV flight trajectory is proved. Further, the analytical expression or its approximate form of the optimal relative distance or position of the UAV relay and the UAV jammer with respect to Willie in different communication modes is derived.

[0016] After the optimization of the transmission power and the flight trajectory of the UAV, the core task of the sub-problem P4 is to determine the operation that the UAV relay should perform at each communication time slot, i.e., whether to select to receive data from Alice and store it in the buffer, or to take data from the buffer and send it to Bob, or to remain silent when the concealment of both links cannot be satisfied. The goal of this decision is still to maximize the long-term average throughput of the system. An important consideration is that, in order to effectively utilize the buffer mechanism, the average data input rate from Alice to the UAV relay should match the average data output rate from the relay to Bob. Based on this, and by comprehensively considering the concealment satisfaction of the current links, the potential maximum achievable transmission rate obtained by the previous two steps of optimization, and the real-time data amount and maximum capacity limit of the buffer in the UAV relay, the optimal logical rule for the transmission or reception decision of the UAV relay is derived. The decision logic is generally as follows: if the concealment of a link cannot be satisfied, no transmission of the link will be performed; if the concealment of both links is satisfied, the potential transmission benefits of the two links will be compared, and the final decision will be made in combination with the state of the buffer.

[0017] The application also provides a buffer-aided UAV relay-based covert communication system, which can perform the buffer-aided UAV relay-based covert communication method described above, and includes a sending end Alice, a receiving end Bob, two UAVs, and a position real-time changing eavesdropper Willie. In the process of covert communication, one UAV acts as a relay UAV, and the other UAV acts as an interference UAV. Alice, Bob, Willie, and the two UAVs are all equipped with a single antenna. Alice realizes covert communication with Bob through the relay UAV, the relay UAV operates in a half-duplex mode, and has a limited buffer capacity. It is assumed that the signal transmission from Alice to the relay UAV and the signal transmission from the relay UAV to Bob will not occur at the same time. The specific position of Willie is uncertain, but it actively moves along a specific trajectory to detect the transmission and reception behavior of the relay UAV in real time.

[0018] The beneficial technical effects of the application include:

[0019] The application constructs a buffer-assisted unmanned aerial vehicle (UAV) wireless relay covert communication framework. Through joint optimization of the transmission power, the UAV trajectory and the UAV relay transmission / reception decision, the end-to-end average system throughput from Alice to Bob is effectively maximized under the premise of strictly meeting the covert communication requirements. The introduction of the buffer enables the UAV relay to actively balance the concealment requirement and the throughput, and adapt to network dynamics. The application enhances the communication concealment performance by accurately modeling and analyzing the active eavesdropper with mobility and location uncertainty. For complex optimization problems, the application derives an optimal or suboptimal analytical solution with a theoretical basis, which provides guidance for system parameter design and ensures the robustness to complex eavesdropping scenarios. The experimental results prove the high efficiency of the proposed scheme in terms of average system throughput and concealment performance. BRIEF DESCRIPTION OF DRAWINGS

[0020] Figure 1 A schematic diagram of the buffer-assisted UAV wireless relay covert communication system model proposed by the application;

[0021] Figure 2 A schematic diagram of the flight trajectory of the eavesdropper Willie (moving along a circular trajectory) and two UAVs in the simulation;

[0022] Figure 3 A dynamic situation of the x-axis coordinate of the UAV relay varying with time (slot) under different buffer capacity conditions in the simulation;

[0023] Figure 4 The relationship between the buffer capacity of the UAV relay and the average system throughput;

[0024] Figure 5 The relationship between the maximum transmission power of Alice and the average system throughput;

[0025] Figure 6 The relationship between the total number of circles of Willie and the average system throughput;

[0026] Figure 7 The relationship between the concealment constraint threshold and the average system throughput;

[0027] Figure 8 The relationship between the flight height of the UAV and the average system throughput;

[0028] Figure 9 The relationship between the maximum jamming power of the UAV jammer and the average system throughput;

[0029] Figure 10 The relationship between the maximum transmission power of Alice and the optimal jamming power;

[0030] Figure 11is the relationship between the distance between Alice and Willie and the optimal interference power;

[0031] Figure 12 is the relationship between the maximum speed of the UAV and the average throughput of the system;

[0032] Figure 13 is the relationship between the noise at the UAV relay and the average system throughput. DETAILED DESCRIPTION

[0033] In order to make the objectives, technical solutions and advantages of the present invention more clear, the specific embodiments of the present invention will be further described in detail below.

[0034] The present invention provides a buffer-assisted UAV wireless relay covert communication method, which includes:

[0035] Step 1: Build a system model, analyze the eavesdropper detection performance and establish stealth constraints.

[0036] Build as Figure 1 The system model shown in Figure 1 includes the transmitter Alice, the receiver Bob, two drones, and the eavesdropper Willie, whose location changes in real time. During covert communication, one drone acts as a relay drone, and the other acts as a jammer drone. Alice, Bob, Willie, and the two drones are all equipped with a single antenna. Alice communicates covertly with Bob via the relay drone, which operates in half-duplex mode and has a limited buffer capacity. It is assumed that signal transmission from Alice to the relay drone and from the relay drone to Bob do not occur simultaneously. Willie's specific location is uncertain, but he actively moves along a specific trajectory to detect the relay drone's transmission and reception behavior in real time.

[0037] The present invention uses a three-dimensional Cartesian coordinate system for system modeling. The drone is operating at a fixed height H, and the remaining nodes are located on the ground. Therefore, the coordinates of Alice and Bob are represented as q a =[0,y a ,0] T and q b =[x b ,y b ,0] T To simplify the analysis and maintain generality, the total flight time T is divided into N time slots, each with a fixed duration of δ. The coordinates of the relay UAV in time slot i are denoted as q r [i]=[x r [i],y r [i],H] T, the coordinate of the interfering UAV in time slot i is denoted as qj[i] = [x j [i], y j [i], H] T , where i ∈ {1, …, N}. In each time slot, the flight distance of the relay UAV satisfies ||q r [i+1] - q r [i]|| ≤ δV max , and the flight distance of the interfering UAV satisfies ||q j [i+1] - q j [i]|| ≤ δV max , where V max represents the maximum flight speed of the UAV. The coordinate position of the eavesdropper Willie has uncertainty to the UAV, and the coordinate is denoted as q w [i] = [x w [i] + Δx w , y w [i] + Δy w ] T . x w [i] and y w [i] represent the estimated position of Willie at time slot i, and Δx w and Δy w represent the estimation errors of the horizontal and vertical coordinates, respectively, where and represent the position estimation error of Willie, and the moving distance of Willie at time slot i satisfies ||q w [i+1] - q w [i]|| ≤ δV w , where V w represents the maximum moving speed thereof.

[0038] At time slot i, Alice sends a covert signal to the relay UAV or the relay UAV sends a covert signal to Bob Meanwhile, the interfering UAV transmits an interfering signal to Willie The signals and satisfy E[·] represents the expected value of a variable, although the UAV maintains a high flight altitude, so that the channel from the UAV to the ground can be approximated as a line-of-sight channel, but the covert communication scenario combines the mobility of the UAV and Willie, which inevitably introduces a non-line-of-sight condition. Based on a large number of previous studies, the present application adopts a mixed channel model, which comprehensively considers the large-scale path loss exponent α and the small-scale Rayleigh fading g. The channel gains of the UAV to Alice and Bob can be represented as and where d au [i] = ||q u [i] - q a || and d ub [i] = ||q u [i] - q b ||. The channel gain from Alice to Willie is denoted as where d uw = ||q u [i] - q w [i]||, β denotes the channel power gain corresponding to the reference distance of 1 m, and g is an independent and identically distributed fading coefficient obeying .

[0039] The signals received by the UAV relay and Bob in the covert communication process are denoted as and where P a [i], P r [i], P j [i] denote the transmission power of Alice, the UAV relay, and the UAV jammer, respectively. h jr [i] denotes the channel gain from the UAV jammer to the UAV relay, and variables n r and n b denote the additive white Gaussian noise at the UAV relay and Bob, respectively, and are denoted as and denote the noise size at the UAV relay and the noise size at Bob, respectively. The signal-to-noise ratio at the UAV relay is and the signal-to-noise ratio at Bob is At time slot i, when Alice transmits information to the UAV relay, the covert transmission rate from Alice to the UAV relay can be denoted as R ar [i] = log2(1 + S r [i]).

[0040] In long-distance covert communication, a UAV relay is introduced to improve the communication quality. However, due to the mobility limitation of the UAV and the threat of the mobile eavesdropper Willie, the channel state from the UAV relay to Alice or from the UAV relay to Bob is often poor. At this time, not only the communication quality will be affected, but also the covert signal is easy to be discovered by the eavesdropper. After introducing the buffer, the UAV relay can select to receive or transmit signals according to the channel state and the covert condition. The maximum buffer of the UAV relay is denoted as C r , and the buffer size of the UAV relay at time slot i is denoted as Q r [i]. Then the rate of the UAV relay when transmitting information to Bob at time slot i should be denoted as the current maximum achievable rate log2(1 + Sb [i]) and Q r [i] is the minimum value of R rb [i] = min{log2(l + S b [i]), Q r [i-1] / δ}, where Q r [i] = Q r [i-1] + H a [i]R ar [i] δ - H r [i]R rb [i] δ is the buffer size of the UAV relay at time slot i, satisfying 0 ≤ Q r [i] ≤ C r . R rb [i] denotes the covert transmission rate of the UAV relay to Bob. The variable H a [i] e {0, 1} denotes whether Alice transmits information to the UAV relay at time slot i, 1 for transmission, and vice versa. The variable H r [i] e {0, 1} denotes whether the UAV relay transmits information to Bob at time slot i, 1 for transmission, and vice versa. At time slot i, if neither the information reception nor the transmission of the UAV relay can satisfy the covert condition, then the equation H a [i] = H r [i] = 0 holds. Otherwise, if the reception but not the transmission satisfies the covert condition, then H a [i] = 1, H r [i] = 0, and vice versa. The system average throughput can be expressed as

[0041] Willie performs a binary hypothesis test. For the Alice-to-UAV relay link, Willie receives the signal y aw [i] as:

[0042]

[0043] h jw [i] denotes the channel gain from the UAV jammer to Willie, n w denotes the additive white Gaussian noise at Willie, H a [i] denotes whether Alice transmits information to the UAV relay.

[0044] Willie computes the average received power over l samples as The decision rule is: if T aw [i] < λ aw , then D a [i] = 0; otherwise D a [i] = 1. λaw , D a [i] represents Willie's decision when Alice transmits a signal, average received power T aw [i]:

[0045]

[0046] represents the noise size at Willie

[0047] The probability of false alarm when Willie detects whether Alice transmits information is denoted by , corresponding to the case where Willie decides D a [i] = 0 given H a [i] = 1. The probability of missed detection is denoted by , corresponding to the case where Willie decides D a [i] = 1 given H a [i] = 0. Thus, the probability of detection error for Willie for the transmission between Alice and the UAV relay is

[0048]

[0049] Theorem 1: If the position of Willie is known, the minimum probability of detection error is

[0050]

[0051] where and

[0052] Theorem 2: If the position of Willie is partially known, the integral expression of the minimum probability of detection error is

[0053]

[0054] where and x and y represent the uncertainty of the position of Alice and the UAV jammer, respectively, to Willie. ε w , represent the position estimation error of Willie, the probability density function of X aw [i], and the probability density function of Y jw [i], respectively.

[0055] Theorem 3: If the position of Willie is partially known, the approximate closed-form expression of the minimum probability of detection error is

[0056]

[0057] where, and

[0058] By taking the first and second order derivatives of , we can find that the optimal detection threshold for Willie is:

[0059]

[0060] Substituting the optimal threshold, we can find the final minimum detection error probability for Willie about Alice-to-drone relay transmission is:

[0061]

[0062] Similarly, for the drone relay-to-Bob link, the received signal y rw [i] for Willie is:

[0063]

[0064] H r [i] is whether the drone relay transmits information to Bob.

[0065] For the transmission between the drone relay and Bob, the detection error probability for Willie is:

[0066]

[0067] and

[0068] Similarly, the minimum detection error probability for Willie about drone relay-to-Bob transmission is:

[0069]

[0070] where, The concealment constraint is and and

[0071] Step 2: Construct the optimization problem to maximize the long-term average system throughput and decompose it. The optimization problem is constructed as follows:

[0072]

[0073] where P = {P a [i], Pa [i], P a [i]} are the transmit powers of Alice, UAV relay and UAV jammer at time slot i, q = {q r [i], q j [i]} are the coordinates of UAV relay and UAV jammer at time slot i, H = {H a [i], H r [i]}. Constraint C1 ensures the concealment requirement when Alice transmits information to the UAV relay, and constraint C2 guarantees the concealment requirement when the UAV relay transmits information to Bob. Constraints C3-C5 are the transmit power size constraints. Constraints C6 and C7 are the movement constraints of the UAV relay and the UAV jammer, respectively, where V max is the maximum movement speed of the UAV. Constraint C8 is the transceiving decision constraint of the UAV relay, and constraint C9 is the buffer size constraint of the UAV relay.

[0074] Step 3: Transform the concealment constraints and derive the optimal solution structure of the transmit power for the transmit power optimization sub-problem.

[0075] Fixing the UAV position and the relay decision, the transmit power is optimized as maxH a [i]R ar [i], H r [i]R rb [i], with constraints C1-C5.

[0076] Theorem 4: When H a [i] = 1, constraint C1 can be transformed as P a [i]A1t1≤ P j [i]B1(1 + t1), where t1 is a constant related to ε. When H r [i] = 1, constraint C2 can be transformed as P r [i]A2t2≤ P j [i]B1(1 + t2), where t2 is a constant related to ε. At this time, the optimal solution when H a [i] = 1 can be obtained as:

[0077]

[0078] represent the optimal transmission power of Alice, the optimal transmission power of the UAV jammer, the derived maximum transmission power of the UAV jammer, and the derived maximum transmission power of Alice, respectively.

[0079] The optimal solution when H r [i] = 1 is:

[0080]

[0081] respectively denote the optimal transmit power of Alice, the optimal transmit power of the UAV jammer, the optimal transmit power of the UAV relay, the derived maximum transmit power of the UAV relay, and the derived maximum transmit power of the UAV jammer.

[0082] Step 4: For the UAV flight trajectory optimization subproblem, the existence of the optimal UAV flight trajectory is proved by analyzing the upper and lower bounds of the system average throughput expression, and the optimal relative positions of the UAV relay and the UAV jammer with respect to the eavesdropper are solved.

[0083] Fixed transmit power and relay decision, optimize UAV trajectory The constraints are C1, C2, C6, and C7.

[0084] Theorem 5: The objective function can be transformed into: where and Thus, the optimal position of the UAV can be obtained.

[0085] Step 5: For the UAV relay transmission and reception decision optimization subproblem, the optimal logic rule for the UAV relay to make transmission / reception decisions is derived under the premise of meeting the concealment constraint and the buffer capacity constraint.

[0086] Optimize UAV relay decision The constraint is D r = D b , C1, C2, C8, and C9. respectively denote the transmission rate from Alice to the UAV relay and the transmission rate from the UAV relay to Bob that have been determined, D r , D b respectively denote the throughput from Alice to the UAV relay and the throughput from the UAV relay to Bob.

[0087] Theorem 7: When the buffer constraint C9 is not considered, the transmission and reception decisions are:

[0088]

[0089] Corollary 1: When the buffer constraint C9 is considered, the transmission and reception decisions are:

[0090]

[0091] ρ denotes the decision threshold.

[0092] Figure 2The flight trajectories of the eavesdropper Willie (moving along a circular trajectory) and two UAVs are shown in a simulation, where the UAV jammer approximately follows the movement of Willie, and the UAV relay moves back and forth between Alice and Bob. Figure 3 The dynamic situation of the x-axis coordinate of the UAV relay varying with time (slot) under different buffer capacity conditions is shown, which shows that the buffer capacity affects the time for the UAV relay to stay above Alice or Bob.

[0093] Figures 4 to 13 The influence of the scheme proposed in the application on the average system throughput under different parameters (such as the maximum transmission power of Alice, the buffer size of the UAV relay, the total number of circles of Willie, the concealment constraint threshold, the flight height of the UAV, the maximum jamming power of the UAV jammer, the maximum flight speed of the UAV, and the noise power of the receiver) is compared, and the performance is compared with that of a benchmark scheme such as random decision. The experimental results show that the introduction of the joint optimization scheme and the buffer mechanism proposed in the application can effectively improve the average system throughput and guarantee the communication concealment, and is superior to the benchmark scheme under various parameter changes.

[0094] The above described is the specific embodiment of the application and the technical principle used, if the change is made according to the concept of the application, the function generated still does not exceed the spirit covered by the specification and drawings, and still should belong to the protection scope of the application.

Claims

1. A covert communication method based on buffer-assisted drone relay, characterized in that: The following steps are involved: Build a system model, determine the network model, communication model, and buffer model, and formulate an optimization problem with the goal of maximizing the average system throughput. The system model includes the sender Alice, the receiver Bob, two drones, and the eavesdropper Willie, whose position changes in real time. The optimization problem is decomposed into three sub-problems, including the UAV transmission power optimization sub-problem and the UAV flight trajectory optimization sub-problem; The sub-problem of optimizing the UAV relay transmission and reception decision; By transforming the stealth constraints, the optimal solutions to the transmission power subproblems of UAV relay and jamming UAV are obtained; By analyzing the upper and lower bounds of the system's average throughput, the optimal relative positions of the drone relay and jamming drone relative to the eavesdropper are solved; Under the premise of satisfying the concealment constraints and buffer capacity constraints, the optimal logical rules for the transmission and reception decisions of the UAV relay are solved.

2. The covert communication method based on buffer-assisted drone relay according to claim 1, characterized in that: The optimization problem aimed at maximizing the average system throughput is: Where P = {P a [i],P r [i],P j [i]} is the transmission power of Alice, UAV relay and UAV jammer in time slot i, q = {q r [i],q j [i]} is the coordinate of the UAV relay and UAV jammer in time slot i, H = {H a [i],H r [i]}, H a [i]∈{0,1} indicates whether Alice transmits information to the drone relay in time slot i, H r [i]∈{0,1} indicates whether the UAV relay transmits information to Bob in time slot i, N indicates the number of time slots, R rb [i] represents the transmission rate from the drone to Bob, represents the probability of Willie’s detection error in relaying from Alice to the drone, represents the probability of Willie’s detection error regarding the transmission relayed from the drone to Bob, ε represents the minimum stealth requirement, They represent the maximum transmission power of Alice, UAV relay, and UAV jammer, respectively, and q r [i] represents the coordinates of the drone relay in time slot i, q j [i] represents the coordinates of the UAV interference in time slot i, δ represents the duration of each time slot, V max is the maximum moving speed of the UAV, H a [i] indicates whether Alice transmits information to the UAV relay in time slot i, H r [i] indicates whether the UAV relay transmits information to Bob in time slot i, Q r [i] represents the size of the UAV relay i time slot buffer, C r Indicates the maximum buffer of the drone relay; Constraint C1 ensures the concealment requirement when Alice sends information to the drone relay, constraint C2 ensures the concealment requirement when the drone relay sends information to Bob, constraints C3-C5 are transmission power constraints, constraints C6 and C7 are the mobility constraints of the drone relay and drone jammer respectively, constraint C8 is the transmission and reception decision constraint of the drone relay, and constraint C9 is the buffer size constraint of the drone relay.

3. The covert communication method based on buffer-assisted drone relay according to claim 2, characterized in that: The UAV transmission power optimization sub-problem is: fix the UAV position and relay decision, optimize the transmission power maxH a [i]R ar [i],H r [i]R rb [i], constrained to C1-C5, R rb [i] represents the transmission rate from the drone to Bob, R ar [i] Covert transmission rate from Alice to the drone relay.

4. The covert communication method based on buffer-assisted drone relay according to claim 3, characterized in that: When H a The optimal solution when [i] = 1 is: They represent Alice’s optimal transmission power, the optimal transmission power of the UAV jammer, the derived maximum transmission power of the UAV jammer, and Alice’s derived maximum transmission power respectively; When H r The optimal solution when [i] = 1 is: They represent Alice’s optimal transmission power, the optimal transmission power of the UAV jammer, the optimal transmission power of the UAV relay, the derived maximum transmission power of the UAV relay, and the derived maximum transmission power of the UAV jammer, respectively.

5. The covert communication method based on buffer-assisted drone relay according to claim 2, characterized in that: The UAV flight trajectory optimization sub-problem is: fixed transmission power and relay decision, optimize the UAV trajectory The constraints are C1, C2, C6, C7, α represents the path loss exponent, d ar , d jr , d rb , d jb , respectively represent the noise at the drone relay, the noise at Bob, the distance between Alice and the drone relay, the distance between the drone jammer and the drone relay, the distance between the drone relay and Bob, and the distance between the drone jammer and Bob.

6. The covert communication method based on buffer-assisted drone relay according to claim 5, characterized in that: The objective function of the UAV flight trajectory optimization sub-problem can be transformed into: Where t1, t2 are constants related to ε, as well as This results in the optimal position of the drone.

7. The covert communication method based on buffer-assisted drone relay according to claim 2, characterized in that: The UAV relay transmission and reception decision optimization sub-problem is: Optimize the UAV relay decision Constraint D r =D b ,C1,C2,C8,C9, They represent the transmission rates from Alice to the drone relay and from the drone relay to Bob, respectively. r , D b They represent the throughput from Alice to the drone relay and the throughput from the drone relay to Bob, respectively.

8. The covert communication method based on buffer-assisted drone relay according to claim 7, characterized in that: The optimal logical rule for the UAV relay to make transmission and reception decisions is: Without considering the buffer constraint C9, the transmission and reception decisions are: When considering the buffer constraint C9, the transmit and receive decisions are: ρ represents the decision threshold.

9. A covert communication system based on a buffer-assisted drone relay, characterized by: The covert communication method based on buffer-assisted drone relay as described in any one of claims 1 to 8 can be executed, comprising: a sending end Alice, a receiving end Bob, two drones, and an eavesdropper Willie whose position changes in real time.

Images