Unmanned aerial vehicle group security communication method based on cooperative beamforming

Abstract

The invention provides an unmanned aerial vehicle group secure communication method based on cooperative beamforming. The method comprises the following steps: constructing an unmanned aerial vehicle auxiliary communication system model, and calculating a system total secrecy rate, propulsion power consumption and unmanned aerial vehicle residual energy of the unmanned aerial vehicle auxiliary communication system model; taking maximization of the total secrecy rate of the system under the condition of unmanned aerial vehicle residual energy limitation as a target, and constructing an optimization problem of an optimal unmanned aerial vehicle group position and beam pointing; and sequentially solving the optimization problem of the optimal unmanned aerial vehicle group position and beam pointing by using an unmanned aerial vehicle group cooperative beam forming optimization algorithm to obtain an optimal arrangement scheme of the unmanned aerial vehicle group position and beam pointing. Optimization of overall performance and communication safety is achieved through a higher degree of freedom of the release system. For unmanned aerial vehicle equipment with limited energy, micro adjustment of the distribution position of each unmanned aerial vehicle in a cluster array is adopted to replace a phase adjustment element to realize beam directivity, so that the overall overhead of the system can be further reduced, and the overall service time is prolonged.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicles, and in particular to a secure communication method for a group of unmanned aerial vehicles based on collaborative beamforming. Background Art

[0002] Due to the flexibility, mobility and strong line-of-sight communication capabilities of drones, when used as relays to assist wireless communications, drones can change their positions in real time as needed, bringing a good line-of-sight communication environment and a more efficient data transmission rate. For situations such as mountainous areas and disaster areas with poor ground conditions or search and rescue, exploration, etc. that require temporary network access to areas without base station coverage, drone-assisted wireless communications can flexibly expand communication coverage and improve the quality of the communication system.

[0003] The wireless channels that drone communications rely on are open and can be easily eavesdropped on by illegal users. At the same time, the limited energy of drones also makes it impossible for them to use the complex security communication solutions commonly used by ground base stations. Research on secure communication technology that is suitable for the characteristics of drone communication networks is an important guarantee for achieving low-altitude communications and air-ground integration.

[0004] Beamforming is a technology that can effectively improve the performance of communication systems. By adjusting the amplitude and phase of antenna units in an antenna array of a certain size, a high-gain, high-directivity beam can be achieved in a specific direction. The UAV communication system has good line-of-sight (LoS) channel conditions. The introduction of beamforming technology can overcome path loss, suppress communication interference, and improve channel quality. At the same time, beamforming technology is also an effective means to achieve physical layer security of communications. The energy-concentrated directional beam can effectively reduce information leakage caused by illegal user eavesdropping from the physical layer and improve the communication security of the system.

[0005] Beamforming technology can greatly improve the performance and overall security of communication systems, but the multi-antenna arrays it requires have disadvantages such as high physical cost and communication overhead compared to single antenna elements. Especially in drone communication systems, drones have characteristics such as energy limitations, weight limitations and size limitations. The addition of multi-antenna arrays will increase the overall system overhead and further reduce the upper limit of drone service time. Therefore, collaborative beamforming (CB) technology is introduced, which can form a virtual antenna array (VAA) with multiple single antenna units, and use collaborative beamforming technology for communication to achieve better communication performance. There are schemes that achieve the optimal beam pattern in a specified direction for a virtual antenna array composed of a large number of distributed nodes in different scenarios, thereby improving the overall communication performance. In terms of system communication security, there are also schemes that study virtual antenna arrays with randomized positions of each node, realize randomization of signals in non-receiving directions, achieve better system confidentiality rates, and analyze the impact of position estimation errors of virtual antenna array nodes on the overall information confidentiality rate.

[0006] While drone equipment is highly flexible, it is subject to strict mass and energy restrictions. The physical equipment and energy overhead carried by drones should be reduced while ensuring system performance. Therefore, using multiple drones carrying single antennas to form a virtual antenna array and using collaborative beamforming technology is a feasible solution to improve system service time and overall performance. There is also a solution that uses a swarm of drones to form a virtual antenna array as an aerial relay, jointly optimizes the bottom base station, drone position and excitation current weight, and maximizes the average achievable rate of the system. Although there is inevitable position jitter during the flight of drones, which will cause performance losses to the system in terms of beam directivity, confidentiality rate and power loss, collaborative beamforming technology will still bring a lot of performance improvements to the system, and with the continuous advancement of drone flight control technology, drone swarm communication using collaborative beamforming technology is still an important solution to enhance overall communication performance.

[0007] The use of collaborative beamforming technology to achieve directional beam gain can enhance system security from the communication physical layer, effectively enhance the confidentiality rate of system information transmission, and realize secure communication of information. For example, there is a solution that uses an improved genetic algorithm to optimize the relative position and excitation current weight of drones in the swarm in the presence of eavesdroppers to achieve secure communication with distant ground base stations. There is also a solution that uses an improved multi-target dragonfly algorithm to implement collaborative beamforming transmission to multiple different base stations in sequence for a static drone swarm, achieving goals such as improving the overall confidentiality rate of the system. There is also a solution that combines drone swarms with self-driving cars to jointly build a virtual antenna array to achieve secure transmission of information. There is also a solution that considers that drones carry limited airborne energy, and a drone array composed of multiple drones that randomly change their positions at each moment uses collaborative beamforming technology to effectively improve the confidentiality rate of transmission for specific users. In addition, the method of actively emitting noise can also be used to improve system security. For example, there is also a solution that uses a drone swarm to build a virtual antenna array to emit artificial noise in directions other than legitimate users, thereby improving the confidentiality rate of the overall system.

[0008] The shortcomings of the drone swarm communication methods in the above-mentioned prior art include: these methods are more targeted at optimizing the adjustment of drone layout positions in static drone swarms, and do not fully consider how to dynamically adjust the swarm array layout and move the overall position of the swarm in real time on demand in energy-constrained drone swarms, and do not fully utilize the high flexibility of drones to achieve better communication performance. Summary of the invention

[0009] An embodiment of the present invention provides a method for secure communication of a drone swarm based on collaborative beamforming to obtain an optimal drone array arrangement and the overall position of the drone swarm.

[0010] In order to achieve the above object, the present invention adopts the following technical scheme.

[0011] A method for secure communication of a drone swarm based on collaborative beamforming, comprising:

[0012] Constructing a UAV-assisted communication system model, and calculating the system total confidentiality rate, propulsion power consumption, and UAV residual energy of the UAV-assisted communication system model;

[0013] With the goal of maximizing the total confidentiality rate of the system under the condition of the remaining energy limit of the drones, the optimization problem of the optimal drone group position and beam pointing is constructed;

[0014] The UAV swarm collaborative beamforming optimization algorithm is used to solve the optimization problems of the optimal UAV swarm position and beam pointing in turn, and the optimal arrangement plan of the UAV swarm position and beam pointing is obtained.

[0015] Preferably, the construction of the UAV-assisted communication system model includes:

[0016] The UAV-assisted communication system model consists of N UAVs and K ground users. All N UAVs form a UAV array. The UAV array communicates with each ground user in turn as a whole. The UAV set is represented as The ground user set is represented as N drones together form a virtual antenna array, and the position of the i-th drone is recorded as The kth ground user position is recorded as D k represents the amount of data required to be transmitted by the kth ground user. Assume that the amount of data required to be transmitted by each ground user is equal and is D0. Assume that the initial energy of each drone is equal and is E0. The position of the eavesdropper is recorded as p. E =[x E y E z E ].

[0017] Preferably, the step of calculating the total system confidentiality rate of the drone-assisted communication system model includes:

[0018] The array vector of the drone swarm array is represented as:

[0019]

[0020] Among them, k c =2π / λ is the phase constant, λ is the wavelength, θ∈[0, π ] and φ∈[- π , π ] are the elevation angle and azimuth angle respectively, I i is the excitation current weight of the i-th UAV, v = [sinθcosφ, sinθsinφ, cosθ] T ;

[0021] The array gain of the UAV array to the ground user k is expressed as:

[0022]

[0023] Where η∈[0,1] is the antenna array efficiency, ω(θ,φ) represents the far-field beam radiation pattern of a single antenna, and the UAV communication system uses an omnidirectional antenna. Figure 1 , (θ k ,φ k ) represents the pitch angle and azimuth angle of the desired pointing direction of the UAV beam, expressed as:

[0024]

[0025]

[0026] Where a=[1 0 0] T ,b=[0 1 0] T ,c=[0 0 1] T ;

[0027] The transmission rate from the UAV array to the ground user k is expressed as:

[0028]

[0029] Where (x i,k ,y i,k ,z i,k ) represents the position coordinates of the i-th UAV when serving the k-th ground user, B represents the channel bandwidth, represents the distance from the UAV array to the kth ground user, P t is the total transmit power of the UAV antenna array, K0 is the path loss constant, σ 2 is the noise power;

[0030] According to equations (1)-(5), the transmission information rate received by the eavesdropper is:

[0031]

[0032] The system information transmission confidentiality rate when the UAV array communicates with the kth ground user is expressed as:

[0033]

[0034] Preferably, the calculation of the propulsion power consumption of the UAV-assisted communication system model and the remaining energy of the UAV includes:

[0035] For a rotorcraft with a speed of V, the propulsion power consumption is modeled as:

[0036]

[0037] In formula (8), P0 and P i They represent the blade profile power constant and induced power constant in the hovering state, U tip represents the UAV rotor tip speed, v0 is the average rotor induced speed in the hovering state, d0 and s are the fuselage drag ratio and rotor solidity, ρ and A are the air density and rotor disc area, respectively;

[0038] Substituting V = 0 into equation (8), we can obtain the hovering energy consumption of the drone:

[0039] P h=P0+P i (9)

[0040] When the flight speed is fixed at V, the energy consumption of the drone hovering and moving is considered, and the remaining energy of the drone is expressed as:

[0041]

[0042] Where E0 is the energy initially carried by the drone, represents the hovering communication time of the UAV at the kth user, It represents the time required for the UAV to move to the kth user.

[0043] Preferably, the optimization problem of constructing the optimal drone group position and beam pointing with the goal of maximizing the total confidentiality rate of the system under the condition of the remaining energy limit of the drones includes:

[0044] With the goal of maximizing the total confidentiality rate of the system under the condition of the remaining energy limit of the drone, the optimization problem of the optimal drone group position and beam pointing is constructed. The expression of the optimization problem is as follows:

[0045]

[0046] In the optimization problem (11), {P i,k} represents the three-dimensional position coordinates of the i-th UAV when communicating with the k-th user. Constraints C1, C2, and C3 represent the position constraints of the UAV, which stipulate the maximum feasible movement range of the UAV. Constraint C4 represents the energy constraint of the UAV, which stipulates that the remaining energy of the UAV must be greater than the minimum energy E min ; Constraint C5 is the information transmission constraint, which stipulates that the drone must meet its minimum transmission information volume at each user; Constraint C6 is the drone distance constraint, which sets the minimum distance between drones to avoid collision;

[0047] The optimization problem (11) is decomposed into two sub-problems, namely, the UAV array arrangement optimization sub-problem under a fixed UAV swarm overall position and the swarm trajectory optimization sub-problem under a fixed UAV array arrangement.

[0048] Preferably, the expression of the drone array arrangement optimization subproblem under the overall position of the fixed drone group is:

[0049]

[0050] The objective function in problem (12) is simplified as follows:

[0051]

[0052] Among them, constraints C7-C10 limit the range within which the drone can move. In constraint C10, L i,j =||p i -p j ||2, this constraint limits the minimum distance between drones;

[0053] set up is the local optimal solution at the rth iteration. For the right side of the objective function in problem (13), let f k =-|AF(θ k ,φ k )| 2 ω(θ k ,φ k ) 2 , and in p ( r ) Taylor expansion is performed at:

[0054]

[0055] in

[0056]

[0057] Thus, we get f k The lower bound function μ (r) .

[0058] For the non-convex constraint C10, at a given local optimal point Perform Taylor expansion at , and get its lower bound function:

[0059]

[0060] in

[0061]

[0062] Through the above processing, problem (13) is transformed into a convex problem (19) with iterative values:

[0063]

[0064] Preferably, the expression of the group trajectory optimization subproblem in the case of fixed UAV array arrangement is:

[0065]

[0066] Among them, constraints C12-C14 represent the position constraints of the drone group, and C15 constraint ensures that the remaining energy of the drone is greater than the minimum value E min , constraint C16 indicates that the amount of information transmitted by the drone to the user must be greater than the minimum value D min ,in

[0067] For the objective function in problem (20), use represents the local optimal solution at the rth iteration, for d in the objective function k -α and d e -α Item, in Taylor expansion is performed at:

[0068]

[0069] in:

[0070]

[0071] The objective function in problem (20) is transformed into:

[0072]

[0073] The right side of (25) exist Perform Taylor expansion at the position and obtain the lower bound function:

[0074]

[0075] Convert the optimization objective function into a convex function:

[0076]

[0077] Simplify constraint (C16) to an equality constraint and substitute it into constraint (C15) to obtain:

[0078]

[0079] By reaching the local optimum Perform Taylor expansion at the position to obtain the lower bound function

[0080]

[0081] in

[0082]

[0083] Convert the problem (20) into a problem (32) involving iterative values;

[0084]

[0085] Preferably, the method of solving the optimization problem of the optimal drone swarm position and beam pointing by using the drone swarm collaborative beamforming optimization algorithm to obtain the optimal arrangement scheme of the drone swarm position and beam pointing includes:

[0086] The UAV swarm cooperative beamforming optimization algorithm is used to solve problems (19) and (32) in sequence. When the difference between the objective function values ​​of two consecutive iterations is less than the set accuracy ε or the maximum number of iterations l is reached, max When , the optimal UAV trajectory is obtained, and the maximum user transmission confidentiality rate is obtained. The specific algorithm flow is as follows:

[0087] Step 1) Initialization Set the number of iterations l = 0 and the error accuracy ε parameter;

[0088] Step 2) Fix the overall position of the drone fleet By solving problem (19), we can obtain the optimal UAV array arrangement

[0089] Step 3) Fix the drone array By solving subproblem (32), the optimal overall position of the UAV fleet is obtained

[0090] Step 4) Determine whether the difference between two iterations is less than the error precision R sec (l+1) -R sec (l) <ε or reaches the maximum number of iterations or or l>l max , if the conditions are met, the optimal solution drone position is output Otherwise jump to step 2).

[0091] It can be seen from the technical solutions provided by the above embodiments of the present invention that the embodiments of the present invention achieve the best overall performance and communication security by releasing a higher degree of freedom of the system. At the same time, for energy-constrained UAV equipment, the beam directivity is achieved by replacing the phase adjustment element with a small adjustment of the distribution position of each UAV in the swarm array, which can further reduce the overall system overhead and enhance the overall service time.

[0092] Additional aspects and advantages of the present invention will be given in part in the following description, which will become obvious from the following description, or may be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0093] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0094] Figure 1 A structural diagram of a drone-assisted communication system model provided by an embodiment of the present invention;

[0095] Figure 2 A processing flow chart of a method for secure communication of a drone group based on collaborative beamforming is provided for an embodiment of the present invention;

[0096] Figure 3 A beam strength diagram obtained by a group of multi-UAV VAA collaborative beamforming provided by an embodiment of the present invention;

[0097] Figure 4 A schematic diagram of a drone flight trajectory of a drone array consisting of 8 drones performing secure communication when there are 6 legitimate user nodes and 1 illegal eavesdropping user provided by an embodiment of the present invention;

[0098] Figure 5 A schematic diagram of the total confidentiality rate of a system under different numbers of UAVs when the total transmission power of a fixed UAV is provided in an embodiment of the present invention;

[0099] Figure 6 A schematic diagram of a comparison of the average confidentiality rate of users under different schemes with the number of users when the initial energy of the same drone is provided in an embodiment of the present invention;

[0100] Figure 7 A schematic diagram comparing the average confidentiality rate of users with different numbers of users as the initial energy of the drone is provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0101] The embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and cannot be interpreted as limiting the present invention.

[0102] It will be understood by those skilled in the art that, unless expressly stated, the singular forms "one", "said", and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present invention refers to the presence of the features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or groups thereof. It should be understood that when we refer to an element as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or there may be intermediate elements. In addition, the "connection" or "coupling" used herein may include wireless connection or coupling. The term "and / or" used herein includes any unit and all combinations of one or more associated listed items.

[0103] It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the art to which the present invention belongs. It should also be understood that terms such as those defined in common dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless defined as herein.

[0104] To facilitate understanding of the embodiments of the present invention, several specific embodiments will be further explained below with reference to the accompanying drawings, and each embodiment does not constitute a limitation on the embodiments of the present invention.

[0105] The embodiment of the present invention utilizes the high mobility of drones and adopts multiple drones carrying fixed-phase single antennas to form a drone swarm. By dynamically adjusting the array arrangement of the swarm and the overall position of the drone swarm in real time, a dynamic drone swarm security communication solution based on collaborative beamforming is proposed.

[0106] The embodiment of the present invention aims at the problem of secure communication of the drone swarm assisted communication system, and jointly considers factors such as drone energy, position, array beam, etc. to establish an optimization problem that maximizes the confidentiality rate of system information transmission. Since this problem is a highly coupled non-convex problem, it cannot be solved directly. By decomposing the original problem into the drone swarm array arrangement optimization problem and the drone swarm trajectory optimization problem, and proposing an iterative optimization algorithm, the local optimal solution of the problem is successfully obtained. Finally, the proposed algorithm is simulated and verified, and the results show that the drone swarm collaborative beamforming optimization scheme proposed in the embodiment of the present invention can effectively improve the confidentiality rate of the system.

[0107] The structure of a UAV-assisted communication system model provided by an embodiment of the present invention is as follows: Figure 1As shown in Figure 1, there are N drones and K ground users. All N drones form a drone array, and the drone array as a whole communicates with each ground user in turn. The drone set is represented by u=={1,2,...,N}, and the ground user set is represented by In order to minimize the cost of UAV equipment, each UAV carries only a single antenna element, and N UAVs will form a virtual antenna array. The position of the i-th UAV is recorded as The kth ground user position is recorded as D k represents the amount of data required to be transmitted by the kth ground user. Since the embodiment of the present invention focuses on the problem of cooperative beamforming secure communication, it is assumed that the amount of data required to be transmitted by each ground user is equal and is D0. Similarly, it is assumed that the initial energy of each drone is equal and is E0. In the embodiment of the present invention, there is an illegal user Eve who eavesdrops on the communication data. The eavesdropper's position is recorded as p E =[x E y E z E ].

[0108] The embodiment of the present invention provides a processing flow of a method for secure communication of a drone group based on collaborative beamforming. Figure 2 As shown, the processing steps include the following:

[0109] Step S10: construct a UAV-assisted communication system model, and calculate the system total confidentiality rate, propulsion power consumption, and UAV residual energy of the UAV-assisted communication system model.

[0110] Step S20, with the goal of maximizing the total confidentiality rate of the system under the condition of the remaining energy limit of the drone, construct an optimization problem of the optimal drone swarm position and beam pointing, and decompose the optimization problem into a drone array arrangement optimization sub-problem under a fixed drone swarm overall position and a swarm trajectory optimization sub-problem under a fixed drone array arrangement.

[0111] Step S30, using the UAV swarm collaborative beamforming optimization algorithm to sequentially solve the UAV array arrangement optimization sub-problem under the fixed UAV swarm overall position and the swarm trajectory optimization sub-problem under the fixed UAV array arrangement, and obtain the optimal arrangement plan of the UAV swarm position and beam pointing.

[0112] The embodiment of the present invention considers that a drone swarm provides services to multiple users distributed in the area. The drone array hovers at a specific location to provide services to user k, and then flies to a new location to provide services to the next user. In order to improve the beam directivity and signal transmission quality, and at the same time achieve a higher information confidentiality rate, the drone swarm uses collaborative beamforming technology for signal transmission. Beamforming technology relies on the regulation of each antenna phase, and the addition of phase shifters will increase system overhead. Therefore, the embodiment of the present invention utilizes the flexibility and high mobility of drones. Under the condition of fixed antenna phase, the required beam directivity is obtained by adjusting the spacing of the drone array.

[0113] The array vector of the drone swarm array can be expressed as:

[0114]

[0115] Among them, k c =2π / λ is the phase constant, λ is the wavelength, θ∈[0,π] and φ∈[-π,π] are the elevation and azimuth angles, respectively, I i is the excitation current weight of the i-th UAV, v = [sinθcosφ, sinθsinφ, cosθ] T .

[0116] The array gain of the UAV array to the ground user at k can be expressed as:

[0117]

[0118] Where η∈[0,1] is the antenna array efficiency, ω(θ,φ) represents the far-field beam radiation pattern of a single antenna. In the embodiment of the present invention, the UAV communication system adopts omnidirectional antennas, and the direction of each antenna element is Figure 1 (θ k ,φ k ) represents the pitch angle and azimuth angle of the desired pointing direction of the UAV beam, which can be expressed as:

[0119]

[0120] Where a=[1 0 0] T ,b=[0 1 0] T ,c=[0 0 1] T .

[0121] Since the UAVs communicate with ground users at high altitudes, the channel can be simplified to a line-of-sight propagation model. Therefore, the transmission rate from the UAV array to the ground user k can be expressed as:

[0122]

[0123] Where (x i,k,y i,k ,z i,k ) represents the position coordinates of the i-th UAV when serving the k-th ground user, B represents the channel bandwidth, represents the distance from the UAV array to the kth ground user, P t is the total transmit power of the UAV antenna array, K0 is the path loss constant, σ 2 is the noise power.

[0124] At the same time, since there are illegal eavesdroppers in the system, according to equations (1)-(5), the transmission information rate received by the eavesdropper can be obtained as:

[0125]

[0126] At this point, the confidentiality rate of system information transmission when the UAV array communicates with the kth ground user can be expressed as:

[0127]

[0128] Since the energy carried by drones is limited, the embodiments of the present invention also need to consider the drone energy consumption model to avoid uncontrollable factors caused by the drone's energy exhaustion during mission execution. The energy consumption of drones includes drone propulsion power consumption, circuit control power consumption, and communication power consumption related to signal transmission and reception. In practical applications, the drone's circuit control power and communication power are much smaller than the propulsion power. The drone's communication-related power can be approximately fixed to P c =5W.

[0129] Generally speaking, the propulsion energy consumption depends on the flight speed and acceleration of the drone. Since the acceleration time of the drone accounts for only a small part of its total motion time, for the convenience of description and analysis, the embodiment of the present invention ignores the energy consumption caused by the acceleration and deceleration of the drone. For a rotor drone with a speed of V, the propulsion power consumption can be modeled as:

[0130]

[0131] In formula (8), P0 and P i They represent the blade profile power constant and induced power constant in the hovering state, U tip represents the rotor tip speed of the UAV, v0 is the average rotor induced speed in the hovering state, d0 and s are the fuselage drag ratio and rotor solidity, respectively, ρ and A represent the air density and rotor disk area, respectively.

[0132] Substituting V = 0 into equation (8), we can get the hovering energy consumption of the drone:

[0133] P h =P0+P i (9)

[0134] Therefore, when the flight speed is fixed at V, the remaining energy of the drone is expressed as follows

[0135]

[0136] Where E0 is the energy initially carried by the drone, represents the hovering communication time of the UAV at the kth user, It represents the time required for the UAV to move to the kth user.

[0137] In the embodiment of the present invention, the positions of ground users and eavesdroppers are fixed. In order to maximize the total confidentiality rate of the system, the positions of drones should be reasonably planned under the limited energy constraints of drones to achieve the optimal drone group position and beam pointing. For the above system, under the constraints of factors such as drone position, energy, and amount of transmitted information, the optimization problem is proposed as follows:

[0138]

[0139] In problem (11), {P i,k} represents the three-dimensional position coordinates of the i-th UAV when communicating with the k-th user. Constraints (C1)(C2)(C3) represent the position constraints of the UAV, which stipulate the maximum feasible movement range of the UAV; constraint (C4) represents the energy constraint of the UAV, which stipulates that the remaining energy of the UAV must be greater than the minimum energy E min ; Constraint (C5) is the information transmission constraint, which stipulates that the drone must meet its minimum transmission information at each user; Constraint (C6) is the drone distance constraint, which sets the minimum distance between drones to avoid collision. Since constraints (C4)(C5)(C6) and the objective function are all non-convex functions and are highly coupled, problem (11) is difficult to solve using standard convex optimization methods.

[0140] The optimization problem (11) proposed in the embodiment of the present invention cannot be directly solved by convex optimization due to the existence of non-convex functions. The embodiment of the present invention decomposes the problem into two sub-problems, namely, the drone array arrangement optimization sub-problem under the fixed overall position of the drone group and the drone group trajectory optimization sub-problem under the fixed drone array arrangement. Then, the two sub-problems are alternately optimized by the convex approximation method, and finally a sub-optimal solution to the problem (11) can be obtained.

[0141] The sub-problem of optimizing the arrangement of drone arrays under the fixed overall position of the drone group

[0142] This sub-problem fixes the position of the drone array, and by adjusting the relative positions between drones, the directional beam strength in the user direction is enhanced, and the beam strength in the eavesdropper direction is reduced, so as to maximize the transmission confidentiality rate. The sub-problem can be expressed as:

[0143]

[0144] Since the position of the drone array is fixed, the objective function in problem (12) can be simplified as follows:

[0145]

[0146] The constraints (C7-C10) limit the range within which the drone can move. In constraint (C10), L i,j =||p i -p j ||2, this constraint limits the minimum distance between drones to avoid collisions. The objective function in problem (13) is a convex function minus a convex function, and the whole is a non-convex function. At the same time, constraint (C10) is also a non-convex constraint. In order to solve this optimization problem, it is necessary to perform convex relaxation on the original problem, and then use continuous convex approximation to approximate the local optimal solution.

[0147] set up is the local optimal solution at the rth iteration. For the right side of the objective function in problem (13), let f k =-|AF(θ k ,φ k )| 2 ω(θ k ,φ k ) 2 , and in p (r) Taylor expansion is performed at:

[0148]

[0149] in

[0150]

[0151] Thus, we can get f k The lower bound function μ (r) .

[0152] For non-convex constraints (C10), at a given local optimal point Perform Taylor expansion at , and get its lower bound function:

[0153]

[0154] in

[0155]

[0156] Through the above processing, problem (13) can be transformed into a problem with iterative values:

[0157]

[0158] At this point, problem (11) is transformed into a convex problem and can be solved by a standard convex optimization algorithm.

[0159] The trajectory optimization subproblem of a fixed UAV array

[0160] This sub-problem fixes the array arrangement of the drone swarm and optimizes the overall confidentiality rate of the system under the energy limit of the drone by adjusting the position and overall trajectory of the drone swarm when serving each user. The sub-problem can be expressed as:

[0161]

[0162] Among them, constraints (C12-C14) represent the position constraints of the drone group, and (C15) constraint ensures that the remaining energy of the drone is greater than the minimum value E min , constraint (C16) indicates that the amount of information transmitted by the drone to the user must be greater than the minimum value D min ,in In this optimization problem, since the objective function is non-convex and constraints (C15) (C16) are non-convex, it cannot be solved directly and it is necessary to introduce appropriate auxiliary variables.

[0163] For the objective function in problem (20), we first use represents the local optimal solution at the rth iteration, for d in the objective function k -α and d e -α Item, in Taylor expansion can be obtained:

[0164]

[0165] in:

[0166]

[0167] The objective function can be transformed into:

[0168]

[0169] This function is transformed into the form of convex function subtraction, and further the right side of exist Taylor expansion is performed at to obtain the lower bound function:

[0170]

[0171] This allows the optimization objective function to be transformed into a convex function:

[0172]

[0173] For constraint (C16), analysis shows that when the amount of transmitted information is greater than the specified minimum amount of information, there is no positive gain for the optimization objective. Therefore, this constraint can be simplified to an equality constraint and brought into constraint (C15) to obtain

[0174]

[0175] Since this constraint exists The term is a non-convex constraint, which is obtained by Taylor expansion can be performed to obtain the lower bound function

[0176]

[0177] in

[0178]

[0179] Therefore, the above problem (20) can be transformed into the problem (32) containing iterative values.

[0180]

[0181] At this point, the non-convex constraints in the above problem are transformed into convex constraints, and the objective function is also a convex function, which can be solved by standard convex optimization or CVX solver.

[0182] Based on the above problem analysis and solution, an embodiment of the present invention proposes a UAV swarm cooperative beamforming optimization algorithm. The algorithm solves problem (19) and problem (32) in sequence, and then solves problem (11). When the difference between the objective function values ​​of two adjacent iterations is less than the set accuracy ε or reaches the maximum number of iterations l max When , the optimal UAV trajectory can be obtained, and the maximum user transmission confidentiality rate can be obtained. The specific algorithm flow is shown below.

[0183] Step 1) Initialization Set the number of iterations l=0, error accuracy ε and other parameters.

[0184] Step 2) Fix the overall position of the drone fleet By solving problem (19), we can obtain the optimal UAV array arrangement

[0185] Step 3) Fix the drone array By solving subproblem (32), the optimal overall position of the UAV fleet is obtained

[0186] Step 4) Determine whether the difference between two iterations is less than the error precision R sec(l+1) -R sec (l) <ε or reaches the maximum number of iterations or or l>l max , if the conditions are met, the optimal solution drone position is output Otherwise jump to step 2).

[0187] In order to verify the effectiveness of the proposed algorithm and evaluate its performance, the present invention uses MATLAB to simulate the proposed algorithm and analyzes the simulation results.

[0188] The simulation scenario is set as a 1 000×1 000×200m 3 The three-dimensional area in which user nodes and eavesdroppers are distributed. Assuming that the initial energy limit of the UAV is E0 = 6 000 J, the initial number of user nodes is 6 and the number of eavesdropping nodes is 1. The other flight and communication related parameters of the UAV are shown in Table 1.

[0189] Table 1 UAV flight and communication related parameters

[0190]

[0191]

[0192] Simulation results analysis: Figure 3 A group of beam strength diagrams obtained by VAA cooperative beamforming of multiple UAVs provided in an embodiment of the present invention. Figure 3 It can be seen that the beam is concentrated in the direction of the user and the signal strength is weakened in the direction of the eavesdropper. This can achieve the purpose of enhancing the overall confidentiality rate of the system.

[0193] Figure 4 A schematic diagram of the flight trajectory of drones provided by an embodiment of the present invention when there are 6 legitimate user nodes and 1 illegal eavesdropping user, and an array of 8 drones performing secure communication. Figure 4 It can be seen that in order to achieve the optimal transmission confidentiality rate, the drone array will tend to approach the user node and stay away from the eavesdropping node under limited energy. When the drone array is hovering for communication, it will construct an optimal virtual antenna array to generate beam gain for the user and suppress the eavesdropper's azimuth beam. Figure 4 The middle image shows the relative position arrangement of the drone array when the drone swarm communicates with three of the ground users. It can be seen that due to the energy limitations of each drone and the directivity requirements of the drone array beam, the array arrangement will change relatively when the drone swarm communicates with different ground users.

[0194] Figure 5A schematic diagram of the total confidentiality rate of the system under different numbers of UAVs when the total power of a fixed UAV transmission is provided in an embodiment of the present invention. At the same time, the optimal confidentiality rates that can be achieved by the system under different flight plans are compared, and the algorithm of the embodiment of the present invention is effectively evaluated. Among them, "Comparison Plan 1" first calculates the fixed optimal UAV array arrangement, and then maintains a fixed VAA to optimize the overall movement trajectory of the UAV array; "Comparison Plan 2" fixes the optimal position of the UAV fleet and optimizes the VAA arrangement to obtain beams with different directionalities. By Figure 5 It can be seen that as the number of drones in the drone array increases, the confidentiality rates of the three algorithms all increase. This is because the more antenna units that make up the VAA, the stronger the beam directivity formed by its collaborative beamforming. The algorithm proposed in the embodiment of the present invention has higher mobility because it adopts a solution of real-time dynamic adjustment of the VAA array arrangement and the movement trajectory of the drone group. The high degree of freedom brought about by this also makes the system have a higher confidentiality rate compared with the two comparison solutions.

[0195] Figure 6 A schematic diagram of the variation of the average confidentiality rate of users with the number of users under different schemes when the initial energy of the same drone is provided in an embodiment of the present invention. Figure 6 It can be seen that for the algorithm proposed in the embodiment of the present invention and the comparative scheme 1, when the number of users increases to a certain extent, the average confidentiality rate will begin to decline. This is because when the number of service users is too large, the UAV transmission and movement energy consumption will increase, and the UAV cannot select the optimal location for data transmission due to energy limitations. The algorithm proposed in the embodiment of the present invention has a higher confidentiality rate than the comparative algorithm under different user node conditions, because in an energy-constrained system, the embodiment of the present invention can achieve a higher confidentiality rate target by dynamically adjusting the VAA arrangement in real time and using the small-range movement of the drone. Comparative scheme 2 adopts a hovering shaping strategy, which requires less UAV propulsion energy consumption, but because its communication position is fixed, in the case of sparse user arrangement, the overall confidentiality rate will show a downward trend as the number of users increases. When the number of ground users is large enough, the energy consumed by the drone group movement in comparative scheme 1 increases significantly, while the initial energy carried by the drone remains unchanged, resulting in a worse selection of the drone group position under this scheme. As the number of ground user nodes increases, the confidentiality rate of comparative scheme 1 will decrease rapidly and even be lower than the confidentiality rate obtained by comparative scheme 2.

[0196] Figure 7 A schematic diagram of comparing the average confidentiality rate of users with different numbers of users and the change of the initial energy of the drone is provided in an embodiment of the present invention. Figure 7It can be seen that when the initial energy carried by the UAV increases, the average confidentiality rate of users will also increase. This is because when the position of the ground user remains unchanged, more energy can support the UAV to operate to a better communication position; when the initial energy exceeds a certain level, the average confidentiality rate growth rate slows down and tends to be the same. The energy required for this stable point increases with the increase in the number of users. This is because the energy at the stable point can already satisfy the UAV to fly to the vicinity of the optimal communication position and perform beamforming for the user. Further energy increase will not improve the overall system security performance.

[0197] In summary, the embodiment of the present invention proposes a drone swarm secure communication algorithm based on collaborative beamforming in a drone-assisted communication system. Under the constraints of drone energy, amount of information transmitted, etc., the confidentiality rate of the system is maximized by optimizing the position and trajectory of each drone in the drone swarm. In view of the non-convex case of the optimization problem, the embodiment of the present invention decomposes the original problem into two sub-problems, and designs a cyclic iterative convex approximation algorithm to solve it through Taylor expansion, convex relaxation, etc. Through simulation and result analysis, the optimization scheme proposed in the embodiment of the present invention makes full use of the high mobility and high degree of freedom of the drone swarm. By dynamically adjusting the swarm array and the overall position in real time, it can more effectively improve the system confidentiality rate and realize physical layer secure communication compared with the traditional static optimization scheme.

[0198] Those skilled in the art can understand that the accompanying drawings are only schematic diagrams of an embodiment, and the modules or processes in the accompanying drawings are not necessarily required to implement the present invention.

[0199] It can be known from the description of the above implementation methods that those skilled in the art can clearly understand that the present invention can be implemented by means of software plus a necessary general hardware platform. Based on such an understanding, the technical solution of the present invention is essentially or the part that contributes to the prior art can be embodied in the form of a software product, which can be stored in a storage medium such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments of the present invention or certain parts of the embodiments.

[0200] Each embodiment in this specification is described in a progressive manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for the device or system embodiment, since it is basically similar to the method embodiment, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiment. The device and system embodiments described above are merely schematic, wherein the units described as separate components may or may not be physically separated, and the components displayed as units may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. Ordinary technicians in this field can understand and implement it without paying creative labor.

[0201] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for secure communication of drone swarms based on collaborative beamforming, characterized in that: include: Constructing a UAV-assisted communication system model, and calculating the system total confidentiality rate, propulsion power consumption, and UAV residual energy of the UAV-assisted communication system model; With the goal of maximizing the total confidentiality rate of the system under the condition of the remaining energy limit of the drones, the optimization problem of the optimal drone group position and beam pointing is constructed; The UAV swarm collaborative beamforming optimization algorithm is used to solve the optimization problems of the optimal UAV swarm position and beam pointing in turn, and the optimal arrangement plan of the UAV swarm position and beam pointing is obtained.

2. The method according to claim 1, characterized in that: The construction of the UAV-assisted communication system model includes: The UAV-assisted communication system model consists of N UAVs and K ground users. All N UAVs form a UAV array. The UAV array communicates with each ground user in turn as a whole. The UAV set is represented as The ground user set is represented as N drones together form a virtual antenna array, and the position of the i-th drone is recorded as The kth ground user position is recorded as D k represents the amount of data required to be transmitted by the kth ground user. Assume that the amount of data required to be transmitted by each ground user is equal and is D0. Assume that the initial energy of each drone is equal and is E0. The position of the eavesdropper is recorded as p. E =[x E y E z E ].

3. The method according to claim 1, characterized in that: The method of calculating the total system confidentiality rate of the drone-assisted communication system model includes: The array vector of the drone swarm array is represented as: Among them, k c =2π / λ is the phase constant, λ is the wavelength, θ∈[0,π] and φ∈[-π,π] are the elevation and azimuth angles, respectively, I i is the excitation current weight of the i-th UAV, v = [sinθcosφ, sinθsinφ, cosθ] T ; The array gain of the UAV array to the ground user k is expressed as: Where η∈[0,1] is the antenna array efficiency, ω(θ,φ) represents the far-field beam radiation pattern of a single antenna, and the UAV communication system uses an omnidirectional antenna with the same radiation pattern for each antenna element. k ,φ k ) represents the pitch angle and azimuth angle of the desired pointing direction of the UAV beam, expressed as: Where a=[1 0 0] T ,b=[0 1 0] T ,c=[0 0 1] T ; The transmission rate from the UAV array to the ground user k is expressed as: Where (x i,k ,y i,k ,z i,k ) represents the position coordinates of the i-th UAV when serving the k-th ground user, B represents the channel bandwidth, represents the distance from the UAV array to the kth ground user, P t is the total transmit power of the UAV antenna array, K0 is the path loss constant, σ 2 is the noise power; According to equations (1)-(5), the transmission information rate received by the eavesdropper is: The system information transmission confidentiality rate when the UAV array communicates with the kth ground user is expressed as:

4. The method according to claim 1, characterized in that: The method of calculating the propulsion power consumption of the UAV auxiliary communication system model and the remaining energy of the UAV includes: For a rotorcraft with a speed of V, the propulsion power consumption is modeled as: In formula (8), P0 and P i They represent the blade profile power constant and induced power constant in the hovering state, U tip represents the UAV rotor tip speed, v0 is the average rotor induced speed in the hovering state, d0 and s are the fuselage drag ratio and rotor solidity, ρ and A are the air density and rotor disc area, respectively; Substituting V = 0 into equation (8), we can obtain the hovering energy consumption of the drone: P h =P0+P i (9) When the flight speed is fixed at V, the energy consumption of the drone hovering and moving is considered, and the remaining energy of the drone is expressed as: Where E0 is the energy initially carried by the drone, represents the hovering communication time of the UAV at the kth user, It represents the time required for the UAV to move to the kth user.

5. The method according to claim 3 and claim 4, characterized in that The optimization problem of constructing the optimal UAV group position and beam pointing with the goal of maximizing the total confidentiality rate of the system under the condition of the remaining energy limit of the UAV includes: With the goal of maximizing the total confidentiality rate of the system under the condition of the remaining energy limit of the drone, the optimization problem of the optimal drone group position and beam pointing is constructed. The expression of the optimization problem is as follows: In the optimization problem (11), {P i,k } represents the three-dimensional position coordinates of the i-th UAV when communicating with the k-th user. Constraints C1, C2, and C3 represent the position constraints of the UAV, which stipulate the maximum feasible movement range of the UAV. Constraint C4 represents the energy constraint of the UAV, which stipulates that the remaining energy of the UAV must be greater than the minimum energy E min ; Constraint C5 is the information transmission constraint, which stipulates that the drone must meet its minimum transmission information volume at each user; Constraint C6 is the drone distance constraint, which sets the minimum distance between drones to avoid collision; The optimization problem (11) is decomposed into two sub-problems, namely, the UAV array arrangement optimization sub-problem under a fixed UAV swarm overall position and the swarm trajectory optimization sub-problem under a fixed UAV array arrangement.

6. The method according to claim 5, characterized in that The expression of the drone array arrangement optimization subproblem under the fixed overall position of the drone group is: The objective function in problem (12) is simplified as follows: Among them, constraints C7-C10 limit the range within which the drone can move. i,j =||p i -p j ||2, this constraint limits the minimum distance between drones; set up is the local optimal solution at the rth iteration. For the right side of the objective function in problem (13), let f k =-|AF(θ k ,φ k )| 2 ω(θ k ,φ k ) 2 , and in p (r) Taylor expansion is performed at: in Thus, we get f k The lower bound function μ (r) . For the non-convex constraint C10, at a given local optimal point Perform Taylor expansion at , and get its lower bound function: in Through the above processing, problem (13) is transformed into a convex problem (19) with iterative values:

7. The method according to claim 5, characterized in that The expression of the group trajectory optimization sub-problem in the case of fixed UAV array arrangement is: Among them, constraints C12-C14 represent the position constraints of the drone group, and C15 constraint ensures that the remaining energy of the drone is greater than the minimum value E min , constraint C16 indicates that the amount of information transmitted by the drone to the user must be greater than the minimum value D min , where D k =R seck t k ′; For the objective function in problem (20), use represents the local optimal solution at the rth iteration, for d in the objective function k -α and d e -α Item, in Taylor expansion is performed at: in: The objective function in problem (20) is transformed into: The right side of (25) exist Perform Taylor expansion at the position and obtain the lower bound function: Convert the optimization objective function into a convex function: Simplify constraint (C16) to an equality constraint and substitute it into constraint (C15) to obtain: By reaching the local optimum Perform Taylor expansion at the position to obtain the lower bound function in Convert the problem (20) into a problem (32) involving iterative values; 8. The method according to claims 5-7, characterized in that: The method of using the UAV swarm collaborative beamforming optimization algorithm to solve the optimization problem of the optimal UAV swarm position and beam pointing to obtain the optimal arrangement scheme of the UAV swarm position and beam pointing includes: The UAV swarm cooperative beamforming optimization algorithm is used to solve problems (19) and (32) in sequence. When the difference between the objective function values ​​of two consecutive iterations is less than the set accuracy ε or the maximum number of iterations l is reached, max When , the optimal UAV trajectory is obtained, and the maximum user transmission confidentiality rate is obtained. The specific algorithm flow is as follows: Step 1) Initialization Set the number of iterations l = 0 and the error accuracy ε parameter; Step 2) Fix the overall position of the drone fleet By solving problem (19), we can obtain the optimal UAV array arrangement Step 3) Fix the drone array By solving subproblem (32), the optimal overall position of the UAV fleet is obtained Step 4) Determine whether the difference between two iterations is less than the error precision R sec (l+1) -R sec (l) <ε or reaches the maximum number of iterations or or l>l max , if the conditions are met, the optimal solution drone position is output Otherwise jump to step 2).

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