CN114698123B - 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 PDFInfo
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- CN114698123B CN114698123B CN202210410331.7A CN202210410331A CN114698123B CN 114698123 B CN114698123 B CN 114698123B CN 202210410331 A CN202210410331 A CN 202210410331A CN 114698123 B CN114698123 B CN 114698123B
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W72/00—Local resource management
- H04W72/04—Wireless resource allocation
- H04W72/044—Wireless resource allocation based on the type of the allocated resource
- H04W72/0473—Wireless resource allocation based on the type of the allocated resource the resource being transmission power
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04B—TRANSMISSION
- H04B7/00—Radio transmission systems, i.e. using radiation field
- H04B7/14—Relay systems
- H04B7/15—Active relay systems
- H04B7/185—Space-based or airborne stations; Stations for satellite systems
- H04B7/18502—Airborne stations
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- 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
- H04K3/822—Jamming or countermeasure characterized by its function related to preventing surveillance, interception or detection by detecting the presence of a surveillance, interception or detection
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
- H04W12/80—Arrangements enabling lawful interception [LI]
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W72/00—Local resource management
- H04W72/04—Wireless resource allocation
- H04W72/044—Wireless resource allocation based on the type of the allocated resource
- H04W72/0446—Resources in time domain, e.g. slots or frames
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- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T10/00—Road transport of goods or passengers
- Y02T10/10—Internal combustion engine [ICE] based vehicles
- Y02T10/40—Engine management systems
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 ensures that the listener is difficult to find the communication between the legal receiving equipment and the unmanned aerial vehicle.
Description
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, conventional fixed base stations are no longer suitable for 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 trend of recent research topics. 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 usually considered that an eavesdropper cannot accurately analyze correct contents after stealing signals; 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, much attention has been paid to research related to covert communication.
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 source of the energy collection technology not only includes 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 can convert the received surrounding wireless signals into electric energy, such as artificially acquired Radio Frequency (RF) signals. Energy harvesting based on RF signals is a research focus because it can be protected from the weather environment 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 sum, the current research of combining the UAV with WPT and WIT does not consider the communication security problem, 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 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 interfering signal for 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 in the combination of the existing UAV wireless communication system and the WPT technology, and adopts the following technical scheme:
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, solving 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-limitation, legal equipment energy limitation 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;
and S7, designing an algorithm to alternately optimize the plurality of sub-problems so as to obtain the optimal solution of the optimization problem.
Further, in step S1, establishing a 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
Where b represents a legal device, k represents the kth legal device, x b，k And y b，k Respectively representing the information of the horizontal and vertical coordinate positions of the kth legal device on the ground;
listener HWs position is indicated as
Where w represents a listener, m represents an mth listener, x w，m And y w，m Respectively representing the horizontal and vertical coordinate position information of the mth listener on the ground;
the flying height of the unmanned plane is H, one task time is T, and the maximum flying speed is V max Unmanned plane in a time slot delta t Has a maximum flight distance of L = V max δ t The trajectory of the drone is represented as
Where a denotes a drone, n denotes the nth slot, q a Representing the trajectory of an unmanned aerial vehicle UAV;
s12: in the nth time slot, using alpha for the k legal device k [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, a k [n]=1 means the device will communicate with drone in nth slot, a k [n]=0 indicates that the device will not communicate with drone and there is one slot per slot
S13: setting the maximum transmitting power and the average transmitting power of the unmanned aerial vehicle;
wherein P is a [n]Indicating unmanned aerial vehicle transmit powerP is the average transmitted power of the unmanned plane, P max The maximum transmitting power of the unmanned aerial vehicle.
Further, step S2 includes the following steps:
s21, obtaining a receiving 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 a scheduling strategy of the legal device b，k [n]Comprises the following steps:
wherein P is a [n]Representing the transmitted power of the drone, z b，k [n]Noise representing the kth legal device LDs; s a [n]A transmission signal representative of the drone; and omega ab，k [n]Representing the channel gain from the drone to the kth legitimate device, further expressed as:
in the formula, Ω 0 Representing a channel gain parameter with a reference distance of 1m, q b，k Denotes the location of the kth legal device, q a[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 slot h，k [n]Comprises the following steps:
P h，k [n]＝ηP a [n]Ω ab，k [n]
wherein P is a [n]Representing the transmitting power of the unmanned aerial vehicle, eta is the energy harvesting coefficient, omega ab，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 strategy a [n]Comprises the following steps:
P b，k [n]representing the transmission power of the kth legal device LDs; z is a radical of a [n]Representing the received noise of the unmanned aerial vehicle UAV; s b，k [n]Representing the modulated signal, Ω, emitted by the kth legal device LDs ab，k [n]Representing the channel gain, a, of the unmanned aerial vehicle UAV to the kth legal device LDs k [n]=1 denotes that the device will communicate with the unmanned aerial vehicle UAV at nth slot, a k [n]=0 indicates that the device will not communicate with the unmanned aerial vehicle UAV and there is one slot per slot
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 end b，k [n]Comprises the following steps:
wherein
i denotes the temporary variable of the sum count, σ a Parametric 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:
wherein Q b，k [n]Denotes the kth sumTotal energy, Q, of the LD in n time slots 0 Represents the initial energy; i is a temporary variable for the sum count; eta is an energy harvesting coefficient; a is k [n]=1 denotes that the device will communicate with the unmanned aerial vehicle UAV at nth slot, a k [n]=0 indicates that the device will not communicate with the unmanned aerial vehicle UAV and there is one slot per slot
Further, step S3 specifically includes the following steps:
s31, obtaining a binary hypothesis model of each listener in each time slot;
setting the listeners HWs to use the joint listening strategy to obtain the binary hypothesis expression of the mth listener in the nth time slot:
wherein
Representing the reception noise of the mth listener; h 0，k Representing the original hypothesis: the intercepted kth legal device is considered to have no transmission information; h 1，k Represent alternative assumptions: the intercepted legitimate device is considered to have transmitted information; j represents a temporary variable of the sum count; r is w，m Representing the received signal of the mth listener; s b，j [n]N (0,1) represents the modulation signal transmitted by the jth legal device LD; a is j [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 b，j [n]Representing the transmission power of the jth legal device; omega aw，m [n]Represents the channel gain of the unmanned aerial vehicle UAV to the mth listener HWs; omega wb，j [n]Representing the channel gain from the mth listener to the jth legitimate device;
the judgment criteria of the listeners are as follows:
wherein P is w，m，k [n]Representing the average value of the power of the ambient signal obtained after the listener HWs measures for l times;
representing the power value of the ambient signal obtained after the listener HWs measures 1 time; p is th，m，k [n]Representing a decision threshold value; d 0 And D 1 Is expressed as corresponding to H 0，k And H 1，k The decision result of (1);
s32, obtaining the missed detection probability and the false detection probability of each listener in each time slot;
wherein the probability ξ of false detection of the mth listener HWs F，m，k [n]And probability xi of missed detection M，m，k [n]Expressed as:
pr represents the mathematically solved probability;
parameter, P, corresponding to received noise representing m-th listener a [n]Denotes the unmanned aerial vehicle transmit power, Ω 0 Denotes a channel gain parameter with a reference distance of 1m, q b，k Indicating the location of the kth legal device, q a[n] Just indicate the trajectory of the drone at the nth time slot, H indicates the altitude of the drone, q w，m Indicating the listener position;
s33, obtaining the total error interception probability of each listener in each time slot;
at angle HWs, listeners know only the transmit power P a [n]Is from 0 to P max Set the range value of (A) to the listener P a [n]Subject to a uniform distribution, its probability density function PDF is written as:
the false detection probability is derived as:
similarly, the probability of missed detection is deduced as:
wherein
In conclusion, the total interception error probability xi can be further obtained m，k [n]Comprises the following steps:
in the scenario of the invention P 3 ≤P 2 Always true, total false intercept probability ξ m，k [n]In [ P ] 1 ，P 3 ]Interval about P th，m，k Is monotonically decreasing; in the interval [ P 2 ，P 4 ]Total false interception probability ξ m，k [n]Is related to a monotonic increase so that the minimum error probability is in the interval [ P ] 3 ，P 2 ]Obtaining; so minimum false intercept probability
Comprises the following steps:
Further, in step S4,
minimum average error probability after adding listener HWs position uncertainty
Write as:
x w，m and y w，m Respectively representing the horizontal and vertical coordinate position information of the mth listener on the ground, and the above formula is approximate:
wherein
x b，k And y b，k Respectively 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
Comprises the following steps:
order to
Then the constraint of covert communication is obtained, where p w Given 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
wherein the optimization problem P1 aims at maximizing the total throughput of the uplink; 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 P2, P3, and P4 for alternative solution, 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 track optimization subproblem P2;
s62, converting the unmanned aerial vehicle track subproblem P2 into a convex problem P2.1 by using continuous convex approximation;
s63, fixing the track of the unmanned aerial vehicle and 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 sub-problem P4;
s65, relaxing the constraint conditions of the scheduling strategy, converting the legal device 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
In order to optimize the optimal solution of the problem, the uplink throughput of all legal devices is obtained according to the suboptimal solution>
Then on upstream throughput>
A non-zero subset K, having>
Will now be>
At the same time, when the upstream 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. </or>
In conclusion, an optimal solution is found for the scheduling policy sub-problem (P4)>
Further, in step S7, the optimal unmanned aerial vehicle is obtained after the algorithm is implementedTrack of
Transmitting power->
Legal device scheduling policy>
Legal device transmitting power->
And an optimal uplink total throughput->
The process of the algorithm is as follows:
s11: firstly, solving a subproblem P3 to obtain the unmanned aerial vehicle transmitting power and the legal equipment transmitting power after one algorithm iteration;
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 path to obtain a latest legal equipment scheduling strategy;
s14: if the solving result is not converged or the precision is not in accordance with the requirement, the step S11 is carried out; otherwise, obtaining a final result;
the optimal unmanned aerial vehicle track can be obtained after the algorithm is implemented
Transmitting power>
Legal device scheduling policy
Legal equipmentShoot power>
And an optimal uplink total throughput->
The resource allocation optimization method of the wireless power supply covert communication system is characterized in that a novel method is designed for the energy supply of legal equipment by introducing covert communication: 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, the system is assumed to have an 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 equipped 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) Interference listener HW s Is detectedAnd (6) listening.
In three-dimensional coordinates, the locations of the legal devices LDs are
Where b represents legal devices LDs, k represents kth legal device LDs, x b，k And y b，k Respectively representing the information of the horizontal and vertical coordinate position of the kth legal device on the ground.
Similarly, listener HWs position may be represented as
Where w represents listener HWs and m represents mth listener HWs, x w，m And y w，m Respectively represent the horizontal and vertical coordinate position information of the mth listener on the ground. Since the location of listener HWs is often not accurately known in a practical scenario, the location of listener HWs can be further expressed as:
wherein
Representing the positional uncertainty of listener HWs, all obeys
And->
Indicating the estimated listener HWs position, ε w Representing 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 V max . Meanwhile, the flight cycle is divided into N time slots, so that the length of each time slot has
When delta t Is enoughIn hours, 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 = V max δ t . Thus, the trajectory of the unmanned aerial vehicle UAV may be expressed as ÷>
Where a denotes an unmanned aerial vehicle UAV. n denotes an nth time slot, q a Representing the trajectory of the unmanned aerial vehicle UAV.
In summary, q is position information, and position information of which device is identified from the lower right corner. Thus, a denotes an unmanned aerial vehicle UAV, then q a Just show the trajectory of the unmanned aerial vehicle UAV, and q above b，k And q is w，m And the corresponding steps are carried out.
S12, in the nth time slot, using alpha for the kth legal equipment LDs k [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 kth legal device LDs, a k [n]=1 denotes that the device will communicate with the unmanned aerial vehicle UAV at nth slot, a k [n]=0 means that the device will not communicate with the drone UAV and there is a slot per time slot
S13, according to the model of S11, the flight track of the unmanned aerial vehicle UAV is as follows: | q a [n]-q a [n-1]|| 2 ≤L 2 (ii) a L represents the maximum flight distance of the unmanned aerial vehicle UAV in one time slot.
The transmit power to the unmanned aerial vehicle UAV is:
wherein P is a [n]Representing the unmanned aerial vehicle UAV transmit power, P being the unmanned aerial vehicle UAV average transmit power, P max For unmanned aerial vehicle UAV maximumThe transmit power.
And S2, solving a signal model of legal equipment and the signal model of 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 unmanned aerial vehicle communication system, as the unmanned aerial vehicle UAV can autonomously control the distance between the UAV and the legal device LDs, the UAV can be regarded as line-of-sight transmission, and 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 LDs b，k [n]Comprises the following steps:
wherein P is a [n]Representing the unmanned aerial vehicle UAV transmit power,
noise representing the kth legal device LDs; s a [n]A transmission signal representative of an Unmanned Aerial Vehicle (UAV); and omega ab，k [n]The channel gain representing the unmanned aerial vehicle UAV to the kth legal device LDs may be expressed as:
in the formula, omega 0 Denotes a channel gain parameter with a reference distance of 1m, q b，k Denotes the location of the kth legal device, q a[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 of each time slot h，k [n]Comprises the following steps:
P h，k [n]＝ηP a [n]Ω ab，k [n]
wherein P is a [n]Representing the UAV launch power, η is the energy harvesting coefficient, Ω ab，k [n]Representing the channel gain of the unmanned aerial vehicle UAV to the kth legal device LDs.
S23, deducing a received signal r of the UAV (unmanned aerial vehicle) through a legal device LDs (laser direct structuring) scheduling strategy a [n]Comprises the following steps:
wherein P is b，k [n]The transmission power representing the kth legal device LDs; z is a radical of formula a [n]Representing the received noise of the unmanned aerial vehicle UAV; s b，k [n]Representing the modulated signal, Ω, emitted by the kth legal device LDs ab，k [n]Representing the channel gain, a, of the unmanned aerial vehicle UAV to the kth legal device LDs k [n]=1 denotes that the device will communicate with the unmanned aerial vehicle UAV at nth slot, a k [n]=0 indicates that the device will not communicate with the unmanned aerial vehicle UAV and there is one slot per slot
S24, further in the nth time slot, the total uplink throughput rate R received by the UAV end b，k [n]Comprises the following steps:
wherein
i denotes a temporary variable of the sum count. Sigma a Parametric information representing the unmanned aerial vehicle UAV received noise.
S25, for all legitimate devices LDs, it must follow the 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:
wherein Q b，k [n]Indicating that the k-th legal device LD is in n time slotsTotal energy of time, Q 0 Representing 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
When delta t Sufficiently small, the position of the unmanned aerial vehicle UAV may be considered to be nearly constant within this time slot. a is a k [n]=1 means the device will communicate with unmanned aerial vehicle UAV at nth slot, a k [n]＝ 0 Means that the device is not communicating with the unmanned aerial vehicle UAV and has ^ er at each time slot>
S3, analyzing the binary hypothesis of the listener HWs, and obtaining the total error listening probability of the listener HWs on the premise of determining the position of the listener HWs.
The method specifically comprises the following steps:
s31, in order to enable the listener HWs not to accurately judge whether the legal device LDs are communicating, the listener HWs needs to stand to analyze binary hypothesis, and the minimum total listening error probability is obtained. Assume that listener HWs uses a joint listening strategy. Therefore, a binary hypothetical representation of the mth listener in the nth slot can be obtained:
wherein
Representing the reception noise of the mth listener. H 0，k Representing the original hypothesis: it is assumed that the intercepted kth legal device does not transmit information, H 0，k It is the original assumption as explained above, howeverFollowed by a colon, indicating that the expression of the latter is H as a whole 0，k . In the same way, H 1，x Represent alternative assumptions: the intercepted legitimate device is considered to have transmitted information. j represents a temporary variable of the sum count to avoid collision with k. r is w，m Representing the received signal of the mth listener.
Hereinbefore, s b，k [n]N (0,1) represents the modulated signal emitted by the kth legal device LDs, corresponding to s b，j [n]N (0,1) represents the modulation signal emitted by the jth legal device LDs, and only the expression mode is changed, so that
Represents the sum of signals of all legitimate devices LDs except j ≠ k, and ≠ k>
Representing the sum of the signals of all legitimate devices LDs containing k.
Hereinbefore, a k [n]=1 denotes that the device will communicate with the unmanned aerial vehicle UAV at nth slot, a k [n]=0 indicates that the device will not communicate with the unmanned aerial vehicle UAV and there is one slot per slot
Corresponding to a j [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, P b，k [n]Representing the transmission power of the kth legal device LDs, correspondingly, P b，j [n]Still representing the transmit power of the jth legitimate device.
Above, Ω ab，k [n]Indicating unmanned aerial vehicle UAV to kth legal device LD s Channel gain of, correspondingly, omega aw，m [n]Representing the channel gain of the unmanned aerial vehicle UAV to the mth listener HWs.
Ω wb，j [n]Representing the channel gain of the (mth) listener to the jth legitimate device.
The judgment criteria of the listeners are:
wherein P is w，m，k [n]Representing the average value of the power of the ambient signal obtained after the listener HWs measures for l times;
representing the power value of the ambient signal obtained after the listener HWs measures 1 time; p is th，m，k [n]Representing a decision threshold value; d 0 And D 1 Is expressed as corresponding to H 0，k And H 1，k The decision result of (1).
S32, further m listener HWs error detection probability xi F，m，k [n]And probability xi of missed detection M，m，k [n]Can be expressed as:
pr represents mathematically solving the probability.
Parameter, P, corresponding to received noise representing m-th listener a [n]Represents the unmanned aerial vehicle UAV transmitted power, omega 0 Denotes a channel gain parameter with a reference distance of 1m, q b，k Denotes the location of the kth legal device, q a[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, q w，m Indicating the location of listener HWs.
S33, in actual scene, all listeners HW s The transmitted power P of the UAV cannot be accurately known a [n]Therefore, a blind condition derivation can be made for listener HWs, and listener HWs only knows the transmit power P a [n]Is from 0 to P max (maximum transmit power) range values, so it can be reasonably assumed that the listener P is a listener a [n]Subject to a uniform distribution, its Probability Density Function (PDF) can be written as:
the false detection probability can be derived as:
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,
similarly, the probability of missed detection can be derived as:
wherein
In conclusion, the total interception error probability ξ can be further obtained m，k [n]Comprises the following steps:
in the scenario of the invention P 3 ≤P 2 This is always true. Easy to find, total false interception probability xi m，k [n]In [ P ] 1 ，P 3 ]Interval about P th，m，k Is monotonically decreasing; in the interval [ P 2 ，P 4 ]Total false interception probability ξ m，k [n]Is related to a monotonic increase, so the minimum error probability isInterval [ P ] 3 ，P 2 ]Obtaining; so minimum false interception probability
Comprises the following steps:
note that this is
Is also an exact position (x) relative to listener HWs w，m ，y w，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. Indeed, the unmanned aerial vehicle UAV cannot know the listener HW s At a precise location, therefore
Is also an exact position (x) relative to listener HWs w，m ，y w，m ) A function of the correlation. And is known from a preceding step->
So the minimum average probability of error is greater or less than the listener HWs position uncertainty added>
Can be written as:
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
The above equation can be approximated as:
wherein
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
Comprises the following steps:
order to
The constraint of covert communication can be obtained, where p w Given covert communication restriction parameters.
S5, proposing and solving the problem of resource allocation: defining an optimization target as uplink throughput of all legal equipment within one-time unmanned aerial vehicle task time, obtaining an optimization problem under the conditions of satisfying communication under hidden conditions, unmanned aerial vehicle self-limitation, legal equipment energy limitation and scheduling, and enabling the optimization problem to be carried out
wherein the optimization problem (P1) aims at maximizing the uplink total throughput; the method comprises the following steps of (a) restricting a scheduling strategy, (b) restricting covert communication, (c) restricting the flight speed of the unmanned aerial vehicle, (d) restricting the maximum transmitting power of the unmanned aerial vehicle, (e) restricting the average transmitting power of the unmanned aerial vehicle, and (f) restricting the causality of energy of legal equipment.
S6, the optimization problem is disassembled into three sub-problems, and each sub-problem is converted into a convex sub-problem through continuous convex approximation.
The method specifically comprises the following steps:
s61, because (P1) is not convex, the optimization tool cannot be directly used for solving, and therefore the alternative optimization mode is considered to convert (P1) into a plurality of different convex sub-problems for solving. Fix { P ] first a ，P b And a } is constant, then (P1) can be converted to:
however, the objective function and covert communication constraints of the subproblem (P2) remain non-convex; but is easy to know
Is about | q a [n]-q b，k | 2 So that it makes->
Representing the result of the iteration after j of the optimization subproblem (P2), the objective function can be expressed as | q a [n]-q b，k | 2 Is integrated in
The dots become convex with a first order taylor expansion. Then the objective function becomes:
to convert constraints to convex, a relaxation variable needs to be introduced
q 1，k[n] ≥|q a [n]-q b，k | 2 and q 2，m [n]≥|q a [n]-q w，m | 2 ；
Then the optimization sub-problem (P2) may become (P2.1):
after the jth unmanned aerial vehicle track iteration result is obtained, the (j + 1) th result can be obtained and written as
In conclusion, the (P2) sub-problem transforms into the (P2.1) sub-problem that can be solved.
S62, fixing { q a And a), obtaining the power optimization subproblem (P3) of the UAV and the LDs of legal equipment, and writing as:
as can be seen, (P3) with respect to P b ，P a The convex problem is solved without further processing, so that the convex optimization tool can be directly used for solving.
S63, fixing { q a ，P a ，P b Get the optimized legal device scheduling subproblem (P4), written as:
however, the sub-problem (P4) is also a non-convex problem, considering relaxing the scheduling policy constraints, i.e. letting α be k [n]The values can be continuous, then (P4) canTo (P4.1):
at this time, the optimization sub-problem (P4.1) becomes convex, and the optimal solution a is solved k [n]Thereafter, the continuous values need to be reshaped into discrete values. The shaping method comprises the following steps: order to
For the optimal solution of the sub-problem (P4.1), the upstream throughputs ≥ of all legal apparatuses are obtained from the sub-optimal solution>
And then on the upstream throughput->
A non-zero subset k, having>
Can now be combined>
At the same time, when the upstream 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. </or>
In summary, an optimal solution for the scheduling policy sub-problem (P4) can be found>
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 sub-problem P2 is still a non-convex optimization problem, so that the direct solution is still unavailable, and then the 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-problems P4 and P2 are the same as the non-convex optimization problem, and the solving is equivalent to P4.1 by using a mathematical method.
P1: original optimization problem, non-convex optimization problem;
p2: a sub-optimization problem of P1, a non-convex optimization problem;
p2.1: the equivalence of P2, convex optimization problem;
p3: p1, sub-optimization problem, convex optimization problem;
p4: a sub-optimization problem of P1, a non-convex optimization problem;
p4.1: p4 equivalence, convex optimization problem.
And S7, designing an algorithm to alternately optimize the three sub-problems to obtain an 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 subproblem 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 solving result is not converged or the precision is not in accordance with 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
Transmitting power->
Legal device scheduling policy
Legal device transmitting power->
And an optimal uplink total throughput->
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 (6)
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;
the establishment of the system model comprises 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
Where b represents a legal device, k represents the kth legal device, x b,k And y b,k Respectively representing the information of the horizontal and vertical coordinate positions of the kth legal device on the ground;
listener HWs position is indicated as
Where w represents a listener, m represents an mth listener, x w,m And y w,m Are respectively provided withThe horizontal and vertical coordinate position information of the mth listener on the ground is represented;
the flying height of the unmanned plane is H, one task time is T, and the maximum flying speed is V max Unmanned plane in a time slot delta t Has a maximum flight distance of L = V max δ t The trajectory of the drone is represented as
Where a denotes the drone, n denotes the nth slot, q a Representing a trajectory of an Unmanned Aerial Vehicle (UAV);
s12: in the nth time slot, a is used for the kth legal device k [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, a k [n]=1 indicates that the device will communicate with drone in nth slot, a k [n]=0 indicates that the device will not communicate with drone and there is one slot per slot
S13: setting the maximum transmitting power and the average transmitting power of the unmanned aerial vehicle;
wherein P is a [n]Which represents the transmitted power of the drone,
for mean transmitted power of drone, P max The maximum transmitting power of the unmanned aerial vehicle;
s2, solving signal models of legal equipment and the unmanned aerial vehicle according to the system model, designing and determining an energy model of the legal equipment, and comprising the following steps:
s21, obtaining a receiving 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 a scheduling strategy of the legal device b，k [n]Comprises the following steps:
wherein P is a [n]Representing the transmitted power of the drone, z b，k [n]Noise representing the kth legal device LDs; s is a [n]A transmission signal representative of the drone; and omega ab，k [n]Representing the channel gain from the drone to the kth legitimate device, further expressed as:
in the formula, Ω 0 Denotes a channel gain parameter with a reference distance of 1m, q b,k Indicating the location of the kth legal device, q a[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 slot h，k [n]Comprises the following steps:
P h，k [n]＝ηP a [n]Ω ab，k [n]
wherein P is a [n]Representing the transmitting power of the unmanned aerial vehicle, eta is the energy harvesting coefficient, omega ab，k [n]Representing the channel gain from 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 strategy a [n]Comprises the following steps:
P b，k [n]representing the transmission power of the kth legal device LDs; z is a radical of a [n]Representing the received noise of the unmanned aerial vehicle UAV; s is b，k [n]Representing the modulated signal, Ω, emitted by the kth legal device LDs ab，k [n]Representing the channel gain from the unmanned aerial vehicle UAV to the kth legal device LDs, a k [n]=1 means the device will communicate with unmanned aerial vehicle UAV at nth slot, a k [n]=0 indicates that the device will not communicate with the unmanned aerial vehicle UAV and there is one slot per slot
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 end b，k [n]Comprises the following steps:
wherein
i denotes the temporary variable of the sum count, σ a Parametric information representing the unmanned aerial vehicle UAV received noise;
s25, designing and determining an energy model of legal equipment;
for all legal devices, it is necessary to follow the 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 is written as:
wherein Q b，k [n]Indicating the kth legal deviceTotal energy, Q, of LD in n time slots 0 Represents the initial energy; i is a temporary variable for the sum count; eta is an energy harvesting coefficient; a is a k [n]=1 denotes that the device will communicate with the unmanned aerial vehicle UAV at nth slot, a k [n]=0 indicates that the device will not communicate with the unmanned aerial vehicle UAV and there is one slot per slot
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 position uncertainty of the listeners in the actual scene to obtain 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-limitation, legal equipment energy limitation 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, designing an algorithm to alternately optimize a plurality of sub-problems to obtain an optimal solution of the optimization problem, and implementing the algorithm to obtain an optimal unmanned aerial vehicle track
Transmitting power->
Legal device scheduling policy>
Legal device transmitting power->
And an optimal uplink total throughput->
The process of the algorithm is as follows:
s71: firstly, solving a subproblem P3 to obtain the unmanned aerial vehicle transmitting power and the legal equipment transmitting power after one algorithm iteration;
s72: 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;
s73: 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;
s74: if the solving result is not converged or the precision is not qualified, the step S11 is carried out; otherwise, obtaining a final result;
the optimal unmanned aerial vehicle track can be obtained after the algorithm is implemented
Transmitting power>
Legal device scheduling policy
Legal device transmitting power->
And an optimal uplink total throughput->
2. The method of claim 1, wherein the method comprises: the step S3 specifically includes the following steps:
s31, obtaining a binary hypothesis model of each listener in each time slot;
setting the listeners HWs to use a joint listening strategy to obtain the binary hypothesis expression of the mth listener in the nth time slot:
wherein
Representing the reception noise of the mth listener; h 0，k Representing the original hypothesis: the intercepted kth legal device is considered not to transmit information; h 1，k Represent alternative assumptions: the intercepted legitimate device is considered to have transmitted information; j represents a temporary variable of the sum count; r is w,m Representing the received signal of the mth listener; s b,j [n]N (0,1) represents the modulation signal transmitted by the jth legal device LD; a is j [n]The j legal device LD is represented in a state that the j legal device LD can communicate with the unmanned aerial vehicle UAV in the nth time slot; p b，j [n]Representing the transmission power of the jth legal device; omega aw，m [n]Represents the channel gain of the unmanned aerial vehicle UAV to the mth listener HWs; omega wb，j [n]Representing the channel gain from the mth listener to the jth legitimate device;
the judgment criteria of the listeners are as follows:
wherein P is w，m，k [n]Representing the average value of the power of the ambient signal obtained after the listener HWs measures for l times;
represents the surroundings obtained after 1 measurement of the listener HWsA signal power value; p th，m，k [n]Representing a decision threshold value; d 0 And D 1 Is expressed as corresponding to H 0，k And H 1，k The decision result of (1);
s32, obtaining the missed detection probability and the false detection probability of each listener in each time slot;
wherein the probability ξ of false detection of the mth listener HWs F，m，k [n]Probability xi of missed detection M，m，k [n]Expressed as:
pr represents the mathematically solved probability;
parameter, P, corresponding to received noise representing m-th listener a [n]Denotes the unmanned aerial vehicle transmit power, Ω 0 Representing a channel gain parameter with a reference distance of 1m, q b,k Indicating the location of the kth legal device, q a[n] Just indicate the trajectory of the drone at the nth slot, H indicates the altitude of the drone, q w，m Indicating the listener position;
s33, obtaining the total error interception probability of each listener in each time slot;
at angle HWs of listener, the transmitted power P a [n]Is from 0 to P max Set the range value of (A) to the listener P a [n]Subject to a uniform distribution, its probability density function PDF is written as:
the false detection probability is derived as:
similarly, the probability of missed detection is deduced as:
wherein
In conclusion, the total interception error probability ξ can be further obtained m，k [n]Comprises the following steps:
P 3 ≤P 2 always true, total false positive probability ξ m，k [n]In [ P ] 1 ，P 3 ]Interval about P th，m，k Is monotonically decreasing; in the interval [ P 2 ，P 4 ]Total false interception probability ξ m，k [n]Is about a monotonous increase, so the minimum error probability is in the interval [ P ] 3 ，P 2 ]Obtaining; so minimum false intercept probability
Comprises the following steps:
3. The method of claim 2, wherein the method comprises: in the step S4, the process is carried out,
minimum average error probability after adding listener HWs position uncertainty
Write as:
x w,m and y w,m Respectively representing the horizontal and vertical coordinate position information of the mth listener on the ground, and the above formula is approximate:
wherein
x b,k And y b,k Respectively 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
Comprises the following steps:
order to
Then the constraint of covert communication is obtained, where p w Given covert communication restriction parameters.
4. The method of claim 2, wherein the method comprises: the 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
(P1)：
s.t.：
||q a [n]-q a [n-1]|| 2 ≤L 2 ，(c)
wherein the optimization problem P1 aims at maximizing the uplink total 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.
5. The method of claim 4, wherein the method comprises: step S6, decomposing the optimization problem P1 into three subproblems of P2, P3 and P4 for alternative solution, and specifically comprising 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 track optimization subproblem P2;
s62, converting the unmanned aerial vehicle track subproblem P2 into a convex problem P2.1 by using continuous convex approximation;
s63, fixing the track of the unmanned aerial vehicle 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 sub-problem P4;
s65, relaxing the constraint conditions of the scheduling strategy, converting the legal device 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.
6. The resource allocation optimization method for the wireless power supply covert communication system according to claim 5, wherein: in step S65, the shaping method includes: order to
For the optimal solution of the optimization problem, the uplink throughput of all legal devices is obtained according to the suboptimal solution>
And then on the upstream throughput->
A non-zero subset K of
Will now be>
At the same time, when the upstream 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. </or>
In conclusion, an optimal solution is found for the scheduling policy sub-problem (P4)>
/>
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