IRS-assisted UAV covert communication method based on trajectory and beam forming joint optimization

Abstract

The invention provides a limited-block-length intelligent reflecting surface (IRS)-assisted multi-antenna unmanned aerial vehicle (UAVCC) covert communication method, in which the covert transmission capability of a mobile multi-antenna unmanned aerial vehicle can be enhanced and the detection capability of a monitor can be weakened by utilizing the IRS. A hidden transmission rate maximization mathematical model of the unmanned aerial vehicle is established by jointly optimizing the trajectory and transmitted beam forming of the multi-antenna unmanned aerial vehicle and a phase shift matrix of the IRS. In order to solve the non-convex problem, the non-convex problem is decomposed into three sub-problems. The method comprises the following steps: firstly, solving two sub-problems of a track of an unmanned aerial vehicle and a phase shift matrix of an IRS by adopting a semi-definite relaxation method; secondly, a successive convex approximation method is applied, and the transmitted beam forming optimization sub-problem of the non-convex multi-antenna unmanned aerial vehicle is converted into a convex sub-problem; and finally, providing an effective block coordinate descent structure to obtain a suboptimal solution of the original problem. On the basis, the invention further provides a gradient projection dual decomposition method with low complexity penalty, and the algorithm complexity can be effectively reduced. A numerical result shows that the algorithm is effective and superior in the IRS-UAVCC with the limited block length.

Description

Technical Field

[0001] The present invention relates to the technical field of UAV covert communication, and in particular to an IRS-assisted UAV covert communication method based on joint optimization of trajectory and beamforming. Background Art

[0002] Unmanned Aerial Vehicle (UAV) can quickly restore communication services and enhance wireless network coverage as aerial communication nodes due to its controllable mobility and flexible deployment capabilities. However, due to the broadcast characteristics of wireless transmission channels in UAV networks (UAVNs), their information may be intercepted by unauthorized eavesdroppers, resulting in the leakage of confidential information. Moreover, when UAVNs require higher security, it becomes crucial to hide the legitimate information of the drone from eavesdroppers. Therefore, it is necessary and critical to explore new technologies to ensure the concealment of UAVNs.

[0003] Existing research on covert communications in UAVNs can be divided into two categories: UAV-enabled covert communications (UAVCC) and IRS-assisted UAV covert communications (IRS-UAVCC). To improve the secure communication performance of UAVNs, the former makes full use of the flexible deployment characteristics of UAVs, while the latter takes advantage of the characteristics of intelligent and controllable wireless propagation environment. 1) UAV-assisted covert communications: Flexible and highly maneuverable UAVs can effectively improve the confidentiality level of communications in the presence of eavesdroppers. However, most studies only consider the assumption of infinite block length (IFB), which is not applicable to low-latency application scenarios. For this reason, finite block length (IFB) is introduced. Blocklength (FB) is used to deal with this problem in UAV-assisted covert communication (UAVCC). 2) IRS-assisted UAV covert communication: IRS can be used to improve the transmission environment of legitimate users while suppressing the detection capability of unauthorized users. Therefore, deploying IRS in UAVNs can further extend the range of covert communication and improve the covert performance, especially in complex urban environments. By adjusting the reflection coefficient of the reflecting surface, IRS can effectively optimize the signal propagation path, improve the signal quality of the legitimate receiver, and reduce the signal strength of the eavesdropper, thereby enhancing the reliability and security of covert communication. However, most studies do not involve UAV self-communication assisted by IRS, which is more vulnerable to security threats. In addition, only single-antenna UAVs are considered, and the impact of finite block length (FB) on IRS-assisted UAV covert communication system (IRS-UAVCC) is ignored.

[0004] In intelligent reflecting surface (IRS)-assisted unmanned aerial vehicle networks (UAVNs), the ultimate goal is to achieve high-speed communication and high security between UAVs and ground legitimate users (GLUs) by hiding the existence of UAVs. However, most of the existing research on IRS-assisted UAV covert communication (IRS-UAVCC) focuses on single-antenna UAVs and infinite block length (IFB) scenarios, which is not applicable in scenarios with high transmission rate and low latency requirements. In finite block length (FB) scenarios, the traditional Shannon capacity formula is no longer applicable. Simply maximizing the signal-to-noise ratio (SNR) cannot guarantee the maximum achievable covert transmission rate (ACTR). Therefore, it is necessary to deeply study the impact of FB on IRS-UAVCC systems. In addition, in order to further improve the achievable ACTR of UAVNs, it is necessary to jointly optimize the multi-antenna UAV's trajectory (UAV-TR) and transmit beam (UAV's transmit beamforming, UAV-TB), as well as the IRS's phase shift matrix (IRS-PSM). It is worth noting that due to the high computational complexity of the multi-antenna UAV transmit beam (UAV-TB) and IRS phase matrix (IRS-PSM), a low-complexity algorithm must be designed to achieve efficient optimization, thereby reducing the computational burden while ensuring the covert communication performance. Summary of the invention

[0005] In view of this, the purpose of the present invention is to provide an IRS-assisted UAV covert communication network design method in a finite block length (FB) scenario, and propose a low-complexity joint optimization algorithm for optimizing the IRS reflection phase shift matrix (IRS-PSM), the trajectory of the mobile multi-antenna UAV (UAV-TR) and the transmit beam (UAV-TB) to maximize the achievable covert transmission rate (ACTR) of the UAV network (UAVNs);

[0006] To achieve the above-mentioned object of the invention, the present invention provides an IRS-assisted UAV covert communication method based on joint optimization of trajectory and beamforming, comprising:

[0007] S1. Establish a joint trajectory and beamforming optimization system model for IRS-assisted multi-antenna UAV finite block length covert communication, including: UAV trajectory discretization, flight period T is evenly divided into N time slots, the duration of each time slot is δ t=T / N; establish a channel model, consider the complex urban environment, all channels are modeled as Rician fading channels; Willie's binary hypothesis test, in covert communication, Willie needs to judge whether the transmission from the drone to Bob occurs based on the observed signal;

[0008] S2. A communication performance optimization problem with the goal of maximizing the average covert transmission rate (ACTR) is established. Under the constraints of UAV mobility, UAV transmission power, intelligent reflection surface phase shift matrix (IRS-PSM) and the covert communication requirements of UAV networks, the covert transmission rate of IRS-assisted UAV networks (UAVNs) with finite block length (FB) is maximized.

[0009] S3. Solve the ACTR maximization problem by building a block coordinate descent-semidefinite relaxation (BCD-SDR) optimization framework;

[0010] S4. In order to reduce the complexity of BCD-SDR in S3, a low-complexity penalized dual decomposition based on gradient projection (PDDGP) method is proposed, which can effectively reduce the computational complexity of the two sub-problems of UAV-TB and IRS-PSM;

[0011] Preferably, in step S1, the system includes a device equipped with N t =N x ×N y There is a transmitter Alice (drone) with 2 antennas, a legal ground user Bob with 1 antenna, a ground monitor Willie with 1 antenna, and an IRS installed on a building with M=M x ×M z A passive reflector unit. With the help of IRS, the drone hopes to communicate covertly with Bob while avoiding detection by Willie.

[0012] S101. Indicates that the drone is The flight period T is evenly divided into N time slots, that is, the duration of each time slot is δ t =T / N. Due to the hardware limitation of the drone, its maximum flight distance in each time slot is limited to V max δ t ,Right now

[0013]

[0014] ||o a [1]-oa,I ||≤V max δ t ,o a [N]=o a,F ;

[0015] S102. time slots, from UAV to IRS link The channel model is:

[0016]

[0017] in Indicates The distance between the UAV and the IRS in the time slot, β0 represents the channel power gain when the reference distance is 1m, α ar and ε ar Respectively represent the path loss exponent and Rician factor of the UAV-IRS link, and the line-of-sight (LoS) channel matrix Non-Line-of-Sight (NLoS) Channel Matrix

[0018] S103.Willie in The signal received by the lth channel in the time slot can be expressed as:

[0019]

[0020] in, represents the null hypothesis, that is, Alice did not send information; represents the alternative hypothesis, that is, Alice sends information to Bob; in addition, represents the additive white Gaussian noise (AWGN) at Willie;

[0021] For covert communication, constraints are often used To ensure the concealment, where ∈ represents a small threshold that defines the concealment level, according to when When , the hidden constraint can be satisfied Therefore, the hidden constraint can be constrained replaced by about is monotonically increasing, so when hour, Can reach maximum value Right now Can be equivalent to

[0023] Considering a finite block length (FB), Bob The average concealed transmission rate (ACTR) achievable in time slots can be expressed as

[0024]

[0025] in, represents the Q function, Q -1 (x) represents its inverse function, δ represents the given maximum permissible decoding error probability, represents the channel dispersion, which is expressed as

[0026] Preferably, in step S2, the covert transmission rate of the IRS-assisted UAV network (UAVNs) with a finite block length (FB) is maximized by considering the mobility constraints of the UAV, the transmission power of the UAV, the intelligent reflection surface phase shift matrix (IRS-PSM) and the covert communication requirements of the UAV network; define Then the ACTR maximization problem of UAVNs can be expressed as

[0027]

[0028] ||o a [1]|o a,I ||≤V max δ t ,o a [N]=o a,F ,

[0029]

[0030] in, represents the transmission power constraint of the UAV, represents the hidden constraint, represents the IRS phase shift matrix (IRS-PSM) constraint;

[0031] Preferably, in step S3, the ACTR maximization problem is solved by constructing a block coordinated descent-semidefinite relaxation (BCD-SDR) optimization framework, and the relaxation variable The ACTR maximization problem is reformulated as

[0032]

[0033] ||o a [1]-o a,I ||≤V max δ t ,o a [N]=o a,F,

[0034]

[0035] In order to solve this complex non-convex ACTR maximization problem, it is divided into three sub-problems, namely, the multi-antenna UAV trajectory (UAV-TR) sub-problem, the UAV transmit beamforming (UAV-TB) sub-problem and the IRS phase shift matrix (IRS-PSM) sub-problem. The optimal solutions of these three sub-problems can be obtained by using the semidefinite relaxation (SDR) method and the continuous convex approximation (SCA) method. Subsequently, an algorithm based on block coordinate descent and semidefinite relaxation (BCD-SDR) is proposed to obtain a high-quality suboptimal solution to the ACTR maximization problem.

[0036] S301. Optimizing the UAV’s transmit beamforming: When Q a When and Φ are given, the UAV-TB subproblem can be transformed into a convex optimization problem using the semidefinite relaxation (SDR) technique. The convex optimization problem is expressed as:

[0037]

[0038] Therefore, the UAV-TB subproblem can be solved efficiently using standard optimization tools such as CVX, and then, by employing the singular value decomposition (SVD) technique, it can be derived that The approximate optimal solution of

[0039] S302. Optimize the phase shift matrix of IRS: When Q a and When given, the rank-one constraint is relaxed using the semidefinite relaxation (SDR) method The IRS-PSM subproblem can be reformulated as the following convex optimization problem:

[0040]

[0041] For this relaxed convex optimization problem, the interior point method can be used to find the optimal solution. Then, by using the standard Gaussian randomization method, we can obtain An approximate solution of

[0042] S303. Optimizing the trajectory of the UAV: ​​When Φ and Given, the UAV trajectory optimization (UAV-TR) subproblem can be formulated as

[0043]

[0044] ||o a [1]-o a,I ||≤V max δ t ,oa [N]=o a,F ,

[0045]

[0046] in, and Respectively and The result at the j-1th iteration is,

[0047] Next, the hiddenness constraint can be rewritten as

[0049] Then, by introducing the slack variable By transforming all non-convex constraints into convex constraints, the UAV-TR subproblem can be further transformed into

[0050]

[0051] ||o a [1]-o a,I ||≤V max δ t ,o a [N]=o a,F ,

[0052]

[0053] Since the problem is a convex optimization problem, it can be solved efficiently using the CVX solver;

[0054] S304. Using the block coordinate descent and semidefinite relaxation (BCD-SDR) optimization framework, the three subproblems of UAV trajectory (UAV-TR) subproblem, UAV transmit beamforming (UAV-TB) subproblem and IRS phase shift matrix (IRS-PSM) subproblem are iteratively solved. Because these three subproblems are finally transformed into convex optimization problems, the concealed transmission rate of the UAV increases monotonically in each iteration, so they finally converge and obtain the suboptimal solution of the ACTR maximization problem;

[0055] Preferably, in step S4, a low-complexity gradient projection-based penalized dual decomposition (PDDGP) method is proposed to solve the UAV-TB and IRS-PSM subproblems, wherein the low-complexity algorithm adopts a double-loop penalized dual decomposition (PDD) method, wherein the inner loop uses the alternating gradient projection (AGP) technique to solve the augmented Lagrangian (AL) problem, and the outer loop updates the dual variables and penalty parameters;

[0056] S401. By introducing The implicit constraint is converted to in Therefore, the augmented Lagrangian function of the ACTR maximization problem can be expressed as

[0057]

[0058] in, ρ represents the penalty parameter, Representation and constraints The related Lagrange multiplier, therefore, the ACTR maximization problem can be equivalently expressed as

[0059]

[0060] Next, a low-complexity penalty dual decomposition with gradient projection-BCD (BCD-PDDGP) optimization method is used to solve the ACTR maximization problem.

[0061] S402. Optimize the phase shift matrix of IRS: Given ρ and It can be expressed as

[0062]

[0063] in, represents the corresponding step size, whose appropriate value can be selected by a backtracking line search scheme based on the Armijo-Goldstein condition, express about The gradient of can be expressed by the following formula:

[0064]

[0065] formula The function of (c) is to Projection to the feasible region in

[0066]

[0067] S403. Optimizing the transmit beamforming of the UAV: ​​Similarly, given ρ and It can be expressed as

[0068]

[0069] in, represents the corresponding step length, express about The gradient of can be expressed as

[0070]

[0071] formula The function of (c) is to Projection to the feasible region

[0072] S404. Optimization In a given ρ and In the case of The optimal solution can be expressed as

[0073]

[0074] S405. Update and ρ: After the inner loop AGP converges, the dual variable and penalty parameter need to be updated in the outer loop. The update method of ρ is ρ = νρ. The dual variable The update method is

[0075]

[0076] Compared with the prior art, the present invention has the following beneficial effects:

[0077] The present invention provides a novel IRS-assisted UAV covert communication method based on joint optimization of trajectory and beamforming, which makes full use of the flexibility and high maneuverability of mobile multi-antenna UAVs, explores the gains brought by active beamforming and passive beamforming, and jointly optimizes the UAV trajectory (UAV-TR) and UAV beamforming (UAV-TB), as well as the passive phase shift matrix of IRS to maximize ACTR while satisfying the constraints of system concealment and UAV transmission power. In addition, the present invention proposes a low-complexity iterative algorithm combining BCD and PDDGP technologies, which can achieve excellent performance with lower complexity compared with the high-quality BCD-SDR algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0078] In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings required for describing the embodiments are briefly introduced below. Obviously, the drawings described below are only preferred embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative work.

[0079] Figure 1It is a model diagram of an IRS-assisted UAV covert communication system based on joint optimization of trajectory and beamforming provided by an embodiment of the present invention;

[0080] Figure 2 It is a convergence diagram of BCD-SDR and BCD-PDDGP algorithms under different IRS reflection units in IRS-assisted multi-antenna UAV finite block length covert communication based on joint optimization of trajectory and beamforming provided by an embodiment of the present invention;

[0081] Figure 3 It is a comparison diagram of ACTR in an IRS-assisted UAV covert communication scheme based on joint optimization of trajectory and beamforming provided by an embodiment of the present invention and other two benchmark schemes; DETAILED DESCRIPTION

[0082] The principles and features of the present invention are described below in conjunction with the accompanying drawings. The examples listed are only used to explain the present invention and are not used to limit the scope of the present invention.

[0083] This embodiment provides an IRS-assisted UAV covert communication method based on joint optimization of trajectory and beamforming, and the specific steps include:

[0084] S1. Figure 1 As shown in the figure, the joint trajectory and beamforming optimization system model of IRS-assisted multi-antenna UAV finite block length covert communication is established. The system includes N t =N x ×N y There is a transmitter Alice (drone) with 2 antennas, a legal ground user Bob with 1 antenna, a ground monitor Willie with 1 antenna, and an IRS installed on a building with M=M x ×M z A passive reflector unit. With the help of IRS, the drone hopes to communicate covertly with Bob while avoiding detection by Willie.

[0085] S101.UAV trajectory discretization: The initial position and final position of the UAV are represented as o a,I =[x a,I ,y a,I ] T and a,F =[x a,F ,y a,F ] T ,set up Indicates that the drone is The discretized trajectory in the time slot (TS) is kept at the altitude H. a , the flight period T is evenly divided into N time slots, that is, the duration of each time slot is δt =T / N. Due to the hardware limitation of the drone, its maximum flight distance in each time slot is limited to V max δ t ,Right now

[0086]

[0087] ||o a [1]-o a,I ||≤V max δ t ,o a [N]=o a,F ,

[0088] S102. Establish channel model: Considering the complex urban environment, all channels are modeled as Rician fading channels. Specifically, in the time slots, from UAV to IRS link The channel model is:

[0089]

[0090] in Indicates The distance between the UAV and the IRS in the time slot, β0 represents the channel power gain when the reference distance is 1m, α ar and ε ar Respectively represent the path loss exponent and Rician factor of the UAV-IRS link, and the line-of-sight (LoS) channel matrix Non-Line-of-Sight (NLoS) Channel Matrix

[0091] In addition, the IRS receive array response vector It is expressed as:

[0092]

[0093] The launch array response of the drone It is expressed as:

[0094]

[0095] in, and denote the vertical and horizontal arrival angles at the IRS, respectively, and and represent the vertical and horizontal departure angles at the UAV, respectively;

[0096] In addition, The IRS phase shift matrix of time slots is expressed as in Drones in the The signal sent in the lth channel of the time slot is and Here, L represents the total number of channels used;

[0097] Drones in the The transmitted signal of a time slot is expressed as in represents the transmit beamforming vector of the UAV, so the transmit power constraint of the UAV can be expressed as:

[0098]

[0099] Among them, P a,max Indicates the maximum transmission power of the drone;

[0100] S103. Willie's binary hypothesis test: In covert communication, Willie needs to judge whether the transmission from the drone to Bob occurs based on the observed signal. Therefore, Willie The received signal of the lth channel of the time slot can be expressed as:

[0101]

[0102] in, represents the null hypothesis, that is, Alice did not send information; represents the alternative hypothesis, that is, Alice sends information to Bob, and in addition, represents the additive white Gaussian noise (AWGN) at Willie;

[0103] In the time slots, false alarm probability and the probability of missed detection They can be defined as:

[0104]

[0105] in, and represents a binary decision for determining whether transmission between the drone and Bob occurs. Therefore, Willie The total detection error probability (DEP) of a time slot can be expressed as:

[0106]

[0107] Among them, π0 and π1 = 1-π0 represent the assumptions and The prior probability of

[0108] However, due to the minimum detection error probability The expression contains an incomplete gamma function, which makes the subsequent analysis more complicated. To solve this problem, we can use Pinsker's inequality to obtain A tractable lower bound for is given by

[0109]

[0110] in, Indicates from arrive The Kullback-Leibler (KL) divergence of is defined as

[0111]

[0112] in,

[0113] For covert communication, constraints are often used To ensure the concealment, where ∈ represents a small threshold that defines the concealment level, according to when When , the hidden constraint can be satisfied Therefore, the hidden constraint can be constrained replaced by about is monotonically increasing, so when hour, Can reach maximum value Right now Can be equivalent to

[0115] Considering a finite block length (FB), Bob The average concealed transmission rate (ACTR) achievable in time slots can be expressed as

[0116]

[0117] in, represents the Q function, Q -1 (x) represents its inverse function, δ represents the given maximum permissible decoding error probability, represents the channel dispersion, which is expressed as

[0118] S2. Establish a communication performance optimization problem with the goal of maximizing the average covert transmission rate (ACTR). Our goal is to maximize the covert transmission rate of IRS-assisted UAV networks (UAVNs) with finite block length (FB) under the consideration of the mobility constraints of UAVs, the transmission power of UAVs, the intelligent reflection surface phase shift matrix (IRS-PSM), and the covert communication requirements of UAV networks. Define Then the ACTR maximization problem of UAVNs can be expressed as

[0119]

[0120] ||o a [1]-o a,I ||≤V max δ t ,o a [N]=o a,F ,

[0121]

[0122] in, represents the transmission power constraint of the UAV, represents the hidden constraint, represents the IRS phase shift matrix (IRS-PSM) constraint;

[0123] S3. The ACTR maximization problem is solved by constructing a block coordinate descent-semidefinite relaxation (BCD-SDR) optimization framework. In order to solve the non-convex ACTR maximization problem in S5, it is necessary to transform the optimization problem in S5 into a more tractable form by introducing relaxation variables. The ACTR maximization problem is reformulated as

[0124]

[0125] ||o a [1]-o a,I ||≤V max δ t ,o a [N]=o a,F ,

[0126] make because About Concave function, in order to deal with non-convex functions can be replaced by its upper bound by using a first-order Taylor expansion, The upper bound of

[0127]

[0128] in, represents the feasible solution obtained in the jth iteration;

[0129] Next, the above ACTR maximization problem can be reformulated as

[0130]

[0131] ||o a [1]-o a,I ||≤V max δ t ,o a [N]=o a,F ,

[0132] In order to solve this complex non-convex ACTR maximization problem, it is divided into three sub-problems, namely, the multi-antenna UAV trajectory (UAV-TR) sub-problem, the UAV transmit beamforming (UAV-TB) sub-problem and the IRS phase shift matrix (IRS-PSM) sub-problem. The optimal solutions of these three sub-problems can be obtained by using the semidefinite relaxation (SDR) method and the continuous convex approximation (SCA) method. Subsequently, an algorithm based on block coordinate descent and semidefinite relaxation (BCD-SDR) is proposed to obtain a high-quality suboptimal solution to the ACTR maximization problem.

[0133] S301. Optimizing the UAV’s transmit beamforming: When Q a When and Φ are given, the UAV transmit beamforming (UAV-TB) subproblem can be expressed as

[0134]

[0135]

[0136] set up and The hiddenness constraint can be restated as:

[0137]

[0138] The UAV-TB subproblem can be transformed into a convex optimization problem using the semidefinite relaxation (SDR) technique. The convex optimization problem is expressed as:

[0139]

[0140] Therefore, the UAV-TB subproblem can be solved efficiently using standard optimization tools such as CVX, and then, by employing the singular value decomposition (SVD) technique, it can be derived that The approximate optimal solution of ;

[0141] S302. Optimize the phase shift matrix of IRS: When Q a and Given, the IRS-PSM subproblem can be expressed as

[0142]

[0143] set up in By definition The implicit constraint is rewritten as

[0144]

[0145] Then the rank-one constraint is relaxed by using the semidefinite relaxation (SDR) method On this basis, the IRS-PSM subproblem can be reformulated as the following convex optimization problem:

[0146]

[0147] For this relaxed convex optimization problem, the interior point method can be used to find the optimal solution. Then, by using the standard Gaussian randomization method, we can obtain An approximate solution of

[0148] S303. Optimizing the trajectory of the UAV: ​​When Φ and Given, the UAV trajectory optimization (UAV-TR) subproblem can be formulated as

[0149]

[0150] ||o a [1]-o a,I ||≤V max δ t ,o a [N]=o a,F ,

[0151]

[0152] Since the UAV-TR subproblem is a non-convex optimization problem, in order to solve this difficult problem, it is necessary to first calculate the LoS component in the objective function The main reason is About variable Q aThe complexity and nonlinearity of make it difficult to optimize the trajectory of the UAV. Specifically, in the jth iteration, can be approximated based on the trajectory of the UAV in the j-1th iteration. Similarly, and In the jth iteration, it is also calculated by the UAV trajectory of the j-1th iteration. Therefore, the UAV-TR subproblem can be restated as follows:

[0153]

[0154] ||o a [1]-o a,I ||≤V max δ t ,o a [N]=o a,F ,

[0155]

[0156] in, and Respectively and The result at the j-1th iteration is,

[0157] Next, the hiddenness constraint can be rewritten as

[0158]

[0159] Then, by introducing the slack variable By transforming all non-convex constraints into convex constraints, the UAV-TR subproblem can be further transformed into

[0160]

[0161] ||o a [1]-o a,I ||≤V max δ t ,o a [N]=o a,F ,

[0162]

[0163] Since the problem is a convex optimization problem, it can be solved efficiently using the CVX solver;

[0164] S304. Using the block coordinate descent and semidefinite relaxation (BCD-SDR) optimization framework, the three subproblems of UAV trajectory (UAV-TR) subproblem, UAV transmit beamforming (UAV-TB) subproblem and IRS phase shift matrix (IRS-PSM) subproblem are iteratively solved. Because these three subproblems are finally transformed into convex optimization problems, the concealed transmission rate of the UAV increases monotonically in each iteration, so they finally converge and obtain the suboptimal solution of the ACTR maximization problem;

[0165] S4. Low-complexity algorithm design: In order to reduce the complexity of BCD-SDR in S6, a low-complexity gradient projection-based penalized dual decomposition (PDDGP) method is proposed to solve the UAV-TB and IRS-PSM sub-problems. The low-complexity algorithm adopts a double-loop penalized dual decomposition (PDD) method, in which the inner loop uses the alternating gradient projection (AGP) technique to solve the augmented Lagrangian (AL) problem, and the outer loop updates the dual variables and penalty parameters.

[0166] S401. By introducing The implicit constraint is converted to in Therefore, the augmented Lagrangian function of the ACTR maximization problem can be expressed as

[0167]

[0168] in, ρ represents the penalty parameter, Representation and constraints The related Lagrange multiplier, therefore, the ACTR maximization problem can be equivalently expressed as

[0169]

[0170] Next, we use a low-complexity penalty dual decomposition with gradient projection-BCD (BCD-PDDGP) optimization method to solve the ACTR maximization problem.

[0171] S402. Optimize the phase shift matrix of IRS: Given ρ and It can be expressed as

[0172]

[0173] in, represents the corresponding step size, whose appropriate value can be selected by a backtracking line search scheme based on the Armijo-Goldstein condition, express about The gradient of can be expressed by the following formula:

[0174]

[0175] formula The function of (c) is to Projection to the feasible region in

[0176]

[0177] S403. Optimizing the transmit beamforming of the UAV: ​​Similarly, given ρ and It can be expressed as

[0178]

[0179] in, represents the corresponding step length, express about The gradient of can be expressed as

[0180]

[0181] formula The function of (c) is to Projection to the feasible region

[0182] S404. Optimization In a given ρ and In the case of The optimal solution can be expressed as

[0183]

[0184] S405. Update and ρ: After the inner loop AGP converges, the dual variable and penalty parameter need to be updated in the outer loop. The update method of ρ is ρ = νρ. The dual variable The update method is

[0185]

[0186] Figure 2 Describes the t=4 and M = {50,80}, it can be observed that the proposed BCD-SDR and BCD-PDDGP algorithms can gradually converge within three iterations, and the low-complexity BCD-PDDGP algorithm can achieve the same performance as the traditional BCD-SDR algorithm. In addition, since more degrees of freedom can be obtained, the ACTR when M = 80 is significantly higher than that when M = 50;

[0187] Figure 3 Comparison of the number of transmitting antennas N of different UAVs t In the following figure, the ACTR performance of Bob in the proposed scheme and the other two baseline schemes is shown. The baseline scheme without IRS and joint optimization of UAV TB and TR is marked as “without IRS”, while the baseline scheme without optimizing UAV trajectory and only executing UAV TB and IRS-PSM design is marked as “straight flight”; Figure 3 As shown in Figure 2, the ACTR of all schemes increases with N t This is because more UAV transmitting antennas can provide greater active beamforming gain, highlighting the importance of optimizing UAV active beamforming. In addition, the low-complexity BCD-PDDGP algorithm can always achieve almost the same performance as the efficient BCD-SDR algorithm. More importantly, in UAVNs, the advantages of the proposed scheme in ACTR have been verified. Therefore, the optimization of UAV TB and TR and the optimization of IRS-PSM play a key role in enhancing covert transmission.

[0188] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. An IRS-assisted UAV covert communication method based on joint optimization of trajectory and beamforming, characterized in that: The following steps are involved: S1. Establish a joint trajectory and beamforming optimization system model for IRS-assisted multi-antenna UAV finite block length covert communication, including: UAV trajectory discretization, flight period T is evenly divided into N time slots, the duration of each time slot is δ t =T / N; establish a channel model, consider the complex urban environment, all channels are modeled as Rician fading channels; Willie's binary hypothesis test, in covert communication, Willie needs to judge whether the transmission from the drone to Bob occurs based on the observed signal; S2. A communication performance optimization problem with the goal of maximizing the average covert transmission rate (ACTR) is established. Under the constraints of UAV mobility, UAV transmission power, intelligent reflection surface phase shift matrix (IRS-PSM) and the covert communication requirements of UAV networks, the covert transmission rate of IRS-assisted UAV networks (UAVNs) with finite block length (FB) is maximized. S3. Solve the ACTR maximization problem by building a block coordinate descent-semidefinite relaxation (BCD-SDR) optimization framework; S4. In order to reduce the complexity of BCD-SDR in S3, a low-complexity penalized dual decomposition based on gradient projection (PDDGP) method is proposed, which can effectively reduce the computational complexity of the two sub-problems of UAV-TB and IRS-PSM.

2. The IRS-assisted UAV covert communication method based on trajectory and beamforming joint optimization according to claim 1 is characterized in that: In step S1, the system includes a device equipped with N t =N x ×N y There is a transmitter Alice (drone) with 2 antennas, a legal ground user Bob with 1 antenna, a ground monitor Willie with 1 antenna, and an IRS installed on a building with M=M x ×M z A passive reflector unit. With the help of IRS, the drone hopes to communicate covertly with Bob while avoiding detection by Willie. S101. Set o a [ι]=[x a [ι],y a [ι]] T , represents the discretized trajectory of the drone in the ιth time slot (TS). The flight period T is evenly divided into N time slots, that is, the duration of each time slot is δ t =T / N. Due to the hardware limitation of the drone, its maximum flight distance in each time slot is limited to V max δ t ,Right now ||o a [1]-o a,I ||≤V max d t ,o a [N]=o a,F ; S102. The ιth time slot, from UAV to IRS link The channel model is: in represents the distance between UAV and IRS in the ιth time slot, β0 represents the channel power gain when the reference distance is 1m, α ar and ε ar Respectively represent the path loss exponent and Rician factor of the UAV-IRS link, and the line-of-sight (LoS) channel matrix Non-Line-of-Sight (NLoS) Channel Matrix S103. The signal received by Willie on the lth channel in the ιth time slot can be expressed as: in, represents the null hypothesis, that is, Alice did not send information; represents the alternative hypothesis, that is, Alice sends information to Bob, and in addition, represents the additive white Gaussian noise (AWGN) at Willie; For covert communication, the constraint ξ is usually used * [ι]≥1-∈ to ensure confidentiality, where ∈ represents a small threshold that defines the confidentiality level, according to when When , the hidden constraint ξ can be satisfied * [ι]≥1-∈, so the hidden constraint can be constrained Replaced by about is monotonically increasing, so when hour, Can reach maximum value Right now Can be equivalent to Considering the finite block length (FB), the average concealed transmission rate (ACTR) that Bob can achieve in the ιth time slot can be expressed as in, represents the Q function, Q -1 (x) represents its inverse function, δ represents the given maximum allowed decoding error probability, Λ[ι] represents the channel dispersion, and its expression is:

3. The IRS-assisted UAV covert communication method based on trajectory and beamforming joint optimization according to claim 1 is characterized in that: In step S2, the covert transmission rate of IRS-assisted UAVNs with finite block length (FB) is maximized under the constraints of UAV mobility, UAV transmission power, intelligent reflection surface phase shift matrix (IRS-PSM) and the covert communication requirements of UAV network. Define Then the ACTR maximization problem of UAVNs can be expressed as st0≤θ m [i]≤2π, ||o a [1]-o a,I ||≤V max d t ,o a [N]=o a,F , in, represents the transmission power constraint of the UAV, represents the hidden constraint, 0≤θ m [ι]≤2π represents the IRS phase shift matrix (IRS-PSM) constraint.

4. The IRS-assisted UAV covert communication method based on trajectory and beamforming joint optimization according to claim 1 is characterized in that: In step S3, the ACTR maximization problem is solved by constructing a block coordinate descent-semidefinite relaxation (BCD-SDR) optimization framework, and the relaxation variable The ACTR maximization problem is reformulated as st0≤θ m [i]≤2π, ||o a [1]-o a,I ||≤V max d t ,o a [N]=o a,F , c b [i]≤t[i], In order to solve this complex non-convex ACTR maximization problem, it is divided into three sub-problems, namely, the multi-antenna UAV trajectory (UAV-TR) sub-problem, the UAV transmit beamforming (UAV-TB) sub-problem and the IRS phase shift matrix (IRS-PSM) sub-problem. The optimal solutions of these three sub-problems can be obtained by using the semidefinite relaxation (SDR) method and the continuous convex approximation (SCA) method. Subsequently, an algorithm based on block coordinate descent and semidefinite relaxation (BCD-SDR) is proposed to obtain a high-quality suboptimal solution to the ACTR maximization problem. S301. Optimizing the UAV’s transmit beamforming: When Q a When and Φ are given, the UAV-TB subproblem can be transformed into a convex optimization problem using the semidefinite relaxation (SDR) technique. The convex optimization problem is expressed as: stTr(W[ι])≤P a,max , W[ι]≥0， Therefore, the UAV-TB subproblem can be solved efficiently using standard optimization tools such as CVX, and subsequently, by employing the singular value decomposition (SVD) technique, a near-optimal solution for w[ι] can be derived; S302. Optimize the phase shift matrix of IRS: When Q a and When , the rank-one constraint rank(V[ι])=1 is relaxed by using the semidefinite relaxation (SDR) method, and the IRS-PSM subproblem can be reformulated as the following convex optimization problem: s.t.V m,m [ι]=1,m=1,…,M+1, V[ι]≥0， For this relaxed convex optimization problem, the interior point method can be used to find the optimal solution, and then the approximate solution of θ[ι] can be obtained by using the standard Gaussian randomization method; S303. Optimizing the trajectory of the UAV: ​​When Φ and Given, the UAV trajectory optimization (UAV-TR) subproblem can be formulated as ||o a [1]-o a,I ||≤V max d t ,o a [N]=o a,F , in, and Respectively and The result at the j-1th iteration is, Next, the hiddenness constraint can be rewritten as Then, by introducing the slack variable By transforming all non-convex constraints into convex constraints, the UAV-TR subproblem can be further transformed into ||o a [1]-o a,I ||≤V max d t ,o a [N]=o a,F , Since the problem is a convex optimization problem, it can be solved efficiently using the CVX solver; S304. Using the block coordinate descent and semidefinite relaxation (BCD-SDR) optimization framework, the three subproblems of UAV trajectory (UAV-TR) subproblem, UAV transmit beamforming (UAV-TB) subproblem and IRS phase shift matrix (IRS-PSM) subproblem are iteratively solved. Because these three subproblems are eventually transformed into convex optimization problems, the covert transmission rate of the UAV increases monotonically in each iteration, so they finally converge to obtain the suboptimal solution of the ACTR maximization problem.

5. The IRS-assisted UAV covert communication method based on trajectory and beamforming joint optimization according to claim 1 is characterized in that: In step S4, a low-complexity penalized dual decomposition based on gradient projection (PDDGP) method is proposed to solve the UAV-TB and IRS-PSM subproblems. The low-complexity algorithm adopts a double-loop penalized dual decomposition (PDD) method, in which the inner loop uses the alternating gradient projection (AGP) technique to solve the augmented Lagrangian (AL) problem, and the outer loop updates the dual variables and penalty parameters. S401. By introducing χ[i]≥0, the hidden constraint is transformed into g(w[ι],θ[ι],χ[ι])=0, where Therefore, the augmented Lagrangian function of the ACTR maximization problem can be expressed as in, ρ represents the penalty parameter, υ[ι] represents the Lagrange multiplier associated with the constraint g(w[ι],θ[ι],χ[ι])=0, so the ACTR maximization problem can be equivalently expressed as stχ[ι]≥0, ||w[i]|| 2 ≤P a,max , 0≤θ m [i]≤2π, Next, a low-complexity penalty dual decomposition with gradient projection-BCD (BCD-PDDGP) optimization method is used to solve the ACTR maximization problem. S402. Optimize the phase shift matrix of IRS: Given w[i], χ[ι], ρ and υ[ι], θ (i+1) [ι] can be expressed as Among them, θ [ι] represents the corresponding step size, whose appropriate value can be selected by a backtracking line search scheme based on the Armijo-Goldstein condition, Represents R ρ The gradient of (w[ι],θ[ι],χ[ι]) with respect to θ[ι] can be expressed by the following formula: Formula θ (i+1) The function of (c) in [ι] is to Projection to the feasible region in S403. Optimize the transmit beamforming of the UAV: ​​Similarly, given θ[ι], χ[ι], ρ and υ[ι], w (i+1) [ι] can be expressed as Among them, w [l] represents the corresponding step size, Represents R ρ The gradient of (w[l],θ[l],χ[ι]) with respect to w[ι] can be expressed as Formula w (i+1) The function of (c) in [l] is to convert Projection to the feasible region S404. Optimize X[l]: Given w[l], θ[l], ρ and υ[ι], the optimal solution of χ[ι] can be expressed as S405. Update υ[ι] and ρ: After the inner loop AGP converges, the dual variable and penalty parameter need to be updated in the outer loop. The update method of ρ is ρ=vρ, and the update method of the dual variable υ[ι] is

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