CN112512037A - Unmanned aerial vehicle active eavesdropping method combining track and interference power optimization - Google Patents

Unmanned aerial vehicle active eavesdropping method combining track and interference power optimization Download PDF

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CN112512037A
CN112512037A CN202011388442.XA CN202011388442A CN112512037A CN 112512037 A CN112512037 A CN 112512037A CN 202011388442 A CN202011388442 A CN 202011388442A CN 112512037 A CN112512037 A CN 112512037A
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eavesdropper
lawful
time slot
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transmitter
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CN112512037B (en
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赵睿
周洁
张孟杰
王培臣
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Huaqiao University
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W28/00—Network traffic management; Network resource management
    • H04W28/02—Traffic management, e.g. flow control or congestion control
    • H04W28/0226—Traffic management, e.g. flow control or congestion control based on location or mobility
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04K—SECRET COMMUNICATION; JAMMING OF COMMUNICATION
    • H04K3/00—Jamming of communication; Counter-measures
    • H04K3/40—Jamming having variable characteristics
    • H04K3/43—Jamming having variable characteristics characterized by the control of the jamming power, signal-to-noise ratio or geographic coverage area
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04K—SECRET COMMUNICATION; JAMMING OF COMMUNICATION
    • H04K3/00—Jamming of communication; Counter-measures
    • H04K3/80—Jamming or countermeasure characterized by its function
    • H04K3/82—Jamming or countermeasure characterized by its function related to preventing surveillance, interception or detection
    • H04K3/825—Jamming or countermeasure characterized by its function related to preventing surveillance, interception or detection by jamming
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
    • H04W12/02—Protecting privacy or anonymity, e.g. protecting personally identifiable information [PII]
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W28/00—Network traffic management; Network resource management
    • H04W28/02—Traffic management, e.g. flow control or congestion control
    • H04W28/0231—Traffic management, e.g. flow control or congestion control based on communication conditions
    • H04W28/0236—Traffic management, e.g. flow control or congestion control based on communication conditions radio quality, e.g. interference, losses or delay
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    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
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Abstract

The invention provides an unmanned aerial vehicle active interception method combining track and interference power optimization, aiming at the influence of track change of an unmanned aerial vehicle on the effective interception rate of a system, an effective active interference scheme is adopted in a model, namely the unmanned aerial vehicle sends an interference signal while intercepting suspicious link information to interfere a suspicious receiver. In order to maximize the effective eavesdropping rate, the track and the sending interference power of the unmanned aerial vehicle are optimized by using the updating rate-assisted block coordinate descent and continuous convex optimization technology, and the effective eavesdropping rate is further improved.

Description

Unmanned aerial vehicle active eavesdropping method combining track and interference power optimization
Technical Field
The invention relates to the technical field of communication monitoring, in particular to an active unmanned aerial vehicle eavesdropping method combining track and interference power optimization.
Background
In recent years, due to the characteristics of high mobility, low cost and the like of the unmanned aerial vehicle, the application requirements in the aspects of public safety, disaster management, monitoring, communication and the like are continuously increased. However, with the popularization of unmanned aerial vehicle communication systems, low-cost wireless services expand the range of activities of criminals or terrorists, and pose a serious threat to national security. To combat criminal or terrorist attacks, government agencies are increasingly required to legally monitor any suspect communication links and detect abnormal behavior in commercial wireless networks.
The trajectory optimization problem of drones is crucial in drone networks, mainly because the high mobility of drones, the inherent broadcast characteristics of wireless communication and the considered channels are controlled by Line of sight (LoS), and the change in the position of a drone can directly affect its reception rate.
In the research of the prior literature, the active monitor is regarded as a node fixed on the ground or an unmanned aerial vehicle with a fixed flight path, and the influence of the track change of the unmanned aerial vehicle as an active eavesdropper on the system eavesdropping rate is almost ignored.
Disclosure of Invention
The invention aims to solve the technical problem of providing an unmanned aerial vehicle active eavesdropping method and device for optimizing joint track and interference power, and the method and device can realize effective active interference by utilizing the characteristics of a suspicious system so as to improve the eavesdropping rate to the maximum extent.
In order to solve the technical problem, the embodiment of the present specification is implemented as follows:
an active unmanned aerial vehicle eavesdropping method combining trajectory and interference power optimization comprises the following steps:
step 10, respectively setting an initial track of a suspicious emitter, initial transmitting power of the suspicious emitter, an initial track of a legal eavesdropper, initial transmitting power of the legal eavesdropper, an initial value of a relaxation variable, a user scheduling rule of the suspicious emitter, a first updating parameter, a second updating parameter, an initial value of iteration times and a threshold value in an active eavesdropping model of the unmanned aerial vehicle;
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 sending power of the legal eavesdropper by using the initial track of the suspicious emitter, the flight track of the legal eavesdropper of the previous iteration, the user scheduling rule of the suspicious emitter and the initial value of the relaxation variable, and then calculating the sending power of the legal eavesdropper of the current iteration by using the first updating parameter, the optimal value of the sending power of the legal eavesdropper and the sending power of the legal eavesdropper of the previous iteration;
step 40, calculating the optimal value of the flight trajectory of the legal eavesdropper by using the sending 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 then calculating the flight trajectory of the legal eavesdropper of the current iteration by using the first updating parameter, the optimal value of the flight trajectory of the legal eavesdropper and the flight trajectory of the legal eavesdropper of the previous iteration;
and step 50, calculating the current average reachable eavesdropping rate, returning to the step 20 if the difference value between the current average reachable eavesdropping rate and the last iterative average reachable eavesdropping rate is greater than or equal to the threshold value, and ending the step if the difference value between the current average reachable eavesdropping rate and the last iterative average reachable eavesdropping rate is less than the threshold value.
Further, in step 10, the active eavesdropping model of the unmanned aerial vehicle specifically includes: in a three-dimensional Cartesian coordinate, a suspicious transmitter sends 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 and is respectively used for eavesdropping the information sent from the suspicious transmitter to the ground users and sending 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 ground users, the served users are selected according to a nearest principle, the whole flight period of the legal eavesdropper is discretized and equally divided into N communication time slots, and in each time slot, the coordinate position of the legal eavesdropper is unchanged.
Further, in 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 γ is a first update parameter, ζ is a second update parameter, and k is the number of iterations.
Further, in step 30, calculating an optimal value of the transmission power of the lawful eavesdropper by using the initial trajectory of the suspected transmitter, the flight trajectory of the lawful eavesdropper of the last iteration, the user scheduling rule of the suspected transmitter, and the initial value of the slack variable specifically includes:
Figure BDA0002810528130000031
Figure BDA0002810528130000032
Figure BDA0002810528130000033
Figure BDA0002810528130000034
Figure BDA0002810528130000035
Figure BDA0002810528130000036
where max is the function of the maximum, ηPowerFor the target value relaxation variable, XmFor introducing a relaxation variable xm[n]Set of (2), YmFor introducing a relaxation variable ym[n]S.t. as constraint, N is total number of communication time slots, xm[n]Is a relaxation variable of the nth slot, ym[n]Is a relaxation variable of the nth time slot, m represents the mth user, n represents the nth communication time slot, PB[n]At the n-thPower transmitted by a slotted suspect transmitter, PE[n]For the interference power transmitted by the lawful eavesdropper at the nth slot,
Figure BDA0002810528130000037
for the channel model between the suspect transmitter at the nth time slot and the mth user,
Figure BDA0002810528130000038
for the channel model between the lawful eavesdropper at the nth time slot and the mth user,
Figure BDA0002810528130000039
for a given initial value of the slack variable, P, in the nth time slotE,maxTransmitting a peak of power, alpha, in the nth time slot for a lawful eavesdropperm[n]The parameters are scheduled for the users and,
Figure BDA00028105281300000310
for receiving rate of mth terrestrial user in nth time slot, RE[n]Is the reception rate of the lawful eavesdropper at the nth time slot.
Further, in the step 30, calculating the transmission power of the lawful eavesdropper of the current iteration by using the first update parameter, the optimal value of the transmission power of the lawful eavesdropper and the transmission power of the lawful eavesdropper of the previous iteration, specifically:
Figure BDA00028105281300000311
where γ is a first update parameter, PEFor the legal eavesdropper to send the optimum value of power,
Figure BDA00028105281300000312
transmitting power for the last iteration of the lawful eavesdropper.
Further, in step 40, the optimal value of the flight trajectory of the lawful eavesdropper is calculated by using the transmission power of the lawful eavesdropper, the initial trajectory of the suspect transmitter, the user scheduling rule of the suspect transmitter, and the initial value of the slack variable, and the formula is as follows:
Figure BDA0002810528130000041
Figure BDA0002810528130000042
Figure BDA0002810528130000043
qE[1]＝qE[N]
Figure BDA0002810528130000044
Figure BDA0002810528130000045
Figure BDA0002810528130000046
Figure BDA0002810528130000047
where max is the function of the maximum, ηtrajFor the target value relaxation variable, XmFor introducing a relaxation variable xm[n]Set of (2), YmFor introducing a relaxation variable ym[n]S.t. as constraint, N is total number of communication time slots, xm[n]Is a relaxation variable of the nth slot, ym[n]Is a relaxation variable of the nth time slot, m represents the mth user, n represents the nth communication time slot, qE[n+1]For the position of the suspect transmitter in the (n + 1) th time slot, qE[n]For the position of lawful eavesdropper at nth time slot, L isMaximum flight distance of legal eavesdropper in each time slot, qE[l]For the position of the lawful eavesdropper in the first time slot, qE[N]For the position of the lawful eavesdropper in the last time slot, PB[n]Transmit power, P, for suspect transmitter in nth time slotE[n]The interference power transmitted in the nth slot for a lawful eavesdropper,
Figure BDA0002810528130000048
for the channel model between the suspect transmitter at the nth time slot and the mth user,
Figure BDA0002810528130000049
is the lower bound obtained after the successive convex optimization of the channel model between the lawful eavesdropper of the nth time slot and the Mth user,
Figure BDA00028105281300000410
in order to introduce the relaxation variables of the process,
Figure BDA00028105281300000411
a lower bound, a, obtained after successive convex optimization of the receiving rate of the legal eavesdropper at the nth time slotm[n]The parameters are scheduled for the user of the suspect transmitter,
Figure BDA00028105281300000412
for receiving rate of mth terrestrial user in nth time slot, PE[n]For interference power transmitted by lawful eavesdropper in the nth time slot, λ0For the signal-to-noise ratio at the reference distance,
Figure BDA00028105281300000413
for the relaxation variable, H is the fly height, ym[n]In order to introduce the relaxation variables of the process,
Figure BDA00028105281300000414
given an initial value of a relaxation variable in the nth time slot, γ n]For introduced relaxation variables, dminThe minimum safe distance between the suspect transmitter and the lawful eavesdropper.
Further, in the step 40, calculating the flight trajectory of the lawful eavesdropper of the current iteration by using the first updated parameter, the optimal flight trajectory value of the lawful eavesdropper and the flight trajectory of the lawful eavesdropper of the previous iteration, specifically:
Figure BDA0002810528130000051
wherein γ is a first update parameter, QEFor the optimum value of the flight trajectory of the lawful eavesdropper,
Figure BDA0002810528130000052
the flight trajectory of the legal eavesdropper of the last iteration is obtained.
Further, in step 50, the current average reachable interception rate is calculated according to the following formula:
Figure BDA0002810528130000053
Figure BDA0002810528130000054
qE[1]＝qE[N]
Figure BDA0002810528130000055
Figure BDA0002810528130000056
Figure BDA0002810528130000057
where max is the function of the maximum, QEFor the optimum value of the flight path of a legal bug, PEIs a law of lawOptimum interference power of the eavesdropper, N being the total number of communication time slots, am[n]Scheduling parameters, R, for users of suspect transmittersEV[n]For effective eavesdropping rate, s.t. as constraint, qE[n+1]For the lawful eavesdropper location at the (n + 1) th time slot, qE[n]For the position of the lawful interception at the nth time slot, L is the maximum flight distance of the lawful interception at each time slot, qE[l]For the position of the lawful eavesdropper in the first time slot, qE[N]For the position of the lawful eavesdropper in the last slot, qE[n]For the position of the lawful eavesdropper in the nth slot, qB[n]For the position of the suspect transmitter in the nth time slot, dminFor minimum security distance between suspect transmitter and lawful eavesdropper, PE[n]Interference power, P, transmitted in the nth time slot for a lawful eavesdropperE,maxTransmitting a peak of interference power, R, for a lawful eavesdropper in the nth time slotEV[N]In order to be able to eavesdrop at a rate efficient,
Figure BDA0002810528130000058
for receiving rate of mth terrestrial user in nth time slot, RE[n]Is the reception rate of the lawful eavesdropper at the nth time slot.
The technical scheme provided by the embodiment of the invention at least has the following technical effects or advantages:
aiming at the influence of the track change of the unmanned aerial vehicle on the effective interception rate of the system, an effective active interference scheme is adopted in the model, namely the unmanned aerial vehicle sends an interference signal while intercepting suspicious link information to interfere a suspicious receiver. In order to maximize the effective eavesdropping rate, the track and the sending interference power of the unmanned aerial vehicle are optimized by using the updating rate-assisted block coordinate descent and continuous convex optimization technology, and the effective eavesdropping rate is further improved.
The foregoing description is only an overview of the technical solutions of the present invention, and the embodiments of the present invention are described below in order to make the technical means of the present invention more clearly understood and to make the above and other objects, features, and advantages of the present invention more clearly understandable.
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The invention will be further described with reference to the following examples with reference to the accompanying drawings.
FIG. 1 is a schematic flow chart of a method according to an embodiment of the present invention;
fig. 2 is a schematic diagram of an active eavesdropping communication system model of an unmanned aerial vehicle according to an embodiment of the invention;
FIG. 3 is a diagram illustrating an average receiving rate of UAV (E) according to an embodiment of the present invention;
fig. 4 shows flight trajectories of uav (b) and uav (e) for 160s according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of the variation of interference power with time for UAV (E) according to the present invention;
fig. 6 is a schematic diagram of the convergence of algorithm 1 according to the embodiment of the present invention.
Detailed Description
The present invention is intended to overcome the above disadvantages of the prior art, and to develop a wireless communication interception scheme of Unmanned Aerial Vehicle (UAV) as a legal eavesdropper (UAV) (e), in which a legal eavesdropper (UAV (e)) is used to intercept suspicious information sent by a suspicious transmitter (UAV (b)) to a ground suspicious receiver. By utilizing the characteristics of a suspicious system, an effective active interference scheme is provided so as to improve the eavesdropping rate to the maximum extent.
Referring to fig. 1, an embodiment of the present invention discloses an active unmanned aerial vehicle eavesdropping method based on joint trajectory and interference power optimization, including:
step 10, respectively setting initial tracks of suspicious emitters in an active eavesdropping model of the unmanned aerial vehicle
Figure BDA0002810528130000061
Initial transmit power P of suspect transmitterBInitial trace of a lawful eavesdropper
Figure BDA0002810528130000062
Initial transmission power of a lawful eavesdropper
Figure BDA0002810528130000063
Initial value of relaxation variable
Figure BDA0002810528130000064
User scheduling rule A of suspicious transmitter, first updating parameter gamma, second updating parameter zeta, iteration number initial value k being 0 and threshold value
Figure BDA0002810528130000065
Step 20, updating the iteration number k to k +1, and then calculating a first update parameter γ to γ/(1+ (k-1) × ζ) by using the updated iteration number and the second update parameter;
step 30, utilizing the initial trajectory of the suspect transmitter
Figure BDA0002810528130000071
Flight path of last iteration legal eavesdropper
Figure BDA0002810528130000072
(when the number of iterations k is 1, the flight trajectory of the lawful eavesdropper of the last iteration
Figure BDA0002810528130000073
I.e. the initial trajectory of the lawful eavesdropper
Figure BDA0002810528130000074
) Calculating the optimal value P of the transmission power of the legal eavesdropper according to the user scheduling rule A of the suspicious transmitter and the initial value of the relaxation variableEThen using the first update parameter gamma, the optimum value P of the transmission power of the lawful eavesdropperEAnd the transmission power of the lawful eavesdropper of the last iteration
Figure BDA0002810528130000075
Calculation book
Figure BDA0002810528130000076
Transmit power of a sub-iterative lawful eavesdropper
Figure BDA0002810528130000077
Step 40, utilizing the transmission power of the lawful eavesdropper
Figure BDA0002810528130000078
Initial trajectory of suspect transmitter
Figure BDA0002810528130000079
User scheduling rule A of suspect transmitter and initial value of slack variable
Figure BDA00028105281300000710
Calculating the optimal value Q of the flight path of the legal eavesdropperEThen, the first updating parameter gamma and the optimal value Q of the flight path of the legal eavesdropper are utilizedEAnd the flight path of the legal eavesdropper of the last iteration
Figure BDA00028105281300000711
(when the number of iterations k is 1, the flight trajectory of the lawful eavesdropper of the last iteration
Figure BDA00028105281300000712
I.e. the initial trajectory of the lawful eavesdropper
Figure BDA00028105281300000713
) Calculating the flight path of the legal eavesdropper of the iteration
Figure BDA00028105281300000714
Step 50, calculating the current average reachable eavesdropping rate, and if the difference value between the current average reachable eavesdropping rate and the last iterative average reachable eavesdropping rate is greater than or equal to a threshold value
Figure BDA00028105281300000715
Returning to step 20, if the difference between the current average reachable eavesdropping rate and the last iteration average reachable eavesdropping rate is less than the threshold value
Figure BDA00028105281300000716
And when so, ending the step.
In one possible implementation, where the model of the communication system is actively intercepted by the drone as shown in fig. 2, in a three-dimensional cartesian coordinate, uav (b) is a suspicious transmitting node that transmits suspicious information to M ground users Dm，
Figure BDA00028105281300000717
The ground user and the UAV (B) are both provided with only one antenna; uav (e) is a lawful eavesdropper equipped with two antennas for eavesdropping on information sent from uav (b) to ground users and for sending interfering signals to interfere with ground users. Uav (e) and uav (b), both drones, are assumed to fly at a constant altitude H, which is the minimum at which a drone requires terrain avoidance, while helping to reduce its energy consumption when ascending or descending. Uav (b) uses Time Division Multiple Access (TDMA) transmission to serve users on the ground, that is, uav (b) serves only one user in each timeslot, and selects the served user according to the closest principle. To simplify the optimization problem and ensure that the receiving rate of the ground user is maximized, the flight trajectory of UAV (B) and the user scheduling rules
Figure BDA0002810528130000081
Determining; the initial trajectory of the uav (e) is a circular flight trajectory with different flight radii set at the center of the geometric midpoint of the user.
Setting the whole flight cycle of the UAV to T, since the continuous time T means infinite speed constraints, which makes the trajectory design of the drone very difficult to handle, the present embodiment discretizes the whole communication process and equally divides it into N very small communication time slots, i.e. T ═ N δt. Due to the communication time slot delta compared with the flight speed of the unmanned aerial vehicletIs small, so it can be considered that at each time slot deltatAnd the coordinate position of the unmanned aerial vehicle is invariable. The position of the drone at each slot can be expressed using discretized slots as:
Figure BDA0002810528130000082
defining M ground users DmThe coordinates on the three-dimensional Cartesian coordinates are respectively
Figure BDA0002810528130000083
Figure BDA0002810528130000084
For the convenience of calculation, the time for takeoff and landing of the unmanned aerial vehicle is ignored. UAV (B) and UAV (E) have a maximum flight speed VmaxThen, the maximum flight distance of the drone in each time slot is L ═ δtVmax. In addition, the last slot of uav (b) and uav (e) will fly to the initial position.
According to the above assumptions, the flight trajectory of uav (b) is determined, and only the movement constraint of uav (e) is considered as:
Figure BDA0002810528130000085
qE[1]＝qE[N]
to avoid collisions during flight for uav (b) and uav (e), the constraint of minimum safe distance is added:
Figure BDA0002810528130000086
wherein d isminRepresents the minimum safe distance between uav (b) and uav (e).
In the wireless communication system of drone-ground communication in this embodiment, assuming that the channels of UAV (b), UAV (e) and all ground nodes are line-of-sight (LoS), in the nth communication slot, the channel model of UAV and all ground nodes is:
Figure BDA0002810528130000087
the channel model between uav (b) and uav (e) is:
Figure BDA0002810528130000088
wherein, beta0Is defined as the distance d0Channel power gain at 1 m.
The transmit power constraint for uav (e) is as follows:
Figure BDA0002810528130000091
wherein, PE[n]Interference power, P, transmitted for UAV (E) in nth time slotE,maxUav (e) sends a peak in power.
In the nth slot, the receiving rate of uav (e) may be expressed as:
Figure BDA0002810528130000092
Figure BDA0002810528130000093
wherein, PB[n]For the transmit power at the nth time slot uav (b),
Figure BDA0002810528130000094
represents the average receiving rate of uav (e).
In the nth time slot, the ground user DmThe reception rate of (d) can be expressed as:
Figure BDA0002810528130000095
wherein the content of the first and second substances,
Figure BDA0002810528130000096
representing the noise power.
Since UAV (E) operates in active eavesdropping mode when
Figure BDA0002810528130000097
UAV (E) can reliably decode messages from UAV (B) when the effective eavesdropping rate is equal to
Figure BDA0002810528130000098
When in use
Figure BDA0002810528130000099
The lawful eavesdropper uav (e) cannot decode the information without error, when the effective eavesdropping rate is equal to 0. Thus, the effective eavesdropping rate of the legitimate eavesdropper uav (e) can be expressed as:
Figure BDA00028105281300000910
the value of the average reachable interception rate is maximized by jointly optimizing the trajectory and interference power of the uav (e) over all time slots.
The optimization problem for the average reachable eavesdropping rate can be expressed as:
Figure BDA00028105281300000911
Figure BDA00028105281300000912
qE[1]＝qE[N]
Figure BDA0002810528130000101
Figure BDA0002810528130000102
Figure BDA0002810528130000103
can be broken down into two sub-problems: 1) optimizing interference power of UAV (E); 2) the trajectory of uav (e) is optimized and then the two sub-problems are solved alternately. The method comprises the following specific steps:
step one, optimizing interference power of UAV (unmanned aerial vehicle) (E)
Given the initial trajectory of UAV (B) and UAV (E), i.e. given
Figure BDA0002810528130000104
User scheduling rule A of UAV (UAV), (B) and transmission power of UAV (B)
Figure BDA0002810528130000105
The uav (e) transmit power is optimized. Introducing a relaxation variable etapower，
Figure BDA0002810528130000106
And
Figure BDA0002810528130000107
and adopting Successive Convex optimization (SCA) technique to use first-order Taylor expansion at given initial value
Figure BDA0002810528130000108
To pair
Figure BDA0002810528130000109
Approximation, the objective function (P1) is transformed into a sub-problem solving the optimal transmit power:
Figure BDA00028105281300001010
Figure BDA00028105281300001011
Figure BDA00028105281300001012
Figure BDA00028105281300001013
Figure BDA00028105281300001014
Figure BDA00028105281300001015
the problem (P2) is a convex optimization problem that can be effectively solved by a convex optimization solver such as CVX.
Step two, optimizing the flight track of UAV (unmanned aerial vehicle) (E)
Initial transmit power given for UAV (B) and UAV (E)
Figure BDA00028105281300001016
Flight trajectory of UAV (B)
Figure BDA00028105281300001017
And user scheduling rules A for UAV (B), for UAV (E) flight trajectory
Figure BDA00028105281300001018
And (6) optimizing. Introducing relaxation variables
Figure BDA00028105281300001019
And ηtrajAnd adopting Successive Convex optimization (SCA) technique to use first-order Taylor expansion at given initial value
Figure BDA0002810528130000111
To pair
Figure BDA0002810528130000112
Approximation, the objective function (P1) is converted into a subproblem solving the optimal flight trajectory:
Figure BDA0002810528130000113
Figure BDA0002810528130000114
Figure BDA0002810528130000115
qE[1]＝qE[N]
Figure BDA0002810528130000116
Figure BDA0002810528130000117
Figure BDA0002810528130000118
Figure BDA0002810528130000119
wherein the content of the first and second substances,
Figure BDA00028105281300001110
and gamma n]Respectively obtained by the following equation under the given initial value to carry out successive convex optimization (SCA) approximation.
Figure BDA00028105281300001111
Figure BDA00028105281300001112
Figure BDA00028105281300001113
Figure BDA00028105281300001114
The problem (P3) is a convex optimization problem that can be effectively solved by a convex optimization solver such as CVX.
The specific algorithm steps are as follows:
Figure BDA0002810528130000121
and 3, assisting the coordinate descent of the block by using the updating rate, and obtaining the sending power of the UAV (E) and the flight track of the UAV (E) by using the updating rate in the steps 4 and 5 to realize rapid convergence.
The following embodiment of the present invention is further described in detail with reference to the simulation diagram, in order to show the performance advantages of the method of the embodiment of the present invention, compared with two optimization schemes:
in the first scheme, the flight track of a fixed UAV (E) is optimized in power;
and in the second scheme, the transmitting power of the UAV (E) is fixed for carrying out track optimization.
The required system parameter settings are as follows: suppose there are 4 users on the ground, the locations are (800), (-800, -800) and (800, -800), respectively, M is 4, Vmax＝40m/s，H＝50m，PB＝16dBm，
Figure BDA0002810528130000122
γ＝0.5，ζ＝0.08
Figure 3 shows uav (e) average receive rate versus duration of flight for the same duration of flight. By comparison, it can be observed that the algorithm provided by the embodiment of the invention is obviously superior to the 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 the joint optimization of the trajectory and the transmission power of the uav (e) in improving the eavesdropping rate. Especially, compared with the UAV (E) power optimization, the average receiving rate is obviously improved. This is because the fixed uav (e) flight trajectory limits its maneuverability potential, and when performing trajectory joint power optimization, the power optimization is superimposed on the pure 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 shows a comparison graph of the flight trajectory of uav (e) and the initial trajectory of uav (e) and the trajectory of uav (b) implemented by the algorithm of the embodiment of the present invention, where the ground user is represented by a square. It can be observed that uav (b) makes individual visits over each user with a fixed flight trajectory, and uav (e) agrees with the flight trajectory of uav (b) after optimization, thereby enabling eavesdropping of the information sent by uav (b).
Fig. 5 shows the time variation trend of the uav (e) transmit interference power realized by the algorithm of the embodiment of the present invention. Fig. 4 in combination with fig. 3 shows that when T is 0s, T is 40s, T is 80s, T is 120s and T is 160s, the corresponding uav (b) and uav (e) fly to the respective user overhead position, where uav (e) is closer to the user, so uav (e) sends interference power down in order to maximize the effective eavesdropping rate.
Fig. 6 shows the convergence of the maximum effective interception rate of the system of the algorithm of the embodiment of the present invention when T is 160 s. As can be seen from the figure, the maximum eavesdropping rate of the proposed algorithm increases rapidly with increasing number of iterations, the algorithm converging after about 18 iterations.
The technical scheme that provides in this application embodiment has adopted an effectual initiative interference scheme to the influence of its track change of unmanned aerial vehicle to the effective rate of eavesdropping of system in the model, and unmanned aerial vehicle sends interfering signal when eavesdropping suspicious link information promptly, disturbs suspicious receiver. In order to maximize the effective eavesdropping rate, the track and the sending interference power of the unmanned aerial vehicle are optimized by using the updating rate-assisted block coordinate descent and continuous convex optimization technology, and the effective eavesdropping rate is further improved.
Although specific embodiments of the invention have been described above, it will be understood by those skilled in the art that the specific embodiments described are illustrative only and are not limiting upon the scope of the invention, and that equivalent modifications and variations can be made by those skilled in the art without departing from the spirit of the invention, which is to be limited only by the appended claims.

Claims (8)

1. An active unmanned aerial vehicle eavesdropping method combining track and interference power optimization is characterized by comprising the following steps:
step 10, respectively setting an initial track of a suspicious emitter, initial transmitting power of the suspicious emitter, an initial track of a legal eavesdropper, initial transmitting power of the legal eavesdropper, an initial value of a relaxation variable, a user scheduling rule of the suspicious emitter, a first updating parameter, a second updating parameter, an initial value of iteration times and a threshold value in an active eavesdropping model of the unmanned aerial vehicle;
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 sending power of the legal eavesdropper by using the initial track of the suspicious emitter, the flight track of the legal eavesdropper of the previous iteration, the user scheduling rule of the suspicious emitter and the initial value of the relaxation variable, and then calculating the sending power of the legal eavesdropper of the current iteration by using the first updating parameter, the optimal value of the sending power of the legal eavesdropper and the sending power of the legal eavesdropper of the previous iteration;
step 40, calculating the optimal value of the flight trajectory of the legal eavesdropper by using the sending 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 then calculating the flight trajectory of the legal eavesdropper of the current iteration by using the first updating parameter, the optimal value of the flight trajectory of the legal eavesdropper and the flight trajectory of the legal eavesdropper of the previous iteration;
and step 50, calculating the current average reachable eavesdropping rate, returning to the step 20 if the difference value between the current average reachable eavesdropping rate and the last iterative average reachable eavesdropping rate is greater than or equal to the threshold value, and ending the step if the difference value between the current average reachable eavesdropping rate and the last iterative average reachable eavesdropping rate is less than the threshold value.
2. The method of claim 1, wherein: in the step 10, the active eavesdropping model of the unmanned aerial vehicle specifically includes: in a three-dimensional Cartesian coordinate, a suspicious transmitter sends 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 and is respectively used for eavesdropping the information sent from the suspicious transmitter to the ground users and sending 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 ground users, the served users are selected according to a nearest principle, the whole flight period of the legal eavesdropper is discretized and equally divided into N communication time slots, and in each time slot, the coordinate position of the legal eavesdropper is unchanged.
3. The method of claim 1, wherein: in 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 γ is a first update parameter, ζ is a second update parameter, and k is the number of iterations.
4. The method of claim 1, wherein: in step 30, calculating an optimal value of the transmission power of the lawful eavesdropper by using the initial trajectory of the suspected transmitter, the flight trajectory of the lawful eavesdropper of the last iteration, the user scheduling rule of the suspected transmitter, and the initial value of the slack variable, specifically including:
Figure FDA0002810528120000021
Figure FDA0002810528120000022
Figure FDA0002810528120000023
Figure FDA0002810528120000024
Figure FDA0002810528120000025
Figure FDA0002810528120000026
where max is the function of the maximum, ηPowerFor the target value relaxation variable, XmFor introducing a relaxation variable xm[n]Set of (2), YmFor introducing a relaxation variable ym[n]S.t. as constraint, N is total number of communication time slots, xm[n]Is a relaxation variable of the nth slot, ym[n]Is a relaxation variable of the nth time slot, m represents the mth user, n represents the nth communication time slot, PB[n]Power, P, transmitted for the suspect transmitter in the nth time slotE[n]For the interference power transmitted by the lawful eavesdropper at the nth slot,
Figure FDA0002810528120000027
for the channel model between the suspect transmitter at the nth time slot and the mth user,
Figure FDA0002810528120000028
for lawful eavesdropping at nth time slot and Mth userThe channel model of the channel between the two,
Figure FDA0002810528120000029
for a given initial value of the slack variable, P, in the nth time slotE,maxTransmitting a peak of power, alpha, in the nth time slot for a lawful eavesdropperm[n]The parameters are scheduled for the users and,
Figure FDA00028105281200000210
for receiving rate of mth terrestrial user in nth time slot, RE[n]Is the reception rate of the lawful eavesdropper at the nth time slot.
5. The method of claim 1, wherein: in step 30, calculating the transmission power of the lawful eavesdropper of the current iteration by using the first update parameter, the optimal value of the transmission power of the lawful eavesdropper and the transmission power of the lawful eavesdropper of the previous iteration, specifically:
Figure FDA0002810528120000031
where γ is a first update parameter, PEFor the legal eavesdropper to send the optimum value of power,
Figure FDA0002810528120000032
transmitting power for the last iteration of the lawful eavesdropper.
6. The method of claim 1, wherein: in step 40, the optimal value of the flight trajectory of the lawful eavesdropper is calculated by using the transmission power of the lawful eavesdropper, the initial trajectory of the suspect transmitter, the user scheduling rule of the suspect transmitter, and the initial value of the slack variable, and the formula is as follows:
Figure FDA0002810528120000033
Figure FDA0002810528120000034
Figure FDA0002810528120000035
qE[1]＝qE[N]
Figure FDA0002810528120000036
Figure FDA0002810528120000037
Figure FDA0002810528120000038
Figure FDA0002810528120000039
where max is the function of the maximum, ηtrajFor the target value relaxation variable, XmFor introducing a relaxation variable xm[n]Set of (2), YmFor introducing a relaxation variable ym[n]S.t. as constraint, N is total number of communication time slots, xm[n]Is a relaxation variable of the nth slot, ym[n]Is a relaxation variable of the nth time slot, m represents the mth user, n represents the nth communication time slot, qE[n+1]For the position of the suspect transmitter in the (n + 1) th time slot, qE[n]For the position of the lawful interception at the nth time slot, L is the maximum flight distance of the lawful interception at each time slot, qE[l]For the position of the lawful eavesdropper in the first time slot, qE[N]For a lawful eavesdropper inPosition of last time slot, PB[n]Transmit power, P, for suspect transmitter in nth time slotE[n]The interference power transmitted in the nth slot for a lawful eavesdropper,
Figure FDA00028105281200000310
for the channel model between the suspect transmitter at the nth time slot and the mth user,
Figure FDA0002810528120000041
is the lower bound obtained after the successive convex optimization of the channel model between the lawful eavesdropper of the nth time slot and the Mth user,
Figure FDA0002810528120000042
in order to introduce the relaxation variables of the process,
Figure FDA0002810528120000043
a lower bound, a, obtained after successive convex optimization of the receiving rate of the legal eavesdropper at the nth time slotm[n]The parameters are scheduled for the user of the suspect transmitter,
Figure FDA0002810528120000044
for receiving rate of mth terrestrial user in nth time slot, PE[n]For interference power transmitted by lawful eavesdropper in the nth time slot, λ0For the signal-to-noise ratio at the reference distance,
Figure FDA0002810528120000045
for the relaxation variable, H is the fly height, ym[n]In order to introduce the relaxation variables of the process,
Figure FDA0002810528120000046
given an initial value of a relaxation variable in the nth time slot, γ n]For introduced relaxation variables, dminThe minimum safe distance between the suspect transmitter and the lawful eavesdropper.
7. The method of claim 1, wherein: in step 40, calculating the flight trajectory of the lawful eavesdropper of the current iteration by using the first updated parameter, the optimal flight trajectory value of the lawful eavesdropper and the flight trajectory of the lawful eavesdropper of the previous iteration, specifically:
Figure FDA0002810528120000047
wherein γ is a first update parameter, QEFor the optimum value of the flight trajectory of the lawful eavesdropper,
Figure FDA0002810528120000048
the flight trajectory of the legal eavesdropper of the last iteration is obtained.
8. The method of claim 1, wherein: in step 50, the current average reachable interception rate is calculated according to the following formula:
Figure FDA0002810528120000049
Figure FDA00028105281200000410
qE[1]＝qE[N]
Figure FDA00028105281200000411
Figure FDA00028105281200000412
Figure FDA00028105281200000413
where max is the function of the maximum, QEFor the optimum value of the flight path of a legal bug, PEFor the optimal interference power of a lawful eavesdropper, N is the total number of communication time slots, am[n]Scheduling parameters, R, for users of suspect transmittersEV[n]For effective eavesdropping rate, s.t. as constraint, qE[n+1]For the lawful eavesdropper location at the (n + 1) th time slot, qE[n]For the position of the lawful interception at the nth time slot, L is the maximum flight distance of the lawful interception at each time slot, qE[l]For the position of the lawful eavesdropper in the first time slot, qE[N]For the position of the lawful eavesdropper in the last slot, qE[n]For the position of the lawful eavesdropper in the nth slot, qB[n]For the position of the suspect transmitter in the nth time slot, dminFor minimum security distance between suspect transmitter and lawful eavesdropper, PE[n]Interference power, P, transmitted in the nth time slot for a lawful eavesdropperE,maxTransmitting a peak of interference power, R, for a lawful eavesdropper in the nth time slotEV[N]In order to be able to eavesdrop at a rate efficient,
Figure FDA0002810528120000051
for receiving rate of mth terrestrial user in nth time slot, RE[n]Is the reception rate of the lawful eavesdropper at the nth time slot.
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