Flexible position antenna enabled unmanned aerial vehicle covert communication resource optimization method

Abstract

The invention particularly relates to an unmanned aerial vehicle covert communication resource optimization method for flexible position antenna enabling. The method comprises the following steps: constructing a joint optimization problem of transmitting beam forming, an unmanned aerial vehicle track and a movable antenna position; a joint optimization problem of transmitting beam forming, an unmanned aerial vehicle track and a movable antenna position is decomposed into three sub-optimization problems, and the three sub-optimization problems include that the transmitting beam forming of the unmanned aerial vehicle is optimized by fixing the unmanned aerial vehicle track and the movable antenna position; the trajectory of the unmanned aerial vehicle is optimized by fixing the transmitting beam forming of the unmanned aerial vehicle and moving the position of the antenna; the position of the movable antenna is optimized by fixing transmitting beam forming of the unmanned aerial vehicle and the track of the unmanned aerial vehicle; and solving the three sub-optimization problems by adopting an alternating optimization algorithm to realize the solving of the joint optimization problem of the transmitted beam forming, the unmanned aerial vehicle track and the movable antenna position. The method provided by the invention has better effectiveness, wider universality and better covert communication performance.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of communication technology, in particular to a flexible location antenna enabled unmanned aerial vehicle (UAV) covert communication resource optimization method, system, device and medium. BACKGROUND

[0002] With the rapid development of communication technology, unmanned aerial vehicles have been widely used in various civilian and military fields. Unmanned aerial vehicles have various advantages, including excellent maneuverability, extensive coverage, and low cost. Due to these advantages, unmanned aerial vehicles can be flexibly moved within a certain range, thereby achieving high-quality communication with users. However, the communication channel used by unmanned aerial vehicles has the characteristic of strong openness, which makes it easy for illegal eavesdroppers to eavesdrop on the transmission of confidential information, which will bring great challenges to the security of unmanned aerial vehicle communication. In order to improve the security of unmanned aerial vehicle communication, covert communication as a new security technology can be used to protect the security of confidential information in unmanned aerial vehicle communication. Unlike traditional methods of encrypting information content, covert communication can hide the process of information transmission, thereby preventing illegal eavesdroppers from obtaining confidential information. However, traditional covert communication usually uses a fixed position antenna (FPA) array, the geometry of which is fixed and cannot make good use of the spatial degrees of freedom. In order to overcome the shortcomings of the FPA array, a movable antenna (MA) array was recently proposed. The MA array can adjust the position of each MA within a certain range, better utilizing the spatial degrees of freedom, thereby achieving flexible beamforming and ultimately improving the communication rate. Therefore, the MA array can enhance the resource optimization performance of unmanned aerial vehicle covert communication, thereby improving the performance of unmanned aerial vehicle covert communication.

[0003] In recent years, covert communication has been widely studied. Hu et al. achieved multi-user covert communication by jointly optimizing the active and passive beamforming alternately (Hu X, Zhao P, Xiao H, et al. Reconfigurable Intelligent Surface-Aided Covert Communications: A Multi-User Scenario[J]. IEEE Trans. Veh. Technol., 2025, 74(6): 10052-10057.). Cheng et al. studied covert communication under multiple illegal eavesdroppers by jointly optimizing the transmit beamforming and frequency offset of array antennas (Cheng Z, Si J, Li Z, et al. FDA-Aided Covert Communication Against Multiple Wardens[J]. IEEE Wireless Commun. Lett., 2024, 13(12): 3305-3309.). In the study of UAV covert communication, Yang et al. used two UAVs to achieve covert communication, one UAV transmitted communication information, and the other UAV provided interference. By jointly optimizing the flight trajectory and transmit power of the two UAVs and the time slot allocation of the communication UAV, the maximization of the average covert rate was achieved (Yang G, Qian Y, Ren K, et al. Covert Wireless Communications for Augmented Reality Systems With Dual Cooperative UAVs[J]. IEEE J. Sel. Top. Signal Process., 2023, 17(5): 1119-1130.). Su et al. used non-orthogonal multiple access (NOMA) to serve both public users and covert users simultaneously to achieve covert communication, and proposed a successive geometric programming approximation (SGPA) algorithm to jointly optimize the UAV hovering height and power allocation (Su Y, Fu S, Si J, et al. Optimal Hovering Height and Power Allocation for UAV-Aided NOMA Covert Communication System[J]. IEEE Wireless Commun. Lett., 2023, 12(6): 937-941.). Currently, there are few studies on applying MA to covert communication. Xie et al. used MA arrays to achieve covert communication with the assistance of intelligent reflective surfaces (IRS).Specifically, the motion trajectory of MA, transmit beamforming and the phase shift of IRS are optimized by using deep reinforcement learning (DRL) and alternating optimization (AO) method, so as to improve the covert communication rate (Xie W, Li Z, Yu C, et al. Movable-Antenna-Assisted Covert Communications With Reconfigurable Intelligent Surfaces [J]. IEEE Internet Things J., 2025, 12(9): 12369-12382.). Liu et al. use MA array to realize the maximization of covert communication rate by joint optimization of transmit beamforming and MA position, and use block coordinate descent (BCD) method to solve the optimization problem (Liu P, Si J, Cheng Z, et al. Movable-Antenna Enabled Covert Communication [J]. IEEE Wireless Commun. Lett., 2025, 14(2): 280-284.).

[0004] Through the above analysis, the problems and defects of the existing technology are:

[0005] (1) In the existing research, there is no technology that applies MA to unmanned aerial vehicle covert communication.

[0006] (2) The existing unmanned aerial vehicle covert communication method has poor covert communication performance. SUMMARY

[0007] The present application provides a flexible position antenna enabled unmanned aerial vehicle covert communication resource optimization method, which can overcome the defects in the prior art to some extent.

[0008] Other characteristics and advantages of the present application will become apparent from the following detailed description, or will be learned by practice of the present application.

[0009] According to a first aspect of the present application, a flexible position antenna enabled unmanned aerial vehicle covert communication resource optimization method is provided, the method comprising:

[0010] Constructing a joint optimization problem of transmit beamforming, unmanned aerial vehicle trajectory and movable antenna position;

[0011] The joint optimization problem of transmit beamforming, unmanned aerial vehicle trajectory and movable antenna position is decomposed into three sub-optimization problems, including:

[0012] Optimizing the transmit beamforming of the unmanned aerial vehicle while fixing the unmanned aerial vehicle trajectory and the movable antenna position;

[0013] The transmit beamforming of the fixed UAV and the position of the movable antenna are used to optimize the UAV's trajectory;

[0014] The transmit beamforming of the fixed UAV and the trajectory of the UAV are optimized for the position of the movable antenna;

[0015] An alternating optimization algorithm is used to solve the three sub-optimization problems, thereby solving the joint optimization problems of transmit beamforming, UAV trajectory, and movable antenna position.

[0016] In some exemplary embodiments, the joint optimization problem based on transmit beamforming, UAV trajectory, and movable antenna position specifically includes:

[0017]

[0018] in, P m d represents the maximum transmit power of the drone transmitter Alice within a single time slot. m R represents the minimum distance between two adjacent movable antennas MA. cmn [q] represents the covert communication rate at the nth Bob in the q-th time slot, where Q represents the total number of time slots, l A [q+1]l A [q]l A [Q+1] represents Alice's horizontal position in the (q+1), (q), and (Q+1)th time slots, respectively. AI Indicates Alice's initial horizontal position, l AF V represents Alice's final horizontal position. max This represents Alice's maximum flight speed within a single time slot, where N represents the number of users, and h... W [q] represents the path vector between Alice and Willie in the q-th time slot, c W [q] represents the steering vector of the MA array from Alice to Willie in the q-th time slot, x k [q] represents the position of the k-th MA in the q-th time slot on Alice, x k+1 [q] represents the position of the (k+1)th MA on Alice in the qth time slot, w[q] is the transmit beamforming vector of Alice in the qth time slot, and r s express The unique solution on [1,+∞), where ε is used to define the degree of concealment. G represents the variance of the noise at Willie. AW[q] represents the signal power received by Willie in the q-th time slot; (C1-1) represents the transmit power constraint; (C1-2) represents the constraint to avoid coupling effects between adjacent MAs; (C1-3) represents the constraint on the feasible range of the movable antenna MA; (C1-4) represents the flight distance constraint of the UAV transmitter Alice in adjacent time slots; (C1-5) represents the initial and final horizontal position constraints of the UAV transmitter Alice; and (C1-6) represents the stealth constraint.

[0019] In some exemplary embodiments, the fixed UAV trajectory and movable antenna position optimize the UAV's transmit beamforming, specifically through the following process:

[0020] Fixed S x and S l To solve S w (P1) is converted to (P4):

[0021]

[0022] st{(C3-1),(C3-2),(C3-3) (C4-1)

[0023] Among them, h Bn [q] represents the path vector between Alice and the nth Bob in the qth time slot, c Bn [q] represents the steering vector of the MA array from Alice to Bob in the q-th time slot. This represents the variance of the noise at the nth Bob.

[0024] (P4) is a convex problem, which can be solved using the CVX toolbox. The optimal solution is obtained by eigenvalue decomposition. This completes the solution to the subproblem.

[0025] In some exemplary embodiments, the fixed UAV's transmit beamforming and movable antenna position optimize the UAV's trajectory, specifically through the following process:

[0026] Fixed S w and S x To solve S l (P1) is converted to (P7):

[0027]

[0028] in, Q0 represents the reference distance d. r Path loss at the location,

[0029] A[q] is a slack variable that satisfies

[0030] A[q]≥||l A [q]-l Bn || 2 +H 2 The horizontal position of the nth Bob is l. Bn =[l Bnx ,l Bny ] T ,n∈{1,2,...,N},H represents the fixed height at which Alice moves in the air;

[0031] (P7) is a convex problem, and S is obtained by solving it using the CVX toolbox. l The optimal solution has been found, therefore the subproblem has been solved.

[0032] In some exemplary embodiments, the transmit beamforming of the fixed UAV and the trajectory of the UAV optimize the position of the movable antenna, specifically through the following process:

[0033] Fixed S w and S l To solve S x (P1) is rewritten as:

[0034]

[0035] st{(C1-2),(C1-3),(C1-6) (C8-1)

[0036] Let w[q] = a[q] + jb[q], where Let w[q] be the vector of the real part. Let w[q] be the imaginary part vector. Furthermore, let...

[0037]

[0038] and

[0039]

[0040] In addition,

[0041]

[0042] in Similarly, let

[0043]

[0044] in Therefore, we get

[0045]

[0046] and

[0047]

[0048] It is possible to know

[0049] (a[q]+jb[q])(a T [q]-jb T [q])

[0050] =a[q]a T [q]-ja[q]b T [q]+jb[q]a T [q]+b[q]b T [q]

[0051] =R1[q]-jR2[q]

[0052] We can obtain:

[0053]

[0054] It can be known that:

[0055]

[0056] Therefore, we can conclude that:

[0057]

[0058] In addition, there are

[0059]

[0060] so

[0061]

[0062] definition And Y satisfies Y T =-Y, therefore we can get

[0063] (y T Yy) T =y T Y T y = -y T Yy = y T Yy

[0064] It is obvious that y T Yy = 0, therefore we know Therefore, we can conclude that:

[0065]

[0066] and

[0067]

[0068] Therefore, we can conclude that:

[0069]

[0070] Therefore, (P8) can be converted to:

[0071]

[0072] The objective function of (P9) is defined as follows: (P9) is solved using the PGA method.

[0073]

[0074] The update rule for the q-th time slot x[q] is expressed as:

[0075]

[0076] and

[0077] x j+1 [q]=ε1{x j+1 [q],d m ,B}[q] (AU1)

[0078] and

[0079] x j+1 [q]=ε2{x j+1 [q],r s}[q] (AU2)

[0080] (NU) represents a necessary update, where x j [q] represents x[q] in the j-th iteration of the q-th time slot, η represents the step size of the PGA method, (AU1) represents additional update 1, which ensures that constraints (C1-2) and (C1-3) are satisfied through the projection function ε1{·}[q]; note that additional update 1 is only executed when the constraints in (C1-2) and (C1-3) are not satisfied; (AU2) is additional update 2, which ensures that constraint (C9-2) is satisfied through the projection function ε2{·}[q]; note that additional update 2 is only executed when constraint (C9-2) is not satisfied;

[0081] It is possible to know It can be calculated using the following formula:

[0082]

[0083] in

[0084]

[0085] Therefore, we can conclude that:

[0086]

[0087] set up

[0088]

[0089] and

[0090]

[0091] Therefore, we can conclude that:

[0092]

[0093] In addition, there are

[0094]

[0095] and

[0096]

[0097] In addition,

[0098]

[0099] Therefore, we can conclude that:

[0100]

[0101] Similarly, we can obtain:

[0102]

[0103] Therefore, we can conclude that:

[0104]

[0105] therefore, It can be obtained; furthermore, to prevent its value from being too small, it needs to be normalized, as shown in the following formula:

[0106]

[0107] Therefore, necessary updates should be made;

[0108] The constraint (C1-2) can be given by the following formula:

[0109]

[0110] It can be transformed into:

[0111]

[0112] Then, by adding constraint (C1-3), we can obtain:

[0113]

[0114] Therefore, we can conclude that:

[0115]

[0116] Where x0[q]=-d m Clearly, (eqJ) satisfies (C1-2) and (C1-3); if after the necessary update, x j+1 [q] If (eqJ) is not satisfied, it means that there are unsatisfied constraints in (C1-2) and (C1-3); then, it is necessary to apply the nearest distance rule to... Projected to Within feasible range The nearest point is represented as:

[0117]

[0118] if If (eqJ) is satisfied, then additional update 1 is not executed; the expression for the projection function in additional update 1 is as follows:

[0119]

[0120] Therefore, (C1-2) and (C1-3) are ultimately satisfied;

[0121] After the MA position of the current time slot converges through the iterative solution of necessary update and additional update 1, if (C9-2) is satisfied, additional update 2 is not performed; if (C9-2) is not satisfied, the latest S is used according to the optimization process of transmit beamforming. x and S l Update S w Update S w Then, constraint (C9-2) is satisfied;

[0122] Based on necessary updates, additional updates 1, and additional updates 2, the PGA method can be used to iteratively update x[q] until the objective function value of (P9) converges, while ensuring that all constraints of (P9) are satisfied; finally, S can be obtained. x The final solution is found, therefore this subproblem is solved.

[0123] In some exemplary embodiments, the alternating optimization algorithm is used to solve the three sub-optimization problems. The specific process is as follows:

[0124] enter: Initial feasible trajectory; Initial feasible MA position; I num : The given number of iterations; I thre Iteration threshold;

[0125] Output: Final solution for transmit beamforming, trajectory, and MA position;

[0126] S1. Let i = 0;

[0127] S2, if i = I num Or the absolute value of the objective function in two adjacent iterations is less than or equal to I. thre If yes, proceed to S7; otherwise, proceed to S3.

[0128] S3, Use and Solving (P4) yields

[0129] S4, Use and Solving (P7) yields

[0130] S5, based on (NU), (AU1), and (AU2), uses and get

[0131] S6. Let i = i + 1, then proceed to S2;

[0132] S7. The final solution for transmitted beamforming was obtained. The final solution of the trajectory The final solution for the position of MA

[0133] According to a second aspect of the present invention, a storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the UAV covert communication resource optimization method with flexible position antenna empowerment described in the first aspect above.

[0134] According to a third aspect of the present invention, a computer program product is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, the method for optimizing covert communication resources of unmanned aerial vehicles with flexible position antennas as described in the first aspect is implemented.

[0135] According to a fourth aspect of the present invention, an electronic device is provided, comprising:

[0136] Processor; and

[0137] Memory for storing the executable instructions of the processor;

[0138] The processor is configured to implement the UAV covert communication resource optimization method with flexible position antenna empowerment as described in the first aspect by executing the executable instructions.

[0139] The embodiment of this invention provides a method for optimizing UAV covert communication resources using flexible position antennas. Compared with the prior art, this invention explores the problems of applying PGA technology to optimize UAV covert communication resources using flexible position antennas, and emphasizes the importance of solving these problems. This invention can be used for resource optimization in any task involving UAV covert communication resource optimization using flexible position antennas. The proposed method for optimizing UAV covert communication resources using flexible position antennas is effective and outperforms benchmark solutions. This invention has better effectiveness and wider versatility.

[0140] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0141] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention. It is obvious that the drawings described below are merely some embodiments of the invention, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0142] Figure 1 This is a flowchart illustrating the method, system, medium, and equipment for optimizing UAV covert communication resources using flexible position antennas, as provided in this embodiment of the invention.

[0143] Figure 2 This is a schematic diagram of simulation results comparing the iterative processes of different methods in the UAV covert communication resource optimization system with flexible position antenna empowerment provided in the embodiments of the present invention. Detailed Implementation

[0144] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that the invention will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0145] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0146] To address the shortcomings and deficiencies of existing technologies, this example implementation provides a method for optimizing UAV covert communication resources using flexible position antennas. A UAV transmits communication signals to multiple users and is equipped with an MA array to enhance covert communication performance. Simultaneously, an unauthorized eavesdropper passively intercepts the wireless channel to determine if the UAV has transmitted a signal. With the objective of maximizing the average covert communication rate for all users across all time slots, an optimization problem is formulated under constraints including transmit power, avoiding coupling effects between adjacent MAs, the feasible range of MAs, Alice's flight distance in adjacent time slots, Alice's initial and final horizontal positions, and covertness. The optimization addresses Alice's transmit beamforming, MA positions, and Alice's trajectory to maximize covert communication performance. During the optimization of MA positions using the Projected Gradient Ascent (PGA) method, an additional update is proposed to address challenging covertness constraints, thus achieving efficient optimization of MA positions. To effectively solve the proposed highly non-convex optimization problem, it is divided into three sub-problems, and an AO algorithm is proposed to iteratively solve them, thereby maximizing covert communication performance; this invention fills a gap in this field.

[0147] refer to Figure 1 As shown, the specific steps may include:

[0148] Step S101: Propose a joint optimization problem that optimizes the transmit beamforming, UAV trajectory, and movable antenna position;

[0149] Step S102: Optimize the transmission beamforming of the UAV by fixing the UAV trajectory and the position of the movable antenna;

[0150] Step S103: Optimize the trajectory of the UAV by fixing the transmit beamforming and the position of the movable antenna.

[0151] Step S104: Optimize the position of the movable antenna by fixing the transmit beamforming of the UAV and the trajectory of the UAV;

[0152] Step S105 proposes an alternating optimization algorithm to solve the joint optimization problem of transmit beamforming, UAV trajectory and movable antenna position.

[0153] The following will describe in more detail each step of the phased array radar design method in this exemplary embodiment, with reference to the accompanying drawings and embodiments.

[0154] In step S101, a joint optimization problem is proposed to optimize the transmitted beamforming, the UAV trajectory, and the position of the movable antenna. The specific process is as follows:

[0155] This invention discusses a scenario for optimizing covert communication resources for unmanned aerial vehicles (UAVs) using flexible position antennas. In this scenario, a UAV transmitter (Alice) is equipped with K movable antennas (MA), N users (Bobs), and a monitor (Willie) are each equipped with a fixed position antenna (FPA). Alice wants to transmit confidential information to Bobs without being detected by Willie, while Willie monitors the channel to determine if Alice is transmitting a signal to Bobs. Alice moves in the air at a fixed altitude H>0, while Bobs and Willie are at fixed positions on the ground. Alice's horizontal position is determined by l. A (t)=[l Ax (t),l Ay (t)] T Given that 0 ≤ t ≤ T, the horizontal position of the nth Bob is l. Bn =[l Bnx ,l Bny ] T Given n∈{1,2,...,N}, Willie's horizontal position is l. W =[l Wx ,l Wy ] T T represents the time required for Alice to complete the covert communication flight mission. T is divided into Q time slots, such that the time t of each time slot is... Q =T / Q is small enough that Alice can be considered stationary in each time slot. Furthermore, Alice's horizontal position in the q-th time slot can be represented as:

[0156] l A [q] = [l Ax [q],l Ay [q] T ,q∈{1,2,...,Q}

[0157] Let x be the position of the k-th MA in the q-th time slot on Alice. k[q]∈[0,B],k∈{1,2,...,K}, where [0,B] represents the feasible movement range of all MAs, and B represents the length of the feasible movement range of all MAs. Without loss of generality, assume that the position of all MAs in the q-th time slot satisfies 0≤x1[q]<x2[q]<...<x K If [q]≤B, then Alice's MA position vector in the q-th time slot can be obtained as follows: Therefore, the steering vector of the MA array in the q-th time slot can be obtained as:

[0158]

[0159] Where λ represents wavelength, i′∈{Bn,W}, i={0,1,2,...,N}. When i′=Bn, we have i={1,2,...,N}=n, and target i refers to the nth Bob. When i′=W, we have i=0, and target i represents Willie. θ i [q]∈[0,π / 2) represents the turning angle of Alice from target i in the q-th time slot, which can be expressed as:

[0160]

[0161] Therefore, we can conclude that:

[0162]

[0163] Furthermore, suppose that Alice, Bobs, and Willie's path vector in the q-th time slot consists of large-scale path fading and turning vectors. Definition

[0164]

[0165] Where Path L This represents large-scale path fading, where Q0 represents the reference distance d. r Path loss at d i [q] represents the distance between Alice and target i in the q-th time slot, α i Let d represent the path loss exponent between Alice and target i. Generally, let d... r =1m and α i =2, so

[0166]

[0167] Therefore, the path vector of path i′ can be represented as:

[0168] h fi' [q] = h i' [q]c i' [q]

[0169] In the q-th time slot θ n The MA array beamforming gains at [q] and θ0[q] are given by the following equations:

[0170]

[0171] in This is Alice's transmit beamforming vector in the q-th time slot. The signal powers received by Bob and Willie in the n-th time slot in the q-th time slot are expressed as:

[0172]

[0173] According to l A [q], we can obtain the distance between Alice's positions in two adjacent time slots as ||l A [q+1]-l A [q]||, therefore Alice should satisfy:

[0174]

[0175] Where V max This represents Alice's maximum flight speed within a single time slot, and Alice should also satisfy...

[0176] l A [1] = l AI ,l A [Q+1]=l AF

[0177] Among them l AI Indicates Alice's initial horizontal position, l AF This indicates Alice's final horizontal position.

[0178] Alice's transmission signal in the q-th time slot is:

[0179]

[0180] in and These are the binary assumptions of Alice sending a signal and not sending a signal. This indicates a confidential message sent by Alice. Additionally, there is...

[0181] The received signal of the nth Bob in the qth time slot is represented as:

[0182]

[0183] in It is the noise at the nth Bob.

[0184] The signal received by Willie in the qth time slot is:

[0185]

[0186] in This represents the noise at Willie.

[0187] Furthermore, the covert communication rate at the nth Bob in the qth time slot is

[0188]

[0189] Willie is a passive warden; it monitors the channel while only receiving signals, without transmitting any. The q-th time slot can be obtained separately. and The likelihood function of the signal received by Willie is:

[0190]

[0191] in Without loss of generality, let's assume and The prior probabilities are consistent. According to the Neyman-Pearson criterion, the likelihood ratio test can be performed as follows:

[0192]

[0193] in and They correspond to respectively and This involves a binary decision. Willie's goal is to minimize the sum of the false alarm rate and the false negative rate (which is also to minimize the overall detection error probability). Therefore, Willie's overall detection error probability in the q-th time slot can be expressed as:

[0194]

[0195] However, the above formula is too complex and difficult to handle in optimization problems. Therefore, using... The lower bound is represented as follows:

[0196]

[0197] in Indicates the q-th time slot from arrive The Kullback-Leibler (KL) divergence is expressed as:

[0198]

[0199] The concealment constraint in covert communication can be expressed as:

[0200]

[0201] Here, ε defines the degree of concealment, and it is a small value. The larger ε is, the looser the concealment constraint, and the less concealment there is. Then, more stringent concealment constraints can be obtained:

[0202]

[0203] Then, let's assume And it is known It is monotonically increasing on [1,+∞), let r be... s for If the solution is unique on [1,+∞), then the hidden constraint can be obtained as follows:

[0204]

[0205] The goal of the optimization problem is to maximize covert communication performance by jointly optimizing Alice's transmit beamforming, Alice's trajectory, and MA's position on Alice. Therefore, under constraints such as transmit power, position, and covertness, the optimization problem is formulated as follows: Maximizing the average covert communication rate for all users across all time slots is the objective function.

[0206]

[0207] in P m d represents Alice's maximum transmit power within a single time slot. m (C1-1) represents the minimum distance between two adjacent MAs, (C1-2) represents the transmit power constraint, (C1-3) represents the constraint to avoid coupling effects between adjacent MAs, (C1-4) represents the constraint of the feasible range of MAs, (C1-5) represents the flight distance constraint of Alice in adjacent time slots, (C1-6) represents the initial and final horizontal position constraints of Alice, and (C1-6) represents the concealment constraint.

[0208] In step S102, the transmission beamforming of the UAV is optimized by fixing the UAV trajectory and the position of the movable antenna. The specific process is as follows:

[0209] Fixed S x and S l To solve S w And (P1) can be converted to:

[0210]

[0211] st{(C1-1),(C1-6) (C2-1)

[0212] set up And W[q] should satisfy W[q]≥0 and rank(W[q])=1, then we can obtain:

[0213]

[0214] Similarly, we can obtain:

[0215]

[0216] Therefore, (P2) can be converted to:

[0217]

[0218] in Clearly, only the rank-one constraint (C3-4) results in (P3) being non-convex. In this case, Gaussian randomization or a penalty-term-based method can be used to solve (P3). However, these methods have high computational complexity and low efficiency. To reduce computational complexity and improve optimization efficiency, (C3-4) in (P3) needs to be removed, and eigenvalue decomposition should be used to obtain the final solution for the transmitted beamforming. Based on this idea, (P3) can be rewritten as follows:

[0219]

[0220] st{(C3-1),(C3-2),(C3-3) (C4-1)

[0221] Therefore, (P4) is a convex problem and can be solved using the CVX toolbox. We can obtain... The optimal solution can be obtained using eigenvalue decomposition. This completes the solution to the subproblem.

[0222] In step S103, the trajectory of the UAV is optimized by fixing the transmit beamforming of the UAV and the position of the movable antenna. The specific process is as follows:

[0223] Fixed S w and S x To solve S l (P1) can be rewritten as:

[0224]

[0225] st{(C1-4),(C1-5),(C1-6) (C5-1)

[0226] It is known that c i′ [q] makes (P5) height non-convex and difficult to solve, so we use l in the j-th iteration of the q-th time slot. A [q] To approximate c in the (j+1)th iteration of the qth time slot i′ [q] It can be represented as follows:

[0227]

[0228] in Therefore, we can conclude that:

[0229]

[0230] in Let a slack variable A[q] satisfy A[q]≥||l A [q]-l Bn || 2 +H 2 , The corresponding value of A[q] is A j [q], where A j [q] represents the value of A[q] in the j-th iteration within the q-th time slot. Using a first-order Taylor expansion, we can obtain...

[0231]

[0232] Therefore, (P5) can be written as:

[0233]

[0234] akin,

[0235]

[0236] in Therefore, (C1-6) can be rewritten as follows:

[0237]

[0238] Using a first-order Taylor expansion, we can obtain

[0239]

[0240] Therefore, (C1-6) can be expressed as:

[0241]

[0242] Then, (P6) can be rewritten as:

[0243]

[0244] It is clear that (P7) is a convex problem, which can be solved using the CVX toolbox. Then, we can obtain S. l The optimal solution has been found, therefore the subproblem has been solved.

[0245] In step S104, the position of the movable antenna is optimized by fixing the transmit beamforming of the UAV and the trajectory of the UAV. The specific process is as follows:

[0246] Next, fix S w and S l To solve S x (P1) can be rewritten as:

[0247]

[0248] st{(C1-2),(C1-3),(C1-6) (C8-1)

[0249] Let w[q] = a[q] + jb[q], where Let w[q] be the vector of the real part. Let represent the imaginary part vector of w[q]. Furthermore, let

[0250]

[0251] and

[0252]

[0253] In addition,

[0254]

[0255] in Similarly, let

[0256]

[0257] in Therefore, we can obtain

[0258]

[0259] and

[0260]

[0261] It is possible to know

[0262] (a[q]+jb[q])(a T [q]-jb T [q])

[0263] =a[q]a T [q]-ja[q]b T [q]+jb[q]a T [q]+b[q]b T [q]

[0264] =R1[q]-jR2[q]

[0265] We can obtain:

[0266]

[0267] It can be known that:

[0268]

[0269] Therefore, we can conclude that:

[0270]

[0271] In addition, there are

[0272]

[0273] so

[0274]

[0275] definition And Y satisfies Y T =-Y, therefore we can get

[0276] (y T Yy) T =y T Y T y = -y T Yy = y T Yy

[0277] It is obvious that y T Yy = 0, therefore we know Therefore, we can conclude that:

[0278]

[0279] and

[0280]

[0281] Therefore, we can conclude that:

[0282]

[0283] Therefore, (P8) can be converted to:

[0284]

[0285] Clearly, (P9) is highly nonconvex and difficult to solve. Therefore, the PGA method is used to solve (P9). The objective function of (P9) is defined as:

[0286]

[0287] The update rule for the q-th time slot x[q] is expressed as:

[0288]

[0289] and

[0290] x j＝1 [q]=ε1{x j+1 [q],d m ,B}[q] (AU1)

[0291] and

[0292] x j+1 [q]=ε2{x j+1 [q],r s}[q] (AU2)

[0293] (NU) represents a necessary update, where x j [q] represents x[q] in the j-th iteration of the q-th time slot, and η represents the step size of the PGA method. (AU1) represents Additional Update 1, which ensures that constraints (C1-2) and (C1-3) are satisfied through the projection function ε1{·}[q]. Note that Additional Update 1 is only executed if the constraints in (C1-2) and (C1-3) are not satisfied. (AU2) is Additional Update 2, which ensures that constraint (C9-2) is satisfied through the projection function ε2{·}[q]. Note that Additional Update 2 is only executed if constraint (C9-2) is not satisfied.

[0294] It is possible to know It can be calculated using the following formula:

[0295]

[0296] in

[0297]

[0298] Therefore, we can conclude that:

[0299]

[0300] set up

[0301]

[0302] and

[0303]

[0304] Therefore, we can conclude that:

[0305]

[0306] In addition, there are

[0307]

[0308] and

[0309]

[0310] In addition,

[0311]

[0312] Therefore, we can conclude that:

[0313]

[0314] Similarly, we can obtain:

[0315]

[0316] Therefore, we can conclude that:

[0317]

[0318] therefore, It can be obtained. Furthermore, to prevent its value from being too small, it needs to be normalized, as shown in the following formula:

[0319]

[0320] Therefore, necessary updates can be made.

[0321] The constraint (C1-2) can be given by the following formula:

[0322]

[0323] It can be transformed into:

[0324]

[0325] Then, by adding constraint (C1-3), we can obtain:

[0326]

[0327] Therefore, we can conclude that:

[0328]

[0329] Where x0[q]=-dm Clearly, (eqJ) satisfies (C1-2) and (C1-3). If, after the necessary update, x j+1 [q] If (eqJ) is not satisfied, it means that there are unmet constraints in (C1-2) and (C1-3). Then, it is necessary to apply the nearest distance rule to... Projected to Within feasible range The nearest point is represented as:

[0330]

[0331] if If (eqJ) is satisfied, then Additional Update 1 is not executed. The expression for the projection function in Additional Update 1 is as follows:

[0332]

[0333] Therefore, (C1-2) and (C1-3) are eventually satisfied.

[0334] After the MA position of the current time slot converges through iterative solutions of necessary updates and additional update 1 (if needed), if (C9-2) is satisfied, additional update 2 is not performed. If (C9-2) is not satisfied, the latest S is used according to the optimization process of transmit beamforming. x and S l Update S w Update S w After that, constraint (C9-2) is satisfied.

[0335] Based on necessary updates, additional updates 1, and additional updates 2, the PGA method can be used to iteratively update x[q] until the objective function value of (P9) converges, while ensuring that all constraints of (P9) are satisfied. Finally, S can be obtained. x The final solution is found, therefore this subproblem is solved.

[0336] In step S105, an alternating optimization algorithm is proposed to solve the joint optimization problem of transmit beamforming, UAV trajectory, and movable antenna position. The specific process is as follows:

[0337] To effectively solve the established optimization problem, an AO algorithm is proposed. By iteratively optimizing the transmitted beamforming, trajectory, and MA position, their final solutions are obtained, and the objective function value of the optimization problem eventually converges. The steps for solving the established optimization problem using the proposed AO algorithm are as follows:

[0338] enter: Initial feasible trajectory; Initial feasible MA position; Inum : The given number of iterations; I thre Iteration threshold.

[0339] Output: Final solution for transmit beamforming, trajectory, and MA position.

[0340] S1. Let i = 0;

[0341] S2, if i = I num Or the absolute value of the objective function in two adjacent iterations is less than or equal to I. thre If yes, proceed to S7; otherwise, proceed to S3.

[0342] S3, Use and Solving (P4) yields

[0343] S4, Use and Solving (P7) yields

[0344] S5, based on (NU), (AU1), and (AU2), uses and get

[0345] S6. Let i = i + 1, then proceed to S2;

[0346] S7. The final solution for transmitted beamforming was obtained. The final solution of the trajectory The final solution for the position of MA

[0347] The resource optimization method provided by this invention can be used to optimize resources for covert communication of UAVs with flexible location antennas.

[0348] The technical effects of the present invention will be described in detail below with reference to simulation experiments.

[0349] To evaluate the performance of this invention, simulation verification was conducted. In the simulation experiment, a flexible position antenna-enabled UAV covert communication resource optimization system was considered. The specific parameters set in the simulation experiment are as follows: Alice's initial horizontal position is (250, 0) m, and her final horizontal position is (225, 300) m. Alice's height is H = 100 m. The horizontal positions of Bob1 (the first user), Bob2 (the second user), and Willie are (200, 200) m, (200, 250) m, and (325, 200) m, respectively. The time t of each time slot... Q=1s, wavelength λ=1, feasible movement range length B=10λ for all MAs, minimum distance d between two adjacent MAs m =λ / 2, Alice's maximum flight speed V within a single time slot max =30m / s, given number of iterations I num =10, iteration threshold I thre =10 -4 , The step size η of the PGA method is 5 × 10 -3 Q0 = -60dB, the baseline scheme is as follows:

[0350] 1. Baseline Scheme 1: Using an FPA array. Specifically, the MA position is not optimized.

[0351] 2. Baseline Scheme 2: A fixed flight path is used. Specifically, the path is not optimized.

[0352] 3. Baseline Solution 3: Employing individual optimization. Specifically, individual optimization involves optimizing only once in the AO (Optical Aspect Ratio).

[0353] Figure 2 This shows a comparison of the iterative processes of different methods. From Figure 2 It can be seen that although baseline scheme 1 converges in the second iteration, its objective function value continues to decrease slightly after the second iteration, indicating poor numerical stability. Meanwhile, the proposed method converges in the ninth iteration, and its numerical stability after convergence is stronger than that of baseline scheme 1. Furthermore, compared with all baseline schemes, the proposed method has the best covert communication performance. Since baseline scheme 2 does not optimize the trajectory, the optimization is incomplete, causing its objective function value to remain unchanged in each iteration. Note that baseline scheme 3 only iterates once, therefore... Figure 2 Each iteration in the algorithm corresponds to each optimization result. It can be seen that due to incomplete optimization, the objective function value of baseline scheme 3 remains unchanged, meaning that the optimization result of baseline scheme 3 is the same in each optimization. The optimization results of baseline schemes 2 and 3 show that incomplete optimization leads to a significant decrease in covert communication performance. In summary, the proposed method is effective and outperforms all baseline schemes. Therefore, the covert communication performance of the resource optimization method proposed in this invention is superior to the baseline schemes, and simulation experiments verify the inventiveness of the resource optimization method proposed in this invention.

[0354] This invention focuses on developing a method for optimizing UAV covert communication resources using flexible position antennas, which offers higher computational efficiency, lower complexity, and better covert communication performance. This invention explores the use of PGA and alternating optimization techniques, which can optimize the resources of UAV covert communication using flexible position antennas.

Claims

1. A flexible position antenna energized UAV stealth communication resource optimization method, characterized in that, The method comprises: constructing a joint optimization problem of transmit beamforming, UAV trajectory and movable antenna position; decomposing the joint optimization problem of transmit beamforming, UAV trajectory and movable antenna position into three sub-optimization problems, comprising: optimizing the transmit beamforming of the UAV by fixing the UAV trajectory and the movable antenna position; optimizing the trajectory of the UAV by fixing the transmit beamforming of the UAV and the movable antenna position; optimizing the movable antenna position by fixing the transmit beamforming of the UAV and the trajectory of the UAV; solving the three sub-optimization problems by using an alternating optimization algorithm to realize the solution of the joint optimization problem of transmit beamforming, UAV trajectory and movable antenna position.

2. The method of claim 1, wherein, The joint optimization problem based on transmit beamforming, UAV trajectory and movable antenna position is specifically: wherein, P m denotes the maximum transmit power of the UAV transmitter Alice in a single time slot, d m denotes the minimum distance between two adjacent movable antennas MA, R cmn denotes the covert communication rate at the nth Bob in the qth time slot, Q denotes the total number of time slots, l A [q+1]l A [q]l A [Q+1] respectively denote the horizontal position of Alice in the q+1th, qth, Q+1th time slot, l AI denotes the initial horizontal position of Alice, l AF denotes the final horizontal position of Alice, V max denotes the maximum flight speed of Alice in a single time slot, N denotes the number of users, h W denotes the path vector of Alice and Willie in the qth time slot, c W denotes the steering vector of the MA array from Alice to Willie in the qth time slot, x k denotes the position of the kth MA on Alice in the qth time slot, x k+1 denotes the position of the k+1th MA on Alice in the qth time slot, w[q] denotes the transmit beamforming vector of Alice in the qth time slot, r s denotes the unique solution on [1, +∞), ε is used to define the degree of concealment, denotes the variance of the noise at Willie, G AW denotes the signal power received by Willie in the qth time slot; (C1-1) denotes the transmit power constraint, (C1-2) denotes the constraint to avoid coupling effects between adjacent MAs, (C1-3) denotes the constraint of the movable antenna MA feasible range, (C1-4) denotes the flight distance constraint of the UAV transmitter Alice in adjacent time slots, (C1-5) denotes the initial and final horizontal position constraint of the UAV transmitter Alice, (C1-6) denotes the concealment constraint.

3. The method of claim 2, wherein, The process of optimizing the transmit beamforming of the UAV by fixing the UAV trajectory and the movable antenna position is specifically: Fixed S x and S l to solve S w , (P1) is converted to (P4): s.t.{(C3-1),(C3-2),(C3-3) (C4-1) where h Bn [q] denotes the path vector of Alice to the nth Bob in the qth time slot, c Bn [q] denotes the steering vector of the MA array from Alice to the nth Bob in the qth time slot, denotes the variance of the noise at the nth Bob; (P4) is a convex problem, which is solved by using CVX toolbox to obtain the optimal solution , and the eigenvalue decomposition is used to obtain , thus completing the solution of the subproblem.

4. The method of claim 3, wherein, The process of optimizing the trajectory of the UAV by fixing the transmit beamforming of the UAV and the movable antenna position is specifically: Fixed S w and S x to solve S l , (P1) is converted to (P7): wherein, Q0represents the path loss at a reference distance d r A[q] is a relaxed variable that satisfies​ A[q] ≥ || l A [q] - l Bn || 2 + H 2 , the horizontal position of the nth Bob is l Bn = [l Bnx , l Bny ] T , n ∈ {1, 2,..., N}, H represents the fixed height of Alice moving in the air; (P7) is a convex problem, which is solved by using CVX toolbox to obtain S l optimal solution, so the sub-problem is solved.

5. The method of claim 4, wherein, The process of optimizing the movable antenna position by fixing the transmit beamforming of the UAV and the trajectory of the UAV is specifically: S is fixed w and S l to solve for S x (P1) is rewritten as: s.t.{(C1-2),(C1-3),(C1-6) (C8-1) Let w[q] = a[q] + jb[q], where Let w[q] be the vector of the real part. Let w[q] be the imaginary part vector. Furthermore, let... And In addition, let wherein Similarly, let wherein So that And It can be known that (a[q] + jb[q]) (a T [q] - jb T [q]) = a[q]a T [q] - ja[q]b T [q] + jb[q]a T [q] + b[q]b T [q] = R1[q] - jR2[q] It can be obtained that: It can be known that: Therefore, it can be obtained that: In addition, there is Therefore Definitions and Y satisfies Y T = -Y, so that (y T Yy) T = y T Y T y = -y T Yy = y T Yy It is clear that y T Yy = 0, it is known that Thus, we have: And Therefore, it can be obtained that: Therefore, (P8) can be converted to: (P9) is solved by using the PGA method, and a target function of (P9) is defined as: The update rule of the qth time slot x[q] is represented as: And x j+1 [q] = ε1{x j+1 [q],d m ,B}[q] (AU1) And x j+1 [q] = ε2{x j+1 [q], r s}[q] (AU2) (NU) is a necessary update, where x j [q] denotes the x[q] of the j-th iteration in the q-th time slot, η denotes the step size of the PGA method, (AU1) denotes an additional update 1 which ensures that the constraints (C1-2) and (C1-3) are satisfied by the projection function ε1{·}[q]; note that the additional update 1 is only performed if the constraints in (C1-2) and (C1-3) are not satisfied; (AU2) is an additional update 2 which ensures that the constraint (C9-2) is satisfied by the projection function ε2{·}[q]; note that the additional update 2 is only performed if the constraint (C9-2) is not satisfied; It can be seen This can be calculated from the equation: Wherein Therefore, it can be obtained that: Let And Therefore, it can be obtained that: In addition, there is And In addition, let Therefore, it can be obtained that: Similarly, it can be obtained that: Therefore, it can be finally obtained that: Thus, may be obtained; furthermore, in order to prevent its value from being too small, it is necessary to normalize its value, as shown in the following equation: Therefore, the necessary update is performed; The constraint (C1-2) can be given by the following formula: It can be converted to: Then, by adding the constraint (C1-3), the following formula can be obtained: Therefore, it can be obtained that: where x0[q] = -d m It is clear that (eqJ) satisfies (C1-2) and (C1-3); if, after the necessary update, x j+1 [q] does not satisfy (eqJ), it means that there is a constraint in (C1-2) and (C1-3) that is not satisfied; then, x needs to be projected onto the nearest point in the feasible region according to the nearest distance rule, denoted as: x0[q] = -d​​ If If (eqJ) is satisfied, no additional update 1 is performed; the expression of the projection function in the additional update 1 is represented as: Therefore, (C1-2) and (C1-3) are finally satisfied; After the MA position of the current time slot converges through the iterative solution of necessary update and additional update 1, if (C9-2) is satisfied, additional update 2 is not performed; if (C9-2) is not satisfied, the latest S is used according to the optimization process of transmit beamforming. x and S l Update S w Update S w Then, constraint (C9-2) is satisfied; Based on the necessary update, the additional update 1 and the additional update 2, the PGA method can be used to iteratively update x[q] until the objective function value of (P9) converges while ensuring that all the constraints of (P9) are satisfied; finally, the final solution of S x can be obtained, thus this sub-problem is solved.

6. The method of claim 5, wherein, The process of solving the three sub-optimization problems by using the alternating optimization algorithm is specifically: Output: initial feasible trajectory; initial feasible MA position; I num : given number of iterations; I thre : iteration threshold; Output: the final solution of the transmit beamforming, trajectory and MA position; S1, let i=0; S2, if i = I num or the absolute value of the objective function value of the two adjacent iterations is less than or equal to I thre then enter S7, otherwise enter S3; S3, using and solving (P4) gives S4, using and solving (P7) gives S5. Based on (NU), (AU1) and (AU2), use and resulting in S6, let i=i+1, enter S2; S7, final solution for transmit beamforming is obtained final solution for trajectory final solution for MA position 7. A storage medium having stored thereon a computer program, characterized in that The computer program, when executed by the processor, implements the flexible position antenna enabled UAV covert communication resource optimization method in any one of claims 1 to 6.

8. A computer program product comprising a computer program, characterized in that, The computer program, when executed by the processor, implements the flexible position antenna enabled UAV covert communication resource optimization method in any one of claims 1 to 6.

9. An electronic device, comprising: Comprise: a processor; and a memory for storing executable instructions of the processor; Wherein, the processor is configured to execute the executable instructions to perform the flexible position antenna enabled UAV covert communication resource optimization method in any one of claims 1 to 6.

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