CN114698123A - Resource allocation optimization method of wireless power supply covert communication system - Google Patents

Resource allocation optimization method of wireless power supply covert communication system Download PDF

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CN114698123A
CN114698123A CN202210410331.7A CN202210410331A CN114698123A CN 114698123 A CN114698123 A CN 114698123A CN 202210410331 A CN202210410331 A CN 202210410331A CN 114698123 A CN114698123 A CN 114698123A
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于秦
张博
胡杰
杨鲲
刘双美
麻泽龙
卢鑫
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HYDRAULIC SCIENCE RESEARCH INSTITUTE OF SICHUAN PROVINCE
University of Electronic Science and Technology of China
Yangtze River Delta Research Institute of UESTC Huzhou
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Abstract

The invention discloses a resource allocation optimization method of a wireless power supply covert communication system supported by an unmanned aerial vehicle, which comprises four parts of system model construction, listener binary assumption, covert condition derivation and resource allocation problem proposing and solving. The invention takes the interference signal emitted by the unmanned aerial vehicle as the energy signal of the legal receiving equipment, realizes the multiplexing of the signal, greatly improves the function of the signal, simultaneously solves the safety problem under the line-of-sight transmission of the unmanned aerial vehicle, realizes the concealment of the information transmission of the legal receiving equipment, and makes it difficult for listeners to find the communication between the legal receiving equipment and the unmanned aerial vehicle.

Description

Resource allocation optimization method of wireless power supply covert communication system
Technical Field
The invention relates to a mobile communication method, in particular to a resource allocation optimization method of a wireless power supply covert communication system supported by an unmanned aerial vehicle.
Background
As communication scenes become more and more complex, traditional fixed base stations will no longer adapt to various communication systems with complex scenes, and Unmanned Aerial Vehicles (UAVs) have the advantages of small size, low consumption, convenience and strong battlefield survivability, and become a hot tide of recent research subjects. The communication network system with the cooperation of the unmanned aerial vehicle also provides a good solution for communication scenes which cannot be covered by the base station. On the other hand, when the unmanned aerial vehicle is used as a mobile base station, the distance between the unmanned aerial vehicle and a legal receiving Device (LD) can be well controlled, so that a Line of Sight (LoS) transmission channel is formed, which can well transmit data, but is easily intercepted by an illegal Device, and therefore, the safety problem of unmanned aerial vehicle communication is more and more important.
In the traditional secure communication, it is often considered that an eavesdropper cannot accurately analyze correct content after stealing a signal; such security measures are obviously not well suited in some scenarios, such as: military scenes; any leakage of information should be avoided in this scenario; therefore, the concept of Covert Communication (CC) comes along, which aims to hide all transmitted information and make an eavesdropper unable to find the transmission of the information, so that the information is naturally prevented from being stolen, and information security is realized. In recent years, research related to covert communication is also increasingly valued by many people.
The Energy Harvesting (EH) technology has a great development prospect because it can provide stable Energy for Energy-limited networks such as wireless sensor networks and the like and prolong the life cycle of the networks. Meanwhile, the energy sources of the energy collection technology include not only most natural energy sources of the surrounding environment, such as solar energy, light energy, wind energy, heat energy, chemical energy, and the like, but also received surrounding wireless signals can be converted into electric energy, such as manually acquired Radio Frequency (RF) signals. Energy harvesting based on RF signals is a research hotspot because it can be immune to weather conditions and provide stable energy. With the rapid development of wireless technology and the rapid increase of the number of mobile devices, user devices such as mobile phones and wearable small devices generate huge data volume, and how to improve portability for the functions of the devices becomes a challenging problem. Wireless Power Transfer (WPT) technology can collect external RF signals and convert them into Direct Current (DC) circuits through circuit design for Wireless Information Transfer (WIT), thereby dealing with some energy bottleneck problems of energy-limited and unstable networks.
In summary, the current research of WPT and WIT combining UAVs does not consider the problem of communication security, which often causes a great security hole; the WPT network scenario is not considered in the related research on covert communication, and because the UAV transmitting power is very large and covert communication is difficult to achieve, the research is extremely important and presents many challenges. On the other hand, in the WPT network, the RF signal does not always carry information, and only has interference effect on LDs, the present invention gives a new effect to the RF signal: as an interference signal of an eavesdropper; therefore, the multiplexing of the signals is realized, and a new solution is provided for the system. Various approximation methods are also provided in the problem solving, and the problem that the non-convex problem is difficult to solve is solved.
Disclosure of Invention
The invention provides a resource allocation optimization method of a wireless power supply covert communication system, which solves the communication safety problem of the existing UAV wireless communication system combined with WPT technology, and the technical scheme is as follows:
a resource allocation optimization method of a wireless power supply covert communication system comprises the following steps:
s1: establishing a system model of an unmanned aerial vehicle, legal equipment and a listener, wherein the unmanned aerial vehicle and the legal equipment have a scheduling strategy;
s2, according to the system model, obtaining signal models of legal equipment and the unmanned aerial vehicle, and designing and determining an energy model of the legal equipment;
s3, analyzing the binary hypothesis of the listeners, and obtaining the total error interception probability of the listeners on the premise of determining the positions of the listeners;
s4, introducing the position uncertainty of the listener in the actual scene to obtain the total error interception probability combined with the position uncertainty;
s5, defining an optimization target as uplink throughput of all legal equipment within one-time unmanned aerial vehicle task time, and obtaining an optimization problem under the conditions of satisfying covert communication, unmanned aerial vehicle self-restriction, legal equipment energy restriction and scheduling;
s6, decomposing the optimization problem into a plurality of sub-problems, and converting each sub-problem into a convex sub-problem by using continuous convex approximation;
s7, alternately optimizing the sub-problems by a design algorithm to obtain the optimal solution of the optimization problem.
Further, in step S1, the establishing the system model includes the following steps:
s11: the set system model comprises an unmanned aerial vehicle, a plurality of legal devices and a plurality of listeners; determining the number and the positions of legal equipment and listeners;
wherein the legal device is located at
Figure BDA0003603905860000031
Where b represents a legitimate device, k represents the kth legitimate device, xb,kAnd yb,kRespectively representing the information of the horizontal and vertical coordinate positions of the kth legal device on the ground;
location of listener HWs is shown as
Figure BDA0003603905860000032
Where w represents a listener, m represents an mth listener, xw,mAnd yw,mRespectively representing the horizontal and vertical coordinate position information of the mth listener on the ground;
the flying height of the unmanned aerial vehicle is H, one task time is T, and the maximum flying speed is VmaxUnmanned plane in a time slot deltatHas a maximum flight distance of L ═ VmaxδtThe trajectory of the drone is represented as
Figure BDA0003603905860000033
Where a denotes a drone, n denotes the nth slot, qaRepresenting a trajectory of an Unmanned Aerial Vehicle (UAV);
s12: in the nth time slot, a is used for the kth legal devicek[n]The scheduling policy parameter is expressed, the scheduling policy is proposed for legal devices, the scheduling policy indicates that only one legal device is allowed to communicate with the unmanned aerial vehicle in one time slot, and for the kth legal device, ak[n]1 indicates that the device will communicate with the drone at the nth slot, ak[n]0 means that the device will not communicate with the drone and there is a slot per slot
Figure BDA0003603905860000041
S13: setting the maximum transmitting power and the average transmitting power of the unmanned aerial vehicle;
Figure BDA0003603905860000042
Figure BDA0003603905860000043
wherein P isa[n]To representThe power of the transmitted unmanned aerial vehicle,
Figure BDA0003603905860000044
for mean transmitted power of drone, PmaxThe maximum transmitting power of the unmanned aerial vehicle.
Further, step S2 includes the following steps:
s21, obtaining the received signal r of the kth legal device in the nth time slot by the distance between the unmanned aerial vehicle autonomous control and the legal device and combining the scheduling strategy of the legal deviceb，k[n]Comprises the following steps:
Figure BDA0003603905860000045
wherein P isa[n]Which represents the transmitted power of the drone,
Figure BDA0003603905860000046
noise representing the kth legal device LDs; s isa[n]A transmission signal representative of the drone; and omegaab，k[n]Representing the channel gain from the drone to the kth legitimate device, further expressed as:
Figure BDA0003603905860000047
in the formula, Ω0Denotes a channel gain parameter with a reference distance of 1m, qb,kIndicating the location of the kth legal device, qa[n]The trajectory of the unmanned aerial vehicle in the nth time slot is represented, and H represents the flight height of the unmanned aerial vehicle;
s22, obtaining the received energy of each legal device of each time slot;
wherein, the received energy P of the kth legal device in each time sloth，k[n]Comprises the following steps:
Ph，k[n]＝ηPa[n]Ωab，k[n]
wherein P isa[n]Representing the transmitting power of the unmanned aerial vehicle, eta is the energy harvesting coefficient, omegaab，k[n]Indicating unmanned aerial vehicle toChannel gain of the kth legal device;
s23, obtaining a receiving signal of each time slot unmanned aerial vehicle;
wherein, the received signal r of the unmanned aerial vehicle is derived by a legal equipment scheduling strategya[n]Comprises the following steps:
Figure BDA0003603905860000048
Pb，k[n]representing the transmission power of the kth legal device LDs;
Figure BDA0003603905860000051
representing the received noise of the unmanned aerial vehicle UAV; sb，k[n]N (0, 1) represents the modulated signal emitted by the kth legal device LDs, omegaab，k[n]Representing the channel gain, a, of the unmanned aerial vehicle UAV to the kth legal device LDsk[n]1 indicates that the device will communicate with the unmanned aerial vehicle UAV at the nth slot, ak[n]0 means that the device will not communicate with the unmanned aerial vehicle UAV and there is a slot per slot
Figure BDA0003603905860000052
S24, obtaining the total uplink throughput rate of all legal devices;
in the nth time slot, the total uplink throughput rate R received by the unmanned aerial vehicle endb，k[n]Comprises the following steps:
Figure BDA0003603905860000053
wherein
Figure BDA0003603905860000054
i denotes the temporary variable of the sum count, σaParametric information representing the unmanned aerial vehicle UAV received noise;
s25, designing and determining an energy model of legal equipment;
for all legitimate devices, it is necessary to follow the causality of energy, i.e. the energy consumed by this slot cannot be greater than the sum of the energy harvested by this slot and the remaining energy of the previous slot, the expression is written as:
Figure BDA0003603905860000055
wherein Qb，k[n]Representing the total energy, Q, of the kth legal device LD in n time slots0Represents the initial energy; i is a temporary variable for the sum count; eta is an energy harvesting coefficient; a isk[n]1 indicates that the device will communicate with the unmanned aerial vehicle UAV at the nth slot, ak[n]0 means that the device will not communicate with the unmanned aerial vehicle UAV and there is a slot per slot
Figure BDA0003603905860000056
Further, step S3 specifically includes the following steps:
s31, obtaining a binary hypothesis model of each listener in each time slot;
setting the listener HWs to use the joint listening strategy to obtain the binary hypothesis expression of the mth listener in the nth time slot:
Figure BDA0003603905860000061
Figure BDA0003603905860000062
wherein
Figure BDA0003603905860000063
Representing the reception noise of the mth listener; h0，kRepresenting the original hypothesis: the intercepted kth legal device is considered not to transmit information; h1，kRepresent alternative assumptions: the intercepted legitimate device is considered to have transmitted information; j represents a temporary variable of the sum count; r isw,mRepresenting the received signal of the mth listener; sb,j[n]～N(0,1) represents the modulated signal transmitted by the jth legitimate device LD; a isj[n]Indicating a state in which the jth legal device LD will communicate with the unmanned aerial vehicle UAV at the nth time slot; pb，j[n]Representing the transmission power of the jth legal device; omegaaw，m[n]Represents the channel gain of the unmanned aerial vehicle UAV to the mth listener HWs; omegawb，j[n]Representing the channel gain from the mth listener to the jth legitimate device;
the judgment criteria of the listeners are as follows:
Figure BDA0003603905860000064
wherein P isw，m，k[n]Represents the average value of the power of the ambient signal obtained after l times of measurement by listener HWs;
Figure BDA0003603905860000065
represents the power value of the ambient signal obtained after the listener HWs measures 1 time; pth，m，k[n]Representing a decision threshold value; d0And D1Is expressed as corresponding to H0，kAnd H1，kThe decision result of (1);
s32, obtaining the missed detection probability and the false detection probability of each listener in each time slot;
where the probability ξ of false detection of the mth listener HWsF，m，k[n]And probability xi of missed detectionM，m，k[n]Expressed as:
Figure BDA0003603905860000066
Figure BDA0003603905860000067
pr represents the mathematically solved probability;
Figure BDA0003603905860000068
parameter, P, corresponding to received noise representing m-th listenera[n]Indicating unmanned aerial vehicle transmit power，Ω0Denotes a channel gain parameter with a reference distance of 1m, qb,kIndicating the location of the kth legal device, qa[n]Just indicate the trajectory of the drone at the nth time slot, H indicates the altitude of the drone, qw，mIndicating the listener position;
s33, obtaining the total error interception probability of each listener in each time slot;
at the angle of the listener HWs, they only know the transmission power Pa[n]Is from 0 to PmaxSet the range value of (A) to the listener Pa[n]Subject to a uniform distribution, its probability density function PDF is written as:
Figure BDA0003603905860000071
the false detection probability is derived as:
Figure BDA0003603905860000072
Figure BDA0003603905860000073
similarly, the probability of missed detection is deduced as:
Figure BDA0003603905860000074
wherein
Figure BDA0003603905860000075
In conclusion, the total interception error probability ξ can be further obtainedm，k[n]Comprises the following steps:
Figure BDA0003603905860000076
in the scenario of the invention P3≤P2Always true, total false positive probability ξm，k[n]In [ P ]1，P3]Interval about Pth，m，kIs monotonically decreasing; in the interval [ P2，P4]Total false interception probability ξm，k[n]Is about a monotonous increase, so the minimum error probability is in the interval [ P ]3，P2]Obtaining; so minimum false intercept probability
Figure BDA0003603905860000077
Comprises the following steps:
Figure BDA0003603905860000078
Figure BDA0003603905860000079
is also an exact position (x) with listener HWsw，m，yw，m) A function of the correlation.
Further, in step S4,
minimum average error probability after adding listener HWs location uncertainty
Figure BDA0003603905860000081
Write as:
Figure BDA0003603905860000082
xw,mand yw,mRespectively representing the horizontal and vertical coordinate position information of the mth listener on the ground, and the above formula is approximate:
Figure BDA0003603905860000083
wherein
Figure BDA0003603905860000084
Figure BDA0003603905860000085
xb,kAnd yb,kRespectively representing the horizontal and vertical coordinate position information of the kth legal device on the ground, wherein X and Y represent uncertain variables;
obtaining the optimal minimum average false interception probability of the added position uncertainty
Figure BDA0003603905860000086
Comprises the following steps:
Figure BDA0003603905860000087
order to
Figure BDA0003603905860000088
Then the constraint of covert communication is obtained, where pwGiven covert communication restriction parameters.
Further, step S5 specifically includes the following steps:
defining an optimization target as uplink throughput of all legal equipment within the task time of the unmanned aerial vehicle, obtaining an optimization problem under the conditions of meeting communication of hidden conditions, self limitation of the unmanned aerial vehicle, energy limitation and scheduling of the legal equipment, and enabling the unmanned aerial vehicle to work
Figure BDA0003603905860000089
The optimization problem is derived as:
Figure BDA00036039058600000912
Figure BDA0003603905860000092
Figure BDA0003603905860000093
||qa[n]-qa[n-1]||2≤L2，(c)
Figure BDA0003603905860000094
Figure BDA0003603905860000095
Figure BDA0003603905860000096
wherein the optimization problem P1 aims to maximize the total upstream throughput; a is a scheduling strategy constraint, b is a covert communication constraint, c is an unmanned aerial vehicle flight speed constraint, d is an unmanned aerial vehicle maximum transmitting power constraint, e is an unmanned aerial vehicle average transmitting power constraint, and f is a legal equipment energy causality constraint.
Further, step S6 decomposes the optimization problem P1 into three sub-problems of P2, P3, and P4, which are solved alternately, and specifically includes the following steps:
s61, fixing the transmitting power of the unmanned aerial vehicle, the transmitting power of all legal equipment and scheduling parameters to obtain an unmanned aerial vehicle trajectory optimization subproblem P2;
s62, converting the unmanned aerial vehicle trajectory sub-problem P2 into a convex problem P2.1 by using continuous convex approximation;
s63, fixing the unmanned aerial vehicle track and the scheduling parameters of legal equipment to obtain a power optimization subproblem P3;
s64, fixing the track of the unmanned aerial vehicle, the transmission power of the unmanned aerial vehicle and the transmission power of legal equipment to obtain a legal equipment scheduling optimization subproblem P4;
s65, relaxing the constraint conditions of the scheduling strategy, converting the legal equipment scheduling optimization sub-problem P4 into a convex problem P4.1, and obtaining the optimal solution of the sub-problem P4 through a shaping algorithm.
Further, in step S65, the shaping method includes: order to
Figure BDA0003603905860000097
Obtaining uplink throughput of all legal devices according to the sub-optimal solution for optimizing the optimal solution of the problem
Figure BDA0003603905860000098
Then to the uplink throughput
Figure BDA0003603905860000099
A non-zero subset K of
Figure BDA00036039058600000910
At this moment will
Figure BDA00036039058600000911
At the same time, when the uplink throughput is too low, the corresponding schedule should also be set to zero, since the communication is no longer meaningful at this time, i.e. it is not meaningful to do so
Figure BDA0003603905860000101
To sum up, an optimal solution of the scheduling policy sub-problem (P4) is obtained
Figure BDA0003603905860000102
Further, in step S7, an optimal trajectory of the drone is obtained after the algorithm is implemented
Figure BDA0003603905860000103
Transmitting power
Figure BDA0003603905860000104
Legal device scheduling policy
Figure BDA0003603905860000105
Legal device transmit power
Figure BDA0003603905860000106
And optimal uplink aggregate throughput
Figure BDA0003603905860000107
The process of the algorithm is as follows:
s11: firstly, solving a subproblem P3 to obtain the emission power of the unmanned aerial vehicle and the emission power of legal equipment after one iteration of the algorithm;
s12: then, introducing newly obtained unmanned aerial vehicle transmitting power and legal equipment transmitting power into a subproblem P2.1 to update the flight trajectory of the unmanned aerial vehicle;
s13: finally, solving a sub-problem P4.1 of latest unmanned aerial vehicle transmitting power, legal equipment transmitting power and unmanned aerial vehicle flight path to obtain a latest legal equipment scheduling strategy;
s14: if the result of the solution result is not converged or the precision is not satisfactory, go to step S11; otherwise, obtaining the final result;
the optimal unmanned aerial vehicle track can be obtained after the algorithm is implemented
Figure BDA0003603905860000108
Transmitting power
Figure BDA0003603905860000109
Legal device scheduling policy
Figure BDA00036039058600001010
Legal device transmit power
Figure BDA00036039058600001011
And optimal uplink aggregate throughput
Figure BDA00036039058600001012
The resource allocation optimization method of the wireless power supply covert communication system is characterized in that covert communication is introduced, and a new method is designed aiming at energy supply of legal equipment: the transmit signal of the UAV is multiplexed for interfering listener interception and for powering legitimate devices.
Drawings
FIG. 1 is a flow chart of a resource allocation optimization method of the wireless power supply covert communication system;
FIG. 2 is a system model diagram of a resource allocation optimization method of the wireless power supply covert communication system;
fig. 3 is an algorithm flow chart of the resource allocation optimization method of the wireless power supply covert communication system.
Detailed Description
The invention provides a resource allocation optimization method of a wireless power supply covert communication system supported by an unmanned aerial vehicle, which comprises four parts of system model construction, listener binary assumption, covert condition derivation, resource allocation problem proposition and solution, and specifically comprises the following steps:
s1, constructing a system model, and determining the number of unmanned aerial vehicles, legal equipment and listeners and the contact state among the unmanned aerial vehicles, the legal equipment and the listeners.
The method specifically comprises the following steps:
s11, suppose the system has one Unmanned Aerial Vehicle (UAV), K Legal Devices (LDs), and M listeners (HWs). Wherein, the unmanned aerial vehicle UAV and the legal equipment LDs are both provided with two antennas to realize full duplex work, and self-interference can be completely eliminated; the listener is provided with only one antenna.
Unmanned aerial vehicle UAV has three functions: (1) providing downlink energy service for legal devices LDs; (2) collecting uplink transmission information of all legal devices LDs; (3) interfering with the listening of listener HWs.
In three-dimensional coordinates, the locations of the legal devices LDs are
Figure BDA0003603905860000111
Where b represents legal devices LDs, k represents the kth legal device LDs, xb,kAnd yb,kRespectively representing the information of the horizontal and vertical coordinate position of the kth legal device on the ground.
Similarly, the location of listener HWs may be expressed as
Figure BDA0003603905860000112
Where w represents listener HWs and m represents the mth listener HWs, xw,mAnd yw,mRespectively represent the horizontal and vertical coordinate position information of the mth listener on the ground. Given that in practical scenarios, the location of listener HWs is often not known accurately, the location of listener HWs can be further expressed as:
Figure BDA0003603905860000113
wherein
Figure BDA0003603905860000114
Representing the uncertainty of the location of listener HWs, all obeys
Figure BDA0003603905860000115
While
Figure BDA0003603905860000116
Indicating the estimated location, ε, of listener HWswRepresenting the corresponding parameter of position uncertainty.
The flying height of the unmanned aerial vehicle UAV is H, one mission time (flight period) is T, and the maximum speed of flight is Vmax. Meanwhile, the flight cycle is divided into N time slots, so that the length of each time slot has
Figure BDA0003603905860000121
When deltatSufficiently small, the position of the unmanned aerial vehicle UAV may be considered to be nearly constant within this time slot. Maximum flight distance of Unmanned Aerial Vehicle (UAV) in one time slot is L ═ Vmaxδt. Thus, the trajectory of the unmanned aerial vehicle UAV may be represented as
Figure BDA0003603905860000122
Where a denotes an unmanned aerial vehicle UAV. n denotes an nth time slot, qaRepresenting the trajectory of the unmanned aerial vehicle UAV.
In summary, q is position information, and position information of which device is distinguished from the lower right corner. Thus, a denotes an unmanned aerial vehicle UAV, then qaJust show the trajectory of the unmanned aerial vehicle UAV, and q aboveb,kAnd q isw,mAnd the corresponding steps are carried out.
S12, in the nth time slot, using a for the kth legal device LDsk[n]Indicating a scheduling policy parameter and n indicates an nth slot of the divided slots. a denotes an unmanned aerial vehicle UAV; the scheduling strategy is proposed for legal devices LDs, and aims to avoid channel congestion, specifically, only one legal device LDs is allowed to communicate with the unmanned aerial vehicle UAV in one time slot; therefore, for the k-th legal device LDs, ak[n]1 indicates that the device will communicate with the unmanned aerial vehicle UAV at the nth slot, ak[n]0 means that the device will not communicate with the unmanned aerial vehicle UAV and there is a slot per slot
Figure BDA0003603905860000123
S13, according to the model of S11, the flight path of the unmanned aerial vehicle UAV is as follows: | qa[n]-qa[n-1]||2≤L2(ii) a L represents the maximum flight distance of the unmanned aerial vehicle UAV in one time slot.
The transmission power to the unmanned aerial vehicle UAV is:
Figure BDA0003603905860000124
Figure BDA0003603905860000125
wherein P isa[n]Representing the unmanned aerial vehicle UAV transmit power,
Figure BDA0003603905860000126
average transmit power, P, for unmanned UAVsmaxThe maximum transmitting power of the unmanned aerial vehicle UAV.
And S2, obtaining signal models of legal equipment and the unmanned aerial vehicle according to the system model, and designing and determining an energy model of the legal equipment.
The method specifically comprises the following steps:
s21, in the UAV communication system, the UAV can autonomously control the distance between the UAV and legal equipment LDs, so that the UAV communication system can be regarded as a UAV communication systemThe line-of-sight transmission is adopted, so that the received signal r of the kth legal device LDs in the nth time slot can be obtained by combining the scheduling strategy of the legal device LDsb，k[n]Comprises the following steps:
Figure BDA0003603905860000131
wherein P isa[n]Representing the unmanned aerial vehicle UAV transmit power,
Figure BDA0003603905860000132
noise representing the kth legal device LDs; sa[n]A transmission signal representative of an Unmanned Aerial Vehicle (UAV); and omegaab，k[n]The channel gain representing the unmanned aerial vehicle UAV to the kth legal device LDs may be expressed as:
Figure BDA0003603905860000133
in the formula, omega0Denotes a channel gain parameter with a reference distance of 1m, qb,kIndicating the location of the kth legal device, qa[n]The trajectory of the unmanned aerial vehicle UAV at the nth time slot is represented, and H represents the flight altitude of the unmanned aerial vehicle UAV.
S22, further knowing the received energy P of the kth legal device LDs in each time sloth，k[n]Comprises the following steps:
Ph，k[n]＝ηPa[n]Ωab，k[n]
wherein P isa[n]Representing the UAV launch power, η is the energy harvesting coefficient, Ωab，k[n]Representing the channel gain of the unmanned aerial vehicle UAV to the kth legal device LDs.
S23, deriving the received signal r of UAV (unmanned aerial vehicle) through legal equipment LDs (laser direct structuring) scheduling strategya[n]Comprises the following steps:
Figure BDA0003603905860000134
wherein P isb，k[n]Representing the kth legal device LDsThe transmit power of (a);
Figure BDA0003603905860000135
representing the received noise of the unmanned aerial vehicle UAV; sb，k[n]N (0, 1) represents the modulated signal emitted by the kth legal device LDs, omegaab，k[n]Representing the channel gain, a, of the unmanned aerial vehicle UAV to the kth legal device LDsk[n]1 indicates that the device will communicate with the unmanned aerial vehicle UAV at the nth slot, ak[n]0 means that the device will not communicate with the unmanned aerial vehicle UAV and there is a slot per slot
Figure BDA0003603905860000136
S24, further in the nth time slot, the total uplink throughput rate R received by the UAV terminalb，k[n]Comprises the following steps:
Figure BDA0003603905860000137
wherein
Figure BDA0003603905860000138
i denotes a temporary variable of the sum count. SigmaaParametric information representing the unmanned aerial vehicle UAV received noise.
S25, for all legitimate devices LDs, it must be energy causality, i.e. the energy consumed by this slot cannot be larger than the sum of the energy harvested by this slot and the remaining energy of the previous slot. The expression can be written as:
Figure BDA0003603905860000141
wherein Qb，k[n]Representing the total energy, Q, of the kth legal device LD in n time slots0Representing the initial energy. i is a temporary variable of the sum count, which has no practical meaning, and the following i, j are all the roles. The flight cycle is divided into N time slots, so that each time slot has a length
Figure BDA0003603905860000142
When deltatSufficiently small, the position of the unmanned aerial vehicle UAV may be considered to be nearly constant within this time slot. a isk[n]1 indicates that the device will communicate with the unmanned aerial vehicle UAV at the nth slot, ak[n]0 means that the device will not communicate with the unmanned aerial vehicle UAV and there is a slot per slot
Figure BDA0003603905860000143
S3, analyzing the binary hypothesis of listener HWs, and obtaining the total probability of the wrong listening of listener HWs under the premise of determining the position of listener HWs.
The method specifically comprises the following steps:
s31, in order to make listener HWs unable to accurately determine whether the LDs are communicating, it is necessary to analyze the binary hypothesis by standing at listener HWs angle and obtain the minimum total listening error probability. Assume that listener HWs uses a joint listening strategy. Therefore, a binary hypothetical representation of the mth listener at the nth slot can be obtained:
Figure BDA0003603905860000144
Figure BDA0003603905860000145
wherein
Figure BDA0003603905860000146
Representing the received noise of the mth listener. H0，kRepresenting the original hypothesis: it is assumed that the intercepted kth legal device does not transmit information, H0，kAs explained above, the primitive assumption is followed by a colon, indicating that the expression following is H overall0，k. In the same way, H0，kRepresent alternative assumptions: the intercepted legitimate device is considered to have transmitted information. j represents a temporary variable for the sum count to avoid collision with k. r isw,mRepresenting mth listenerA signal is received.
Hereinbefore, sb，k[n]N (0, 1) represents the modulated signal emitted by the kth legitimate device LDs, corresponding to sb，j[n]N (0, 1) represents the modulated signal emitted by the jth legitimate device LDs, only the representation has been changed, so
Figure BDA0003603905860000151
Represents the sum of the signals of all legitimate devices LDs except j ≠ k,
Figure BDA0003603905860000152
representing the sum of the signals of all legitimate devices LDs containing k.
Hereinbefore, ak[n]1 indicates that the device will communicate with the unmanned aerial vehicle UAV at the nth slot, ak[n]0 means that the device will not communicate with the unmanned aerial vehicle UAV and there is a slot per slot
Figure BDA0003603905860000153
Corresponding to aj[n]It still represents the state that the jth legal device LDs will communicate with the unmanned aerial vehicle UAV at the nth time slot.
In the above, Pb，k[n]Representing the transmission power of the kth legal device LDs, correspondingly, Pb，j[n]Still representing the transmit power of the jth legitimate device.
Above, Ωab，k[n]Representing the channel gain from the unmanned aerial vehicle UAV to the kth legal device LDs, corresponding to Ωaw，m[n]Representing the channel gain of the unmanned aerial vehicle UAV to the mth listener HWs.
Ωwb，j[n]Representing the channel gain of the (mth) listener to the jth legitimate device.
The judgment criteria of the listeners are:
Figure BDA0003603905860000154
wherein P isw，m，k[n]Represents the average value of the power of the ambient signal obtained after l times of measurement by listener HWs;
Figure BDA0003603905860000155
represents the power value of the ambient signal obtained after the listener HWs measures 1 time; pth，m，k[n]Representing a decision threshold value; d0And D1Is expressed as corresponding to H0，kAnd H1，kAnd (4) judging results.
S32, and further mth listener HWsF，m，k[n]And probability xi of missed detectionM，m，k[n]Can be expressed as:
Figure BDA0003603905860000161
Figure BDA0003603905860000162
pr represents mathematically solving the probability.
Figure BDA0003603905860000163
Parameter, P, corresponding to received noise representing m-th listenera[n]Represents the unmanned aerial vehicle UAV transmitted power, omega0Representing a channel gain parameter with a reference distance of 1m, qb,kIndicating the location of the kth legal device, qa[n]Just denote the trajectory of the unmanned aerial vehicle UAV at the nth time slot, H denotes the flight altitude of the unmanned aerial vehicle UAV, qw，mIndicating the location of listener HWs.
S33, in actual scene, all listeners HWs cannot accurately know the transmission power P of the UAVa[n]Therefore, blind condition derivation can be performed for listener HWs, who only knows the transmit power P at angle HWsa[n]Is from 0 to Pmax(maximum transmit power) range values, so it can be reasonably assumed that the listener P is a listenera[n]Subject to a uniform distribution, its Probability Density Function (PDF) can be written as:
Figure BDA0003603905860000164
the false detection probability can be derived as:
Figure BDA0003603905860000165
wherein, the complex expression is replaced by a plurality of variables with equivalent, the expression of the variables is the expression meaning on the right side of the equation,
Figure BDA0003603905860000166
similarly, the probability of missed detection can be derived as:
Figure BDA0003603905860000167
wherein
Figure BDA0003603905860000171
In conclusion, the total interception error probability ξ can be further obtainedm，k[n]Comprises the following steps:
Figure BDA0003603905860000172
in the scenario of the invention P3≤P2This is always true. Easy to find, total false interception probability xim，k[n]In [ P ]1，P3]Interval about Pth，m，kIs monotonically decreasing; in the interval [ P2，P4]Total false interception probability ξm，k[n]Is related to a monotonic increase so that the minimum error probability is in the interval [ P ]3，P2]Obtaining; so minimum false intercept probability
Figure BDA0003603905860000173
Comprises the following steps:
Figure BDA0003603905860000174
note that this is
Figure BDA0003603905860000175
Is also an exact position (x) with listener HWsw，m，yw，m) A function of the correlation.
And S4, introducing the position uncertainty of the listener HWs in the actual scene, and further obtaining the total error interception probability combined with the position uncertainty. In fact, the unmanned aerial vehicle UAV cannot know the exact location of listener HWs, so
Figure BDA0003603905860000176
Is also an exact position (x) with listener HWsw，m，yw，m) A function of the correlation. From the previous step
Figure BDA0003603905860000177
So adding listener HWs location uncertainty, minimum average error probability
Figure BDA0003603905860000178
Can be written as:
Figure BDA0003603905860000179
the direct solving complexity is quite high, and the accurate minimum error interception probability cannot be obtained, so the optimal minimum average error interception probability is approximately obtained by considering
Figure BDA00036039058600001710
The above equation can be approximated as:
Figure BDA00036039058600001711
wherein
Figure BDA0003603905860000181
Figure BDA0003603905860000182
X and Y represent the abscissa uncertainty variable and the ordinate uncertainty variable of the listener, respectively.
Further, the optimal minimum average error interception probability added with the position uncertainty is finally obtained
Figure BDA0003603905860000183
Comprises the following steps:
Figure BDA0003603905860000184
order to
Figure BDA0003603905860000185
The constraint of covert communication can be obtained, where ρwGiven covert communication restriction parameters.
S5, solving the resource allocation problem: defining an optimization target as uplink throughput of all legal equipment within the task time of the unmanned aerial vehicle, obtaining an optimization problem under the conditions of meeting communication of hidden conditions, self limitation of the unmanned aerial vehicle, energy limitation and scheduling of the legal equipment, and enabling the unmanned aerial vehicle to work
Figure BDA0003603905860000186
The optimization problem can be derived as:
Figure BDA00036039058600001813
Figure BDA0003603905860000188
Figure BDA0003603905860000189
||qa[n]-qa[n-1]||2≤L2，(c)
Figure BDA00036039058600001810
Figure BDA00036039058600001811
Figure BDA00036039058600001812
wherein the optimization problem (P1) aims at maximizing the uplink total throughput; (a) the method comprises the following steps of (a) scheduling policy constraint, (b) covert communication constraint, (c) unmanned plane flight speed constraint, (d) unmanned plane maximum transmission power constraint, (e) unmanned plane average transmission power constraint, and (f) legal equipment energy causality constraint.
S6, decomposing the optimization problem into three sub-problems, and converting each sub-problem into a convex sub-problem by using continuous convex approximation.
The method specifically comprises the following steps:
s61, because (P1) is non-convex, the solution cannot be directly solved by using an optimization tool, so the problem that (P1) is converted into a plurality of different convex sub-problems in an alternating optimization mode is considered to be solved. Fix { P firsta，PbAnd a } is constant, then (P1) can be converted to:
Figure BDA0003603905860000198
Figure BDA0003603905860000192
Figure BDA0003603905860000193
||qa[n]-qa[n-1]||2≤L2，(c)
however, the objective function and covert communication constraints of the sub-problem (P2) remain non-convex; but is easy to know
Figure BDA0003603905860000194
Is about | qa[n]-qb，k|2A convex function of
Figure BDA0003603905860000195
Representing the result of the iteration after j of the optimization sub-problem (P2), the objective function can be expressed as | q |a[n]-qb，k|2Is integrated in
Figure BDA0003603905860000196
The dots become convex with a first order taylor expansion. Then the objective function becomes:
Figure BDA0003603905860000197
to convert constraints to convex, a relaxation variable needs to be introduced
q1，k[n]≥|qa[n]-qb,k|2and q2，m[n]≥|qa[n]-qw，m|2
Then the optimization sub-problem (P2) may become (P2.1):
Figure BDA00036039058600002014
Figure BDA0003603905860000202
Figure BDA0003603905860000203
q1，k[n]≥|qa[n]-qb，k|2
||qa[n]-qa[n-1]||2≤L2
q2，m[n]≥|qa[n]-qw，m|2
after the jth unmanned aerial vehicle track iteration result is obtained, the (j +1) th result can be obtained and written as
Figure BDA0003603905860000204
To sum up (P2) the subproblem translates into the (P2.1) subproblem that can be solved.
S62, fix { qaA }, the drone UAV power and legal device LDs power optimization subproblem (P3) may be obtained, written as:
Figure BDA00036039058600002015
Figure BDA0003603905860000206
Figure BDA0003603905860000207
Figure BDA0003603905860000208
Figure BDA0003603905860000209
as can be seen, (P3) with respect to Pb，PaThe convex problem is solved without further processing, so that the convex optimization tool can be directly used for solving.
S63, fix { qa，Pa，PbGet the optimized legal device scheduling subproblem (P4), written as:
Figure BDA00036039058600002016
Figure BDA00036039058600002011
Figure BDA00036039058600002012
Figure BDA00036039058600002013
however, the sub-problem (P4) is also a non-convex problem, considering that the scheduling policy constraint is relaxed, i.e. let ak[n]Values can be continuous, then (P4) can become (P4.1):
(
Figure BDA00036039058600002112
Figure BDA0003603905860000212
Figure BDA0003603905860000213
Figure BDA0003603905860000214
at this time, the optimization sub-problem (P4.1) becomes convex, and the optimal solution a is solvedk[n]Thereafter, the continuous values need to be reshaped into discrete values. The shaping method comprises the following steps: order to
Figure BDA0003603905860000215
For the optimal solution of the subproblem (P4.1), the uplink throughput of all legal devices is obtained according to the suboptimal solution
Figure BDA0003603905860000216
Then to the uplink throughput
Figure BDA0003603905860000217
A non-zero subset K of
Figure BDA0003603905860000218
At this time can be
Figure BDA0003603905860000219
At the same time, when the uplink throughput is too low, the corresponding schedule should also be set to zero, since the communication is no longer meaningful at this time, i.e. it is not meaningful to do so
Figure BDA00036039058600002110
In summary, an optimal solution to the scheduling policy sub-problem (P4) can be obtained
Figure BDA00036039058600002111
In summary, P1 is the original optimization problem, i.e., the optimization problem to be solved initially. However, since P1 is a non-convex optimization problem and cannot be solved, P1 is decomposed into three sub-problems of P2, P3 and P4, which are solved alternately. Then the decomposed subproblem P2 is still a non-convex optimization problem, so that the subproblem is still not solved directly, and then P2 is equivalent to P2.1 by adopting a mathematical technique; finally, P2.1 is a convex optimization problem which can be solved. The sub-problem P3 is a convex optimization problem and can therefore be solved directly. The sub-problem P4 is a non-convex optimization problem, as is P2, and is solved for P4.1 using a mathematical method.
P1: the original optimization problem, the non-convex optimization problem;
p2: a sub-optimization problem of P1, a non-convex optimization problem;
p2.1: the equivalent of P2, convex optimization problem;
p3: the sub-optimization problem of P1, the convex optimization problem;
p4: a sub-optimization problem of P1, a non-convex optimization problem;
p4.1: equivalent of P4, convex optimization problem.
And S7, alternately optimizing the three sub-problems by a design algorithm to obtain the optimal solution of the optimization problem. The detailed algorithm is shown in fig. 3. For the algorithm provided in fig. 3, the following is stated:
the method comprises the following steps: firstly, solving a subproblem P (3) to obtain the emission power of the unmanned aerial vehicle and the emission power of legal equipment after one iteration of the algorithm;
step two: then, introducing newly obtained unmanned aerial vehicle transmitting power and legal equipment transmitting power into a subproblem P (2.1) to update the flight trajectory of the unmanned aerial vehicle;
step three: finally, solving a sub-problem P (4.1) of latest unmanned aerial vehicle transmitting power, legal equipment transmitting power and unmanned aerial vehicle flight trajectory to obtain a latest legal equipment scheduling strategy;
step four: if the result of the solution result is not converged or the precision does not meet the requirement, turning to the first step; otherwise, the final result is obtained.
The optimal unmanned aerial vehicle track can be obtained after the algorithm is implemented
Figure BDA0003603905860000221
Transmitted power
Figure BDA0003603905860000222
Legal device scheduling policy
Figure BDA0003603905860000223
Legal device transmit power
Figure BDA0003603905860000224
And optimal uplink aggregate throughput
Figure BDA0003603905860000225
It will be appreciated by those of ordinary skill in the art that the embodiments described herein are intended to assist the reader in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited embodiments and examples. Those skilled in the art can make various other specific changes and combinations based on the teachings of the present invention without departing from the spirit of the invention, and these changes and combinations are within the scope of the invention.

Claims (9)

1. A resource allocation optimization method of a wireless power supply covert communication system comprises the following steps:
s1: establishing a system model of an unmanned aerial vehicle, legal equipment and a listener, wherein the unmanned aerial vehicle and the legal equipment have a scheduling strategy;
s2, obtaining signal models of legal equipment and the unmanned aerial vehicle according to the system model, and designing and determining an energy model of the legal equipment;
s3, analyzing the binary hypothesis of the listeners, and obtaining the total error interception probability of the listeners on the premise of determining the positions of the listeners;
s4, introducing the position uncertainty of the listener in the actual scene to obtain the total error interception probability combined with the position uncertainty;
s5, defining an optimization target as uplink throughput of all legal equipment within one-time unmanned aerial vehicle task time, and obtaining an optimization problem under the conditions of satisfying covert communication, unmanned aerial vehicle self-restriction, legal equipment energy restriction and scheduling;
s6, decomposing the optimization problem into a plurality of sub-problems, and converting each sub-problem into a convex sub-problem by using continuous convex approximation;
s7, alternately optimizing the sub-problems by a design algorithm to obtain the optimal solution of the optimization problem.
2. The method of claim 1, wherein the method comprises: in step S1, the establishing of the system model includes the following steps:
s11: the set system model comprises an unmanned aerial vehicle, a plurality of legal devices and a plurality of listeners; determining the number and the positions of legal equipment and listeners;
wherein the legal device is located at
Figure FDA0003603905850000011
Where b represents a legitimate device, k represents the kth legitimate device, xb，kAnd yb，kRespectively representing the information of the horizontal and vertical coordinate positions of the kth legal device on the ground;
location of listener HWs is shown as
Figure FDA0003603905850000012
Where w represents a listener, m represents an mth listener, xw，mAnd yw，mRespectively representing the horizontal and vertical coordinate position information of the mth listener on the ground;
the flying height of the unmanned aerial vehicle is H, one task time is T, and the maximum flying speed is VmaxUnmanned plane in a time slot deltatHas a maximum flight distance of L ═ VmaxδtThe trajectory of the drone is represented as
Figure FDA0003603905850000021
Where a denotes a drone, n denotes the nth slot, qaRepresenting a trajectory of an Unmanned Aerial Vehicle (UAV);
s12: in the nth time slot, a is used for the kth legal devicek[n]The scheduling policy parameter is expressed, the scheduling policy is proposed for legal devices, the scheduling policy indicates that only one legal device is allowed to communicate with the unmanned aerial vehicle in one time slot, and for the kth legal device, ak[n]1 indicates that the device will communicate with the drone at the nth slot, ak[n]0 means that the device will not communicate with the drone and there is a slot per slot
Figure FDA0003603905850000022
S13: setting the maximum transmitting power and the average transmitting power of the unmanned aerial vehicle;
Figure FDA0003603905850000023
Figure FDA0003603905850000024
wherein P isa[n]Which represents the transmitted power of the drone,
Figure FDA0003603905850000025
for mean transmitted power of drone, PmaxThe maximum transmitting power of the unmanned aerial vehicle.
3. The method of claim 1, wherein the method comprises: in step S2, the method includes the steps of:
s21, obtaining the received signal r of the kth legal device in the nth time slot by the distance between the unmanned aerial vehicle autonomous control and the legal device and combining the scheduling strategy of the legal deviceb，k[n]Comprises the following steps:
Figure FDA0003603905850000026
wherein P isa[n]Which represents the transmitted power of the drone,
Figure FDA0003603905850000027
noise representing the kth legal device LDs; sa[n]A transmission signal representative of the drone; and omegaab，k[n]Representing the channel gain from the drone to the kth legitimate device, further expressed as:
Figure FDA0003603905850000028
in the formula, omega0Presentation GinsengConsidering the channel gain parameter, q, at a distance of 1mb，kIndicating the location of the kth legal device, qa[n]The trajectory of the unmanned aerial vehicle in the nth time slot is represented, and H represents the flight height of the unmanned aerial vehicle;
s22, obtaining the receiving energy of each legal device of each time slot;
wherein, the received energy P of the kth legal device in each time sloth，k[n]Comprises the following steps:
Ph，k[n]＝ηPa[n]Ωab，k[n]
wherein P isa[n]Representing the transmitting power of the unmanned aerial vehicle, eta is the energy harvesting coefficient, omegaab，k[n]Representing the channel gain of the drone to the kth legitimate device;
s23, obtaining a receiving signal of each time slot unmanned aerial vehicle;
wherein, the received signal r of the unmanned aerial vehicle is derived by a legal equipment scheduling strategya[n]Comprises the following steps:
Figure FDA0003603905850000031
Pb，k[n]representing the transmission power of the kth legal device LDs;
Figure FDA0003603905850000032
representing the received noise of the unmanned aerial vehicle UAV; sb，k[n]N (0, 1) represents the modulated signal emitted by the kth legal device LDs, omegaab，k[n]Representing the channel gain, a, of the unmanned aerial vehicle UAV to the kth legal device LDsk[n]1 indicates that the device will communicate with the unmanned aerial vehicle UAV at the nth slot, ak[n]0 means that the device will not communicate with the unmanned aerial vehicle UAV and there is a slot per slot
Figure FDA0003603905850000033
S24, obtaining the total uplink throughput rate of all legal devices;
total uplink throughput received by the drone end in the nth time slotRate Rb，k[n]Comprises the following steps:
Figure FDA0003603905850000034
wherein
Figure FDA0003603905850000035
i denotes the temporary variable of the sum count, σaParametric information representing the unmanned aerial vehicle UAV receiving noise;
s25, designing and determining an energy model of legal equipment;
for all legitimate devices, it is necessary to follow the causality of energy, i.e. the energy consumed by this slot cannot be greater than the sum of the energy harvested by this slot and the remaining energy of the previous slot, the expression is written as:
Figure FDA0003603905850000036
wherein Qb，k[n]Representing the total energy, Q, of the kth legal device LD in n time slots0Represents the initial energy; i is a temporary variable for the sum count; eta is an energy harvesting coefficient; a isk[n]1 indicates that the device will communicate with the unmanned aerial vehicle UAV at the nth slot, ak[n]0 means that the device will not communicate with the unmanned aerial vehicle UAV and there is a slot per slot
Figure FDA0003603905850000041
4. The method of claim 1, wherein the method comprises: step S3 specifically includes the following steps:
s31, obtaining a binary hypothesis model of each listener in each time slot;
setting the listener HWs to use the joint listening strategy to obtain the binary hypothesis expression of the mth listener in the nth time slot:
Figure FDA0003603905850000042
Figure FDA0003603905850000043
wherein
Figure FDA0003603905850000044
Representing the reception noise of the mth listener; h0，kRepresenting the original hypothesis: the intercepted kth legal device is considered not to transmit information; h1，kRepresent alternative assumptions: the intercepted legitimate device is considered to have transmitted information; j represents a temporary variable of the sum count; r is a radical of hydrogenw，mRepresenting the received signal of the mth listener; sb，j[n]N (0, 1) represents the modulation signal transmitted by the jth legal device LD; a isj[n]Indicating a state in which the jth legal device LD will communicate with the unmanned aerial vehicle UAV at the nth time slot; p isb，j[n]Representing the transmission power of the jth legal device; omegaaw，m[n]Represents the channel gain of the unmanned aerial vehicle UAV to the mth listener HWs; omegawb，j[n]Representing the channel gain from the mth listener to the jth legitimate device;
the judgment criteria of the listeners are as follows:
Figure FDA0003603905850000045
wherein P isw，m，k[n]Represents the average value of the power of the ambient signal obtained after l times of measurement by listener HWs;
Figure FDA0003603905850000046
represents the power value of the ambient signal obtained after the listener HWs measures 1 time; pth，m，k[n]Representing a decision threshold value; d0And D1Is expressed as corresponding to H0，kAnd H1，kIs determined byThe result is;
s32, obtaining the missing detection probability and the false detection probability of each listener in each time slot;
where the probability ξ of false detection of the mth listener HWsF，m，k[n]And probability xi of missed detectionM，m，k[n]Expressed as:
Figure FDA0003603905850000051
Figure FDA0003603905850000052
pr represents the mathematically solved probability;
Figure FDA0003603905850000053
parameter, P, corresponding to received noise representing m-th listenera[n]Represents the transmitted power of the drone, Ω0Representing a channel gain parameter with a reference distance of 1m, qb，kIndicating the location of the kth legal device, qa[n]Just indicate the trajectory of the drone at the nth time slot, H indicates the altitude of the drone, qw，mIndicating the listener position;
s33, obtaining the total error interception probability of each listener in each time slot;
at the angle of the listener HWs, they only know the transmission power Pa[n]Is from 0 to PmaxSet a range value for the listener Pa[n]Subject to a uniform distribution, its probability density function PDF is written as:
Figure FDA0003603905850000054
the false detection probability is derived as:
Figure FDA0003603905850000055
Figure FDA0003603905850000056
similarly, the probability of missed detection is deduced as:
Figure FDA0003603905850000057
wherein
Figure FDA0003603905850000058
In conclusion, the total interception error probability ξ can be further obtainedm，k[n]Comprises the following steps:
Figure FDA0003603905850000061
in the scenario of the invention P3≤P2Always true, total false positive probability ξm，k[n]In [ P ]1，P3]Interval about Pth，m，kIs monotonically decreasing; in the interval [ P2，P4]Total false interception probability ξm，k[n]Is related to a monotonic increase so that the minimum error probability is in the interval [ P ]3，P2]Obtaining; so minimum false intercept probability
Figure FDA0003603905850000062
Comprises the following steps:
Figure FDA0003603905850000063
Figure FDA0003603905850000064
is also an exact position (x) with listener HWsw，m，yw，m) A function of the correlation.
5. The method of claim 4, wherein the method comprises: in the step S4, in the step S,
minimum average error probability after adding listener HWs location uncertainty
Figure FDA0003603905850000065
Write as:
Figure FDA0003603905850000066
xw，mand yw，mRespectively representing the horizontal and vertical coordinate position information of the mth listener on the ground, and the above formula is approximate:
Figure FDA0003603905850000067
wherein
Figure FDA0003603905850000068
Figure FDA0003603905850000069
xb，kAnd yb，kRespectively representing the horizontal and vertical coordinate position information of the kth legal device on the ground, wherein X and Y represent uncertain variables;
obtaining the optimal minimum average false interception probability of the added position uncertainty
Figure FDA00036039058500000610
Comprises the following steps:
Figure FDA0003603905850000071
order to
Figure FDA0003603905850000072
Then the constraint of covert communication is obtained, where pwFor a given covert communication restriction parameter.
6. The method of claim 4, wherein the method comprises: step S5 specifically includes the following steps:
defining an optimization target as uplink throughput of all legal equipment within the task time of the unmanned aerial vehicle, obtaining an optimization problem under the conditions of meeting communication of hidden conditions, self limitation of the unmanned aerial vehicle, energy limitation and scheduling of the legal equipment, and enabling the unmanned aerial vehicle to work
Figure FDA0003603905850000073
The optimization problem is derived as:
Figure FDA0003603905850000074
Figure FDA0003603905850000075
Figure FDA0003603905850000076
Figure FDA0003603905850000077
Figure FDA0003603905850000078
Figure FDA0003603905850000079
Figure FDA00036039058500000710
wherein the optimization problem P1 aims to maximize the total upstream throughput; a is a scheduling strategy constraint, b is a covert communication constraint, c is an unmanned aerial vehicle flight speed constraint, d is an unmanned aerial vehicle maximum transmitting power constraint, e is an unmanned aerial vehicle average transmitting power constraint, and f is a legal equipment energy causality constraint.
7. The resource allocation optimization method for the wireless power supply covert communication system according to claim 6, wherein: step S6 decomposes the optimization problem P1 into three sub-problems of P2, P3, and P4, and solves the sub-problems alternately, specifically includes the following steps:
s61, fixing the transmitting power of the unmanned aerial vehicle, the transmitting power of all legal equipment and scheduling parameters to obtain an unmanned aerial vehicle trajectory optimization subproblem P2;
s62, converting the unmanned aerial vehicle trajectory sub-problem P2 into a convex problem P2.1 by using continuous convex approximation;
s63, fixing the unmanned aerial vehicle track and the scheduling parameters of legal equipment to obtain a power optimization subproblem P3;
s64, fixing the track of the unmanned aerial vehicle, the transmission power of the unmanned aerial vehicle and the transmission power of legal equipment to obtain a legal equipment scheduling optimization subproblem P4;
s65, relaxing the constraint conditions of the scheduling strategy, converting the legal equipment scheduling optimization sub-problem P4 into a convex problem P4.1, and obtaining the optimal solution of the sub-problem P4 through a shaping algorithm.
8. The method of claim 7, wherein the method comprises: in step S65, moldingThe forming method comprises the following steps: order to
Figure FDA0003603905850000081
Obtaining uplink throughput of all legal devices according to the sub-optimal solution for optimizing the optimal solution of the problem
Figure FDA0003603905850000082
Then to the uplink throughput
Figure FDA0003603905850000083
A non-zero subset K of
Figure FDA0003603905850000084
At this moment will
Figure FDA0003603905850000085
At the same time, when the uplink throughput is too low, the corresponding schedule should also be set to zero, since the communication is no longer meaningful at this time, i.e. it is not meaningful to do so
Figure FDA0003603905850000086
To sum up, an optimal solution of the scheduling policy sub-problem (P4) is obtained
Figure FDA0003603905850000087
9. The method of claim 7, wherein the method comprises: in step S7, an optimal unmanned aerial vehicle track is obtained after an algorithm is implemented
Figure FDA0003603905850000088
Transmitting power
Figure FDA0003603905850000089
Legal device scheduling policy
Figure FDA00036039058500000810
Legal device transmit power
Figure FDA00036039058500000811
And optimal uplink aggregate throughput
Figure FDA00036039058500000812
The process of the algorithm is as follows:
s11: firstly, solving a subproblem P3 to obtain the emission power of the unmanned aerial vehicle and the emission power of legal equipment after one iteration of the algorithm;
s12: then bringing the newly obtained unmanned plane transmitting power and legal equipment transmitting power into a subproblem P2.1 to update the flight trajectory of the unmanned plane;
s13: finally, solving a sub-problem P4.1 of latest unmanned aerial vehicle transmitting power, legal equipment transmitting power and unmanned aerial vehicle flight trajectory to obtain a latest legal equipment scheduling strategy;
s14: if the result of the solution result is not converged or the precision is not satisfactory, go to step S11;
otherwise, obtaining a final result;
the optimal unmanned aerial vehicle track can be obtained after the algorithm is implemented
Figure FDA0003603905850000091
Transmitting power
Figure FDA0003603905850000092
Legal device scheduling policy
Figure FDA0003603905850000093
Legal device transmit power
Figure FDA0003603905850000094
And optimal uplink aggregate throughput
Figure FDA0003603905850000095
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