Unmanned aerial vehicle covert communication resource optimization method based on intelligent reflecting surface assistance

Abstract

The invention relates to an unmanned aerial vehicle covert communication resource optimization method based on intelligent reflecting surface assistance, which constructs a covert communication scene in which an intelligent reflecting surface and an unmanned aerial vehicle cooperate, and establishes an unmanned aerial vehicle covert communication model for maximizing the maximum average rate of a legal user on the premise of meeting the minimum detection probability of an eavesdropper. Initializing configuration information of a legal user, an eavesdropper, a jammer and an unmanned aerial vehicle; an eavesdropper detection probability model is constructed; initializing and calculating the trajectory of the unmanned aerial vehicle and the initial phase of the intelligent reflecting surface; the phase shift of the reflecting element of the reconfigurable intelligent reflecting surface and the track of the unmanned aerial vehicle are optimized; if the target function converges, the maximum average rate, the optimal phase shift and the optimal unmanned aerial vehicle trajectory of the user are obtained, and otherwise, one is added to the number of iterations, and all the variables continue to be optimized. According to the method, the maneuverability of the unmanned aerial vehicle and the mobility of the reconfigurable intelligent reflecting surface are fully considered, and the jammer is arranged to influence detection of legal signals by an eavesdropper so as to improve the average information rate of a user.

Description

Technical Field

[0001] The present invention relates to the technical field of computer wireless communication, and in particular to a resource optimization method for unmanned aerial vehicle covert communication assisted by a reconfigurable intelligent reflective surface. Background Art

[0002] Traditional drone communications usually require the installation of signal transceiver equipment on the drone to act as an aerial relay or base station to forward signals. Since signal transceiver equipment is generally active and has high energy loss, the drone's working time in the air is limited and the communication efficiency of the system is reduced. In 6G mobile communications, a key technology is the smart reflective surface, which is an emerging technology that uses a large number of low-cost passive reflective elements to intelligently reflect signals. It can effectively improve the quality of signal transmission and has significant advantages in improving data rate and energy efficiency. Therefore, mounting smart reflective surfaces on drones for communication can not only achieve flexible deployment and expand coverage, but also effectively reduce energy consumption and costs, and improve communication quality. It is a new technology with development potential.

[0003] In addition to the energy consumption problem of drones, the air-to-ground channel of the drone network is dominated by line-of-sight links, which are easily eavesdropped by illegal users or receive signal interference. Compared with traditional ground channels, it faces more severe information security challenges. How to ensure the secure transmission of information is an urgent problem that needs to be solved in drone networks. Traditional cryptography technology and physical layer security technology both attempt to ensure the security of the content of transmitted information, that is, the transmitted information cannot be stolen by illegal users. Illegal users can detect the transmission of information and interfere with or destroy the communication process, causing great harm to the normal communication of legitimate users. As legitimate users increase their requirements for transmission security performance, it is necessary to further ensure the security of the information transmission process.

[0004] Covert communication is a secure communication technology that "hides" the information transmission process. It hides the information transmission process in the environmental noise, making it impossible for the monitor to judge the information transmission situation, thereby achieving the purpose of hiding the information transmission process. The traditional UAV system is combined with a reconfigurable smart reflective surface of appropriate size. In the existing work, a UAV covert communication scheme assisted by a smart reflective surface is proposed to maximize the covert transmission rate. The ground transmitter secretly sends private information to the legitimate receiver through the UAV-smart reflective surface, hoping that the transmission signal will not be noticed by the eavesdropper. However, in the study, the UAV is fixed in one position, and only the height is optimized, ignoring the application value of the maneuverability and flexibility of the UAV in reality. Others have proposed a scheme in which a UAV carrying a smart reflective surface is used as a relay node to assist the covert communication system. When the positions of the UAV, base station and eavesdropper are known, it is assumed that the eavesdropper can minimize the probability of detection error and improve the data rate of the smart reflective surface-UAV assisted covert communication. However, only the case of illegal eavesdroppers is considered, and other active signal interference signals are not considered to effectively affect the eavesdropper's detection of legitimate user communications. Summary of the invention

[0005] In view of the shortcomings of the above-mentioned prior art, the present invention proposes a resource optimization method for covert communication of unmanned aerial vehicles assisted by reconfigurable intelligent reflective surfaces. The eavesdropper with a known position works in a passive eavesdropping mode, does not send any external interference signals, and only passively receives the signals sent by the transmitter. With the addition of the interference signal of the active jammer, the motion trajectory of the unmanned aerial vehicle and the phase shift of the intelligent reflective surface are jointly optimized to maximize the average covert information rate of the legitimate user under the covert constraint.

[0006] A resource optimization method for covert communication of unmanned aerial vehicles assisted by a reconfigurable intelligent reflective surface, the method comprising the following steps:

[0007] Step 1: According to the geographical locations of the UAV, the jammer, the legitimate users and the eavesdroppers on the ground, an air-to-ground channel fading model and a signal-to-noise ratio model from the legitimate users to the UAV are established;

[0008] Step 2, under the condition that the power of the jammer's noise is random and uniformly distributed, calculate the false detection probability of the eavesdropper;

[0009] Step 3, construct an optimization problem under the premise that the false detection probability of the eavesdropper is minimized;

[0010] Step 4, the optimization problem is divided into two optimization sub-problems: in the first sub-problem, the phases of the received signals from different channels at the user side and the eavesdropper are coherently combined to achieve the maximum average rate; in the second sub-problem, the trajectory scheduling of the UAV is optimized using the relaxation variable method and the successive convex approximation method;

[0011] Step 5: Use convex optimization tools to find local approximate solutions to the above two sub-optimization problems respectively, iterate the three local approximate solutions, and obtain the approximate optimal solution to the legitimate user weighted sum rate maximization problem.

[0012] Furthermore, in step 1, the direct channel from the base station to the user is blocked by a building, and the drone carrying the intelligent reflective surface acts as a relay. The air-to-ground channel fading model and the signal-to-noise ratio model from the legitimate user to the drone include the following information:

[0013] A drone with a smart reflective surface, a legitimate user, an eavesdropper, and a jammer; the trajectory of the drone is shown u s and u f is the initial and final position of the trajectory, u[0] = u s ,u[N]=u f , the vertical height of the drone is fixed at H, the flight period is T, T is divided into N time slots, T = Nδ, δ is the time slot length, and the drone trajectory satisfies:

[0014] ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (1)

[0015] Where D = Vδ, V is the flight speed of the drone.

[0016] The horizontal position of the legitimate user is denoted as q B =[x b ,y b ] T ; The horizontal position of the eavesdropper is denoted by q W =[x w ,y w ] T , the horizontal position of the jammer is denoted as q J =[x j ,y j ] T .

[0017] The phase shift matrix of the smart reflection surface in the nth time slot is:

[0018]

[0019] The phase shift of the mth reflective element is:

[0020]

[0021] The channel gain from the base station to the legitimate user is expressed as:

[0022]

[0023] in

[0024]

[0025] ρ represents the path loss at a unit distance d = 1m, λ is the wavelength, d is the antenna length, and η is the path loss exponent.

[0026] is the distance from the base station to the drone,

[0027] is the distance from the drone to the legal user.

[0028] is the cosine of the angle of arrival of the signal from the base station to the drone in the nth time slot.

[0029] is the cosine of the angle of arrival of the signal from the drone to the legitimate user in the nth time slot.

[0030] The channel gain from the base station to the eavesdropper is expressed as:

[0031]

[0032] in

[0033]

[0034] is the distance from the drone to the eavesdropper,

[0035] is the cosine of the angle of arrival of the signal from the drone to the eavesdropper in the nth time slot.

[0036] Due to the fast fading caused by multipath propagation, the signal gain from the jammer to the user and from the jammer to the eavesdropper is modeled by the Rayleigh channel:

[0037]

[0038] where μ 1 , μ 2 is the path loss exponent, ξ JW and JB Each element follows an independent and identical distribution, that is, is the distance from the jammer to the eavesdropper, is the distance from the jammer to the legitimate user.

[0039] Signal gain from jammer to user and eavesdropper:

[0040]

[0041] in represents the cosine of the arrival angle of the signal from the jammer to the drone in the nth time slot, is the distance from the jammer to the drone.

[0042] The signal-to-noise ratio of a legitimate user in each time slot is:

[0043]

[0044] The average rate of the legitimate user in the nth time slot:

[0045]

[0046] Among them, P b is the base station transmission power, P j is the jammer transmit power, σ b 2 is the noise power of the legitimate user.

[0047] Furthermore, in step 2, when the locations of the eavesdropper, jammer, and base station are known, the most false detection probability of the eavesdropper is derived:

[0048] The probability density function of the jammer's artificial noise is:

[0049]

[0050] When the drone is flying, the eavesdropper can directly detect the drone's trajectory and accurately know the drone's location information. The signal received by the eavesdropper is:

[0051]

[0052] H 0 Indicates that there is no communication between the drone and the legitimate user, H 1 Indicates that communication has occurred, x j (n) represents the transmission signal of the jammer, x b represents the transmission signal of the base station, n w is the Gaussian white noise at the eavesdropper, and the base station transmits power P in each time slot b is fixed, P j is the transmit power of the jammer.

[0053] Received power at the eavesdropper:

[0054]

[0055] The eavesdropper determines whether the drone is communicating with a legitimate user by comparing the average power with the preset threshold (binary judgment).

[0056]

[0057] Γ 1 Indicates that the judgment is H 1 (communication has occurred), Γ 0 Indicates that the judgment is H 0 (no communication occurs), where τ is a detection threshold with no definite value, used to distinguish the intervals.

[0058] False alarm probability

[0059]

[0060]

[0061] Missed detection probability

[0062] in

[0063]

[0064] Furthermore, in step 3, under the premise that the false detection probability of the eavesdropper is minimized, an optimization problem is constructed:

[0065] The false detection probability of the eavesdropper is composed of the false alarm probability and the missed detection probability. Considering the jammer as a strong user, we only consider In the case of , the total false detection probability is expressed as:

[0066]

[0067] when When ξ[n] decreases monotonically, , ξ[n] increases monotonically, so the minimum value ξ[n] * [n] must be a value in Inside.

[0068] Minimum

[0069] Confidentiality performance must meet the following requirements:

[0070] ξ*[n]≥1-ε

[0071] Right now:

[0072]

[0073] The value of ε is 0.01.

[0074] With the goal of maximizing the concealment rate, the phase of the smart reflective surface (smart reflective surface) and the trajectory of the UAV are optimized under the constraint of the detection error probability.

[0075] Detection probability and concealment rate are two key metrics for covert communication systems. However, these two metrics are constrained by each other. If the concealment rate of a covert communication system is increased, which means that more covert bits are transmitted in a given time slot, the covert bits are more easily detected, resulting in a higher detection probability. On the contrary, a lower detection probability means that the covert communication is not easily detected, which limits the concealment rate of the communication system. Therefore, under the constraint of a certain detection probability of the eavesdropper, the flight trajectory of the drone and the phase shift of the smart reflective surface are optimized to achieve the maximum average concealment rate.

[0076] Let the UAV trajectory U={u[n],n=1,2,…,N},

[0077] Smart reflector phase shift Θ = {θ m ,m=1,2,…,M}.

[0078] The optimization problem is expressed as:

[0079] (P):

[0080]

[0081] θ m ∈[0,2π) m=1,2,…,M-1 (19c)

[0082] u[0]=u s ,u[N]=u f (19d)

[0083] ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (19e)

[0084] Furthermore, in step 4, the optimization problem is divided into two optimization sub-problems:

[0085] In the first sub-problem the phases of the received signals from different channels at the user and the eavesdropper are coherently combined to achieve the maximum average rate:

[0086] Written as:

[0087]

[0088] Combine signals from different paths through smart reflective surfaces:

[0089]

[0090] Get the optimal reflection coefficient of the mth reflection element in the nth time slot:

[0091]

[0092] Written as:

[0093]

[0094] Written as:

[0095]

[0096] Written as:

[0097]

[0098] The trajectory of the drone is optimized as follows:

[0099] P can be rewritten as:

[0100] (P1):

[0101]

[0102] θ m ∈[0,2π) m=1,2,…,M-1 (25c)

[0103] u[0]=u s ,u[N]=u f (25d)

[0104] ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (25e)

[0105] P1 is non-convex, and the trajectory of the drone is optimized using the slack variable method and the successive convex approximation method:

[0106] Define e[n] as The upper bound of s[n] is The lower bound of v[n] is The upper bound of q[n] is The lower bound of

[0107] P(1) can be rewritten as:

[0108] P(2):

[0109]

[0110] u[0]=u s ,u[N]=u f (26g)

[0111] ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (26h)

[0112] For P2, first solve (26a), P b ρ 2 M 2 >0,P j ρ 2 M 2 >0,P j h JB +σ b 2 >0, when e[n]>0, s[n]>0, function

[0113] The Hessian matrix of is a positive definite matrix, so the function is a convex function. and The Taylor expansion of is:

[0114]

[0115]

[0116] Among them, C, C 1 and C 2 Respectively represent P b ρ 2 M 2 , (P j h JB +σ b 2 ) and P j ρ 2 M 2 .

[0117] (26c)-(26f) The convexity of is unknown. For (26c), first prove is convex:

[0118]

[0119] exist and Perform a first-order Taylor expansion on equation (28):

[0120]

[0121] The first-order Taylor display of is T(u[n]), The first-order Taylor display of is Y(u[n]), The first-order Taylor display of is W(u[n]).

[0122] At the point Perform the first-order Taylor expansion of (26e) and (26f):

[0123]

[0124] P2 is rewritten as:

[0125] P3:

[0126]

[0127]

[0128] u[0]=u s ,u[N]=u f (32g)

[0129] ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (32h)

[0130] (32a) is a linear function, and all constraints are convex constraints. Convex optimization is used to solve problem P3.

[0131] Furthermore, in step 5, the convex optimization tool is used to find local approximate solutions to the above two sub-problems respectively, and the two local solutions are iterated to obtain the approximate optimal solution of the system as a whole:

[0132] 1: Initialize the drone trajectory U 0 , phase Θ 0 、UAV initial coordinates u 0 , auxiliary variables {e 0 、s 0 、v 0 ,q 0}, set the initial number of iterations L = 1,

[0133] repeat:

[0134] 2: Fixed θ L-1 , update U through (32) L ,u L , e L 、s L 、v L ,q L The value of

[0135] 3: Fixed U L , update Θ by (21) L The value of

[0136] 4: Fixed U L and θ L , update R by (10) L The value of

[0137] Until:|R L -R L-1 |<κ,

[0138] The constant κ is set to 10 -5 .

[0139] An electronic device comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method for optimizing covert communication resources of an unmanned aerial vehicle based on the assistance of an intelligent reflective surface is implemented.

[0140] A computer-readable storage medium stores computer instructions, which, when executed by a processor, implement a method for optimizing covert communication resources of an unmanned aerial vehicle based on the assistance of an intelligent reflective surface.

[0141] Compared with the prior art, the present invention has the following advantages:

[0142] 1. Smart reflective surfaces (smart reflective surfaces) are widely used as an emerging technology to assist wireless communications. Smart reflective surfaces improve the signal-to-noise ratio of communication by intelligently controlling the direction of reflected signals. However, existing work usually fixes smart reflective surfaces on the surface of buildings or fixed points of drones, limiting the flexibility and coverage of the system. The present invention combines smart reflective surfaces with drones (UAVs). Through the collaborative design of smart reflective surfaces and drones, the system can adjust the flight trajectory of the drone according to the dynamic changes of the user's position and environment to enhance the dynamic optimization capability. At the same time, the drone carries smart reflective surfaces, which enables the system to overcome the obstacle restrictions in fixed scenes and better adapt to actual application scenarios. Since the optimization problem is non-convex, it is difficult to solve it directly. Therefore, we designed an alternating iterative optimization algorithm based on the successive convex approximation technology, which converts the optimization problem into a series of convex optimization sub-problems, and solves the approximate optimal solution of the optimization problem by alternating optimization sub-problems. Through simulation results, compared with the traditional fixed smart reflective surface solution, the average communication rate of users is increased by 10%-12%.

[0143] 2. The core goal of covert communication is to ensure the security of information, so that eavesdroppers cannot detect the existence of legitimate communication. Detection probability and covert communication rate are two key indicators in the system. There is usually a mutual constraint relationship between these two indicators: reducing the detection probability will sacrifice part of the communication rate. The present invention proposes to use the interference signal of the jammer to affect the detection ability of the eavesdropper. Since the drone is non-fixed, the jammer's signal will also be transmitted to the user and the eavesdropper through the intelligent reflective surface, which makes the channel model more complicated, further strengthens the coupling between constraints, and converts the optimization problem into a linear function by using the first-order Taylor expansion formula multiple times. By introducing multiple auxiliary variables, the drone trajectory constraint is transformed into a convex constraint. The minimum detection probability of the eavesdropper is also used as a constraint to optimize the rate of the legitimate user. The simulation results show that after the introduction of the jammer, the detection probability of the eavesdropper is reduced by 15%-20%, and the covert communication rate is increased by 10%-15% relative to the covert communication system without interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0144] Figure 1 It is a system model diagram of the present invention;

[0145] Figure 2 It is a schematic diagram of the process of the present invention;

[0146] Figure 3 is a comparison chart of the number of reflective elements of the reconfigurable smart reflective surface and the average covert information rate of the user;

[0147] Figure 4 It is a comparison chart of the average hidden information rate of three different optimization schemes when the concealment parameter increases. DETAILED DESCRIPTION

[0148] The invention is further described below in conjunction with the accompanying drawings. Figure 1 The specific steps of the method of the present invention are described as follows:

[0149] like Figure 1 As shown in the figure, the base station sends secret messages to legitimate users through the smart reflective surface carried by the drone. The base station is the signal transmission site, and the legitimate user is the receiver of the signal. The drone carrying the smart reflective surface relays the signal sent from the base station to the user, and the transmitted secret signal may be eavesdropped by the monitor.

[0150] UAV trajectory representation u s and u f is the initial and final position of the trajectory, u[0] = u s ,u[N]=u f, the vertical height of the drone is fixed at H, the flight period is T, T is divided into N time slots, T = Nδ, δ is the time slot length, and the drone trajectory satisfies:

[0151] ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (1)

[0152] Where D = Vδ, V is the flight speed of the drone.

[0153] The horizontal position of the legitimate user is denoted as q B =[x b ,y b ] T ; The horizontal position of the eavesdropper is denoted by q W =[x w ,y w ] T , the horizontal position of the jammer is denoted as q J =[x j ,y j ] T .

[0154] The phase shift matrix of the smart reflection surface in the nth time slot is:

[0155]

[0156] The phase shift of the mth reflective element is:

[0157]

[0158] Among the numerous secret communication methods, introducing artificial noise interference is an effective method. Due to the interference of artificial noise, illegal eavesdroppers cannot determine whether the energy change is due to the occurrence of communication behavior or the change of interference signal.

[0159] In practical applications, the direct links between the base station and the user and the eavesdropper are often blocked by obstacles. Therefore, it is assumed that there is no direct channel between the base station and the user and between the base station and the eavesdropper.

[0160]

[0161] in

[0162]

[0163] ρ represents the path loss at a unit distance d = 1m, λ is the wavelength, d is the antenna length, and η is the path loss exponent.

[0164] is the distance from the base station to the drone,

[0165] is the distance from the drone to the legal user.

[0166] is the cosine of the angle of arrival of the signal from the base station to the drone in the nth time slot.

[0167] is the cosine of the angle of arrival of the signal from the drone to the legitimate user in the nth time slot.

[0168] The channel gain from the base station to the eavesdropper is expressed as:

[0169]

[0170] in

[0171]

[0172] is the distance from the drone to the eavesdropper,

[0173] is the cosine of the angle of arrival of the signal from the drone to the eavesdropper in the nth time slot.

[0174] Due to the fast fading caused by multipath propagation, the signal gain from the jammer to the user and from the jammer to the eavesdropper is modeled by the Rayleigh channel:

[0175]

[0176] where μ 1 , μ 2 is the path loss exponent, ξ JW and JB Each element follows an independent and identical distribution, that is, is the distance from the jammer to the eavesdropper, is the distance from the jammer to the legitimate user.

[0177] Signal gain from jammer to user and eavesdropper:

[0178]

[0179] in represents the cosine of the arrival angle of the signal from the jammer to the drone in the nth time slot, is the distance from the jammer to the drone.

[0180] The signal-to-noise ratio of a legitimate user in each time slot is:

[0181]

[0182] The average rate of the legitimate user in the nth time slot:

[0183]

[0184] Among them, P b is the base station transmission power, P j is the jammer transmit power, σ b 2 is the noise power of the legitimate user.

[0185] The power of the jammer's artificial noise is randomly and evenly distributed, and its probability density function is:

[0186]

[0187] Received power at the eavesdropper:

[0188]

[0189] The eavesdropper determines whether the drone is communicating with a legitimate user by comparing the average power with the preset threshold (binary judgment).

[0190]

[0191] Γ 1 Indicates that the judgment is H 1 (communication has occurred), Γ 0 Indicates that the judgment is H 0 (no communication occurs), where τ is a detection threshold with no definite value, used to distinguish the intervals.

[0192] Consider the jammer as a strong user, so only consider In the case of , the total false detection probability is expressed as:

[0193]

[0194] in

[0195]

[0196] when When ξ[n] decreases monotonically, , ξ[n] increases monotonically, so the minimum value ξ[n] * [n] must be a value in Inside.

[0197] Minimum

[0198] Confidentiality performance must meet the following requirements:

[0199] ξ*[n]≥1-ε

[0200] Right now:

[0201]

[0202] At this time, the optimization problem is expressed as:

[0203]

[0204] θ m ∈[0,2π) m=1,2,…,M-1 (16c)

[0205] u[0]=u s ,u[N]=u f (16d)

[0206] ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (16e)

[0207] The trajectory of the UAV is U = {u[n], n = 1, 2, ..., N},

[0208] Smart reflector phase shift Θ = {θ m ,m=1,2,…,M}

[0209] (a) Optimizing the phase of the smart reflector:

[0210] The phases of the received signals from different channels on the user side are coherently combined to achieve the maximum average rate: Written as:

[0211]

[0212] Combine signals from different paths through smart reflective surfaces:

[0213]

[0214]

[0215] Get the optimal reflection coefficient of the mth reflection element in the nth time slot:

[0216]

[0217] Among them and and Represents the cosine of the signal arrival angle.

[0218] (b) Optimizing UAV trajectories:

[0219] After merging the phases, the problem can be rewritten as:

[0220]

[0221] θ m ∈[0,2π) m=1,2,…,M-1 (19c)

[0222] u[0]=u s ,u[N]=u f (19d)

[0223] ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (19e)

[0224] Use the slack variable method to optimize the trajectory of the drone:

[0225] Define e[n] as The upper bound of s[n] is The lower bound of v[n] is The upper bound of q[n] is The lower bound of

[0226] The optimization problem can be rewritten as:

[0227]

[0228] u[0]=u s ,u[N]=u f (20g)

[0229] ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (20h)

[0230] After the first-order Taylor expansion of the objective function and constraints, the problem can be rewritten as:

[0231]

[0232] u[0]=u s ,u[N]=u f (21g)

[0233] ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (21h)

[0234] The objective function is a linear function, and the constraints are all convex constraints. Convex optimization is used to solve the problem.

[0235] Use convex optimization tools to find local approximate solutions to the above two sub-problems respectively, and iterate the two local solutions to obtain the approximate optimal solution of the system as a whole:

[0236] 1: Initialize the drone trajectory U 0 , phase Θ 0 、UAV initial coordinates u 0 , auxiliary variables {e 0 、s 0 、v 0 ,q 0}, set the initial number of iterations L = 1,

[0237] repeat:

[0238] 2: Fixed θ L-1 , update U through (32) L ,u L , e L 、s L 、v L ,q L The value of

[0239] 3: Fixed U L , update Θ by (21) L The value of

[0240] 4: Fixed U L and θ L , update R by (10) L The value of

[0241] Until:|R L -R L-1 |<κ,

[0242] The constant κ is set to 10 -5 .

[0243] The effect of the present invention is further described below in conjunction with simulation experiments.

[0244] 1. Simulation conditions and parameter settings:

[0245] The base station coordinates (0, 0), the initial coordinates of the drone are u S =(-400, 0), ending coordinate u f = (400, 0), and equipped with a reconfigurable intelligent reflective surface carrying M = 15 reflective elements, flying speed V = 40m / s, height H = 50m. Eavesdropper coordinates q B =(-100, 200), q W =(-100, 150), q J =(-200, 150). The power of the base station is set to P b=34dBm, the jammer power is set to P j =37dBm, the noise power is set to σ w 2 =σ b 2 =-100dBm. Finally, assume that the channel power gain at a reference distance of 1m is ρ = -40dB, η = 2, β = 10 -3 , μ 1 =μ 2 =3,ε=0.01,σ=10 -5 , period T = 10s, divided into 10 time slots, each time slot is 1s.

[0246] 2. Simulation content:

[0247] Figure 3 It is a comparison chart of the number of reflective elements of the reconfigurable smart reflective surface and the average hidden information rate of the user, presenting the average rate of the proposed algorithm with different numbers of reflective elements. We set the number of reflective elements M = 20, 25 and 30 respectively. It can be seen from the figure that with the increase of the number of reflective elements M of the smart reflective surface, 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 12 iterations.

[0248] Figure 4 The figure is a comparison of the average covert information rate of three different optimization schemes when the concealment parameter increases. Fixed phase: optimize the trajectory of the drone. Fixed drone trajectory: The drone flies along a uniform straight trajectory and optimizes the phase. Joint optimization: drone trajectory and smart reflector phase. According to the scheme proposed by P3, the phase of the smart reflector and the drone trajectory are jointly optimized. The joint optimization effectively improves the average covert information rate, but as the concealment parameter increases, the performance improvement effect gradually saturates. This is because as the concealment parameter increases, the detection rate constraint becomes more stringent and the performance gain gradually converges.

[0249] Based on the above simulation results and analysis, the present invention improves the average information rate of users by jointly optimizing the phase of the reflective elements of the reconfigurable smart reflective surface and the trajectory of the drone, and by introducing interference signals to reduce the efficiency of eavesdroppers monitoring legitimate signals. In addition, the system performance can be improved by increasing the number of reflective elements of the reconfigurable smart reflective surface.

Claims

1. A method for optimizing UAV covert communication resources based on intelligent reflective surface assistance, characterized in that: The method comprises the following steps: Step 1: According to the geographical locations of the UAV, the jammer, the legitimate users and the eavesdroppers on the ground, an air-to-ground channel fading model and a signal-to-noise ratio model from the legitimate users to the UAV are established; Step 2, under the condition that the power of the jammer's noise is random and uniformly distributed, calculate the false detection probability of the eavesdropper; Step 3, construct an optimization problem under the premise that the false detection probability of the eavesdropper is minimized; Step 4, the optimization problem is divided into two optimization sub-problems: in the first sub-problem, the phases of the received signals from different channels at the user side and the eavesdropper are coherently combined to achieve the maximum average rate; in the second sub-problem, the trajectory scheduling of the UAV is optimized using the relaxation variable method and the successive convex approximation method; Step 5: Use the convex optimization toolbox to find local approximate solutions to the above two sub-optimization problems respectively, iterate the three local approximate solutions, and obtain the approximate optimal solution to the legitimate user weighted sum rate maximization problem.

2. According to claim 1, a method for optimizing UAV covert communication resources based on intelligent reflective surface assistance is characterized in that: In step 1, the direct channel from the base station to the user is blocked by a building, and a drone carrying a smart reflective surface is used as a relay. The air-to-ground channel fading model and the signal-to-noise ratio model from a legitimate user to a drone eavesdropper include the following information: a drone carrying a smart reflective surface, a legitimate user, an eavesdropper, and a jammer; the trajectory of the drone is represented by u[n] = [x[n], y[n]] T , u s and u f is the initial and final position of the trajectory, u[0] = u s ,u[N]=u f , the vertical height of the drone is fixed at H, the flight period is T, T is divided into N time slots, T = Nδ, δ is the time slot length, and the drone trajectory satisfies: ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (1) Where D = Vδ, V is the flight speed of the drone, The horizontal position of the legitimate user is denoted as q B =[x b ,y b ] T ; The horizontal position of the eavesdropper is denoted by q W =[x w ,y w ] T , the horizontal position of the jammer is denoted as q J =[x j ,y j ] T . The phase shift matrix of the smart reflection surface in the nth time slot is: The phase shift of the mth reflective element is: The channel gain from the base station to the legitimate user is expressed as: in ρ represents the path loss at a unit distance d = 1m, λ is the wavelength, d is the antenna length, and η is the path loss exponent. is the distance from the base station to the drone, is the distance from the drone to the legal user. is the cosine of the angle of arrival of the signal from the base station to the drone in the nth time slot. is the cosine of the angle of arrival of the signal from the drone to the legitimate user in the nth time slot. The channel gain from the base station to the eavesdropper is expressed as: in is the distance from the drone to the eavesdropper, is the cosine of the angle of arrival of the signal from the drone to the eavesdropper in the nth time slot. Due to the fast fading caused by multipath propagation, the signal gain from the jammer to the user and from the jammer to the eavesdropper is modeled by the Rayleigh channel: where μ1, μ2 are path loss exponents, ξ JW and JB Each element follows an independent and identical distribution, that is, is the distance from the jammer to the eavesdropper, is the distance from the jammer to the legitimate user. Signal gain from jammer to user and eavesdropper: in represents the cosine of the arrival angle of the signal from the jammer to the drone in the nth time slot, is the distance from the jammer to the drone. The signal-to-noise ratio of a legitimate user in each time slot is: The average rate of the legitimate user in the nth time slot: Among them, P b is the base station transmission power, P j is the jammer transmit power, σ b 2 is the noise power of the legitimate user.

3. According to claim 1, a method for optimizing UAV covert communication resources based on intelligent reflective surface assistance is characterized in that: In step 2, when the locations of the eavesdropper, jammer, and base station are known, the minimum false detection probability of the eavesdropper is derived: The artificial noise model of the jammer obeys uniform distribution, and the probability density function is: When the drone is flying, the eavesdropper can directly detect the drone's trajectory and accurately know the drone's location information. The signal received by the eavesdropper is: H0 means there is no communication between the drone and the legitimate user, H1 means there is communication, x j (n) represents the transmission signal of the jammer, x b represents the transmission signal of the base station, n w is the Gaussian white noise at the eavesdropper, and the base station transmits power P in each time slot b is fixed, P j is the transmit power of the jammer. The received power of the eavesdropper: The eavesdropper compares the average power with the preset threshold to determine whether the drone is communicating with the legitimate user, making a binary judgment. Γ1 indicates that the judgment is H1 (communication occurs), and Γ0 indicates that the judgment is H0 (no communication occurs), where τ is a detection threshold with no definite value, which is used to distinguish the intervals. False alarm probability Missed detection probability in 4. According to claim 1, a method for optimizing UAV covert communication resources based on intelligent reflective surface assistance is characterized in that: In step 3, under the premise that the false detection probability of the eavesdropper is minimized, the optimization problem is constructed: From step 3, we can get the false alarm probability and missed detection probability of the eavesdropper's detection signal. The jammer is a strong user. In the case of , the total false detection probability is expressed as: ξ[n]=P FA [n]+P MD [n] when When ξ[n] decreases monotonically, , ξ[n] increases monotonically, so the minimum value ξ[n] * [n] must be a value in Inside. Minimum Confidentiality performance must meet the following requirements: ξ*[n]≥1-ε Right now: The value of ε is 0.

01. Let the UAV trajectory U={u[n],n=1,2,…,N}, Smart reflector phase shift Θ = {θ m ,m=1,2,…,M} The optimization problem is expressed as: (P)： i m ∈[0,2π)m=1,2,…,M-1 (19c) u[0]=u s ,u[N]=u f (19d) ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (19e)。 5. According to claim 1, a method for optimizing UAV covert communication resources based on intelligent reflective surface assistance is characterized in that: In step 4, the optimization problem is divided into two optimization sub-problems: In the first sub-problem the phases of the received signals from different channels at the user and the eavesdropper are coherently combined to achieve the maximum average rate: Written as: Combine signals from different paths through smart reflective surfaces: Get the optimal reflection coefficient of the mth reflection element in the nth time slot: Written as: Written as: Written as: Next, we optimize the trajectory of the drone: P is rewritten as: (P1)： i m ∈[0,2π)m=1,2,…,M-1 (25c) u[0]=u s ,u[N]=u f (25d) ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (25e) P1 is non-convex, and the trajectory of the drone is optimized using the slack variable method and the successive convex approximation method: Define e[n] as The upper bound of s[n] is The lower bound of v[n] is The upper bound of q[n] is The lower bound of P(1) can be rewritten as: P(2): u[0]=u s ,u[N]=u f (26g) ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (26h) For P2, first solve (26a), P b ρ 2 M 2 >0,P j ρ 2 M 2 >0,P j h JB +σ b 2 >0, when e[n]>0, s[n]>0, function The Hessian matrix of is a positive definite matrix, so the function is a convex function. and The first-order Taylor expansion of is: Where C, C1 and C2 represent P b ρ 2 M 2 , (P j h JB +σ b 2 ) and P j ρ 2 M 2 . (26c)-(26f) The convexity of is unknown. For (26c), first prove is convex: exist and Perform a first-order Taylor expansion on equation (28): The first-order Taylor display of is T(u[n]), The first-order Taylor display of is Y(u[n]), The first-order Taylor display of is W(u[n]). At the point Perform the first-order Taylor expansion of (26e) and (26f): P2 is rewritten as: P3： u[0]=u s ,u[N]=u f (32g) ||u[n+1]-u[n]|| 2 ≤D 2 n=1,2,…,N-1 (32h) (32a) is a linear function, and all constraints are convex constraints. Convex optimization is used to solve problem P3.

6. According to claim 1, a method for optimizing UAV covert communication resources based on intelligent reflective surface assistance is characterized in that: In step 5, the convex optimization tool is used to find local approximate solutions to the above two sub-problems respectively, and the two local optimal solutions are alternately iteratively optimized to obtain the overall approximate optimal solution of the system: 1: Initialize the drone trajectory U0, phase Θ0, drone initial coordinates u0, auxiliary variables {e0, s0, v0, q0}, and set the initial iteration number L = 1, repeat: 2: Fixed θ L-1 , update U through (32) L ,u L , e L 、s L 、v L ,q L The value of 3: Fixed U L , update Θ by (21) L The value of 4: Fixed U L and θ L , update R by (10) L The value of Until:|R L -R L-1 |<κ, The constant κ is set to 10 -5 .

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, it implements a method for optimizing covert communication resources of unmanned aerial vehicles based on the assistance of intelligent reflective surfaces as described in any one of claims 1 to 6 above.

8. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the computer instruction is executed by the processor, a method for optimizing covert communication resources of a UAV based on the assistance of an intelligent reflective surface is implemented as described in any one of claims 1-6.

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