Unmanned aerial vehicle covert communication system and method

Abstract

The invention discloses an unmanned aerial vehicle covert communication system and method, and belongs to the technical field of wireless communication, secret communication and unmanned aerial vehicle communication. The unmanned aerial vehicle covert communication system comprises an unmanned aerial vehicle Alice, an eavesdropper Willie and a receiver Bob. The unmanned aerial vehicle covert communication system comprises a wireless channel link from an unmanned aerial vehicle Alice to a receiver Bob and a wireless channel link from the unmanned aerial vehicle Alice to an eavesdropper Willie, the two channels are air-to-ground wireless channels, and channel uncertainty and environmental noise uncertainty exist at the eavesdropper Willie at the same time. The transmitting power and the flight position of the unmanned aerial vehicle are jointly optimized, so that the energy efficiency of covert communication of the unmanned aerial vehicle is improved to the maximum extent, certain communication quality is kept, and the unmanned aerial vehicle can communicate with a receiver. By designing the covert communication of the unmanned aerial vehicle, the limited battery capacity of the unmanned aerial vehicle can be utilized as much as possible while the information security is guaranteed, and the endurance as long as possible is realized. According to the invention, a brand new solution is provided for endurance and safety of unmanned aerial vehicle communication in a complex environment.

Description

Technical Field

[0001] The present invention belongs to the technical fields of wireless communication, confidential communication and unmanned aerial vehicle communication, and in particular relates to a covert communication system and method for unmanned aerial vehicles. Background Art

[0002] Drones have been widely used in military and civilian fields, such as military reconnaissance, remote sensing, rescue operations, and the Internet of Things, due to their small size, low cost, simple and flexible operation, and strong battlefield survivability. At present, the use of drones for auxiliary communications faces two major challenges. On the one hand, since the channel between the drone and the ground terminal is usually considered to be a line-of-sight channel LoS (Line-of-Sight), signal transmission is vulnerable to interception and attack by monitoring personnel. On the other hand, due to the limitation of battery capacity, the energy carried by drones is very limited, which requires minimizing energy consumption while maintaining communication performance. Traditional encryption technology requires high computational complexity, resulting in high energy consumption, and cannot hide transmission behavior, which may not be suitable for drone communications. As an emerging lightweight information security technology, covert communication can solve the above two problems at the same time.

[0003] As a more thorough confidentiality communication technology, covert communication aims to hide the communication behavior itself. Specifically, covert communication introduces uncertainty at the eavesdropper to hide the transmitted signal in the environment or artificial noise, thereby hiding the wireless transmission behavior of the signal sender to the legitimate receiver from the detection of the eavesdropper. Covert communication technology analyzes the detection performance of the eavesdropper through signal detection theory, uses certain strategies or system parameter optimization to reduce the detection probability of the eavesdropper, and then builds a certain covert communication network.

[0004] The present invention considers a practical application scenario, that is, long-term military surveillance of the ground from an aerial platform. Specifically, the monitor dispatches a drone equipped with imaging equipment to monitor the ground area for a long time, and then secretly transmits the imaging results back to the legitimate recipient. Considering the counter-reconnaissance and battlefield deception in military operations, the exposure of the transmission itself alone may pose an unpredictable and serious threat. It is therefore necessary to hide the existence of the transmission behavior so as to covertly feed back continuous information to the ground receiver. In addition, the surveillance actor also hopes to maintain the drone surveillance for as long as possible, which requires energy-efficient drone covert communication. In order to effectively utilize limited resources, it is necessary to strike a balance between service quality and energy consumption. Therefore, it is of great significance to study the energy-efficient covert communication of drones. Summary of the invention

[0005] The present invention aims to solve the problems existing in the prior art and provide a covert communication system based on drone assistance in a wireless communication network and an optimization method for maximizing the drone's concealed energy efficiency. The present invention evaluates the concealment of the system by calculating the probability of false detection and missed detection from the perspective of the eavesdropper, and then deriving the minimum detection error probability; the signal-to-interference-noise ratio and the probability of communication interruption are calculated from the perspective of the receiving end, and the expression of the effective transmission rate is obtained to evaluate the performance of the communication; the concept of energy efficiency is proposed to reflect the trade-off between communication performance and energy consumption, and on this basis, the optimization problem of maximizing concealed energy efficiency is proposed. By jointly optimizing the transmission power and flight position of the drone, the proposed concealed energy efficiency maximization problem is solved while meeting the concealment requirements and ensuring a certain degree of communication service quality.

[0006] A drone covert communication system comprises: a drone Alice, an eavesdropper Willie and a legitimate receiver Bob; the drone is equipped with an imaging device, and the eavesdropper Willie detects transmission in the monitored area; the drone Alice monitors the eavesdropper Willie and communicates with the receiver Bob at the same time; the drone covert communication system comprises a wireless channel link from the drone Alice to the receiver Bob and a wireless channel link from the drone Alice to the eavesdropper Willie, and both the channels from the drone Alice to the receiver Bob and from the drone Alice to the eavesdropper Willie have the properties of air-to-ground wireless channels, and the eavesdropper Willie has both channel uncertainty caused by the inability to estimate channel state information and noise uncertainty caused by random changes in environmental noise.

[0007] Drone Alice, receiver Bob, and eavesdropper Willie are each equipped with an antenna. The flight position of drone Alice is determined by the distance and angle between it and eavesdropper Willie. In the system model, drone Alice monitors eavesdropper Willie and communicates with receiver Bob at the same time. Drone Alice, as the transmitter, monitors the ground facilities for a long time and feeds information back to the intended receiver Bob while ensuring a certain degree of communication performance and will not be discovered by eavesdropper Willie of the ground facilities.

[0008] As a preferred embodiment of the present invention, the air-to-ground wireless channel is an air-to-ground wireless channel having both NLoS and LoS component probabilities, and the path loss of the air-to-ground wireless channel is:

[0009]

[0010] Among them, PL krepresents the path loss between the UAV and the target k, k∈{b,w}, b is the receiver Bob, w is the eavesdropper Willie; d k represents the distance from drone Alice to receiver Bob or eavesdropper Willie, ξ L is the path loss exponent of the LoS channel component, ξ N is the path loss exponent of the NLoS channel component, p k is the probability that a LoS component appears in the two channels from drone Alice to receiver Bob or from drone Alice to eavesdropper Willie, p k Depending on the environmental parameters and the angle between the drone Alice and the receiver Bob or the eavesdropper Willie, the calculation formula is:

[0011]

[0012] Among them, a and B are curve parameters that depend on the communication environment, θ k is the elevation angle of drone Alice relative to receiver Bob or eavesdropper Willie, in degrees. In various application scenarios of drones, the LoS component dominates the NLoS component, so the NLoS component modeling can be ignored.

[0013] As a preferred embodiment of the present invention, there is environmental noise uncertainty at the eavesdropper Willie, where the noise power of the eavesdropper Willie is The noise power at the eavesdropper Willie is log-uniformly distributed. The probability density function of is as follows:

[0014]

[0015] in, Indicates the noise power The probability density function of α represents the uncertainty of the noise. is the nominal noise power, x represents the noise power The possible values ​​of .

[0016] The present invention also claims a method for covert communication of an unmanned aerial vehicle, comprising the following steps:

[0017] (1) Establish a covert communication system for UAVs;

[0018] (2) According to the signal received by eavesdropper Willie in time slot i and the detection strategy of eavesdropper Willie, the total detection error probability of eavesdropper Willie is obtained;

[0019] (3) Based on the total detection error probability of eavesdropper Willie, derive the optimal detection threshold λ of eavesdropper Willie * and the minimum detection error probability ξ min ;

[0020] (4) According to the received signal and signal-to-interference-noise ratio of the receiver Bob, the probability of signal transmission interruption from the drone Alice to the receiver Bob is obtained, and then the effective covert transmission rate from the drone Alice to the receiver Bob and the communication energy efficiency of the drone Alice are obtained;

[0021] (5) By optimizing the position and transmission power of the UAV, the optimization problem of maximizing the concealed energy efficiency is proposed, and then the optimal power under unconstrained conditions is obtained. and optimal location And given the monotonicity of the objective and constraint functions, the feasible position range of the drone Alice is narrowed down to simplify the optimization problem;

[0022] (6) Decompose the simplified optimization problem into two sub-problems and solve the sub-problems;

[0023] (7) Use the alternating optimization method to solve the optimization problem.

[0024] As a preferred embodiment of the present invention, the eavesdropper Willie receives the signal y in time slot i w [i] is:

[0025]

[0026] Among them, P is the transmission power of the drone Alice, H0 means that the drone Alice does not transmit signals, and H1 means that the drone Alice transmits signals. is the complex Gaussian noise at the eavesdropper Willie, is the noise power at the eavesdropper Willie, H aw represents the channel fading of the air-to-ground channel from drone Alice to eavesdropper Willie, h aw is the channel fading coefficient from drone Alice to eavesdropper Willie, p w is the probability of the LoS component in the air-to-ground channel from drone Alice to eavesdropper Willie, and x[i] is the transmitted signal of drone Alice;

[0027] As a preferred embodiment of the present invention, based on the eavesdropper Willie receiving the signal y in time slot i w [i], the detection strategy of the eavesdropper Willie is:

[0028]

[0029] Among them, T w represents the average power received by the eavesdropper Willie, λ represents the detection threshold, D0 and D1 represent the binary decision of the eavesdropper Willie on whether the drone Alice transmits, and n is the total number of channels used.

[0030] As a preferred embodiment of the present invention, under the uniform prior probability assumption of H0 and H1, the sum of the probability of false detection and missed detection is

[0031]

[0032] Where ξ is the total detection error probability of the eavesdropper Willie, P FA =Pr{D1|H0} is the false detection probability of the eavesdropper Willie, P MD =Pr{D0|H1} is the probability of missed detection of the eavesdropper Willie.

[0033] Define P w is the received power at the eavesdropper Willie, According to equations (3) and (6), the total detection error probability ξ is

[0034]

[0035] where dx is |h aw | 2 The differential of dy is the noise power The differential of x is |h aw | 2 The possible values ​​of y are The possible values ​​of .

[0036] As a preferred embodiment of the present invention, the optimal detection threshold λ of the eavesdropper Willie is * and the minimum detection error probability ξ min The calculation includes:

[0037] S3-1: According to formula (7), if ξ=1; if ξ will increase with the increase of λ, thus obtaining the optimal detection threshold λ that minimizes the probability of detection error * Must be in Therefore, for λ in In the interval, the total detection error probability ξ is:

[0038]

[0039] S3-2, the total detection error probability ξ is derived with respect to the detection threshold λ:

[0040]

[0041]

[0042] is a solution where the first-order derivative of ξ with respect to λ is equal to 0. have Thus further obtaining

[0043]

[0044]

[0045] It is thus proved that ξ is a strictly pseudoconvex function of λ if Optimal detection threshold if In summary, the optimal detection threshold λ * for:

[0046]

[0047] in is the solution of equation (11).

[0048] S3-3, according to equation (8) and equation (13), the optimal detection threshold λ * Substituting the total detection error probability ξ into the total detection error probability ξ, the minimum detection error probability ξ of the eavesdropper Willie can be obtained. min for:

[0049]

[0050] As a preferred embodiment of the present invention, the effective concealed transmission rate from the drone Alice to the receiver Bob and the communication energy efficiency of the drone Alice are specifically calculated including the following steps:

[0051] S4-1: Receiver Bob’s received signal y b [i] is:

[0052]

[0053] Among them, n b [i] represents the Gaussian white noise received by the base station, The mean is 0 and the variance is Gaussian normal distribution, is the noise power at the receiver Bob; H ab represents the channel fading of the air-to-ground channel from drone Alice to receiver Bob, h abis the channel fading coefficient from drone Alice to receiver Bob, p b is the probability of the LoS component in the air-to-ground channel from drone Alice to receiver Bob.

[0054] S4-2: Based on formula (16), the signal-to-interference-noise ratio of the receiver Bob is:

[0055]

[0056] Among them, f(d w ,θ w ) is the same as d w and θ w The function defined, θ w is the elevation angle of drone Alice relative to eavesdropper Willie;

[0057]

[0058] L is the distance between the eavesdropper Willie and the receiver Bob, and a and B are curve parameters that depend on the communication environment.

[0059] S4-3: When the transmission rate R of drone Alice is fixed, when the channel capacity is less than the fixed transmission rate, a transmission interruption occurs between drone Alice and receiver Bob. The transmission interruption probability δ from drone Alice to receiver Bob is:

[0060]

[0061] S4-4: Assume that the transmission probability of drone Alice is 1 / 2. Therefore, under the fixed signal transmission rate R, the effective concealed transmission rate R c for:

[0062]

[0063] S4-5: The communication energy efficiency of drone Alice is

[0064]

[0065] As a preferred embodiment of the present invention, the optimization problem is:

[0066]

[0067] Where P≤P m is the maximum transmission power constraint of UAV Alice, P m is the maximum transmission power of drone Alice; and Together they represent constraints on the monitoring quality and flight position of the drone Alice. is the minimum distance allowed between drone Alice and eavesdropper Willie, is the maximum distance allowed between drone Alice and eavesdropper Willie, is the minimum elevation angle of drone Alice to eavesdropper Willie; specifically, the constraint Make sure the drone doesn't get too far away from the monitored eavesdropper Willie. Ensure that the drone Alice can get a good enough view of the eavesdropper Willie. These two points together ensure that the drone Alice has good monitoring quality; Constraint This is to prevent the drone Alice from being visually detected by the eavesdropper Willie when the drone is too close to Willie, and This is because the drone Alice will stay between the eavesdropper Willie and the receiver Bob; in the most common practical scenario we consider, the distance L between Bob and Willie is much larger than Therefore, assuming that in this case ξ min ≥1-∈ is the concealment constraint, ∈ is the tolerable detection probability reflecting the concealment level; R c ≥R m is the transmission rate constraint to ensure a certain communication quality, R m Indicates the minimum effective covert transmission rate required for covert communication.

[0068] As a preferred embodiment of the present invention, in step (5), the optimal power and optimal position under no constraints are obtained, and the communication energy efficiency η and the minimum detection error probability ξ are given. min For the transmission power P and distance d of drone Alice respectively w and the elevation angle θ w The changing trend of , and then simplify and decompose the optimization problem, including:

[0069] S5-1: Given the position of UAV Alice without any constraints, find the optimal transmission power that maximizes the communication energy efficiency of UAV Alice

[0070]

[0071] when When , the communication energy efficiency reaches the maximum value; when When , the communication energy efficiency η increases monotonically with the transmission power P of the drone Alice; when When , the communication energy efficiency η decreases monotonically with the transmission power P of UAV Alice.

[0072] S5-2: Given a transmission power P and without restrictions, if the optimal angle and distance between the drone Alice and the eavesdropper Willie are jointly optimized, then the best position for the drone to maximize communication energy efficiency is the position closest to the receiver Bob on the ground, so,

[0073] For a given transmit power P and elevation angle θ w , the optimal distance between drone Alice and eavesdropper Willie is expressed as This distance is unique and is given by the following equation d w The unique solution of is given by:

[0074]

[0075] Among them, p b (d w ,θ w ) is the probability of the LoS component in the channel between drone Alice and receiver Bob,

[0076]

[0077] The only solution of formula (24) is the optimal distance Therefore, in d w ≤Lcos(θ w ), the communication energy efficiency η increases with the distance d w Monotonically increasing.

[0078] S5-3: At a given transmission power P and distance d w Under the condition of , the optimal elevation angle between drone Alice and eavesdropper Willie is expressed as is unique, given by the following equation θ w The unique solution of is given by:

[0079]

[0080] The only solution of formula (25), namely the optimal elevation angle Therefore, when When the communication energy efficiency η changes with the elevation angle θ w Monotonically decreasing.

[0081] S5-4, minimum detection error probability ξ min is a monotonically decreasing function of P, which is d w is a monotonically increasing function of θ w A monotone decreasing function: The derivation process is as follows:

[0082] According to equations (11) and (14), for The implicit function F(P w ,ξ min )=0, given by:

[0083]

[0084] Because min YesP w function, then both sides of the implicit function are simultaneously w The derivation of is:

[0085]

[0086] According to α>1 and P w >0, we get This makes When min Follow P w Monotonically decreasing.

[0087] Then, when When ξ min P w The first-order derivative of is:

[0088]

[0089] In formula (28), the inequality d>c>0, where x is the independent variable of the integral, c and d are the upper and lower limits of the integral respectively. w >0, yes

[0090]

[0091] Thus, it is deduced When min Follow P w is monotonically decreasing, so ξ min YesP w is a monotonically decreasing function of .

[0092] In addition, Willie's received power P w Specifically:

[0093]

[0094] It can be observed that P w is a monotonically increasing function of P, which is d w is a monotonically decreasing function of θ w is a monotonically increasing function. Therefore, we can conclude that ξ min is a monotonically decreasing function of P, which is d wA monotonically increasing function, θ w is a monotonically decreasing function of .

[0095] S5-5: Narrow the flight position range where the drone has the best communication energy efficiency, and obtain the optimal distance between the drone Alice and the eavesdropper Willie:

[0096] First, when the elevation angle between drone Alice and eavesdropper Willie is For distance When, therefore, According to S5-2, for a fixed θ w , when d w ≤Lcos(θ w ), the objective function communication energy efficiency η changes with d w Monotonically increasing, and the effective transmission rate R in the constraint condition c =ηP with d w is monotonically increasing; in addition, according to S5-4, the minimum detection error probability ξ in the constraint condition min Follow w Monotonically increasing, therefore, according to get is the optimal distance at a given elevation angle, which has nothing to do with the transmit power, that is, the range of the optimal position is and

[0097] Second, when the distance between drone Alice and eavesdropper Willie is For elevation According to S5-2, for a fixed θ w , when d w ≤Lcos(θ w ), the objective function communication energy efficiency η changes with d w Monotonically increasing, and the effective transmission rate R in the constraint condition c =ηP with d w is monotonically increasing; in addition, according to S5-4, the minimum detection error probability ξ in the constraint condition min Follow w Monotonically increasing, Lcos(θ w ) is the optimal distance at a given elevation angle, that is, the range of the optimal position at this time is d w =Lcos(θ w )and

[0098] Third, when the distance between drone Alice and eavesdropper Willie is For elevation When d is fixed w, when the elevation angle between drone Alice and eavesdropper Willie is θ w ≥arccos(d w / L), according to S5-3, η and R c With θ w is monotonically decreasing; in addition, according to S5-4, ξ min Follow w monotonically decreasing; therefore, based on arccos(d w / L)≤θ w ≤π / 2, for a given d w , the optimal elevation angle is arccos(d w / L), that is, the range of the optimal position is and θ w =arccos(d w / L), and this is also related to d w =Lcos(θ w )and equivalence;

[0099] Fourth, for the range d where the optimal position of the second and third points is located w =Lcos(θ w )and have So according to S5-2, for the elevation angle Given an angle, the optimal distance should be greater than Lcos(θ w ), therefore, the optimal flight position for the communication energy efficiency of the drone Alice is not within the range of the optimal positions in the second and third points.

[0100] In summary, the optimal flight position of drone Alice is in the range of and

[0101] S5-6: The optimization problem is simplified to:

[0102]

[0103] As a preferred embodiment of the present invention, in step (6), the simplified optimization problem is decomposed into two sub-problems, and the sub-problems are solved, specifically including:

[0104] S6-1: The simplified optimization problem is divided into two sub-problems, where sub-problem 1 is to optimize the elevation angle θ under a given transmission power P. w Maximize the concealment energy efficiency; Subproblem 2 is to w Under the condition of , solve the optimization problem of transmission power P.

[0105] S6-2: Given the transmission power, the eavesdropper Willie makes an angle θ to the drone Alice. w The optimization problem is expressed as:

[0106]

[0107] in is the equation ξ min (θ w )=1-∈, and is the equation R c (θ w )=R m The root of According to S5-4, the ξ in the constraint condition min is θ w is a monotonically decreasing function; when ξ min =1-, θ w Get the maximum value According to the optimal θ in S5-3 w The uniqueness of When R c With θ w increases monotonically, and when When R c With θ w is monotonically decreasing; therefore, when R c =R m When θ w Get the maximum value and minimum value Without considering the existence of empty sets, combined with the constraints in the optimization problem formula (32), the solution to subproblem 1 is obtained as follows:

[0108]

[0109] in is the unconstrained optimal elevation angle, which is the solution of equation (25), θ LL yes and The larger value of and The smaller value of

[0110] when When , the hidden constraint will not be satisfied; when the closed interval and When the intersection of is empty, it means that the performance constraint cannot be achieved under the current circumstances; in the above case, the optimization problem has no solution.

[0111] S6-3, given elevation angle θw , the optimization problem of power P is expressed as:

[0112]

[0113] Where P∈ is the equation ξ min (P) = 1-∈ root, P c is the equation R c (P) = R m The root of is:

[0114]

[0115] According to S5-4, the ξ in the constraint condition min is a monotonically decreasing function of P; when ξ min =1-∈, the obtained P is the maximum value P ∈ According to formula (20), R c As P increases monotonically, when R c =R m When P is the minimum value P c ; Without considering the existence of the empty set, combined with the constraints in the optimization problem formula (35), the solution to subproblem 2 is obtained as follows:

[0116]

[0117] in is the optimal power under no constraints in equation (22); the above solution does not consider the case of an empty set. When P c >min{P∈,P m}, it means that there is an empty set of solutions, which means that the hidden constraints and performance constraints cannot be achieved simultaneously under the current circumstances, that is, this optimization problem has no solution.

[0118] As a preferred embodiment of the present invention, in step (7), based on the solutions of the two sub-problems, an alternating optimization method is adopted to solve the optimization problem formula (31), and the optimal power P is obtained by iteratively optimizing the elevation angle and the power until the algorithm converges. * With the optimal elevation angle Combined with the optimal distance The solution to the optimization problem formula (31) is completed; the algorithm converges to

[0119] Compared with the prior art, the present invention has the following beneficial effects:

[0120] The present invention jointly optimizes the transmission power and flight position of the drone to maximize the energy efficiency of the drone's covert communication while maintaining a certain communication quality so that it can communicate with legitimate ground receivers outside the surveillance area. By designing energy-efficient drone covert communications, the limited battery capacity of the drone can be utilized as much as possible while ensuring information security, achieving the longest possible endurance. This innovative design will provide a new solution for the endurance and security of drone communications in complex environments, making drones more valuable in the execution of military missions and bringing important technological breakthroughs to the field of modern communications. BRIEF DESCRIPTION OF THE DRAWINGS

[0121] Figure 1 This is a model diagram of the UAV covert communication system.

[0122] Figure 2 Schematic diagram of the relative position of the UAV covert communication system in two-dimensional coordinates.

[0123] Figure 3 is the concealment energy efficiency η of the UAV under different maximum distance constraints * With the change of tolerable detection probability ∈.

[0124] Figure 4 is the optimal power P under different maximum distance constraints * With the optimal elevation angle With the change of tolerable detection probability. DETAILED DESCRIPTION

[0125] In order to better illustrate the purpose, technical solutions and advantages of the present invention, the present invention will be further described below in conjunction with specific embodiments.

[0126] Example 1

[0127] A method for covert communication of an unmanned aerial vehicle comprises the following steps:

[0128] (1) Establishing a UAV covert communication system:

[0129] like Figure 1 As shown, the present invention considers a two-dimensional drone monitoring application scenario. The model consists of a drone equipped with an imaging device as the sender Alice, an eavesdropper Willie who detects the presence of the monitored area and transmits, and a legal receiver Bob. In this system model, the drone Alice monitors the eavesdropper Willie and communicates with the receiver Bob at the same time. As the sender, the drone Alice monitors the ground facilities for a long time and feeds back information to the intended receiver Bob while ensuring a certain degree of communication performance and will not be discovered by the eavesdropper Willie of the ground facilities.

[0130] The UAV covert communication system of the present invention is a two-dimensional scene, that is, the UAV Alice flies directly above the axis determined by the receiver Bob and the eavesdropper Willie, and the distance between the UAV Alice and the eavesdropper Willie is d w , the distance between the eavesdropper Willie and the receiver Bob is d b , the drone Alice’s looking up angle relative to the eavesdropper Willie is θ w The drone Alice, the receiver Bob, and the eavesdropper Willie are each equipped with an antenna. The channel fading coefficients from the drone Alice to the receiver Bob and from the drone Alice to the eavesdropper Willie are denoted as h ab and h aw , the channel fading coefficient remains unchanged in the current time slot and varies independently between different time slots. The channel coefficient follows quasi-static Rayleigh fading, where h ab and h aw is a circularly symmetric complex Gaussian variable, that is, h ab , Since the channel changes in different time slots are independent, the eavesdropper Willie cannot use the knowledge of previous time slots to improve the detection performance. In general, whether the eavesdropper Willie can obtain channel state information (CSI) depends on the channel estimation method used. In practice, it is difficult for the eavesdropper Willie to obtain perfect CSI, so the present invention assumes that the eavesdropper Willie does not know the instantaneous CSI.

[0131] In addition, the channels from drone Alice to receiver Bob and from drone Alice to eavesdropper Willie are modeled as air-to-ground wireless channels with both NLoS (Non-Line-of-Sight) and LoS component probabilities. The path loss of the air-to-ground wireless channel is:

[0132]

[0133] Among them, PL k represents the path loss between drone Alice and target k, k∈{b,w}, where b represents the receiver Bob, w represents the eavesdropper Willie, and d k represents the distance from the drone to the receiver Bob or the eavesdropper Willie, ξ L is the path loss exponent of the LoS channel component, ξ N is the path loss exponent of the NLoS channel component. kis the probability of the LoS component appearing in the two air-to-ground channels from drone Alice to receiver Bob or from drone Alice to eavesdropper Willie, which depends on the environmental parameters and the angle between the drone and receiver Bob or eavesdropper Willie. The calculation formula is:

[0134]

[0135] Among them, the constants a and B in formula (2) are curve parameters that depend on the communication environment, θ k is the elevation angle of the drone relative to the receiver Bob or the eavesdropper Willie (unit: degree). In various application scenarios of drones, the LoS component dominates the NLoS component, so the NLoS component modeling can be ignored.

[0136] Taking into account the background noise variation or calibration error at the eavesdropper Willie, the present invention considers a widely used bounded noise uncertainty model, where the eavesdropper Willie noise power It obeys the logarithmic uniform distribution, and its probability density function (PDF) is as follows:

[0137]

[0138] in, Indicates the noise power The probability density function of α represents the uncertainty of the noise. is the nominal noise power, x represents the noise power The possible values ​​of .

[0139] (2) According to the signal received by the eavesdropper Willie in time slot i and the detection strategy of the eavesdropper Willie, the total detection error probability of the eavesdropper Willie is obtained, which specifically includes:

[0140] S2-1: Define the transmission power of drone Alice as P, H0 means that drone Alice does not transmit signals, H1 means that drone Alice transmits signals, y w [i] represents the received signal at the eavesdropper Willie, and its formula is

[0141]

[0142] According to formula (1), and is the complex Gaussian noise at the eavesdropper Willie, is the noise power at the eavesdropper Willie, and its probability density function is given by equation (3); aw represents the channel fading of the air-to-ground channel from drone Alice to eavesdropper Willie, h aw is the channel fading coefficient from drone Alice to eavesdropper Willie, p w is the probability of the LoS component in the air-to-ground channel from drone Alice to eavesdropper Willie, and x[i] is the sending signal of drone Alice.

[0143] S2-2, the eavesdropper Willie performs energy detection (optimal detection) to detect the hidden signal from the received signal. Based on the average received power, the detection strategy of the eavesdropper Willie is:

[0144]

[0145] Among them, T w represents the average power received by the eavesdropper Willie, λ represents the detection threshold, D0 and D1 represent the binary decision of the eavesdropper Willie on whether the drone Alice transmits, and n is the total number of channels used. Assuming that the eavesdropper Willie can observe an infinite number of samples, the present invention applies the strong law of large numbers, T w It is expressed as:

[0146]

[0147] S2-3, the detection error probability is used to measure the detection performance of the eavesdropper Willie. Under the uniform prior probability assumptions of H0 and H1, the sum of the probability of false detection and missed detection is

[0148]

[0149] Where ξ is the total detection error probability of the eavesdropper Willie, P FA =Pr{D1|H0} is the probability of false detection, P MD =Pr{D0|H1} is the probability of missed detection. Define the received power at the eavesdropper Willie According to equations (3) and (6), the total detection error probability is

[0150]

[0151] where dx is |h aw | 2 The differential of dy is the noise power The differential of x is |h aw | 2 The possible values ​​of y are The possible values ​​of .

[0152] (3) In order to ensure that the transmission is not detected, the worst case is considered, that is, adjusting its detection threshold to obtain the best detection performance, that is, the minimum detection error probability. To this end, the present invention makes a pessimistic assumption that the eavesdropper Willie will try to choose the best detection threshold with the minimum detection error probability. Therefore, the present invention further considers Willie's minimum detection error probability to evaluate the concealment of the communication. The optimal detection threshold λ of the eavesdropper Willie is derived based on the total detection error probability of the eavesdropper Willie. * and the minimum detection error probability ξ min , specifically including:

[0153] S3-1: According to formula (7), it can be deduced that if ξ=1; if ξ will increase with the increase of λ, so that the optimal detection threshold λ that minimizes the probability of detection error can be obtained. * Must be in In the above equation, for λ in this interval, the probability of detection error ξ can be derived as:

[0154]

[0155] S3-2, if it is proved that ξ is a strictly pseudo-convex function, so there is a unique optimal threshold λ * To minimize the probability of detection error. Specifically:

[0156]

[0157]

[0158] is a solution where the first-order derivative of ξ with respect to λ is equal to 0. have Thus further obtaining

[0159]

[0160]

[0161] Therefore, it is proved that ξ is a strictly pseudoconvex function of λ. Optimal detection threshold if In summary, the optimal detection threshold λ * for:

[0162]

[0163] in is the solution of equation (11).

[0164] S3-3, according to equations (8) and (13), the optimal detection threshold λ * Substituting the total detection error probability into the total detection error probability, we can get the minimum detection error probability ξ of the eavesdropper Willie. min for:

[0165]

[0166] (4) According to the received signal and signal-to-interference-noise ratio of the receiver Bob, the probability of signal transmission interruption from the drone Alice to the receiver Bob is obtained, and then the effective covert transmission rate from the drone Alice to the receiver Bob and the communication energy efficiency of the drone Alice are obtained, which specifically includes:

[0167] S4-1,y b [i] is the signal received by the receiver Bob in any time slot i, and its formula is:

[0168]

[0169] Among them, n b [i] represents the Gaussian white noise received by the base station, The mean is 0 and the variance is Gaussian normal distribution, is the noise power at the receiver Bob; H ab represents the channel fading of the air-to-ground channel from drone Alice to receiver Bob, h ab is the channel fading coefficient from drone Alice to receiver Bob, p b is the probability of the LoS component in the air-to-ground channel from drone Alice to receiver Bob.

[0170] S4-2, according to formula (15), the signal-to-interference-noise ratio γ of the signal received by the receiver Bob is obtained b for:

[0171]

[0172] Among them, f(d w ,θ w ) is the same as d w and θ w The function defined. w is the elevation angle of drone Alice relative to eavesdropper Willie, You can use f(d w ,θ w ) indicates that following Figure 1 The geometric position relationship in:

[0173]

[0174] L is the distance between the eavesdropper Willie and the receiver Bob, and a and B are curve parameters that depend on the communication environment.

[0175] S4-3, when the transmission rate R of drone Alice is fixed, when the channel capacity is less than the fixed transmission rate, transmission interruption will occur between drone Alice and receiver Bob. δ represents the transmission interruption probability from drone Alice to receiver Bob, and its formula is:

[0176]

[0177] S4-4, the effective covert transmission rate is used to measure the performance of covert communication, which is affected by the transmission interruption probability and the transmission prior probability. Assume that the transmission prior probability of drone Alice is 1 / 2. Therefore, under the fixed signal transmission rate R, the effective covert transmission rate R c The calculation formula is:

[0178]

[0179] S4-5, in order to make full use of the performance of the limited energy used by the drone Alice and achieve energy-efficient covert communication, energy efficiency is used as a measurement standard, which is characterized by the number of covert bits that can be successfully transmitted per unit energy. η represents the communication energy efficiency of the drone, and its formula is:

[0180]

[0181] The coefficient 1 / 2 is due to the fact that the drone Alice transmits with a prior probability of 1 / 2. In fact, the essence of using communication energy efficiency as an evaluation indicator is to make a trade-off between covert transmission performance and energy consumption.

[0182] (5) By optimizing the position and transmission power of the drone Alice, an optimization problem of maximizing the concealed energy efficiency is proposed, and then the optimal power under unconstrained conditions is obtained. and optimal location And given the monotonicity of the objective and constraint functions, the feasible position range of the drone Alice is narrowed to simplify the optimization problem, including:

[0183] S5-0: Improve the energy efficiency of UAV covert communication while ensuring the concealment and performance of communication. Specifically, the present invention proposes an optimization problem of maximizing the concealment energy efficiency by optimizing the position and transmission power of the UAV. The optimization problem can be expressed as:

[0184]

[0185] Where P≤P m is the maximum transmission power constraint of UAV Alice, P m is the maximum transmission power of UAV Alice. and Together they represent constraints on the monitoring quality and flight position of the drone Alice. is the minimum distance allowed between drone Alice and eavesdropper Willie, is the maximum distance allowed between drone Alice and eavesdropper Willie, is the minimum elevation angle of the drone to the eavesdropper Willie. Specifically, the constraint Make sure the drone doesn't get too far away from the monitored eavesdropper Willie. Ensure that the drone Alice can get a good enough view of the eavesdropper Willie. These two points together ensure that the drone Alice has good monitoring quality. This is to prevent the drone Alice from being visually detected by the eavesdropper Willie when the drone is too close to Willie, and Because Figure 1 As shown in Figure 2, the drone will stay between the eavesdropper Willie and the receiver Bob. In the most common practical scenario considered, the distance L between the receiver Bob and the eavesdropper Willie is much larger than So assuming that in this case ξ min ≥1- ∈ is the concealment constraint, and ∈ is the tolerable detection probability reflecting the concealment level. c ≥R m is the transmission rate constraint to ensure a certain communication quality, R m Indicates the minimum effective covert transmission rate required for covert communication.

[0186] S5-1: In the case of no constraints, the present invention will determine some properties of optimizing the remaining variable between two known variables to maximize the communication energy efficiency η, and these properties will be used to simplify and solve the optimization problem:

[0187] Without any constraints, given the position of the drone Alice, the optimal transmission power that maximizes the communication energy efficiency of the drone Alice can be obtained.

[0188]

[0189] when When , the communication energy efficiency η reaches its maximum value; when When , η increases monotonically with P; when When , η decreases monotonically with P.

[0190] S5-2, given the transmission power of drone Alice and without restrictions, if the optimal angle and distance between drone Alice and eavesdropper Willie are jointly optimized, then the optimal position of drone Alice to maximize η will be the position closest to Bob on the ground. Therefore, determine the given θ w , the optimal d of P w and given d w , the optimal θ of P w some properties of .

[0191] For a given transmission power P and angle θ w , the optimal distance between drone Alice and eavesdropper Willie is expressed as This distance is unique and is given by the following equation d w The unique solution of is given by:

[0192]

[0193] Among them, p b (d w ,θ w ) is the probability of the LoS component in the channel between drones Alice and Bob, and its calculation formula is:

[0194]

[0195] The only solution of formula (24) is the optimal distance Therefore, in d w ≤Lcos(θ w ),η changes with d w Monotonically increasing.

[0196] S8-3, at a given transmission power P and distance d w Under the condition of , the optimal angle between drone Alice and eavesdropper Willie is expressed as is unique, given by the following equation θ w The only solution is given by

[0197]

[0198] The only solution of formula (25) is the optimal angle Therefore, when When η changes with θ w Monotonically decreasing.

[0199] S5-4, minimum detection error probability ξ min is a monotonically decreasing function of P, which is d w is a monotonically increasing function of θw The monotonically decreasing function of is derived as follows:

[0200] According to equations (11) and (14), for The implicit function F(P w ,ξ min )=0, given by:

[0201]

[0202] Because min YesP w function, then both sides of the implicit function are simultaneously w The derivation of is:

[0203]

[0204] According to α>1 and P w >0, we get This makes When min Follow P w Monotonically decreasing;

[0205] Then, when When ξ min P w The first-order derivative of is:

[0206]

[0207] In formula (28), the inequality d>c>0, where x is the independent variable of the integral, c and d are the upper and lower limits of the integral respectively. w >0, yes

[0208]

[0209] It is deduced from this When min Follow P w is monotonically decreasing, so ξ min YesP w A monotonically decreasing function of ;

[0210] In addition, the received power P of the eavesdropper Willie w Specifically:

[0211]

[0212] From formula (30), we can see that P w is a monotonically increasing function of P, which is d w is a monotonically decreasing function of θ wA monotonically increasing function of ;

[0213] Therefore, min is a monotonically decreasing function of P, which is d w A monotonically increasing function, θ w A monotonically decreasing function of ;

[0214] S5-5, based on steps S5-1 to S5-3, can significantly reduce the range of flight positions for the drone to achieve optimal energy efficiency. Figure 2 It is a schematic diagram of the relative position of the system model in two-dimensional polar coordinates, combined with Figure 2 The specific instructions are as follows:

[0215] Figure 2 The EFGH region in is the UAV flight position determined by the position constraints. And ∠BJW=90°.

[0216] First, in region ① (i.e., region EFKJ), it is proved that the optimal point must be located on the EJ arc. Since the elevation angle between the point in region ① and Willie is so According to S5-2, for a fixed θ w , when d w ≤Lcos(θ w ), the objective function energy efficiency η changes with d w monotonically increasing, and the effective transmission rate R in the constraint condition c =ηP with d w In addition, according to S5-4, the minimum detection error probability ξ in the constraint condition min Follow w is monotonically increasing. Therefore, according to It can be concluded that The optimal distance for a given angle is independent of the transmitted power, which means that the optimal point in the area lies on the EJ arc.

[0217] Next, in region ② (i.e., JKM region), we prove that the optimal point must be located on the JM arc. For a given θ w , This shows that the point P(Lcos(θ w ),θ w ) is farther from Willie than the point at the same angle. Therefore, we can get the same result as before: Lcos(θ w ) is the optimal d under given angle conditions w , which means that the optimal point of the region lies on the JM arc.

[0218] Then, in area ③ (i.e., JMGH), it is proved that the optimal point must also be located on the JM arc. w The elevation angle between the points in this area and Willie is θ w ≥arccos(d w / L), so according to S5-3, when θ w ≥arccos(d w / L), η and R c With θ w is monotonically decreasing. In addition, according to S5-4, ξ min Follow w monotonically decreasing. Therefore, considering arccos(d w / L)≤θ w ≤π / 2, for a given d w , we can conclude that arccos(d w / L) is the optimal angle, which means that the optimal point of this area is also located on the JM arc.

[0219] Finally, it is proved that the point on the JM arc is definitely not the optimal point. The points on the JM arc are But according to S5-2, the optimal distance It can be concluded that the point on the JM arc is not the optimal point of energy efficiency.

[0220] In summary, the best flight position of the drone is on the EJ arc, that is, and

[0221] S5-6, from the above, the best position for the drone Located on the EJ arc, that is, regardless of other constraints, and Therefore, the optimization problem is simplified to:

[0222]

[0223] (6) In fact, the optimization problem (31) is an NP-hard problem and is difficult to solve directly. Therefore, in order to solve this optimization problem with lower complexity, the present invention divides it into two sub-problems and then adopts an alternating iterative algorithm, where sub-problem 1 is to optimize the angle θ under a given transmission power P. w Maximize the concealment energy efficiency; Subproblem 2 is to w In the case of , solve the optimization problem of transmit power P, specifically including:

[0224] S6-1, based on the analysis of the nature of the constraints, under a given transmission power, Willie's elevation angle θ of the UAVw The optimization problem is expressed as:

[0225]

[0226] in is the equation ξ min (θ w )=1-∈, and is the equation R c (θ w )=R m The root of According to S5-4, the ξ in the constraint condition min is θ w is a monotonically decreasing function. min =1-∈, θ w The maximum value can be obtained According to the optimal θ in S5-3 w The uniqueness of When R c With θ w increases monotonically, and when When R c With θ w is monotonically decreasing. Therefore, when R c =R m When θ w The maximum value can be obtained and minimum value Without considering the existence of empty sets, combined with the constraints in the optimization problem (32), the solution to subproblem 1 can be obtained as follows:

[0227]

[0228] in is the unconstrained optimal elevation angle, which is the solution of equation (25), and The above solution does not consider the case of an empty set. When , the hidden constraint will not be satisfied. and When the intersection of is empty, it means that the performance constraint cannot be achieved under the current circumstances. In the above case, the optimization problem has no solution.

[0229] S6-2, based on the analysis of the nature of the constraints, given the elevation angle θ w , the optimization problem of power P can be expressed as:

[0230]

[0231] Where P∈ is the equation ξ min(P) = the root of 1-∈. c is the equation R c (P) = R m The root of is:

[0232]

[0233] According to S5-4, the ξ in the constraint condition min is a monotonically decreasing function of P. When ξ min =1-∈, the obtained P is the maximum value P. According to formula (20), R c As P increases monotonically, when R c =R m When P is the minimum value P c Without considering the existence of empty sets, combined with the constraints in the optimization problem (35), the solution to subproblem 2 can be obtained as follows:

[0234]

[0235] in is the optimal power under no constraints in equation (22). The above solution does not consider the case of an empty set. c >min{P∈,P m}, it means that there is an empty set of solutions, which means that the hidden constraints and performance constraints cannot be achieved simultaneously under the current circumstances, that is, this optimization problem has no solution.

[0236] (7) Use the alternating optimization method to solve the optimization problem.

[0237] Based on the solutions of the two sub-problems, the present invention adopts an alternating optimization method to solve the optimization problem formula (31), and obtains the optimal power P by iteratively optimizing the angle and power until the algorithm converges. * With the optimal angle Combined with the optimal distance determined previously The solution to the entire optimization problem is completed. The alternating optimization algorithm has similar performance and lower complexity than the exhaustive solution, and can solve the optimization problem more effectively.

[0238] S7-1: The alternating iterative optimization process for solving the optimization problem formula (31) is as follows: Algorithm 1, where τ represents the convergence accuracy.

[0239]

[0240] S7-2: Determine the convergence of Algorithm 1. According to step 4 of the algorithm, According to step 3 of the algorithm, Further deducing This ensures the convergence of Algorithm 1.

[0241] S7-3, determine the complexity of Algorithm 1. The complexity of Algorithm 1 mainly depends on the solution equation, that is, ξ in formula (32) min (θ w )=1-∈、R c (θ w )=R m and ξ in formula (36) min (P) = 1-∈. The computational complexity of solving these three equations is recorded as and Therefore, the final complexity of Algorithm 1 is Where N represents the number of iterations.

[0242] In order to facilitate those skilled in the art to understand the specific implementation of the present invention, the following examples, simulation parameters and numerical results are provided.

[0243] Regarding the selection of simulation parameters, in order to keep it general, a suburban military scenario is considered, in which there is a surveillance drone (Alice), an eavesdropper (Willie) in the monitored area, and a legitimate receiver (Bob). MATLAB is used for simulation, and the simulation parameters are shown in Table 1.

[0244] Table 1. System simulation parameters

[0245]

[0246]

[0247] The simulation results are now described. Figure 3 Shows different maximum distances The concealment efficiency of the drone is * The relationship between the concealment constraint level, i.e., the tolerable detection probability ∈, is given by the concealment energy efficiency η. * represents the maximum communication energy efficiency that satisfies the covert communication requirements obtained by solving the optimization problem (31). Figure 3 First, it can be observed that the exhaustive sampling points are consistent with the proposed scheme, which means that the proposed scheme can achieve similar performance as the exhaustive search. The complexity of the exhaustive search method is too high, and the proposed scheme can achieve similar performance as the exhaustive search with a smaller complexity, indicating that the proposed scheme is more efficient than the exhaustive search. Then it can be observed that as ∈ increases, the hidden energy efficiency η * It first increases, and then remains constant. This is because the larger ∈ is, the looser the concealment constraint is, which means that more information can be transmitted with greater power, thus achieving higher concealment energy efficiency, until it stabilizes. And when ∈ is small enough, η *There will be null values, because too small ∈ means that the concealment constraint is too strict, in which case the concealment constraint and the performance constraint cannot be satisfied at the same time. In addition, a larger It has greater concealment energy efficiency and can achieve covert communication at a lower ∈. This is because the farther the drone is from Willie, the closer it is to Bob, and the harder it is for Willie to detect its transmission, resulting in higher concealment energy efficiency for covert communication under stricter concealment constraints. Therefore, the maximum distance constraint is relaxed as much as possible to achieve better concealment energy efficiency performance while ensuring monitoring quality and position relationship.

[0248] Figure 4 The optimal power P corresponding to the hidden energy efficiency is shown * and the best angle Relationship with ∈. Hidden energy efficiency η * By the optimal power P * and the best angle Determined from Figure 4 As can be seen from the figure, as ∈ increases, the optimal power P * First increase and then remain unchanged, and the optimal angle The power changes because looser privacy constraints mean that more power can be used to transmit information until the unconstrained optimal power is reached. It is worth noting that regardless of the concealment constraint, All remain at a fixed value, which is the optimal angle without constraints According to S5-3, the optimal angle It is independent of the transmit power P, which means that in the current scenario, regardless of the concealment constraint and transmit power, there is a same optimal angle. This is because the change of angle has a significant impact on the minimum detection error probability ξ min The influence of is small, so the influence on communication concealment is weak, but the change of transmission power will have a significant impact on communication concealment, so this means that the optimization problem proposed by the present invention mainly depends on the optimal transmission power, and the optimal position is fixed. In addition, when ∈ is small enough, P * and There will be null values ​​because covert communication cannot be achieved while satisfying all constraints. * and the best angle The changing trend of ∈ explains the hidden energy efficiency η * 's changing trend.

[0249] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the scope of protection of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the essence and scope of the technical solution of the present invention.

Claims

1. A UAV covert communication system, characterized in that: include: There is a drone Alice, an eavesdropper Willie, and a receiver Bob. The drone is equipped with imaging equipment, and the eavesdropper Willie detects transmissions in the monitored area. The drone Alice simultaneously monitors the eavesdropper Willie and communicates with the receiver Bob. The UAV covert communication system includes a wireless channel link from the UAV Alice to the receiver Bob and a wireless channel link from the UAV Alice to the eavesdropper Willie. The two channels from the UAV Alice to the receiver Bob and from the UAV Alice to the eavesdropper Willie are both air-to-ground wireless channels. There is both channel uncertainty and noise uncertainty at the eavesdropper Willie.

2. The UAV covert communication system as claimed in claim 1, characterized in that: The air-to-ground wireless channel is an air-to-ground wireless channel having both NLoS and LoS component probabilities, and the path loss of the air-to-ground wireless channel is: Among them, PL k represents the path loss between the UAV and the target k, k∈{b,w}, b is the receiver Bob, w is the eavesdropper Willie; d k represents the distance from drone Alice to receiver Bob or eavesdropper Willie, ξ L is the path loss exponent of the LoS channel component, ξ N is the path loss exponent of the NLoS channel component, p k is the probability of the LoS component appearing in the two air-to-ground channels from drone Alice to receiver Bob or from drone Alice to eavesdropper Willie, p k Depending on the environmental parameters and the angle between the drone Alice and the receiver Bob or the eavesdropper Willie, the calculation formula is: Among them, a and B are curve parameters that depend on the communication environment, θ k is the elevation angle of drone Alice relative to receiver Bob or eavesdropper Willie, in degrees; There is environmental noise uncertainty at the eavesdropper Willie, where the noise power at the eavesdropper Willie is The noise power at the eavesdropper Willie is log-uniformly distributed. The probability density function of is as follows: in, Indicates the noise power The probability density function of α represents the uncertainty of the noise. is the nominal noise power, x represents the noise power The possible values ​​of .

3. A covert communication method for unmanned aerial vehicles, characterized in that: The steps include: (1) Establishing the UAV covert communication system as described in claim 2; (2) According to the signal received by eavesdropper Willie in time slot i and the detection strategy of eavesdropper Willie, the total detection error probability of eavesdropper Willie is obtained; (3) Based on the total detection error probability of eavesdropper Willie, derive the optimal detection threshold λ of eavesdropper Willie * and the minimum detection error probability ξ min ; (4) According to the received signal and signal-to-interference-noise ratio of the receiver Bob, the probability of signal transmission interruption from the drone Alice to the receiver Bob is obtained, and then the effective covert transmission rate from the drone Alice to the receiver Bob and the communication energy efficiency of the drone Alice are obtained; (5) By optimizing the position and transmission power of the drone Alice, an optimization problem of maximizing the concealed energy efficiency is proposed, and then the optimal power under unconstrained conditions is obtained. and optimal location And given the monotonicity of the objective and constraint functions, the feasible position range of the drone Alice is narrowed down to simplify the optimization problem; (6) Decompose the simplified optimization problem into two sub-problems and solve the sub-problems; (7) Use the alternating optimization method to solve the optimization problem.

4. The UAV covert communication method as claimed in claim 3, characterized in that: The eavesdropper Willie receives signal y in time slot i w [i] is: Among them, P is the transmission power of the drone Alice, H0 means that the drone Alice does not transmit signals, and H1 means that the drone Alice transmits signals. is the complex Gaussian noise at the eavesdropper Willie, is the noise power at Willie, H aw represents the channel fading of the air-to-ground channel from drone Alice to eavesdropper Willie, h aw is the channel fading coefficient from drone Alice to eavesdropper Willie, p w is the probability of the LoS component in the air-to-ground channel from drone Alice to eavesdropper Willie, and x[i] is the transmitted signal of drone Alice; Based on the eavesdropper Willie receiving signal y in time slot i w [i], the detection strategy of the eavesdropper Willie is: Among them, T w represents the average power received by the eavesdropper Willie, λ represents the detection threshold, D0 and D1 represent the binary decision of the eavesdropper Willie on whether the drone Alice transmits, and n is the total number of channels used.

5. The UAV covert communication method as claimed in claim 4, characterized in that: Under the uniform prior probability assumptions of H0 and H1, the sum of the probabilities of false positives and false negatives is Where ξ is the total detection error probability of the eavesdropper Willie, P FA =Pr{D1|H0} is the false detection probability of the eavesdropper Willie, P MD =Pr{D0|H1} is the probability of missed detection of the eavesdropper Willie; P w is the received power at the eavesdropper Willie; Define the received power at the eavesdropper Willie Then, according to equations (3) and (6), the total detection error probability ξ is obtained as where dx is |h aw | 2 The differential of dy is the noise power The differential of x is |h aw | 2 The possible values ​​of y are The possible values ​​of .

6. The UAV covert communication method as claimed in claim 5, characterized in that: The optimal detection threshold λ of the eavesdropper Willie * and the minimum detection error probability ξ min The calculation includes: S3-1: According to formula (7), if ξ=1; if ξ will increase with the increase of λ, thus obtaining the optimal detection threshold λ that minimizes the probability of detection error * Must be in Therefore, for λ in In the interval, the total detection error probability ξ is: S3-2, the total detection error probability ξ is derived with respect to the detection threshold λ: is a solution where the first-order derivative of ξ with respect to λ is equal to 0. have Thus we can further obtain: It is thus proved that ξ is a strictly pseudoconvex function of λ if Optimal detection threshold if In summary, the optimal detection threshold λ * for: in is the solution of equation (11); S3-3, according to equations (8) and (13), the optimal detection threshold λ * Substituting the total detection error probability ξ into the total detection error probability ξ, the minimum detection error probability ξ of the eavesdropper Willie can be obtained. min for:

7. The UAV covert communication method as claimed in claim 3, characterized in that: The effective concealed transmission rate from the drone Alice to the receiver Bob and the communication energy efficiency of the drone Alice are calculated in the following steps: S4-1: Receiver Bob’s received signal y b [i] is: Among them, n b [i] represents the Gaussian white noise received by the base station, The mean is 0 and the variance is Gaussian normal distribution, is the noise power at the receiver Bob; H ab represents the channel fading of the air-to-ground channel from drone Alice to receiver Bob, h ab is the channel fading coefficient from drone Alice to receiver Bob, p b is the probability of the LoS component in the air-to-ground channel from drone Alice to receiver Bob; S4-2: Based on formula (15), the signal-to-interference-noise ratio of the receiver Bob is: Among them, f(d w ,θ w ) is the same as d w and θ w The function defined, θ w is the elevation angle of drone Alice relative to eavesdropper Willie; L is the distance between the eavesdropper Willie and the receiver Bob, a and B are curve parameters that depend on the communication environment; S4-3: When the transmission rate R of drone Alice is fixed, when the channel capacity is less than the fixed transmission rate, a transmission interruption occurs between drone Alice and receiver Bob. The transmission interruption probability δ from drone Alice to receiver Bob is: S4-4: Assume that the transmission probability of drone Alice is 1 / 2. Therefore, under the fixed signal transmission rate R, the effective concealed transmission rate R c for: S4-5: The communication energy efficiency of drone Alice is 8. The UAV covert communication method as claimed in claim 7, characterized in that: The optimization problem is: Where P≤P m is the maximum transmission power constraint of UAV Alice, P m is the maximum transmission power of drone Alice; and Together they represent constraints on the monitoring quality and flight position of the drone Alice. d w is the minimum distance allowed between drone Alice and eavesdropper Willie, is the maximum distance allowed between drone Alice and eavesdropper Willie, θ w is the minimum elevation angle of drone Alice to eavesdropper Willie; min ≥1-∈ is the concealment constraint, ∈ is the tolerable detection probability reflecting the concealment level; R c ≥R m is the transmission rate constraint, R m Indicates the minimum effective covert transmission rate required for covert communication.

9. The UAV covert communication method as claimed in claim 8, characterized in that: In step (5), the optimal power and optimal position under no constraints are obtained, and the communication energy efficiency η and the minimum detection error probability ξ are given. min For the transmission power P and distance d of drone Alice respectively w and the elevation angle θ w The changing trend of , and then simplify and decompose the optimization problem, including: S5-1: Given the position of UAV Alice without any constraints, find the optimal transmission power that maximizes the communication energy efficiency of UAV Alice when When , the communication energy efficiency η reaches the maximum value; when When , the communication energy efficiency η increases monotonically with the transmission power P of the drone Alice; when When , the communication energy efficiency η decreases monotonically with the transmission power P of the drone Alice; S5-2: Given the transmission power P of the drone Alice and without restrictions, if the optimal angle and distance between the drone Alice and the eavesdropper Willie are jointly optimized, then the optimal position of the drone to maximize communication energy efficiency is the position closest to the receiver Bob on the ground, so, For a given transmit power P and elevation angle θ w , the optimal distance between drone Alice and eavesdropper Willie is expressed as This distance is unique and is given by the following equation d w The unique solution of is given by: Among them, p b (d w ,θ w ) is the probability of the LoS component in the channel between drone Alice and receiver Bob, The only solution of formula (24) is the optimal distance Therefore, in d w ≤Lcos(θ w ), the communication energy efficiency η increases with the distance d w monotonically increasing; S5-3: At a given transmission power P and distance d w Under the condition of , the optimal elevation angle between drone Alice and eavesdropper Willie is expressed as is unique, given by the following equation θ w The unique solution of is given by: The only solution of equation (25) is the optimal elevation angle Therefore, when When the communication energy efficiency η changes with the elevation angle θ w Monotonically decreasing; S5-4, according to equations (11) and (14), for The implicit function F(P w ,ξ min )=0, given by: Because min YesP w function, then both sides of the implicit function are simultaneously w The derivation of is: According to α>1 and P w >0, we get This makes When min Follow P w Monotonically decreasing; Then, when When ξ min P w The first-order derivative of is: In formula (28), the inequality d>c>0, where x is the independent variable of the integral, c and d are the upper and lower limits of the integral respectively. w >0, yes It is deduced from this When min Follow P w is monotonically decreasing, so ξ min YesP w A monotonically decreasing function of ; In addition, the received power P of the eavesdropper Willie w Specifically: From formula (30), we can see that P w is a monotonically increasing function of P, which is d w is a monotonically decreasing function of θ w A monotonically increasing function of ; Therefore, min is a monotonically decreasing function of P, which is d w A monotonically increasing function, θ w A monotonically decreasing function of ; S5-5: Narrow the flight position range where the drone has the best communication energy efficiency, and obtain the optimal distance between the drone Alice and the eavesdropper Willie: First, when the elevation angle between drone Alice and eavesdropper Willie is For the distance When, therefore, According to S5-2, for a fixed θ w , when d w ≤Lcos(θ w ), the objective function communication energy efficiency η changes with d w Monotonically increasing, and the effective transmission rate R in the constraint condition c =ηP with d w is monotonically increasing; in addition, according to S5-4, the minimum detection error probability ξ in the constraint condition min Follow w Monotonically increasing, therefore, according to get is the optimal distance at a given elevation angle, which has nothing to do with the transmit power, that is, the range of the optimal position is and Second, when the distance between drone Alice and eavesdropper Willie is For elevation According to S5-2, for a fixed θ w , when d w ≤Lcos(θ w ), the objective function communication energy efficiency η changes with d w Monotonically increasing, and the effective transmission rate R in the constraint condition c =ηP with d w is monotonically increasing; in addition, according to S5-4, the minimum detection error probability ξ in the constraint condition min Follow w Monotonically increasing, Lcos(θ w ) is the optimal distance at a given elevation angle, that is, the range of the optimal position is d w =Lcos(θ w )and Third, when the distance between drone Alice and eavesdropper Willie is For elevation When d is fixed w , when the elevation angle between drone Alice and eavesdropper Willie is θ w ≥arccos(d w / L), according to S5-3, η and R c With θ w is monotonically decreasing; in addition, according to S5-4, ξ min Follow w monotonically decreasing; therefore, based on arccos(d w / L)≤θ w ≤π / 2, for a given d w , the optimal elevation angle is arccos(d w / L), that is, the range of the optimal position is and θ w =arccos(d w / L); Fourth, for the range d where the optimal position of the second and third points is located w =Lcos(θ w )and have So according to S5-2, for the elevation angle Given an angle, the optimal distance should be greater than Lcos(θ w ); Therefore, the optimal flight position of UAV Alice is in the range of and S5-6: The optimization problem is simplified to:

10. The UAV covert communication method as claimed in claim 9, characterized in that: In step (6), the simplified optimization problem is decomposed into two sub-problems, and the sub-problems are solved, specifically including: S6-1: The simplified optimization problem is divided into two sub-problems, where sub-problem 1 is to optimize the elevation angle θ under a given transmission power P. w Maximize the concealment energy efficiency; Subproblem 2 is to w Under the condition of , solve the optimization problem of transmission power P; S6-2: Given the transmission power, the eavesdropper Willie makes an angle θ to the drone Alice. w The optimization problem is expressed as: in is the equation ξ min (θ w )=1-∈, and is the equation R c (θ w )=R m The root of According to S5-4, the ξ in the constraint condition min is θ w is a monotonically decreasing function; when ξ min =1-∈, θ w Get the maximum value According to the optimal θ in S5-3 w The uniqueness of When R c With θ w increases monotonically, and when When R c With θ w is monotonically decreasing; therefore, when R c =R m When θ w Get the maximum value and minimum value Without considering the existence of empty sets, combined with the constraints in the optimization problem formula (32), the solution to subproblem 1 is obtained as follows: in is the unconstrained optimal elevation angle, which is the solution of equation (25), θ LL yes θ w and The larger value of θ UL yes and The smaller value of S6-3, given elevation angle θ w , the optimization problem of power P is expressed as: Among them, P ∈ is the equation ξ min (P) = 1-∈ root, P c is the equation R c (P) = R m The root of is: According to S5-4, the ξ in the constraint condition min is a monotonically decreasing function of P; when ξ min =1-∈, the obtained P is the maximum value P ∈ According to formula (19), R c As P increases monotonically, when R c =R m When P is the minimum value P c ; Without considering the existence of empty sets, combined with the constraints in the optimization problem formula (34), the solution to subproblem 2 is obtained as follows: in is the optimal power without constraints in equation (22).

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