Data and Energy Transmission Method and System for Dual Unmanned Aerial Vehicles in the Presence of Eavesdroppers

Abstract

The present application discloses a method and system for data and energy transmission between two UAVs in the context of an eavesdropper. The method for data and energy transmission between two UAVs in the context of an eavesdropper includes: the WET UAV and the WIT UAV respectively obtain preset dual UAV control strategies; the WIT UAV performs uplink data transmission with each of the ground devices according to the preset dual UAV control strategy; the WET UAV performs downlink energy transmission with each of the ground devices according to the preset dual UAV control strategy. The method for data and energy transmission between two UAVs in the context of an eavesdropper of the present application can solve the problem of an eavesdropper monitoring the data uploaded by the ground device and determining the working status. At the same time, the two UAVs can work together to meet the communication needs while charging the ground device, solving the problem of insufficient energy supply for the equipment.

Description

Technical Field

[0001] The present application relates to the technical field of unmanned aerial vehicle communication, and particularly relates to a data and energy transmission method for two unmanned aerial vehicles in the presence of eavesdroppers and a data and energy transmission system for two unmanned aerial vehicles in the presence of eavesdroppers. Background Art

[0002] With the rapid development of wireless communication technology, the problem of energy consumption in communication systems has become increasingly serious. The problem of energy consumption of devices in traditional wireless communication systems is solved by rechargeable or replaceable batteries, which results in communication devices being fixed in one place and also incurs relatively high costs. As a new type of wireless communication, wireless energy harvesting communication can achieve the simultaneous transmission of wireless information and energy, that is, while interacting with wireless devices for information, it provides energy for wireless devices, which well solves the problem of limited node energy.

[0003] In many remote areas or disaster areas, it is often difficult for traditional ground devices to establish communication with users in a timely manner. Moreover, due to a large amount of path loss during the propagation of radio frequency signals, the coverage range of wireless energy supply is very limited and it is difficult to continuously provide stable energy. To solve this problem, unmanned aerial vehicles can be added to the communication system. Utilizing the characteristics of high maneuverability and rapid deployment of unmanned aerial vehicles, the communication range can be greatly increased, and a line-of-sight link can be provided, which will greatly improve communication performance and solve the problem of continuously increasing infrastructure costs.

[0004] However, due to the openness and broadcast nature of wireless channels, the communication between unmanned aerial vehicles and ground users is easily monitored by hostile eavesdroppers. To solve this problem, the radio frequency signals transmitted by unmanned aerial vehicles can be dynamically adjusted to interfere with the eavesdroppers' determination of the working state of ground devices, which will ensure the data privacy of ground devices.

[0005] Currently, for unmanned aerial vehicle energy harvesting communication, mainly the transmission of data and energy is considered, and the protection of the data privacy of ground devices is not involved. Some existing papers and works are limited to single unmanned aerial vehicles and do not consider the coordinated cooperation of multiple unmanned aerial vehicles to complete the task of simultaneous data and energy transmission under the threat of hostile eavesdroppers.

[0006] Therefore, it is desirable to have a technical solution to overcome or at least mitigate at least one of the above-mentioned defects of the prior art. Summary of the Invention

[0007] The object of the present invention is to provide a data and energy transmission method for two unmanned aerial vehicles in the presence of eavesdroppers to overcome or at least mitigate at least one of the above-mentioned defects of the prior art.

[0008] Glossary of Terms:

[0009] WET represents Wireless Energy Transfer, and WIT represents Wireless Information Transfer.

[0010] In one aspect of the present invention, a data and energy transmission method for dual unmanned aerial vehicles (UAVs) in the presence of eavesdroppers is provided, which is used to control the WET UAV and the WIT UAV to perform data and energy transmission with various ground devices. The data and energy transmission method for dual UAVs in the presence of eavesdroppers includes:

[0011] The WET UAV and the WIT UAV respectively obtain a preset dual-UAV control strategy.

[0012] The WIT UAV performs uplink data transmission with each of the ground devices according to the preset dual-UAV control strategy.

[0013] The WET UAV performs downlink energy transmission with each of the ground devices according to the preset dual-UAV control strategy.

[0014] Optionally, the dual-UAV control strategy includes:

[0015] Obtain an objective function to be optimized.

[0016] Obtain preset constraint conditions.

[0017] According to the objective function to be optimized and the preset constraint conditions, obtain the transmit power control strategy of the WET UAV, the transmit power control strategy of the ground device, the scheduling control strategy between the WIT UAV and the ground device, the flight trajectory control strategy of the WIT UAV, and the flight trajectory control strategy of the WET UAV. The transmit power control strategy of the WET UAV, the transmit power control strategy of the ground device, the scheduling control strategy between the WIT UAV and the ground device, the flight trajectory control strategy of the WIT UAV, and the flight trajectory control strategy of the WET UAV constitute the dual-UAV control strategy.

[0018] Optionally, the objective function to be optimized is:

[0019] Wherein,

[0020] represents the transmit power of the WET UAV, P b represents the transmit power of the ground device, a k represents the scheduling between the WIT UAV and the ground device, represents the flight trajectory of the WIT UAV and represents the flight trajectory of the WET UAV; R b，k[n] represents the data transmission rate of the k-th ground device for uplink transmission.

[0021] Optionally, the preset constraint conditions include:

[0022] Among them,

[0023] represents the horizontal position of the UAV; N represents the time slot; when i = 1, it represents the WIT UAV, and when i = 2, it represents the WET UAV.

[0024] Optionally, the preset constraint conditions further include:

[0025] Among them,

[0026] The horizontal positions of the two UAVs can be expressed as and L i represents the maximum flight distance of the UAV in the i-th time slot; n represents the n-th time slot; when i = 1, it represents the WIT UAV, and when i = 2, it represents the WET UAV.

[0027] Optionally, the preset constraint conditions further include:

[0028] Among them,

[0029] represents the horizontal distance between the UAV and the k-th ground device in the n-th time slot; when i = 1, it represents the WIT UAV, and when i = 2, it represents the WET UAV.

[0030] Optionally, the preset constraint conditions further include:

[0031] Among them,

[0032] represents the transmission power of the WET UAV; P max represents the maximum transmission power of the WET UAV.

[0033] Optionally, the preset constraint conditions further include:

[0034] Among them,

[0035] represents the average transmission power of the WET UAV; represents the transmission power of the WET UAV; N represents the total number of equal intervals obtained by evenly dividing the flight cycle T of the UAV into N equal intervals of time slots.

[0036] Optionally, the preset constraint conditions further include:

[0037]

[0038]

[0039]

[0040] a k [n] = {0, 1};

[0041] Wherein,

[0042] represents the flight trajectory of the WET UAV, represents the horizontal distance between the UAV and the k-th ground device in the n-th time slot, H represents the altitude of the UAV, a k represents the scheduling between the WIT UAV and the ground device, represents the transmission power of the WET UAV, Q 0 represents the initial energy storage of the ground device, P b,k [n] represents the transmission power of the k-th ground device in the n-th time slot; represents the constraint that the average minimum false detection rate of the desired hostile eavesdroppers HWs should be as close as possible to the case of random judgment.

[0043] Optionally, the obtaining of the transmission power control strategy of the WET UAV, the transmission power control strategy of the ground device, the scheduling control strategy between the WIT UAV and the ground device, the flight trajectory control strategy of the WIT UAV, and the flight trajectory control strategy of the WET UAV according to the objective function to be optimized and the preset constraint conditions includes:

[0044] Initialize the iteration number m = 0,

[0045] Initialize the user scheduling strategy and the initial trajectory of the UAV

[0046] For a given and the optimization variables of the optimization problem are only the transmission power of the WET UAV and the transmission power of the ground device. Use the convex optimization toolbox to solve for the optimal and

[0047] For a given and the optimization variables of the optimization problem are only the flight trajectories of the two UAVs. Use the continuous convex approximation algorithm to solve for the optimal UAV trajectories

[0048] For a given and The optimization variables for the optimization problem are only the scheduling of WIT drones and ground devices. Using the convex optimization toolbox, the optimal

[0049] Use and To obtain the maximum uplink data transmission rate of the current iteration and Let ε 1 Be the set iteration accuracy. If Update the iteration count m = m + 1, and return to step A3; otherwise, end directly.

[0050] This application also provides a dual - drone data and energy transmission system. The dual - drone data and energy transmission system includes a WET drone, a WIT drone, and ground devices. The WET drone, WIT drone, and ground devices cooperate to implement the data and energy transmission method of the dual - drone in the presence of an eavesdropper as described above.

[0051] Beneficial effects:

[0052] The data and energy transmission method of the dual - drone in the presence of an eavesdropper in this application can solve the problem of the eavesdropper monitoring the data uploaded by the ground device and determining its working state. At the same time, the dual drones can cooperate, meet the communication requirements while charging the ground device, and solve the problem of insufficient energy supply of the device. The method of the present invention has the following advantages:

[0053] 1. The WET drone uses radio frequency signals to interfere with the work of the eavesdropper, ensuring the privacy of the data of the ground device.

[0054] 2. The transmission powers of the WET drone and the ground device are designed to ensure energy causality and improve the uplink data transmission rate and.

[0055] 3. A scheduling scheme for the WIT drone and the ground device in the presence of an eavesdropper is designed to ensure that the ground device can upload data to the WIT drone orderly and without conflict, improving the uplink data transmission rate and.

[0056] 4. Through the trajectory optimization of the dual drones, the uplink data transmission rate of the ground device is further improved and.

[0057] 5. The proposed algorithm is applicable to the data and energy transmission system of multiple drones in the presence of an eavesdropper. Brief description of the drawings

[0058] Figure 1Schematic flowchart of the data and energy transmission method for dual unmanned aerial vehicles (UAVs) in the presence of eavesdroppers according to an embodiment of the present application;

[0059] Figure 2 System model diagram of the data and energy transmission system for dual UAVs in the presence of eavesdroppers according to the present application;

[0060] Figure 3 Principle diagram of covert communication for the data and energy transmission system of dual UAVs in the presence of eavesdroppers according to the present application;

[0061] Figure 4 Algorithm flowchart of the data and energy transmission method for dual UAVs in the presence of eavesdroppers according to the present application;

[0062] Figure 5 Graph of the uplink information transmission rate of the ground device varying with time under different flight cycles. Among them, the three curves from top to bottom at the 160-slot position represent 100 s, 80 s, and 60 s respectively;

[0063] Figure 6 Graph of the uplink transmission rate of the ground device varying with time under different initial conditions. Among them, the five curves from top to bottom at the 160-slot position represent noWPT5 (the two curves of WPT5 and noWPT5 completely overlap), WPT1, WPT05, and noWPT1;

[0064] Figure 7 Flight trajectory diagram of WIT and WET UAVs. Detailed implementation manners

[0065] To make the objectives, technical solutions, and advantages of the implementation of the present application clearer, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the accompanying drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements with the same or similar functions from beginning to end. The described embodiments are some but not all of the embodiments of the present application. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to explain the present application and should not be construed as limiting the present application. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present application without creative efforts shall fall within the scope of protection of the present application. The embodiments of the present application will be described in detail below with reference to the accompanying drawings.

[0066] It should be noted that in the description of the present invention, the terms "first" and "second" are only used for descriptive purposes and should not be construed as indicating or implying relative importance.

[0067] Figure 1Schematic flowchart of the data and energy transmission method for a dual-UAV under the eavesdropper background in an embodiment of the present application; Figure 2 System model diagram of the data and energy transmission system for a dual-UAV under the eavesdropper background in the present application; Figure 3 Principle diagram of covert communication of the data and energy transmission system for a dual-UAV under the eavesdropper background in the present application; Figure 4 Algorithm flowchart of the data and energy transmission method for a dual-UAV under the eavesdropper background in the present application; Figure 5 Graph of the uplink information transmission rate of the ground device varying with time under different flight cycles; Figure 6 Curve graph of the uplink transmission rate of the ground device varying with time under different initial conditions; Figure 7 Flight trajectory diagram of WIT and WET UAVs.

[0068] As Figure 1 The data and energy transmission method for a dual-UAV under the eavesdropper background as shown in

[0069] Step 1: The WET UAV and the WIT UAV respectively obtain a preset dual-UAV control strategy;

[0070] Step 2: The WIT UAV performs uplink data transmission with each of the ground devices according to the preset dual-UAV control strategy;

[0071] Step 3: The WET UAV performs downlink energy transmission with each of the ground devices according to the preset dual-UAV control strategy.

[0072] The data and energy transmission method for a dual-UAV under the eavesdropper background in the present application can solve the problem that the eavesdropper monitors the data uploaded by the ground device and determines the working state. At the same time, the dual-UAVs can cooperate with each other, meet the communication requirements and charge the ground device, solving the problem of insufficient energy supply of the device. The method of the present invention has the following advantages:

[0073] 1. The WET UAV uses radio frequency signals to interfere with the work of the eavesdropper, ensuring the privacy of the data of the ground device.

[0074] 2. The transmission powers of the WET UAV and the ground device are designed to ensure energy causality and improve the uplink data transmission rate sum.

[0075] 3. A scheduling scheme for the WIT UAV and the ground device under the eavesdropper background is designed to ensure that the ground devices can upload data to the WIT UAV orderly and without conflict, improving the uplink data transmission rate sum.

[0076] 4. The uplink data transmission rate sum of the ground device is further improved through the trajectory optimization of the dual-UAVs.

[0077] 5. The proposed algorithm is applicable to the data and energy transmission system of multiple UAVs in the presence of eavesdroppers.

[0078] In this embodiment, the dual-UAV control strategy includes:

[0079] Obtain the objective function to be optimized;

[0080] Obtain the preset constraint conditions;

[0081] According to the objective function to be optimized and the preset constraint conditions, obtain the transmit power control strategy of the WET UAV, the transmit power control strategy of the ground device, the scheduling control strategy between the WIT UAV and the ground device, the flight trajectory control strategy of the WIT UAV, and the flight trajectory control strategy of the WET UAV. The transmit power control strategy of the WET UAV, the transmit power control strategy of the ground device, the scheduling control strategy between the WIT UAV and the ground device, the flight trajectory control strategy of the WIT UAV, and the flight trajectory control strategy of the WET UAV constitute the dual-UAV control strategy.

[0082] In this embodiment, the objective function to be optimized is:

[0083] Where,

[0084] represents the transmit power of the WET UAV, P b represents the transmit power of the ground device, a k represents the scheduling between the WIT UAV and the ground device, represents the flight trajectory of the WIT UAV and represents the flight trajectory of the WET UAV; R b，k [n] represents the data transmission rate of the uplink transmission of the k-th ground device.

[0085] In this embodiment, the preset constraint conditions include:

[0086] Where,

[0087] represents the horizontal position of the UAV; N represents the time slot; when i = 1, it represents the WIT UAV, and when i = 2, it represents the WET UAV.

[0088] In this embodiment, the preset constraint conditions further include:

[0089] Where,

[0090] The horizontal positions of the two UAVs can be expressed as and Li represents the maximum flight distance of the UAV in the \(i\)-th time slot; \(n\) represents the \(n\)-th time slot; when \(i = 1\), it represents the WIT UAV, and when \(i = 2\), it represents the WET UAV.

[0091] In this embodiment, the preset constraint conditions further include:

[0092] Among them,

[0093] represents the horizontal distance between the UAV and the \(k\)-th ground device in the \(n\)-th time slot; when \(i = 1\), it represents the WIT UAV, and when \(i = 2\), it represents the WET UAV.

[0094] In this embodiment, the preset constraint conditions further include:

[0095] Among them,

[0096] represents the transmission power of the WET UAV; \(P\) max represents the maximum transmission power of the WET UAV.

[0097] In this embodiment, the preset constraint conditions further include:

[0098] Among them,

[0099] represents the average transmission power of the WET UAV; represents the transmission power of the WET UAV; \(N\) represents the total number of equal intervals obtained by evenly dividing the flight period \(T\) of the UAV into \(N\) equal intervals of time slots.

[0100] In this embodiment, the preset constraint conditions further include:

[0101]

[0102]

[0103]

[0104] a k [n] = {0, 1};

[0105] Among them,

[0106] represents the flight trajectory of the WET UAV, represents the horizontal distance between the UAV and the \(k\)-th ground device in the \(n\)-th time slot, \(H\) represents the height of the UAV, \(a\) kDenote the scheduling between WIT UAVs and ground devices, Denote the transmission power of WET UAVs, Q 0 Denote the initial energy storage of ground devices, P b,k [n] Denote the transmission power of the k-th ground device in the n-th time slot; q b，k Refers to the location of the k-th ground device; Denote the constraint that the average minimum miss detection rate of the desired hostile eavesdroppers HWs should be as close as possible to the case of random judgment.

[0107] See Figure 4 , in this embodiment, the obtaining of the transmission power control strategy of WET UAVs, the transmission power control strategy of ground devices, the scheduling control strategy between WIT UAVs and ground devices, the flight trajectory control strategy of WIT UAVs, and the flight trajectory control strategy of WET UAVs according to the objective function to be optimized and the preset constraint conditions includes:

[0108] Initialize the iteration number m = 0,

[0109] Initialize the user scheduling strategy and the initial trajectory of the UAV

[0110] For a given and The optimization variables of the optimization problem are only the transmission power of WET UAVs and the transmission power of ground devices. Use the convex optimization toolbox to solve for the optimal and

[0111] For a given and The optimization variables of the optimization problem are only the flight trajectories of the two UAVs. Use the continuous convex approximation algorithm to solve for the optimal UAV trajectories

[0112] For a given and The optimization variables of the optimization problem are only the scheduling between WIT UAVs and ground devices. Use the convex optimization toolbox to solve for the optimal

[0113] Use and To obtain the maximum uplink data transmission rate of the current iteration and Let ε 1 Be the set iteration accuracy. If Update the iteration number m = m + 1, and return to step A3; otherwise, directly end.

[0114] In this embodiment, the flight cycle T of the UAV is evenly divided into N time slots with equal intervals, and the length of each time slot is δ t = T / N. During each time slot in the flight of the UAV, the WIT UAV collects the data uploaded by the ground device. At the same time, the WET UAV transmits a radio frequency signal to interfere with the eavesdropper's determination of the working state of the ground device and performs wireless energy transfer to the ground devices within its coverage area. Let a k [n] represent the scheduling of the WIT UAV and the ground device in the nth time slot. a k [n]=1 indicates that the kth ground device uploads data to the WIT UAV in the nth time slot. The horizontal positions of the two UAVs can be expressed as and

[0115] In this embodiment, the exact position of the eavesdropper cannot be known by the UAV (in this embodiment, it is defaulted that there is an eavesdropper), and the UAV only knows the possible positions where the eavesdropper may be distributed. The position uncertainty is expressed as which independently follows the same Gaussian distribution The exact position of the UAV can be expressed as where and represent the approximate position of the mth eavesdropper.

[0116] In this embodiment, the channel gain between the UAV and the kth ground device in the nth time slot is where α 0 represents the channel power gain with a reference distance of 1m, β represents the path loss, and its value is 2, represents the horizontal distance between the UAV and the kth ground device in the nth time slot. i = 1 represents the WIT UAV, i = 2 represents the WET UAV, and H represents the height of the UAV.

[0117] In this embodiment, for the kth ground device, the energy collected in the nth time slot is where η represents the energy collection efficiency, represents the transmission power of the WET UAV. The operation of the ground device follows the energy causality theorem: The data transmission rate when the kth ground device uploads data to the WIT UAV in the nth time slot can be expressed as where P b,k [n] represents the transmission power of the kth ground device in the nth time slot, represents the received noise of the WIT UAV.

[0118] In this embodiment, use Η 0,k and Η 1,kRespectively indicating that the k-th ground device has not uploaded data or has uploaded data, the average signal power received by the m-th eavesdropper in the n-th time slot can be expressed as Where represents the i-th sample signal collected by the m-th eavesdropper in the n-th time slot, and l represents the number of times the eavesdropper samples the received signal. The criterion for the m-th eavesdropper to determine whether the k-th ground device uploads data in the n-th time slot is: Where P th,m,k [n] is the decision threshold set by the eavesdropper, and D 0 and D 1 represent two decision results of the eavesdropper. D 0 indicates that the eavesdropper believes that the ground device has not uploaded information to the WIT UAV, and D 1 indicates that the eavesdropper believes that the ground device has uploaded information to the WIT UAV.

[0119] In this embodiment, the ground devices include sensors, Internet of Things devices, mobile users, etc.

[0120] The following further elaborates on this application by way of example. It can be understood that this example does not constitute any limitation to this application.

[0121] Figure 2 is the system model diagram of the data and energy transmission system of the dual UAVs of this application under the background of eavesdroppers. As Figure 2 shown, the algorithm implementation of the present invention is based on the following system: Two UAVs fly over a large number of ground devices. The ground devices upload data to the WIT UAV. At the same time, the eavesdropper will also monitor the activities of the ground devices to determine whether they are uploading data. The WET UAV will emit radio frequency signals to interfere with the decision of the eavesdropper and at the same time perform wireless energy transmission to the ground devices.

[0122] Figure 3 is the schematic diagram of the covert communication of the dual UAV data and energy transmission of the present invention under the background of eavesdroppers. The specific details are as follows:

[0123] A1. As Figure 3 shown, S k is the signal uploaded by the ground device to the WIT UAV, and S a is the signal used by the WET UAV to interfere with the work of the eavesdropper. Use Η 0,k and Η 1,k to respectively indicate that the k-th ground device has not uploaded data or has uploaded data. After multiple samplings, the eavesdropper obtains the average power P w,m [n], which can be expressed as:

[0124]

[0125] The criterion for the m-th eavesdropper to determine the working state of the k-th ground device in the n-th time slot is as follows: where P th,m,k [n] is the decision threshold set by the eavesdropper, and D 0 and D 1 represent two decision results of the eavesdropper. D 0 means that the eavesdropper believes that the ground device has not uploaded information to the WIT UAV, and D 1 means that the eavesdropper believes that the ground device has uploaded information to the WIT UAV.

[0126] A2. To achieve the effect of covert communication, the following two situations need to be realized:

[0127]

[0128] P F,m,k [n] represents the false detection rate of the m-th eavesdropper in the n-th time slot. At this time, the k-th ground device has not uploaded data, but the eavesdropper determines that it has uploaded data; P M,m,k [n] represents the missed detection rate of the m-th eavesdropper in the n-th time slot. At this time, the k-th ground device has uploaded data, but the eavesdropper determines that it has not uploaded data. Combining the decision criterion of the eavesdropper, the two misdetection probabilities can be expressed as:

[0129]

[0130] A3. Assume that the probabilities of the two working states of the ground device P{Η 0,k} = P{Η 1,k} = 0.5. Assume that the hostile eavesdropper knows the transmission power of the WET UAV is between 0 and P max , and believes that obeys a uniform distribution, and its probability density function is expressed as:

[0131]

[0132] Then the false detection rate can be expressed as:

[0133]

[0134] where represents the sum of the noise power received by the m-th eavesdropper and the signal power transmitted by the remaining ground devices when the k-th ground device has not uploaded information to the WIT UAV, represents the sum of the noise power received by the m-th eavesdropper, the signal power transmitted by the remaining ground devices and the maximum transmission power of the WET UAV when the k-th ground device has not uploaded information to the WIT UAV.

[0135] The undetected rate can be expressed as:

[0136]

[0137] Where represents the sum of the noise power received by the m-th eavesdropper and the signal power transmitted by the k-th ground device when the k-th ground device uploads information to the WIT UAV, represents the sum of the noise power received by the m-th eavesdropper, the signal power transmitted by the k-th ground device, and the maximum transmission power of the WET UAV when the k-th ground device uploads information to the WIT UAV.

[0138] Then the total false detection rate can be expressed as:

[0139] P m,k [n] = P F,m,k [n] + P M,m,k [n];

[0140] A4. In real life, P max >> P b , then there is P 3 < P 2 , P 1 < P 4 . When P 1 < P 3 , the total false detection rate can be expressed as:

[0141]

[0142] Take the lowest false detection rate as the false detection rate ξ m,k [n]:

[0143]

[0144] A5. For the WET UAV, the exact location of the eavesdropper is often unknown. Due to the uncertainty of the eavesdropper's location independently follows the same Gaussian distribution Therefore, the average lowest false detection rate can be expressed as:

[0145]

[0146] Using the lemma: If there is a binary function Y = g(X 1 , X 2 ), and E(X 1 ) = m 1 , E(X 2 ) = m 2 , D(X 1 ), D(X 2) and Cov(X 1 , X 2 ) are both known, then E(Y) = E(g(X 1 , X 2 )) can be approximated as:

[0147]

[0148] In the formula, the left side is greater than the right side. Substituting ξ m,k (X, Y) into g(X 1 , X 2 ) can obtain the lower bound of the average minimum miss detection rate

[0149]

[0150] A6. Generally speaking, if the hostile eavesdropper HWs is not working, then the result of its judgment on the working condition of the legitimate ground device LDs is random, with a probability of 0.5. In order to better achieve the effect of covert communication, it is hoped that the average minimum misdetection rate of the hostile eavesdropper HWs should be as close as possible to the situation of random judgment, that is:

[0151]

[0152] Figure 4 is the algorithm flow chart of the present invention, and the specific operation steps are as follows:

[0153] A1. Initialize the number of iterations m = 0,

[0154] A2. Initialize the user scheduling strategy and the initial trajectory of the UAV

[0155] A3. For the given and For the optimization variables of the optimization problem, there are only the transmission power of the WET UAV and the transmission power of the ground device,

[0156]

[0157]

[0158]

[0159]

[0160]

[0161] Use the convex optimization toolbox to solve the optimal and​

[0162] A4. For the given and the optimization variables for the optimization problem are only the flight trajectories of two UAVs, and the optimal UAV trajectories are solved using the successive convex approximation algorithm.

[0163]

[0164]

[0165]

[0166]

[0167]

[0168]

[0169] Using the successive convex approximation technique, the non-convex part in the above problem is converted into a convex function with respect to as follows:

[0170] A41. Define to represent the flight trajectory of UAV1 after the j-th optimization, and then find the first-order Taylor expansion of R b,k [n] at as λ k [n]: as follows:

[0171]

[0172] λ k [n] is the lower bound of R b,k [n], and λ k [n] is a linear function with respect to and is also a concave function. Introducing a slack variable will result in:

[0173]

[0174] where is a convex function with respect to q 1 and can be first-order Taylor expanded at q 1 to obtain:

[0175]

[0176] Therefore, the energy causality constraint satisfies the convex constraint condition:

[0177]

[0178] By introducing slack variables, the hidden constraint conditions can be transformed into linear functions of q1 and q2 as follows:

[0179]

[0180] A42. Therefore, by using the lower bound λ k [n], we can transform the problem of solving the trajectory optimization of the UAV into the following problem:

[0181]

[0182]

[0183]

[0184]

[0185]

[0186]

[0187]

[0188]

[0189] The objective function and constraint conditions of this problem are both concave functions of the trajectory and the slack variables q1 and q2. This problem is transformed into a convex problem and can be solved by a standard convex optimization solver to obtain the optimized trajectory and

[0190] A5. For the given and the optimization variables of the optimization problem are only the scheduling of the WIT UAV and the ground equipment,

[0191]

[0192]

[0193]

[0194]

[0195] a k [n] = {0, 1};

[0196]

[0197] By relaxing the binary variable a k to make it a continuous variable between [0, 1], the optimization problem becomes a linear programming problem, and the optimal is solved using a convex optimization toolkit. Then, through the following method, the continuous is converted back to a binary variable

[0198] A51. Substitute to obtain Let Let R th be the given transmission rate threshold. If then let Otherwise, let

[0199] A6. Use and to obtain the maximum uplink data transmission rate of the current iteration and Let ε 1 be the set iteration accuracy. If update the iteration count m = m + 1 and return to step A3; otherwise, end directly.

[0200] During the simulation of the present invention, it is assumed that the UAV maintains a constant flight altitude throughout the flight cycle, the initial and final positions of the UAV are the same, and its initial trajectory is a circular trajectory when covering the maximum number of ground devices. The maximum transmission power P of the WET UAV max = 10W, the average transmission power The maximum flight speed V of the UAV max1 = V max2 = 10 m / s, the flight altitude H of the two UAVs is 5 m, the flight cycle T is 80 s, the number of time slots N is 160, the average noise power of the hostile eavesdropper and the UAV The path loss α at a reference distance of 1 m 0 = 10 -2 The initial energy Q of the ground legitimate device 0 = 0.001 J, the energy conversion efficiency η of the RF - DC is 0.8, the position uncertainty of the eavesdropper The threshold ρ of the detection probability constraint w = 10 -5 , the threshold R of the uplink throughput of each ground legitimate device th = 0.01 bit / Hz, the minimum distance d between the two UAVs min = 10 m. We simulated the scenario of 6 ground devices and 6 eavesdroppers, and the specific process is as follows:

[0201] Figure 5It is a graph showing the uplink information transmission rate of the ground equipment and its variation over time under different flight cycles. From Figure 5 it can be seen that as the duty cycle increases, the uplink information transmission rate also increases. This is because when the duty cycle becomes longer, the WIT drones and WET drones can execute flight tasks at a more "appropriate" speed: the WIT drones, as WIT-Stations, can adjust their flight positions and speeds in real time to pursue better channel conditions, and the WET drones, as WET-Stations, can provide more sufficient power to the ground equipment to support the latter's communication tasks.

[0202] Figure 6 It is a curve graph showing the uplink transmission rate of the ground equipment and its variation over time under different initial conditions. The initial conditions are as follows in the table:

[0203]

[0204] From Figure 6 it can be seen that when the initial energy is limited, compared with the situation without wireless energy transmission, the algorithm model proposed by the present invention can effectively improve the performance of the communication system and increase the uplink information transmission rate of the ground equipment.

[0205] Figure 7 It is a flight trajectory graph of WIT and WET drones. Through the method of the present application, in order to seek better channel conditions and form a line-of-sight link, the WIT drones will fly over the ground equipment as much as possible. When the communication time is limited, in order to maximize the uplink information transmission rate of the ground equipment, the WIT drones will selectively approach the ground equipment in remote areas and leave better communication opportunities for the ground equipment with better channel conditions; in order to avoid the radio frequency signals transmitted from interfering with the data collected by the WIT drones from the ground equipment and ensure that each ground equipment has sufficient energy to work properly, the trajectory of the WET drones is finally optimized to the center of the map.

[0206] The present application also provides a dual-drone data and energy transmission system, which includes a WET drone, a WIT drone and a ground equipment. The WET drone, the WIT drone and the ground equipment cooperate to implement the data and energy transmission method of the dual drones under the background of eavesdroppers as described above.

[0207] Although the present invention has been described in detail above with general descriptions and specific implementation schemes, based on the present invention, some modifications or improvements can be made, which are obvious to those skilled in the art. Therefore, these modifications or improvements made without departing from the spirit of the present invention all fall within the scope of protection required by the present invention.

Claims

1. A data and energy transmission method for dual unmanned aerial vehicles (UAVs) in the presence of eavesdroppers, which is used to control the wireless energy transfer (WET) UAV and the wireless information transfer (WIT) UAV to perform data and energy transmission with various ground devices. Characterized in that, The data and energy transmission method for dual UAVs in the presence of eavesdroppers includes: The WET UAV and the WIT UAV respectively obtain a preset dual-UAV control strategy; The WIT UAV performs uplink data transmission with each of the ground devices according to the preset dual-UAV control strategy; The WET UAV performs downlink energy transmission with each of the ground devices according to the preset dual-UAV control strategy; The dual-UAV control strategy includes: Obtaining an objective function to be optimized; Obtaining preset constraint conditions; According to the objective function to be optimized and the preset constraint conditions, obtaining the transmit power control strategy of the WET UAV, the transmit power control strategy of the ground device, the scheduling control strategy between the WIT UAV and the ground device, the flight trajectory control strategy of the WIT UAV, and the flight trajectory control strategy of the WET UAV. The transmit power control strategy of the WET UAV, the transmit power control strategy of the ground device, the scheduling control strategy between the WIT UAV and the ground device, the flight trajectory control strategy of the WIT UAV, and the flight trajectory control strategy of the WET UAV constitute the dual-UAV control strategy; The objective function to be optimized is: ; wherein, Indicates the transmission power of the WET UAV, Indicates the transmission power of the ground equipment, Indicates the scheduling between the WIT UAV and the ground equipment, Indicates the flight trajectory of the WIT UAV and Indicates the flight trajectory of the WET UAV; Indicates the k data transmission rate of the uplink transmission of the N Indicates dividing the flight cycle of the UAV T evenly into N the total number of equal intervals in The obtaining of the transmit power control strategy of the WET UAV, the transmit power control strategy of the ground device, the scheduling control strategy between the WIT UAV and the ground device, the flight trajectory control strategy of the WIT UAV, and the flight trajectory control strategy of the WET UAV according to the objective function to be optimized and the preset constraint conditions includes: A1. Initialize the number of iterations , ; A2. Initialize the user scheduling policy and the initial trajectory of the UAV , ; A3. For a given , and , the optimization variables of the optimization problem are only the transmission power of the WET UAV and the transmission power of the ground equipment. The optimal and are solved using a convex optimization toolbox; A4. For a given , and , the optimization variables of the optimization problem are only the flight trajectories of two UAVs, and the continuous convex approximation algorithm is used to solve the optimal UAV trajectory , ; A5. For a given , , and , the optimization variable of the optimization problem is only the scheduling of WIT drones and ground equipment, and the optimal ; A6. Use , , , and to obtain the maximum uplink data transmission rate of the current iteration and . Let be the set iteration accuracy. If , update the iteration count , and return to step A3; otherwise, end directly.

2. The data and energy transmission method for dual UAVs in the presence of eavesdroppers according to claim 1, Characterized in that, The preset constraint conditions include: ; wherein, Indicates the horizontal position of the UAV; N Indicates the flight cycle of the UAV T Evenly divided into N The total number of equal gaps in the number of equal intervals of the time slots; when Indicates the WIT UAV, Indicates the WET UAV; The preset constraint conditions further include: , , ; wherein, The horizontal positions of two UAVs can be expressed as and ; represents the maximum flight distance of the UAV in the i th time slot; n represents the n th time slot; when represents the WIT UAV, represents the WET UAV.

3. The data and energy transmission method for dual UAVs in the presence of eavesdroppers according to claim 2, Characterized in that, The preset constraint conditions further include: ; wherein, Indicates the horizontal distance between the UAV and the n th ground device in the k th time slot; when represents a WIT UAV, represents a WET UAV.

4. The data and energy transmission method for dual UAVs in the presence of eavesdroppers according to claim 3, Characterized in that, The preset constraint conditions further include: ; wherein, Indicates the transmission power of the WET drone; Indicates the maximum transmission power of the WET drone.

5. The data and energy transmission method for dual UAVs in the presence of eavesdroppers according to claim 4, Characterized in that, The preset constraint conditions further include: ; wherein, Denote the average transmission power of the WET UAV; Denote the transmission power of the WET UAV; N Denote the total number of equal intervals in the T equally divide N flight cycle of the UAV into equal intervals of time slots.

6. The data and energy transmission method for dual UAVs in the presence of eavesdroppers according to claim 5, Characterized in that, The preset constraint conditions further include: ； ； ； ； ; wherein, Indicates the flight trajectory of the WET UAV, Indicates at the n th time slot, the horizontal distance between the UAV and the k th ground device, H Indicates the height of the UAV, Indicates the scheduling between the WIT UAV and the ground device, Indicates the transmit power of the WET UAV, Indicates the initial energy storage of the ground device, Indicates at the n th time slot, the transmit power of the k th ground device; Refers to the position of the k th ground device; Indicates the constraint that the average minimum false detection rate of the desired hostile eavesdroppers HWs should be as close as possible to the case of random judgment.

7. A dual-UAV data and energy transmission system, Characterized in that, The dual-UAV data and energy transmission system includes a WET UAV, a WIT UAV, and ground devices. The WET UAV, the WIT UAV, and the ground devices cooperate to implement the data and energy transmission method for dual UAVs in the presence of eavesdroppers according to any one of claims 1 to 6; The dual-UAV control strategy includes: Obtaining an objective function to be optimized; Obtaining preset constraint conditions; Obtain the transmit power control strategy of the WET UAV, the transmit power control strategy of the ground device, the scheduling control strategy between the WIT UAV and the ground device, the flight trajectory control strategy of the WIT UAV, and the flight trajectory control strategy of the WET UAV according to the objective function to be optimized and the preset constraint conditions. The transmit power control strategy of the WET UAV, the transmit power control strategy of the ground device, the scheduling control strategy between the WIT UAV and the ground device, the flight trajectory control strategy of the WIT UAV, and the flight trajectory control strategy of the WET UAV constitute the dual-UAV control strategy; The objective function to be optimized is: ; wherein, Indicates the transmission power of the WET UAV, Indicates the transmission power of the ground equipment, Indicates the scheduling between the WIT UAV and the ground equipment, Indicates the flight trajectory of the WIT UAV and Indicates the flight trajectory of the WET UAV; Indicates the k data transmission rate of the uplink transmission of the - th ground equipment; N Indicates dividing the flight cycle of the UAV T evenly into N the total number of equal intervals in equal - interval time slots; The obtaining of the transmit power control strategy of the WET UAV, the transmit power control strategy of the ground device, the scheduling control strategy between the WIT UAV and the ground device, the flight trajectory control strategy of the WIT UAV, and the flight trajectory control strategy of the WET UAV according to the objective function to be optimized and the preset constraint conditions includes: Initial number of iterations , ; Initialize the user scheduling strategy and the initial trajectory of the UAV , ; For a given , and , the optimization variables for the optimization problem are only the transmission power of the WET UAV and the transmission power of the ground equipment. The optimal and are solved using the convex optimization toolbox; For a given , and , the optimization variables of the optimization problem are only the flight trajectories of two UAVs, and the optimal UAV trajectories are obtained by using the continuous convex approximation algorithm , ; For a given , , and , the optimization variable of the optimization problem is only the scheduling of WIT drones and ground equipment, and the optimal ; Use , , , and to obtain the maximum uplink data transmission rate of the current iteration and , let be the set iteration accuracy. If , update the iteration count , and return to step A3; otherwise, end directly.

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