Irs-aided uav covert communication method based on trajectory and beamforming joint optimization

Abstract

The application provides a limited block length intelligent reflecting surface (IRS) assisted multi-antenna unmanned aerial vehicle covert communication (UAVCC) method, wherein 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. By jointly optimizing the trajectory and transmit beamforming of the multi-antenna unmanned aerial vehicle and the phase shift matrix of the IRS, a mathematical model for maximizing the covert transmission rate of the unmanned aerial vehicle is established. In order to solve the non-convex problem, the problem is decomposed into three sub-problems. Firstly, the semi-definite relaxation method is adopted to solve the two sub-problems of the trajectory of the unmanned aerial vehicle and the phase shift matrix of the IRS. Secondly, the non-convex multi-antenna unmanned aerial vehicle transmit beamforming optimization sub-problem is converted into a convex sub-problem by applying the successive convex approximation method. Finally, an effective block coordinate descent structure is proposed to obtain a suboptimal solution of the original problem. On this basis, further, a low-complexity penalty gradient projection dual decomposition method is proposed, which can effectively reduce the algorithm complexity. Numerical results show that the algorithm is effective and superior in the limited block length IRS-UAVCC.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of UAV covert communication, and particularly relates to an IRS assisted UAV covert communication method based on trajectory and beamforming joint optimization. BACKGROUND

[0002] As unmanned aerial vehicles (UAVs) have controllable mobility and flexible deployment capability, they can quickly restore communication services and enhance wireless network coverage as air communication nodes. However, due to the broadcast nature of wireless transmission channels in UAV networks (UAVNs), the information may be intercepted by unauthorized eavesdroppers, thereby leading to confidential information leakage. Moreover, when higher security is required for UAVNs, it is crucial to hide the legal information of the UAVs in front of the 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 security of UAVNs, the former takes full advantage of the flexible deployment characteristics of UAVs, while the latter takes advantage of the intelligent controllable wireless propagation environment characteristics. 1) UAV-enabled covert communications: Flexible and highly mobile 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 suitable for low-latency application scenarios. Therefore, finite block length (FB) is introduced to address this issue in UAV-enabled covert communications (UAVCC). 2) IRS-assisted UAV covert communications: IRS can be used to improve the transmission environment of legitimate users while suppressing the detection ability of unauthorized users. Therefore, deploying IRS in UAVNs can further expand the range of covert communications 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 communications. However, most studies do not involve IRS-assisted UAV communication, which is more susceptible to security threats, and only consider single-antenna UAVs and ignore the impact of finite block length (FB) on IRS-assisted UAV covert communication systems (IRS-UAVCC).

[0004] In the intelligent reflecting surface (IRS)-assisted unmanned aerial networks (UAVNs), the ultimate goal is to achieve high-rate communication and high security between the UAVs and the ground legal users (GLUs) by hiding the presence of the UAVs, however, most of the existing researches on IRS-assisted UAV covert communication (IRS-UAVCC) focus on the single-antenna UAV and the infinite block length (IFB) scenario, which is not applicable in the scenario of high transmission rate and low delay demand, in the finite block length (FB) scenario, the traditional Shannon capacity formula is no longer applicable, and merely maximizing the signal-to-noise ratio (SNR) cannot guarantee the maximization of the average covert transmission rate (ACTR), therefore, it is necessary to further study the influence of FB on the IRS-UAVCC system. In addition, in order to further improve the ACTR of the UAVNs, it is necessary to jointly optimize the trajectory of the multi-antenna UAV (UAV's trajectory, UAV-TR) and the transmit beamforming of the UAV (UAV's transmit beamforming, UAV-TB), and the phase shift matrix of the IRS (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 the IRS phase matrix (IRS-PSM), it is necessary to design a low-complexity algorithm to realize efficient optimization, so as to reduce the computational burden while guaranteeing the performance of the covert communication. SUMMARY

[0005] In view of this, the purpose of the present application is to provide an IRS-assisted UAV covert communication network design method in the finite block length (FB) scenario, and to propose a low-complexity joint optimization algorithm for optimizing the reflection phase shift matrix of the IRS (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 purpose of the application, the present application provides an IRS-assisted UAV covert communication method based on trajectory and beamforming joint optimization, comprising:

[0007] S1. Establish a joint trajectory and beamforming optimization system model of IRS-assisted multi-antenna UAV finite block length covert communication, including: UAV trajectory discretization, the flight period T is uniformly divided into N time slots, and the time length of each time slot is δ tT / N; a channel model is established, considering 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 UAV to Bob occurs according to the observed signal;

[0008] S2. A communication performance optimization problem is established to maximize the average covert transmission rate (ACTR), under the constraints of the mobility of the UAV, the transmission power of the UAV, the phase shift matrix of the intelligent reflecting surface (IRS-PSM) and the covert communication requirements of the UAV network, the covert transmission rate of the IRS-assisted UAV network (UAVN) with a finite block length (FB) is maximized;

[0009] S3. For the ACTR maximization problem constructed, it is decomposed into three non-convex sub-problems: multi-antenna UAV trajectory optimization sub-problem, UAV transmit beamforming optimization sub-problem and IRS phase shift matrix optimization sub-problem, and the semi-definite relaxation (SDR) method and the successive convex approximation (SCA) method are used to convert the three non-convex sub-problems into three convex optimization sub-problems, and finally the block coordinate descent-semi-definite relaxation (BCD-SDR) optimization framework is used to iteratively solve the three convex optimization sub-problems to obtain the solution of the ACTR maximization problem;

[0010] S4. In the iteration process of the BCD-SDR optimization framework, in order to reduce the computational complexity, a low-complexity penalty dual decomposition (PDDGP) algorithm based on gradient projection is used to solve the UAV transmit beamforming sub-problem and the IRS phase shift matrix optimization sub-problem, and the low-complexity algorithm uses a double-loop penalty dual decomposition method, in which the inner loop uses the alternating gradient projection technique to solve the augmented Lagrangian problem, and the outer loop updates the dual variables and the penalty parameter.

[0011] Preferably, in step S1, the system includes an unmanned aerial vehicle (UAV) equipped with N t = N x × N y antennas, a single-antenna ground legitimate user Bob, a single-antenna ground monitor Willie, and an IRS installed on a building, equipped with M = M x × M z passive reflecting elements, with the help of the IRS, the UAV hopes to carry out covert communication with Bob while avoiding being detected by Willie;

[0012] S101. Let denote the discretized trajectory of the UAV in the ith time slot (TS), and the flight period T is evenly divided into N time slots, i.e. the time length of each time slot is δ t= T / N, due to the hardware limitation of the UAV, its maximum flight distance in each time slot is limited to V max δ t , i.e.

[0013]

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

[0015] S102. The channel model for the link from the UAV to the IRS in the ith time slot is

[0016]

[0017] where d denotes the distance between the UAV and the IRS in the ith time slot, β0denotes the channel power gain when the reference distance is 1 m, α ar and ε ar denote the path loss exponent and the Rician factor of the UAV-IRS link, respectively, the line-of-sight (LoS) channel matrix the non-line-of-sight (NLoS) channel matrix

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

[0019]

[0020] where, denotes the null hypothesis, i.e., the UAV does not send information; denotes the alternative hypothesis, i.e., the UAV sends information to Bob; in addition, denotes the additive white Gaussian noise (AWGN) at Willie;

[0021] For covert communication, the constraint ξ * [i] ≥ 1 - ∈ is usually used to ensure the covertness, where ∈ denotes a small threshold that defines the level of covertness, according to When , the covertness constraint ξ * [i] ≥ 1 - ∈ can be satisfied, thus, the covertness constraint can be replaced by the constraint Since is monotonically increasing with respect to , when ,​ can reach a maximum value i.e. can be equivalent to

[0022]

[0023] Considering the finite block length (FB), the average covert transmission rate (ACTR) that Bob can achieve in the ith time slot can be expressed as

[0024]

[0025] where, denotes the Q function, Q -1 (x) denotes its inverse function, δ denotes a given maximum allowed decoding error probability, and Λ[i] denotes the channel dispersion, whose expression is

[0026] Preferably, in step S2, the covert transmission rate of the intelligent reflecting surface (IRS) assisted unmanned aerial network (UAVN) with a finite block length (FB) is maximized, considering the mobility constraint of the UAV, the transmission power of the UAV, the phase shift matrix (IRS-PSM) of the intelligent reflecting surface, and the covert communication requirement of the UAVN; and the ACTR of the UAVN is defined as The ACTR maximization problem of the UAVN can be expressed as

[0027]

[0028] where, denotes the transmission power constraint of the UAV, denotes the covert constraint, 0≤θ m [i]≤2π denotes the IRS phase shift matrix (IRS-PSM) constraint;

[0029] Preferably, in step S3, the ACTR maximization problem is solved by constructing a block coordinate descent-semidefinite relaxation (BCD-SDR) optimization framework, and by introducing a relaxation variable The ACTR maximization problem is re-expressed as

[0030]

[0031]

[0032] To solve this complex non-convex ACTR maximization problem, it is divided into three sub-problems, namely, the UAV-TR sub-problem, the UAV-TB sub-problem and the IRS-PSM sub-problem, and the optimal solution of these three sub-problems can be obtained by using the semi-definite relaxation (SDR) method and the successive convex approximation (SCA) method. Subsequently, a block coordinate descent and semi-definite relaxation based algorithm (BCD-SDR) is proposed to obtain a high-quality suboptimal solution of the ACTR maximization problem.

[0033] S301. Optimizing the transmit beamforming of UAVs: When Q a and Φ are given, the UAV-TB sub-problem can be transformed into a convex optimization problem by using the semi-definite relaxation (SDR) technique, which is expressed as

[0034]

[0035] Therefore, the UAV-TB sub-problem can be effectively solved by using a standard optimization tool such as CVX, and subsequently, the approximate optimal solution of w[i] can be derived by using the singular value decomposition (SVD) technique.

[0036] S302. Optimizing the phase shift matrix of IRS: When Q a and are given, the IRS-PSM sub-problem can be reformulated as the following convex optimization problem by relaxing the rank-one constraint rank(V[i]) = 1 using the semi-definite relaxation (SDR) method:

[0037]

[0038] For this relaxed convex optimization problem, the interior point method can be used to obtain its optimal solution, and subsequently, the approximate solution of θ[i] can be obtained by using the standard Gaussian randomization method.

[0039] S303. Optimizing the trajectory of UAVs: When Φ and are given, the UAV-TR sub-problem can be expressed as

[0040]

[0041] where, and represent and respectively.

[0042] Next, the concealment constraint can be rewritten as

[0043]

[0044] Then, by introducing the slack variable By converting all non-convex constraints into convex constraints, the UAV-TR subproblem can be further converted into

[0045]

[0046] Since the problem is a convex optimization problem, the CVX solver can be effectively used to solve it;

[0047] S304. The UAV trajectory (UAV-TR) subproblem, the UAV transmit beamforming (UAV-TB) subproblem, and the IRS phase shift matrix (IRS-PSM) subproblem are iteratively solved using the block coordinate descent and semidefinite relaxation (BCD-SDR) optimization framework, because these three subproblems are eventually converted into convex optimization problems, and the concealment transmission rate of the UAV is monotonically increasing in each iteration, so it eventually converges to obtain a suboptimal solution to the ACTR maximization problem;

[0048] Preferably, in step S4, a low-complexity penalty dual decomposition based on gradient projection (PDDGP) method is proposed to solve the UAV-TB and IRS-PSM subproblems, which adopts a double-loop penalty dual decomposition (PDD) method, where the inner loop solves the augmented Lagrangian (AL) problem using an alternating gradient projection (AGP) technique, and the outer loop updates the dual variables and the penalty parameter;

[0049] S401. By introducing χ[i]≥0, the concealment constraint is converted into g(w[i], θ[i], χ[i])=0, where Therefore, the augmented Lagrangian function of the ACTR maximization problem can be expressed as

[0050]

[0051] where, ρ represents the penalty parameter, and υ[i] represents the Lagrange multiplier related to the constraint condition g(w[i], θ[i], χ[i])=0, so the ACTR maximization problem can be equivalently expressed as

[0052]

[0053] Next, a low-complexity penalty dual decomposition based on gradient projection and block coordinate descent (BCD-PDDGP) optimization method is used to solve the ACTR maximization problem;

[0054] S402. Optimizing the phase shift matrix of IRS: Given w[i], χ[i], ρ, and υ[i], θ (i+1) [ι] can be represented as

[0055]

[0056] where ζ θ [ι] represents the corresponding step size, which can be chosen by a backtracking line search scheme based on the Armijo-Goldstein condition, R ρ The gradient of (w[i], θ[i], χ[i]) with respect to θ[i], which can be represented by

[0057]

[0058] The formula θ (i+1) The role of (c) in θ[i] is to project to the feasible region where

[0059]

[0060] S403. Optimizing the transmit beamforming of UAV: Similarly, given θ[i], χ[i], ρ, and υ[i], w (i+1) [ι] can be represented as

[0061]

[0062] where ζ w [ι] represents the corresponding step size, R ρ The gradient of (w[i], θ[i], χ[i]) with respect to w[i], which can be represented by

[0063]

[0064] The formula w (i+1) The role of (c) in w[i] is to project to the feasible region

[0065] S404. Optimizing χ[i]: Given w[i], θ[i], ρ, and υ[i], the optimal solution of χ[i] can be represented as

[0066]

[0067] S405. Update υ[i] and p: After the inner loop AGP converges, the dual variable and the penalty parameter p need to be updated in the outer loop, the update method of p is p = v p, and the update method of the dual variable υ[i] is

[0068]

[0069] Compared with the prior art, the present application has the beneficial effects that:

[0070] The present application provides a novel IRS-assisted UAV covert communication method based on trajectory and beamforming joint optimization, which fully utilizes the flexibility and high mobility of mobile multi-antenna UAVs, and explores the gain brought by active beamforming and passive beamforming, jointly optimizes the UAV trajectory (UAV-TR) and UAV beamforming (UAV-TB), and the passive phase shift matrix of IRS, to maximize the ACTR while satisfying the system concealment and UAV transmission power constraints. In addition, the present application proposes a low-complexity iterative algorithm combining BCD and PDDGP technology, which can achieve excellent performance with lower complexity compared with the high-quality BCD-SDR algorithm. BRIEF DESCRIPTION OF DRAWINGS

[0071] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only preferred embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0072] Figure 1 is a model diagram of an IRS-assisted UAV covert communication system based on trajectory and beamforming joint optimization provided by the embodiments of the present application;

[0073] Figure 2 is a convergence diagram of BCD-SDR and BCD-PDDGP algorithms under different IRS reflecting elements in an IRS-assisted multi-antenna UAV finite block length covert communication based on trajectory and beamforming joint optimization provided by the embodiments of the present application;

[0074] Figure 3 is a comparison diagram of ACTR in the proposed scheme and other two reference schemes in an IRS-assisted UAV covert communication based on trajectory and beamforming joint optimization provided by the embodiments of the present application; DETAILED DESCRIPTION

[0075] The principles and characteristics of the present application are described below in combination with the drawings, and the listed embodiments are only used to explain the present application and not to limit the scope of the present application;

[0076] This embodiment provides an IRS-assisted UAV covert communication method based on joint optimization of trajectory and beamforming, the specific steps of which include:

[0077] S1. As Figure 1 As shown, a joint trajectory and beamforming optimization system model for IRS-assisted multi-antenna UAV finite block long covert communication is established. The system includes N... t =N x ×N y A drone with one antenna, Bob, a ground-based lawful user with one antenna, Willie, a ground-based monitor with one antenna, and an IRS mounted on a building, equipped with M=M x ×M z With the help of the IRS, the drone hopes to communicate covertly with Bob while avoiding detection by Willie.

[0078] S101. UAV Trajectory Discretization: The initial and final positions of the UAV are represented as o a,I =[x a,I ,y a,I ] T and o a,F =[x a,F ,y a,F ] T Let o a [ι]=[x a [ι],y a [ι]] T , This represents the discretized trajectory of the UAV within the ι-th time slot (TS), with the UAV maintaining a flight altitude of H. a The flight period T is uniformly divided into N time slots, with each time slot having a duration of δ. t =T / N, due to the hardware limitations of the drone, its maximum flight distance within each time slot is limited to V. max δ t ,Right now

[0079]

[0080] ||o a [1]-o a,I ||≤V max δ t ,o a [N] = o a,F ;

[0081] S102. Establishing the Channel Model: Considering the complex urban environment, all channels are modeled as Rician fading channels. Specifically, in the ιth time slot, from the UAV to the IRS link... The channel model for the ith time slot is given as

[0082]

[0083] where denotes the distance between the UAV and the IRS in the ith time slot, denotes the channel power gain when the reference distance is 1 m, and ar and ar denote the path loss exponent and the Rician factor of the UAV-IRS link, respectively, the line-of-sight (LoS) channel matrix the non-line-of-sight (NLoS) channel matrix

[0084] In addition, the receive array response vector of the IRS is denoted as

[0085]

[0086] The transmit array response of the UAV is denoted as

[0087]

[0088] where and denote the vertical and horizontal angles of arrival at the IRS, respectively, and and denote the vertical and horizontal angles of departure at the UAV, respectively;

[0089] In addition, the phase shift matrix of the IRS in the ith time slot is denoted as where The signal transmitted by the UAV in the lth channel use in the ith time slot is denoted as and Here, L denotes the total number of channel uses;

[0090] The transmit signal of the UAV in the ith time slot is denoted as x[i] = w[i]x l [i], where denotes the transmit beamforming vector of the UAV, and thus, the transmit power constraint of the UAV can be denoted as

[0091]

[0092] where a,max denotes the maximum transmit power of the UAV;

[0093] ​​S103. Willie's binary hypothesis test: In covert communications, Willie needs to determine whether the transmission from the UAV to Bob occurred based on the observed signal, thus, the received signal at Willie at the / -th time slot and the / -th channel can be represented as:

[0094]

[0095] where, represents the null hypothesis, i.e., the UAV did not transmit information; represents the alternative hypothesis, i.e., the UAV transmitted information to Bob, and represents the additive white Gaussian noise (AWGN) at Willie;

[0096] The false alarm probability and the missed detection probability at the / -th time slot can be defined as

[0097] where, and represent the binary decisions for determining whether the transmission between the UAV and Bob occurred, thus, the total detection error probability (DEP) at Willie at the / -th time slot can be represented as

[0098]

[0099] where, π0and π1= 1 - π0represent the prior probabilities of the hypotheses and respectively;

[0100] However, since the expression of the minimum detection error probability ξ * [ι] contains the incomplete gamma function, which makes the subsequent analysis more complicated, to solve this problem, an easily handled lower bound of ξ * [ι] can be obtained by using the Pinsker inequality, which is represented as

[0101]

[0102] where, represents the Kullback-Leibler (KL) divergence from to , which is defined as

[0103]

[0104] where,

[0105] For covert communications, it is usually used to constrain ξ *[ι] ≥ 1 - ∈ to ensure concealment, where ∈ denotes a small threshold value defining the level of concealment, according to When the concealment constraint ξ * [ι] ≥ 1 - ∈, thus, the concealment constraint can be replaced by ; since is monotonically increasing, thus, when , the maximum value can be achieved; i.e. can be equivalent to

[0106]

[0107] Considering the finite block length (FB), the average concealment transmission rate (ACTR) that Bob can achieve in the ith time slot can be expressed as

[0108]

[0109] where, denotes the Q function, Q -1 (x) denotes its inverse function, δ denotes the given maximum allowed decoding error probability, Λ[ι] denotes the channel dispersion, whose expression is

[0110] S2. Establish a communication performance optimization problem with the goal of maximizing the average concealment transmission rate (ACTR), our goal is to maximize the concealment transmission rate of the IRS-assisted unmanned aerial vehicle network (UAVN) with a finite block length (FB) while considering the mobility constraints of the unmanned aerial vehicle, the transmission power of the unmanned aerial vehicle, the phase shift matrix of the intelligent reflecting surface (IRS-PSM), and the concealment communication requirements of the unmanned aerial vehicle network, define Then the ACTR maximization problem of the UAVN can be expressed as

[0111]

[0112] where, denotes the transmission power constraint of the unmanned aerial vehicle, denotes the concealment constraint, 0 ≤ θ m [ι] ≤ 2π denotes the IRS phase shift matrix (IRS-PSM) constraint;

[0113] S3. The ACTR maximization problem is solved by a block coordinate descent-semidefinite relaxation (BCD-SDR) optimization framework; in order to solve the non-convex ACTR maximization problem in S2, the optimization problem in S2 needs to be transformed into a more tractable form by introducing a relaxation variable The ACTR maximization problem is reformulated as

[0114]

[0115]

[0116] Let Since f(τ[i]) is a concave function with respect to τ[i], in order to handle the non-convex function -f(τ[i]), f(τ[i]) can be replaced by its upper bound, which is

[0117]

[0118] where τ (j) [i] represents the feasible solution obtained in the jth iteration;

[0119] Next, the above ACTR maximization problem can be reconfigured as

[0120]

[0121] In order to solve this complex non-convex ACTR maximization problem, it is divided into three sub-problems, namely, a multi-antenna UAV trajectory (UAV-TR) sub-problem, a UAV transmit beamforming (UAV-TB) sub-problem, and an IRS phase shift matrix (IRS-PSM) sub-problem, and the optimal solution of the three sub-problems can be obtained by using a semidefinite relaxation (SDR) method and a successive convex approximation (SCA) method, and then a block coordinate descent and semidefinite relaxation (BCD-SDR) algorithm is proposed to obtain a high-quality suboptimal solution of the ACTR maximization problem;

[0122] S301. Optimize the transmit beamforming of the UAV: when Q a and Φ are given, the transmit beamforming (UAV-TB) sub-problem of the UAV can be expressed as

[0123]

[0124] Let and W[i] = w[i]w H[ι], the concealment constraint can be re-expressed as

[0125]

[0126] The UAV-TB subproblem can be transformed into a convex optimization problem by using the semidefinite relaxation (SDR) technique, which can be expressed as

[0127]

[0128] Therefore, the UAV-TB subproblem can be solved efficiently using standard optimization tools such as CVX, and subsequently, the approximate optimal solution of w[ι] can be derived by employing the singular value decomposition (SVD) technique;

[0129] S302. Optimizing the phase shift matrix of the IRS: when Q a and Given Φ and Q, the IRS-PSM subproblem can be expressed as

[0130]

[0131] Let where By defining V[ι] = μ[ι] μ H [ι], μ[ι] = [θ T [ι], 1] T , the concealment constraint is rewritten as

[0132]

[0133] Then, by relaxing the rank-one constraint rank(V[ι]) = 1 using the semidefinite relaxation (SDR) method, the IRS-PSM subproblem can be re-expressed as the following convex optimization problem:

[0134]

[0135] For this relaxed convex optimization problem, the interior point method can be employed to solve it optimally, and subsequently, the approximate solution of θ[ι] can be obtained by using the standard Gaussian randomization method;

[0136] S303. Optimizing the trajectory of the UAV: when Φ and Given Φ and Q, the UAV trajectory optimization (UAV-TR) subproblem can be expressed as

[0137]

[0138] Since the UAV-TR subproblem is a non-convex optimization problem, in order to solve this challenging problem, it is necessary to first calculate the LoS component in the objective function The main reason is Regarding the variable Q a The complexity and nonlinearity of the problem make it difficult to optimize the UAV trajectory; specifically, in the jth iteration, can be calculated based on the UAV trajectory approximation in the j-1th iteration, similarly, and is also calculated by the UAV trajectory in the j-1th iteration in the jth iteration, therefore, the UAV-TR subproblem can be re-expressed as follows:

[0139]

[0140]

[0141] where, and respectively represent and the results of the j-1th iteration,

[0142] Next, the concealment constraint can be rewritten as

[0143]

[0144] Then, by introducing the relaxation variable convert all non-convex constraints to convex constraints, the UAV-TR subproblem can be further converted to

[0145]

[0146] Since the problem is a convex optimization problem, the CVX solver can be effectively used to solve it;

[0147] S304. Using the block coordinate descent and semi-definite relaxation (BCD-SDR) optimization framework, the UAV trajectory (UAV-TR) subproblem, the UAV transmit beamforming (UAV-TB) subproblem and the IRS phase shift matrix (IRS-PSM) subproblem are iteratively solved, because the three subproblems are finally converted into convex optimization problems, the concealment transmission rate of the UAV is monotonically increased in each iteration, so it finally converges, obtaining the suboptimal solution of the ACTR maximization problem;

[0148] S4. Low-complexity algorithm design: To reduce the complexity of BCD-SDR in S3, a low-complexity penalty dual decomposition with gradient projection (PDDGP) method is proposed to solve the UAV-TB and IRS-PSM subproblems, which adopts a double-loop penalty dual decomposition (PDD) method, where the inner loop solves the augmented Lagrangian (AL) problem by using an alternating gradient projection (AGP) technique, and the outer loop updates the dual variables and the penalty parameter;

[0149] S401. By introducing χ[i] ≥ 0, the concealment constraint is converted to g(w[i], θ[i], χ[i]) = 0, where Therefore, the augmented Lagrangian function of the ACTR maximization problem can be expressed as

[0150]

[0151] where, ρ represents the penalty parameter, and υ[i] represents the Lagrange multiplier associated with the constraint g(w[i], θ[i], χ[i]) = 0. Therefore, the ACTR maximization problem can be equivalently expressed as

[0152]

[0153] Next, a low-complexity penalty dual decomposition with gradient projection and block coordinate descent (BCD-PDDGP) optimization method is adopted to solve the ACTR maximization problem,

[0154] S402. Optimizing the phase shift matrix of IRS: Given w[i], χ[i], ρ, and υ[i], θ (i+1) [i] can be expressed as

[0155]

[0156] where, ζ θ [i] represents the corresponding step size, which can be selected by a backtracking line search scheme based on the Armijo-Goldstein condition, represents R ρ (w[i], θ[i], χ[i]) with respect to θ[i], which can be expressed by the following formula:

[0157]

[0158] The formula θ (i+1) The role of (c) in θ[i] is to project to the feasible region where

[0159]

[0160] S403. Optimizing the transmit beamforming of UAV: Similarly, given θ[i], χ[i], ρ and υ[i], w (i+1) [i] can be represented as

[0161]

[0162] where, ζ w [i] represents the corresponding step size, represents R ρ The gradient of (w[i], θ[i], χ[i]) with respect to w[i], which can be represented as

[0163]

[0164] The role of (c) in formula w (i+1) [i] is to project to the feasible region

[0165] S404. Optimizing χ[i]: Given w[i], θ[i], ρ and υ[i], the optimal solution of χ[i] can be represented as

[0166]

[0167] S405. Updating υ[i] and ρ: After the inner loop AGP converges, it is necessary to update the dual variables and the penalty parameter in the outer loop, the update method of ρ is ρ = vρ, and the update method of the dual variable υ[i] is

[0168]

[0169] Figure 2 The convergence of the proposed algorithm under N t = 4 and M = {50, 80} is described, 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;

[0170] Figure 3 The number of UAV transmit antennas N tNext, the ACTR performance of Bob in the proposed scheme, the baseline scheme without IRS and jointly optimizing the UAV TB and TR is marked as "no IRS", and the baseline scheme without optimizing the UAV trajectory and only performing the UAV TB and IRS-PSM design is marked as "straight flight"; as Figure 3 shown, the ACTR of all schemes increases with the increase of N t , because more UAV transmitting antennas can provide greater active beamforming gain, which highlights the importance of optimizing the UAV active beamforming, in addition, the low-complexity BCD-PDDGP algorithm can always achieve almost the same performance as the high-efficiency BCD-SDR algorithm, and more importantly, in UAVNs, the advantage of the proposed scheme in ACTR is verified, therefore, the optimization of UAV TB and TR and the optimization of IRS-PSM play a key role in enhancing covert transmission;

[0171] The above only describes the preferred embodiments of the present application and is not intended to limit the present application, any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. An IRS-assisted UAV covert communication method based on joint optimization of trajectory and beamforming, characterized in that, Includes the following steps: 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, the flight period T is uniformly divided into N time slots, and the duration of each time slot is δ. t =T / N; Establish a channel model, considering the complex urban environment, all channels are modeled as Rician fading channels; Willie's binary hypothesis test, in covert communication, Willie needs to determine whether the transmission from the UAV to Bob has occurred based on the observed signal; S2. Establish a communication performance optimization problem with the goal of maximizing the average covert transmission rate (ACTR). Under the constraints of UAV mobility, UAV transmission power, intelligent reflector phase shift matrix (IRS-PSM), and covert communication requirements of UAV network, maximize the covert transmission rate of IRS-assisted UAVNs with finite block length (FB). S3. For the constructed ACTR maximization problem, it is decomposed into three non-convex sub-problems: multi-antenna UAV trajectory optimization sub-problem, UAV transmit beamforming optimization sub-problem, and IRS phase shift matrix optimization sub-problem. Semidefinite relaxation (SDR) is adopted, and finally the block coordinate descent-semi-positive definite relaxation (BCD-SDR) optimization framework is used to iterate the three convex optimization sub-problems alternately to obtain the solution of the ACTR maximization problem. S4. In the iterative process of the BCD-SDR optimization framework, in order to reduce computational complexity, a low-complexity gradient projection-based penalized dual decomposition (PDDGP) algorithm is adopted when solving the UAV transmit beamforming subproblem and the IRS phase shift matrix optimization subproblem. This low-complexity algorithm adopts a double-loop penalized dual decomposition method, in which the inner loop uses alternating gradient projection technology to solve the augmented Lagrange problem, while the outer loop updates the dual variables and penalty parameters.

2. The IRS-assisted UAV covert communication method based on trajectory and beamforming joint optimization according to claim 1, characterized in that, In step S1, the system includes N t =N x ×N y A drone with one antenna, Bob, a ground-based lawful user with one antenna, Willie, a ground-based monitor with one antenna, and an IRS mounted on a building, equipped with M=M x ×M z With the help of the IRS, the drone hopes to communicate covertly with Bob while avoiding detection by Willie. S101. Let... Let represent the discretized trajectory of the UAV in the ι-th time slot (TS), where the flight period T is uniformly divided into N time slots, and the duration of each time slot is δ. t =T / N, due to the hardware limitations of the drone, its maximum flight distance within 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 α represents the distance between the UAV and the IRS in the ιth time slot, β0 represents the channel power gain when the reference distance is 1m, and α ar and ε ar Represent the path loss exponent and Rician factor of the UAV-IRS link, respectively, and the line-of-sight (LoS) channel matrix. Non-line-of-sight (NLoS) channel matrix S103. The signal received by Willie in the l-th channel of the l-th time slot can be represented as: in, This represents the null hypothesis, meaning that the drone did not send any information; This indicates the alternative hypothesis, namely that the drone sends information to Bob. Furthermore, This represents the additive white Gaussian noise (AWGN) at Willie. For covert communication, constraint ξ is typically used. * [l]≥1-∈ to ensure concealment, where ∈ represents the small threshold defining the concealment level, according to when At that time, the concealment constraint ξ can be satisfied. * [ι]≥1-∈, therefore, the hidden constraint can be constrained. Replaced, due to about Monotonically increasing, therefore, when hour, It can reach the maximum value Right now It can be equivalent to Considering a finite block length (FB), Bob's achievable average covert transmission rate (ACTR) in the ι-th time slot can be expressed as: in, Denotes the Q function, Q -1 (x) represents its inverse function, δ represents the given maximum allowable decoding error probability, and Λ[ι] represents the channel dispersion, its expression is:

3. The IRS-assisted UAV covert communication method based on joint optimization of trajectory and beamforming according to claim 1, characterized in that, In step S2, under the constraints of UAV mobility, UAV transmission power, Intelligent Reflector Phase Shift Matrix (IRS-PSM), and the covert communication requirements of the UAV network, the covert transmission rate of the IRS-assisted UAVNs with a finite block length (FB) is maximized, defining... The ACTR maximization problem of UAVNs can then 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, This indicates the transmission power constraint of the drone. This represents a hidden constraint, 0 ≤ θ m [ι]≤2π indicates the IRS phase shift matrix (IRS-PSM) constraint.

4. The IRS-assisted UAV covert communication method based on joint optimization of trajectory and beamforming according to claim 1, 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 introducing relaxation variables. The ACTR maximization problem is reformulated as follows: 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], To solve this complex non-convex ACTR maximization problem, it is divided into three subproblems: the multi-antenna UAV trajectory (UAV-TR) subproblem, the UAV transmit beamforming (UAV-TB) subproblem, and the IRS phase shift matrix (IRS-PSM) subproblem. The optimal solutions to these three subproblems 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. Optimize the UAV's transmit beamforming: When Q a Given Φ, the UAV-TB subproblem can be transformed into a convex optimization problem using the semidefinite relaxation (SDR) technique, which is expressed as: stTr(W[ι])≤P a,max , W[ι]≥0， Therefore, standard optimization tools such as CVX can be used to effectively solve the UAV-TB subproblem. Subsequently, by employing singular value decomposition (SVD) techniques, an approximate optimal solution for w[ι] can be derived. S302. Optimize the phase shift matrix of the IRS: when Q a and Given that the rank-one constraint rank(V[ι]) = 1 is relaxed using the semidefinite relaxation (SDR) method, 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. Then, by using the standard Gaussian randomization method, an approximate solution for θ[ι] can be obtained. S303. Optimize the drone's trajectory: when Φ and Given a time limit, the UAV trajectory optimization (UAV-TR) subproblem can be formulated as follows: ||o a [1]-o a,I ||≤V max d t ,o a [N]=o a,F , in, and They represent and The result of the (j-1)th iteration, Next, the concealment constraint can be rewritten as Then, by introducing slack variables 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 effectively 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), UAV transmit beamforming (UAV-TB), and IRS phase shift matrix (IRS-PSM) are solved iteratively. Since these three subproblems are eventually transformed into convex optimization problems, and the UAV's covert transmission rate increases monotonically in each iteration, they eventually converge, yielding a suboptimal solution to the ACTR maximization problem.

5. The IRS-assisted UAV covert communication method based on joint optimization of trajectory and beamforming according to claim 1, characterized in that, 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. This low-complexity algorithm adopts the double-loop penalized dual decomposition (PDD) method, in which the inner loop uses the alternating gradient projection (AGP) technique to solve the augmented Lagrange (AL) problem, while the outer loop updates the dual variables and penalty parameters. S401. By introducing χ[ι]≥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, and υ[ι] represents the Lagrange multiplier associated with the constraint g(w[ι],θ[ι],χ[ι])=0. Therefore, the ACTR maximization problem can be equivalently expressed as stχ[ι]≥0, ||in[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 the IRS: Given w[ι], χ[ι], ρ and υ[ι], θ (i+1) [ι] can be represented as Where, ζ θ [ι] represents the corresponding step size, and its appropriate value can be selected through a backtracking search scheme based on the Armijo-Goldstein condition. R represents 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... Projected onto feasible area 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 represented as Where, ζ w [ι] indicates the corresponding step size. R represents ρ The gradient of (w[ι],θ[ι],χ[ι]) with respect to w[ι] can be expressed as: Formula w (i+1) The function of (c) in [ι] is to... Projected onto feasible area S404. Optimizing χ[ι]: Given w[ι], θ[ι], 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. ρ is updated as ρ = νρ, and the dual variable υ[δ] is updated as follows:

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