A UAV trajectory design method and system based on mechanical equivalence in Rice channel

Abstract

The present invention provides a method and system for designing UAV trajectories based on mechanical equivalence under Ricean channels. The covert communication requirements under Ricean channels are re-derived, and the optimal transmission power implicit expression of the UAV under the covert communication requirements is introduced and numerically solved. For the continuous trajectory optimization of the UAV, an artificial potential field is designed to obtain a rope shape characterization problem equivalent to the continuous trajectory problem of the UAV. According to the physical properties of the optimal rope shape, the mechanical principle is cleverly used to obtain a closed-form expression of the optimal continuous rope shape, that is, a closed-form expression of the equivalent optimal UAV trajectory. This method is based on the theory of artificial potential field, and equates the non-convex trajectory problem of the UAV with continuous infinite variables to the minimum potential energy problem of the rope under the artificial potential field. It will obtain the closed-form expression of the optimal trajectory of the UAV for the first time in the covert communication scenario of the Ricean channel, which greatly reduces the search space for the solution of the UAV trajectory problem and has broad application prospects.

Description

Technical Field

[0001] The present application relates to the field of wireless communications, and more specifically to a method and system for designing a continuous trajectory of an unmanned aerial vehicle based on mechanical equivalence under a Rice channel. Background Art

[0002] In recent years, with the explosive growth of wireless services, communication security has become a key requirement for wireless networks. In particular, concealing the transmission of secret information is crucial to achieving communication confidentiality. Covert Communication (CC), as an emerging security technology, can prevent other communication nodes from detecting the communication behavior of a wireless transmitter. It can use noise, artificial noise, and power control techniques to make it impossible for an eavesdropper to determine whether the two parties are communicating, thereby hiding the existence of wireless transmission.

[0003] To further expand the scope of wireless services, UAVs (Unmanned Aerial Vehicles, UAVs) can be used as relay platforms to achieve longer-distance communications and meet more stringent communication requirements. Compared with ground wireless networks, UAVs have the characteristics of high mobility and high flexibility in three-dimensional space, and can provide higher communication performance. Therefore, they are widely used in a variety of real-world scenarios, such as data collection, environmental monitoring, and agricultural irrigation.

[0004] It is worth noting that drones are very suitable for covert communications. However, due to the possible line-of-sight conditions between drones and ground eavesdroppers, they are vulnerable to attacks by malicious nodes, and the transmission of information also increases the risk of being detected by malicious nodes. To solve this problem, we explored the application of drones in covert communications. By carefully designing the transmission power and trajectory of the drone, the communication behavior of the drone to the target user node can be hidden from malicious nodes. Since the transmission power and trajectory of the drone are continuous in time and space, and contain the drone position information corresponding to an infinite number of time points, how to obtain the optimal continuous power and trajectory expression of the drone in the world with a low-complexity algorithm is also one of the research difficulties.

[0005] As far as we know, most of the existing UAV covert communication works use simplified line-of-sight channels, often without considering channel fading, and adopt an idealized representation of real-world scenarios. This motivates us to use more realistic and accurate Rician fading to study the performance of UAVs in covert communications. Gaussian white noise in the Rician channel characteristics can effectively confuse the detection of malicious nodes on the ground. However, in the face of UAV trajectory optimization in more complex channel environments, current work mostly obtains suboptimal solutions through discrete optimization or heuristic design, and the complexity increases exponentially with the increase of the area of ​​the UAV service area.

[0006] The present invention first re-derives the covert communication requirements under the Ricean channel, and introduces an implicit expression of the optimal transmission power of the UAV under the covert communication requirements and proposes an efficient numerical solution method. Furthermore, for the continuous trajectory optimization of the UAV, a method based on mechanical equivalence is proposed, which obtains the rope shape characterization problem equivalent to the continuous trajectory problem of the UAV by designing an appropriate artificial potential field. According to the physical properties of the optimal rope shape, the mechanical principle is cleverly used to obtain the closed-form expression of the optimal continuous clue shape, that is, the closed-form expression of the equivalent optimal UAV trajectory. This trajectory design method is based on the theory of artificial potential field, with extremely low complexity, greatly reduces the search space for the solution of the UAV trajectory problem, and has broad application prospects. Summary of the invention

[0007] The present invention first proposes a method based on mechanical equivalence to optimize the design of the optimal joint power and trajectory design of UAVs under Ricean channels. First, by utilizing the channel uncertainty under Ricean channels, the transmission behavior of the UAV is protected from detection by malicious nodes by maximizing the covert communication error rate, thereby deriving the implicit expression of the optimal transmission power of the UAV under covert communication requirements and proposing an efficient numerical solution method. Furthermore, for the continuous trajectory optimization of the UAV, this method cleverly equates the non-convex trajectory problem of the UAV with continuous infinite variables to the minimum potential energy problem of the rope under the artificial potential energy field, and uses the force balance characteristics of the optimal rope to obtain the closed-form expression of the optimal rope shape, that is, the closed-form expression of the optimal UAV trajectory. This method can greatly reduce the time for solving the UAV trajectory solution, and its optimality also shows that this method can be expanded in single-user networks with many complex models and targets (such as obstacle avoidance, mobile user nodes, etc.).

[0008] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0009] A UAV trajectory design method based on mechanical equivalence under Rice channel includes the following steps:

[0010] Step 1: The UAV starts from a given starting point, establishes a covert communication Rice channel, and obtains the relevant parameters of the UAV and the Rice channel;

[0011] Step 2: Malicious nodes are tested using the likelihood ratio criterion, and the optimal test threshold and the optimal detection error rate under the optimal test threshold are obtained according to the Rice channel noise distribution;

[0012] Step 3: Based on the optimal detection error rate in step 2, the numerical solution of the optimal transmission power under covert communication is obtained through local binary search;

[0013] Step 4: By optimizing the trajectory of the UAV to maximize the information throughput when the UAV communicates with the ground node, a joint optimization problem of jointly optimizing the trajectory and transmission power of the UAV is established and the joint optimization problem is converted into a pure trajectory design problem;

[0014] Step 5: Equivalent the pure trajectory design problem to a mechanical problem under an artificial potential energy field;

[0015] Step 6: Based on the optimal trajectory expression obtained by solving the equivalent problem, the UAV flies and adjusts the transmission power in a timely manner, and the optimization result is successfully extracted.

[0016] Furthermore, the drone-related parameters in step 1 include: the maximum speed limit V of the drone flight max , Maximum transmit power limit P max , the minimum flight altitude of the drone H, the starting and ending position information of the drone are D1=(ω 1,x ,ω 1,y )、D2=(ω 2,x ,ω 2,y ), the location information of the ground user node and the malicious node D0 = (ω 0,x ,ω 0,y )、D3=(ω 3,x ,ω 3,y ), the communication duration T between the UAV and the ground user

[0017] Rice channel related parameters include: channel power gain β at unit distance, environmental characteristic parameters a, b, κ0, The basic path loss coefficients ξ0, ξ1 represent random variables of the scattering component

[0018] Furthermore, the optimal detection error rate ξ under the optimal test threshold in step 2 * (τ * )for:

[0019]

[0020] Among them, τ * is the optimal test threshold, P FA (τ * ) is the false alarm probability under the optimal detection threshold, P MD (τ * ) is the false detection probability under the optimal test threshold, and Θ(τ * ) refers to the intermediate parameter under the optimal test threshold,

[0021]

[0022]

[0023] Optimal test threshold τ * By solving get,

[0024] Where I0(·) is the first kind of zero-order modified Bessel function; K is the Rice factor, τ is the given detection threshold, ξ(τ) is the detection error rate under the given detection threshold, c1 and c2 are intermediate parameters, and e is a natural constant.

[0025] Q1(x,y) is the standard Marcum Q function, is the variance of the signal received at the malicious node, σ 2 is the noise variance, and P is the received power.

[0026] Furthermore, the step 3 comprises:

[0027] 1) Set the search range: Given the drone flight range [x min ,x max ],[y min ,y max ], the transmission power search range is [P wmin ,P wmax ], x min ,y min are the horizontal and vertical coordinates of the lower left point of the UAV flight area, x max ,y max are the horizontal and vertical coordinates of the upper right point of the UAV flight area, P wmin ,P wmax are the minimum and maximum values ​​of concealed transmission power, respectively;

[0028] Given the position of the drone, the optimal detection error rate is only related to the optimal transmission power and is monotonic.

[0029] At time t∈[0,T], the optimal transmission power P of the drone under covert communication * (t) can be expressed as:

[0030] P * (t) = min{P w ,P max}

[0031] Among them, P w The transmission power at the malicious node that meets the minimum detection error rate is the required power for covert communication;

[0032] 2) Parameter initialization: Initialize covert communication required power and initialize the optimal transmission power of the neighboring locations

[0033] 3) The optimal transmission power [x, y, P for a given location and its neighboring locations lw ], if the optimal transmission power P of the neighboring location lw = 0, the transmit power search range remains [P wmin ,P wmax ]; if P lw ≠0, the hidden power search range at this location is further narrowed according to the power of the adjacent location [P wmin ,P wmax ]=[P lw -ΔP,P lw +ΔP], where ΔP is the given power error;

[0034] 4) Order And calculate the corresponding detection error rate. If the detection error rate is less than the set value, then P wmax =P w , and repeat step 4); if the detection error rate is greater than the set value, then P wmin =P w , and repeat step 4); if the detection error rate is equal to the set value, continue to step 5);

[0035] 5) If P w ≤P max , then the optimal transmission power at the current position is P * =P w ; On the contrary, the optimal transmission power at the current position is P * =P max ; Continue to search for the next position and update P lw =P * , get the new position and the optimal transmission power of the new position, and jump back to step 3); when all positions are searched, get the numerical solution of the optimal transmission power under covert communication.

[0036] Furthermore, the joint optimization problem OP of jointly optimizing the trajectory of the UAV and the transmission power in step 4 is:

[0037]

[0038] The optimal transmission power is characterized by the maximum hardware probability constraint C1 and the covert communication requirement constraint C2 in the original problem OP, and the joint optimization problem OP of jointly optimizing the trajectory of the UAV and the transmission power is transformed into a pure trajectory design problem P1:

[0039]

[0040] Among them, x(t) and y(t) are the horizontal and vertical coordinates of the UAV at time t, P(t) represents the transmission power of the UAV at time t; R ab (t) and They represent the information transmission rate and the flight speed of the UAV at time t respectively. Constraints C1 and C3 represent the maximum hardware power constraint and maximum speed constraint of the UAV respectively. C2 is the covert communication requirement constraint. C4 and C5 represent the starting point and ending point position constraints of the UAV respectively.

[0041] Furthermore, the information transmission rate R at time t ab (t) is:

[0042]

[0043] Among them, f n To achieve the rate R ab Under the interruption probability requirement, the effective fading power to ensure reliable transmission of the UAV is expressed as p out = the only solution of η, where p out represents the channel outage probability, η is the given maximum tolerable outage probability, β n is the channel gain between the UAV and the user,

[0044] f n Expressed as a function of the drone trajectory:

[0045]

[0046] Where Q -1 () represents the inverse function of Marcum Q.

[0047] Furthermore, in step 5, the pure trajectory design problem is transformed into a mechanical problem MP. The continuous trajectory design problem of the UAV is equivalent to the variable density rope balance problem in the artificial potential field, which is expressed as follows:

[0048]

[0049] The path variable s represents the path from a given starting point along the trajectory {x(t), y(t)} to The path length is s∈[0,S], where is the total length of the rope, are the x- and y-coordinates of the equivalent rope shape in space, ρ(s) represents the rope linear density, and the inverse of the rope linear density is Equivalent to the speed v(s) of the drone, the minimum line density of the rope is limited to ρ min and the total mass of the rope m correspond to the maximum speed limit of the drone V max and the total task time T, are the x- and y-coordinates of the starting point of the equivalent rope, are the x- and y-coordinates of the end point of the equivalent rope, respectively;

[0050] By constructing an artificial potential energy field R″(x,y), the maximum information transmission rate of the UAV air-to-ground communication is characterized, and the equivalence of P1 and the physical problem is found. The potential energy field expression is as follows:

[0051]

[0052] Among them, P(x,y) is obtained by converting P(t)=P(x(t),y(t))=P(x(s),y(s))=P(x,y) in the expression of the drone transmission power at time t.

[0053] Furthermore, in step 6, the negative gradient of the scalar potential function is used to describe the force field in the potential energy field, and the force field can be expressed as:

[0054]

[0055] Among them, g(x,y) represents the force field, represents the negative gradient, g1(q(t),P(t)) is the force field under the maximum hardware power limit, and g 2x (q(t),P(t)),g 2y (q(t), P(t)) are the force field scalars in the x and y directions respectively under the power limit required for covert communication;

[0056] Based on the numerical solution of the optimal transmission power in the UAV flight area obtained in step 3, the force field size corresponding to each UAV position, i.e. the rope position, in the corresponding area is obtained.

[0057] Under the optimal rope shape, the distance from the starting point D1 of the drone to any point on the rope is The combined force on the x and y axes of the part is 0.

[0058] At the optimal initial rope tension and the optimal tension angle of the rope When the optimal solution is known, the rope shape is combined Initial value conditions of the equivalent problem MP, rope shape when the rope mass is insufficient for:

[0059]

[0060] Among them, A1 * (s) represents the sum of the gravitational force and the projection of the initial rope tension in the x-axis direction, A2 * (s) is the sum of the gravity and the projection of the initial rope tension in the y-axis direction;

[0061] The optimal initial rope tension corresponding to the optimal solution of rope shape can be solved by binary search, and the solution process is:

[0062] 1) Given an initial rope tension and angle;

[0063] 2) Construct the mechanical expressions of the rope in the x and y directions according to the pre-designed force field table and force balance conditions, and simplify the rope shape;

[0064] 3) If the condition that the path through the destination point is equal to the rope length and the tension or angle is changed does not meet the requirement, then return to step (2). If the condition is met, then the search ends and the optimal rope shape and the corresponding optimal rope tension are output;

[0065] Based on the optimal rope shape Solve the optimal trajectory q of the UAV * (t) = {x*(t), y*(t)}:

[0066]

[0067] Among them, s = Vt. As the UAV flies, the UAV's transmission power is adjusted in time, P * (t) = min{P w (q * (t)),P max}, P w (q * (t)) is the function of the covert communication power requirement with respect to the optimal trajectory of the UAV.

[0068] On the other hand, the present invention provides a UAV trajectory design system based on mechanical equivalence under Rice channel, comprising:

[0069] Module 1 is used for the UAV to start from a given starting point, establish a covert communication Rice channel, and obtain the relevant parameters of the UAV and the Rice channel;

[0070] Module 2 is used to detect malicious nodes using the likelihood ratio criterion, and obtains the optimal detection threshold and the optimal detection error rate under the optimal detection threshold according to the Rice channel noise distribution;

[0071] Module 3 is used to obtain the numerical solution of the optimal transmission power in covert communication through local binary search based on the optimal detection error rate;

[0072] Module 4 is used to maximize the information throughput when the UAV communicates with the ground node by optimizing the trajectory of the UAV, establish a joint optimization problem of jointly optimizing the trajectory and transmission power of the UAV and convert the joint optimization problem into a pure trajectory design problem;

[0073] Module 5, which is used to convert pure trajectory design problems into mechanical problems under artificial potential energy fields;

[0074] Module six is ​​used to fly the drone according to the optimal trajectory expression obtained by solving the equivalent problem, and adjust the transmission power in time to successfully extract the optimization result;

[0075] Compared with the prior art, the present invention has the following beneficial effects:

[0076] The present invention provides an efficient solution to the joint power and continuous trajectory design of UAVs in the Ricean channel covert communication scenario. First, the present invention proposes an efficient numerical solution to the optimal detection probability of covert communication after introducing complex integrals under the Ricean channel. Secondly, the present invention proposes a method based on mechanical equivalence, which obtains a rope shape characterization problem equivalent to the UAV continuous trajectory problem by designing an appropriate artificial potential field, and obtains the optimal solution to the UAV continuous trajectory using the principle of mechanics. By jointly optimizing the trajectory and transmission power of the UAV, the covert system can maximize the information throughput while meeting the minimum concealment requirements. This method can obtain a closed-form expression of the optimal continuous trajectory with extremely low complexity, which greatly reduces the search space for solutions to the UAV trajectory problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0078] Figure 1 This is a model diagram of the UAV system under the covert communication Rice channel.

[0079] Figure 2 Flowchart for the implementation of a covert communication method involving drones.

[0080] Figure 3 for Figure 2 Flowchart for finding the optimal solution to equivalent mechanical problems.

[0081] Figure 4 for Figure 3 Flowchart of the program for binary search to obtain the optimal initial rope tension. DETAILED DESCRIPTION

[0082] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0083] Example 1

[0084] This embodiment takes a covert communication network with a single user node and a single malicious node as an example, and a drone is used as a mobile base station. Figure 1 As shown. The user node is placed in D0 = (ω 0,x ,ω 0,y ), the malicious node is placed in D3 = (ω 3,x ,ω 3,y ), are located on the ground. The drone starts from a given starting position D1 = (ω 1,x ,ω 1,y ) and flies at a fixed altitude H>0 to a given destination D2=(ω 2,x ,ω 2,y ), and communicate wirelessly with ground users while minimizing information leakage. The horizontal position of the drone at time t ≥ 0 is represented by (x(t), y(t)), where t is a continuous variable.

[0085] Reference Figure 2 , the design method and system of continuous trajectory of UAV in concealed communication environment based on mechanical equivalence mainly include the following steps:

[0086] Step 1: The UAV starts from a given starting point, establishes a covert communication Ricean channel, and obtains relevant parameters, including UAV-related parameters and Ricean channel-related parameters.

[0087] The obtained drone related parameters include the maximum speed limit V of the drone flight max , Maximum transmit power limit P max , the minimum flight altitude of the drone H, the starting and ending position information of the drone are D1=(ω 1,x ,ω 1,y )、D2=(ω 2,x ,ω 2,y ), the location information of the ground user node and the malicious node D0 = (ω 0,x ,ω 0,y )、D3=(ω 3,x ,ω 3,y ), the communication duration between the UAV and the ground user is T.

[0088] The obtained Rice channel related parameters include the channel power gain β0 at unit distance, environmental characteristic parameters a, b, κ0, The basic path loss coefficients ξ0, ξ1 represent random variables of the scattering component

[0089] The starting and ending points of the drone, the flight altitude, and the positions of the ground nodes are all known. When the drone departs from the starting point, it begins to establish a covert communication channel. Based on the relative position information, the channel-related parameters from the drone to the user node and the malicious node can be obtained, including the channel power gain per unit distance, environmental characteristic parameters, and basic path loss coefficient.

[0090] When the drone starts from the starting point, it starts to establish a covert communication Rice channel. All wireless channels experience large-scale path loss and small-scale fading, so the channel coefficient from the drone to the user node (malicious node) can be modeled as:

[0091]

[0092] Among them, β n =βd -a represents the large-scale average channel power, and d represents the horizontal distance from the drone to the target user node (malicious node). In addition, the path loss index α can be calculated using the angle-dependent probability model as follows:

[0093]

[0094] Among them, the elevation angle H represents the fixed flight altitude of the drone.

[0095] In addition, the small-scale Rice fading coefficient g can be modeled as follows, satisfying

[0096]

[0097] in, is the deterministic line-of-sight channel component, satisfying is a zero-mean unit-variance cyclically symmetric complex Gaussian (CSCG) random variable of the scattered component. Therefore, the Rice fading coefficient exhibits a complex Gaussian distribution, satisfying In addition, the Ricean factor K is a function of the elevation angle θ and can be given by:

[0098]

[0099] Among them, κ0 and It is a parameter related to the environment. It can be seen that when K = 0, Rice fading can be simplified to Rayleigh fading, which is often used to describe small-scale fading.

[0100] About complex Gaussian distribution: In probability theory, complex Gaussian distribution is used to describe composite random variables (real and imaginary parts are random variables with joint normal distribution). Assuming X and Y are random vectors in k-dimensional real space, and vector [XY] is a 2k-dimensional normal random vector, then the composite random variable Z = X + iY has a complex Gaussian distribution, which can be represented by the following three parameters: location parameter μ = E [Z], covariance matrix The correlation matrix C = E[(Z-μ)(Z-μ)′], where Z′ represents the matrix transpose, denotes complex conjugation, and the location parameter μ can be any k-dimensional complex vector. The covariance matrix Γ must be Hermitian and nonnegative definite, and the correlation matrix C is symmetric.

[0101] Step 2: Malicious nodes are tested using the likelihood ratio criterion, and the optimal test threshold and the optimal detection error rate under the optimal test threshold are obtained according to the Rice channel noise distribution;

[0102] This embodiment intends to consider that the received signal and noise of the malicious node obey the complex Gaussian distribution. In order to detect whether the drone has transmission behavior, the malicious node uses the likelihood ratio criterion for inspection, samples N times for inspection within the mission time, and takes the average received power T w as a test statistic.

[0103] At time t, the signal received by the malicious node can be expressed as (5):

[0104]

[0105] Among them, n w (t) is the Gaussian noise at the malicious node, with variance σ 2 P(t) is the transmission power of the UAV at time t, represents the null hypothesis that the drone does not launch, and represents the alternative hypothesis of the drone transmission. In order to detect whether the drone has transmission behavior, the malicious node uses the likelihood ratio criterion to test and takes the average received power T w As the test statistic. Sample N times for testing within the task time, the decision rule can be expressed as:

[0106]

[0107] Among them, τ represents the test threshold. Based on this threshold, the corresponding covert communication error rate ξ at the malicious node can be obtained. The detection error rate consists of two parts, including the false alarm probability P FA and the false detection probability P MD , respectively expressed as:

[0108]

[0109] P MD =Pr(P w ≤τ|H1)=Pr(Pβg 2 +σ 2 ≤τ|H1) (8)

[0110] P MD Involves the joint distribution of two independent random variables. For ease of reading, let λ1 = Pβg 2 ,λ2=σ 2 According to the mathematical relationship, the latter obeys the Γ distribution, and the former obeys the non-central chi-square distribution with the Rice factor K. The probability density function can be given by the following formula:

[0111]

[0112] in, I0(·) is the first kind of zero-order modified Bessel function. From this, we can get a further expression of the false detection probability:

[0113]

[0114] in, Q1(x, y) is the standard Marcum Q function. For ease of reading, the present invention defines the parameters to make the formula more concise.

[0115] About Γ distribution: Γ distribution is a continuous probability function in statistics and a very important distribution in probability statistics. The parameter α in the distribution is called the shape parameter, and β is called the inverse scale parameter. The mean and variance are Regarding the additivity of Γ distribution, for two independent random variables X and Y, and X~Γ(a,γ), Y~Γ(b,γ), then Z=X+Y~Γ(a+b,γ).

[0116] Therefore, for a given test threshold τ, the total error probability can be expressed as:

[0117]

[0118] For covert communication, the ground malicious node aims to minimize the probability of detection error. At this time, the given detection threshold is optimal, that is, τ * . We can solve To obtain. Due to the integral of the random fading of the Rice channel, the optimal detection threshold at the ground malicious node has an expression in the form of Marcum Q function, so the detection error probability is characterized by Marcum Q function. Based on this, the optimal detection error rate ξ can be obtained * (τ *)for:

[0119]

[0120] Among them, the covert communication requirements must meet * (τ * )≥1-∈, ∈ is the set concealment requirement value. It should be noted that, according to the definition, the optimal detection error rate under the optimal threshold is only related to the current position (x, y) and the transmission power P(t).

[0121] Step 3: Based on the optimal detection error rate in step 2, the numerical solution of the optimal transmission power under covert communication is obtained through local binary search;

[0122] Due to the integral of random fading of the Rice channel, the optimal detection threshold at the ground malicious node in step 2 has an expression in the form of Marcum Q function. Therefore, through the approximate function of formula (17) in step 4, the optimal threshold at a given drone position can be obtained as an approximate expression of power, that is,

[0123] Given the approximate closed-form expression of the optimal threshold, the optimal detection error rate defined in formula (12) is only related to the optimal transmission power and is monotonic under a given drone position. Therefore, the present invention uses a binary search method to use ξ * = 1-∈, the transmission power P of the malicious node that satisfies the minimum detection error rate can be obtained w Combined with the maximum hardware power constraint P of the UAV max , the optimal transmission power P(t) for UAV under covert communication can be expressed as:

[0124] P * (t) = min{P w ,P max} (13)

[0125] Among them, P w is the implicit function related to the current position of the UAV, P max is the set value. By traversing the UAV flight area (this is a pre-design determined before flying from the starting point), the optimal transmission power at the corresponding position can be obtained. Due to the continuity of the UAV flight process in space and time, the optimal transmission power between adjacent positions is continuous and related. Further, in order to optimize the operation rate of the algorithm, the present invention adopts a local two-search method to obtain the algorithm process of the optimal transmission power under a given concealment requirement value:

[0126] 1) Set the search range: Given the drone flight range [x min ,x max ],[y min ,ymax ], the transmission power search range is [P wmin ,P wmax ], x min ,y min are the horizontal and vertical coordinates of the lower left point of the UAV flight area, x max ,y max are the horizontal and vertical coordinates of the upper right point of the UAV flight area, P wmin ,P wmax are the minimum and maximum values ​​of concealed transmission power, respectively;

[0127] Given the position of the drone, the optimal detection error rate is only related to the optimal transmission power and is monotonic.

[0128] At time t∈[0,T], the optimal transmission power P of the drone under covert communication * (t) can be expressed as:

[0129] P * (t) = min{P w ,P max}

[0130] Among them, P w The transmission power at the malicious node that meets the minimum detection error rate is the required power for covert communication;

[0131] 2) Parameter initialization: Initialize covert communication required power and initialize the optimal transmission power of the neighboring locations

[0132] 3) The optimal transmission power [x, y, P for a given location and its neighboring locations lw ], if the optimal transmission power P of the neighboring location lw = 0, the transmit power search range remains [P wmin ,P wmax ]; if P lw ≠0, the hidden power search range at this location is further narrowed according to the power of the adjacent location [P wmin ,P wmax ]=[P lw -ΔP,P lw +ΔP], where ΔP is the given power error;

[0133] 4) Order And calculate the corresponding detection error rate. If the detection error rate is less than the set value, then P wmax =P w , and repeat step 4); if the detection error rate is greater than the set value, then P wmin =P w, and repeat step 4); if the detection error rate is equal to the set value, continue to step 5);

[0134] 5) If P w ≤P max , then the optimal transmission power at the current position is P * =P w ; On the contrary, the optimal transmission power at the current position is P * =P max ; Continue to search for the next position and update P lw =P * , get the new position and the optimal transmission power of the new position, and jump back to step 3); when all positions are searched, get the numerical solution of the optimal transmission power under covert communication.

[0135] Step 4: By optimizing the trajectory of the UAV to maximize the information throughput when the UAV communicates with the ground node, a joint optimization problem of jointly optimizing the trajectory and transmission power of the UAV is established and the joint optimization problem is converted into a pure trajectory design problem;

[0136] The present invention optimizes the flight trajectory and power control jointly, so that the UAV concealed system can further improve the communication quality while meeting the minimum concealed communication performance requirements. However, due to the channel uncertainty of the Ricean channel and the unknown channel capacity, we need to consider the impact of the interruption probability to model the optimization problem.

[0137] For time t, the maximum achievable rate from the drone to the target node can be expressed as:

[0138]

[0139] Among them, h ab represents the channel coefficient between the UAV and the target node in formula (1), P * (t) represents the optimal transmission power of the UAV at time t. For the trajectory design of the UAV, due to the lack of knowledge of the instantaneous channel of the UAV during flight, that is, g ab The knowledge at time t is unknown and the above rates are not completely known.

[0140] For time t, the fixed information transmission rate R between the UAV and the target node is given ab (t), when the maximum achievable rate C is lower than R ab When , the transmission information is considered to be interrupted. The interruption probability of information can be expressed as:

[0141]

[0142] Among them, Q1(x,y) is the standard Marcum Q function. In order to maximize the communication performance, it is often given by out=η(0<η≤0.1) to select the fixed information transmission rate R ab Combining formula (14), we can get the information transmission rate R at time t ab The expression of (t) is:

[0143]

[0144] Among them, f n Indicates p out =η, which can be understood as the only solution that can achieve the rate R ab Under the interruption probability requirement, the effective fading power to ensure reliable transmission of the UAV is also called effective fading power. Note that f n It can be expressed as a function of the trajectory of the UAV, That is to say Since the inverse function of the Marcum Q function is difficult to express mathematically, the present invention further approximates it with elementary functions, which can be expressed as:

[0145]

[0146] Among them, x0 can be obtained by the equation Get. Q -1 (y) is the inverse Q function.

[0147] Therefore, the present invention maximizes the information transmission throughput between the UAV and the target user by jointly optimizing the UAV trajectory and the transmission power. The joint optimization problem is modeled as (18):

[0148]

[0149] The optimal transmission power is characterized by the maximum hardware probability constraint C1 and the covert communication requirement constraint C2 in the original problem OP, and the joint optimization problem OP of jointly optimizing the trajectory of the UAV and the transmission power is transformed into a pure trajectory design problem P1:

[0150]

[0151] Among them, x(t) and y(t) are the horizontal and vertical coordinates of the UAV at time t, P(t) represents the transmission power of the UAV at time t; R ab (t) and They represent the information transmission rate and the flight speed of the UAV at time t respectively. Constraints C1 and C3 represent the maximum hardware power constraint and maximum speed constraint of the UAV respectively. C2 is the covert communication requirement constraint. C4 and C5 represent the starting point and ending point position constraints of the UAV respectively.

[0152] Compared with the existing traditional optimization algorithm, which cannot handle the convex approximation problem of drone trajectory design under the Rice channel in the covert communication scenario, the mechanical analysis strategy proposed in this embodiment is still applicable to this Rician random fading scenario. The key difference is that, based on the above discussion, the present invention needs to define an artificial potential field (APF) for characterizing the achievable rate between the drone and the ground user. In this fading case, the expression of the APF involves two Marcum Q functions (from the characteristics of two Rician fading links, namely the drone-ground malicious node link and the drone-ground user link). Note that the Marcum Q function, as an integral function, lacks a standard derivative expression in mathematics, which makes it different when calculating the force field generated by the APF. There are two possible ways to obtain this force field: one is to use numerical methods or numerical integration techniques to approximate the solution. The other is that specific mathematical techniques and approximation methods can be used to simplify the problem and approximate the derivative of the MarcumQ function. However, both introduce additional approximation errors, making it impossible to obtain the optimal continuous trajectory and the corresponding optimal resource allocation solution. Therefore, it is more likely not to be a closed-form optimal solution, but an approximate solution that is finally achieved. However, under the existing traditional optimization algorithm, when there is no closed-form solution for the optimal power, it is impossible to handle the convex approximation of the information transmission rate between infinite UAV positions and ground users at infinite time points, and thus cannot handle the problem. Therefore, the trajectory design method based on the artificial potential field still has great significance in dealing with the solution ideas provided by the random fading of the Rice channel, including the elementary function approximation introduced by formula (17) and the use of numerical methods to obtain the force field size at the corresponding position through formula (22).

[0153] Step 5: Equivalent the pure trajectory design problem to a mechanical problem under an artificial potential energy field;

[0154] According to the equivalence of the problem, the present invention cleverly transforms the continuous trajectory design problem of the UAV into the design of the shape of the variable density rope to solve the problem of minimizing the artificial potential field. The present invention constructs an artificial potential field R″(x,y) to characterize the maximum information transmission rate of the UAV during air-to-ground communication, and finds the equivalence of P1 with the physical problem. The potential field expression is as follows:

[0155]

[0156] Therefore, the original trajectory design problem P1 can be completely transformed into the mechanical problem MP. The UAV continuous trajectory design problem is equivalent to the variable density rope balance problem in the artificial potential field, which can be expressed as follows:

[0157]

[0158] The path variable s represents the path from a given starting point along the trajectory {x(t), y(t)} to The path length is s∈[0,S], where is the total length of the rope, are the x- and y-coordinates of the equivalent rope shape in space, ρ(s) represents the rope linear density, and the inverse of the rope linear density is Equivalent to the speed v(s) of the drone, the minimum line density of the rope is limited to ρ min and the total mass of the rope m correspond to the maximum speed limit of the drone V max and the total task time T, are the x- and y-coordinates of the starting point of the equivalent rope, are the x-coordinate and y-coordinate of the end point of the equivalent rope respectively.

[0159] Step 6: Based on the optimal trajectory expression obtained by solving the equivalent problem, the UAV flies and adjusts the transmission power in a timely manner, and the optimization result is successfully extracted.

[0160] The present invention uses the negative gradient of the scalar potential function to describe the force field in the potential energy field. The force field can be expressed as:

[0161]

[0162] Note that the force field has a direction. According to formula (13), outside the hidden field P w >P max , the transmission power is subject to the maximum hardware constraint rather than the covert communication power constraint, expressed as P = P max At this time, the UAV is considered to be free from interference from malicious nodes on the ground, g(x,y)=g1(q(t),P(t)), and the force field size is only related to the distance from the UAV to the target node. w ≤P max , the transmission power is subject to the covert communication power constraint rather than the maximum hardware constraint, expressed as P = P w At this time, the UAV is considered to be interfered by malicious nodes on the ground, g(x,y) = g 2x (q(t),P(t))x+g 2y (q(t), P(t))y, the force field size is related to the distance from the drone to the target node and the distance from the drone to the malicious node. Note that since the optimal transmission power is the numerical solution table for the drone flight area obtained by step 3), according to formula (22), the present invention can obtain the force field size (including x direction and y direction) corresponding to each drone position (rope position) in the corresponding area in advance.

[0163] According to the principle of minimum total potential energy, if the total potential energy field of the rope is minimized, then the rope must be balanced 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. From D1 to any point on the rope The resultant force on the x and y axes is 0, and the expression is as follows:

[0164]

[0165] The solution flow chart is as follows Figure 3 :

[0166] 1) Describe and define the force field properties in the potential energy field under covert communication and determine the optimal rope tension range: As a mechanical concept, the negative gradient of the scalar potential function can be used to describe the force field in the potential energy field. In the equivalent problem MP of UAV trajectory design under covert communication, the force field can be given by formula (22).

[0167] Assume that the optimal rope design shape is The initial rope tension at D1 is The angle between the tension and the positive direction of the x-axis is a*. Considering the general situation, the total mission execution time of the drone is limited (not large enough), that is, when the rope quality is insufficient, the optimal rope shape is Will be strictly limited to D i , i∈[0,1,2], therefore, the optimal angle corresponding to the optimal initial tension Q0*

[0168] 2) Construct a mechanical expression based on the force balance condition, and obtain the optimal initial rope tension through binary search. Substituting it into the optimal rope shape expression, we can get the corresponding expression: According to the principle of minimum total potential energy, if the total potential energy field of the rope is the minimum, the rope must be balanced everywhere (the net force and torque are zero). Under the optimal rope shape, from D1 to The resultant force on the x and y axes is 0, and the expressions are given by formulas (23) and (24).

[0169] According to the force balance formula, we can get but It can be expressed as:

[0170]

[0171] At the optimal initial rope tension and Known cases, combined The optimal solution of the equivalent problem MP under the condition of insufficient rope quality It can be constructed from formula (25):

[0172]

[0173] After establishing the optimal solution for the rope shape, it is necessary to obtain the optimal initial tension through design. The optimal initial tension and rope shape satisfy the following relationship: On the one hand, when a is fixed, the larger Q0 is, the closer the constructed rope will be to the user node D0. Therefore, for any given a, there is only one |Q0(a)| that just makes the rope pass through the destination D2, which is Q0*. On the other hand, when Q0=Q0*(a), the rope length increases monotonically with respect to a. Therefore, for any given rope tension |Q0(a)|, the optimal initial tension Q0* can be obtained by searching a. The flowchart of the binary search solution program is as follows Figure 4 , which can be briefly described as: i. Given an initial rope tension and angle ii. Construct the mechanical expression of the rope in the x and y directions according to the force balance condition, and obtain the rope shape through a series of simplifications iii. If the condition that the rope length is equal to the destination point and the path is not satisfied, change the tension size or angle, and return to step ii. If it is satisfied, end the search and output the optimal rope shape and the corresponding optimal rope tension.

[0174] 3) According to s = Vt, the optimal trajectory of the drone {x*(t), y*(t)} can be obtained from the optimal rope shape Constructed, the expression is formula (26).

[0175]

[0176] As the drone flies, the transmission power of the drone will be adjusted in time. In order to maximize the throughput, the maximum transmission power is always P * (t) = min{P w (q * (t)),P max}.

[0177] As the drone flies, the transmission power of the drone will be adjusted in time, P * (t) = min{P w (q * (t)),P max}

[0178] When the drone reaches the given destination, the covert communication ends.

[0179] It should be understood that parts not elaborated in detail in this specification belong to the prior art.

[0180] It should be understood that the above description of the preferred embodiment is relatively detailed, and it cannot be considered as limiting the scope of protection of the patent of the present invention. It is not necessary and impossible to list all the embodiments here. Under the enlightenment of the present invention, ordinary technicians in this field can also make substitutions or modifications without departing from the scope of protection of the claims of the present invention, which all fall within the scope of protection of the present invention. The scope of protection of the present invention shall be based on the attached claims.

Claims

1. A UAV trajectory design method based on mechanical equivalence under Rice channel, characterized in that: The steps include: Step 1: The UAV starts from a given starting point, establishes a covert communication Rice channel, and obtains the relevant parameters of the UAV and the Rice channel; including: the maximum speed limit V of the UAV flight max , Maximum transmit power limit P max , the minimum flight altitude of the drone H, the starting and ending position information of the drone are D1=(ω 1,x ,ω 1,y )、D2=(ω 2,x ,ω 2,y ), the location information of the ground user node and the malicious node D0 = (ω 0,x ,ω 0,y )、D3=(ω 3,x ,ω 3,y ), the communication duration T between the UAV and the ground user; Rice channel related parameters include: channel power gain β at unit distance, environmental characteristic parameters a, b, κ0, The basic path loss coefficients ξ0, ξ1 represent random variables of the scattering component Step 2: Malicious nodes are tested using the likelihood ratio criterion. According to the Rice channel noise distribution, the optimal test threshold and the optimal detection error rate under the optimal test threshold are obtained; the optimal detection error rate ξ under the optimal test threshold is * (τ * )for: Among them, τ * is the optimal test threshold, P FA (τ * ) is the false alarm probability under the optimal detection threshold, P MD (τ * ) is the false detection probability under the optimal test threshold, and Θ(τ * ) refers to the intermediate parameter under the optimal test threshold, Optimal test threshold τ * By solving get, Where I0(·) is the first kind of zero-order modified Bessel function; K is the Rice factor, For a given detection threshold, is the detection error rate under a given detection threshold, c1 and c2 are intermediate parameters, and e is a natural constant. Q1(x,y) is the standard Marcum Q function, is the variance of the signal received at the malicious node, σ 2 is the noise variance, P is the received power; Step 3: Based on the optimal detection error rate in step 2, the numerical solution of the optimal transmission power under covert communication is obtained through local binary search; Step 4: By optimizing the trajectory of the UAV to maximize the information throughput when the UAV communicates with the ground node, a joint optimization problem of jointly optimizing the trajectory and transmission power of the UAV is established and the joint optimization problem is converted into a pure trajectory design problem; Step 5: Equivalent the pure trajectory design problem to a mechanical problem under an artificial potential energy field; Step 6: Based on the optimal trajectory expression obtained by solving the equivalent problem, the UAV flies and adjusts the transmission power in a timely manner, and the optimization result is successfully extracted.

2. The method for designing a UAV trajectory based on mechanical equivalence under a Rice channel as claimed in claim 1, characterized in that: The step 3 comprises: 1) Set the search range: Given the drone flight range [x min ,x max ],[y min ,y max ], the transmission power search range is [P wmin ,P wmax ], x min ,y min are the horizontal and vertical coordinates of the lower left point of the UAV flight area, x max ,y max are the horizontal and vertical coordinates of the upper right point of the UAV flight area, P wmin ,P wmax are the minimum and maximum values ​​of concealed transmission power, respectively; Given the position of the drone, the optimal detection error rate is only related to the optimal transmission power and is monotonic. At time t∈[0,T], the optimal transmission power P of the drone under covert communication * (t) can be expressed as: P * (t)=min{P w ,P max } Among them, P w The transmission power at the malicious node that meets the minimum detection error rate is the required power for covert communication; 2) Parameter initialization: Initialize covert communication required power and initialize the optimal transmission power of the neighboring locations 3) The optimal transmission power [x, y, P for a given location and its neighboring locations lw ], if the optimal transmission power P of the neighboring location lw = 0, the transmit power search range remains [P wmin ,P wmax ]; if P lw ≠0, the hidden power search range at this location is further narrowed according to the power of the adjacent location [P wmin ,P wmax ]=[P lw -ΔP,P lw +ΔP], where ΔP is the given power error; 4) Order And calculate the corresponding detection error rate. If the detection error rate is less than the set value, then P wmax =P w , and repeat step 4); if the detection error rate is greater than the set value, then P wmin =P w , and repeat step 4); if the detection error rate is equal to the set value, continue to step 5); 5) If P w ≤P max , then the optimal transmission power at the current position is P * =P w ; On the contrary, the optimal transmission power at the current position is P * =P max ; Continue to search for the next position and update P lw =P * , get the new position and the optimal transmission power of the new position, and jump back to step 3); when all positions are searched, get the numerical solution of the optimal transmission power under covert communication.

3. The method for designing a UAV trajectory based on mechanical equivalence under a Rice channel as claimed in claim 2, characterized in that: The joint optimization problem OP of jointly optimizing the trajectory and transmission power of the UAV in step 4 is: s.t.C1:P(t)≤P max , C2:ξ*≥1-∈, C4:(x(0),y(0))=(ω 1,x ,ω 1,y ), C5:(x(T),y(T))=(ω 2,x ,ω 2,y ). ∈ is the set concealment requirement value, T is the communication duration between the UAV and the ground user; The optimal transmission power is characterized by the maximum hardware probability constraint C1 and the covert communication requirement constraint C2 in the original problem OP, and the joint optimization problem OP of jointly optimizing the trajectory of the UAV and the transmission power is transformed into a pure trajectory design problem P1: C2:(x(0),y(0))=(ω 1,x ,oh 1,y ), C3:(x(T),y(T))=(ω 2,x ,ω 2,y ). Among them, x(t) and y(t) are the horizontal and vertical coordinates of the UAV at time t, P(t) represents the transmission power of the UAV at time t; R ab (t) and They represent the information transmission rate and the flight speed of the UAV at time t respectively. Constraints C1 and C3 represent the maximum hardware power constraint and maximum speed constraint of the UAV respectively. C2 is the covert communication requirement constraint. C4 and C5 represent the starting point and ending point position constraints of the UAV respectively.

4. The method for designing a UAV trajectory based on mechanical equivalence under a Rice channel as claimed in claim 3, characterized in that: The information transmission rate R at time t ab (t) is: Among them, f n To achieve the rate R ab Under the interruption probability requirement, the effective fading power to ensure reliable transmission of the UAV is expressed as p out = the only solution of η, where p out represents the channel outage probability, η is the given maximum tolerable outage probability, β n is the channel gain between the UAV and the user, f n Expressed as a function of the drone trajectory: Where Q -1 () represents the inverse function of Marcum Q.

5. The method for designing a UAV trajectory based on mechanical equivalence under a Rice channel as claimed in claim 4, characterized in that: In step 5, the pure trajectory design problem is transformed into a mechanical problem MP. The continuous trajectory design problem of the UAV is equivalent to the variable density rope balance problem in the artificial potential field, which is expressed as follows: The path variable s represents the path from a given starting point along the trajectory {x(t), y(t)} to The path length is s∈[0,S], where is the total length of the rope, are the x- and y-coordinates of the equivalent rope shape in space, ρ(s) represents the rope linear density, and the inverse of the rope linear density is Equivalent to the speed v(s) of the drone, the minimum line density of the rope is limited to ρ min and the total mass of the rope m correspond to the maximum speed limit of the drone V max and the total task time T, are the x- and y-coordinates of the starting point of the equivalent rope, are the x- and y-coordinates of the end point of the equivalent rope, respectively; By constructing an artificial potential energy field R″(x,y), the maximum information transmission rate of the UAV air-to-ground communication is characterized, and the equivalence of P1 and the physical problem is found. The potential energy field expression is as follows: Among them, P(x,y) is obtained by converting P(t)=P(x(t),y(t))=P(x(s),y(s))=P(x,y) in the expression of the drone transmission power at time t.

6. The method for designing a UAV trajectory based on mechanical equivalence under a Rice channel as claimed in claim 5, characterized in that: In step 6, the negative gradient of the scalar potential function is used to describe the force field in the potential energy field. The force field can be expressed as: Among them, g(x,y) represents the force field, represents the negative gradient, g1(q(t),P(t)) is the force field under the maximum hardware power limit, and g 2x (q(t),P(t)),g 2y (q(t), P(t)) are the force field scalars in the x and y directions respectively under the power limit required for covert communication; Based on the numerical solution of the optimal transmission power in the UAV flight area obtained in step 3, the force field size corresponding to each UAV position, i.e. the rope position, in the corresponding area is obtained. Under the optimal rope shape, the distance from the starting point D1 of the drone to any point on the rope is The combined force on the x and y axes of the part is 0. At the optimal initial rope tension and the optimal rope tension angle α ＊ When the optimal solution is known, the rope shape is combined Initial value conditions of the equivalent problem MP, rope shape when the rope mass is insufficient for: Among them, A1 * (s) represents the sum of the gravitational force and the projection of the initial rope tension in the x-axis direction, A2 * (s) is the sum of the gravity and the projection of the initial rope tension in the y-axis direction; The optimal initial rope tension corresponding to the optimal solution of rope shape can be solved by binary search, and the solution process is: 1) Given an initial rope tension and angle; 2) Construct the mechanical expressions of the rope in the x and y directions according to the pre-designed force field table and force balance conditions, and simplify the rope shape; 3) If the condition that the path through the destination point is equal to the rope length and the tension or angle is changed does not meet the requirement, then return to step (2). If the condition is met, then the search ends and the optimal rope shape and the corresponding optimal rope tension are output; Based on the optimal rope shape Solve the optimal trajectory q of the UAV * (t) = {x*(t), y*(t)}: Among them, s = Vt. As the UAV flies, the UAV's transmission power is adjusted in time, P * (t) = min{P w (q * (t)),P max }, P w (q * (t)) is the function of the covert communication power requirement with respect to the optimal trajectory of the UAV.

7. A UAV trajectory design system based on mechanical equivalence under Rice channel, characterized in that: include: Module 1 is used for the UAV to start from a given starting point, establish a covert communication Rice channel, and obtain the relevant parameters of the UAV and the Rice channel; Module 2 is used to detect malicious nodes using the likelihood ratio criterion, and obtains the optimal detection threshold and the optimal detection error rate under the optimal detection threshold according to the Rice channel noise distribution; Module 3 is used to obtain the numerical solution of the optimal transmission power in covert communication through local binary search based on the optimal detection error rate; Module 4 is used to maximize the information throughput when the UAV communicates with the ground node by optimizing the trajectory of the UAV, establish a joint optimization problem of jointly optimizing the trajectory and transmission power of the UAV and convert the joint optimization problem into a pure trajectory design problem; Module 5, which is used to convert pure trajectory design problems into mechanical problems under artificial potential energy fields; Module six is ​​used to fly the drone according to the optimal trajectory expression obtained by solving the equivalent problem, and adjust the transmission power in time to successfully extract the optimization result; The UAV trajectory design system based on mechanical equivalence under the Ricean channel is used to execute the steps in the UAV trajectory design method based on mechanical equivalence under the Ricean channel described in any one of claims 1-6.

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