CN112512037B - Unmanned aerial vehicle active eavesdropping method based on joint track and interference power optimization - Google Patents
Unmanned aerial vehicle active eavesdropping method based on joint track and interference power optimization Download PDFInfo
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Abstract
The application provides an unmanned aerial vehicle active eavesdropping method with combined track and interference power optimization, aiming at the influence of track change of an unmanned aerial vehicle on the effective eavesdropping rate of a system, an effective active interference scheme is adopted in a model, namely the unmanned aerial vehicle transmits interference signals while eavesdropping suspicious link information, and a suspicious receiver is interfered. In order to maximize the effective eavesdropping rate, the track and the transmitting interference power of the unmanned aerial vehicle are optimized by using the block coordinate descent and continuous convex optimization technology assisted by the update rate, so that the effective eavesdropping rate is improved.
Description
Technical Field
The application relates to the technical field of communication monitoring, in particular to an unmanned aerial vehicle active eavesdropping method with combined track and interference power optimization.
Background
In recent years, due to the characteristics of high maneuverability, low cost and the like of unmanned aerial vehicles, the application demands in public security, disaster management, monitoring, communication and the like are continuously increasing. However, with the popularization of unmanned aerial vehicle communication systems, low-cost wireless services expand the range of criminals or terrorists, and pose a serious threat to national security. To combat crime or terrorist attacks, government agencies are increasingly required to legally monitor any suspected communication links and detect abnormal behavior in commercial wireless networks.
The problem of trajectory optimization of the drone is of major importance in the drone network, mainly because the high mobility of the drone, the inherent broadcasting characteristics of the wireless communication and the channel under consideration are controlled by the Line of sight (LoS), the position variation of which can directly affect its receiving rate.
In the studies of the prior literature, active monitors were considered as nodes fixed to the ground, or unmanned aerial vehicles with fixed flight paths, and the influence of the trajectory change of unmanned aerial vehicles as active eavesdroppers on the system eavesdropping rate was almost ignored.
Disclosure of Invention
The application aims to solve the technical problem of providing an unmanned aerial vehicle active eavesdropping method and device with combined track and interference power optimization, which utilize the characteristics of a suspicious system to realize effective active interference so as to furthest improve eavesdropping rate.
In order to solve the above technical problems, the embodiments of the present specification are implemented as follows:
an unmanned aerial vehicle active eavesdropping method with combined track and interference power optimization, comprising:
step 10, in an unmanned aerial vehicle active eavesdropping model, respectively setting an initial track of a suspicious emitter, an initial transmitting power of the suspicious emitter, an initial track of a legal eavesdropper, an initial transmitting power of the legal eavesdropper, a relaxation variable initial value, a user scheduling rule of the suspicious emitter, a first updating parameter, a second updating parameter, an iteration number initial value and a threshold value;
step 20, updating the iteration times, and then calculating a first updating parameter by using the updated iteration times and a second updating parameter;
step 30, calculating the optimal value of the transmission power of the legal eavesdropper by using the initial track of the suspicious emitter, the flight track of the legal eavesdropper in the last iteration, the user scheduling rule of the suspicious emitter and the initial value of the relaxation variable, and then calculating the transmission power of the legal eavesdropper in the current iteration by using the first updated parameter, the optimal value of the transmission power of the legal eavesdropper and the transmission power of the legal eavesdropper in the last iteration;
step 40, calculating the optimal value of the flight track of the legal eavesdropper by using the transmission power of the legal eavesdropper, the initial track of the suspicious emitter, the user scheduling rule of the suspicious emitter and the initial value of the relaxation variable, and then calculating the flight track of the legal eavesdropper in the iteration by using the first updated parameter, the optimal value of the flight track of the legal eavesdropper and the flight track of the legal eavesdropper in the previous iteration;
step 50, calculating the current average available eavesdropping rate, returning to step 20 if the difference between the current average available eavesdropping rate and the last iteration average available eavesdropping rate is greater than or equal to the threshold value, and ending the step if the difference between the current average available eavesdropping rate and the last iteration average available eavesdropping rate is less than the threshold value.
Further, in the step 10, the active eavesdropping model of the unmanned aerial vehicle is specifically: in a three-dimensional Cartesian coordinate, a suspicious transmitter transmits suspicious information to M ground users, the ground users and the suspicious transmitter are respectively provided with an antenna, a legal eavesdropper is provided with two antennas for eavesdropping on the information transmitted from the suspicious transmitter to the ground users and for transmitting interference signals to interfere with the ground users, the legal eavesdropper and the suspicious transmitter are assumed to fly at a constant height, the suspicious transmitter adopts a time division multiple access transmission mode to serve the users on the ground, the served users are selected according to the principle of distance nearest, the whole flight cycle of the legal eavesdropper is discretized, the legal eavesdropper is equally divided into N communication time slots, and the coordinate position of the legal eavesdropper is unchanged in each time slot.
Further, in the step 20, the first update parameter is calculated by using the updated iteration number and the second update parameter, and the formula is as follows:
γ＝γ/(1+(k-1)×ζ)
wherein, gamma is a first updating parameter, ζ is a second updating parameter, and k is the iteration number.
Further, in the step 30, the calculating the optimal value of the transmission power of the legal eavesdropper by using the initial trajectory of the suspicious emitter, the flight trajectory of the legal eavesdropper in the last iteration, the user scheduling rule of the suspicious emitter and the initial value of the relaxation variable specifically includes:
wherein max is the maximum function, η Power To target value of relaxation variable X m For introduced relaxation variable x m [n]Is set of (1), Y m For introduced relaxation variable y m [n]Is the constraint, N is the total number of communication time slots, x m [n]Is the relaxation variable of the nth time slot, y m [n]As a relaxation variable of the nth time slot, m represents the mth user, n represents the nth communication time slot, P B [n]For the power transmitted by the suspicious transmitter in the nth time slot, P E [n]For the interference power transmitted by the legal eavesdropper in the nth time slot,for the channel model between the suspicious transmitter and the Mth user in the nth time slot +.>For the channel model between the n-th time slot legal eavesdropper and the M-th user +.>To give the initial value of the relaxation variable at the nth slot, P E,max Peak value of transmitting power at nth time slot for legal eavesdropper, alpha m [n]Scheduling parameters for a user->For the receiving rate of the mth ground user in the nth time slot, R E [n]Is the rate of reception by a lawful eavesdropper in the nth time slot.
Further, in the step 30, the transmission power of the legal eavesdropper in the present iteration is calculated by using the first updated parameter, the transmission power optimum value of the legal eavesdropper and the transmission power of the legal eavesdropper in the last iteration, specifically:
wherein, gamma is the first updating parameter, P E The power optimum value is transmitted for a legitimate eavesdropper,power is transmitted for the legal eavesdropper of the last iteration.
Further, in the step 40, the optimal value of the flight trajectory of the legal eavesdropper is calculated by using the transmission power of the legal eavesdropper, the initial trajectory of the suspicious emitter, the user scheduling rule of the suspicious emitter and the initial value of the relaxation variable, and the formula is as follows:
q E [1]＝q E [N]
wherein max is the maximum function, η traj To target value of relaxation variable X m For introduced relaxation variable x m [n]Is set of (1), Y m For introduced relaxation variable y m [n]Is the constraint, N is the total number of communication time slots, x m [n]Is the relaxation variable of the nth time slot, y m [n]Is a relaxation variable of the nth time slot, m represents the mth user, n represents the nth communication time slot, q E [n+1]To suspect transmitter position in the n+1th slot, q E [n]For the position of the legal eavesdropper in the nth time slot, L is the maximum flight distance of the legal eavesdropper in each time slot, q E [l]For the position of the legal eavesdropper in the first time slot, q E [N]P for the position of the legal eavesdropper in the last slot B [n]For the transmission power of the suspicious transmitter in the nth time slot, P E [n]The interference power transmitted in the nth time slot for a legitimate eavesdropper,for the channel model between the suspicious transmitter and the Mth user in the nth time slot +.>For the lower bound obtained by successive convex optimization of the channel model between the nth time slot legal eavesdropper and the Mth user->For the introduced relaxation variable, ++>A is the lower bound obtained by successive convex optimization of the receiving rate of the legal eavesdropper in the nth time slot m [n]Scheduling parameters for users of suspicious transmitters, < >>For the receiving rate of the mth ground user in the nth time slot, P E [n]For interference power, lambda, transmitted by legal eavesdroppers in the nth time slot 0 For the signal-to-noise ratio at the reference distance, +.>As relaxation variable, H is flying height, y m [n]For the introduced relaxation variable, ++>For a given initial value of the relaxation variable in the nth slot, γn]D for the introduced relaxation variable min Is the minimum safe distance between the suspicious transmitter and the legitimate eavesdropper.
Further, in the step 40, the flight path of the legal eavesdropper in the iteration is calculated by using the first updated parameter, the flight path optimal value of the legal eavesdropper and the flight path of the legal eavesdropper in the previous iteration, specifically:
wherein, gamma is a first update parameter, Q E For the optimum value of the legal eavesdropper flight trajectory,is the legal eavesdropper flight trajectory of the last iteration.
Further, in the step 50, the current average achievable eavesdropping rate is calculated as follows:
q E [1]＝q E [N]
wherein max is a maximum function, Q E Is the optimal value of the flight path of the legal eavesdropper, P E For optimal interference power of legal eavesdropper, N is total number of communication time slots, a m [n]Scheduling parameters for users of suspicious transmitters, R EV [n]For effective eavesdropping rate, s.t. is a constraint, q E [n+1]To the position of legal eavesdropper in the n+1th time slot, q E [n]For the position of the legal eavesdropper in the nth time slot, L is the maximum flight distance of the legal eavesdropper in each time slot, q E [l]For the position of the legal eavesdropper in the first time slot, q E [N]For the position of the legal eavesdropper in the last time slot, q E [n]Is legalThe position of the eavesdropper in the nth slot, q B [n]D, for the position of the suspicious transmitter in the nth time slot min For minimum security distance between suspicious emitter and legal eavesdropper, P E [n]Interference power, P, transmitted in the nth time slot for a legitimate eavesdropper E,max Transmitting the peak of interference power at the nth time slot for a legitimate eavesdropper, R EV [N]In order to be able to effectively tap the rate,for the receiving rate of the mth ground user in the nth time slot, R E [n]Is the rate of reception by a lawful eavesdropper in the nth time slot.
The technical scheme provided by the embodiment of the application has at least the following technical effects or advantages:
aiming at the influence of the track change of the unmanned aerial vehicle on the effective eavesdropping rate of the system, an effective active interference scheme is adopted in the model, namely, the unmanned aerial vehicle transmits interference signals while eavesdropping on suspicious link information, and a suspicious receiver is interfered. In order to maximize the effective eavesdropping rate, the track and the transmitting interference power of the unmanned aerial vehicle are optimized by using the block coordinate descent and continuous convex optimization technology assisted by the update rate, so that the effective eavesdropping rate is improved.
The foregoing description is only an overview of the present application, and is intended to be implemented in accordance with the teachings of the present application in order that the same may be more clearly understood and to make the same and other objects, features and advantages of the present application more readily apparent.
Drawings
The application will be further described with reference to examples of embodiments with reference to the accompanying drawings.
FIG. 1 is a schematic flow chart of a method according to an embodiment of the application;
fig. 2 is a schematic diagram of an active eavesdropping communication system model of an unmanned aerial vehicle according to an embodiment of the present application;
FIG. 3 is a diagram illustrating average received rates of UAVs (E) according to an embodiment of the present application;
fig. 4 shows flight trajectories of UAV (B) and UAV (E) for example t=160 s;
FIG. 5 is a graph showing the variation of UAV (E) interference power with time according to an embodiment of the present application;
fig. 6 is a schematic diagram illustrating convergence of algorithm 1 according to an embodiment of the present application.
Detailed Description
The aim of the application is to overcome the drawbacks of the prior art described above, and to develop a wireless communication interception scheme for unmanned aerial vehicles (Unmanned Aerial Vehicle, UAV) as legal eavesdroppers UAV (E), in which a legal eavesdropper (UAV (E)) is used to eavesdrop on suspicious information sent by suspicious transmitters (UAV (B)) to suspicious receivers on the ground. By utilizing the characteristics of the suspicious system, an effective active interference scheme is provided to furthest improve the eavesdropping rate.
Referring to fig. 1, the embodiment of the application discloses an unmanned aerial vehicle active eavesdropping method with combined track and interference power optimization, which comprises the following steps:
step 10, respectively setting initial tracks of suspicious transmitters in an unmanned aerial vehicle active eavesdropping modelInitial transmit power P of suspicious transmitter B Initial trajectory of legal eavesdropper +.>Initial transmit power of legal eavesdropper>Initial value of relaxation variable->User scheduling rule a of suspicious transmitter, first update parameter y, second update parameter ζ, iteration number initial value k=0, and threshold +.>
Step 20, updating the iteration number k=k+1, and then calculating a first updating parameter gamma=gamma/(1+ (k-1) x ζ) by using the updated iteration number and a second updating parameter;
step 30, utilizing the initial trajectory of the suspected transmitterThe flight trajectory of legal eavesdropper of last iteration +.>(when the number of iterations k is 1, the flight trajectory of the legal eavesdropper of the last iteration +.>I.e. the initial trajectory of a legitimate eavesdropper) Calculation of the optimal value P of the transmission power of a legal eavesdropper from the initial value of the relaxation variable, the user scheduling rule A of the suspicious transmitter E Then using the first update parameter gamma, the optimal value P of the transmission power of the legal eavesdropper E And the transmit power of the legal eavesdropper of the last iteration +.>Calculation book->Transmission power of legal eavesdropper of the next iteration +.>
Step 40, utilizing the transmitting power of legal eavesdropperInitial trajectory of suspicious emitter->User scheduling rules a for suspicious transmitters and relaxation changesInitial value of quantity->Calculating the optimal value Q of the flight path of a legal eavesdropper E Then using the first updated parameter gamma, the optimum value Q of the flight trajectory of the legal eavesdropper E And the flight trajectory of the legal eavesdropper of the last iteration +.>(when the number of iterations k is 1, the flight trajectory of the legal eavesdropper of the last iteration +.>I.e. the initial trajectory of a legal eavesdropper +.>) Calculating the flight track of legal eavesdropper of the iteration>
Step 50, calculating the current average available eavesdropping rate, if the difference between the current average available eavesdropping rate and the last iteration average available eavesdropping rate is greater than or equal to the threshold valueReturning to step 20, if the difference between the current average available eavesdropping rate and the average available eavesdropping rate of the previous iteration is less than the threshold +.>And ending the step.
In one possible implementation, the unmanned aerial vehicle active eavesdropping communication system model is as shown in fig. 2, and in a three-dimensional cartesian coordinate, the UAV (B) is a suspicious transmitting node that transmits suspicious information to M ground users D m ，Only one antenna is equipped for both the ground user and the UAV (B); the UAV (E) is a legal eavesdropper provided with two antennas for eavesdropping on information transmitted from the UAV (B) to the ground user and for transmitting interfering signals to interfere with the ground user, respectively. Both UAV (E) and UAV (B) are unmanned aerial vehicles, which are assumed to fly at a constant altitude H, which is the minimum value that unmanned aerial vehicles need terrain avoidance while helping to reduce energy consumption as they ascend or descend. The UAV (B) serves users on the ground using a time division multiple access (Time Division Multiple Access, TDMA) transmission, i.e. the UAV (B) serves only one user per time slot, the served users being selected according to the closest principle. To simplify the optimization problem and ensure that the receiving rate of ground users is maximized, the flight trajectory of UAV (B) and the user scheduling rules +.>Determining; and the initial trajectory of the UAV (E) is a circular flight trajectory with different flight radii set by the center of the geometric midpoint of the user.
The present embodiment discretizes the whole communication process into N very small communication slots equally dividing it into N very small communication slots, i.e. t=nδ, since the continuous time T means an infinite number of speed constraints, which makes the trajectory design of the unmanned aerial vehicle very difficult to handle t . Due to the communication time slot delta compared to the flight speed of the unmanned aerial vehicle t Is small, so it can be considered that in each time slot delta t The coordinate position of the unmanned aerial vehicle is unchanged. The position of the drone at each slot can be represented by the discretized slot:definition of M terrestrial subscribers D m The coordinates on three-dimensional Cartesian coordinates are +.> For ease of calculation, unmanned aerial vehicle is ignoredTake-off and landing times. The maximum flight speeds of UAV (B) and UAV (E) are V max The maximum flight distance of the unmanned aerial vehicle in each time slot is L=delta t V max . Furthermore, the last time slot of UAVs (B) and UAVs (E) flies to the initial position.
Based on the above assumptions, the flight trajectory of UAV (B) is defined, considering only the movement constraints of UAV (E) as:
q E [1]＝q E [N]
in order to avoid collisions between UAV (B) and UAV (E) during flight, the constraint of minimum safe distance is added:
wherein d min Representing the minimum safe distance between UAV (B) and UAV (E).
In the wireless communication system of the unmanned aerial vehicle-ground communication in the present embodiment, it is assumed that channels of the UAV (B), the UAV (E) and all ground nodes are line of sight links (LoS), and in the nth communication slot, a channel model of the UAV and all ground nodes is:
the channel model between UAV (B) and UAV (E) is:
wherein beta is 0 Defined as distance d 0 Channel power gain at=1m.
The transmit power constraints of the UAV (E) are as follows:
wherein P is E [n]For interference power, P, transmitted in the nth time slot UAV (E) E,max The peak of power is transmitted for UAV (E).
In the nth slot, the reception rate of the UAV (E) can be expressed as:
wherein P is B [n]For the transmit power of UAV (B) at the nth slot,representing the average received rate of the UAV (E).
At the nth time slot, ground user D m The reception rate of (2) can be expressed as:
wherein,representing the noise power.
Since UAV (E) is operating in active eavesdropping mode, whenThe UAV (E) can reliably decode the message from the UAV (B) at an effective eavesdropping rate equal to +.>When->At this point, the lawful eavesdropper UAV (E) cannot decode the information without error, where the effective eavesdropping rate is equal to 0. Thus, the effective eavesdropping rate of the legitimate eavesdropper UAV (E) can be expressed as:
the value of the average achievable eavesdropping rate is maximized by jointly optimizing the trajectory and interference power of the UAV (E) over all slots.
The optimization problem of the average achievable eavesdropping rate can be expressed as:
q E [1]＝q E [N]
can be broken down into two sub-problems: 1) Optimizing the interference power of the UAV (E); 2) The trajectory of the UAV (E) is optimized and then the two sub-problems are solved alternately. The method comprises the following specific steps:
step one, optimizing the interference power of the UAV (E)
Given the initial trajectories of UAVs (B) and UAVs (E), i.e. givenUser scheduling rule A of UAV (B) and transmit power of UAV (B)>The UAV (E) transmit power is optimized. Introducing a relaxation variable η power ，/>And->And using a first-order taylor expansion at a given initial value using a successive convex optimization (Successive Convex Approximation (SCA)) technique>For->Approximately, the objective function (P1) is converted into a sub-problem of solving the optimal transmit power:
the problem (P2) is a convex optimization problem that can be effectively solved by a convex optimization solver such as CVX.
Optimizing the flight path of the UAV (E)
Given initial transmit power of UAVs (B) and UAVs (E)Flight trajectory of UAV (B)And user scheduling rules A for UAV (B), for UAV (E) flight trajectory +.>And (5) optimizing. Introducing relaxation variable->And eta traj And using a first-order taylor expansion at a given initial value using a successive convex optimization (Successive Convex Approximation (SCA)) technique>For->Approximately, the objective function (P1) is converted into a sub-problem of solving the optimal flight trajectory:
q E [1]＝q E [N]
wherein,and gamma [ n ]]Each of the results is obtained by successive convex optimization (SCA) approximation at a given initial value by the following equation.
The problem (P3) is a convex optimization problem that can be effectively solved by a convex optimization solver such as CVX.
The specific algorithm comprises the following steps:
and (3) utilizing the update rate to assist the block coordinate to descend, and obtaining the transmitting power of the UAV (E) and the flight trajectory of the UAV (E) through the update rate in the step (4) and the step (5) to realize rapid convergence.
The following describes the embodiments of the present application in further detail with reference to simulation diagrams, and in order to show the performance advantages of the method according to the embodiments of the present application, the following description is compared with two optimization schemes:
the method comprises the steps that firstly, a flight track of a UAV (E) is fixed to perform power optimization;
and secondly, fixing the transmitting power of the UAV (E) to perform track optimization.
The required system parameters are set as follows: assuming that there are 4 users on the ground, the locations are (800 ), (-800, -800) and (800, -800), respectively, m=4, v max ＝40m/s，H＝50m，P B ＝16dBm，γ＝0.5，ζ＝0.08
Fig. 3 illustrates UAV (E) average reception rate versus duration of flight for the same duration of flight. By comparison, the algorithm provided by the embodiment of the application is obviously superior to two reference schemes of power optimization of the flight trajectory of the fixed UAV (E) and trajectory optimization of the fixed transmission power, which proves the effectiveness of joint optimization of the trajectory and the transmission power of the UAV (E) in improving the eavesdropping rate. In particular, the average reception rate is significantly improved compared to UAV (E) power optimization alone. This is because the fixed UAV (E) flight trajectory limits its mobility potential, while when trajectory joint power optimization is performed, power optimization is superimposed on the simple trajectory optimization, so that UAV (E) is more flexible, and therefore the average receiving rate of UAV (E) is higher than that of the other two methods.
FIG. 4 illustrates a comparison of the flight trajectory of UAV (E) with the initial trajectory of UAV (E) and the trajectory of UAV (B), represented by squares, implemented by the algorithm of an embodiment of the present application. The UAV (B) can be observed to access above each user one by one in a fixed flight path, and the flight path of the UAV (E) after optimization is consistent with the flight path of the UAV (B), so that interception of information sent by the UAV (B) is realized.
Figure 5 illustrates the trend of UAV (E) transmit interference power over time as implemented by the algorithm of an embodiment of the present application. As can be seen in fig. 4 in combination with fig. 3, when t=0s, t=40s, t=80s, t=120s and t=160s, the corresponding UAV (B) and UAV (E) fly to the respective user's upper free position, where UAV (E) is closer to the user, so UAV (E) transmits a reduced interference power in order to maximize the effective eavesdropping rate.
Fig. 6 shows a convergence graph of the system maximum effective eavesdropping rate for the algorithm of an embodiment of the present application when t=160 s. As can be seen from the figure, the maximum eavesdropping rate of the proposed algorithm increases rapidly with increasing number of iterations, and the algorithm converges after about 18 iterations.
The technical scheme provided by the embodiment of the application aims at the influence of the track change of the unmanned aerial vehicle on the effective eavesdropping rate of the system, and an effective active interference scheme is adopted in the model, namely, the unmanned aerial vehicle transmits interference signals while eavesdropping suspicious link information, and the suspicious receiver is interfered. In order to maximize the effective eavesdropping rate, the track and the transmitting interference power of the unmanned aerial vehicle are optimized by using the block coordinate descent and continuous convex optimization technology assisted by the update rate, so that the effective eavesdropping rate is improved.
While specific embodiments of the application have been described above, it will be appreciated by those skilled in the art that the specific embodiments described are illustrative only and not intended to limit the scope of the application, and that equivalent modifications and variations of the application in light of the spirit of the application will be covered by the claims of the present application.
Claims (1)
1. An unmanned aerial vehicle active eavesdropping method with combined track and interference power optimization is characterized by comprising the following steps:
step 10, in an unmanned aerial vehicle active eavesdropping model, respectively setting an initial track of a suspicious emitter, an initial transmitting power of the suspicious emitter, an initial track of a legal eavesdropper, an initial transmitting power of the legal eavesdropper, a relaxation variable initial value, a user scheduling rule of the suspicious emitter, a first updating parameter, a second updating parameter, an iteration number initial value and a threshold value; the unmanned aerial vehicle initiative eavesdropping model specifically is: in a three-dimensional Cartesian coordinate, a suspicious emitter sends suspicious information to M ground users, the ground users and the suspicious emitter are respectively provided with an antenna, a legal eavesdropper is provided with two antennas for eavesdropping on the information sent from the suspicious emitter to the ground users and for sending interference signals to interfere with the ground users, the legal eavesdropper and the suspicious emitter are assumed to fly at a constant height, the suspicious emitter adopts a time division multiple access transmission mode to serve the users on the ground, the served users are selected according to the principle of closest distance, the whole flight cycle of the legal eavesdropper is discretized, the legal eavesdropper is equally divided into N communication time slots, and the coordinate position of the legal eavesdropper is unchanged in each time slot;
step 20, updating the iteration times, and then calculating a first updating parameter by using the updated iteration times and a second updating parameter; and calculating a first updating parameter by using the updated iteration times and the second updating parameter, wherein the formula is as follows:
γ＝γ/(1+(k-1)×ζ)
wherein, gamma is a first updating parameter, ζ is a second updating parameter, and k is the iteration number;
step 30, calculating the optimal value of the transmission power of the legal eavesdropper by using the initial track of the suspicious emitter, the flight track of the legal eavesdropper in the last iteration, the user scheduling rule of the suspicious emitter and the initial value of the relaxation variable, and then calculating the transmission power of the legal eavesdropper in the current iteration by using the first updated parameter, the optimal value of the transmission power of the legal eavesdropper and the transmission power of the legal eavesdropper in the last iteration; calculating the optimal value of the sending power of the legal eavesdropper by using the initial track of the suspicious emitter, the flight track of the legal eavesdropper in the last iteration, the user scheduling rule of the suspicious emitter and the initial value of the relaxation variable, wherein the method specifically comprises the following steps:
wherein max is the maximum function, η Power To target value of relaxation variable X m For introduced relaxation variable x m [n]Is set of (1), Y m For introduced relaxation variable y m [n]Is the constraint, N is the total number of communication time slots, x m [n]Is the relaxation variable of the nth time slot, y m [n]As a relaxation variable of the nth time slot, m represents the mth user, n represents the nth communication time slot, P B [n]For the power transmitted by the suspicious transmitter in the nth time slot, P E [n]For the interference power transmitted by the legal eavesdropper in the nth time slot,for the channel model between the suspicious transmitter and the Mth user in the nth time slot +.>For the channel model between the n-th time slot legal eavesdropper and the M-th user +.>To give the initial value of the relaxation variable at the nth slot, P E,max Peak value of transmitting power at nth time slot for legal eavesdropper, alpha m [n]Scheduling parameters for a user->For the receiving rate of the mth ground user in the nth time slot, R E [n]Is the reception rate of a legal eavesdropper in the nth time slot;
calculating the transmission power of the legal eavesdropper in the iteration by using the first updated parameter, the transmission power optimal value of the legal eavesdropper and the transmission power of the legal eavesdropper in the previous iteration, wherein the transmission power of the legal eavesdropper in the iteration specifically comprises the following steps:
wherein, gamma is the first updating parameter, P E The power optimum value is transmitted for a legitimate eavesdropper,transmitting power for the legal eavesdropper of the last iteration;
step 40, calculating the optimal value of the flight track of the legal eavesdropper by using the transmission power of the legal eavesdropper, the initial track of the suspicious emitter, the user scheduling rule of the suspicious emitter and the initial value of the relaxation variable, and then calculating the flight track of the legal eavesdropper in the iteration by using the first updated parameter, the optimal value of the flight track of the legal eavesdropper and the flight track of the legal eavesdropper in the previous iteration; and calculating the optimal value of the flight track of the legal eavesdropper by using the transmission power of the legal eavesdropper, the initial track of the suspicious emitter, the user scheduling rule of the suspicious emitter and the initial value of the relaxation variable, wherein the formula is as follows:
q E [1]＝q E [N]
wherein max is the maximum function, η traj To target value of relaxation variable X m For introduced relaxation variable x m [n]Is set of (1), Y m For introduced relaxation variable y m [n]Is the constraint, N is the total number of communication time slots, x m [n]Is the relaxation variable of the nth time slot, y m [n]Is a relaxation variable of the nth time slot, m represents the mth user, n represents the nth communication time slot, q E [n+1]To suspect transmitter position in the n+1th slot, q E [n]For the position of the legal eavesdropper in the nth time slot, L is the maximum flight distance of the legal eavesdropper in each time slot, q E [l]For the position of the legal eavesdropper in the first time slot, q E [N]P for the position of the legal eavesdropper in the last slot B [n]For the transmission power of the suspicious transmitter in the nth time slot, P E [n]The interference power transmitted in the nth time slot for a legitimate eavesdropper,for the channel model between the suspicious transmitter and the Mth user in the nth time slot +.>For the lower bound obtained by successive convex optimization of the channel model between the nth time slot legal eavesdropper and the Mth user->For the introduced relaxation variable, ++>A is the lower bound obtained by successive convex optimization of the receiving rate of the legal eavesdropper in the nth time slot m [n]Scheduling parameters for users of suspicious transmitters, < >>For the receiving rate of the mth ground user in the nth time slot, P E [n]For interference power, lambda, transmitted by legal eavesdroppers in the nth time slot 0 For the signal-to-noise ratio at the reference distance, +.>As relaxation variable, H is flying height, y m [n]For the introduced relaxation variable, ++>To give in the nth time slotInitial value of relaxation variable of [ gamma ] [ n ]]D for the introduced relaxation variable min Is the minimum safe distance between the suspected transmitter and the legitimate eavesdropper; calculating the flight path of the legal eavesdropper in the iteration by using the first updated parameter, the flight path optimal value of the legal eavesdropper and the flight path of the legal eavesdropper in the previous iteration, wherein the flight path of the legal eavesdropper in the iteration is specifically as follows:
wherein, gamma is a first update parameter, Q E For the optimum value of the legal eavesdropper flight trajectory,the method is characterized in that the method is a legal eavesdropper flight track of the last iteration;
step 50, calculating the current average reachable interception rate, returning to step 20 if the difference between the current average reachable interception rate and the last iteration average reachable interception rate is greater than or equal to a threshold value, and ending the step if the difference between the current average reachable interception rate and the last iteration average reachable interception rate is less than the threshold value; the current average achievable eavesdropping rate is calculated as follows:
q E [1]＝q E [N]
wherein max is a maximum function, Q E Is the optimal value of the flight path of the legal eavesdropper, P E For optimal interference power of legal eavesdropper, N is total number of communication time slots, a m [n]Scheduling parameters for users of suspicious transmitters, R EV [n]For effective eavesdropping rate, s.t. is a constraint, q E [n+1]To the position of legal eavesdropper in the n+1th time slot, q E [n]For the position of the legal eavesdropper in the nth time slot, L is the maximum flight distance of the legal eavesdropper in each time slot, q E [l]For the position of the legal eavesdropper in the first time slot, q E [N]For the position of the legal eavesdropper in the last time slot, q E [n]For the position of the legal eavesdropper in the nth time slot, q B [n]D, for the position of the suspicious transmitter in the nth time slot min For minimum security distance between suspicious emitter and legal eavesdropper, P E [n]Interference power, P, transmitted in the nth time slot for a legitimate eavesdropper E,max Transmitting the peak of interference power at the nth time slot for a legitimate eavesdropper, R EV [N]In order to be able to effectively tap the rate,for the receiving rate of the mth ground user in the nth time slot, R E [n]Is the rate of reception by a lawful eavesdropper in the nth time slot.
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