Multi-user covert communication method based on time slot allocation and 3D trajectory optimization

Abstract

The invention discloses a multi-user covert communication method based on time slot allocation and 3D trajectory optimization. The method comprises the following steps: S1, constructing a communication system for serving multiple users by an unmanned aerial vehicle base station; s2, establishing an optimization problem for maximizing the average concealment rate by jointly optimizing user service time slot allocation, a sender beam forming vector and a 3D flight trajectory; s3, dividing the optimization problem into a user service time slot allocation sub-problem, a beam forming vector sub-problem and a 3D flight path optimization sub-problem; s4, solving an alternate user service time slot allocation sub-problem, a beam forming vector sub-problem and a 3D flight path optimization sub-problem through an alternate optimization algorithm to obtain a communication strategy including optimal user service time slot allocation, beam forming vector and 3D flight path; and S5, guiding the communication system to realize multi-user covert communication through the communication strategy. According to the invention, the security, concealment and reliability of multi-user covert communication are improved through the unmanned aerial vehicle base station.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication security, and in particular to a multi-user covert communication method based on time slot allocation and 3D trajectory optimization. Background Art

[0002] In the information age, covert communication, as an important means to ensure the security of information transmission, has attracted increasing attention from researchers. Traditional covert communication methods mostly focus on ensuring the concealment between single-user pairs, but in practical applications, multi-user communication scenarios based on multiple legitimate receivers are more common and universal. However, covert communication methods for this scenario are still in the early stages of development and face many challenges.

[0003] A significant challenge is that existing multi-user covert communication methods often assume that the channel state information (CSI) is perfectly known. This assumption may be feasible in theoretical analysis, but it is difficult to achieve in actual communication environments. In particular, when the illegal detection party (Willie) acts as a passive detection user, it is difficult for legitimate users to obtain its accurate CSI due to the concealment of its identity and location. Therefore, studying multi-user covert communication methods under imperfect CSI conditions is of great significance to improving the practicality and security of communication systems.

[0004] Under imperfect CSI conditions, the challenge of multi-user covert communication lies in how to effectively allocate time slots, optimize the 3D trajectory of the UAV-BS, and design beamforming vectors to ensure the secure transmission of information. Among them, the allocation of time slots for multiple users is a key issue. Since each user needs to receive information within a specific time slot, the allocation of time slots needs to take into account the user's priority, the concealment of information transmission, and the overall performance of the system. However, this allocation process often brings about integer programming problems, making it extremely complicated to solve the optimal solution.

[0005] In addition, the 3D trajectory optimization of UAV-BS is also an important challenge. Compared with traditional fixed base stations, UAV-BS has higher flexibility and coverage, but the optimization of its trajectory needs to take into account multiple factors, such as the user's geographical location, the need for information transmission, and the complexity of the communication environment. At the same time, 3D trajectory optimization is also closely related to beamforming vectors and time slot allocation. Beamforming vectors are used to adjust the transmission direction of the signal to improve the concealment and transmission efficiency of information; while time slot allocation determines the timing and order in which each user receives information. These three factors are coupled with each other, further increasing the difficulty of solving the optimal solution.

[0006] To address these challenges, researchers have proposed a variety of solutions. An effective approach is to use advanced optimization algorithms, such as heuristic algorithms and genetic algorithms, to solve integer programming problems. These algorithms can find approximately optimal solutions within an acceptable time to meet the needs of multi-user covert communication. Another approach is to predict and estimate Willie's CSI through machine learning techniques. Although this method may not be able to obtain perfect CSI, it can improve the accuracy and reliability of the estimate by learning from historical data and the characteristics of the communication environment. In addition, in order to optimize the 3D trajectory and beamforming vector of the UAV-BS, researchers have also proposed solutions based on dynamic programming, gradient descent and other methods. These methods can gradually approach the optimal solution while taking into account the coupling of multiple factors. At the same time, through a reasonable time slot allocation strategy, the system performance and user fairness can be further balanced.

[0007] In summary, multi-user covert communication is a complex and challenging research field. Under imperfect CSI conditions, how to ensure the secure transmission of information through effective time slot allocation, 3D trajectory optimization and beamforming vector design is a technical problem that needs to be solved urgently. Summary of the invention

[0008] In view of the above-mentioned deficiencies of the prior art, the technical problem to be solved by the present invention is: how to provide a multi-user covert communication method based on time slot allocation and 3D trajectory optimization, build a communication system in which a UAV base station serves multiple users, and at the same time establish an optimization problem of maximizing the average covert rate by jointly optimizing the user service time slot allocation, the sender beamforming vector and the 3D flight trajectory, thereby improving the security, concealment and reliability of multi-user covert communication.

[0009] In order to solve the above technical problems, the present invention adopts the following technical solutions:

[0010] A multi-user covert communication method based on time slot allocation and 3D trajectory optimization, comprising:

[0011] S1: Build a communication system where drone base stations serve multiple users;

[0012] S2: Based on the communication system, an optimization problem is established to maximize the average concealment rate by jointly optimizing the user service time slot allocation, the transmitter beamforming vector and the 3D flight trajectory;

[0013] S3: Split the optimization problem into the user service time slot allocation sub-problem, the beamforming vector sub-problem and the 3D flight trajectory optimization sub-problem;

[0014] S4: Solve the alternating user service time slot allocation subproblem, beamforming vector subproblem and 3D flight trajectory optimization subproblem through the alternating optimization algorithm to obtain the communication strategy including the optimal user service time slot allocation, beamforming vector and 3D flight trajectory;

[0015] S5: The communication system is guided by a communication strategy including optimal user service time slot allocation, beamforming vectors and 3D flight trajectory to achieve multi-user covert communication.

[0016] Preferably, in step S1, the communication system constructed is:

[0017] A multi-antenna drone base station serves L users; there is an illegal detection party to detect whether there is legal communication;

[0018] The 3D coordinates of the ground user, i.e. the user and the illegal detection party, are p C =[x C ,y C ,0] T ,C={1,...,L,W}, {1,...,L} represents the user set, and W represents the illegal detection party;

[0019] Let the total flight time of the drone base station be T U , and is equally divided into M time slots δ U , that is, T U =Mδ U , each time slot can only serve one user, using a l [m]∈{0,1} represents the user served in the mth time slot. l [m] = 1 means that the UAV base station in the mth time slot serves the lth user, then there exists

[0020] The flight altitude of the drone base station is H, and its horizontal and vertical coordinates are p xy [m]=[x[m],y[m]] T , the 3D coordinates are p[m]=[x[m],y[m],H[m]] T , There is a cylindrical no-fly zone within the communication area, the bottom of which is p nf =[x nf ,y nf ] T The center is r and the radius is nf The airspace above the circle is a no-fly zone.

[0021] Preferably, in step S2, the formula of the optimization problem P1 is expressed as:

[0022]

[0023] Where: represents the user service time slot coefficient set, a l [m]∈{0,1} represents the user served by the drone base station in the mth time slot. l [m] = 1 means that the UAV base station in the mth time slot serves the lth user; represents the beamforming vector set of the UAV base station, w[m] represents the beamforming vector of the UAV base station; represents the channel with error term, g U,W [m] represents the link from the drone base station to the user, Δg[m] represents the error term, δ g Indicates the error level; Represents the 3D flight trajectory set of the drone base station, p[m] = [x[m], y[m], H[m]] T represents the 3D coordinates of the drone base station, H represents the flight altitude of the drone base station; R l [m] represents the achievable rate of the mth time slot; Δg represents the channel uncertainty; C1 represents the location constraint of the no-fly zone, where the no-fly zone is a cylinder with the bottom of the cylinder at p nf =[x nf ,y nf ] T The center is r and the radius is nf The airspace above the circle is a no-fly zone; xy [m]=[x[m],y[m]] T represents the horizontal and vertical coordinates of the drone base station; C2 represents the covert communication constraint, τ β represents the detection threshold of the illegal detection party; C3 represents the transmission power constraint of the drone base station, P U represents the maximum transmission power; C4 and C5 represent the user service time slot coefficient constraints; C6 represents the flight speed constraint of the UAV, δ U represents the time slot; C7 represents the location constraint of the drone base station, p I and p F They represent the starting and ending positions of the UAV base station respectively; C8 represents the flight altitude constraint of the UAV base station, H min and H max They represent the minimum and maximum flight altitudes of the UAV base station respectively.

[0024] Preferably, in step S2, a slack variable μ is introduced to transform the optimization problem P1 into the optimization problem P2:

[0025]

[0026] Where: M represents the total flight time T of the drone base station U Divide into time slots δU The total number of g U,l [m] represents the link from the drone base station to the lth user; Represents the variance of the background noise.

[0027] Preferably, in step S3, the beamforming vector set W and the 3D flight trajectory set P are fixed, and the optimization problem P2 is converted into a user service time slot allocation sub-problem P3:

[0028]

[0029] Preferably, in step S3, the user service time slot coefficient set A and the 3D flight trajectory set P are fixed, and the optimization problem P2 is converted into a beamforming vector quantum problem P4:

[0030]

[0031] Preferably, the beamforming vector quantum problem P4 is transformed into the beamforming vector quantum problem P5:

[0032]

[0033] Where: The dimension is N U The identity matrix of (k),H [m] is the conjugate transpose of the k-th iteration value of the m-time slot beamforming vector; is the conjugate transpose of the m-slot UAV to user channel.

[0034] Preferably, the user service time slot coefficient set A and the beamforming vector set W are fixed, and the optimization problem P2 is converted into a 3D flight trajectory optimization sub-problem P6:

[0035]

[0036] Preferably, the 3D flight trajectory optimization sub-problem P6 is converted into the 3D flight trajectory optimization sub-problem P7:

[0037]

[0038] Where: is the introduced slack variable; α is the channel attenuation coefficient.

[0039] Preferably, in step S4, the processing steps of the alternating optimization algorithm are as follows:

[0040] S401: Initialization: Setting the number of cycles k=0, the cutoff parameter and the maximum number of cycles N max And the initial 3D flight trajectory set P (0) and the beamforming vector set W (0) ;

[0041] S402: For a given 3D flight trajectory set P (k) and the beamforming vector set W (k) , solve the user service time slot allocation subproblem P3, and obtain the optimal user service time slot coefficient set A (k+1) =A (*) ;

[0042] S403: For a given 3D flight trajectory set P (k) and user service slot coefficient set A (k+1) , solve the beamforming vector quantum problem P5 and obtain the optimal beamforming vector set W (k+1) =W (*) ;

[0043] S404: For a given user service time slot coefficient set A (k+1) and the beamforming vector set W (k+1) , solve the 3D flight trajectory optimization subproblem P7 and obtain the optimal 3D flight trajectory set P (k+1) =P (*) ;

[0044] S405: Set the number of loops k=k+1;

[0045] S406: If the cut-off parameter or the maximum number of cycles is reached, execute step S407; otherwise, return to step S402;

[0046] S407: Output the optimal user service time slot coefficient set A (*) , beamforming vector set W (*) and the 3D flight trajectory set P (*) and the optimal objective function value.

[0047] Compared with the prior art, the multi-user covert communication method based on time slot allocation and 3D trajectory optimization in the present invention has the following beneficial effects:

[0048] The present invention constructs a communication system in which a drone base station serves multiple users. First, due to its high mobility and flexibility, the drone base station (UAV-BS) can quickly change its position and service area, thereby reducing the risk of being monitored and located by illegal detection parties, and helping to better achieve multi-user covert communication. Secondly, the drone base station can be deployed in areas that are difficult to cover or inaccessible to traditional base stations, such as mountainous areas, remote areas, or temporary activity areas, to ensure the continuity and concealment of multi-user communications. Finally, the drone base station can adjust its service scope and service quality according to real-time needs, provide personalized covert communication services for different users, and improve resource utilization efficiency.

[0049] Based on the UAV base station communication system, the present invention establishes an optimization problem of maximizing the average concealment rate by jointly optimizing the user service time slot allocation, the sender beamforming vector and the 3D flight trajectory. First, by jointly optimizing the time slot allocation, the beamforming vector and the 3D flight trajectory, the communication signal can be hidden more effectively, while maximizing the data transmission rate to ensure the efficiency and reliability of multi-user covert communication. Secondly, the optimized beamforming vector can accurately control the transmission direction of the signal, reduce signal leakage, and reduce the risk of being intercepted by the enemy, while the optimization of the 3D flight trajectory can ensure that the UAV base station is always in the best position to provide the best communication quality and concealment, thereby improving the performance of the entire communication system, thereby improving the security and concealment of multi-user covert communication.

[0050] The optimization problem constructed by the present invention is a non-convex optimization problem. Therefore, when solving the optimization problem, the optimization problem is divided into a user service time slot allocation sub-problem, a beamforming vector sub-problem and a 3D flight trajectory optimization sub-problem, and the problem is solved alternately through an alternating optimization algorithm. First, the complex optimization problem is decomposed into multiple sub-problems and solved separately, which can reduce the overall difficulty of the solution and improve the solution efficiency. Secondly, through the alternating optimization algorithm, the global optimal solution can be gradually approached to ensure that the obtained user service time slot allocation, beamforming vector and 3D flight trajectory are optimal, thereby maximizing the efficiency and security of covert communication. Finally, the alternating optimization algorithm allows the adjustment of parameters and strategies according to actual needs during the solution process, so that the communication system can more flexibly respond to different covert communication needs and environmental changes, thereby further improving the reliability of multi-user covert communication. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to make the purpose, technical solution and advantages of the invention more clear, the present invention will be further described in detail below with reference to the accompanying drawings, in which:

[0052] Figure 1 The logical block diagram of the multi-user covert communication method based on time slot allocation and 3D trajectory optimization.

[0053] Figure 2 This is a network architecture diagram for the communication system.

[0054] Figure 3 is the variation of average concealment rate with transmit power.

[0055] Figure 4 3D trajectory of the UAV base station UAV-BS. DETAILED DESCRIPTION

[0056] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. The components of the embodiments of the present invention generally described and shown in the drawings here can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the claimed invention, but only represents selected embodiments of the present invention. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work belong to the scope of protection of the present invention.

[0057] The following is a further detailed description through specific implementation methods:

[0058] Example:

[0059] This embodiment discloses a multi-user covert communication method based on time slot allocation and 3D trajectory optimization.

[0060] like Figure 1 As shown, a multi-user covert communication method based on time slot allocation and 3D trajectory optimization includes:

[0061] S1: Build a communication system where drone base stations serve multiple users;

[0062] S2: Based on the communication system, an optimization problem is established to maximize the average concealment rate by jointly optimizing the user service time slot allocation, the transmitter beamforming vector and the 3D flight trajectory;

[0063] S3: Split the optimization problem into the user service time slot allocation sub-problem, the beamforming vector sub-problem and the 3D flight trajectory optimization sub-problem;

[0064] S4: Solve the alternating user service time slot allocation subproblem, beamforming vector subproblem and 3D flight trajectory optimization subproblem through the alternating optimization algorithm to obtain the communication strategy including the optimal user service time slot allocation, beamforming vector and 3D flight trajectory;

[0065] S5: The communication system is guided by a communication strategy including optimal user service time slot allocation, beamforming vectors and 3D flight trajectory to achieve multi-user covert communication.

[0066] The present invention constructs a communication system in which an unmanned aerial vehicle base station serves multiple users. First, due to its high mobility and flexibility, the unmanned aerial vehicle base station (UAV-BS) can quickly change its position and service area, thereby reducing the risk of being monitored and located by illegal detection parties, and helping to better realize multi-user covert communication. Secondly, the unmanned aerial vehicle base station can be deployed in areas that are difficult to cover or inaccessible to traditional base stations, such as mountainous areas, remote areas, or temporary activity areas, to ensure the continuity and concealment of multi-user communications. Finally, the unmanned aerial vehicle base station can adjust its service scope and service quality according to real-time needs, provide personalized covert communication services for different users, and improve resource utilization efficiency.

[0067] Based on the UAV base station communication system, the present invention establishes an optimization problem of maximizing the average concealment rate by jointly optimizing the user service time slot allocation, the sender beamforming vector and the 3D flight trajectory. First, by jointly optimizing the time slot allocation, the beamforming vector and the 3D flight trajectory, the communication signal can be hidden more effectively, while maximizing the data transmission rate to ensure the efficiency and reliability of multi-user covert communication. Secondly, the optimized beamforming vector can accurately control the transmission direction of the signal, reduce signal leakage, and reduce the risk of being intercepted by the enemy, while the optimization of the 3D flight trajectory can ensure that the UAV base station is always in the best position to provide the best communication quality and concealment, thereby improving the performance of the entire communication system, thereby improving the security and concealment of multi-user covert communication.

[0068] The optimization problem constructed by the present invention is a non-convex optimization problem. Therefore, when solving the optimization problem, the optimization problem is divided into a user service time slot allocation sub-problem, a beamforming vector sub-problem and a 3D flight trajectory optimization sub-problem, and the problem is solved alternately through an alternating optimization algorithm. First, the complex optimization problem is decomposed into multiple sub-problems and solved separately, which can reduce the overall difficulty of the solution and improve the solution efficiency. Secondly, through the alternating optimization algorithm, the global optimal solution can be gradually approached to ensure that the obtained user service time slot allocation, beamforming vector and 3D flight trajectory are optimal, thereby maximizing the efficiency and security of covert communication. Finally, the alternating optimization algorithm allows the adjustment of parameters and strategies according to actual needs during the solution process, so that the communication system can more flexibly respond to different covert communication needs and environmental changes, thereby further improving the reliability of multi-user covert communication.

[0069] In order to better introduce the technical aspects of the present invention, this embodiment is described through the following parts.

[0070] 1. Communication system based on UAV base station (UAV-BS)

[0071] In the communication system constructed:

[0072] A multi-antenna UAV-BS serves L users (Bob); the UAV-BS has N U Antennas are arranged along the x-axis, the distance between adjacent antennas is d, and λ represents the carrier wavelength; there is an illegal detection party (Willie) to detect whether there is legal communication. The illegal detection party poses a security threat to the communication system. All ground users, i.e. users and illegal detection parties, are single-antenna users, such as Figure 2 shown.

[0073] The vertical height of the ground user can be ignored and set to 0. The 3D coordinate of the ground user is p C =[x C ,y C ,0] T ,C∈{1,...,L,W}, {1,...,L} represents the user set, and W represents the illegal detection party;

[0074] Let the total flight time of the drone base station be T U , and is equally divided into M time slots δ U , that is, T U =Mδ U , each time slot can only serve one user, using a l [m]∈{0,1} represents the user served in the mth time slot. l [m] = 1 means that the UAV base station in the mth time slot serves the lth user, then there exists

[0075] The flight altitude of the drone base station is H, and its horizontal and vertical coordinates are p xy [m]=[x[m],y[m]] T , the 3D coordinates are p[m]=[x[m],y[m],H[m]] T ,

[0076] Due to bad weather, high-altitude buildings and other reasons, there is a cylindrical no-fly zone in the communication area. The bottom of the cylinder is p nf =[x nf ,y nf ] T The center is r and the radius is nf The airspace above the circle is a no-fly zone.

[0077] Since the drone base station has a certain flying altitude when flying, the channel between the drone base station and the ground user is considered to be controlled by the LoS link. In addition, it is assumed that the Doppler effect caused by the mobility of the drone is well compensated. Therefore, the link from the drone base station to the ground user is modeled as in represents the Euclidean distance from the drone base station to the ground user, α is the attenuation factor, It is a direct link. It should be noted that for legitimate users, the illegal detection party is a non-cooperative hidden node and it is difficult to obtain perfect CSI (Channel State Information). Therefore, even if the channel is estimated through the reflected signal, only imperfect CSI with errors can be obtained. We use an uncertain channel with error terms to represent the channel between the drone base station and the illegal detection party.

[0078] 2. Optimization Issues

[0079] Specifically, the optimization problem is established through the following steps:

[0080] For the lth user, the received signal in the mth time slot is y l [m] = a l [m]g U,l [m]w[m]x[m]+n l [m], where w[m] represents the beamforming vector of the drone base station, x[m] and P U represent the transmitted data signal and the maximum transmission power respectively, and satisfy E[|x[m]| 2 ]=1,||w[m]|| 2 ≤P U ; use a l [m]∈{0,1} represents the user served in the mth time slot. l [m]=1 means that the drone base station serves the lth user in the mth time slot.

[0081] Since the background noise of the legitimate receiving user will not affect the communication performance, it is assumed that its noise variance is stable, that is, C∈{1,...,L}. However, due to the real-time changes in the environment, the background noise n W [m] has uncertainty. The background noise uncertainty provides a covert cover for covert communication. The present invention applies a bounded uncertainty model to the noise power at the illegal detection party, and its probability density function (PDF) can be given by the following formula:

[0082]

[0083] Where: λ is the noise uncertainty coefficient, is the standard noise variance.

[0084] The achievable rate of the mth time slot is expressed as

[0085] For the illegal detection party, in order to achieve covert communication, it is necessary to ensure that the detection error probability at the illegal detection party is not less than 1-β. Combined with the expression of the detection error probability, it is equivalent to in It is the detection threshold at the illegal detection party.

[0086] Due to the existence of a no-fly zone, the trajectory of the drone cannot appear in the no-fly zone, so |p xy [m]-p nf |≥r nf .

[0087] The optimization problem P1 is formulated as:

[0088]

[0089] Where: represents the user service time slot coefficient set, a l [m]∈{0,1} represents the user served by the drone base station in the mth time slot. l [m] = 1 means that the UAV base station in the mth time slot serves the lth user; represents the beamforming vector set of the UAV base station, w[m] represents the beamforming vector of the UAV base station; represents the channel with error term, g U,W [m] represents the link from the drone base station to the user, Δg[m] represents the error term, δ g Indicates the error level; Represents the 3D flight trajectory set of the drone base station, p[m] = [x[m], y[m], H[m]] T represents the 3D coordinates of the drone base station, H represents the flight altitude of the drone base station; R l [m] represents the achievable rate of the mth time slot; Δg represents the channel uncertainty; C1 represents the location constraint of the no-fly zone, where the no-fly zone is a cylinder with the bottom of the cylinder at p nf =[x nf ,y nf ] T The center is r and the radius is nf The airspace above the circle is a no-fly zone; xy [m]=[x[m],y[m]] T represents the horizontal and vertical coordinates of the drone base station; C2 represents the covert communication constraint, τ β represents the detection threshold of the illegal detection party; C3 represents the transmission power constraint of the drone base station, P U represents the maximum transmission power; C4 and C5 represent the user service time slot coefficient constraints; C6 represents the flight speed constraint of the UAV, δ Urepresents the time slot; C7 represents the location constraint of the drone base station, p I and p F They represent the starting and ending positions of the UAV base station respectively; C8 represents the flight altitude constraint of the UAV base station, H min and H max They represent the minimum and maximum flight altitudes of the UAV base station respectively.

[0090] Specifically, the slack variable μ is introduced to transform the optimization problem P1 into the optimization problem P2:

[0091]

[0092] Where: M represents the total flight time T of the drone base station U Divide into time slots δ U The total number of g U,l [m] represents the link from the drone base station to the lth user; represents the variance of background noise;

[0093] The optimal solution of optimization problem P2 is equivalent to optimization problem P1, and the objective function of optimization problem P1 is equivalent to the objective function of optimization problem P2 and C9; at the optimal solution, the equation of C9 holds, otherwise the equation can be made valid by increasing μ, and such an operation will not reduce the optimal objective value of the optimization problem. For optimization problem P2, this optimization problem has non-convex operations such as maximization and integer programming, and there are infinite constraints and non-convex constraints caused by uncertain CSI. At the same time, there is a coupling relationship between the user service time slot coefficient, the beamforming vector and the 3D flight trajectory of the UAV-BS, which makes it difficult to obtain an effective closed solution. This paper decomposes the non-convex optimization problem into three sub-problems. When solving each sub-problem, the other two sub-problems are fixed respectively and solved in turn.

[0094] 3. User Service Slot Allocation Sub-Problem

[0095] In this embodiment, the beamforming vector set W and the 3D flight trajectory set P are fixed, and the constraints irrelevant to the user service time slot coefficient are removed, and the optimization problem P2 is converted into the user service time slot allocation sub-problem P3:

[0096]

[0097] This optimization problem is a 0-1 integer programming problem and can be solved using the optimization software package cvx.

[0098] 4. Beamforming to the Quantum Problem

[0099] In this embodiment, the user service time slot coefficient set A and the 3D flight trajectory set P are fixed, and the optimization problem P2 is converted into the beamforming vector quantum problem P4:

[0100]

[0101] Specifically, the beamforming vector quantum problem P4 is converted into the beamforming vector quantum problem P5 through the following steps:

[0102] The CSI (Channel State Information) in constraint C2 of the beamforming quantum problem P4 is uncertain and is converted using the Schur complement theorem:

[0103]

[0104] Will Substituting into the above formula, it can be further converted into:

[0105]

[0106] Substitute the above formula into the General Sign-Definiteness lemma and introduce the slack variable Combined with ||Δg[m]||≤δ g Equivalent to LMI:

[0107]

[0108] in, The dimension is N U The identity matrix of

[0109] For non-convex constraint C9, slack variables are introduced Convert C9 to and C10:

[0110]

[0111] Among them, C10 is further processed using the first-order Taylor inequality as follows:

[0112]

[0113] Among them, w (k),H [m] is the conjugate transpose of the k-th iteration value of the m-time slot beamforming vector; is the conjugate transpose of the m-slot UAV to user channel.

[0114] Finally, the beamforming vector quantum problem P5 is expressed as:

[0115]

[0116] This optimization subproblem is a convex optimization problem and can be solved using the optimization package cvx.

[0117] 5. 3D flight trajectory optimization sub-problem

[0118] In this embodiment, the user service time slot coefficient set A and the beamforming vector set W are fixed, and the optimization problem P2 is converted into a 3D flight trajectory optimization sub-problem P6:

[0119]

[0120] Specifically, the 3D flight trajectory optimization sub-problem P6 is converted into the 3D flight trajectory optimization sub-problem P7 through the following steps:

[0121] For non-convex constraints C1, square both sides of the constraint Its left side can be expressed as a lower bound:

[0122]

[0123] in, is a feasible solution for the kth time. Therefore, C1 can be transformed into the following C1:

[0124]

[0125] For the non-convex constraint C2, according to the triangle and Cauchy-Schwarz inequality:

[0126]

[0127] It should be noted that A2[m] is a constant that is independent of the trajectory, and the expression of A1[m] is a non-convex expression that contains the flight trajectory P, which is a tricky constraint. To solve this problem, considering that the change in distance from the k-1th iteration to the kth iteration is much smaller than the distance from the UAV-BS to the ground node, we use the result P of the k-1th iteration (k - 1) To approximate the trajectory information in A1[m].

[0128] Squaring both sides of the above equation yields:

[0129]

[0130] To further process the above equation, we introduce the slack variable And satisfy u Q [m]≤s U,W [m]. For D1[m], For D2[m], we have Therefore, C2 can be transformed into the following C2:

[0131]

[0132] in, is the introduced slack variable; α is the channel attenuation coefficient.

[0133] On the other hand, for the u brought by the slack variable Q [m]≤s U,W [m], converting it to Further:

[0134]

[0135] Where P (k) [m] is the result of the kth trajectory optimization. Therefore, it is equivalent to:

[0136]

[0137] For the non-convex constraint C9, similar to the previous section, we introduce the slack variable Convert C9 to and C10.

[0138] For C10, we further introduce variables satisfy It can be transformed into:

[0139]

[0140] right Performing a first-order Taylor expansion, C10 eventually becomes:

[0141]

[0142] The infinite constraints and non-convex constraints in the optimization problem P6 are processed, and the k-th recursive optimization problem eventually becomes the 3D flight trajectory optimization sub-problem P7:

[0143]

[0144] The solution algorithm for this optimization subproblem is similar to the previous two problems and can be solved using the optimization software package cvx.

[0145] 6. Alternating Optimization Algorithm

[0146] In this embodiment, the processing steps of the alternating optimization algorithm are as follows:

[0147] S401: Initialization: Setting the number of cycles k=0, the cutoff parameter and the maximum number of cycles N max And the initial 3D flight trajectory set P(0) and the beamforming vector set W (0) ;

[0148] S402: For a given 3D flight trajectory set P (k) and the beamforming vector set W (k) , (using CVX software package) solve the user service time slot allocation subproblem P3 and obtain the optimal user service time slot coefficient set A (k+1) =A (*) ;

[0149] S403: For a given 3D flight trajectory set P (k) and user service slot coefficient set A (k+1) , solve the beamforming vector quantum problem P5 (using the CVX software package) and obtain the optimal beamforming vector set W (k+1) =W (*) ;

[0150] S404: For a given user service time slot coefficient set A (k+1) and the beamforming vector set W (k+1) , (using CVX software package) solve the 3D flight trajectory optimization subproblem P7 and obtain the optimal 3D flight trajectory set P (k+1) =P (*) ;

[0151] S405: Set the number of loops k=k+1;

[0152] S406: If the cut-off parameter or the maximum number of cycles is reached, execute step S407; otherwise, return to step S402;

[0153] S407: Output the optimal user service time slot coefficient set A (*) , beamforming vector set W (*) and the 3D flight trajectory set P (*) and the optimal objective function value.

[0154] VII. Example

[0155] The system simulation of this embodiment adopts Matlab software, and the solution of the optimization problem adopts CVX software package.

[0156] The following example examines the effectiveness of a multi-user covert communication method based on time slot allocation and 3D trajectory optimization designed by the present invention.

[0157] This example verifies the effectiveness of the proposed algorithm through simulation results. On a three-dimensional plane with a horizontal and vertical coordinate length of 100m, L users Bob and illegal detection party Willie are randomly distributed on the three-dimensional plane, and their height is fixed at 1.5m. The initial and final positions of the drone are (0,0,50) and (100,100,50) respectively.

[0158] By default, typical values ​​of the parameters are as follows: d / λ = 0.5, cutoff parameter ε = 0.01 and maximum number of cycles K max =30, channel error δ g =0.01, attenuation factor α=2, N U =4, M = 10s, L = 5, v max =25m / s, r nf =10, v max =25m / s, the maximum power of UAV-BS P U =30dBm, background noise Noise uncertainty λ = 5, detection error probability 1-β = 0.98. The initial value of the beamforming vector is a random vector with maximum power, and the initial value of the flight trajectory is uniformly distributed at the initial position and the end position.

[0159] In order to demonstrate the superiority of the covert communication method proposed in the present invention, Figure 3 The average concealment rate of different schemes is compared with the change of transmission power. The comparison schemes include the 2D trajectory optimization scheme and the single antenna scheme. The 2D trajectory optimization scheme only considers the horizontal and vertical coordinates of the UAV-BS, and the flight altitude is fixed at 50m. The single antenna scheme means that the number of antennas of the UAV-BS is 1. When the transmission power increases, the average concealment rate of the proposed scheme increases accordingly. When there is channel uncertainty, when the transmission power is small, the UAV-BS can use all the power to send signals. As the transmission power increases, the UAV-BS cannot use all the power due to the concealment constraint, and the average concealment rate tends to be stable. By comparing the two curves of the proposed scheme and the 2D trajectory optimization scheme, the performance of the proposed 3D trajectory optimization scheme is better than that of the 2D trajectory optimization scheme, which reflects the performance advantage brought by the 3D trajectory optimization. By comparing the proposed scheme and the single antenna scheme, the performance of the scheme based on multiple antennas is better than that of the single antenna scheme, which reflects the beam directional gain of multiple antennas.

[0160] Figure 4The 3D trajectory of the UAV-BS of the proposed scheme is depicted. First, all three trajectories can effectively avoid the no-fly zone. Second, the height of the flight trajectory tends to the ground after the initial point. This is because the height of the legitimate receiving user is fixed at 1.5. The UAV-BS will try to get close to the user while satisfying the concealment constraint, thereby improving the communication performance. When the communication duration gradually increases, the UAV-BS has more time to serve the user, that is, more trajectory points are close to some users, thereby improving the average concealment rate of the minimum user.

[0161] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit the technical solution. Those skilled in the art should understand that those modifications or equivalent substitutions of the technical solution of the present invention that do not depart from the purpose and scope of the technical solution should be included in the scope of the claims of the present invention.

Claims

1. A multi-user covert communication method based on time slot allocation and 3D trajectory optimization, characterized in that: include: S1: Build a communication system where drone base stations serve multiple users; S2: Based on the communication system, an optimization problem is established to maximize the average concealment rate by jointly optimizing the user service time slot allocation, the transmitter beamforming vector and the 3D flight trajectory; S3: Split the optimization problem into the user service time slot allocation sub-problem, the beamforming vector sub-problem and the 3D flight trajectory optimization sub-problem; S4: Solve the alternating user service time slot allocation subproblem, beamforming vector subproblem and 3D flight trajectory optimization subproblem through the alternating optimization algorithm to obtain the communication strategy including the optimal user service time slot allocation, beamforming vector and 3D flight trajectory; S5: The communication system is guided by a communication strategy including optimal user service time slot allocation, beamforming vectors and 3D flight trajectory to achieve multi-user covert communication.

2. The multi-user covert communication method based on time slot allocation and 3D trajectory optimization as claimed in claim 1, characterized in that: In step S1, the communication system constructed is: A multi-antenna drone base station serves L users; there is an illegal detection party to detect whether there is legal communication; The 3D coordinates of the ground user, i.e. the user and the illegal detection party, are p C =[x C ,y C ,0] T ,C∈{1,...,L,W}, {1,...,L} represents the user set, and W represents the illegal detection party; Let the total flight time of the drone base station be T U , and is equally divided into M time slots δ U , that is, T U =Mδ U , each time slot can only serve one user, using a l [m]∈{0,1} represents the user served in the mth time slot. l [m] = 1 means that the UAV base station in the mth time slot serves the lth user, then there exists The flight altitude of the drone base station is H, and its horizontal and vertical coordinates are p xy [m]=[x[m],y[m]] T , the 3D coordinates are p[m]=[x[m],y[m],H[m]] T , There is a cylindrical no-fly zone within the communication area, the bottom of which is p nf =[x nf ,y nf ] T The center is r and the radius is nf The airspace above the circle is a no-fly zone.

3. The multi-user covert communication method based on time slot allocation and 3D trajectory optimization as claimed in claim 1, characterized in that: In step S2, the formula of the optimization problem P1 is expressed as: Where: represents the user service time slot coefficient set, a l [m]∈{0,1} represents the user served by the drone base station in the mth time slot. l [m] = 1 means that the UAV base station in the mth time slot serves the lth user; represents the beamforming vector set of the UAV base station, w[m] represents the beamforming vector of the UAV base station; represents the channel with error term, g U,W [m] represents the link from the drone base station to the user, Δg[m] represents the error term, δ g Indicates the error level; Represents the 3D flight trajectory set of the drone base station, p[m] = [x[m], y[m], H[m]] T represents the 3D coordinates of the drone base station, H represents the flight altitude of the drone base station; R l [m] represents the achievable rate of the mth time slot; Δg represents the channel uncertainty; C1 represents the location constraint of the no-fly zone, where the no-fly zone is a cylinder with the bottom of the cylinder at p nf =[x nf ,y nf ] T The center is r and the radius is nf The airspace above the circle is a no-fly zone; xy [m]=[x[m],y[m]] T represents the horizontal and vertical coordinates of the drone base station; C2 represents the covert communication constraint, τ β represents the detection threshold of the illegal detection party; C3 represents the transmission power constraint of the drone base station, P U represents the maximum transmission power; C4 and C5 represent the user service time slot coefficient constraints; C6 represents the flight speed constraint of the UAV, δ U represents the time slot; C7 represents the location constraint of the drone base station, p I and p F They represent the starting and ending positions of the UAV base station respectively; C8 represents the flight altitude constraint of the UAV base station, H min and H max They represent the minimum and maximum flight altitudes of the UAV base station respectively.

4. The multi-user covert communication method based on time slot allocation and 3D trajectory optimization as claimed in claim 3, characterized in that: In step S2, the slack variable μ is introduced to transform the optimization problem P1 into the optimization problem P2: Where: M represents the total flight time T of the drone base station U Divide into time slots δ U The total number of g U,l [m] represents the link from the drone base station to the lth user; Represents the variance of the background noise.

5. The multi-user covert communication method based on time slot allocation and 3D trajectory optimization as claimed in claim 4, characterized in that: In step S3, the beamforming vector set W and the 3D flight trajectory set P are fixed, and the optimization problem P2 is converted into the user service time slot allocation sub-problem P3:

6. The multi-user covert communication method based on time slot allocation and 3D trajectory optimization as claimed in claim 5, characterized in that: In step S3, the user service time slot coefficient set A and the 3D flight trajectory set P are fixed, and the optimization problem P2 is converted into the beamforming vector quantum problem P4:

7. The multi-user covert communication method based on time slot allocation and 3D trajectory optimization as claimed in claim 6, characterized in that: Transform the beamforming vector quantum problem P4 into the beamforming vector quantum problem P5: Where: The dimension is N U The identity matrix of (k),H [m] is the conjugate transpose of the k-th iteration value of the m-time slot beamforming vector; is the conjugate transpose of the m-slot UAV to user channel.

8. The multi-user covert communication method based on time slot allocation and 3D trajectory optimization as claimed in claim 7, characterized in that: Fix the user service time slot coefficient set A and the beamforming vector set W, and transform the optimization problem P2 into the 3D flight trajectory optimization sub-problem P6:

9. The multi-user covert communication method based on time slot allocation and 3D trajectory optimization as claimed in claim 8, characterized in that: Convert the 3D flight trajectory optimization subproblem P6 to the 3D flight trajectory optimization subproblem P7: Where: is the introduced slack variable; α is the channel attenuation coefficient.

10. The multi-user covert communication method based on time slot allocation and 3D trajectory optimization as claimed in claim 9, characterized in that: In step S4, the processing steps of the alternating optimization algorithm are as follows: S401: Initialization: Setting the number of cycles k=0, the cutoff parameter and the maximum number of cycles N max And the initial 3D flight trajectory set P (0) and the beamforming vector set W (0) ; S402: For a given 3D flight trajectory set P (k) and the beamforming vector set W (k) , solve the user service time slot allocation subproblem P3, and obtain the optimal user service time slot coefficient set A (k+1) =A (*) ; S403: For a given 3D flight trajectory set P (k) and user service slot coefficient set A (k+1) , solve the beamforming vector quantum problem P5 and obtain the optimal beamforming vector set W (k+1) =W (*) ; S404: For a given user service time slot coefficient set A (k+1) and the beamforming vector set W (k+1) , solve the 3D flight trajectory optimization subproblem P7 and obtain the optimal 3D flight trajectory set P (k+1) =P (*) ; S405: Set the number of loops k=k+1; S406: If the cut-off parameter or the maximum number of cycles is reached, execute step S407; Otherwise, return to step S402; S407: Output the optimal user service time slot coefficient set A (*) , beamforming vector set W (*) and the 3D flight trajectory set P (*) and the optimal objective function value.

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