A cooperative secure communication method for multiple unmanned aerial vehicles (UAVs) based on intelligent reflective surfaces and non-orthogonal multiple access technology

Abstract

This invention provides a multi-UAV cooperative secure communication method based on intelligent reflectors and non-orthogonal multiple access (NOMA) technology. The method initializes configuration information for ground users, eavesdroppers, and UAVs; initializes the iteration count variable; enters the iteration process based on the initial configuration information; optimizes the transmit power and flight trajectory of the source UAV, the interference power and flight trajectory of the interfering UAV, and the phase of the intelligent reflector; calculates the objective function value for this iteration and determines whether the difference between the objective function of this iteration and the previous iteration is less than a threshold. If so, the optimal transmit power and flight trajectory of the source UAV, the optimal interference power and flight trajectory of the interfering UAV, the optimal phase of the intelligent reflector, and the average security rate of the system are obtained; otherwise, the iteration count is incremented and each variable is optimized. This invention employs non-orthogonal multiple access (NOMA) technology, which can maximize the security of the system.

Description

Technical Field

[0001] This invention relates to the field of computer wireless communication technology, and specifically to a multi-UAV cooperative secure communication method based on intelligent reflective surfaces and non-orthogonal multiple access technology. Background Technology

[0002] Unmanned aerial vehicles (UAVs) are widely used in wireless communication systems due to their high mobility, rapid deployment, and low cost. Compared to traditional terrestrial wireless channels, which are susceptible to path loss, shadowing, and multipath fading in urban environments, UAVs offer the advantage of altitude and facilitate line-of-sight connections with ground equipment to establish aerial base stations. However, due to the broadcast nature of wireless channels and the existence of line-of-sight links, ground-based eavesdroppers can more easily intercept information transmitted by UAVs to ground users, leading to information leaks and posing security risks.

[0003] Smart reflectors, with their advantages of enhanced signal coverage and low cost, are widely used in various wireless communication scenarios. Furthermore, by adjusting the phase of the reflected signal, it can cancel out the direct signal upon reception, thereby reducing information leakage. At the physical layer security level, jammers are introduced to reduce the risk of eavesdropping. Jammers can also be deployed on drones to transmit interference signals to eavesdroppers, further mitigating the risk of eavesdropping.

[0004] Drone communication requires high wireless transmission rates. Non-orthogonal multiple access technology can further improve transmission speed in multi-user scenarios and maximize the security performance of drone communication. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a secure communication method involving multiple drones working together. In the presence of eavesdroppers, this method utilizes a multi-drone collaborative approach: one drone acts as a base station transmitting information to ground users, while another drone acts as a jammer, emitting interference signals to disrupt the eavesdropper. Furthermore, a smart reflector improves the channel environment of the link, and ground users employ non-orthogonal addressing technology when receiving information, further enhancing the confidentiality of drone-to-ground communication and significantly improving the system's security performance.

[0006] A multi-UAV cooperative secure communication method based on intelligent reflective surfaces and non-orthogonal multiple access technology includes the following steps:

[0007] Step 1: Based on the geographical locations of the source UAV, jamming UAV, smart reflector, ground users, and eavesdroppers, establish an air-to-ground channel fading model and a reachability rate model from the source UAV to ground users and from the source UAV to the eavesdroppers.

[0008] Step 2: Construct an optimization problem with the goal of maximizing the average confidentiality rate of all ground users;

[0009] Step 3: Using the alternating optimization algorithm, the model for maximizing the average security rate of the system is decoupled into the source UAV's transmit power optimization sub-problem and flight trajectory optimization sub-problem, the interference power optimization sub-problem and trajectory optimization sub-problem of the interfering UAV, and the intelligent reflector phase shift optimization sub-problem;

[0010] Step 4: Use the CVX tool to find local approximate solutions for the five sub-optimization problems mentioned above. Iterate the five local solutions to obtain the overall approximate optimal solution, and obtain the transmission power and flight trajectory of the source UAV, the interference power and flight trajectory of the interfering UAV, and the phase of the smart reflector in each time slot.

[0011] Further, in step 1, the geographic location information for the UAV secure communication includes: K ground terminal users, one ground eavesdropper, one source UAV, one jamming UAV, and one smart reflector; the location of the kth user is represented as... The location of the ground eavesdropper is known, and can be represented as follows: The source drone and the jamming drone simultaneously operate at a fixed altitude H above the ground within a time period T. u Flight, dividing T into N hour slots, the horizontal position of the source UAV is represented as The horizontal position of the jamming drone is represented as The first element of the intelligent reflective surface is considered as a reference point, located at a fixed height H. r horizontal position The intelligent reflective surface consists of M=M x M y It consists of a uniform planar array of reflective elements, where M x and M y These represent the number of elements along the x-axis and y-axis, respectively. The phase shift matrix of the smart reflector in the nth time slot is expressed as... in This represents the phase shift generated by the m-th reflecting element within the n-th time slot. Furthermore, the source drone, jamming drone, all ground users, and eavesdroppers are all equipped with only a single antenna. All channels are Ricean channels.

[0012] The channel gain from the source UAV to the smart reflector is expressed as:

[0013]

[0014] in α is the path loss exponent, β0 is the channel power gain at the reference distance d0 = 1m, and λ0 is the carrier wavelength. It is the azimuth and elevation angle, K sr It is the Rice factor, d sr [n] is the distance from the UAV in the nth time slot to the smart reflector. Let represent a set of M×1 dimensional composite matrices. This represents the line-of-sight link component from the source drone to the smart reflector. This represents the non-line-of-sight link component from the source drone to the smart reflector. CN(0,1) represents a circularly symmetric complex Gaussian distribution with zero mean and unit variance.

[0015] The channel gains from the source drone to the k-th user and the eavesdropper are respectively:

[0016]

[0017] Where K sk It is the Rice factor, d sk [n] is the distance from the source drone in the nth time slot to the kth user. This represents the line-of-sight link component from the source drone to the k-th user. K represents the non-line-of-sight link component from the source drone to the k-th user; se It is the Rice factor, d se [n] is the distance from the source drone to the eavesdropper in the nth time slot. This indicates the line-of-sight link components from the source drone to the eavesdropper. This represents the non-line-of-sight link components from the source drone to the eavesdropper;

[0018] The channel gains from the jamming drone to the smart reflector, the k-th user, and the eavesdropper are respectively:

[0019]

[0020] Where K jr It is the Rice factor, d jr [n] represents the distance from the interfering UAV to the smart reflector in the nth time slot. This represents the line-of-sight link component from the interfering drone to the smart reflector. K represents the non-line-of-sight link component from the interfering drone to the smart reflector. jk It is the Rice factor, d jk [n] represents the distance from the interfering drone to the k-th user in the nth time slot. This represents the line-of-sight link component from the interfering drone to the k-th user. This represents the non-line-of-sight link component from the interfering drone to the k-th user; K je It is the Rice factor, d je[n] represents the distance from the interfering drone to the eavesdropper in the nth time slot. This indicates interference with the line-of-sight link components from the drone to the eavesdropper. This indicates the non-line-of-sight link component that interferes with the drone's connection to the eavesdropper.

[0021] The total channel gain from the source drone to the k-th user and the eavesdropper are respectively:

[0022]

[0023] The total channel gain from the jamming drone to the k-th user and the eavesdropper are respectively:

[0024]

[0025] The channel gains from the smart reflector to the k-th user and the eavesdropper are respectively

[0026]

[0027] Where K rk It is the Rice factor, d rk [n] is the distance from the intelligent reflective surface in the nth time slot to the kth user. This represents the line-of-sight link component from the smart reflector to the k-th user. K represents the non-line-of-sight link component from the smart reflector to the k-th user; re It is the Rice factor, d re [n] is the distance from the intelligent reflective surface to the eavesdropper in the nth time slot. This represents the line-of-sight link component from the smart reflector to the eavesdropper. This represents the non-line-of-sight link component from the smart reflector to the eavesdropper.

[0028] The source UAV and ground users employ non-orthogonal multiple access technology. The reachable rates of the k-th ground user and the eavesdropper in the n-th time slot are respectively expressed as:

[0029]

[0030] Where p k [n] represents the transmission power of the source UAV when transmitting information to the k-th user in the n-th time slot, p l [n] is the transmission power of the source UAV transmitting information to the l-th user in the n-th time slot, p j [n] represents the interference power of the UAV in the nth time slot. This represents the power of the additive white Gaussian noise at the ground user location. λ represents the power of the additive white Gaussian noise at the eavesdropper's location; k,l[n](l≠k) is a binary variable. When the channel gain of the k-th user is worse than that of the l-th user, λ k,l [n] = 1, otherwise λ k,l [n] = 0.

[0031] The confidentiality rate of the k-th ground user in the n-th time slot is represented by R. sec,k [n] = [R] k [n]-R e [n] + , where [x] + =max{x,0}, if R L [n]-R e The value of [n] is negative in the nth time slot, which allows the UAV-S transmit power p to be set to a negative value. k If [n] = 0, then R sec,k [n] = R k [n]-R e [n], thus ensuring that the system's confidentiality rate remains non-negative in any time slot.

[0032] Furthermore, in step 2, the established optimization problem specifically includes an objective function and constraints;

[0033]

[0034] In P1, Q s Q represents the flight trajectory of the source drone. j P represents the flight trajectory of the source drone. k P represents the transmit power of the source drone. k The value represents the interference power of the interfering drone, and ψ represents the phase of the smart reflector.

[0035] The constraints specifically include:

[0036] Within time T, the initial and final positions of the source and interfering drones are fixed; within a time slot, the distance flown by the drones is less than the maximum distance, and to ensure that the two drones do not collide during flight, there are constraints:

[0037]

[0038]

[0039]

[0040] Where, q u [0] = q uI q represents the initial position of the drone. u [N] = q uFIndicates the final position of the drone, V max d represents the maximum flight speed of the source drone and the interfering drone. min This indicates the minimum distance that must be maintained between two drones;

[0041] The phase constraint of the intelligent reflective surface is:

[0042]

[0043] Within any time slot, the source UAV's transmit power guarantees that its transmission power to the k-th user is greater than the transmission power to other users, and guarantees that the source UAV's transmit power does not exceed its maximum transmit power. The source UAV's transmit power constraint is as follows:

[0044]

[0045] Where p s max Indicates the maximum transmit power of the source UAV; λ k,l [n] satisfies λ k,l [n]+λ l,k [n]=1,λ k,l [n]∈{1,0},d sl [n] represents the distance from the source drone to the l-th user.

[0046] The interference power constraint for interfering with drones is

[0047]

[0048] in p represents the average jamming power of the jamming drone. jmax This indicates the maximum jamming power of the interfering drone.

[0049] Based on the above analysis, the optimization problem in this invention can be modeled as problem P1:

[0050]

[0051] To simplify the objective function, we introduce the variable t. The objective function and constraints are then expressed as follows:

[0052]

[0053] st(15a), (15b), (15c), (15d), (15f), (15g), (15h), (15i) (16b)

[0054]

[0055] Furthermore, in step 3, the established optimization problem is decoupled into five sub-problems using an alternating optimization algorithm. The specific steps are as follows:

[0056] a. The source UAV's transmit power optimization subproblem includes optimizing the source UAV's transmit power to maximize the system's security rate; introducing auxiliary variables and using Taylor expansion to optimize the source UAV's transmit power allocation. The source UAV transmit power optimization subproblem is expressed as:

[0057]

[0058] st(16c) (17b)

[0059] (15e), (15f), (15g), (17c)

[0060] In this optimization subproblem, (17b) is a non-convex constraint, which can be transformed into a convex constraint using auxiliary variables; R k [n], R e [n] in p k (i) A first-order Taylor expansion at [n] yields...

[0061]

[0062] Where, p k (i) [n] represents the transmit power optimized by the source UAV in the i-th iteration. R obtained through SCA technology k [n] lower bound, It is R e [n] is a convex approximation of the upper bound, a n b n The expressions for the introduced auxiliary variables are as follows:

[0063]

[0064] The transformation of the non-convex constraint (17b) is expressed by the formula: Then constraint (17b) becomes a convex set.

[0065] P2 is rewritten as:

[0066]

[0067] (15e), (15f), (15g) (20c)

[0068] b. The sub-problem of optimizing the jamming power of the jamming UAV includes optimizing the transmission power of the jamming UAV to maximize the system's security rate; introducing auxiliary variables and using Taylor expansion to optimize the jamming power allocation of the jamming UAV. The sub-problem of optimizing the jamming power of the jamming UAV is expressed as:

[0069]

[0070] st(16c) (21b)

[0071] (15h), (15i) (21c)

[0072] In this optimization subproblem, (21b) is a non-convex constraint, which can be transformed into a convex constraint using auxiliary variables; R k [n], R e [n] in p j (i) A first-order Taylor expansion at [n] yields...

[0073]

[0074] Where, p j (i) [n] represents the transmit power optimized by the source UAV in the i-th iteration. R obtained through SCA technology k [n] lower bound, It is R e [n] is a convex approximation of the upper bound, c n ,d n ,e n ,f n The expressions for the introduced auxiliary variables are as follows:

[0075]

[0076] The transformation of the non-convex constraint (21b) is expressed by the formula: Then constraint (21b) becomes a convex set.

[0077] P4 rewritten as:

[0078]

[0079] (15h), (15i) (24c)

[0080] c. The sub-problem of optimizing the flight trajectory of the source UAV includes optimizing the flight trajectory of the source UAV to maximize the system's security rate; introducing slack variables and using SCA to perform a local convex approximation of the source UAV's flight trajectory optimization problem. The sub-problem of optimizing the flight trajectory of the source UAV is expressed as:

[0081]

[0082] st(16c) (25b)

[0083] (15c) (25c)

[0084]

[0085] In this optimization subproblem, (25b) and (25c) are both non-convex constraints. For the non-convex constraint (25b), slack variables need to be introduced and Taylor expansion method is used to transform (25b) into a convex set. The specific steps are as follows: For R k [n], introducing variable s k [n]z k [n], whose constraints are respectively

[0086]

[0087] (26) and (27) make And variable s k [n],z k The constraint [n] is non-convex. Then, we introduce slack variables a1[n], a2[n], a3[n], a4[n] such that a1[n] ≥ d. sk [n], a2[n]≥d sr [n], a3[n]≤d sk [n], a4[n]≤d sr [n], then (27)205 is represented as

[0088]

[0089] in

[0090]

[0091] Related items The value can be positive or negative, depending on the phase difference between the signals. If the coherence term is positive, it helps increase the channel gain; if it is negative, it weakens the channel gain. A binary variable F is introduced for the coherence term. k [n], which satisfies when

[0092] At that time, F k [n] = 1 indicates that the coherent term is positive, which enhances the signal strength and satisfies the condition.

[0093]

[0094] when At that time, Fk [n] = 0 indicates that the coherent term is negative, which strengthens or weakens the effect, satisfying the condition.

[0095]

[0096] Then variable s k The constraint (28) of [n] transforms into a convex set, expressed as follows:

[0097]

[0098] Then R k [n] in z k A first-order Taylor expansion at [n] yields...

[0099]

[0100] in R obtained through SCA technology k [n] Lower bound.

[0101] For R e [n], and R k The optimization method for [n] is similar to introducing slack variables s. e [n], z e [n], with constraints respectively

[0102]

[0103] And s e [n], z e The constraint [n] is still non-convex. Further slack variables b1[n] and b2[n] are introduced, satisfying b1[n] ≥ d. se [n],b2[n]≤d se [n], such that (31) is represented as

[0104]

[0105] Among them when At that time, F e [n] = 1, indicating an increase in signal strength. This yields...

[0106]

[0107] when At that time, F e [n] = 0 indicates a weakening of the signal strength. This yields...

[0108]

[0109] Then R e [n] in z e A first-order Taylor expansion at [n] yields...

[0110]

[0111] in R obtained through SCA technology e [n] Upper bound.

[0112] The slack variables a1[n], a2[n], a3[n], a4[n], b1[n], b2[n] in the first-order Taylor expansion of the i-th iteration satisfy the following constraints:

[0113]

[0114] The transformation of the non-convex constraint (25b) is expressed by the following formula: At this point, constraint (25b) becomes a convex set.

[0115] For the non-convex constraint (25c), the safe flight distance d between the two drones is also considered. min Perform a first-order Taylor expansion at the i-th iteration:

[0116] At this point, the non-convex constraint (25c) becomes a convex set.

[0117] P6 is rewritten as:

[0118]

[0119] (25d), (25f), (35)-(40) (41d)

[0120] d. The sub-problem of optimizing the flight trajectory of the source UAV is expressed as:

[0121]

[0122] st(16c) (42b)

[0123] (15c) (42c)

[0124]

[0125] In this optimization subproblem, (42b) and (42c) are both non-convex constraints. For the non-convex constraint (42c), the method is the same as in the trajectory optimization of the source UAV, and the safe flight distance d between the two UAVs is... min Perform a first-order Taylor expansion at the i-th iteration: d min 2 +||q s (i) [n]|| 2 -2(q s (i)[n]-q j (i) [n])(q s [n]) T -||q j (i) [n]|| 2 ≤0

[0126] For the non-convex constraint (42b), similar to the method in the trajectory optimization of the source UAV, the specific steps are as follows: For R k [n], introducing slack variable s jk [n], whose constraints are

[0127]

[0128] but in

[0129] And variable s jk The constraint [n] is still non-convex. We then introduce slack variables c1[n], c2[n], c3[n], and c4[n] such that c1[n] ≥ d. jk [n],c2[n]≥d jr [n],c3[n]≤d jk [n],c4[n]≤d jr [n], s jk [n] is obtained by performing a first-order Taylor expansion on the i-th iteration:

[0130]

[0131] in

[0132] because Possible values ​​can be positive or negative; introduce a binary variable F. jk [n], which satisfies the following conditions:

[0133] when At that time, F jk [n] = 1 indicates that the coherent term is positive, which enhances the signal strength.

[0134]

[0135] when At that time, F jk [n] = 0 indicates that the coherent term is negative, which weakens the signal strength.

[0136]

[0137] Then R k [n] in s jk Perform a Taylor first-order expansion at [n], i.e.

[0138]

[0139] in R obtained through SCA technology k [n] Lower bound.

[0140] Similarly, for R e [n] Introducing variable s je [n], which satisfies the following constraints:

[0141]

[0142] but in

[0143] And variable s je The constraint [n] is still non-convex. We then introduce slack variables d1[n] and d2[n] such that d1[n] ≥ d2[n]. je [n],d2[n]≤d je [n], and introduce F jk [n], then for s je [n] is expanded using a first-order Taylor series to obtain:

[0144]

[0145] Where F jk [n] satisfies: when At that time, F je [n] = 1 indicates that the coherent term is positive, which enhances the signal strength.

[0146]

[0147] when At that time, F jk [n] = 0 indicates that the coherent term is negative, which weakens the signal strength.

[0148]

[0149] Then R e [n] in s je Perform a Taylor first-order expansion at [n], i.e.

[0150]

[0151] in R obtained through SCA technology e [n] Upper bound.

[0152] The slack variables c1[n], c2[n], c3[n], c4[n], d1[n], d2[n] in the first-order Taylor expansion of the i-th iteration satisfy the following constraints:

[0153] d jk 2 [n]≤-(c1 (i) [n]) 2 +2c1 (i) [n]c1[n] (49)

[0154] d jr 2 [n]≤-(c2 (i) [n]) 2 +2c2 (i) [n]c2[n] (50)

[0155] d je 2 [n]≤-(d1 (i) [n]) 2 +2d1 (i) [n]d1[n] (51)

[0156] c3 2 [n]≤(d jk (i) [n]) 2 +2(q j (i) [n]) T (q j [n]-q j (i) [n]) (52)

[0157] c4 2 [n]≤(d jk (i) [n]) 2 +2(q j (i) [n]) T (q j [n]-q j (i) [n]) (53)

[0158] d2 2 [n]≤(d je (i) [n]) 2 +2(q j (i) [n]) T (q j [n]-q j (i) [n]) (54)

[0159] The transformation of the non-convex constraint (42b) is expressed by the following formula: At this point, constraint (42b) becomes a convex set.

[0160] P8 rewritten as:

[0161]

[0162] d min 2 +||q s (i) [n]|| 2 -2(q s (i) [n]-q j (i) [n])(q s [n]) T -||q j (i) [n]|| 2 ≤0 (55c)

[0163] (42d), (42f), (49)-(54) (55d)

[0164] e. The phase optimization sub-problem of the intelligent reflector includes optimizing the phase of the intelligent reflector to maximize the system's security rate. The phase optimization sub-problem of the intelligent reflector is expressed as:

[0165]

[0166] st(16c) (56b)

[0167]

[0168] P10 is non-convex. The phase shift matrix of the smart reflector is optimized using the Successive Convex Approximation (SCA) method and the Semidefinite Relaxation (SDR) method: a semidefinite matrix is ​​introduced, and we set... v[n]=[v1[n],v2[n],...,v M [n]], Substituting v[n] into P10, then (55c) is equivalent to transforming the constraint of the vector modulus into

[0169] To simplify the problem and constraints, and to convert them all into quadratic forms, we introduce...

[0170]

[0171] in At this time

[0172]

[0173] At point At R k [n] and R e [n] is expanded using a first-order Taylor series:

[0174]

[0175]

[0176] in R obtained through SCA technology k [n] lower bound, R obtained through SCA technology e [n] is the upper bound. Then the non-convex constraint (56b) is transformed into the formula: At this point, constraint (56b) becomes a convex set.

[0177] P10 rewritten as

[0178]

[0179] Further, in step 4, the CVX tool is used to find local approximate solutions to the five sub-problems, and the five local solutions are iterated to obtain the overall approximate optimal solution of the system. Specifically, this involves: initializing the values ​​of variables for maximizing the system's security rate; substituting the initialized variables into the source UAV's transmit power optimization sub-problem to obtain a local approximate solution for the i-th iteration of the source UAV's transmit power optimization sub-problem; substituting the local approximate solution of the i-th iteration of the source UAV's interference power optimization sub-problem and other initialized variables into the interference UAV's interference power optimization sub-problem to obtain a local approximate solution; substituting the local approximate solutions of the i-th iteration of the source UAV's interference power optimization sub-problem, the interference UAV's interference power optimization sub-problem, and other initialized variables into the source UAV's flight trajectory optimization sub-problem to obtain a local approximate solution; and then iterating the i-th iteration... Substituting the local approximate solutions of the source UAV interference power optimization subproblem, the interference UAV interference power optimization subproblem, the source UAV flight trajectory optimization subproblem, and other initialized variables into the interference UAV flight trajectory optimization subproblem, we obtain a local approximate solution to the interference UAV flight trajectory optimization subproblem. Substituting the local approximate solutions of the source UAV transmit power optimization subproblem, the interference UAV interference power optimization subproblem, the source UAV flight trajectory optimization subproblem, the interference UAV flight trajectory optimization subproblem, and other initialized variables into the intelligent reflector phase shift optimization subproblem, we obtain a local approximate solution to the intelligent reflector phase shift optimization subproblem. Continuously increasing the iteration count until the iteration convergence condition is met, we obtain the transmit power and flight trajectory of the source UAV, the interference power and flight trajectory of the interference UAV, and the phase shift of the intelligent reflector, thus obtaining the overall approximate optimal solution.

[0180] Compared with the prior art, the present invention has the following advantages:

[0181] First, this invention considers the impact of eavesdroppers on wireless communication transmission rates. It introduces interfering drones to send jamming signals, reducing the eavesdropping rate. The system can adjust the flight trajectory of the interference drone based on dynamic changes in the user's location and environment to enhance dynamic optimization capabilities, thereby increasing the reachability rate from the source drone to the ground user. In cases with multiple ground users, non-orthogonal multiple access technology is considered to further improve the user's reachability rate.

[0182] Second, this invention designs an alternating iterative optimization algorithm that transforms the optimization problem into a series of convex optimization subproblems and solves these subproblems using Successive Convex Approximation (SCA) and Semidefinite Relaxation (SDR). This solves the problem of jointly optimizing the flight trajectory of the source UAV, the trajectory of the interfering UAV, the transmission power of the source UAV, the interference power of the interfering UAV, and the phase shift of the intelligent reflector in such systems. The joint solution of the optimization problem, the system's security level, and simulation experiments also verify the effectiveness and fast convergence of the method of this invention. Attached Figure Description

[0183] Figure 1 This is a system model diagram in an embodiment of the present invention;

[0184] Figure 2 This is a flowchart illustrating an embodiment of the present invention;

[0185] Figure 3 This is a comparison chart of the number of reflective elements in the intelligent reflective surface and the average security rate of the system;

[0186] Figure 4 This is a graph showing the variation of the system's average security level with the source UAV's transmission power under intelligent reflective surface conditions with different numbers of reflective elements. Detailed Implementation

[0187] The present invention will be further illustrated below with reference to the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. It should be noted that the terms "front," "rear," "left," "right," "up," and "down" used in the following description refer to directions in the accompanying drawings, and the terms "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

[0188] Combined with attachment Figure 1 and Figure 2 The specific steps of the method of the present invention are described below.

[0189] Step 1: Based on the geographical locations of the source drone, the jamming drone, the ground user, and the eavesdropper, establish an air-to-ground channel fading model and a reachability rate model from the source drone to the ground user and from the source drone to the eavesdropper.

[0190] Step 2: Construct an optimization problem with the goal of maximizing the average confidentiality rate of all ground users;

[0191] Step 3: Using the alternating optimization algorithm, the model for maximizing the average security rate of the system is decoupled into the source UAV's transmit power optimization sub-problem and flight trajectory optimization sub-problem, the interference power optimization sub-problem and trajectory optimization sub-problem of the interfering UAV, and the intelligent reflector phase shift optimization sub-problem;

[0192] Step 4: Use the CVX tool to find local approximate solutions for the five sub-optimization problems mentioned above. Iterate the five local solutions to obtain the overall approximate optimal solution, and obtain the transmission power and flight trajectory of the source UAV, the interference power and flight trajectory of the interfering UAV, and the phase of the smart reflector in each time slot.

[0193] Furthermore, this invention considers a multi-UAV cooperative secure communication system based on intelligent reflective surfaces and non-orthogonal multiple access technology, such as... Figure 1 Regarding step 1: Figure 1 The specific model of the present invention is illustrated, including: K ground terminal users, a ground eavesdropper, a source drone, a jamming drone, and a smart reflector; the position of the kth user is represented as... The location of the ground eavesdropper is known, and can be represented as follows: The source drone and the jamming drone simultaneously operate at a fixed altitude H above the ground within a time period T. u Flight, dividing T into N hour slots, the horizontal position of the source UAV is represented as The horizontal position of the jamming drone is represented as The first element of the intelligent reflective surface is considered as a reference point, located at a fixed height H. r horizontal position The intelligent reflective surface consists of M=M x M y It consists of a uniform planar array of reflective elements, where M x and M y These represent the number of elements along the x-axis and y-axis, respectively. The phase shift matrix of the smart reflector in the nth time slot is expressed as... in This represents the phase shift generated by the m-th reflecting element within the n-th time slot. Furthermore, the source drone, jamming drone, all ground users, and eavesdroppers are all equipped with only a single antenna. All channels are Ricean channels.

[0194] The channel gain from the source UAV to the smart reflector is expressed as:

[0195]

[0196] in α is the path loss exponent, β0 is the channel power gain at the reference distance d0 = 1m, and λ0 is the carrier wavelength. It is the azimuth and elevation angle, K sr It is the Rice factor, d sr [n] is the distance from the UAV in the nth time slot to the smart reflector. Let represent a set of M×1 dimensional composite matrices. This represents the line-of-sight link component from the source drone to the smart reflector. This represents the non-line-of-sight link component from the source drone to the smart reflector. CN(0,1) represents a circularly symmetric complex Gaussian distribution with zero mean and unit variance.

[0197] The channel gains from the source drone to the k-th user and the eavesdropper are respectively:

[0198]

[0199] Where K sk It is the Rice factor, d sk [n] is the distance from the source drone in the nth time slot to the kth user. This represents the line-of-sight link component from the source drone to the k-th user. K represents the non-line-of-sight link component from the source drone to the k-th user; se It is the Rice factor, d se [n] is the distance from the source drone to the eavesdropper in the nth time slot. This indicates the line-of-sight link components from the source drone to the eavesdropper. This represents the non-line-of-sight link components from the source drone to the eavesdropper;

[0200] The channel gains from the jamming drone to the smart reflector, the k-th user, and the eavesdropper are respectively:

[0201]

[0202]

[0203] Where K jr It is the Rice factor, d jr [n] represents the distance from the interfering UAV to the smart reflector in the nth time slot. This represents the line-of-sight link component from the interfering drone to the smart reflector. K represents the non-line-of-sight link component from the interfering drone to the smart reflector. jk It is the Rice factor, d jk [n] represents the distance from the interfering drone to the k-th user in the nth time slot. This represents the line-of-sight link component from the interfering drone to the k-th user. This represents the non-line-of-sight link component from the interfering drone to the k-th user; K je It is the Rice factor, d je [n] represents the distance from the interfering drone to the eavesdropper in the nth time slot. This indicates interference with the line-of-sight link components from the drone to the eavesdropper. This indicates the non-line-of-sight link component that interferes with the drone's connection to the eavesdropper.

[0204] The total channel gain from the source drone to the k-th user and the eavesdropper are respectively:

[0205]

[0206] The total channel gain from the jamming drone to the k-th user and the eavesdropper are respectively:

[0207]

[0208] The channel gains from the smart reflector to the k-th user and the eavesdropper are respectively

[0209]

[0210] Where K rk It is the Rice factor, d rk [n] is the distance from the intelligent reflective surface in the nth time slot to the kth user. This represents the line-of-sight link component from the smart reflector to the k-th user. K represents the non-line-of-sight link component from the smart reflector to the k-th user; re It is the Rice factor, d re [n] is the distance from the intelligent reflective surface to the eavesdropper in the nth time slot. This represents the line-of-sight link component from the smart reflector to the eavesdropper. This represents the non-line-of-sight link component from the smart reflector to the eavesdropper.

[0211] The source UAV and ground users employ non-orthogonal multiple access technology. The reachable rates of the k-th ground user and the eavesdropper in the n-th time slot are respectively expressed as:

[0212]

[0213] Where p k [n] represents the transmission power of the source UAV when transmitting information to the k-th user in the n-th time slot, p l [n] is the transmission power of the source UAV transmitting information to the l-th user in the n-th time slot, p j [n] represents the interference power of the UAV in the nth time slot. This represents the power of the additive white Gaussian noise at the ground user location. λ represents the power of the additive white Gaussian noise at the eavesdropper's location; k,l [n](l≠k) is a binary variable. When the channel gain of the k-th user is worse than that of the l-th user, λ k,l [n] = 1, otherwise λ k,l [n] = 0.

[0214] The confidentiality rate of the k-th ground user in the n-th time slot is represented by R. sec,k [n] = [R] k [n]-R e [n] + , where [x] + =max{x,0}, if R L [n]-R e The value of [n] is negative in the nth time slot, which allows the UAV-S transmit power p to be set to a negative value. k If [n] = 0, then R sec,k [n] = R k [n]-R e [n], thus ensuring that the system's confidentiality rate remains non-negative in any time slot. For step 2, an optimization problem is constructed with the objective of maximizing the confidentiality rate of ground users. Based on the above description, the following mathematical model is established:

[0215] The objective function is expressed as:

[0216] In P1, Q s Q represents the flight trajectory of the source drone. j P represents the flight trajectory of the source drone. k P represents the transmit power of the source drone. k The value represents the interference power of the interfering drone, and ψ represents the phase of the smart reflector.

[0217] The constraints specifically include:

[0218] Within time T, the initial and final positions of the source and interfering drones are fixed; within a time slot, the distance flown by the drones is less than the maximum distance, and to ensure that the two drones do not collide during flight, there are constraints:

[0219]

[0220]

[0221]

[0222] Where, q u [0] = q uI q represents the initial position of the drone. u [N] = q uF Indicates the final position of the drone, V max d represents the maximum flight speed of the source drone and the interfering drone. min This indicates the minimum distance that must be maintained between two drones;

[0223] The phase constraint of the intelligent reflective surface is:

[0224]

[0225] Within any time slot, the source UAV's transmit power guarantees that its transmission power to the k-th user is greater than the transmission power to other users, and guarantees that the source UAV's transmit power does not exceed its maximum transmit power. The source UAV's transmit power constraint is as follows:

[0226]

[0227]

[0228] Where p s max Indicates the maximum transmit power of the source UAV; λ k,l [n] satisfies λ k,l [n]+λ l,k [n]=1,λ k,l [n]∈{1,0},d sl [n] represents the distance from the source drone to the l-th user.

[0229] The interference power constraint for interfering with drones is

[0230]

[0231] Where p j p represents the average jamming power of the jamming drone. jmax Let represent the maximum interference power of the interfering drone. To simplify the objective function, we introduce the variable t, then the objective function and constraints are expressed as follows:

[0232]

[0233] st(15a), (15b), (15c), (15d), (15f), (15g), (15h), (15i) (16b)

[0234]

[0235] Step 3 involves jointly optimizing the source UAV's transmit power and flight trajectory, the interfering UAV's interference power and trajectory, and the phase shift of the smart reflector using the relaxation variable method, successive convex approximation (SCA), and semidefinite relaxation (SDR) method. This method updates one variable block at a time when solving the optimization problem, iteratively solving five sub-problems by alternately optimizing them to obtain an approximate solution to the original problem.

[0236] (a) Optimize the source UAV's transmit power:

[0237] The subproblem of optimizing the transmit power of the UAV source is expressed as:

[0238]

[0239] st(16c) (17b)

[0240] (15e), (15f), (15g), (17c)

[0241] For non-convex constraints (17b), auxiliary variables can be used to transform them into convex constraints; R k [n], R e [n] in p k (i) A first-order Taylor expansion at [n] yields...

[0242]

[0243] Where, p k (i) [n] represents the transmit power optimized by the source UAV in the i-th iteration. R obtained through SCA technology k [n] lower bound, It is R e [n] is a convex approximation of the upper bound, a n b n The expressions for the introduced auxiliary variables are as follows:

[0244]

[0245] The transformation of the non-convex constraint (17b) is expressed by the formula: Then constraint (17b) becomes a convex set.

[0246] P2 is rewritten as:

[0247]

[0248] (15e), (15f), (15g) (20c)

[0249] (b) Optimize the jamming power of interfering drones:

[0250] The subproblem of optimizing the transmit power of the UAV source is expressed as:

[0251]

[0252] st(16c) (21b)

[0253] (15h), (15i) (21c)

[0254] For non-convex constraints (21b), auxiliary variables can be used to transform them into convex constraints; R k [n], R e [n] in p j (i) A first-order Taylor expansion at [n] yields...

[0255]

[0256] Where, p j (i) [n] represents the transmit power optimized by the source UAV in the i-th iteration. R obtained through SCA technology k [n] lower bound, It is R e [n] is a convex approximation of the upper bound, c n ,d n ,e n ,f n The expressions for the introduced auxiliary variables are as follows:

[0257]

[0258] The transformation of the non-convex constraint (21b) is expressed by the formula: Then constraint (21b) becomes a convex set.

[0259] P4 rewritten as:

[0260]

[0261] (15h), (15i) (21c)

[0262] (c) Optimize the power of the source UAV flight trajectory:

[0263] The subproblem of optimizing the flight trajectory of the source UAV is expressed as:

[0264]

[0265] st(16c) (25b)

[0266] (15c) (25c)

[0267]

[0268] For the non-convex constraint (25b), slack variables need to be introduced and Taylor expansion needs to be used to transform (25b) into a convex set. The specific steps are as follows: For R k [n], introducing variable s k [n]z k [n], whose constraints are respectively

[0269]

[0270] make And variable s k [n], z k The constraint [n] is non-convex. Then, we introduce slack variables a1[n], a2[n], a3[n], a4[n] such that a1[n] ≥ d. sk [n], a2[n]≥d sr [n], a3[n]≤d sk [n], a4[n]≤d sr [n], then (27) is represented as

[0271]

[0272] in Related items The value can be positive or negative, depending on the phase difference between the signals. If the coherence term is positive, it helps increase the channel gain; if it is negative, it weakens the channel gain. A binary variable F is introduced for the coherence term. k [n], which satisfies when At that time, F k [n] = 1 indicates that the coherent term is positive, which enhances the signal strength and satisfies the condition.

[0273]

[0274] when At that time, F k [n] = 0 indicates that the coherent term is negative, which strengthens or weakens the effect, satisfying the condition.

[0275]

[0276] Then variable s k The constraint (28) of [n] transforms into a convex set, expressed as follows:

[0277]

[0278] Then R k [n] in z k A first-order Taylor expansion at [n] yields...

[0279]

[0280] in R obtained through SCA technology k [n] Lower bound.

[0281] For R e [n], and Rk The optimization method for [n] is similar to introducing slack variables s. e [n],z e [n], with constraints respectively

[0282]

[0283]

[0284] And s e [n],z e The constraint [n] is still non-convex. Further slack variables b1[n] and b2[n] are introduced, satisfying b1[n] ≥ d. se [n],b2[n]≤d se [n], such that (31) is represented as

[0285]

[0286] Among them when At that time, F e [n] = 1, indicating an increase in signal strength. This yields...

[0287]

[0288] when At that time, F e [n] = 0 indicates a weakening of the signal strength. This yields...

[0289]

[0290] Then R e [n] in z e A first-order Taylor expansion at [n] yields...

[0291]

[0292] in R obtained through SCA technology e [n] Upper bound.

[0293] The slack variables a1[n], a2[n], a3[n], a4[n], b1[n], b2[n] in the first-order Taylor expansion of the i-th iteration satisfy the following constraints:

[0294] d sk 2 [n]≤-(a1 (i) [n]) 2 +2a1 (i) [n]a1[n] (35)

[0295] d sr 2[n]≤-(a2 (i) [n]) 2 +2a2 (i) [n]a2[n] (36)

[0296] d se 2 [n]≤-(b1 (i) [n]) 2 +2b1 (i) [n]b1[n] (37)

[0297] a3 2 [n]≤(d sk (i) [n]) 2 +2(q s (i) [n]) T (q s [n]-q s (i) [n]) (38)

[0298] a4 2 [n]≤(d sr (i) [n]) 2 +2(q s (i) [n]) T (q s [n]-q s (i) [n]) (39)

[0299] b2 2 [n]≤(d se (i) [n]) 2 +2(q s (i) [n]) T (q s [n]-q s (i) [n]) (40)

[0300] The transformation of the non-convex constraint (25b) is expressed by the following formula: At this point, constraint (25b) becomes a convex set.

[0301] For the non-convex constraint (25c), the safe flight distance d between the two drones is also considered. min Perform a first-order Taylor expansion at the i-th iteration: d min 2 +||q s (i) [n]|| 2-2(q s (i) [n]-q j (i) [n])(q s [n]) T -||q j (i) [n]|| 2 If ≤0, the non-convex constraint (25c) becomes a convex set.

[0302] P6 is rewritten as:

[0303]

[0304] (25d), (25f), (35)-(40) (41d)

[0305] (d) Optimize the source UAV's transmit power:

[0306] The subproblem of optimizing the flight trajectory of a drone under interference is expressed as:

[0307]

[0308] st(16c) (42b)

[0309] (15c) (42c)

[0310]

[0311] In this optimization subproblem, (42b) and (42c) are both non-convex constraints. For the non-convex constraint (42c), the method is the same as in the trajectory optimization of the source UAV, and the safe flight distance d between the two UAVs is... min Perform a first-order Taylor expansion at the i-th iteration: d min 2 +||q s (i) [n]|| 2 -2(q s (i) [n]-q j (i) [n])(q s [n]) T -||q j (i) [n]|| 2 ≤0

[0312] For the non-convex constraint (42b), similar to the method in the trajectory optimization of the source UAV, the specific steps are as follows: For R k [n], introducing slack variable s jk [n], whose constraints are

[0313]

[0314] but in

[0315] And variable s jk The constraint [n] is still non-convex. We then introduce slack variables c1[n], c2[n], c3[n], and c4[n] such that c1[n] ≥ d. jk [n],c2[n]≥d jr [n],c3[n]≤d jk [n],c4[n]≤d jr [n], s jk [n] is obtained by performing a first-order Taylor expansion on the i-th iteration:

[0316]

[0317] in

[0318] because Possible values ​​can be positive or negative; introduce a binary variable F. jk [n], which satisfies the following condition: when At that time, F jk [n] = 1 indicates that the coherent term is positive, which enhances the signal strength.

[0319]

[0320] when At that time, F jk [n] = 0 indicates that the coherent term is negative, which weakens the signal strength.

[0321]

[0322] Then R k [n] in s jk Perform a Taylor first-order expansion at [n], i.e.

[0323]

[0324] in R obtained through SCA technology k [n] Lower bound.

[0325] Similarly, for R e [n] Introducing variable s je [n], which satisfies the following constraints:

[0326]

[0327] but in

[0328] And variable s je The constraint [n] is still non-convex. We then introduce slack variables d1[n] and d2[n] such that d1[n] ≥ d2[n]. je [n],d2[n]≤d je [n], and introduce F jk [n], then for s je [n] is expanded using a first-order Taylor series to obtain:

[0329]

[0330] Where F jk [n] satisfies: when At that time, F je [n] = 1 indicates that the coherent term is positive, which enhances the signal strength.

[0331]

[0332] when At that time, F jk [n] = 0 indicates that the coherent term is negative, which weakens the signal strength.

[0333]

[0334] Then R e [n] in s je Perform a Taylor first-order expansion at [n], i.e.

[0335]

[0336] in R obtained through SCA technology e [n] Upper bound.

[0337] The slack variables c1[n], c2[n], c3[n], c4[n], d1[n], d2[n] in the first-order Taylor expansion of the i-th iteration satisfy the following constraints:

[0338] d jk 2 [n]≤-(c1 (i) [n]) 2 +2c1 (i) [n]c1[n] (49)

[0339] d jr 2 [n]≤-(c2 (i) [n]) 2 +2c2 (i) [n]c2[n] (50)

[0340] d je 2 [n]≤-(d1 (i) [n]) 2 +2d1 (i) [n]d1[n] (51)

[0341] c3 2 [n]≤(d jk (i) [n]) 2 +2(q j (i) [n]) T (q j [n]-q j (i) [n]) (52)

[0342] c4 2 [n]≤(d jk (i) [n]) 2 +2(q j (i) [n]) T (q j [n]-q j (i) [n]) (53)

[0343] d2 2 [n]≤(d je (i) [n]) 2 +2(q j (i) [n]) T (q j [n]-q j (i) [n]) (54)

[0344] The transformation of the non-convex constraint (42b) is expressed by the following formula: At this point, constraint (42b) becomes a convex set.

[0345] P8 rewritten as:

[0346]

[0347] (42d), (42f), (49)-(54) (55d)

[0348] (e) Optimize the phase shift of the smart reflector:

[0349] The phase optimization subproblem of the smart reflector is expressed as:

[0350]

[0351] st(16c) (56b)

[0352]

[0353] P10 is non-convex. The phase shift matrix of the smart reflector is optimized using the Successive Convex Approximation (SCA) method and the Semidefinite Relaxation (SDR) method: a semidefinite matrix is ​​introduced, and we set... v[n]=[v1[n],v2[n],...,v M [n]], Substituting v[n] into P10, then (55c) is equivalent to transforming the constraint of the vector modulus into To simplify the problem and constraints, and to convert them all into quadratic forms, we introduce...

[0354]

[0355] in At this time

[0356]

[0357] At point At R k [n] and R e [n] is expanded using a first-order Taylor series:

[0358]

[0359]

[0360] in R is obtained through successive convex approximation technique k [n] lower bound, R is obtained through successive convex approximation technique e [n] is the upper bound. Then the non-convex constraint (56b) is transformed into the formula: At this point, constraint (56b) becomes a convex set.

[0361] P10 rewritten as

[0362]

[0363] In step 4, the CVX tool is used to find local approximate solutions to the five sub-problems, and these five local solutions are iterated to obtain the overall approximate optimal solution of the system. Specifically, this involves: initializing the values ​​of variables for maximizing the system's security rate; substituting the initialized variables into the source UAV's transmit power optimization sub-problem to obtain a local approximate solution for the i-th iteration of the source UAV's transmit power optimization sub-problem; substituting the local approximate solution of the i-th iteration of the source UAV's interference power optimization sub-problem and other initialized variables into the interference UAV's interference power optimization sub-problem to obtain a local approximate solution; and substituting the local approximate solutions of the i-th iteration of the source UAV's interference power optimization sub-problem, the interference UAV's interference power optimization sub-problem, and other initialized variables into the source UAV's flight trajectory optimization sub-problem to obtain the source UAV's flight trajectory. The local approximate solution of the trajectory optimization subproblem is obtained by substituting the local approximate solutions of the source UAV interference power optimization subproblem, the interference UAV interference power optimization subproblem, the source UAV flight trajectory optimization subproblem, and other initialized variables into the interference UAV flight trajectory optimization subproblem. The local approximate solution of the interference UAV flight trajectory optimization subproblem is then obtained by substituting the local approximate solutions of the source UAV transmission power optimization subproblem, the interference UAV interference power optimization subproblem, the source UAV flight trajectory optimization subproblem, the interference UAV flight trajectory optimization subproblem, and other initialized variables into the intelligent reflector phase shift optimization subproblem. The number of iterations is continuously increased until the iteration convergence condition is met, yielding the overall approximate optimal solution.

[0364] The effects of the present invention will be further explained below with reference to simulation experiments.

[0365] 1. Simulation conditions and parameter settings:

[0366] The number of ground users is 3. The smart reflector equipped with M=8 reflective elements is located at coordinates 0,0 and altitude 10m. The eavesdropper's location is at coordinates 25,0. Both the source UAV and the jamming UAV are at altitude 20m. The time period is 2s, divided into 10 time slots. The maximum flight speed of both the source UAV and the jamming UAV is 100m / s, and their average flight speed is 50m / s. The initial and final positions of the source UAV are -50,20 and 50,20, respectively. The initial and final positions of the jamming UAV are -50,-20 and 50,-20, respectively. The maximum transmission power of the source UAV is p. smax =30dBm, the maximum interference power for interfering with drones is p j max=20dBm, the noise power spectral density of both ground users and eavesdroppers is -80dBm, all Rice factors are 10dBm, and the channel power gain β0 is -50dB at a reference distance d=1m.

[0367] 2. Simulation content:

[0368] Figure 3 This is a comparison graph of the number of reflective elements in the intelligent reflective surface and the average security rate of the system, showing the average speed of the proposed algorithm with different numbers of reflective elements. We set the number of reflective elements M to 8 and 32 respectively. As can be seen from the graph, as the number of reflective elements M in the intelligent reflective surface increases, the average speed at the legitimate user location increases, indicating that increasing the number of intelligent reflective surface elements can significantly improve the average speed of legitimate users. The optimization algorithm of this invention converges to the maximum speed within 10 iterations.

[0369] Figure 4 The figure shows the variation of the system's average security level with the source UAV's transmission power under intelligent reflective surface conditions with different numbers of reflective elements. As can be seen from the figure, the system's average security level improves when the source UAV's transmission power increases. Increasing the jamming power of the jamming UAV also improves the system's average security level.

[0370] Based on the simulation results and analysis above, this invention improves the average information rate for users by jointly optimizing the trajectory and transmission power of the source UAV, the trajectory and interference power of the jamming UAV, and the phase of the intelligent reflector, and by introducing jamming signals emitted by the jamming UAV to reduce the efficiency of eavesdroppers in intercepting legitimate signals. Furthermore, increasing the number of reflective elements on the intelligent reflector can further enhance system performance. Simultaneously, employing non-orthogonal multiple access technology when ground users receive signals further improves the system's average security rate. The simulation results effectively demonstrate the rapid convergence and high feasibility of the method presented in this invention.

[0371] The technical means disclosed in this invention are not limited to those disclosed in the above embodiments, but also include technical solutions composed of any combination of the above technical features.

Claims

1. A multi-UAV cooperative secure communication method based on intelligent reflective surfaces and non-orthogonal multiple access technology, characterized in that: Specifically, the steps include the following: Step 1: Based on the geographical locations of the source UAV, the jamming UAV, the ground user, and the eavesdropper, establish an air-to-ground channel fading model and a reachability rate model from the source UAV to the ground user and from the source UAV to the eavesdropper. In step 1, the establishment of the air-to-ground channel fading model and the reachability rate from the source UAV to the user, and the reachability rate model from the source UAV to the eavesdropper, includes the following information: K ground terminal users, one ground eavesdropper, one source UAV, one jamming UAV, and one smart reflector; the location of the kth user is represented as... The location of the ground eavesdropper is known, represented as The source drone and the jamming drone simultaneously operate at a fixed altitude H above the ground within a time period T. u Flight, dividing T into N hour slots, the horizontal position of the source UAV is represented as The horizontal position of the jamming drone is represented as The first element of the intelligent reflective surface is considered as a reference point, located at a fixed height H. r horizontal position The intelligent reflective surface is composed of M=M x M y It consists of a uniform planar array of reflective elements, where M x and M y Let x and y represent the number of elements along the x-axis and y-axis, respectively; the phase shift matrix of the smart reflector in the nth time slot is expressed as... in This represents the phase shift generated by the m-th reflecting element within the n-th time slot. Furthermore, the source drone, jamming drone, all ground users, and eavesdroppers are equipped with only a single antenna; all channels are Ricean channels. The channel gain from the source UAV to the smart reflector is expressed as: in α is the path loss exponent, β0 is the channel power gain at the reference distance d0 = 1m, and λ0 is the carrier wavelength. It is the azimuth and elevation angle, K sr It is the Rice factor, d sr [n] is the distance from the UAV in the nth time slot to the smart reflector. Let represent a set of M×1 dimensional composite matrices. This represents the line-of-sight link component from the source drone to the smart reflector. This represents the non-line-of-sight link component from the source drone to the smart reflector. CN(0,1) represents a circularly symmetric complex Gaussian distribution with zero mean and unit variance. The channel gains from the source UAV to the k-th user and the eavesdropper are respectively: Where K sk It is the Rice factor, d sk [n] is the distance from the source drone in the nth time slot to the kth user. This represents the line-of-sight link component from the source drone to the k-th user. K represents the non-line-of-sight link component from the source drone to the k-th user; se It is the Rice factor, d se [n] is the distance from the source drone to the eavesdropper in the nth time slot. This indicates the line-of-sight link components from the source drone to the eavesdropper. This represents the non-line-of-sight link components from the source drone to the eavesdropper; The channel gains from the jamming drone to the smart reflector, the k-th user, and the eavesdropper are respectively: Where K jr It is the Rice factor, d jr [n] represents the distance from the interfering UAV to the smart reflector in the nth time slot. This represents the line-of-sight link component from the interfering drone to the smart reflector. K represents the non-line-of-sight link component from the interfering drone to the smart reflector. jk It is the Rice factor, d jk [n] represents the distance from the interfering drone to the k-th user in the nth time slot. This represents the line-of-sight link component from the interfering drone to the k-th user. This represents the non-line-of-sight link component from the interfering drone to the k-th user; K je It is the Rice factor, d je [n] represents the distance from the interfering drone to the eavesdropper in the nth time slot. This indicates interference with the line-of-sight link components from the drone to the eavesdropper. This indicates the non-line-of-sight link component that interferes with the drone's connection to the eavesdropper. The total channel gain from the source drone to the k-th user and the eavesdropper are respectively: The total channel gain from the jamming drone to the k-th user and the eavesdropper are respectively: The channel gains from the smart reflector to the k-th user and the eavesdropper are respectively Where K rk It is the Rice factor, d rk [n] is the distance from the intelligent reflective surface in the nth time slot to the kth user. This represents the line-of-sight link component from the smart reflector to the k-th user. K represents the non-line-of-sight link component from the smart reflector to the k-th user; re It is the Rice factor, d re [n] is the distance from the intelligent reflective surface to the eavesdropper in the nth time slot. This represents the line-of-sight link component from the smart reflector to the eavesdropper. This represents the non-line-of-sight link component from the smart reflector to the eavesdropper. The source UAV and ground users use non-orthogonal multiple access technology; the reachability rates of the k-th ground user and the eavesdropper in the n-th time slot are respectively represented as: Where p k [n] represents the transmission power of the source UAV when transmitting information to the k-th user in the n-th time slot, p l [n] is the transmission power of the source UAV transmitting information to the l-th user in the n-th time slot, p j [n] represents the interference power of the UAV in the nth time slot. This represents the power of the additive white Gaussian noise at the ground user location. λ represents the power of the additive white Gaussian noise at the eavesdropper's location; k,l [n], l≠k is a binary variable. When the channel gain of the k-th user is worse than that of the l-th user, λ k,l [n] = 1, otherwise λ k,l [n] = 0; The confidentiality rate of the k-th ground user in the n-th time slot is represented by R. sec,k [n] = [R] k [n]-R e [n] + , where [x] + =max{x,0}, if R L [n]-R e The value of [n] is negative in the nth time slot, let the UAV-S transmit power p k If [n] = 0, then R sec,k [n] = R k [n]-R e [n], thus ensuring that the system's confidentiality rate remains non-negative in any time slot; Step 2: To maximize the average confidentiality rate of all ground users, an optimization problem is constructed. Step 2 involves establishing a model that maximizes the confidentiality capacity of all ground users, including building a model with the objective function of maximizing the confidentiality rate of ground users. The objective function is expressed as: In P1, Q s Q represents the flight trajectory of the source drone. j P indicates interference with the flight path of the drone. k p represents the transmit power of the source drone. j The value represents the interference power of the interfering drone, and ψ represents the phase of the smart reflector. The constraints specifically include: Within time T, the initial and final positions of the source and interfering drones are fixed; within a time slot, the distance flown by the drones is less than the maximum distance, and to ensure that the two drones do not collide during flight, there are constraints: Where, q u [0] = q uI q represents the initial position of the drone. u [N] = q uF Indicates the final position of the drone, V max d represents the maximum flight speed of the source drone and the interfering drone. min This indicates the minimum distance that must be maintained between two drones; The phase constraint of the intelligent reflective surface is: Within any time slot, the source UAV's transmit power guarantees that its transmission power to the k-th user is greater than the transmission power to other users, and guarantees that the source UAV's transmit power does not exceed its maximum transmit power. The source UAV's transmit power constraint is as follows: Where p smax Indicates the maximum transmit power of the source UAV; λ k,l [n] satisfies λ k,l [n]+λ l,k [n]=1,λ k,l [n]∈{1,0},d sl [n] represents the distance from the source drone to the l-th user; The interference power constraint for interfering with drones is in p represents the average jamming power of the jamming drone. jmax This indicates the maximum jamming power of the interfering drone; To simplify the objective function, we introduce the variable t. The objective function and constraints are then expressed as follows: st(15a),(15b),(15c),(15d),(15e),(15f),(15g),(15h),(15i)(16b) Step 3: Using the alternating optimization algorithm, the model for maximizing the average security rate of the system is decoupled into the source UAV's transmit power optimization sub-problem and flight trajectory optimization sub-problem, the interference power optimization sub-problem and trajectory optimization sub-problem of the interfering UAV, and the intelligent reflector phase shift optimization sub-problem; Step 4: Use the CVX tool to find local approximate solutions for the five sub-optimization problems mentioned above. Iterate the five local solutions to obtain the overall approximate optimal solution, and obtain the transmission power and flight trajectory of the source UAV, the interference power and flight trajectory of the interfering UAV, and the phase of the smart reflector in each time slot.

2. The multi-UAV cooperative secure communication method based on intelligent reflective surface and non-orthogonal multiple access technology according to claim 1, characterized in that: Step 3, the source UAV's transmit power optimization sub-problem, includes optimizing the source UAV's transmit power. Auxiliary variables are introduced, and the Taylor expansion method is used to optimize the source UAV's transmit power allocation. The source UAV transmit power optimization sub-problem is expressed as: st(16c) (17b) (15e), (15f), (15g), (17c) In this optimization subproblem (17b), the constraint is non-convex. Auxiliary variables are used to transform the non-convex constraint into a convex constraint; R... k [n], R e [n] in p k (i) A first-order Taylor expansion at [n] yields... Where, p k (i) [n] represents the transmit power optimized by the source UAV in the i-th iteration. R obtained through SCA technology k [n] lower bound, It is R e [n] is a convex approximation of the upper bound, a n b n The expressions for the introduced auxiliary variables are as follows: The transformation of the non-convex constraint (17b) is expressed by the formula: Then constraint (17b) becomes a convex set; P2 is rewritten as: (15e), (15f), (15g)(20c) where, p k (i) [n] represents the transmit power optimized by the source UAV in the i-th iteration. R obtained through SCA technology k [n] lower bound, It is R e [n] is a convex approximation of the upper bound, a n b n The expressions for the introduced auxiliary variables are as follows: The transformation of the non-convex constraint (17b) is expressed by the formula: Then constraint (17b) becomes a convex set; P2 is rewritten as: (15e), (15f), (15g)(20c).

3. The multi-UAV cooperative secure communication method based on intelligent reflective surface and non-orthogonal multiple access technology according to claim 1, characterized in that: Step 3, the sub-problem of optimizing the interference power of the jamming drone, includes optimizing the transmission power of the jamming drone. It introduces auxiliary variables and uses Taylor expansion to optimize the interference power allocation of the jamming drone. The sub-problem of optimizing the interference power of the jamming drone is expressed as: st(16c) (21b) (15h), (15i) (21c) In this optimization subproblem (21b), the constraint is non-convex. Auxiliary variables are used to transform the non-convex constraint into a convex constraint; R... k [n], R e [n] in p j (i) A first-order Taylor expansion at [n] yields... Where, p j (i) [n] represents the transmit power optimized by the source UAV in the i-th iteration. R obtained through SCA technology k [n] lower bound, It is R e [n] is a convex approximation of the upper bound, c n ,d n ,e n ,f n The expressions for the introduced auxiliary variables are as follows: The transformation of the non-convex constraint (21b) is expressed by the formula: Then constraint (21b) becomes a convex set; P4 rewritten as: (15h), (15i)(21c).

4. The multi-UAV cooperative secure communication method based on intelligent reflective surface and non-orthogonal multiple access technology as described in claim 1, characterized in that: The sub-problem of optimizing the flight trajectory of the source UAV includes optimizing the flight trajectory of the source UAV, incorporating relaxation variables, and using SCA to perform a local convex approximation on the flight trajectory optimization problem of the source UAV; the sub-problem of optimizing the flight trajectory of the source UAV is expressed as: st(16c)(25b) (15c)(25c) In this optimization subproblem, both (25b) and (25c) are non-convex constraints. For the non-convex constraint (25b), slack variables need to be introduced and Taylor expansion needs to be used to transform (25b) into a convex set. The specific steps are as follows: For R k [n], introducing variable s k [n]z k [n], whose constraints are respectively make And variable s k [n], z k The constraint [n] is non-convex. Then, we introduce slack variables a1[n], a2[n], a3[n], a4[n] such that a1[n] ≥ d. sk [n], a2[n]≥d sr [n], a3[n]≤d sk [n], a4[n]≤d sr [n], then (27) is represented as in Related items The value can be positive or negative, depending on the phase difference between the signals; if the coherence term is positive, it helps increase the channel gain; if it is negative, it weakens the channel gain; a binary variable F is introduced for the coherence term. k [n], which satisfies when At that time, F k [n] = 1 indicates that the coherent term is positive, which enhances the signal strength and satisfies the condition. when At that time, F k [n] = 0 indicates that the coherent term is negative, which strengthens or weakens the effect, satisfying the condition. Then variable s k The constraint (28) of [n] transforms into a convex set, expressed as follows: Then R k [n] in z k A first-order Taylor expansion at [n] yields... in R obtained through SCA technology k [n] lower bound; For R e [n], and R k The optimization method for [n] is similar to introducing slack variables s. e [n], z e [n], with constraints respectively And s e [n], z e The constraint [n] is still non-convex. Further slack variables b1[n] and b2[n] are introduced, satisfying b1[n] ≥ d. se [n],b2[n]≤d se [n], such that (31) is represented as Among them when At that time, F e [n] = 1, indicating that the signal strength is enhanced; thus, we obtain... when At that time, F e [n] = 0 indicates that the signal strength is weakened; thus, we obtain... Then R e [n] in z e A first-order Taylor expansion at [n] yields... in R obtained through SCA technology e [n] is the upper bound; the slack variables a1[n], a2[n], a3[n], a4[n], b1[n], b2[n] are the first-order Taylor expansions in the i-th iteration, which satisfy the constraints: d sk 2 [n]≤-(a1 (i) [n]) 2 +2a1 (i) [n]a1[n] (35) d sr 2 [n]≤-(a2 (i) [n]) 2 +2a2 (i) [n]a2[n] (36) d se 2 [n]≤-(b1 (i) [n]) 2 +2b1 (i) [n]b1[n] (37) a3 2 [n]≤(d sk (i) [n]) 2 +2(q s (i) [n]) T (q s [n]-q s (i) [n]) (38) a4 2 [n]≤(d sr (i) [n]) 2 +2(q s (i) [n]) T (q s [n]-q s (i) [n]) (39) b2 2 [n]≤(d se (i) [n]) 2 +2(q s (i) [n]) T (q s [n]-q s (i) [n]) (40) The transformation of the non-convex constraint (25b) is expressed by the following formula: At this point, constraint (25b) becomes a convex set; For the non-convex constraint (25c), the safe flight distance d between the two drones is also considered. min Perform a first-order Taylor expansion at the i-th iteration: d min 2 +||q s (i) [n]|| 2 -2(q s (i) [n]-q j (i) [n])(q s [n]) T -||q j (i) [n]|| 2 ≤0 At this point, the non-convex constraint (25c) becomes a convex set; P6 is rewritten as: d min 2 +||q s (i) [n]|| 2 -2(q s (i) [n]-q j (i) [n])(q s [n]) T -||q j (i) [n]|| 2 ≤0 (41c) (25d), (25f), (35)-(40) (41d).

5. A multi-UAV cooperative secure communication method based on intelligent reflective surface and non-orthogonal multiple access technology as described in claim 1, characterized in that: The sub-problem of optimizing the flight trajectory of the interfering UAV in step 3 includes optimizing the flight trajectory of the interfering UAV, introducing slack variables, and using SCA to perform a local convex approximation of the flight trajectory optimization problem of the interfering UAV; the sub-problem of optimizing the flight trajectory of the interfering UAV is expressed as: st(16c)(42b) (15c)(42c) In this optimization subproblem, (42b) and (42c) are both non-convex constraints. For the non-convex constraint (42c), the method is the same as in the trajectory optimization of the source UAV, and the safe flight distance d between the two UAVs is... min Perform a first-order Taylor expansion at the i-th iteration: d min 2 +||q s (i) [n]|| 2 -2(q s (i) [n]-q j (i) [n])(q s [n]) T -||q j (i) [n]|| 2 ≤0 For the non-convex constraint (42b), similar to the method in the trajectory optimization of the source UAV, the specific steps are as follows: For R k [n], introducing slack variable s jk [n], whose constraints are but in And variable s jk The constraint [n] is still non-convex. We then introduce slack variables c1[n], c2[n], c3[n], and c4[n] such that c1[n] ≥ d. jk [n],c2[n]≥d jr [n],c3[n]≤d jk [n],c4[n]≤d jr [n], s jk [n] is obtained by performing a first-order Taylor expansion on the i-th iteration: in because Possible values ​​can be positive or negative; introduce a binary variable F. jk [n], which satisfies the following conditions: when At that time, F jk [n] = 1 indicates that the coherent term is positive, which enhances the signal strength; when At that time, F jk [n] = 0 indicates that the coherent term is negative, which weakens the signal strength; Then R k [n] in s jk Perform a first-order Taylor expansion at [n], i.e. in R obtained through SCA technology k [n] lower bound; Similarly, for R e [n] Introducing variable s je [n], which satisfies the following constraints: but in And variable s je The constraint [n] is still non-convex. We then introduce slack variables d1[n] and d2[n] such that d1[n] ≥ d2[n]. je [n],d2[n]≤d je [n], and introduce F jk [n], then for s je [n] is expanded using a first-order Taylor series to obtain: Where F jk [n] satisfies: when At that time, F je [n] = 1 indicates that the coherent term is positive, which enhances the signal strength; when At that time, F jk [n] = 0 indicates that the coherent term is negative, which weakens the signal strength; Then R e [n] in s je Perform a first-order Taylor expansion at [n], i.e. in R obtained through SCA technology e [n] Upper bound; The slack variables c1[n], c2[n], c3[n], c4[n], d1[n], d2[n] in the first-order Taylor expansion of the i-th iteration satisfy the following constraints: d jk 2 [n]≤-(c1 (i) [n]) 2 +2c1 (i) [n]c1[n] (49) d jr 2 [n]≤-(c2 (i) [n]) 2 +2c2 (i) [n]c2[n] (50) d je 2 [n]≤-(d1 (i) [n]) 2 +2d1 (i) [n]d1[n] (51) c3 2 [n]≤(d jk (i) [n]) 2 +2(q j (i) [n]) T (q j [n]-q j (i) [n]) (52) c4 2 [n]≤(d jk (i) [n]) 2 +2(q j (i) [n]) T (q j [n]-q j (i) [n]) (53) d2 2 [n]≤(d je (i) [n]) 2 +2(q j (i) [n]) T (q j [n]-q j (i) [n]) (54) The transformation of the non-convex constraint (42b) is expressed by the following formula: At this point, constraint (42b) becomes a convex set; P8 rewritten as: d min 2 +||q s (i) [n]|| 2 -2(q s (i) [n]-q j (i) [n])(q s [n]) T -||q j (i) [n]|| 2 ≤0 (55c) (42d), (42f), (49)-(54) (55d).

6. The multi-UAV cooperative secure communication method based on intelligent reflective surface and non-orthogonal multiple access technology as described in claim 1, characterized in that: The phase optimization subproblem of the intelligent reflector includes optimizing the phase of the intelligent reflector to maximize the system's security rate; the phase optimization subproblem of the intelligent reflector is expressed as: st(16c) (56b) P10 is non-convex. The phase shift matrix of the smart reflector is optimized using the Successive Convex Approximation (SCA) method and the Semidefinite Relaxation (SDR) method: a semidefinite matrix is ​​introduced, and we set... v[n]=[v1[n],v2[n],...,v M [n]], Substituting v[n] into P10, then (55c) is equivalent to transforming the constraint of the vector modulus into V[n]≥0; To simplify the problem and constraints, and to convert them all into quadratic forms, we introduce... in At this time At point At R k [n] and R e [n] is expanded using a first-order Taylor series: in R obtained through SCA technology k [n] lower bound, R obtained through SCA technology e [n] is the upper bound; then the non-convex constraint (56b) is transformed into the formula: At this point, constraint (56b) becomes a convex set; P10 rewritten as 7. The multi-UAV cooperative secure communication method based on intelligent reflective surface and non-orthogonal multiple access technology as described in claim 1, characterized in that: Step 4, maximizing security, includes: initializing the values ​​of variables for maximizing system security; substituting the initialized variables into the source UAV transmit power optimization subproblem to obtain a local approximate solution to the i-th iteration source UAV transmit power optimization subproblem; substituting the local approximate solution of the i-th iteration source UAV interference power optimization subproblem and other initialized variables into the interference UAV interference power optimization subproblem to obtain a local approximate solution to the interference UAV interference power optimization subproblem; substituting the local approximate solutions of the i-th iteration source UAV interference power optimization subproblem, the interference UAV interference power optimization subproblem, and other initialized variables into the source UAV flight trajectory optimization subproblem to obtain a local approximate solution to the source UAV flight trajectory optimization subproblem; and ...; and substituting the local approximate solutions of the i-th iteration source UAV interference power optimization subproblem, the interference UAV interference power optimization subproblem, and other initialized variables into the source UAV flight trajectory optimization subproblem; and substituting the local approximate solutions of the i-th iteration source UAV interference power optimization subproblem, the interference UAV interference power optimization subproblem, and other initialized variables into the source UAV flight trajectory optimization subproblem; and substituting the local approximate solutions of the i-th iteration source UAV interference power optimization subproblem, the interference UAV interference power optimization subproble Substituting the local approximate solutions of the source UAV flight trajectory optimization subproblem, the source UAV flight trajectory optimization subproblem, and other initialized variables into the interference UAV flight trajectory optimization subproblem, we obtain the local approximate solution of the interference UAV flight trajectory optimization subproblem. Substituting the local approximate solutions of the source UAV transmit power optimization subproblem, the interference UAV interference power optimization subproblem, the source UAV flight trajectory optimization subproblem, the interference UAV flight trajectory optimization subproblem, and other initialized variables into the intelligent reflector phase shift optimization subproblem, we obtain the local approximate solution of the intelligent reflector phase shift optimization subproblem. Continuously increasing the number of iterations until the iteration convergence condition is met, we obtain the transmit power and flight trajectory of the source UAV, the interference power and flight trajectory of the interference UAV, and the phase shift of the intelligent reflector, thus obtaining the overall approximate optimal solution and ending the process.

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