A robust method for secure terahertz communication for unmanned aerial vehicles

Abstract

This invention discloses a robust terahertz secure communication method for unmanned aerial vehicles (UAVs). The method first establishes a UAV terahertz secure communication system; then, with the goal of minimizing the total transmit power of the UAV flight base station, it establishes an optimization problem involving the joint UAV trajectory Q, artificial noise vector f, and transmit beamforming vector w; finally, using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, it transforms the optimization problem into a solution, obtaining the optimal UAV trajectory set Q corresponding to minimizing the total transmit power P of the UAV flight base station. b Optimal artificial noise vector f b and the optimal transmit beamforming vector w b This communication method provides accurate channel estimation, resulting in low energy consumption for UAV base stations.

Description

Technical Field

[0001] This invention relates to the field of communications, and more specifically, to a robust method for secure terahertz communication for unmanned aerial vehicles (UAVs). Background Technology

[0002] Terahertz technology, as a potential 6G technology, holds promise for solving the problems of spectrum scarcity and capacity limitations in current wireless systems. However, terahertz communication is subject to severe propagation loss and molecular absorption, thus limiting transmission distance and communication capacity. Furthermore, obstacles in the propagation environment can directly block communication. Drones, due to their air-to-ground link characteristics, are well-suited for using terahertz channels for information transmission.

[0003] Traditional UAV terahertz communication methods assume overly ideal channel conditions, often failing to meet the needs of real-world environments. The existence of eavesdroppers in reality leads to imperfect channel conditions. Furthermore, UAVs are affected by environmental factors such as wind speed, causing instability and resulting in channel estimation errors for both users and eavesdroppers. Consequently, UAVs consume significant energy to compensate for these errors.

[0004] Existing technology discloses a downlink channel estimation method for UAV communication. This method estimates the channel state information by using a learned Long Short-Term Memory (LSTM) network based on the pilot signal and the channel frequency response at the pilot position. However, this method does not consider the actual channel state. Summary of the Invention

[0005] This invention addresses the shortcomings of existing technologies, such as errors in channel estimation leading to high energy consumption, by providing a robust UAV terahertz secure communication method.

[0006] The primary objective of this invention is to solve the aforementioned technical problems. The technical solution of this invention is as follows:

[0007] A robust method for secure terahertz communication for unmanned aerial vehicles (UAVs) includes:

[0008] S1: Establish a drone terahertz secure communication system, which includes a drone flight base station, multiple users, and an eavesdropper;

[0009] S2: Based on the aforementioned UAV terahertz secure communication system, and with the goal of minimizing the total transmit power of the UAV flight base station, establish a joint UAV trajectory. The optimization problem of artificial noise vector f and transmitted beamforming vector w;

[0010] S3: Using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, the optimization problem is transformed and solved to obtain the optimal UAV trajectory set corresponding to the minimum total transmit power P of the UAV flight base station. Optimal artificial noise vector f b and the optimal transmit beamforming vector w b .

[0011] Furthermore, in the aforementioned UAV terahertz secure communication system, the UAV base station communicates with each user through a first channel, and the UAV base station communicates with the eavesdropper through a second channel;

[0012] The estimation of the first channel uncertainty gain for the nth time slot is as follows:

[0013]

[0014] The terahertz path gain of the first channel is as follows:

[0015]

[0016] The transmission rate of the first channel in the nth time slot for the kth user is as follows:

[0017]

[0018] The eavesdropping rate of the eavesdropper on the first channel of the k-th user in the n-th time slot is as follows:

[0019]

[0020] Where j and k represent user sequence numbers, and n represents time slot sequence numbers. This represents the terahertz path gain of the first channel. The frequency represents the communication frequency, C represents the speed of light, and d represents the speed of light. k [n] represents the distance from the k-th user in the n-th time slot to the drone base station, k f Indicates the medium absorption factor; This represents the conjugate transpose of the channel uncertainty gain for the k-th user in the n-th time slot. The conjugate transpose of the second channel uncertainty gain of the eavesdropper in the nth time slot; w k [n] represents the transmit beamforming vector of the k-th user in the n-th time slot, f[n] represents the artificial noise vector in the n-th time slot, σ e σ represents the power spectral density of the white noise in the second channel; k This represents the white noise power spectral density of the first channel for the k-th user. This represents the guidance vector from the drone base station to the k-th user.

[0021] Furthermore, the optimization problem is as follows:

[0022]

[0023] The constraints are as follows:

[0024] (x[n+1]-x[n]) 2 +(y[n+1]-y[n]) 2 ≤(v max ·ΔT) 2

[0025]

[0026] q[0]=q0

[0027] k represents the user sequence number, k represents all users; n represents the time slot sequence number, N represents all time slots; w k [n] represents the beamforming vector for the k-th user in the n-th time slot; w k Let w represent the beamforming vector of the k-th user. k ={w k [1],w k [2],…,w k [N]};w represents the user's beamforming vector w={w1,w2,…,w K};f[n] represents the artificial noise vector sent by the UAV base station in the nth time slot; f[n] represents the artificial noise vector sent by the UAV base station in the nth time slot, f represents the artificial noise vector sent by the UAV base station, f={f[1],f[2],…,f[N]}; Let x[n] represent the set of trajectories of the UAV; x[n] represents the x-coordinate of the UAV in the nth time slot, and y[n] represents the y-coordinate of the UAV in the nth time slot; v max ΔT represents the maximum speed of the drone; ΔT represents the duration of each time slot; Δh k [n] represents the channel gain estimation error of the first time slot for the k-th user, Δh e [n] represents the second channel gain estimation error in the nth time slot; ε k [n] represents the upper limit of the channel gain estimation error for the first channel in the nth time slot for the kth user, ε e [n] represents the upper limit of the second channel gain estimation error in the nth time slot; R k [n] represents the transmission rate of the first channel in the nth time slot for the kth user. This represents the eavesdropping rate of the eavesdropper on the first channel of the k-th user in the n-th time slot; This represents the minimum transmission rate of the first channel for the k-th user. The second channel transmission rate is represented by q[0] and q0, which represent the initial trajectory of the UAV.

[0028] Further, in step S3, the optimization problem is transformed and solved using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, including:

[0029] S301: Based on the aforementioned joint drone trajectory The optimization problem of artificial noise vector f and transmitted beamforming vector w is solved, and the first optimization objective and the second optimization objective are derived.

[0030] S302: Using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, solve for the first and second optimization objectives; obtain the optimal UAV trajectory set corresponding to the minimum total transmit power P of the UAV flight base station. Optimal artificial noise vector f b and the optimal transmit beamforming vector w b .

[0031] Furthermore, the first optimization objective is as follows:

[0032]

[0033] The constraints are as follows:

[0034] W k [n]≥0,F[n]≥0

[0035]

[0036] rank(W k [n])=1,rank(F[n])=1

[0037] k represents the user sequence number, K represents all users; n represents the time slot sequence number, N represents all time slots; w k [n] represents the beamforming vector of the k-th user in the n-th time slot, W k [n] represents the beamforming vector product of the k-th user in the n-th time slot. w k Let w represent the beamforming vector of the k-th user. k ={w k [1],w k [2],…,w k [N]};w represents the user's beamforming vector w={w1,w2,…,w K};f[n] represents the artificial noise vector sent by the UAV base station in the nth time slot, and F[n] represents the product of the artificial noise vectors sent by the UAV base station in the nth time slot; λ k [n] represents the non-negative relaxation variable of the k-th user in the n-th time slot, I M Γ represents the identity matrix; k[n] represents the gamma function of the k-th user in the n-th time slot; Let represent the conjugate transpose of the estimated first channel uncertainty gain for the k-th user in the n-th time slot. λ represents the estimated first channel uncertainty gain for the k-th user in the n-th time slot; e [n] represents the second channel relaxation variable in the nth time slot, W e [n] represents the product of the eavesdropper beamforming vectors in the nth time slot. Let represent the conjugate transpose of the estimated second channel uncertainty gain for the nth time slot. Γ represents the estimated second channel uncertainty gain for the nth time slot; e [n] represents the gamma function of the eavesdropper in the nth time slot.

[0038] Furthermore, the second optimization objective is as follows:

[0039]

[0040] The constraints are as follows:

[0041] (x[n+1]-x[n]) 2 +(y[n+1]-y[n]) 2 ≤(v max ·ΔT) 2

[0042]

[0043] l represents the current iteration number; 2 represents the set of drone trajectories; k represents the user sequence number; n represents the time slot sequence number; x[n] represents the x-coordinate of the drone's nth time slot. (l-1) Let y[n] represent the x-coordinate of the UAV in the (l-1)th time slot, and let y[n] represent the y-coordinate of the UAV in the nth time slot. (l-1) This represents the ordinate of the nth time slot of the UAV in the (l-1)th iteration, (x k ,y k (x, 0) represents the position of the k-th user, (x e ,y e () indicates the location of the eavesdropper; v max The maximum speed of the drone is represented by ΔT; the duration of each time slot is represented by β. 1,k [n] represents the first intermediate value of the nth time slot for the kth user; β 2,k [n] represents the second intermediate value of the nth time slot for the kth user; β 3,k [n] represents the third intermediate value of the k-th user in the n-th time slot; u represents the square of the slack variable for the k-th user in the n-th time slot. k [n] represents the slack variable for the k-th user in the n-th time slot. u represents the square of the slack variable for the k-th user in the n-th time slot during the (l-1)-th iteration. k [n] (l-1) Let represent the slack variable for the k-th user in the n-th time slot during the (l-1)-th iteration; This represents the minimum transmission rate of the first channel for the k-th user; k f The medium absorption factor is represented by H, which represents the height of the UAV; β 1,e [n] represents the first intermediate value of the eavesdropper in the nth time slot, β 2,e [n] represents the second intermediate value of the eavesdropper in the nth time slot, β 3,e [n] represents the third intermediate value of the eavesdropper in the nth time slot; Indicates the maximum transmission rate of the second channel; u e [n] represents the slack variable of the eavesdropper in the nth time slot. u represents the square of the slack variable in the nth time slot of the eavesdropper. e [n] (l-1) Let n be the relaxation variable of the eavesdropper in the (l-1)th iteration. Let represent the square of the slack variable of the eavesdropper in the nth time slot during the (l-1)th iteration.

[0044] Furthermore, the first intermediate value β of the k-th user in the n-th time slot 1,k [n] is as follows:

[0045]

[0046] The second intermediate value β of the k-th user in the n-th time slot 2,k [n] is as follows:

[0047]

[0048] The third intermediate value β of the k-th user in the n-th time slot 3,k [n] is as follows:

[0049]

[0050] Where ρ1 represents the first probability of error; j and k represent user serial numbers; n represents time slot serial number; and l represents the current iteration number. w represents the trajectory variable of the k-th user in the n-th time slot during the (l-1)-th iteration. k [n] represents the beamforming vector of the k-th user in the n-th time slot, and f[n] represents the artificial noise vector sent by the UAV base station in the n-th time slot.

[0051] Furthermore, the first intermediate value β of the eavesdropper in the nth time slot 1,e [n] is as follows:

[0052]

[0053] The second intermediate value β of the eavesdropper in the nth time slot 2,e [n] is as follows:

[0054]

[0055] The third intermediate value β of the eavesdropper in the nth time slot 3,e [n] is as follows:

[0056]

[0057] Where ρ2 represents the second error probability; j and k represent user serial numbers, n represents time slot serial number, and l represents the current iteration number. w represents the trajectory variable of the eavesdropper in the nth time slot during the (l-1)th iteration. k [n] represents the beamforming vector of the k-th user in the n-th time slot, and f[n] represents the artificial noise vector sent by the UAV base station in the n-th time slot.

[0058] Furthermore, the first error probability ρ1 is as follows:

[0059]

[0060] The second error probability ρ2 is as follows:

[0061]

[0062] Where f represents the artificial noise vector sent by the drone base station, C represents the speed of light, and σ e σ represents the power spectral density of the white noise in the second channel; k This represents the white noise power spectral density of the first channel for the k-th user.

[0063] Further, in step S302, the first optimization objective and the second optimization objective are solved using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, including:

[0064] S30201: Initialize the trajectory set of the first UAV First artificial noise vector f 1 and the first user beamforming vector w 1 And calculate the first total transmit power P. 1 ;

[0065] S30202: Based on the trajectory set of the first UAV Solving the first optimization objective yields the second artificial noise vector f. 2 Second user beamforming vector w 2 ;

[0066] S30203: According to the second artificial noise vector f 2 Second user beamforming vector w 2 Solve the second optimization objective to obtain the trajectory set of the second UAV.

[0067] S30204: According to the second artificial noise vector f 2 Second user beamforming vector w 2 The trajectory set of the second UAV Calculate the second total transmit power P 2 ;

[0068] S30205: Judgment Is it greater than a preset value? If so, then set the trajectory of the second UAV. As a new first drone trajectory set Execute step S30202; if not, collect the trajectories of the second UAV. As the optimal set of drone trajectories The second artificial noise vector f 2 As the optimal artificial noise vector f b The second user beamforming vector w 2 w, as the optimal transmit beamforming vector b .

[0069] Compared with the prior art, the beneficial effects of the present invention are:

[0070] This invention establishes an optimization problem by setting up a UAV terahertz secure communication system and minimizing the total transmission power of the UAV flight base station. Finally, the optimization problem is solved to make the channel estimation of the UAV flight base station more accurate, thereby reducing the energy consumption of the UAV flight base station. Attached Figure Description

[0071] Figure 1 A flowchart illustrating a robust UAV terahertz secure communication method provided for an embodiment.

[0072] Figure 2 The flowchart provided for the embodiment uses the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm to transform and solve the optimization problem.

[0073] Figure 3The flight trajectory diagram of the drone provided for the embodiment.

[0074] Figure 4 The convergence polygon provided in the embodiment is a line graph of the solution to the optimization problem using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm. Detailed Implementation

[0075] The accompanying drawings are for illustrative purposes only and should not be construed as limiting the scope of this patent.

[0076] To better illustrate this embodiment, some parts in the accompanying drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions;

[0077] It will be understood by those skilled in the art that certain well-known structures and their descriptions may be omitted in the accompanying drawings.

[0078] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0079] Example

[0080] like Figure 1 As shown, a robust UAV terahertz secure communication method includes:

[0081] S1: Establish a drone terahertz secure communication system, which includes a drone flight base station, multiple users, and an eavesdropper;

[0082] S2: Based on the aforementioned UAV terahertz secure communication system, and with the goal of minimizing the total transmit power of the UAV flight base station, establish a joint UAV trajectory. The optimization problem of artificial noise vector f and transmitted beamforming vector w;

[0083] S3: Using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, the optimization problem is transformed and solved to obtain the optimal UAV trajectory set corresponding to the minimum total transmit power P of the UAV flight base station. Optimal artificial noise vector f b and the optimal transmit beamforming vector w b .

[0084] Furthermore, in the aforementioned UAV terahertz secure communication system, the UAV base station communicates with each user through a first channel, and the UAV base station communicates with the eavesdropper through a second channel;

[0085] The estimation of the first channel uncertainty gain for the nth time slot is as follows:

[0086]

[0087] The terahertz path gain of the first channel is as follows:

[0088]

[0089] The transmission rate of the first channel in the nth time slot for the kth user is as follows:

[0090]

[0091] The eavesdropping rate of the eavesdropper on the first channel of the k-th user in the n-th time slot is as follows:

[0092]

[0093] Where j and k represent user sequence numbers, and n represents time slot sequence numbers. This represents the terahertz path gain of the first channel. The frequency represents the communication frequency, C represents the speed of light, and d represents the speed of light. k [n] represents the distance from the k-th user in the n-th time slot to the drone base station, k f Indicates the medium absorption factor; This represents the conjugate transpose of the channel uncertainty gain for the k-th user in the n-th time slot. The conjugate transpose of the second channel uncertainty gain of the eavesdropper in the nth time slot; w k [n] represents the transmit beamforming vector of the k-th user in the n-th time slot, f[n] represents the artificial noise vector in the n-th time slot, σ e σ represents the power spectral density of the white noise in the second channel; k This represents the white noise power spectral density of the first channel for the k-th user. This represents the guidance vector from the drone base station to the k-th user.

[0094] In one specific embodiment, the guidance vector from the drone base station to the k-th user is as follows:

[0095]

[0096] The estimation of the second channel uncertainty gain for the nth time slot is as follows:

[0097]

[0098] The terahertz path gain of the second channel is as follows:

[0099]

[0100] The guidance vector from the drone base station to the eavesdropper is as follows:

[0101]

[0102] sinφ k[n] represents the angle of arrival from the k-th user in the n-th time slot to the drone base station, where d and λ are constants, and M is the total number of users. e [n] represents the distance from the eavesdropper to the drone base station. The terahertz path gain of the second channel is represented by sinφ. e [n] represents the angle of arrival from the eavesdropper's household in the nth time slot to the drone base station.

[0103] Furthermore, the optimization problem is as follows:

[0104]

[0105] The constraints are as follows:

[0106] (x[n+1]-x[n]) 2 +(y[n+1]-y[n]) 2 ≤(v max ·ΔT) 2

[0107]

[0108] q[0]=q0

[0109] k represents the user sequence number, K represents all users; n represents the time slot sequence number, N represents all time slots; w k [n] represents the beamforming vector for the k-th user in the n-th time slot; w k Let w represent the beamforming vector of the k-th user. k ={w k [1],w k [2],…,w k [N]};w represents the user's beamforming vector w={w1,w2,…,w K};f[n] represents the artificial noise vector sent by the UAV base station in the nth time slot; f[n] represents the artificial noise vector sent by the UAV base station in the nth time slot, f represents the artificial noise vector sent by the UAV base station, f={f[1],f[2],…,f[N]};2 represents the trajectory set of the UAV; x[n] represents the horizontal coordinate of the UAV in the nth time slot, y[n] represents the vertical coordinate of the UAV in the nth time slot; v max ΔT represents the maximum speed of the drone; ΔT represents the duration of each time slot; Δh k [n] represents the channel gain estimation error of the first time slot for the k-th user, Δh e [n] represents the second channel gain estimation error in the nth time slot; ε k [n] represents the upper limit of the channel gain estimation error for the first channel in the nth time slot for the kth user, ε e[n] represents the upper limit of the second channel gain estimation error in the nth time slot; R k [n] represents the transmission rate of the first channel in the nth time slot for the kth user. This represents the eavesdropping rate of the eavesdropper on the first channel of the k-th user in the n-th time slot; This represents the minimum transmission rate of the first channel for the k-th user. The second channel transmission rate is represented by q[0] and q0, which represent the initial trajectory of the UAV.

[0110] In one specific embodiment, the first channel gain estimation error Δh for the k-th user in the n-th time slot k [n], the estimated first channel uncertainty gain for the k-th user in the n-th time slot. The first channel uncertainty gain h for the k-th user in the n-th time slot k [n], the upper limit of the first channel gain estimation error ε for the k-th user in the n-th time slot. k [n] satisfies:

[0111]

[0112] In one specific embodiment, the second channel gain estimation error Δh in the nth time slot e [n], the estimated second channel uncertainty gain for the nth time slot. The eavesdropper's second channel uncertainty gain h in the nth time slot e [n], the upper limit of the second channel gain estimation error ε in the nth time slot. e [n] satisfies:

[0113]

[0114] In one specific embodiment, the signal transmitted by the drone is as follows:

[0115]

[0116] The signal received by the k-th user in the n-th time slot is as follows:

[0117]

[0118] The signal received by the eavesdropper in the nth time slot is as follows:

[0119]

[0120] n k [n] represents the Gaussian white noise received by the k-th user in the n-th time slot, n e [n] represents the Gaussian white noise received by the eavesdropper in the nth time slot, and s[n] represents a constant.

[0121] In one specific embodiment, constraints

[0122]

[0123] Can be written as:

[0124]

[0125] This can be further deduced as follows:

[0126]

[0127] In one specific embodiment, the optimization problem can be further transformed into:

[0128]

[0129] The constraints are as follows:

[0130]

[0131] rank(W k [n])=1,rank(F[n])=1

[0132] W k [n]≥0,F[n]≥0

[0133] In one specific embodiment, q[n] = (x[n], y[n], H), and the location of the drone is the location of the drone base station.

[0134] Furthermore, such as Figure 2 As shown, in step S3, the optimization problem is transformed and solved using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, including:

[0135] S301: Based on the aforementioned joint drone trajectory The optimization problem of artificial noise vector f and transmitted beamforming vector w is solved, and the first optimization objective and the second optimization objective are derived.

[0136] S302: Using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, solve for the first and second optimization objectives; obtain the optimal UAV trajectory set corresponding to the minimum total transmit power P of the UAV flight base station. Optimal artificial noise vector f b and the optimal transmit beamforming vector w b .

[0137] Furthermore, the first optimization objective is as follows:

[0138]

[0139] The constraints are as follows:

[0140] W k [n]≥0,F[n]≥0

[0141]

[0142] rank(w k [n])=1,rank(F[n])=1

[0143] k represents the user sequence number, K represents all users; n represents the time slot sequence number, n represents all time slots; w k [n] represents the beamforming vector of the k-th user in the n-th time slot, W k [n] represents the beamforming vector product of the k-th user in the n-th time slot. w k Let w represent the beamforming vector of the k-th user. k ={w k [1],w k [2],…,w k [N]};w represents the user's beamforming vector w={w1,w2,…,w K};f[n] represents the artificial noise vector sent by the UAV base station in the nth time slot, and F[n] represents the product of the artificial noise vectors sent by the UAV base station in the nth time slot; λ k [n] represents the non-negative relaxation variable of the k-th user in the n-th time slot, I M Γ represents the identity matrix; k [n] represents the gamma function of the k-th user in the n-th time slot; Let represent the conjugate transpose of the estimated first channel uncertainty gain for the k-th user in the n-th time slot. λ represents the estimated first channel uncertainty gain for the k-th user in the n-th time slot; e [n] represents the second channel relaxation variable in the nth time slot, W e [n] represents the product of the eavesdropper beamforming vectors in the nth time slot. Let represent the conjugate transpose of the estimated second channel uncertainty gain for the nth time slot. Γ represents the estimated second channel uncertainty gain for the nth time slot; e [n] represents the gamma function of the eavesdropper in the nth time slot.

[0144] Furthermore, the second optimization objective is as follows:

[0145]

[0146] The constraints are as follows:

[0147] (x[n+1]-x[n]) 2 +(y[n+1]-y[n]) 2 ≤(v max ·ΔT) 2

[0148]

[0149] l represents the current iteration number; Let represent the set of drone trajectories; k represents the user sequence number, n represents the time slot sequence number; x[n] represents the x-coordinate of the drone's nth time slot. (l-1) Let y[n] represent the x-coordinate of the UAV in the (l-1)th time slot, and let y[n] represent the y-coordinate of the UAV in the nth time slot. (l-1) This represents the ordinate of the nth time slot of the UAV in the (l-1)th iteration, (x k ,y k (x, 0) represents the position of the k-th user, (x e ,y e () indicates the location of the eavesdropper; v max The maximum speed of the drone is represented by ΔT; the duration of each time slot is represented by β. 1,k [n] represents the first intermediate value of the nth time slot for the kth user; β 2,k [n] represents the second intermediate value of the nth time slot for the kth user; β 3,k [n] represents the third intermediate value of the k-th user in the n-th time slot; u represents the square of the slack variable for the k-th user in the n-th time slot. k [n] represents the slack variable for the k-th user in the n-th time slot. u represents the square of the slack variable for the k-th user in the n-th time slot during the (l-1)-th iteration. k [n] (l-1) Let represent the slack variable for the k-th user in the n-th time slot during the (l-1)-th iteration; This represents the minimum transmission rate of the first channel for the k-th user; k f The medium absorption factor is represented by H, which represents the height of the UAV; β 1,e [n] represents the first intermediate value of the eavesdropper in the nth time slot, β 2,e [n] represents the second intermediate value of the eavesdropper in the nth time slot, β 3,e [n] represents the third intermediate value of the eavesdropper in the nth time slot; Indicates the maximum transmission rate of the second channel; u e [n] represents the slack variable of the eavesdropper in the nth time slot. u represents the square of the slack variable in the nth time slot of the eavesdropper. e [n] (l-1) Let n be the relaxation variable of the eavesdropper in the (l-1)th iteration. Let represent the square of the slack variable of the eavesdropper in the nth time slot during the (l-1)th iteration.

[0150] Furthermore, the first intermediate value β of the k-th user in the n-th time slot 1,k [n] is as follows:

[0151]

[0152] The second intermediate value β of the k-th user in the n-th time slot 2,k [n] is as follows:

[0153]

[0154] The third intermediate value β of the k-th user in the n-th time slot 3,k [n] is as follows:

[0155]

[0156] Where ρ1 represents the first probability of error; j and k represent user serial numbers; n represents time slot serial number; and l represents the current iteration number. w represents the trajectory variable of the k-th user in the n-th time slot during the (l-1)-th iteration. k [n] represents the beamforming vector of the k-th user in the n-th time slot, and f[n] represents the artificial noise vector sent by the UAV base station in the n-th time slot.

[0157] Furthermore, the first intermediate value β of the eavesdropper in the nth time slot 1,e [n] is as follows:

[0158]

[0159] The second intermediate value β of the eavesdropper in the nth time slot 2,e [n] is as follows:

[0160]

[0161] The third intermediate value β of the eavesdropper in the nth time slot 3,e [n] is as follows:

[0162]

[0163] Where ρ2 represents the second error probability; j and k represent user serial numbers, n represents time slot serial number, and l represents the current iteration number. w represents the trajectory variable of the eavesdropper in the nth time slot during the (l-1)th iteration. k [n] represents the beamforming vector of the k-th user in the n-th time slot, and f[b] represents the artificial noise vector sent by the UAV base station in the n-th time slot.

[0164] Furthermore, the first error probability ρ1 is as follows:

[0165]

[0166] The second error probability ρ2 is as follows:

[0167]

[0168] Where f represents the artificial noise vector sent by the drone base station, C represents the speed of light, and σ e σ represents the power spectral density of the white noise in the second channel; k This represents the white noise power spectral density of the first channel for the k-th user.

[0169] Further, in step S302, the first optimization objective and the second optimization objective are solved using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, including:

[0170] S30201: Initialize the trajectory set of the first UAV First artificial noise vector f 1 and the first user beamforming vector w 1 And calculate the first total transmit power P. 1 ;

[0171] S30202: Based on the trajectory set of the first UAV Solving the first optimization objective yields the second artificial noise vector f. 2 Second user beamforming vector w 2 ;

[0172] S30203: According to the second artificial noise vector f 2 Second user beamforming vector w 2 Solve the second optimization objective to obtain the trajectory set of the second UAV.

[0173] S30204: According to the second artificial noise vector f 2 Second user beamforming vector w 2 The second set of drone trajectories Calculate the second total transmit power P 2 ;

[0174] S30205: Judgment Is it greater than a preset value? If so, then set the trajectory of the second UAV. As a new first drone trajectory set Execute step S30202; if not, collect the trajectories of the second UAV. As the optimal set of drone trajectories The second artificial noise vector f 2 As the optimal artificial noise vector f b The second user beamforming vector w 2 w, as the optimal transmit beamforming vector b .

[0175] In one specific embodiment, the total number of users K is set to 2, the drone flight time T is 20s, the drone flight altitude H is 15m, and the drone's maximum speed v is... max It is 4 m / s; such as Figure 3 As shown, the drone flies from the starting point (0m, 0m, 15m) to the ending point (0m, 30m, 15m). The user's positions are (6m, 5m) and (6m, 25m), and the eavesdropper's position is (-2m, 15m). The upper limit of the channel normalization uncertainty is... Minimum transmission rate of the first channel for the kth user Maximum transmission rate of the second channel Medium absorption factor k f =0.05, communication frequency The value is 0.8 THZ; the square of the white noise power spectral density in the second channel is σ. e 2 The square of the white noise power spectral density of the first channel for the k-th user, σ k 2 All are -110dBm.

[0176] like Figure 4 As shown, the algorithm converges under different security rate thresholds, demonstrating good convergence. Furthermore, as the minimum security rate threshold for users increases, the total transmit power required by the base station increases, necessitating greater transmit power to meet higher security performance requirements.

[0177] The same or similar labels correspond to the same or similar parts;

[0178] The terms used to describe positional relationships in the accompanying drawings are for illustrative purposes only and should not be construed as limiting this patent.

[0179] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the implementation of the present invention. Those skilled in the art can make other variations or modifications based on the above description. It is neither necessary nor possible to exhaustively describe all embodiments here. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the claims of the present invention.

Claims

1. A robust terahertz secure communication method for unmanned aerial vehicles (UAVs), characterized in that, include: S1: Establish a drone terahertz secure communication system, which includes a drone flight base station, multiple users, and an eavesdropper; S2: Based on the aforementioned UAV terahertz secure communication system, and with the goal of minimizing the total transmit power of the UAV flight base station, establish a joint UAV trajectory. The optimization problem of artificial noise vector f and transmitted beamforming vector w; S3: Using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, the optimization problem is transformed and solved to obtain the optimal UAV trajectory set corresponding to the minimum total transmit power P of the UAV flight base station. Optimal artificial noise vector f b and the optimal transmit beamforming vector w b ; In step S3, the optimization problem is transformed and solved using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, including: S301: Based on the aforementioned joint drone trajectory The optimization problem of artificial noise vector f and transmitted beamforming vector w is solved, and the first optimization objective and the second optimization objective are derived. S302: Using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, solve for the first and second optimization objectives; obtain the optimal UAV trajectory set corresponding to the minimum total transmit power P of the UAV flight base station. Optimal artificial noise vector f b and the optimal transmit beamforming vector w b ; In step S302, the first and second optimization objectives are solved using the block coordinate descent method and the S-process semidefinite relaxation successive convex approximation algorithm, including: S30201: Initialize the trajectory set of the first UAV First artificial noise vector f 1 and the first user beamforming vector w 1 And calculate the first total transmit power P. 1 ; S30202: Based on the trajectory set of the first UAV Solving the first optimization objective yields the second artificial noise vector f. 2 Second user beamforming vector w 2 ; S30203: According to the second artificial noise vector f 2 Second user beamforming vector w 2 Solve the second optimization objective to obtain the trajectory set of the second UAV. S30204: According to the second artificial noise vector f 2 Second user beamforming vector w 2 The trajectory set of the second UAV Calculate the second total transmit power P 2 ; S30205: Judgment Is it greater than a preset value? If so, then set the trajectory of the second UAV. As a new first drone trajectory set Execute step S30202; if not, collect the trajectories of the second UAV. As the optimal set of drone trajectories The second artificial noise vector f 2 As the optimal artificial noise vector f b The second user beamforming vector w 2 w, as the optimal transmit beamforming vector b .

2. The robust UAV terahertz secure communication method according to claim 1, characterized in that, In the aforementioned UAV terahertz secure communication system, the UAV base station communicates with each user through a first channel, and the UAV base station communicates with the eavesdropper through a second channel. The estimation of the first channel uncertainty gain for the nth time slot is as follows: The terahertz path gain of the first channel is as follows: The transmission rate of the first channel in the nth time slot for the kth user is as follows: The eavesdropping rate of the eavesdropper on the first channel of the nth time slot of the kth user is as follows: Where j and k represent user sequence numbers, and n represents time slot sequence numbers. This represents the terahertz path gain of the first channel. The frequency represents the communication frequency, C represents the speed of light, and d represents the speed of light. k [n] represents the distance from the k-th user in the n-th time slot to the drone base station, k f Indicates the medium absorption factor; This represents the conjugate transpose of the channel uncertainty gain for the k-th user in the n-th time slot. The conjugate transpose of the second channel uncertainty gain of the eavesdropper in the nth time slot; w k [n] represents the transmit beamforming vector of the k-th user in the n-th time slot, f[n] represents the artificial noise vector in the n-th time slot, σ e σ represents the power spectral density of the white noise in the second channel; k This represents the white noise power spectral density of the first channel for the k-th user. This represents the guidance vector from the drone base station to the k-th user.

3. The robust UAV terahertz secure communication method according to claim 2, characterized in that, The optimization problem is as follows: The constraints are as follows: q[0]=q0 k represents the user sequence number, K represents all users; n represents the time slot sequence number, N represents all time slots; w k [n] represents the beamforming vector for the k-th user in the n-th time slot; w k Let w represent the beamforming vector of the k-th user. k ={w k [1],w k [2],…,w k [N]};w represents the user's beamforming vector w={w1,w2,…,w K };f[n] represents the artificial noise vector sent by the UAV base station in the nth time slot; f[n] represents the artificial noise vector sent by the UAV base station in the nth time slot, f represents the artificial noise vector sent by the UAV base station, f={f[1],f[2],…,f[N]}; Let x[n] represent the set of trajectories of the UAV; x[n] represents the x-coordinate of the UAV in the nth time slot, and y[n] represents the y-coordinate of the UAV in the nth time slot; v max ΔT represents the maximum speed of the drone; ΔT represents the duration of each time slot; Δh k [n] represents the channel gain estimation error of the first time slot for the k-th user, Δh e [n] represents the second channel gain estimation error in the nth time slot; ε k [n] represents the upper limit of the channel gain estimation error for the first channel in the nth time slot for the kth user, ε e [n] represents the upper limit of the second channel gain estimation error in the nth time slot; R k [n] represents the transmission rate of the first channel in the nth time slot for the kth user. This represents the eavesdropping rate of the eavesdropper on the first channel of the k-th user in the n-th time slot; This represents the minimum transmission rate of the first channel for the k-th user. The second channel transmission rate is represented by q[0] and q0, which represent the initial trajectory of the UAV.

4. The robust UAV terahertz secure communication method according to claim 1, characterized in that, The first optimization objective is as follows: The constraints are as follows: rank(W k [n])=1,rank(F[n])=1 k represents the user sequence number, K represents all users; n represents the time slot sequence number, N represents all time slots; w k [n] represents the beamforming vector of the k-th user in the n-th time slot, W k [n] represents the beamforming vector product of the k-th user in the n-th time slot. w k Let w represent the beamforming vector of the k-th user. k ={w k [1],w k [2],…,w k [N]};w represents the user's beamforming vector w={w1,w2,…,w K };f[n] represents the artificial noise vector sent by the UAV base station in the nth time slot, and F[n] represents the product of the artificial noise vectors sent by the UAV base station in the nth time slot; λ k [n] represents the non-negative relaxation variable of the k-th user in the n-th time slot, I M Γ represents the identity matrix; k [n] represents the gamma function of the k-th user in the n-th time slot; Let represent the conjugate transpose of the estimated first channel uncertainty gain for the k-th user in the n-th time slot. λ represents the estimated first channel uncertainty gain for the k-th user in the n-th time slot; e [n] represents the second channel relaxation variable in the nth time slot, W e [n] represents the product of the eavesdropper beamforming vectors in the nth time slot. Let represent the conjugate transpose of the estimated second channel uncertainty gain for the nth time slot. Γ represents the estimated second channel uncertainty gain for the nth time slot; e [n] represents the gamma function of the eavesdropper in the nth time slot.

5. A robust UAV terahertz secure communication method according to claim 1, characterized in that, The second optimization objective is as follows: The constraints are as follows: l represents the current iteration number; Let represent the set of drone trajectories; k represents the user sequence number, n represents the time slot sequence number; x[n] represents the x-coordinate of the drone's nth time slot. (l-1) Let y[n] represent the x-coordinate of the UAV in the (l-1)th time slot, and let y[n] represent the y-coordinate of the UAV in the nth time slot. (l-1) This represents the ordinate of the nth time slot of the UAV in the (l-1)th iteration, (x k ,y k (x, 0) represents the position of the k-th user, (x, 0) e ,y e () indicates the location of the eavesdropper; v max The maximum speed of the drone is represented by ΔT; the duration of each time slot is represented by β. 1,k [n] represents the first intermediate value of the nth time slot for the kth user; β 2,k [n] represents the second intermediate value of the nth time slot for the kth user; β 3,k [n] represents the third intermediate value of the k-th user in the n-th time slot; u represents the square of the slack variable for the k-th user in the n-th time slot. k [n] represents the slack variable for the k-th user in the n-th time slot. u represents the square of the slack variable for the k-th user in the n-th time slot during the (l-1)-th iteration. k [n] (l-1) Let represent the slack variable for the k-th user in the n-th time slot during the (l-1)-th iteration; This represents the minimum transmission rate of the first channel for the k-th user; k f The medium absorption factor is represented by H, which represents the height of the UAV; β 1,e [n] represents the first intermediate value of the eavesdropper in the nth time slot, β 2,e [n] represents the second intermediate value of the eavesdropper in the nth time slot, β 3,e [n] represents the third intermediate value of the eavesdropper in the nth time slot; Indicates the maximum transmission rate of the second channel; u e [n] represents the slack variable of the eavesdropper in the nth time slot. u represents the square of the slack variable in the nth time slot of the eavesdropper. e [n] (l-1) Let n be the relaxation variable of the eavesdropper in the (l-1)th iteration. Let represent the square of the slack variable of the eavesdropper in the nth time slot during the (l-1)th iteration.

6. A robust UAV terahertz secure communication method according to claim 5, characterized in that, The first intermediate value β of the k-th user in the n-th time slot 1,k [n] is as follows: The second intermediate value β of the k-th user in the n-th time slot 2,k [n] is as follows: The third intermediate value β of the k-th user in the n-th time slot 3,k [n] is as follows: Where ρ1 represents the first probability of error; j and k represent user serial numbers; n represents time slot serial number; and l represents the current iteration number. w represents the trajectory variable of the k-th user in the n-th time slot during the (l-1)-th iteration. k [n] represents the beamforming vector of the k-th user in the n-th time slot, and f[n] represents the artificial noise vector sent by the UAV base station in the n-th time slot.

7. A robust UAV terahertz secure communication method according to claim 6, characterized in that, The first intermediate value β of the eavesdropper in the nth time slot 1,e [n] is as follows: The second intermediate value β of the eavesdropper in the nth time slot 2,e [n] is as follows: The third intermediate value β of the eavesdropper in the nth time slot 3,e [n] is as follows: Where ρ2 represents the second error probability; j and k represent user serial numbers, n represents time slot serial number, and l represents the current iteration number. w represents the trajectory variable of the eavesdropper in the nth time slot during the (l-1)th iteration. k [n] represents the beamforming vector of the k-th user in the n-th time slot, and f[n] represents the artificial noise vector sent by the UAV base station in the n-th time slot.

8. A robust UAV terahertz secure communication method according to claim 7, characterized in that, The first error probability ρ1 is as follows: The second error probability ρ2 is as follows: Where f represents the artificial noise vector sent by the drone base station, C represents the speed of light, and σ e σ represents the power spectral density of the white noise in the second channel; k This represents the white noise power spectral density of the first channel for the k-th user.

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