Multi-unmanned aerial vehicle cooperative security communication method based on intelligent reflecting surface and non-orthogonal multiple access technology

Abstract

The invention provides a multi-unmanned aerial vehicle cooperative security communication method based on an intelligent reflecting surface and a non-orthogonal multiple access technology. The method comprises the following steps: initializing configuration information of a ground user, an eavesdropper and an unmanned aerial vehicle; initializing an iteration frequency variable; according to the initial configuration information, iteration is carried out; optimizing the transmitting power and the flight path of the source unmanned aerial vehicle, the interference power and the flight path of the interference unmanned aerial vehicle and the phase of the intelligent reflecting surface; and calculating an objective function value of the current iteration, and judging whether the difference between the objective function of the current iteration and the objective function of the last iteration is smaller than a threshold value or not. If yes, the optimal transmitting power and the optimal flight path of the source unmanned aerial vehicle, the optimal interference power and the optimal flight path of the interference unmanned aerial vehicle, the optimal phase of the intelligent reflecting surface and the average secrecy rate of the system are obtained; otherwise, continuously adding one to the number of iterations, and optimizing each variable. The non-orthogonal multiple access technology (NOMA) is adopted, and the safety of the system can be improved to the maximum extent.

Description

Technical Field

[0001] The present invention relates to the field of computer wireless communication technology, and in particular to a multi-UAV collaborative secure communication method based on an intelligent reflective surface and non-orthogonal multiple access technology. Background Art

[0002] Drones are widely used in wireless communication systems due to their high mobility, fast deployment speed and low cost. Compared with traditional ground wireless channels that are susceptible to path loss, shadowing and multipath fading in urban environments, drones take advantage of their height and are more likely to establish aerial base stations through line-of-sight connections with ground equipment. However, due to the broadcast nature of wireless channels and the existence of line-of-sight link channels, it is easier for ground eavesdroppers to illegally intercept information sent by drones to ground users, resulting in information leakage and security risks.

[0003] Smart reflective surfaces can enhance signal coverage and are low-cost, and are widely used in various wireless communication scenarios. At the same time, the phase of the reflected signal of the smart reflective surface can be adjusted to offset the direct signal when it is received, thereby reducing information leakage. At the physical layer security technology level, jammers are introduced to reduce the risk of eavesdropping. Jammers can also be deployed on assisting drones to transmit jamming signals to eavesdroppers, further reducing the risk of eavesdropping.

[0004] The wireless transmission rate requirement for drone communications is high. Non-orthogonal multiple access technology can further improve the transmission speed in multi-user scenarios and maximize the security performance of drone communications. Summary of the invention

[0005] In view of the shortcomings of the above-mentioned prior art, the present invention proposes a multi-UAV collaborative secure communication method. In the presence of an eavesdropper, the multi-UAV collaborative method is used, one UAV acts as a base station to transmit information to the user on the ground, and another UAV acts as a jammer to transmit a jamming signal to interfere with the eavesdropper. In addition, the channel environment of the link is improved by an intelligent reflective surface, and the ground user uses non-orthogonal addressing technology when receiving information, which further improves the confidentiality of the communication between the UAV and the ground, and greatly improves the confidentiality performance of the system.

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

[0007] Step 1: According to the geographical locations of the source UAV, the jamming UAV, the intelligent reflective surface, the users on the ground, and the eavesdropper, an air-to-ground channel fading model and a reachable rate model from the source UAV to the ground user and a reachable rate model from the source UAV to the eavesdropper are established;

[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 system average confidentiality rate maximization model is decoupled into the source UAV transmission power optimization subproblem and flight trajectory optimization subproblem, the interference UAV interference power optimization subproblem and trajectory optimization subproblem, and the smart reflection surface phase shift optimization subproblem.

[0010] Step 4: Use the CVX tool to find local approximate solutions to the above five sub-optimization problems respectively, 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 interference UAV, and the phase of the smart reflective surface in each time slot.

[0011] Furthermore, in step 1, the geographical location information of the secure communication of the UAV includes: K ground terminal users, a ground eavesdropper, a source UAV, a jammer UAV and a smart reflective surface; the location of the kth user is expressed as The location of the ground eavesdropper is known and can be expressed as The source UAV and the jammer UAV simultaneously fly at a fixed height H above the ground within a time period T. u Flight, T is divided into N small time slots, and the horizontal position of the source drone is expressed as The horizontal position of the jamming drone is expressed as The first element of the smart reflective surface is considered as the reference point, which is located at a fixed height H. r Horizontal position The intelligent reflective surface has M=M x M y A uniform planar array of reflective elements, where M x and M y denotes the number of elements along the x-axis and y-axis respectively. The phase shift matrix of the smart reflector at the nth time slot is expressed as in represents the phase shift produced by the mth reflective element in the nth time slot, In addition, the source drone, jammer drone, all ground users and eavesdroppers are equipped with only single antennas. All channels are Ricean channels.

[0012] The channel gain from the source drone to the smart reflective surface is expressed as:

[0013]

[0014] in α is the path loss exponent, β0 is the channel power gain at the reference distance d0=1m, λ0 is the carrier wavelength, are the azimuth and elevation angle of arrival, K sr is the Rice factor, d sr [n] is the distance from the source drone to the smart reflective surface in the nth time slot, represents a set of M×1 dimensional composite matrices, represents the line-of-sight link component from the source UAV to the smart reflector, represents the non-line-of-sight link component from the source UAV to the smart reflective surface, 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 kth user and the eavesdropper are:

[0016]

[0017] Where K sk is the Rice factor, d sk [n] is the distance from the source drone to the kth user in the nth time slot, represents the line-of-sight link component from the source UAV to the kth user, K represents the non-line-of-sight link component from the source UAV to the kth user; se is the Rice factor, d se [n] is the distance from the source drone to the eavesdropper at the nth time slot, represents the line-of-sight link component from the source UAV to the eavesdropper, represents the non-line-of-sight link component from the source UAV to the eavesdropper;

[0018] The channel gains from the jammer UAV to the smart reflective surface, the kth user, and the eavesdropper are:

[0019]

[0020] Where K jr is the Rice factor, d jr [n] is the distance from the jammer drone to the smart reflective surface in the nth time slot, represents the line-of-sight link component from the jammer UAV to the smart reflector, K represents the non-line-of-sight link component from the jammer UAV to the smart reflective surface; jk is the Rice factor, d jk [n] is the distance from the interfering drone to the kth user in the nth time slot, represents the line-of-sight link component from the interfering UAV to the kth user, K represents the non-line-of-sight link component from the interfering UAV to the kth user; je is the Rice factor, d je[n] is the distance from the jammer drone to the eavesdropper at the nth time slot, represents the line-of-sight link component from the jammer UAV to the eavesdropper, Represents the non-line-of-sight link component from the jamming UAV to the eavesdropper.

[0021] The total channel gains from the source drone to the kth user and the eavesdropper are:

[0022]

[0023] The total channel gains from the jammer UAV to the kth user and the eavesdropper are:

[0024]

[0025] The channel gains from the smart reflector to the kth user and the eavesdropper are

[0026]

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

[0028] Non-orthogonal multiple access technology is used between the source UAV and the ground user. The achievable rates of the kth ground user and the eavesdropper in the nth time slot are respectively expressed as:

[0029]

[0030] where p k [n] is the transmission power of the source UAV when transmitting information to the kth user in the nth time slot, p l [n] is the transmission power of the source UAV when transmitting information to the lth user in the nth time slot, p j [n] is the jamming power of the UAV in the nth time slot, represents the power of additive white Gaussian noise at the ground user, represents the power of additive Gaussian white noise at the eavesdropper; λ k,l[n](l≠k) is a binary variable. When the channel gain of the kth user is worse than the channel gain of the lth user, λ k,l [n]=1, otherwise λ k,l [n]=0.

[0031] The confidentiality rate of the kth ground user in the nth time slot is expressed as 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 can make the UAV-S transmit power p k [n]=0, then R sec,k [n] = R k [n]-R e [n], thus ensuring that the system confidentiality rate remains non-negative in any time slot.

[0032] Further, in step 2, the established optimization problem specifically includes an objective function and constraint conditions;

[0033]

[0034] In P1, Q s represents the flight trajectory of the source UAV, Q j represents the flight trajectory of the source UAV, P k represents the transmission power of the source UAV, P k represents the interference power of the jamming UAV, and ψ represents the phase of the smart reflective surface.

[0035] The constraints include:

[0036] In time T, the initial and final positions of the source UAV and the interference UAV are fixed; in a time slot, the distance flown by the UAV is less than the maximum distance, and in order to ensure that the two UAVs do not collide during the flight, there are constraints:

[0037]

[0038]

[0039]

[0040] Among them, q u [0] = q uI represents the initial position of the drone, q u [N] = q uFIndicates the end position of the drone, V max represents the maximum flight speed of the source UAV and the jammer UAV, d min Indicates the minimum distance between two drones;

[0041] The phase constraint of the smart reflector is:

[0042]

[0043] In any time slot, the transmission power of the source UAV ensures that the transmission power to the kth user is greater than the transmission power of other users, and ensures that the transmission power of the source UAV is not higher than its maximum transmission power. The transmission power constraint of the source UAV is

[0044]

[0045] where p s max represents the maximum transmission power of the source UAV; k,l [n] Satisfaction λ k,l [n]+λ l,k [n]=1,λ k,l [n]∈{1,0},d sl [n] represents the distance from the source UAV to the lth user.

[0046] The jamming power constraint of the jamming UAV is

[0047]

[0048] in represents the average interference power of the jamming UAV, p jmax Indicates the maximum jamming power of the jamming drone.

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

[0050]

[0051] In order to simplify the objective function, the variable t is introduced, and the objective function and constraints are expressed as

[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 optimization sub-problems using an alternating optimization algorithm. The specific steps are as follows:

[0056] a. The transmission power optimization sub-problem of the source UAV includes optimizing the transmission power of the source UAV to maximize the confidentiality rate of the system; introducing auxiliary variables and using the Taylor expansion method to optimize the transmission power allocation of the source UAV. The transmission power optimization sub-problem of the source UAV is expressed as:

[0057]

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

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

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

[0061]

[0062] Among them, p k (i) [n] represents the transmission power optimized by the source UAV at the i-th iteration, is obtained by SCA technology k [n] lower bound, YesR e [n] Convex approximation of the upper bound, a n , b n are the auxiliary variables introduced, and their expressions are

[0063]

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

[0065] P2 is rewritten as:

[0066]

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

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

[0069]

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

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

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

[0073]

[0074] Among them, p j (i) [n] represents the transmission power optimized by the source UAV at the i-th iteration, is obtained by SCA technology k [n] lower bound, YesR e [n] Convex approximation of the upper bound, c n ,d n ,e n ,f n are the auxiliary variables introduced, and their expressions are

[0075]

[0076] The non-convex constraint (21b) is transformed into the formula: Then constraint (21b) becomes a convex set.

[0077] P4 is 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 confidentiality rate of the system; introducing slack 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:

[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), it is necessary to introduce slack variables and use the Taylor expansion method to convert (25b) into a convex set. The specific steps are as follows: For R k [n], introduce variable s k [n]z k [n], whose constraints are

[0086]

[0087] (26), (27) The variable s k [n],z k The constraint of [n] is non-convex, and then introduce slack variables a1[n], a2[n], a3[n], a4[n] to make a1[n] ≥ d sk [n],a2[n]≥d sr [n],a3[n]≤d sk [n],a4[n]≤d sr [n], then (27)205 is expressed as

[0088]

[0089] in

[0090]

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

[0092] When F k [n] = 1, indicating that the coherence term is positive, enhancing the signal strength, satisfying

[0093]

[0094] when When Fk [n] = 0, indicating that the coherence term is negative, strengthening the weakening strength, satisfying

[0095]

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

[0097]

[0098] Then R k [n] in z k The first-order Taylor expansion at [n] gives

[0099]

[0100] in is obtained by SCA technology k [n] Lower bound.

[0101] For R e [n], with R k The optimization method of [n] is similar to introducing the slack variable s e [n],z e [n], the constraints are

[0102]

[0103] And s e [n],z e The constraint of [n] is still non-convex. Then, slack variables b1[n] and b2[n] are introduced to satisfy b1[n]≥d se [n],b2[n]≤d se [n], so that (31) can be expressed as

[0104]

[0105] Among them When F e [n] = 1, indicating enhanced signal strength.

[0106]

[0107] when When F e [n] = 0, which means the signal strength is weakened.

[0108]

[0109] Then R e [n] in z e The first-order Taylor expansion at [n] gives

[0110]

[0111] in is obtained by SCA technology e [n] Upper bound.

[0112] The slack variables a1[n], a2[n], a3[n], a4[n], b1[n], b2[n] are first-order Taylor expansions at the i-th iteration, which satisfy the constraints:

[0113]

[0114] Then the non-convex constraint (25b) is transformed into the formula: At this time, constraint (25b) becomes a convex set.

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

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

[0117] P6 is rewritten as:

[0118]

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

[0120] d. The flight trajectory optimization sub-problem 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 safe flight distance d of the two UAVs is calculated in the same way as in the trajectory optimization of the source UAV. 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), the method is similar to that in the trajectory optimization of the source UAV. The specific steps are as follows: k [n], introduce slack variable s jk [n], whose constraints are

[0127]

[0128] but in

[0129] The variable s jk The constraint of [n] is still non-convex, and slack variables c1[n], c2[n], c3[n], c4[n] are introduced to make c1[n] ≥ d jk [n],c2[n]≥d jr [n],c3[n]≤d jk [n],c4[n]≤d jr [n],s jk [n] Perform a first-order Taylor expansion at the i-th iteration to obtain:

[0130]

[0131] in

[0132] because Can be positive or negative, introduce binary variable F jk [n], which satisfies the following conditions:

[0133] when When F jk [n] = 1, indicating that the coherence term is positive, which enhances the signal strength.

[0134]

[0135] when When F jk [n] = 0, indicating that the coherence term is negative, which weakens the signal strength.

[0136]

[0137] Then R k [n] in s jk [n] is a Taylor first-order expansion, that is,

[0138]

[0139] in is obtained by SCA technology k [n] Lower bound.

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

[0141]

[0142] but in

[0143] The variable s je [n], the constraint is still non-convex, and then introduce slack variables d1[n], d2[n] to make d1[n]≥d je [n],d2[n]≤d je [n], and introduce F jk [n], then for s je [n] Perform a first-order Taylor expansion to obtain:

[0144]

[0145] where F jk [n] Satisfy: when When F je [n] = 1, indicating that the coherence term is positive, which enhances the signal strength.

[0146]

[0147] when When F jk [n] = 0, indicating that the coherence term is negative, which weakens the signal strength.

[0148]

[0149] Then R e [n] in s je [n] is a Taylor first-order expansion, that is

[0150]

[0151] in is obtained by SCA technology e [n] Upper bound.

[0152] The slack variables c1[n], c2[n], c3[n], c4[n], d1[n], d2[n] are first-order Taylor expansions at the i-th iteration, which satisfy the 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] Then the non-convex constraint (42b) is transformed into the formula: At this time, constraint condition (42b) becomes a convex set.

[0160] P8 is 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 smart reflective surface includes optimizing the phase of the smart reflective surface to maximize the confidentiality rate of the system. The phase optimization sub-problem of the smart reflective surface is expressed as:

[0165]

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

[0167]

[0168] P10 is non-convex, and the phase shift matrix of the smart reflector is optimized using the successive convex approximation (SCA) method and semidefinite relaxation (SDR): a semidefinite matrix is ​​introduced, and v[n]=[v1[n],v2[n],...,v M [n]], Substituting v[n] into P10, (55c) is equivalent to the vector norm constraint being transformed into

[0169] In order to simplify the problem and constraints and convert them into quadratic form, we introduce

[0170]

[0171] in At this time, get

[0172]

[0173] At the point At R k [n] and R e [n] Perform a first-order Taylor expansion:

[0174]

[0175]

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

[0177] P10 is rewritten as

[0178]

[0179] Further, in step 4, the CVX tool is used to respectively find local approximate solutions to the above five sub-problems, and the five local solutions are iterated to obtain the approximate optimal solution of the system as a whole. The specific method refers to: initializing the values ​​of the variables of the system confidentiality rate maximization problem; substituting the initialized variables into the source UAV transmission power optimization sub-problem to obtain the local approximate solution of the source UAV transmission power optimization sub-problem of the i-th iteration; substituting the local approximate solution of the i-th iteration source UAV interference power optimization sub-problem and other initialized variables into the interference UAV interference power optimization sub-problem to obtain the local approximate solution of the interference UAV interference power optimization sub-problem; substituting the local approximate solution of the i-th iteration source UAV interference power optimization sub-problem, the local approximate solution of the interference UAV interference power optimization sub-problem and other initialized variables into the source UAV flight trajectory optimization sub-problem to obtain the local approximate solution of the source UAV flight trajectory optimization sub-problem; the i-th iteration The local approximate solution of the source UAV interference power optimization subproblem, the local approximate solution of the interference UAV interference power optimization subproblem, the local approximate solution of the source UAV flight trajectory optimization subproblem and other initialized variables are substituted into the interference UAV flight trajectory optimization subproblem to obtain the local approximate solution of the interference UAV flight trajectory optimization subproblem; the local approximate solution of the i-th iteration source UAV transmission power optimization subproblem, the local approximate solution of the interference UAV interference power optimization subproblem, the local approximate solution of the source UAV flight trajectory optimization subproblem, the local approximate solution of the interference UAV flight trajectory optimization subproblem and other initialized variables are substituted into the intelligent reflection surface phase shift optimization subproblem to obtain the local approximate solution of the intelligent reflection surface phase shift optimization subproblem; the number of iterations is continuously increased until the iteration convergence condition is met, the transmission 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 reflection surface are obtained, and the overall approximate optimal solution is obtained.

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

[0181] First, the present invention takes into account the impact of eavesdroppers on the wireless communication transmission rate, introduces interference drones to send interference signals to reduce the eavesdropping rate, and the system can adjust the interference flight trajectory according to the dynamic changes of the user's location and environment to enhance the dynamic optimization capability, thereby increasing the achievable rate from the source drone to the ground user. In the case of multiple ground users, non-orthogonal multiple access technology is considered to further improve the user's achievable rate.

[0182] Second, the present invention designs an alternating iterative optimization algorithm, transforms the optimization problem into a series of convex optimization sub-problems and uses successive convex approximation (SCA) and semidefinite relaxation (SDR) to solve the sub-problems, solving the joint optimization of the flight trajectory of the source UAV, the trajectory source of the jamming UAV, the transmission power of the source UAV, the jamming power of the jamming UAV, and the phase shift of the intelligent reflective surface under such a system. Jointly solving the optimization problem, the confidentiality rate of the system, and the simulation experiment also verified the effectiveness and rapid convergence of the method of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0184] Figure 2 It is a schematic diagram of a flow chart in an embodiment of the present invention;

[0185] Figure 3 It is a comparison chart between the number of reflective elements of the intelligent reflective surface and the average confidentiality rate of the system;

[0186] Figure 4 This is a graph showing how the average confidentiality rate of the system changes with the transmission power of the source UAV under the conditions of the intelligent reflective surface with different numbers of reflective elements of the present invention. DETAILED DESCRIPTION

[0187] The present invention is further explained below in conjunction with the accompanying drawings and specific embodiments. It should be understood that the following specific embodiments are only used to illustrate the present invention and are not used to limit the scope of the present invention. It should be noted that the words "front", "rear", "left", "right", "upper" and "lower" used in the following description refer to directions in the accompanying drawings, and the words "inner" and "outer" refer to directions toward or away from the geometric center of a specific component, respectively.

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

[0189] Step 1: According to the geographical locations of the source UAV, the interfering UAV, the users on the ground, and the eavesdropper, an air-to-ground channel fading model and a reachable rate model from the source UAV to the ground user and a reachable rate model from the source UAV to the eavesdropper are established;

[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 system average confidentiality rate maximization model is decoupled into the source UAV transmission power optimization subproblem and flight trajectory optimization subproblem, the interference UAV interference power optimization subproblem and trajectory optimization subproblem, and the smart reflection surface phase shift optimization subproblem.

[0192] Step 4: Use the CVX tool to find local approximate solutions to the above five sub-optimization problems respectively, 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 interference UAV, and the phase of the smart reflective surface in each time slot.

[0193] Furthermore, the present invention considers a multi-UAV cooperative secure communication system based on intelligent reflective surfaces and non-orthogonal multiple access technology, such as Figure 1 As mentioned above, for step 1: Figure 1 The specific model of the present invention is shown, including: K ground terminal users, a ground eavesdropper, a source drone, a jammer drone and a smart reflective surface; the position of the kth user is expressed as The location of the ground eavesdropper is known and can be expressed as The source UAV and the jammer UAV simultaneously fly at a fixed height H above the ground within a time period T. u Flight, T is divided into N small time slots, and the horizontal position of the source drone is expressed as The horizontal position of the jamming drone is expressed as The first element of the smart reflective surface is considered as the reference point, which is located at a fixed height H. r Horizontal position The intelligent reflective surface has M=M x M y A uniform planar array of reflective elements, where M x and M y denotes the number of elements along the x-axis and y-axis respectively. The phase shift matrix of the smart reflector at the nth time slot is expressed as in represents the phase shift produced by the mth reflective element in the nth time slot, In addition, the source drone, jammer drone, all ground users and eavesdroppers are equipped with only single antennas. All channels are Ricean channels.

[0194] The channel gain from the source drone to the smart reflective surface is expressed as:

[0195]

[0196] in α is the path loss exponent, β0 is the channel power gain at the reference distance d0=1m, λ0 is the carrier wavelength, are the azimuth and elevation angle of arrival, K sr is the Rice factor, d sr [n] is the distance from the source drone to the smart reflective surface in the nth time slot, represents a set of M×1 dimensional composite matrices, represents the line-of-sight link component from the source UAV to the smart reflector, represents the non-line-of-sight link component from the source UAV to the smart reflective surface, 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 kth user and the eavesdropper are:

[0198]

[0199] Where K sk is the Rice factor, d sk [n] is the distance from the source drone to the kth user in the nth time slot, represents the line-of-sight link component from the source UAV to the kth user, K represents the non-line-of-sight link component from the source UAV to the kth user; se is the Rice factor, d se [n] is the distance from the source drone to the eavesdropper at the nth time slot, represents the line-of-sight link component from the source UAV to the eavesdropper, represents the non-line-of-sight link component from the source UAV to the eavesdropper;

[0200] The channel gains from the jammer UAV to the smart reflective surface, the kth user, and the eavesdropper are:

[0201]

[0202]

[0203] Where K jr is the Rice factor, d jr [n] is the distance from the jammer drone to the smart reflective surface in the nth time slot, represents the line-of-sight link component from the jammer UAV to the smart reflector, K represents the non-line-of-sight link component from the jammer UAV to the smart reflective surface; jk is the Rice factor, d jk [n] is the distance from the interfering drone to the kth user in the nth time slot, represents the line-of-sight link component from the interfering UAV to the kth user, K represents the non-line-of-sight link component from the interfering UAV to the kth user; je is the Rice factor, d je [n] is the distance from the jammer drone to the eavesdropper at the nth time slot, represents the line-of-sight link component from the jammer UAV to the eavesdropper, Represents the non-line-of-sight link component from the jamming UAV to the eavesdropper.

[0204] The total channel gains from the source drone to the kth user and the eavesdropper are:

[0205]

[0206] The total channel gains from the jammer UAV to the kth user and the eavesdropper are:

[0207]

[0208] The channel gains from the smart reflector to the kth user and the eavesdropper are

[0209]

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

[0211] Non-orthogonal multiple access technology is used between the source UAV and the ground user. The achievable rates of the kth ground user and the eavesdropper in the nth time slot are respectively expressed as:

[0212]

[0213] where p k [n] is the transmission power of the source UAV when transmitting information to the kth user in the nth time slot, p l [n] is the transmission power of the source UAV when transmitting information to the lth user in the nth time slot, p j [n] is the jamming power of the UAV in the nth time slot, represents the power of additive white Gaussian noise at the ground user, represents the power of additive Gaussian white noise at the eavesdropper; λ k,l [n](l≠k) is a binary variable. When the channel gain of the kth user is worse than the channel gain of the lth user, λ k,l [n]=1, otherwise λ k,l [n]=0.

[0214] The confidentiality rate of the kth ground user in the nth time slot is expressed as 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 can make the UAV-S transmit power p k [n]=0, then R sec,k [n] = R k [n]-R e [n], thus ensuring that the system confidentiality rate remains non-negative in any time slot. For step 2, an optimization problem is constructed with the goal 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 represents the flight trajectory of the source UAV, Q j represents the flight trajectory of the source UAV, P k represents the transmission power of the source UAV, P k represents the interference power of the jamming UAV, and ψ represents the phase of the smart reflective surface.

[0217] The constraints include:

[0218] In time T, the initial and final positions of the source UAV and the interference UAV are fixed; in a time slot, the distance flown by the UAV is less than the maximum distance, and in order to ensure that the two UAVs do not collide during the flight, there are constraints:

[0219]

[0220]

[0221]

[0222] Among them, q u [0] = q uI represents the initial position of the drone, q u [N] = q uF Indicates the end position of the drone, V max represents the maximum flight speed of the source UAV and the jammer UAV, d min Indicates the minimum distance between two drones;

[0223] The phase constraint of the smart reflector is:

[0224]

[0225] In any time slot, the transmission power of the source UAV ensures that the transmission power to the kth user is greater than the transmission power of other users, and ensures that the transmission power of the source UAV is not higher than its maximum transmission power. The transmission power constraint of the source UAV is

[0226]

[0227]

[0228] where p s max represents the maximum transmission power of the source UAV; k,l [n] Satisfaction λ k,l [n]+λ l,k [n]=1,λ k,l [n]∈{1,0}, d sl [n] represents the distance from the source UAV to the lth user.

[0229] The jamming power constraint of the jamming UAV is

[0230]

[0231] where p j represents the average interference power of the jamming UAV, p jmax In order to simplify the objective function, the variable t is introduced, and the objective function and constraints are expressed as

[0232]

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

[0234]

[0235] Step 3, the source UAV transmission power and flight trajectory, the jamming UAV interference power and trajectory, and the phase shift of the smart reflector are jointly optimized 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, and iteratively solves the five sub-problems by alternately optimizing them to obtain an approximate solution to the original problem.

[0236] (a) Optimize the source UAV transmission power:

[0237] The source UAV transmission power optimization sub-problem is expressed as:

[0238]

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

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

[0241] For the non-convex constraint (17b), auxiliary variables can be used to transform it into a convex constraint; k [n],R e [n] in p k (i) The first-order Taylor expansion at [n] gives

[0242]

[0243] Among them, p k (i) [n] represents the transmission power optimized by the source UAV at the i-th iteration, is obtained by SCA technology k [n] lower bound, YesR e [n] Convex approximation of the upper bound, a n , b n are the auxiliary variables introduced, and their expressions are

[0244]

[0245] The transformation of the non-convex constraint (17b) is expressed as: 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 UAVs:

[0250] The source UAV transmission power optimization sub-problem 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; k [n], R e [n] in p j (i) The first-order Taylor expansion at [n] gives

[0255]

[0256] Among them, p j (i) [n] represents the transmission power optimized by the source UAV at the i-th iteration, is obtained by SCA technology k [n] lower bound, YesR e [n] Convex approximation of the upper bound, c n ,d n ,e n ,f n are the auxiliary variables introduced, and their expressions are

[0257]

[0258] The non-convex constraint (21b) is transformed into the formula: Then constraint (21b) becomes a convex set.

[0259] P4 is rewritten as:

[0260]

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

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

[0263] The sub-problem of source UAV flight trajectory optimization is expressed as:

[0264]

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

[0266] (15c) (25c)

[0267]

[0268] For the non-convex constraint (25b), it is necessary to introduce slack variables and use the Taylor expansion method to transform (25b) into a convex set. The specific steps are as follows: k [n], introduce variable s k [n]z k [n], whose constraints are

[0269]

[0270] make The variable s k [n],z k The constraint of [n] is non-convex, and then introduce slack variables a1[n], a2[n], a3[n], a4[n] to make a1[n] ≥ d sk [n],a2[n]≥d sr [n],a3[n]≤d sk [n],a4[n]≤d sr [n], then (27) can be expressed as

[0271]

[0272] in Related items It can be positive or negative, depending on the phase difference between the signals. If the coherence term is positive, it helps to increase its channel gain; if it is negative, it weakens its channel gain. A binary variable F is introduced for the coherence term k [n], which satisfies When F k [n] = 1, indicating that the coherence term is positive, enhancing the signal strength, satisfying

[0273]

[0274] when When F k [n] = 0, indicating that the coherence term is negative, strengthening the weakening strength, satisfying

[0275]

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

[0277]

[0278] Then R k [n] in z k The first-order Taylor expansion at [n] gives

[0279]

[0280] in is obtained by SCA technology k [n] Lower bound.

[0281] For R e [n], with Rk The optimization method of [n] is similar to introducing the slack variable s e [n],z e [n], the constraints are

[0282]

[0283]

[0284] And s e [n],z e The constraint of [n] is still non-convex. Then, slack variables b1[n] and b2[n] are introduced to satisfy b1[n]≥d se [n],b2[n]≤d se [n], so that (31) can be expressed as

[0285]

[0286] Among them When F e [n] = 1, indicating enhanced signal strength.

[0287]

[0288] when When F e [n] = 0, which means the signal strength is weakened.

[0289]

[0290] Then R e [n] in z e The first-order Taylor expansion at [n] gives

[0291]

[0292] in is obtained by SCA technology e [n] Upper bound.

[0293] The slack variables a1[n], a2[n], a3[n], a4[n], b1[n], b2[n] are first-order Taylor expansions at the i-th iteration, which satisfy the 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] Then the non-convex constraint (25b) is transformed into the formula: At this time, constraint (25b) becomes a convex set.

[0301] For the non-convex constraint (25c), the safe flight distance d between the two drones 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, then 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 transmission power:

[0306] The sub-problem of interference UAV flight trajectory optimization 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 safe flight distance d of the two UAVs is calculated in the same way as in the trajectory optimization of the source UAV. 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), the method is similar to that in the trajectory optimization of the source UAV. The specific steps are as follows: k [n], introduce slack variable s jk [n], whose constraints are

[0313]

[0314] but in

[0315] The variable s jk The constraint of [n] is still non-convex, and slack variables c1[n], c2[n], c3[n], c4[n] are introduced to make c1[n] ≥ d jk [n],c2[n]≥d jr [n],c3[n]≤d jk [n],c4[n]≤d jr [n],s jk [n] Perform a first-order Taylor expansion at the i-th iteration to obtain:

[0316]

[0317] in

[0318] because Can be positive or negative, introduce binary variable F jk [n], which satisfies the following conditions: When F jk [n] = 1, indicating that the coherence term is positive, which enhances the signal strength.

[0319]

[0320] when When F jk [n] = 0, indicating that the coherence term is negative, which weakens the signal strength.

[0321]

[0322] Then R k [n] in s jk [n] is a Taylor first-order expansion, that is

[0323]

[0324] in is obtained by SCA technology k [n] Lower bound.

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

[0326]

[0327] but in

[0328] The variable s je [n], the constraint is still non-convex, and then introduce slack variables d1[n], d2[n] to make d1[n]≥d je [n],d2[n]≤d je [n], and introduce F jk [n], then for s je [n] Perform a first-order Taylor expansion to obtain:

[0329]

[0330] Among them, F jk [n] Satisfy: when When F je [n] = 1, indicating that the coherence term is positive, which enhances the signal strength.

[0331]

[0332] when When F jk [n] = 0, indicating that the coherence term is negative, which weakens the signal strength.

[0333]

[0334] Then R e [n] in s je [n] is a Taylor first-order expansion, that is,

[0335]

[0336] in is obtained by SCA technology e [n] Upper bound.

[0337] The slack variables c1[n], c2[n], c3[n], c4[n], d1[n], d2[n] are first-order Taylor expansions at the i-th iteration, which satisfy the 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] Then the non-convex constraint (42b) is transformed into the formula: At this time, constraint condition (42b) becomes a convex set.

[0345] P8 is rewritten as:

[0346]

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

[0348] (e) Optimizing smart reflector phase shift:

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

[0350]

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

[0352]

[0353] P10 is non-convex, and the phase shift matrix of the smart reflector is optimized using the successive convex approximation (SCA) method and semidefinite relaxation (SDR): a semidefinite matrix is ​​introduced, and v[n]=[v1[n],v2[n],...,v M [n]], Substituting v[n] into P10, (55c) is equivalent to the vector norm constraint being transformed into In order to simplify the problem and constraints and convert them into quadratic form, we introduce

[0354]

[0355] in At this time, get

[0356]

[0357] At the point At R k [n] and R e [n] Perform a first-order Taylor expansion:

[0358]

[0359]

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

[0361] P10 is rewritten as

[0362]

[0363] In step 4, the CVX tool is used to respectively find local approximate solutions to the above five sub-problems, and the five local solutions are iterated to obtain the approximate optimal solution of the system as a whole. The specific method is as follows: initialize the values ​​of the variables of the system confidentiality rate maximization problem; substitute the initialized variables into the source UAV transmission power optimization sub-problem to obtain the local approximate solution of the source UAV transmission power optimization sub-problem of the i-th iteration; substitute the local approximate solution of the i-th iteration source UAV interference power optimization sub-problem and other initialized variables into the interference UAV interference power optimization sub-problem to obtain the local approximate solution of the interference UAV interference power optimization sub-problem; substitute the local approximate solution of the i-th iteration source UAV interference power optimization sub-problem, the local approximate solution of the interference UAV interference power optimization sub-problem and other initialized variables into the source UAV flight trajectory optimization sub-problem to obtain the source UAV flight trajectory. The local approximate solution of the trajectory optimization subproblem is obtained; the local approximate solution of the interference power optimization subproblem of the source UAV in the i-th iteration, the local approximate solution of the interference power optimization subproblem of the interference UAV, the local approximate solution of the flight trajectory optimization subproblem of the source UAV and other initialized variables are substituted into the interference UAV flight trajectory optimization subproblem to obtain the local approximate solution of the interference UAV flight trajectory optimization subproblem; the local approximate solution of the i-th iteration source UAV transmission power optimization subproblem, the local approximate solution of the interference power optimization subproblem of the interference UAV, the local approximate solution of the flight trajectory optimization subproblem of the source UAV, the local approximate solution of the flight trajectory optimization subproblem of the interference UAV and other initialized variables are substituted into the smart reflection surface phase shift optimization subproblem to obtain the local approximate solution of the smart reflection surface phase shift optimization subproblem; the number of iterations is continuously increased until the iteration convergence condition is met to obtain the overall approximate optimal solution.

[0364] The effect of the present invention is further described below in conjunction with simulation experiments.

[0365] 1. Simulation conditions and parameter settings:

[0366] The number of ground users is 3, the position coordinates of the smart reflective surface carrying M = 8 reflective elements are 0,0 and the height is 10m, the position coordinates of the eavesdropper are 25,0, the heights of the source UAV and the jammer UAV are both 20m, the time period is 2s, divided into 10 time slots, the maximum flight speed of the source UAV and the jammer UAV are both 100m / s and the average flight speed is 50m / s, the initial and final position coordinates of the source UAV are -50,20 and 50,20 respectively, the initial and final position coordinates of the jammer UAV are -50,-20 and 50,-20 respectively, and the maximum transmission power of the source UAV is p smax =30dBm, the maximum interference power of the UAV is p j max=20dBm, the noise power spectral density of the ground user and the eavesdropper is -80dBm, all Rice factors are 10dBm, and the channel power gain β0 at the reference distance d=1m is -50dB.

[0367] 2. Simulation content:

[0368] Figure 3 It is a comparison chart of the number of reflective elements of the smart reflective surface and the average confidentiality rate of the system, presenting the average rate of the proposed algorithm with different numbers of reflective elements. We set the number of reflective units M = 8 and 32 respectively. It can be seen from the figure that as the number of reflective elements M of the smart reflective surface increases, the average rate at the legitimate user becomes larger, indicating that increasing the number of smart reflective surface elements can significantly improve the average rate of legitimate users. The optimization algorithm of the present invention converges to the maximum rate within 10 iterations.

[0369] Figure 4 The average confidentiality rate of the system changes with the transmission power of the source drone under the condition of intelligent reflective surfaces with different numbers of reflective elements. As can be seen from the figure, when the transmission power of the source drone increases, the average confidentiality rate of the system will increase. When the interference power of the interference drone is increased, the average confidentiality rate of the system will also increase.

[0370] Based on the above simulation results and analysis, the present invention improves the average information rate of users by jointly optimizing the trajectory and transmission power of the source drone, the trajectory and interference power of the interference drone, and the phase of the intelligent reflection surface, and by introducing interference signals emitted by the interference drone to reduce the efficiency of eavesdroppers eavesdropping on legitimate signals. In addition, the system performance can be improved by increasing the number of reflective elements of the intelligent reflection surface. At the same time, when the ground user receives the signal, the non-orthogonal multiple access technology is used to further improve the average confidentiality rate of the system. At the same time, the simulation results effectively illustrate the rapid convergence and high feasibility of the method of the present invention.

[0371] The technical means disclosed in the scheme of the present invention are not limited to the technical means disclosed in the above-mentioned implementation mode, but also include technical schemes composed of any combination of the above technical features.

Claims

1. An optimization design method for multi-UAV cooperative secure communication based on intelligent reflective surface and non-orthogonal multiple access technology, characterized by: The specific steps include: Step 1: According to the geographical locations of the source UAV, the interfering UAV, the ground user, and the eavesdropper, an air-to-ground channel fading model and a reachable rate model from the source UAV to the ground user and a reachable rate model from the source UAV to the eavesdropper are established; Step 2, construct an optimization problem with the goal of maximizing the average confidentiality rate of all ground users; Step 3: Using the alternating optimization algorithm, the system average confidentiality rate maximization model is decoupled into the source UAV transmission power optimization subproblem and flight trajectory optimization subproblem, the interference UAV interference power optimization subproblem and trajectory optimization subproblem, and the smart reflection surface phase shift optimization subproblem. Step 4: Use the CVX tool to find local approximate solutions to the above five sub-optimization problems respectively, 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 interference UAV, and the phase of the smart reflective surface in each time slot.

2. The optimization design method for multi-UAV cooperative secure communication based on intelligent reflective surface and non-orthogonal multiple access technology according to claim 1 is characterized by: In step 1, the air-to-ground channel fading model and the achievable rate model from the source drone to the user and the achievable rate model from the source drone to the eavesdropper are established. The model includes the following information: K ground terminal users, one ground eavesdropper, one source drone, one jammer drone, and one smart reflective surface; the position of the kth user is expressed as The location of the ground eavesdropper is known and is expressed as The source UAV and the jammer UAV simultaneously fly at a fixed height H above the ground within a time period T. u Flight, T is divided into N small time slots, and the horizontal position of the source drone is expressed as The horizontal position of the jamming drone is expressed as The first element of the smart reflective surface is considered as the reference point, which is located at a fixed height H. r Horizontal position The intelligent reflective surface has M=M x M y A uniform planar array of reflective elements, where M x and M y denote the number of elements along the x-axis and y-axis respectively; the phase shift matrix of the smart reflection surface in the nth time slot is expressed as in represents the phase shift produced by the mth reflective element in the nth time slot, In addition, the source drone, jammer drone, all ground users and eavesdroppers are equipped with only single antennas; all channels are Rice channels; The channel gain from the source drone to the smart reflective surface is expressed as: in α is the path loss exponent, β0 is the channel power gain at the reference distance d0=1m, λ0 is the carrier wavelength, are the azimuth and elevation angle of arrival, K sr is the Rice factor, d sr [n] is the distance from the source drone to the smart reflective surface in the nth time slot, represents a set of M×1 dimensional composite matrices, represents the line-of-sight link component from the source UAV to the smart reflector, represents the non-line-of-sight link component from the source UAV to the smart reflective surface, CN(0,1) represents a circularly symmetric complex Gaussian distribution with zero mean and unit variance; The channel gains from the source drone to the kth user and the eavesdropper are: Where K sk is the Rice factor, d sk [n] is the distance from the source drone to the kth user in the nth time slot, represents the line-of-sight link component from the source UAV to the kth user, K represents the non-line-of-sight link component from the source UAV to the kth user; se is the Rice factor, d se [n] is the distance from the source drone to the eavesdropper at the nth time slot, represents the line-of-sight link component from the source UAV to the eavesdropper, represents the non-line-of-sight link component from the source UAV to the eavesdropper; The channel gains from the jammer UAV to the smart reflective surface, the kth user, and the eavesdropper are: Where K jr is the Rice factor, d jr [n] is the distance from the jammer drone to the smart reflective surface in the nth time slot, represents the line-of-sight link component from the jammer UAV to the smart reflector, K represents the non-line-of-sight link component from the jammer UAV to the smart reflective surface; jk is the Rice factor, d jk [n] is the distance from the interfering drone to the kth user in the nth time slot, represents the line-of-sight link component from the interfering UAV to the kth user, K represents the non-line-of-sight link component from the interfering UAV to the kth user; je is the Rice factor, d je [n] is the distance from the jammer drone to the eavesdropper at the nth time slot, represents the line-of-sight link component from the jammer UAV to the eavesdropper, It represents the non-line-of-sight link component from the jammer UAV to the eavesdropper; The total channel gains from the source drone to the kth user and the eavesdropper are: The total channel gains from the jammer UAV to the kth user and the eavesdropper are: The channel gains from the smart reflector to the kth user and the eavesdropper are Where K rk is the Rice factor, d rk [n] is the distance from the smart reflector to the kth user in the nth time slot, represents the line-of-sight link component from the smart reflector to the kth user, represents the non-line-of-sight link component from the smart reflector to the kth user; K re is the Rice factor, d re [n] is the distance from the smart reflector to the eavesdropper in the nth time slot, represents the line-of-sight link component from the smart reflector to the eavesdropper, It represents the non-line-of-sight link component from the smart reflective surface to the eavesdropper; Non-orthogonal multiple access technology is used between the source UAV and the ground user. The achievable rates of the kth ground user and the eavesdropper in the nth time slot are expressed as: where p k [n] is the transmission power of the source UAV when transmitting information to the kth user in the nth time slot, p l [n] is the transmission power of the source UAV when transmitting information to the lth user in the nth time slot, p j [n] is the jamming power of the UAV in the nth time slot, represents the power of additive white Gaussian noise at the ground user, represents the power of additive Gaussian white noise at the eavesdropper; λ k,l [n](l≠k) is a binary variable. When the channel gain of the kth user is worse than the channel gain of the lth user, λ k,l [n]=1, otherwise λ k,l [n] = 0; The confidentiality rate of the kth ground user in the nth time slot is expressed as 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, so let the UAV-S transmit power p k [n]=0, then R sec,k [n] = R k [n]-R e [n], thus ensuring that the system confidentiality rate remains non-negative in any time slot.

3. The optimization design method for multi-UAV cooperative secure communication based on intelligent reflective surface and non-orthogonal multiple access technology according to claim 1 is characterized by: In the step 2, a confidentiality capacity maximization model for all ground users is established, including establishing a model with the objective function of maximizing the confidentiality rate of ground users, and the objective function is expressed as: In P1, Q s represents the flight trajectory of the source UAV, Q j represents the flight trajectory of the source UAV, P k represents the transmission power of the source UAV, P k represents the interference power of the jamming UAV, ψ represents the phase of the smart reflective surface; The constraints include: In time T, the initial and final positions of the source UAV and the interference UAV are fixed; in a time slot, the distance flown by the UAV is less than the maximum distance, and in order to ensure that the two UAVs do not collide during the flight, there are constraints: Among them, q u [0] = q uI represents the initial position of the drone, q u [N] = q uF Indicates the end position of the drone, V max represents the maximum flight speed of the source UAV and the jammer UAV, d min Indicates the minimum distance between two drones; The phase constraint of the smart reflector is: In any time slot, the transmission power of the source UAV ensures that the transmission power to the kth user is greater than the transmission power of other users, and ensures that the transmission power of the source UAV is not higher than its maximum transmission power. The transmission power constraint of the source UAV is where p smax represents the maximum transmission power of the source UAV; k,l [n] Satisfaction d sl [n] represents the distance from the source UAV to the lth user; The jamming power constraint of the jamming UAV is in represents the average interference power of the jamming UAV, p jmax Indicates the maximum jamming power of the jamming drone. In order to simplify the objective function, the variable t is introduced, and the objective function and constraints are expressed as st(15a),(15b),(15c),(15d),(15f),(15g),(15h),(15i)(16b) 4. The optimization design method for multi-UAV cooperative secure communication based on intelligent reflective surface and non-orthogonal multiple access technology according to claim 1 is characterized by: The transmission power optimization sub-problem of the source UAV in step 3 includes optimizing the transmission power of the source UAV, introducing auxiliary variables and using the Taylor expansion method to optimize the transmission power allocation of the source UAV. The transmission power optimization sub-problem of the source UAV is expressed as: st(16c)(17b) (15e), (15f), (15g), (17c) Among them, (17b) in this optimization subproblem is a non-convex constraint, which can be transformed into a convex constraint by using auxiliary variables; k [n],R e [n] in p k (i) The first-order Taylor expansion at [n] gives Among them, p k (i) [n] represents the transmission power optimized by the source UAV at the i-th iteration, is obtained by SCA technology k [n] lower bound, YesR e [n] Convex approximation of the upper bound, a n 、b n are the auxiliary variables introduced, and their expressions are The non-convex constraint (17b) is transformed into the formula: Then constraint (17b) becomes a convex set; P2 is rewritten as: (15e), (15f), (15g), (20c) Among them, p k (i) [n] represents the transmission power optimized by the source UAV at the i-th iteration, is obtained by SCA technology k [n] lower bound, YesR e [n] Convex approximation of the upper bound, a n , b n are the auxiliary variables introduced, and their expressions are The non-convex constraint (17b) is transformed into the formula: Then constraint (17b) becomes a convex set. P2 is rewritten as: (15e), (15f), (15g)(20c).

5. The optimization design method for multi-UAV cooperative secure communication based on intelligent reflective surface and non-orthogonal multiple access technology according to claim 1 is characterized by: The step 3 is to optimize the interference power of the UAV, including optimizing the transmission power of the UAV, introducing auxiliary variables and using the Taylor expansion method to optimize the distribution of interference power of the UAV. The optimization sub-problem of the interference power of the UAV is expressed as: st(16c)(21b) (15h), (15i)(21c) Among them, (21b) in this optimization subproblem is a non-convex constraint, which can be transformed into a convex constraint by using auxiliary variables; k [n],R e [n] in p j (i) The first-order Taylor expansion at [n] gives Among them, p j (i) [n] represents the transmission power optimized by the source UAV at the i-th iteration, is obtained by SCA technology k [n] lower bound, YesR e [n] Convex approximation of the upper bound, c n ,d n ,e n ,f n are the auxiliary variables introduced, and their expressions are The non-convex constraint (21b) is transformed into the formula: Then constraint (21b) becomes a convex set; P4 is rewritten as: (15h), (15i)(21c).

6. The optimization design method for multi-UAV cooperative secure communication based on intelligent reflective surface and non-orthogonal multiple access technology as claimed in claim 1, characterized in that: The flight trajectory optimization sub-problem of the source UAV includes optimizing the flight trajectory of the source UAV, entering slack variables, and using SCA to perform a local convex approximation on the flight trajectory optimization problem of the source UAV; the flight trajectory optimization sub-problem of the source UAV is expressed as: st(16c) (25b) (15c) (25c) In this optimization subproblem, (25b) and (25c) are both non-convex constraints. For the non-convex constraint (25b), it is necessary to introduce slack variables and use the Taylor expansion method to transform (25b) into a convex set. The specific steps are as follows: k [n], introduce variable s k [n]z k [n], whose constraints are make The variable s k [n],z k The constraint of [n] is non-convex, and then introduce slack variables a1[n], a2[n], a3[n], a4[n] to make a1[n] ≥ d sk [n],a2[n]≥d sr [n],a3[n]≤d sk [n],a4[n]≤d sr [n], then (27) can be expressed as in Related items It may be positive or negative, depending on the phase difference between the signals. If the coherence term is positive, it helps to increase its channel gain; if it is negative, it weakens its channel gain; a binary variable F is introduced for the coherence term k [n], which satisfies When F k [n] = 1, indicating that the coherence term is positive, enhancing the signal strength, satisfying when When F k [n] = 0, indicating that the coherence term is negative, strengthening the weakening strength, satisfying Then the variable s k The constraint (28) of [n] transforms into a convex set, expressed as Then R k [n] in z k The first-order Taylor expansion at [n] gives in is obtained by SCA technology k [n] Lower bound. For R e [n], with R k The optimization method of [n] is similar to introducing the slack variable s e [n],z e [n], the constraints are And s e [n],z e The constraint of [n] is still non-convex. Then, slack variables b1[n] and b2[n] are introduced to satisfy b1[n]≥d se [n],b2[n]≤d se [n], so that (31) can be expressed as Among them When F e [n] = 1, indicating enhanced signal strength; when When F e [n] = 0, indicating that the signal strength is weakened; Then R e [n] in z e The first-order Taylor expansion at [n] gives in is obtained by SCA technology e [n] upper bound; the slack variables a1[n], a2[n], a3[n], a4[n], b1[n], b2[n] are first-order Taylor expansions at the i-th iteration, which satisfy the constraints: d sk 2 [n]≤-(a1 (i) [n]) 2 +2a1 (i) [n]a1[n] (35) <h2 style=";text-align:left;direction:ltr">d<h2 style=";text-align:left;direction:ltr"> sr <h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> [n]≤-(a2<h2 style=";text-align:left;direction:ltr"> (i) <h2 style=";text-align:left;direction:ltr"> [n])<h2 style=";text-align:left;direction:ltr"> 2 <h2 style=";text-align:left;direction:ltr"> +2a2<h2 style=";text-align:left;direction:ltr"> (i) <h2 style=";text-align:left;direction:ltr"> [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) Then the non-convex constraint (25b) is transformed into the formula: At this time, constraint (25b) becomes a convex set. For the non-convex constraint (25c), the safe flight distance d between the two drones 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 At this time, 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).

7. The optimization design method for multi-UAV cooperative secure communication based on intelligent reflective surface and non-orthogonal multiple access technology as claimed in claim 1, characterized in that: The sub-problem of optimizing the flight trajectory of the jamming UAV in step 3 includes optimizing the flight trajectory of the jamming UAV, introducing slack variables, and using SCA to perform a local convex approximation on the flight trajectory optimization problem of the jamming UAV; the sub-problem of optimizing the flight trajectory of the jamming 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 safe flight distance d of the two UAVs is calculated in the same way as in the trajectory optimization of the source UAV. 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), the method is similar to that in the trajectory optimization of the source UAV. The specific steps are as follows: k [n], introduce slack variable s jk [n], whose constraints are but in The variable s jk The constraint of [n] is still non-convex, and slack variables c1[n], c2[n], c3[n], c4[n] are introduced to make c1[n] ≥ d jk [n],c2[n]≥d jr [n],c3[n]≤d jk [n],c4[n]≤d jr [n],s jk [n] Perform a first-order Taylor expansion at the i-th iteration to obtain: in because Can be positive or negative, introduce binary variable F jk [n], which satisfies the following conditions: When F jk [n] = 1, indicating that the coherence term is positive, which enhances the signal strength; when When F jk [n] = 0, indicating that the coherence term is negative, weakening the signal strength; Then R k [n] in s jk [n] is a Taylor first-order expansion, that is, in is obtained by SCA technology k [n] lower bound; Similarly, for R e [n]Introduce variable s je [n], which satisfies the constraints: but in The variable s je [n], the constraint is still non-convex, and then introduce slack variables d1[n], d2[n] to make d1[n]≥d je [n],d2[n]≤d je [n], and introduce F jk [n], then for s je [n] Perform a first-order Taylor expansion to obtain: where F jk [n] Satisfy: when When F je [n] = 1, indicating that the coherence term is positive, which enhances the signal strength. when When F jk [n] = 0, indicating that the coherence term is negative, which weakens the signal strength. Then R e [n] in s je [n] is a Taylor first-order expansion, that is, in is obtained by SCA technology e [n] Upper bound. The slack variables c1[n], c2[n], c3[n], c4[n], d1[n], d2[n] are first-order Taylor expansions at the i-th iteration, which satisfy the 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) Then the non-convex constraint (42b) is transformed into the formula: At this time, constraint (42b) becomes a convex set; P8 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 (55c) (42d), (42f), (49)-(54) (55d).

8. The optimization design method for multi-UAV cooperative secure communication based on intelligent reflective surface and non-orthogonal multiple access technology as claimed in claim 3, characterized in that: The phase optimization sub-problem of the smart reflective surface includes optimizing the phase of the smart reflective surface to maximize the confidentiality rate of the system. The phase optimization sub-problem of the smart reflective surface is expressed as: st(16c) (56b) P10 is non-convex, and the phase shift matrix of the smart reflector is optimized using the successive convex approximation (SCA) method and semidefinite relaxation (SDR): a semidefinite matrix is ​​introduced, and v[n]=[v1[n],v2[n],...,v M [n]], Substituting v[n] into P10, (55c) is equivalent to the vector norm constraint being transformed into V[n]≥0. In order to simplify the problem and constraints and convert them into quadratic form, we introduce in At this time, get At the point At R k [n] and R e [n] Perform a first-order Taylor expansion: in is obtained by SCA technology k [n] lower bound, is obtained by SCA technology e [n] upper bound. Then the non-convex constraint (56b) is transformed into the formula: At this time, constraint condition (56b) becomes a convex set. P10 is rewritten as 9. The multi-UAV cooperative secure communication method based on intelligent reflective surface and non-orthogonal multiple access technology as claimed in claim 1, characterized in that: The step 4 of maximum confidentiality rate optimization includes initializing the values ​​of the variables of the system confidentiality rate maximization problem; substituting the initialized variables into the source UAV transmission power optimization subproblem to obtain the local approximate solution of the i-th iteration source UAV transmission 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 the local approximate solution of the interference UAV interference power optimization subproblem; substituting the local approximate solution of the i-th iteration source UAV interference power optimization subproblem, the local approximate solution of the interference UAV interference power optimization subproblem and other initialized variables into the source UAV flight trajectory optimization subproblem to obtain the local approximate solution of the source UAV flight trajectory ... Substitute the local approximate solution of the optimization subproblem, the local approximate solution of the source UAV flight trajectory optimization subproblem and other initialized variables into the interference UAV flight trajectory optimization subproblem to obtain the local approximate solution of the interference UAV flight trajectory optimization subproblem; substitute the local approximate solution of the i-th iteration source UAV transmission power optimization subproblem, the local approximate solution of the interference UAV interference power optimization subproblem, the local approximate solution of the source UAV flight trajectory optimization subproblem, the local approximate solution of the interference UAV flight trajectory optimization subproblem and other initialized variables into the intelligent reflection surface phase shift optimization subproblem to obtain the local approximate solution of the intelligent reflection surface phase shift optimization subproblem; continuously increase the number of iterations until the iteration convergence conditions are met, obtain the transmission 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 reflection surface, obtain the overall approximate optimal solution, and end the process.

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