A method and system for designing a trajectory of a UAV in covert communication based on mechanical equivalence

Abstract

The present application provides a kind of unmanned aerial vehicle trajectory design method and system under covert communication based on mechanical equivalence, comprising: step 1. Unmanned aerial vehicle establishes covert communication channel, obtains communication parameter;Step 2: obtain optimal decision distribution and minimum detection error rate according to noise distribution;Step 3: calculate the maximum signal-to-noise ratio, can obtain the constraint on power under covert communication;Step 4: by jointly optimizing the trajectory of unmanned aerial vehicle and resource allocation to maximize the information throughput of unmanned aerial vehicle and ground node communication;Step 5: the original trajectory problem is equivalent to the mechanical problem under artificial potential field;Step 6: unmanned aerial vehicle flies according to the optimal trajectory obtained by solving equivalent problem, and adjusts transmission power in time;Step 7: unmanned aerial vehicle reaches the given terminal point, and covert communication ends.The present application equates the non-convex trajectory problem of continuous infinite variables of unmanned aerial vehicle to the minimum potential problem of rope under artificial potential field, greatly reduces the time of solving the trajectory solution of unmanned aerial vehicle.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of wireless communication, in particular to a method and system for designing the trajectory of unmanned aerial vehicles (UAVs) in covert communication based on mechanical equivalence. BACKGROUND

[0002] In recent years, unmanned aerial vehicles (UAVs) have shown great application prospects in various fields, including wireless communication, data collection, public safety, traffic monitoring, environmental monitoring, and smart agriculture. In particular, in communication applications, the high mobility of UAVs in three-dimensional space makes the probability of line-of-sight (LOS) between the UAVs and ground nodes higher, and the channel gain stronger, which can provide higher communication performance than ground wireless networks. Meanwhile, UAVs have high controllability, and the optimization of the static deployment position of UAVs can further improve the communication performance of the network. In particular, by optimizing the continuous trajectory of UAVs, the wireless network can obtain additional performance increment space. In addition, the optimization of the trajectory of UAVs can also improve the communication capacity and energy efficiency of the wireless communication network assisted by UAVs, enhance the communication reliability and security, and improve the energy transmission efficiency of the wireless energy transmission network, etc.

[0003] In particular, due to the potential line-of-sight condition between UAVs and ground potential eavesdroppers, unmanned aerial vehicle networks are more vulnerable to communication security threats than ground wireless networks, and physical layer security is a promising technology that can improve the confidentiality of data transmission in UAV systems with carefully designed transmission power and trajectory. In practice, physical layer security only focuses on protecting the transmission content from being eavesdropped, while in some cases it is also desirable to hide the communication behavior of the wireless transmitter from other communication nodes.

[0004] Covert communication technology is becoming a promising technology to overcome this challenge, as it can use noise, artificial noise, and power control to make it impossible for the listener to determine whether the communication parties are communicating, thereby hiding the existence of wireless transmission. However, the trajectory of UAVs is continuous in time and space, containing an infinite number of UAV position information corresponding to time points (velocity information can be obtained by continuous position information). Therefore, this continuous trajectory design problem with an infinite number of variables needs to be optimized to meet the needs of communication users and the threats of potential eavesdroppers, which is not only cutting-edge but also extremely challenging.

[0005] Current techniques reduce the complexity of solving the continuous trajectory problem (containing an infinite number of variables), and obtain suboptimal solutions through quantization, approximation, substitution optimization, and heuristic design. The method based on discrete point solving problem has an exponential increase in complexity as the area of the UAV service area increases. SUMMARY

[0006] The present application firstly aims at the optimal trajectory design problem of single user and single eavesdropper network under covert communication, and proposes a method based on mechanical equivalent artificial potential field to design the continuous trajectory of the unmanned aerial vehicle. The method ingeniously equates the non-convex trajectory problem of the unmanned aerial vehicle with continuous infinite variables to the minimum potential problem of the rope under the artificial potential field, first obtains the closed expression of the optimal trajectory of the unmanned aerial vehicle, can greatly reduce the time of solving the trajectory solution of the unmanned aerial vehicle, and the optimality also shows that the method can be extended in the single user network with many complex models and targets.

[0007] To solve the above technical problems, the present application adopts the following technical scheme:

[0008] A mechanical equivalent based trajectory design method of unmanned aerial vehicle under covert communication, comprising the following steps:

[0009] Step S1. The unmanned aerial vehicle starts from a given starting point, establishes a covert communication channel, and obtains communication parameters;

[0010] Step S2: According to the noise distribution, the optimal decision distribution and the minimum detection error rate are obtained;

[0011] Step S3: The maximum signal-to-noise ratio is calculated, so that the constraint on the power under covert communication can be obtained;

[0012] Step S4: The information throughput when the unmanned aerial vehicle communicates with the ground node is maximized by jointly optimizing the trajectory of the unmanned aerial vehicle and the resource allocation;

[0013] Step S5: The original trajectory problem is equivalent to a mechanical problem under the artificial potential field;

[0014] Step S6: According to the optimal trajectory expression obtained by solving the equivalent problem, the unmanned aerial vehicle flies and adjusts the transmission power in time;

[0015] Step S7: The unmanned aerial vehicle reaches the given terminal point, and the covert communication ends.

[0016] Further, in the step S1, the obtained communication parameters include the maximum speed limit V max of the unmanned aerial vehicle flight, the maximum transmission power limit P max , the minimum flight height H of the unmanned aerial vehicle, and the position information of the starting point and the terminal point of the unmanned aerial vehicle D1=(ω 1,x ,ω 1,y ), D2=(ω 2,x ,ω 2,y ), the position information of the ground user node and the eavesdropping node D0=(ω 0,x ,ω 0,y ), and D3=(ω 3,x ,ω 3,y), the communication duration T between the UAV and the ground user.

[0017] Further, in step S1, when the UAV starts from the starting point, the covert communication channel is established. According to the relative position information of the UAV to the user node, the channel gain of the UAV to the user node can be obtained, which is represented as (1):

[0018]

[0019] wherein β represents the channel gain with a reference distance of 1m, r(x(t), y(t)) represents the horizontal distance of the UAV to the ground user node,

[0020] According to the relative position information of the UAV to the eavesdropping node, the channel gain of the UAV to the eavesdropping node can be obtained, which is represented as (2):

[0021]

[0022] wherein β represents the channel gain with a reference distance of 1m, r w (x(t), y(t)) represents the horizontal distance of the UAV to the eavesdropping node,

[0023] Further, in step S2, the received signal of the eavesdropping node and the noise are subject to complex Gaussian distribution. The total flight communication time is divided into N time slots, and L times of decisions are made in each time slot to determine whether the eavesdropper receives the signal sent by the UAV. For time slot n, the signal received by the eavesdropper for the Lth time can be represented as (3):

[0024]

[0025] wherein σ 2 is the noise power, P[n] is the transmission power of the UAV in the nth time slot, h w [n] is the discrete channel gain of the UAV to the eavesdropping node, represents the zero hypothesis that the UAV does not transmit, and represents the alternative hypothesis that the UAV transmits;

[0026] The optimal decision adopted is the decision that can obtain the minimum error rate. Since the complex Gaussian distribution and the additivity of the Gamma distribution, the distribution of the optimal decision can be obtained, which is represented as (4):

[0027]

[0028] wherein, T w [n] can be regarded as the total received power of L observations in the nth time slot;

[0029] The total detection error rate can be represented by (5):

[0030]

[0031] where ρ is the set concealment requirement value, P F is the false alarm probability, P M is the missed detection probability, and when the optimal decision is τ*, and the minimum detection error rate ξ* is only related to γ w is the maximum signal-to-noise ratio at the eavesdropping node that satisfies the minimum detection error rate.

[0032] Further, in the step S3, the constraint on the power under covert communication is obtained by a binary search method, and the maximum signal-to-noise ratio γ w at the eavesdropping node that satisfies the minimum detection error rate is obtained. The constraint on the unmanned aerial vehicle transmission power P[n] under covert communication is obtained from (5), and is represented as (6):

[0033]

[0034] where γ w is the maximum signal-to-noise ratio at the eavesdropping node that satisfies the minimum detection error rate, σ 2 is the noise power, β is the channel gain with a reference distance of 1 m, H is the fixed flight height of the unmanned aerial vehicle, P max is the maximum transmission power limit set by the unmanned aerial vehicle, and the vector r3=(ω 3,x ,ω 3,y ). When the time slot n tends to infinity, the discrete transmission power P[n] can be converted into continuous transmission power P(t).

[0035] Further, in the step S4, the joint optimization of the flight trajectory and the power control makes the unmanned aerial vehicle concealment system further improve the communication quality while meeting the minimum covert communication performance requirement. The problem can be modeled as (7):

[0036]

[0037] where B represents the bandwidth, σ 2 is the noise power, and U({x(t),y(t)},P(t)) is the information throughput between the unmanned aerial vehicle and the user node at the two-dimensional coordinates {x(t),y(t)} and the transmission power P(t).

[0038] Further, in the step S5, the continuous trajectory design problem of the unmanned aerial vehicle is converted into a variable density rope shape design, a new path and speed information model is considered, and a new problem model (8) is obtained:

[0039]

[0040] where, for any UAV trajectory {x(t),y(t)}, the corresponding UAV path is denoted as s is a given path variable, v(s) is the corresponding UAV speed for any given path variable s, is the transmit power of the UAV located at is the information throughput between the UAV and the user node when the UAV is located at the two-dimensional coordinate with transmit power .

[0041] Then consider the minimum gravitational potential energy field with variable density rope, and the problem description in formula (9):

[0042]

[0043] where, s is a given path variable, s∈[0,S′], S′ represents the total length of the rope, represents the shape of the rope, ρ(s) is the density of the rope, G is the gravitational constant, M0 is the mass of the point at the user node, represents the distance from point to D0, is the gravitational potential energy field of the rope when the point at the user node is located at with rope density ρ(s);

[0044] By constructing an artificial potential energy field R″(x,y), the information transmission rate of the UAV air-ground communication is characterized, the equivalence of P1 and P2 problems is found, and the definition is given by formula (10):

[0045]

[0046] where, R″(x,y) is the artificial potential energy field representing the information transmission rate of the UAV and the user node communication, R(x,y) is the information transmission rate of the UAV and the user node communication, B is the signal bandwidth, β is the channel gain with a reference distance of 1m, P(x,y) is the transmit power of the UAV at , σ 2 is the noise power, r(x,y) is the distance from the UAV to the user node, H is the fixed flight height of the UAV.

[0047] Therefore, the original trajectory design problem P1 can be completely transformed into the mechanical problem P3 equivalent to the variable density rope balance problem in the artificial potential field, expressed as formula (11):

[0048] ​

[0049] where, is the artificial potential field of the rope with the rope density ρ(s) at the location of the user node.

[0050] Further, in the step S6,

[0051] The force field in the potential field is described by the negative gradient of the scalar potential function. In the equivalent problem P3 of the UAV trajectory design under covert communication, the force field can be given by formula (12):

[0052]

[0053] where, γ w is the maximum signal-to-noise ratio at the eavesdropping node D3 that satisfies the minimum detection error rate mentioned in step S3, in addition, P w ≤P max can be mathematically transformed into that is, |r(x,y)-r3| 2 <R W 2 , where r w =r3-r(x,y), the bold symbol is a vector, and R w is the shielding range around the eavesdropper D3, the value of which is

[0054] According to the principle of minimum total potential energy, if the total potential field of the rope is minimum, the rope must be balanced everywhere, that is, the net force and torque are zero, otherwise, under the action of non-zero net force or non-zero net torque, a better solution with lower potential energy will be found. Under the optimal rope shape, the rope density should be the lowest, that is, ρ(s)=ρ min The partial x,y-axis force from D1 to is 0, and the expression is as formula (13):

[0055]

[0056] where, is the absolute value of the optimal solution of the initial rope tension value, α ★ is the optimal solution of the initial rope tension angle, is the optimal rope shape solution, is the absolute value of the force field size at the corresponding position of the optimal rope shape, ρ min is the minimum rope density, (ω 0,x ,ω 0,y ) is the position of the user node, is the optimal rope position ​distance to the user node, s is a variable for any given path, s∈[0,S'], S' represents the total length of the rope, Q(s) is the rope tension at the optimal rope position is the sum of the projection of the initial rope tension and the gravity in the x-axis direction, is the sum of the projection of the initial rope tension and the gravity in the y-axis direction;

[0057] the optimal rope initial tension value and the angle α of the tension to the positive direction of the x-axis ★ under the known condition, combined with the initial value condition, the optimal solution of the equivalent problem P3 under the condition of insufficient rope mass can be constructed by formula (14):

[0058]

[0059] wherein s is a variable for any given path, s∈[0,S'], S' * represents the total length of the rope under the optimal solution, m is the total mass of the rope, ρ min is the minimum rope density, (ω 1,x ,ω 1,y ) is the starting position of the unmanned aerial vehicle flight;

[0060] According to s=Vt, the optimal trajectory {x*(t),y*(t)} of the unmanned aerial vehicle can be constructed from the optimal rope shape , which is represented as (15):

[0061]

[0062] Further, as the unmanned aerial vehicle flies, the optimal transmission power of the unmanned aerial vehicle will be adjusted in time, in order to maximize the throughput, the total is its maximum transmission power, that is

[0063] The application also provides a mechanical equivalent-based unmanned aerial vehicle trajectory design system under covert communication, comprising a parameter acquisition module, a decision distribution module, a power-constrained communication module under covert communication, a trajectory optimization module, a potential field equivalent module, a transmission power acquisition module and a covert communication end module, wherein

[0064] The parameter acquisition module acquires the communication parameters in the establishment of the covert communication channel by the unmanned aerial vehicle starting from a given starting point;

[0065] The decision distribution module is used to obtain the optimal decision distribution and the minimum detection error rate according to the noise distribution;

[0066] ​The covert communication under power constraint communication module is used for calculating the maximum signal-to-noise ratio, so that the constraint on power under covert communication can be obtained;

[0067] The trajectory optimization module maximizes the information throughput of the unmanned aerial vehicle and the ground node in communication by jointly optimizing the trajectory of the unmanned aerial vehicle;

[0068] The potential field equivalent module equivalent the original trajectory problem to a mechanical problem in an artificial potential field;

[0069] The transmission power acquisition module acquires the optimal trajectory expression obtained by solving the equivalent problem, and the unmanned aerial vehicle flies and adjusts the transmission power in time;

[0070] The covert communication end module is used for ending the covert communication when the unmanned aerial vehicle reaches a given terminal point.

[0071] Compared with the prior art, the present application has at least the following beneficial effects:

[0072] The present application proposes a mechanical equivalent-based method, which obtains a rope shape representation problem equivalent to the continuous trajectory problem of the unmanned aerial vehicle by designing an appropriate artificial potential field. Through joint optimization of the trajectory of the unmanned aerial vehicle and the transmission power, the concealment system realizes the maximization of the information throughput under the condition of meeting the minimum concealment requirement. The method can obtain a closed expression of the optimal continuous trajectory, has extremely low complexity, and greatly reduces the search space of the solution of the trajectory problem of the unmanned aerial vehicle.

[0073] The present application proposes a mechanical equivalent-based method, which obtains a rope shape representation problem equivalent to the continuous trajectory problem of the unmanned aerial vehicle by designing an appropriate artificial potential field. Through joint optimization of the trajectory of the unmanned aerial vehicle and the transmission power, the concealment system realizes the maximization of the information throughput under the condition of meeting the minimum concealment requirement. The method can obtain a closed expression of the optimal continuous trajectory, has extremely low complexity, and greatly reduces the search space of the solution of the trajectory problem of the unmanned aerial vehicle. BRIEF DESCRIPTION OF DRAWINGS

[0074] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0075] Figure 1 The figure is a model of the trajectory of the unmanned aerial vehicle in covert communication;

[0076] Figure 2 The figure is a shape model of the rope in an artificial potential field;

[0077] Figure 3 The figure is an implementation flowchart of the covert communication method participated by the unmanned aerial vehicle;

[0078] Figure 4 The figure is an implementation flowchart of the covert communication method participated by the unmanned aerial vehicle; Figure 3Flowchart for optimal solution of a medium-effort mechanical problem

[0079] Figure 5 To Figure 4 Flowchart for binary search to find optimal initial cable tension. DETAILED DESCRIPTION

[0080] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0081] It should be noted that, in the following embodiments, the experimental methods described are conventional methods unless otherwise specified, and the reagents and materials described are commercially available unless otherwise specified. In the description of the present application, the terms "lateral", "longitudinal", "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like indicate the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as limiting the present application.

[0082] In addition, the terms "horizontal", "vertical", "overhanging", and the like do not mean that the components must be absolutely horizontal or overhanging, but can be slightly inclined. For example, "horizontal" only means that it is more horizontal relative to "vertical", and does not mean that the structure must be completely horizontal, but can be slightly inclined.

[0083] In the description of the present application, it should also be noted that, unless otherwise explicitly specified and limited, the terms "arrangement", "installation", "connection", "connection" should be understood broadly, for example, it can be fixedly connected, or it can be detachably connected, or integrally connected; it can be mechanically connected, or it can be electrically connected; it can be directly connected, or it can be indirectly connected through an intermediate medium; it can be the communication between two elements inside. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0084] As Figure 1 As shown in the figure, the present application considers a single-user, single-eavesdropper network, with a UAV as a mobile base station. The user node is placed at D0=(ω 0,x ,ω 0,y ), and the eavesdropper node is placed at D3=(ω 3,x ,ω 3,y), all are located on the ground. The UAV departs from a given starting point D1=(ω 1,x ,ω 1,y ), flies at a fixed height H>0, flies to a given end point D2=(ω 2,x ,ω 2,y ), and performs wireless communication with the ground user while minimizing information leakage. The horizontal position of the UAV at time point t>0 is represented by (x(t), y(t)), where t is a continuous variable.

[0085] As shown in Figure 3 , the UAV continuous trajectory design method based on mechanical equivalence in the face of covert communication environment mainly includes the following steps:

[0086] Step S1. The UAV departs from a given starting point, establishes a covert communication channel, and obtains communication parameters.

[0087] The starting point and the end point of the UAV, the flight height, and the position of the ground node are known. When the UAV departs from the starting point, it begins to establish a covert communication channel. According to the relative position information, the channel gain of the UAV to the user node and the eavesdropping node can be obtained.

[0088] Step S2: Obtain the optimal decision distribution and the minimum detection error rate according to the noise distribution.

[0089] The present application considers that the received signal and the noise of the eavesdropping node are subject to complex Gaussian distribution. The total flight communication time is divided into N time slots (1st, 2nd, …, Nth time slots), and L times of decision are made in each time slot to determine whether the eavesdropper receives the signal sent by the UAV. The decision with the minimum error rate is the optimal decision adopted by the present application.

[0090] Step S3: Calculate the maximum signal-to-noise ratio, so that the power constraint under covert communication can be obtained.

[0091] Through mathematical derivation, the present application finds that the total detection error rate is monotonically decreasing with respect to the signal-to-noise ratio when L>1, so the present application can obtain the maximum signal-to-noise ratio γ w that satisfies the minimum detection error rate at the eavesdropping node by means of binary search.

[0092] Step S4: Maximize the information throughput when the UAV communicates with the ground node by jointly optimizing the trajectory of the UAV and the resource allocation.

[0093] Step S5: Equivalent the original trajectory problem to a mechanical problem in an artificial potential field.

[0094] According to the problem equivalence, the present application ingeniously converts the continuous trajectory design problem of the UAV into the design of a variable density rope shape, as shown in Figure 1 , 2, which is solved by minimizing the artificial potential field.

[0095] Step S6: According to the optimal trajectory expression obtained by solving the equivalent problem, the unmanned aerial vehicle flies and adjusts the transmission power in time;

[0096] The equivalent problem solving flowchart is as shown in Figure 4 , wherein the optimal initial rope tension corresponding to the optimal rope shape solution can be solved by binary search, and the solving program flowchart is as shown in Figure 5 , which is briefly described as:

[0097] 1) An initial rope tension and angle are given;

[0098] 2) The mechanical expressions of the rope in x and y directions are constructed according to the force balance condition, and a series of simplifications are obtained to obtain the rope shape;

[0099] 3) If it does not satisfy that the path through the destination point is equal to the rope length, the tension size or angle is changed, then return to step (2), if it satisfies, then end the search, and output the optimal rope shape and the corresponding optimal rope tension.

[0100] Step S7: The unmanned aerial vehicle reaches the given terminal point, and the covert communication ends.

[0101] In the above embodiment, the unmanned aerial vehicle starts from a given starting point, establishes a covert communication channel, and obtains channel parameters: the unmanned aerial vehicle is a mobile sending end, starts from a known starting point D1, the ground user node D0 is a receiving end, and there is a eavesdropping node D3 on the ground, which can eavesdrop the information sent by the unmanned aerial vehicle. The unmanned aerial vehicle flies at a fixed height H>0, realizes the covert communication with the ground user D0 in the case that there is an eavesdropping node D3 on the ground, and reaches a given terminal point D2. The obtained communication parameters include the maximum speed limit V max of the unmanned aerial vehicle, the maximum transmission power limit P max , the minimum flight height H of the unmanned aerial vehicle, the position information of the starting point and the terminal point of the unmanned aerial vehicle D1=(ω 1,x ,ω 1,y ), D2=(ω 2,x ,ω 2,y ), the position information of the ground user node and the eavesdropping node D0=(ω 0,x ,ω 0,y ), D3=(ω 3,x ,ω 3,y ), and the communication duration T between the unmanned aerial vehicle and the ground user.

[0102] In this embodiment, the channel gain is used to represent the channel quality, and since the line-of-sight probability of the unmanned aerial vehicle and the ground node in a short distance is high, the free space path loss model is adopted. For time t, the channel gains of the unmanned aerial vehicle to the ground user node and the eavesdropping node are represented by formulas (1) and (2) respectively.

[0103] When the UAV starts from the starting point, it begins to establish a covert communication channel. According to the relative position information of the UAV to the user node, the channel gain of the UAV to the user node can be obtained and is expressed as (1):

[0104]

[0105] wherein β represents the channel gain with a reference distance of 1 m, r(x(t), y(t)) represents the horizontal distance of the UAV to the ground user node,

[0106] According to the relative position information of the UAV to the eavesdropping node, the channel gain of the UAV to the eavesdropping node can be obtained and is expressed as (2):

[0107]

[0108] wherein β represents the channel gain with a reference distance of 1 m, r w (x(t), y(t)) represents the horizontal distance of the UAV to the eavesdropping node,

[0109] In the above embodiment, in step S2,

[0110] 1) Since the Gaussian distribution is more widely used in real life, this embodiment considers that the received signal and noise of the eavesdropping node are subject to complex Gaussian distribution. The eavesdropping node can only determine whether the UAV is transmitting useful information according to the received signal of L times sensing in each time slot n. For time slot n, the signal received by the eavesdropper for the Lth time can be expressed as formula (3).

[0111]

[0112] wherein σ 2 is the noise power, P[n] is the transmission power of the UAV in the nth time slot, represents the zero hypothesis that the UAV does not transmit, h w [n] is the discrete channel gain of the UAV to the eavesdropping node, and represents the alternative hypothesis that the UAV transmits.

[0113] 2) Obtain the optimal decision distribution under , and express the L signals received at the guard as The likelihood functions under the conditions of are respectively:

[0114]

[0115]

[0116] wherein,

[0117] When , the optimal decision is τ*, which is expressed in the following equation:

[0118]

[0119] where D1and D0represent the binary decision of the eavesdropping node on whether the UAV has transmitted a message, T w [n] can be regarded as the total received power of L observations in the nth time slot.

[0120] According to the probability density function of the received signal , the probability density function of the received signal power is Since obeys the sub-Gaussian distribution and the additivity of the Γ distribution, the distribution of the optimal decision is obtained, which is expressed in equation (4).

[0121]

[0122] where T w [n] can be regarded as the total received power of L observations in the nth time slot.

[0123] 3) Obtain the minimum detection error rate: Based on statistical decision theory, the total detection error probability of the eavesdropper, denoted as ξ, is composed of two parts, i.e., the false alarm probability, denoted as P F[n] , which can be expressed in equation (19). The missed detection probability, denoted as P M[n] , can be expressed in equation (20).

[0124]

[0125]

[0126] where τ* is the optimal decision made by the eavesdropping node.

[0127] Therefore, the total detection error rate can be expressed in equation (5).

[0128]

[0129] where ρ is the set shielding requirement value, when , the optimal decision is τ*, and the minimum detection error rate ξ* is only related to , and γ w is the maximum signal-to-noise ratio at the eavesdropping node that satisfies the minimum detection error rate.

[0130] 3. Calculate the maximum signal-to-noise ratio, so that the power constraint under covert communication can be obtained: Through mathematical derivation, the present application finds that the total detection error rate is monotonically decreasing with respect to the signal-to-noise ratio at L>1. Therefore, the present application can obtain the maximum signal-to-noise ratio γ that satisfies the minimum detection error rate at the eavesdropping node by means of bisection search w . By the power constraint of the unmanned aerial vehicle transmission power P[n] under covert communication can be obtained, which can be represented by formula (6).

[0131]

[0132] wherein γ w is the maximum signal-to-noise ratio that satisfies the minimum detection error rate at the eavesdropping node, σ 2 is the noise variance, β is the channel gain with a reference distance of 1m, H is the fixed flight height of the unmanned aerial vehicle, P max is the maximum transmission power limit set by the unmanned aerial vehicle, and vector r3=(ω 3,x ,ω 3,y ). When the time slot n tends to infinity, the discrete transmission power P[n] can be converted into continuous transmission power P(t).

[0133] 4. Optimize the trajectory for the purpose of maximizing the information throughput of the unmanned aerial vehicle and the ground node communication: For the wireless communication between the unmanned aerial vehicle and the ground node, the corresponding throughput within the period T in which the unmanned aerial vehicle performs the task is represented by formula (21).

[0134]

[0135] wherein B represents the bandwidth, and σ 2 is the noise power level.

[0136] According to the above system model, our goal is to maximize the throughput U({x(t),y(t)}) by optimizing the unmanned aerial vehicle trajectory {x(t),y(t)} under the maximum speed limit V max of the unmanned aerial vehicle. Therefore, the original problem is described as:

[0137]

[0138] wherein v is the flight speed of the unmanned aerial vehicle at time t, vector r=(ω 0,x ,ω 0,y ), and vector r3=(ω 3,x ,ω 3,y ).

[0139] 5. Equivalence of original trajectory problem to mechanical problem in artificial potential field: Obviously, the original problem (OP) contains infinite variables, and the UAV trajectory is continuous in time and spatial position, which makes the trajectory design very challenging. In addition, the objective function is obviously non-convex, which means that it is impossible to obtain an effective optimal solution by convex optimization techniques. In order to construct the optimal UAV trajectory, we introduce the concept of an equivalent potential field, which equivalently transforms the continuous infinite variable UAV non-convex trajectory problem into a minimum potential problem of a rope in an artificial potential field. As shown in FIG. 1. Figure 1 、 2 The equivalence of the problem and the uniqueness of the optimal solution are proved below.

[0140] 1) Consider a new path and velocity information model, and restate the original problem: At each time point, the entire UAV trajectory can be described by two sets of information, namely path information and velocity information. For any UAV trajectory {x(t), y(t)}, the corresponding UAV path can be defined as:

[0141]

[0142] where the path variable s represents the path length from the given starting point D1 along the trajectory {x(t), y(t)} to . Obviously, s ∈ [0, S'], where represents the total length of the rope. Therefore, the path also ends at point D2 from point D1, then The velocity information can also be expressed based on the path model. For any given path variable s, there is a unique corresponding UAV velocity when , and

[0143] According to the above path and velocity information model, the overall throughput is described by equation (24):

[0144]

[0145] The problem (OP) can be equivalently restated as:

[0146]

[0147] 2) Use variable density rope to minimize the gravitational potential field problem: The present invention considers a mechanical problem in a space with a single force field, as shown in FIG. 2. Figure 2 A mass point with M0 is located at a fixed position D0, i.e. Figure 2Earth in the space. Meanwhile, there is a mass point with mass M3located at a fixed position D3in the space. In addition, a variable density rope with mass m is placed in the space, and the two ends of the rope are fixed at positions D1and D2.

[0148] The gravitational potential generated by mass point M0at any other position is given by equation (26).

[0149]

[0150] where G is the gravitational constant, denotes the distance from point to D0.

[0151] We assume that the rope is thin enough and soft enough, so it can be regarded as a single straight line, and each rope segment can be concentrated at a point, denoted by a continuous function representing the shape of the rope. Where s ∈ [0, S'], represents the length of the rope from D1to point , and S' represents the total length of the rope. In addition, the rope linear density p(s) can vary, with a lower limit of p min > 0 and

[0152] Therefore, the total gravitational potential energy of the rope is represented by equation (27):

[0153]

[0154] In order to study the static rope shape (i.e. the flight trajectory of the UAV), a problem of jointly optimizing the rope shape and the rope density p(s) to minimize the total potential energy field can be established as:

[0155]

[0156] According to the principle of minimum total potential energy, if the total potential energy field of the rope is minimized, the rope must be in equilibrium everywhere (net force and torque are zero). Otherwise, under the action of non-zero net force or non-zero net torque, a better solution with lower potential energy will be found.

[0157] 3) Construct an artificial potential energy field to find the equivalence of problems P1 and P2: After careful comparison, we can find the equivalence of the trajectory design problem P1 and the mechanical problem P2. The UAV path total path length S and the UAV speed v(s) can be equivalent to the total rope length S' and the inverse of the rope linear density the maximum speed limit V max of the UAV and the total task time T correspond to the minimum linear density limit p min of the rope and the total mass m of the rope, respectively. Therefore, the maximum information throughput The negative value of the minimum gravitational potential energy Since the expression of the gravitational potential energy field is completely different from that of the information throughput, a new potential energy field needs to be artificially constructed.

[0158] Since the problem P2 is constructed in the gravitational potential field, we can also represent the maximum information transmission rate of the UAV air-ground communication by defining another artificial potential energy field R''(x, y), as shown in equation (10).

[0159]

[0160] Therefore, the original trajectory design problem P1 can be completely transformed into a mechanical problem P3, which is equivalent to the variable density rope balance problem in the artificial potential field, and the problem P3 is represented as:

[0161]

[0162] 6. The UAV flies according to the optimal trajectory expression obtained by solving the equivalent problem, and adjusts the transmission power in time: the optimal solution solving process of the equivalent problem is shown in Figure 4 .

[0163] 1) Describe the force field properties in the potential energy field under covert communication, and determine the optimal rope tension range: as a mechanical concept, the force field in the potential energy field can be described by the negative gradient of the scalar potential function. In the equivalent problem P3 of the UAV trajectory design under covert communication, the force field can be given by equation (12).

[0164]

[0165] where γ w is the maximum signal-to-noise ratio that satisfies the minimum detection error rate at the eavesdropping node mentioned in step S3, in addition, the case of P w ≤ P max can be mathematically transformed into that is, |r(x, y)-r3| 2 <R W 2 , where r w =r3-r(x, y), the bold symbol is a vector, and R w is the shielding range around the eavesdropper D3, and its value is

[0166] It can be observed from the force field that within the shielding range, the force field is superimposed by the force field pointing to the user D0 and the force field pointing to the eavesdropper D3 in the opposite direction; outside the shielding range, the force field only points to the user D0.

[0167] Assuming that the optimal rope design shape is The initial rope tension at D1 is Q0*, and the angle between the tension and the positive direction of the x-axis is a*. Considering the general case that the total task execution time of the UAV is limited (not large enough), i.e., the mass of the rope is insufficient, the optimal rope shape will be strictly limited within the triangular region formed by D i , i∈[0, 1, 2], therefore, the optimal angle a corresponding to the optimal initial tension Q0*

[0168] 2) According to the force balance condition, the mechanical expression is constructed, and the optimal initial rope tension is obtained according to the dichotomy search, which is substituted into the corresponding optimal rope shape expression: In the P2 problem, it is also mentioned that according to the principle of minimum total potential energy, if the total potential energy field of the rope is minimum, the rope must be in force balance everywhere (net force and torque are zero). Under the optimal rope shape, the partial x, y-axis force of D1 to is 0, and the expression is given by formula (13).

[0169]

[0170] wherein, is the absolute value of the optimal solution of the initial rope tension value, a ★ is the optimal solution of the initial rope tension angle, is the optimal rope shape solution, is the absolute value of the force field size at the corresponding position of the optimal rope shape, p min is the minimum rope density, (w 0,x , w 0,y ) is the position of the user node, is the distance from the optimal rope position to the user node. s is for any given path variable, s∈[0, S'], and S' represents the total length of the rope. Q(s) is the rope tension at the optimal rope position . is the sum of the projection of the initial rope tension in the x-axis direction, is the sum of the projection of the initial rope tension in the y-axis direction.

[0171] By formula (13), we can get and by , which can be represented by formula (30):

[0172]

[0173] wherein, s is for any given path variable, s∈[0, S'], and S' represents the total length of the rope. is the position where the optimal rope shape of the rope length at s is located. is the sum of the projections of the gravity and the initial string tension in the x-axis direction, is the sum of the projections of the gravity and the initial string tension in the y-axis direction.

[0174] According to formula (13), as long as the optimal string initial tension value and α ＊ are known, combined with the initial value condition of , the optimal solution of the equivalent problem P3 under the condition of insufficient string mass can be constructed by formula (14).

[0175]

[0176] where s is for any given path variable, s ∈ [0, S'], S' * represents the total length of the string under the optimal solution, m is the total mass of the string, and ρ min is the minimum string density. is the sum of the projections of the gravity and the initial string tension in the x-axis direction, is the sum of the projections of the gravity and the initial string tension in the y-axis direction. (ω 1,x , ω 1,y ) is the starting position of the unmanned aerial vehicle flight.

[0177] After establishing the optimal solution of the string shape, it is necessary to obtain the optimal initial tension through design. The optimal initial tension and the string shape satisfy the following relationship: on the one hand, when the initial string tension angle a is fixed, the larger the initial string tension value |Q0(a)|, the closer the constructed string to the user node D0. Therefore, for any given a, there is only one |Q0(a)| that makes the string pass through the destination D2, which is the optimal initial string tension Q0*. On the other hand, when Q0 = Q0*(a), the string length is monotonically increasing with respect to a. Therefore, for any given string tension value |Q0(a)|, the optimal initial tension Q0* can be obtained by searching a. The solution procedure flowchart of the bisection search is as follows Figure 5 , which can be briefly expressed as: i. Given an initial string tension and angle ii. According to the force balance condition, the mechanical expressions of the string in the x and y directions are constructed, and a series of simplifications are obtained to obtain the string shape iii. If it does not satisfy the condition of passing through the destination and the path being equal to the string length, change the tension size or angle, then return to step ii, if it satisfies, then end the search and output the optimal string shape and the corresponding optimal string tension.

[0178] 3) According to s = Vt, the optimal trajectory {x*(t), y*(t)} of the unmanned aerial vehicle can be constructed from the optimal string shape , and the expression is formula (15).

[0179]

[0180] As the UAV flies, the optimal transmit power of the UAV will be adjusted in time. To achieve the maximization of the throughput, it is always at its maximum transmit power, i.e.

[0181] 7. The UAV reaches the given end point, and the covert communication ends.

[0182] The above embodiments are only examples of the technical solutions of the present application. The method and device involved in the present application are not limited to the content described in the above embodiments, but are subject to the scope defined in the claims. Any modification or supplement or equivalent replacement made by the skilled in the art on the basis of the above embodiments is within the scope claimed by the claims of the present application.

Claims

1. A method for designing a trajectory of an unmanned aerial vehicle (UAV) in covert communication based on mechanical equivalence, characterized in that, The method comprises the following steps: Step S1. The unmanned aerial vehicle sets up a covert communication channel from a given starting point and obtains communication parameters; Step S2: obtaining optimal decision distribution and minimum detection error rate according to noise distribution; the received signal of the eavesdropping node and the noise are subject to complex Gaussian distribution, the total flight communication time is divided into slots, and times of decisions are made in each slot to determine whether the eavesdropper receives the signal sent by the UAV, for the slot , the signal received by the eavesdropper for the time is represented as (3): （3） wherein is the noise power, is the transmit power of the UAV at the th time slot, is the discrete channel gain from the UAV to the eavesdropping node, represents the null hypothesis that the UAV does not transmit, while represents the alternative hypothesis that the UAV transmits. The optimal decision is the one that gives the minimum error rate, since subject to the complex Gaussian distribution and the additivity of the distribution, the distribution of the optimal decision is given by (4): （4） wherein , , may be seen as the total received power of the second observation at the time slot. The total detection error rate can be represented by (5): （5） wherein, is a set masking requirement value, is a false alarm probability, is a missed detection probability, when the optimal decision is the minimum detection error rate is only related to , is a maximum signal-to-noise ratio at the eavesdropping node that satisfies the minimum detection error rate; Step S3: The maximum signal-to-noise ratio is calculated, so that the power constraint under covert communication can be obtained; Step S4: The information throughput of the unmanned aerial vehicle in communication with the ground node is maximized by jointly optimizing the trajectory of the unmanned aerial vehicle and resource allocation; Step S5: The original trajectory problem is equivalent to a mechanical problem in an artificial potential field; Step S6: According to the optimal trajectory expression obtained by solving the equivalent problem, the unmanned aerial vehicle flies and adjusts the transmission power in a timely manner; Step S7: The unmanned aerial vehicle reaches the given end point, and the covert communication ends.

2. The method of claim 1, wherein the method is based on mechanical equivalence. In step S1, the obtained communication parameters include maximum speed limit of the UAV flight , maximum transmit power limit , minimum flight height of the UAV , starting point and ending point position information of the UAV , , position information of the ground user node and the eavesdropping node , , communication duration between the UAV and the ground user .

3. The method of claim 2, wherein the method is based on mechanical equivalence. In step S1, when the unmanned aerial vehicle starts from the starting point, the covert communication channel is established. According to the relative position information of the unmanned aerial vehicle to the user node, the channel gain of the unmanned aerial vehicle to the user node can be obtained, which is represented by (1): （1） wherein, represents a channel gain with a reference distance of 1 m, represents a horizontal distance from the UAV to the ground user node, ; According to the relative position information of the unmanned aerial vehicle to the eavesdropping node, the channel gain of the unmanned aerial vehicle to the eavesdropping node can be obtained, which is represented by (2): （2） wherein, denotes the channel gain with a reference distance of 1m, denotes the horizontal distance from the drone to the eavesdropping node, .

4. The method of claim 2, wherein the method is based on mechanical equivalence. In the step S3, the constraint on the power under covert communication is obtained by a dichotomy search, to get the maximum signal-to-noise ratio at the eavesdropping node satisfying the minimum detection error rate , which is expressed as (6): The constraint on the power of the unmanned aerial vehicle under covert communication is obtained, which is expressed as (6): P n ]​ （6） wherein is the maximum signal-to-noise ratio at the eavesdropping node that satisfies a minimum detection error rate, is the noise power, is the channel gain for a reference distance of 1 m, is the fixed flight altitude of the UAV, is the maximum transmit power limit set for the UAV, vector when the time slot tends to infinity, the discrete transmit power can be converted to the continuous transmit power .

5. The method of claim 3, wherein the method is based on mechanical equivalence. In step S4, the joint optimization of the flight trajectory and the power control makes the unmanned aerial vehicle covert system further improve the communication quality under the condition of meeting the minimum covert communication performance requirement. The problem can be modeled as (7): （7） wherein, represents a bandwidth, is a noise power, is an information throughput between the UAV and the user node at a two-dimensional coordinate at a transmission power .

6. The method of claim 5, wherein the method is based on mechanical equivalence. In step S5, the continuous trajectory design problem of the unmanned aerial vehicle is converted into variable density rope shape design. Considering the new path and speed information model, a new problem model (8) is obtained: （8） wherein, for any drone trajectory , the corresponding drone path is represented as , for any given path variable, for any given path variable the unique corresponding drone velocity, is the transmit power of the drone located at , is the information throughput between the drone and the user node at two-dimensional coordinates , transmit power . Then consider using a variable density rope to minimize the gravitational potential field, and describe the problem in formula (9): （9） wherein, is the total length of the rope for any given path variable, , denotes the total length of the rope, denotes the shape of the rope, is the density of the rope, is the gravitational constant, is the mass of the particle at the user node, denotes the distance from the point to , and is the gravitational potential energy field of the rope for a particle at the user node to the rope with density located at . By constructing an artificial potential field , the information transmission rate of UAV air-ground communication is characterized, and the equivalence of the problem is found and The formula (10) is given: （10） in, An artificial potential field is used to characterize the information transmission rate when a drone communicates with a user node. For the information transmission rate of communication between the drone and the user node, For signal bandwidth, For the channel gain at a reference distance of 1m, For drones The transmission power at that location, It is noise power. The distance from the drone to the user node. This refers to the fixed flight altitude of the drone. Thus, the original trajectory design problem can be completely transformed into a mechanical problem is equivalent to a variable-density rope balancing problem in artificial potential fields, expressed as equation (11): （11） wherein, is the artificial potential field for a user node to a rope located at with a rope density of .

7. The method of claim 2, wherein the method is based on mechanical equivalence. In step S6, The force field in the potential field is described by the negative gradient of the scalar potential function. In the equivalent problem P3 of the trajectory design of the unmanned aerial vehicle under covert communication, the force field can be given by formula (12): （12） wherein is the maximum signal-to-noise ratio at the eavesdropping node mentioned in step S3 that fulfills the minimum detection error rate, and the case can be mathematically transformed into i.e. with the definition with bold symbols being vectors, is the shadowing range around the eavesdropper with the value ; The lowest rope density under the optimal rope shape, i.e. From to The x, y axis force of the part is 0, expression like (13): （13） wherein, is the absolute value of the optimal solution for the initial rope tension value, is the optimal solution for the initial rope tension angle, is the optimal rope shape solution, is the absolute value of the force field magnitude at the corresponding position for the optimal rope shape, is the minimum rope density, is the position of the user node, is the optimal rope position is the distance to the user node, is for any given path variable, , denotes the total length of the rope, is the rope tension at the optimal rope position is the sum representing the projection of the attractive force and the initial rope tension in the axis direction, is the sum representing the projection of the attractive force and the initial rope tension in the axis direction, is the sum representing the projection of the attractive force and the initial rope tension in the at the optimal rope initial tension value and the tension to the angle of the axis positive direction known, combined with the initial value condition, the equivalent problem the optimal solution in the case of insufficient rope mass can be constructed by formula (14): （14） wherein, is the total length of the tether for any given path variable, , represents the total length of the tether under the optimal solution, is the total mass of the tether, is the minimum tether density, is the starting position of the UAV flight; According to optimal trajectory may be constructed by the optimal rope shape can be constructed, denoted as (15): （15）。 8. The method of claim 7, wherein the method is based on mechanical equivalence. As the UAV flies, the optimal transmit power of the UAV will be adjusted in time, and the total transmit power will be maximized for the throughput maximization, i.e. . 9.A system for designing trajectories of unmanned aerial vehicles (UAVs) in covert communications based on mechanical equivalence, comprising: The system comprises a parameter acquisition module, a decision distribution module, a power constraint communication module under covert communication, a trajectory optimization module, a potential field equivalent module, a transmission power acquisition module, and a covert communication end module, wherein The parameter acquisition module acquires the communication parameters in the establishment of the covert communication channel by the unmanned aerial vehicle starting from the given starting point; The decision distribution module is used to obtain the optimal decision distribution and the minimum detection error rate according to the noise distribution; The power constraint communication module under covert communication is used to calculate the maximum signal-to-noise ratio, so that the power constraint under covert communication can be obtained; The trajectory optimization module maximizes the information throughput of the unmanned aerial vehicle in communication with the ground node by jointly optimizing the trajectory of the unmanned aerial vehicle and resource allocation; The potential field equivalent module equivalent the original trajectory problem to a mechanical problem in an artificial potential field; The transmission power acquisition module acquires the optimal trajectory expression obtained by solving the equivalent problem, and the unmanned aerial vehicle flies and adjusts the transmission power in a timely manner; The covert communication end module is used to end the covert communication when the unmanned aerial vehicle reaches the given end point. The unmanned aerial vehicle trajectory design system based on mechanical equivalence under covert communication is used to execute the steps in the unmanned aerial vehicle trajectory design method based on mechanical equivalence under covert communication in any one of claims 1-8.

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