Beam forming and horizontal trajectory joint optimization method in covert communication of unmanned aerial vehicle

Abstract

The embodiment of the invention relates to the technical field of communication, in particular to a beam forming and horizontal trajectory joint optimization method in unmanned aerial vehicle covert communication, and the method comprises the steps: constructing a beam forming and horizontal trajectory joint optimization problem in unmanned aerial vehicle covert communication based on a communication-interference integrated signal; based on the joint optimization problem, fixing the horizontal trajectory of the unmanned aerial vehicle to optimize the beam forming of the unmanned aerial vehicle transmitted signal, and obtaining an optimization sub-problem of the beam forming of the unmanned aerial vehicle transmitted signal; based on a joint optimization problem and beam forming of a fixed unmanned aerial vehicle transmitting signal, optimizing the horizontal trajectory of the unmanned aerial vehicle to obtain an optimization sub-problem of the horizontal trajectory of the unmanned aerial vehicle; alternative optimization is carried out based on the two optimization sub-problems, and joint optimization of beam forming and horizontal trajectory of covert communication of the unmanned aerial vehicle in the non-ground network is achieved. According to the method, the communication transmission process and the communication information content can be protected at the same time, the maximization of the overall performance is realized, and the method has very high universality and universality.

Description

Technical Field

[0001] Embodiments of the present application relate to the field of communication technologies, and particularly to a joint optimization method for beamforming and horizontal trajectory in UAV covert communication. Background Art

[0002] In recent years, due to the rapid development of communication technologies, the Non Terrestrial Network (NTN) has attracted extensive research due to its many advantages such as large coverage area, strong bandwidth capacity, and flexible deployment. These advantages have made the NTN not only an important part of the 6G network but also an important part of satellite communication networks. Therefore, the NTN provides indispensable technical support for a wide range of applications that require global coverage and ultra-high-capacity data sharing. However, the inherent openness of the NTN greatly challenges the security of the information transmitted within it. Traditional methods for protecting information content include encryption, physical layer security, authentication, etc. Although these technologies protect the communication content, their transmission behaviors are completely exposed to illegal eavesdroppers and there is a risk of being decrypted. If these communication messages are decrypted, their security will be completely lost. To protect the transmission process of communication information, some research teams have proposed covert communication technologies. The main purpose of covert communication technologies is to hide the transmission process of communication information on the premise of ensuring the demodulation performance of the receiver, so that eavesdroppers cannot detect the communication behavior. By using covert communication technologies, the communication information in the NTN can be made more secure.

[0003] Currently, many domestic and foreign research teams have conducted in-depth and detailed research on covert communication technologies. To prevent eavesdropping and monitoring, Li et al. proposed a joint covert and secure transmission method using Artificial Noise (AN) assistance in a Non-Orthogonal Multiple Access (NOMA) network. To maximize the covert rate, Cheng et al. jointly optimized the transmit beamformer and frequency offset on the array antenna. Du et al. optimized the transmit and interference powers to maximize the covert rate of users, and at the same time used a jammer to assist the communication of the UAV covert communication system. Wang et al. improved covert communication using cooperative radar and jointly designed the transmit beamforming vector and radar waveform of the transmitter. Ma et al. proposed a covert beamforming design framework that realizes radar detection and covert communication in two cases where the channel state information of the eavesdropper (Willie) is accurately known and the error can only be estimated. Luo et al. proposed a covert communication method with strong anti-detection ability and robustness based on Bitcoin transactions.

[0004] However, the inventors of the present application have found that there are still some defects in the above-mentioned covert communication technology.

[0005] First, most of the current covert communication technologies only conceal the transmission process of communication information, and there is little research on protecting the content of communication information while transmitting the covert communication information.

[0006] Second, the current methods for jointly optimizing beamforming and horizontal trajectory in UAV covert communication under non-terrestrial networks have poor performance, slow convergence speed, and high complexity. Summary of the Invention

[0007] In view of this, the embodiments of the present application propose a method for jointly optimizing beamforming and horizontal trajectory in UAV covert communication, which can protect both the communication transmission process and the content of communication information. By jointly optimizing beamforming and horizontal trajectory, the overall performance is maximized, and it has strong universality and generality.

[0008] In a first aspect, the embodiments of the present application propose a method for jointly optimizing beamforming and horizontal trajectory in UAV covert communication, which is applicable to integrated communication and interference signals. The method includes: constructing a joint optimization problem of beamforming and horizontal trajectory in UAV covert communication based on the integrated communication and interference signals; optimizing the beamforming of the UAV transmitted signal by fixing the horizontal trajectory of the UAV based on the joint optimization problem to obtain an optimization sub-problem of the beamforming of the UAV transmitted signal; optimizing the horizontal trajectory of the UAV by fixing the beamforming of the UAV transmitted signal based on the joint optimization problem to obtain an optimization sub-problem of the horizontal trajectory of the UAV; and alternately optimizing based on the two optimization sub-problems to achieve the joint optimization of beamforming and horizontal trajectory in UAV covert communication under non-terrestrial networks.

[0009] A joint optimization method of beamforming and horizontal trajectory in UAV covert communication proposed in this application innovatively considers the multi-user covert communication scenario in NTN, can protect both the communication transmission process and the communication information content simultaneously, and the total detection error probability of Willie always meets the requirements of covert communication. Under the constraints of transmit power, distance constraint of Alice in adjacent time slots, initial and final horizontal position constraints of Alice, effective interference power constraint at Willie, and covertness constraint, an optimization problem aiming to maximize the overall performance is proposed, and the overall performance is maximized through the joint optimization of beamforming and horizontal trajectory. Alice sends ICAJ signals, and the interference signals in the ICAJ signals can protect the content of the communication information and enhance the security of covert communication. This application also designs an alternating optimization algorithm based on quadratic transformation and penalty term method to solve the proposed non-convex optimization problem. This alternating optimization algorithm has good effectiveness and low complexity, and its performance is superior to the benchmark scheme, filling the gap in this field.

[0010] The research of this application focuses on developing a joint optimization of beamforming and horizontal trajectory in UAV covert communication under non-terrestrial networks with faster convergence speed, better covert communication performance and lower complexity, explores the use of ICAJ technology and alternating optimization algorithm technology, and can jointly optimize the beamforming and horizontal trajectory in UAV covert communication under non-terrestrial networks.

[0011] In summary, compared with traditional covert communication technologies, the research of this application discusses the application of ICAJ technology in UAV covert communication under non-terrestrial networks, and emphasizes the importance of solving the problem of joint optimization of beamforming and horizontal trajectory in UAV covert communication under non-terrestrial networks when applying ICAJ technology. Any task involving the joint optimization of beamforming and horizontal trajectory in UAV covert communication under non-terrestrial networks can use the method proposed in this application for joint optimization. The joint optimization method proposed in this application is effective, with performance superior to the benchmark scheme, and has better performance and wider generality.

[0012] Second aspect, an embodiment of the present application proposes a joint optimization system for beamforming and horizontal trajectory in UAV stealth communication, which is applicable to integrated communication and jamming signals. The system includes: a joint optimization problem establishment module, a beamforming optimization module, a horizontal trajectory optimization module, and an alternating optimization module; the joint optimization problem establishment module is used to construct a joint optimization problem for beamforming and horizontal trajectory in UAV stealth communication based on the integrated communication and jamming signals; the beamforming optimization module is used to optimize the beamforming of the UAV transmitted signal by fixing the horizontal trajectory of the UAV based on the joint optimization problem, and obtain an optimization sub-problem of the beamforming of the UAV transmitted signal; the horizontal trajectory optimization module is used to optimize the horizontal trajectory of the UAV by fixing the beamforming of the UAV transmitted signal based on the joint optimization problem, and obtain an optimization sub-problem of the horizontal trajectory of the UAV; the alternating optimization module is used to perform alternating optimization based on the two optimization sub-problems to realize the joint optimization of beamforming and horizontal trajectory in UAV stealth communication under a non-terrestrial network.

[0013] Third aspect, an embodiment of the present application proposes an electronic device, including: at least one processor; and a memory communicatively connected to the at least one processor; wherein, the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to execute a method for joint optimization of beamforming and horizontal trajectory in UAV stealth communication as described in the first aspect above.

[0014] Fourth aspect, an embodiment of the present application proposes a computer-readable storage medium storing a computer program, which when executed by a processor, can implement a method for joint optimization of beamforming and horizontal trajectory in UAV stealth communication as described in the first aspect above.

[0015] It can be understood that the beneficial effects of the second to fourth aspects above can refer to the relevant descriptions in the first aspect above, and will not be repeated here. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the related art, the following will briefly introduce the drawings required for use in the description of the embodiments of the present application or the related technology. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0017] Figure 1 It is a flowchart of a method for joint optimization of beamforming and horizontal trajectory in UAV stealth communication provided in an embodiment of the present application; Figure 2It is a schematic diagram of the comparison simulation experiment results of the objective function values of different methods for the joint optimization of beamforming and horizontal trajectory in UAV covert communication under non-terrestrial networks provided in an embodiment of the present application; Figure 3 It is a schematic structural diagram of a system for the joint optimization of beamforming and horizontal trajectory in UAV covert communication provided in another embodiment of the present application; Figure 4 It is a schematic structural diagram of an electronic device provided in another embodiment of the present application. Detailed implementation manners

[0018] To make the objectives, technical solutions, and advantages of the embodiments of the present application clearer, the embodiments of the present application will be elaborated in detail below with reference to the accompanying drawings. In various embodiments of the present application, many technical details are proposed for the reader to better understand the present application. However, even without these technical details and various changes and modifications based on the following embodiments, the technical solutions required to be protected by the present application can be implemented. The division of the following embodiments is only for convenient description and should not constitute any limitation on the specific implementation manner of the present application. The various embodiments can be combined and cross-referenced with each other on the premise of not being contradictory.

[0019] To solve the defects existing in the covert communication technology, an embodiment of the present application proposes a method for the joint optimization of beamforming and horizontal trajectory in UAV covert communication, which is applicable to communication-jamming integrated signals and is applied to a server. The implementation details of a method for the joint optimization of beamforming and horizontal trajectory in UAV covert communication proposed in this embodiment will be specifically described below. The following content is only the implementation details provided for convenient understanding and is not necessary for implementing this solution.

[0020] The specific process of a method for the joint optimization of beamforming and horizontal trajectory in UAV covert communication proposed in this embodiment can be as Figure 1 shown, including: Step 101, construct a joint optimization problem of beamforming and horizontal trajectory in UAV covert communication based on communication-jamming integrated signals.

[0021] In specific implementation, in the face of the UAV covert communication scenario, the server first needs to construct a joint optimization problem of beamforming and horizontal trajectory in UAV covert communication based on communication-jamming integrated signals.

[0022] This embodiment discusses a scenario of UAV covert communication under a non-terrestrial network. In this scenario, there is a UAV Alice for transmitting signals, several UAV users Bobs, and a UAV warden Willie.

[0023] Alice moves horizontally at a fixed altitude in the air. Bobs hovers in the air, and Willie also hovers in the air. Alice hopes to transmit the integrated communication and jamming signal (ICAJ) to Bobs while hiding the process of signal transmission for covert communication. Willie monitors the channel and tries to detect whether Alice's transmission is taking place.

[0024] Suppose Alice is equipped with antennas, each Bob is equipped with one antenna, and Willie is equipped with one antenna. In the horizontal coordinate system, the horizontal positions of Alice, the th Bob, and Willie are , and respectively, and the altitudes are , and , , , , .

[0025] Let be the time required for Alice to complete a flight mission. Divide evenly into time slots, and the time in each time slot is , , is small enough to consider Alice's position constant in each time slot. Based on this, the horizontal position of Alice in the th time slot can be given as: ; ; where represents Alice's horizontal position in the th time slot.

[0026] Based on this, the distance between the positions of Alice corresponding to two adjacent time slots can be calculated as . Let the maximum flight speed of Alice be , then .

[0027] Let Alice's initial horizontal position be , and the final horizontal position be , then , .

[0028] In addition, we can know that in the th time slot, the distance between Alice and the th Bob is , the distance between Alice and Willie is , and is expressed by the formula: ; .

[0029] To simplify the process, assume that all channel states in the scenario are known, and define the path as , is the path between Alice and Willie, is the path between Alice and the th Bob.

[0030] Let represent the large-scale path fading of the path in the th time slot, and its expression is: ; where is the path loss at the reference distance d_0, is the th time slot, the path corresponding distance, is corresponding path loss exponent.

[0031] Based on this, we can obtain the channel vector of the path in the th time slot as: ; where each term in is , represents random numbers between.

[0032] Alice sends an ICAJ signal to achieve covert communication while protecting the information content. The ICAJ signal sent by Alice in the th time slot is expressed by the formula: ; where is the hypothesis that Alice does not send a signal, is the hypothesis that Alice sends a signal, is the communication beamforming vector for sending a signal in the nth time slot, and the signal sent is , , The interference beamforming vector for transmitting spoofing signals in the nth time slot, where the transmitted spoofing signal is , .

[0033] The th Bob's received signal in the th time slot is expressed by the formula: ; where represents the noise at the th Bob in the th time slot, .

[0034] The signal received by Willie in the nth time slot is expressed by the formula: ; where represents the noise at Willie in the th time slot, .

[0035] The th Bob's secrecy communication rate in the th time slot is expressed by the formula: ; ; where represents the signal-to-noise ratio of the th Bob in the th time slot.

[0036] Let represent Alice's transmit power in the th time slot, then we can get: .

[0037] The effective interference power at Willie in the th time slot is expressed as: .

[0038] The communication power at Willie in the th time slot is expressed as: .

[0039] Willie does not actively transmit signals but judges whether Alice is transmitting signals by listening to the spatial channel. We can get and The likelihood function of the signal received by Willie and are respectively: ; ; ; ; Generally speaking, and are considered to be equal.

[0040] From Willie's perspective, its goal is to minimize the detection error to improve the surveillance performance. According to the Neyman-Pearson criterion, the likelihood ratio test can be obtained as: ; where, and are respectively the binary decisions corresponding to and , indicating that Alice does not send a signal and Alice sends a signal respectively.

[0041] Let represent the false alarm probability of Willie in the -th time slot, and let represent the miss detection probability of Willie in the -th time slot. Then the total detection error probability of Willie in the -th time slot is: .

[0042] However, the above formula cannot be used for the analysis of subsequent optimization problems. Therefore, we set the lower bound of as: ; where, represents the KL divergence from to .

[0043] After calculation, it can be obtained that: ; Based on the basic concealment constraint , the strict concealment degree is defined as:

[0044] where, is a small value used to define the concealment degree. The concealment degree varies with increases as the

[0045] However, when solving the optimization problem, the concealment of the lattice is still insufficient. Therefore, it is necessary to continue the calculation to obtain: ; Let , and we can obtain .

[0046] Since is monotonically increasing on , let be the unique solution of on , and we can calculate .

[0047] Based on this, the final concealment constraint is obtained as: .

[0048] The objective of the joint optimization problem of beamforming and horizontal trajectory in UAV covert communication is to balance the covert communication performance and interference performance. The constraint conditions include transmit power constraint, distance constraint, position constraint, interference constraint, and the final concealment constraint. The joint optimization problem of beamforming and horizontal trajectory in UAV covert communication is expressed by the formula as: ; ; where the constraint conditions from top to bottom are the transmit power constraint, the distance constraint of Alice in adjacent time slots, the initial and final horizontal position constraints of Alice, the effective interference power constraint at Willie, and the final concealment constraint, represents the beamforming of the UAV transmitting signal, represents the interference beamforming of the UAV transmitting spoofing signals, represents the horizontal trajectory of the UAV, , , , is a scaling factor used to make the dimensions of the covert communication performance and interference performance consistent, represents the maximum transmit power of Alice in a single time slot.

[0049] Step 102: Based on the joint optimization problem, fix the horizontal trajectory of the UAV and optimize the beamforming of the UAV transmitting signal to obtain the optimization sub-problem of the beamforming of the UAV transmitting signal.

[0050] In a specific implementation, the joint optimization problem needs to be decomposed into two sub-optimization problems for solution. First, the server needs to optimize the beamforming of the signals transmitted by the UAV based on the joint optimization problem by fixing the horizontal trajectory of the UAV, and obtain the sub-optimization problem of the beamforming of the signals transmitted by the UAV.

[0051] For the joint optimization problem, we fix to solve and , and obtain the first intermediate sub-optimization problem as follows: ; ; Obviously, the interference signal term in the objective function makes the above problem non-convex and difficult to solve. Therefore, we use the null space method to remove the interference signal term in the first intermediate sub-optimization problem. Since is the interference signal term, when the objective function is maximized, the interference signal term must be minimized simultaneously. Let be the new constraint condition, and we can obtain , thus transforming the objective function of the first intermediate sub-optimization problem into: ; Let , and we can get . Next, let , and we can get , remove the constraint , and let , and we can obtain the second intermediate sub-optimization problem as follows: ; ; Next, let , , , , and , and . Based on this, we can obtain: ; ; ; ; ; We know that the second intermediate sub-optimization problem obtained now is a multi-ratio fractional programming problem. Therefore, we use the quadratic transformation method to process the second intermediate sub-optimization problem and introduce the auxiliary variable set , by using to transform the objective function of the second intermediate optimization sub-problem. When is fixed, the objective function of the transformed second intermediate optimization sub-problem is a convex function. The update formula for the th is: ; When solving, first use the latest to obtain the solution, and then use the obtained solution to update . Iterate repeatedly until convergence, and the third intermediate optimization sub-problem can be obtained as follows: ; ; Obviously, only the rank-one constraint makes the optimization problem non-convex. To solve this problem, we use the penalty term method Taking as an example, we know that the rank of a matrix is the number of its non-zero singular values. So when , has 1 non-zero singular value. So the sum of all singular values is equal to the largest singular value in ; Therefore, the rank-one constraint can be rewritten as , where represents the nuclear norm, represents the spectral norm, represents taking the sum of all singular values in represents taking the maximum value of all singular values in

[0052] When , there is . In the maximization problem, we can introduce the penalty term , where represents the penalty factor, . When tends to 0, tends to . Therefore, when is not a rank-one matrix and tends to 0, the penalty term is infinitesimal, and the objective function containing the penalty term is infinitesimal. Therefore, a rank-one solution satisfying can be obtained. In addition, is non-convex, so we use the first-order Taylor expansion at the point to obtain The upper bound of ; where denotes the eigenvector corresponding to the maximum eigenvalue of

[0053] Therefore, the penalty term can be expressed as: .

[0054] Similarly, we will also introduce the penalty term , denotes taking the sum of all singular values in denotes the upper bound of denotes taking the maximum value of all singular values in

[0055] Based on this, we can obtain the following optimization sub-problem for the beamforming of the UAV transmitted signal: ; ; The optimization sub-problem of the beamforming of the UAV transmitted signal is a convex problem, which can be solved by CVX, and then the eigenvalue decomposition is used to obtain and , which is obtained from .

[0056] Step 103: Based on the joint optimization problem, fix the beamforming of the UAV transmitted signal and optimize the horizontal trajectory of the UAV to obtain the optimization sub-problem of the horizontal trajectory of the UAV.

[0057] In specific implementation, in addition to the optimization sub-problem of the beamforming of the UAV transmitted signal, the server also needs to optimize the horizontal trajectory of the UAV based on the joint optimization problem by fixing the beamforming of the UAV transmitted signal to obtain the optimization sub-problem of the horizontal trajectory of the UAV.

[0058] For the joint optimization problem, fix and to solve , and the following fourth intermediate optimization sub-problem can be obtained: ; ; Let , and , and at the same time assume , assume the reference distance is , with the unit of meter, , based on this, we can obtain: ; ; ; ; ; ; Obviously, the above equation is still non-convex. Therefore, we assume that represents Alice's horizontal position in the \(n\)th time slot and the \(i\)th iteration. Using the first-order Taylor expansion, we can obtain: ; Let ; Let ; Then ; Based on this, the following fifth intermediate optimization sub-problem is obtained: ; ; Assume that , and we can obtain: ; ; Based on this, the objective function of the fifth intermediate optimization sub-problem is transformed into: ; Set a first slack variable , , corresponding to 's value is . Let , , and we can obtain: ; Then set a second slack variable , , corresponding to 's value is . Let , , and we can obtain: ; Based on this, the following optimization sub-problem for the horizontal trajectory of the UAV is obtained: ; ; The optimization sub - problem of the horizontal trajectory of the UAV is a convex problem and can be solved by CVX.

[0059] Step 104: Based on the two optimization sub - problems, perform alternating optimization to achieve the joint optimization of beamforming and horizontal trajectory for UAV covert communication in a non - terrestrial network.

[0060] In specific implementation, after the server obtains the two optimization sub - problems, it can perform alternating optimization based on the two optimization sub - problems to achieve the joint optimization of beamforming and horizontal trajectory for UAV covert communication in a non - terrestrial network.

[0061] The process of alternating optimization of the two optimization sub - problems is implemented based on the alternating optimization algorithm.

[0062] Let the input of the alternating optimization algorithm include the initial feasibility , the initial feasible horizontal trajectory of Alice , the threshold of the quadratic transformation is , the threshold of the alternating optimization algorithm is , the maximum number of iterations of the quadratic transformation is , the maximum number of iterations of the alternating optimization algorithm is .

[0063] Let the output of the alternating optimization algorithm be , and .

[0064] The alternating optimization algorithm includes the following steps: S1: Let ; S2: If the number of iterations of the alternating optimization algorithm reaches or the absolute value of the difference between the objective function values of two adjacent iterations is less than or equal to , then go to S10; otherwise, go to S3; S3: Let ; S4: If the number of iterations of the quadratic transformation reaches or the absolute value of the difference between the objective function values of two adjacent iterations is less than or equal to , then go to S7; otherwise, go to S5; S5: Let , and solve the optimization sub - problem of beamforming for the UAV - transmitted signal through using to obtain and ; S6: Use the update formula of to update , enter S4; S7, through obtain , through and obtain ; S8, use and to solve the optimization sub - problem of the horizontal trajectory of the UAV, thus obtaining ; S9, let , enter S2; S10, output , , and .

[0065] A joint optimization method of beamforming and horizontal trajectory in UAV covert communication proposed in this embodiment innovatively considers the multi - user covert communication scenario in NTN, can protect both the communication transmission process and the communication information content simultaneously, and the total detection error probability of Willie always meets the requirements of covert communication. Under the constraints of transmit power, distance constraint between Alice in adjacent time slots, initial and final horizontal position constraints of Alice, effective interference power constraint at Willie, and concealment constraint, an optimization problem aiming to maximize the overall performance is proposed, and through the joint optimization of beamforming and horizontal trajectory, the maximization of the overall performance is achieved. Alice sends ICAJ signals, and the interference signals in the ICAJ signals can protect the content of the communication information and enhance the security of covert communication. This embodiment also designs an alternating optimization algorithm based on quadratic transformation and penalty term method to solve the proposed non - convex optimization problem. The proposed alternating optimization algorithm has good effectiveness and low complexity, and its performance is superior to the benchmark scheme, filling the gap in this field.

[0066] The research of this embodiment focuses on developing a joint optimization of beamforming and horizontal trajectory in UAV covert communication under non - terrestrial networks with faster convergence speed, better covert communication performance, and lower complexity, explores the use of ICAJ technology and alternating optimization algorithm technology, and can jointly optimize the beamforming and horizontal trajectory in UAV covert communication under non - terrestrial networks.

[0067] In summary, compared with traditional covert communication technologies, the research in this embodiment explores the application of the ICAJ technology to the covert communication of unmanned aerial vehicles (UAVs) in non-terrestrial networks, and emphasizes the importance of solving the problem of joint optimization of beamforming and horizontal trajectory in the application of the ICAJ technology to the covert communication of UAVs in non-terrestrial networks. Any task involving the joint optimization of beamforming and horizontal trajectory in the covert communication of UAVs in non-terrestrial networks can use the method proposed in this embodiment for joint optimization. The joint optimization method proposed in this embodiment is effective, with performance superior to the benchmark scheme, and has better performance and wider generality.

[0068] The step division of the above various methods is only for clear description. When implemented, they can be combined into one step or some steps can be split into multiple steps. As long as the same logical relationship is included, they are all within the protection scope of this application; adding insignificant modifications to the algorithm or process or introducing insignificant designs, but without changing the core design of its algorithm and process, are all within the protection scope of this application.

[0069] In one embodiment, in order to evaluate the performance of a method for joint optimization of beamforming and horizontal trajectory in the covert communication of UAVs proposed in this application, we conducted simulation experiments for verification.

[0070] In the simulation experiment, the parameters are set as follows: the number of Bobs , the heights of Alice, Bobs, and Willie are 400 meters, 300 meters, and 300 meters respectively. The initial horizontal position of Alice is , the final horizontal position of Alice is , the horizontal position of Bob1 is , the horizontal position of Bob2 is , the horizontal position of Willie is , the noise variances of Bobs and Willie are , the time of each time slot , the maximum flight speed of Alice is , the maximum transmit power of Alice in a single time slot is , the path loss at the reference distance is , the quadratic transformation threshold is , the threshold of the alternating optimization algorithm is , the penalty factor is specifically , the scaling factor is specifically .

[0071] All the benchmark schemes are as follows: 1. benchmark1: Only the horizontal trajectory of Alice is optimized, and beamforming is not optimized.

[0072] 2. benchmark2: Adopt a separate design.

[0073] Specifically, the number of antennas in Alice is half of that in the joint design, that is . The transmit power constraint becomes that the communication transmit power and interference transmit power at Alice are respectively less than or equal to .

[0074] Figure 2 Shows the comparison of the objective function values of different methods. From Figure 2 It can be seen that the method proposed in this application can converge within 5 iterations, proving the effectiveness and fast convergence speed of the proposed method, and also indicating that the complexity of the proposed method is relatively low. In addition, the objective function value of the method proposed in this application can converge to approximately , while the objective function values of benchmark1 and benchmark2 can only converge to approximately and approximately . Therefore, the performance of the method proposed in this application is much higher than that of the two benchmark schemes, proving the superiority of the method proposed in this application. Therefore, the covert communication performance of the joint optimization method proposed in this application is better than that of the benchmark scheme, and the simulation experiment verifies the creativity of the joint optimization method proposed in this application.

[0075] Correspondingly, another embodiment of this application proposes a joint optimization system for beamforming and horizontal trajectory in UAV covert communication, which is applicable to integrated communication and interference signals. The implementation details of the joint optimization system for beamforming and horizontal trajectory in UAV covert communication proposed in this embodiment are specifically described below. The following content is only relevant implementation details provided for convenience of understanding and is not necessary for implementing this embodiment. Figure 3 Is the structural schematic diagram of a joint optimization system for beamforming and horizontal trajectory in UAV covert communication proposed in this embodiment. The system includes: a joint optimization problem establishment module 201, a beamforming optimization module 202, a horizontal trajectory optimization module 203, and an alternating optimization module 204.

[0076] The joint optimization problem establishment module 201 is used to construct a joint optimization problem for beamforming and horizontal trajectory in UAV covert communication based on integrated communication and interference signals.

[0077] The beamforming optimization module 202 is used to optimize the beamforming of the UAV transmitted signal by fixing the horizontal trajectory of the UAV based on the joint optimization problem, and obtain an optimization sub-problem for the beamforming of the UAV transmitted signal.

[0078] The horizontal trajectory optimization module 203 is configured to optimize the horizontal trajectory of the UAV based on the joint optimization problem by fixing the beamforming of the signal transmitted by the UAV, and obtain an optimization sub-problem of the horizontal trajectory of the UAV.

[0079] The alternating optimization module 204 is configured to perform alternating optimization based on the two optimization sub-problems, so as to realize the joint optimization of the beamforming and the horizontal trajectory of the UAV in the non-terrestrial network for covert communication.

[0080] It is worth mentioning that each module involved in this embodiment is a logical module. In practical applications, a logical unit can be a physical unit, a part of a physical unit, or can be implemented by a combination of multiple physical units. In addition, in order to highlight the innovative part of this application, units that are not closely related to solving the technical problems proposed in this application are not introduced in this embodiment, but this does not mean that there are no other units in this embodiment.

[0081] It is not difficult to find that this embodiment is a system embodiment corresponding to the above method embodiment. This embodiment can be implemented in cooperation with the above method embodiment. The relevant technical details and technical effects mentioned in the above method embodiment are still valid in this embodiment. In order to reduce repetition, they will not be elaborated here. Correspondingly, the relevant technical details mentioned in this embodiment can also be applied to the above method embodiment.

[0082] Another embodiment of this application proposes an electronic device, and its specific structure is as Figure 4 shown, including: at least one processor 301; and a memory 302 communicatively connected to the at least one processor 301; wherein, the memory 302 stores instructions executable by the at least one processor 301, and the instructions are executed by the at least one processor 301, so that the at least one processor 301 can execute a method for joint optimization of beamforming and horizontal trajectory in UAV covert communication as described in the above method embodiment.

[0083] Among them, the memory and the processor can be connected in a bus manner. The bus can include any number of interconnected buses and bridges, and the bus connects various circuits of one or more processors and the memory together. The bus can also connect various other circuits such as peripheral devices, voltage regulators, and power management circuits together, which are well known in the art and will not be further described herein. The bus interface is responsible for providing an interface between the bus and the transceiver. The transceiver can be one element or multiple elements, such as multiple receivers and transmitters, and provides a unit for communicating with various other devices on the transmission medium. The data processed by the processor is transmitted on the wireless medium through the antenna. Further, the antenna also receives data and transmits the data to the processor.

[0084] The processor is responsible for managing the bus and general processing, and can also provide various functions, including timing, peripheral interfaces, voltage regulation, power management, and other control functions. The memory can be used to store data used by the processor when executing operations.

[0085] Another embodiment of the present application proposes a computer-readable storage medium storing a computer program, which when executed by a processor, can implement a method for jointly optimizing beamforming and horizontal trajectory in stealth communication of an unmanned aerial vehicle as described in the above method embodiment.

[0086] That is, those skilled in the art can understand that all or part of the steps in the above method embodiments can be completed by instructing relevant hardware through a program. This program is stored in a storage medium and includes several instructions to enable a device (such as a single-chip microcomputer, chip, etc.) or a processor to execute all or part of the steps of the methods described in various embodiments of the present application. The foregoing storage medium includes: USB flash drives, mobile hard disks, ROM (Read-Only Memory), RAM (Random Access Memory), magnetic disks, or optical discs and other various media that can store program codes.

[0087] Those of ordinary skill in the art can understand that the above embodiments are specific embodiments for implementing the present application, and in actual applications, various changes can be made in form and details without departing from the spirit and scope of the present application.

Claims

1. A joint optimization method for beamforming and horizontal trajectory in UAV stealth communication, characterized in that Applicable to integrated communication and interference signals, the method includes: Based on the integrated communication and interference signals, construct a joint optimization problem of beamforming and horizontal trajectory in UAV covert communication; Based on the joint optimization problem, fix the horizontal trajectory of the UAV and optimize the beamforming of the UAV transmitted signal to obtain an optimization sub-problem of the beamforming of the UAV transmitted signal; Based on the joint optimization problem, fix the beamforming of the UAV transmitted signal and optimize the horizontal trajectory of the UAV to obtain an optimization sub-problem of the horizontal trajectory of the UAV; Based on the two optimization sub-problems, perform alternating optimization to achieve the joint optimization of beamforming and horizontal trajectory in UAV covert communication under non-terrestrial networks.

2. The joint optimization method of beamforming and horizontal trajectory in UAV stealth communication according to claim 1, characterized in that In the scenario of UAV covert communication, there is a UAV Alice for transmitting signals, a number of UAV users Bobs, and a UAV warden Willie; Alice moves horizontally at a fixed altitude in the air, Bobs hovers in the air, Willie hovers in the air. Alice hopes to transmit an integrated communication and interference signal to Bobs while hiding the transmission process for covert communication. Willie monitors the channel and tries to detect whether Alice's transmission is occurring; Assume that Alice is equipped with antennas, each Bob is equipped with one antenna, and Willie is equipped with one antenna. In the horizontal coordinate system, the horizontal positions of Alice, the th Bob, and Willie are , and , respectively, and the heights are , and , , , , ; Let be the time required for Alice to complete a flight mission. Divide evenly into time slots, and the time in each time slot is . . is small enough that it can be considered that Alice's position is constant in each time slot. Based on this, the horizontal position of Alice in the th time slot is given as: ； ； Among them, represents the horizontal position of Alice at the th time slot; Based on this, the distance between the positions of Alice corresponding to two adjacent time slots can be calculated as , and let the maximum flying speed of Alice be , then ; Let Alice's initial horizontal position be , and the final horizontal position be . It can be obtained that , ; Suppose in the -th time slot, the distance between Alice and the -th Bob is , and the distance between Alice and Willie is , and are expressed by the formula as: ； ； To simplify the process, assume that all channel states in the scenario are known, and define the paths as , the path between Alice and Willie, and the path between Alice and the Let represent the path in the th time slot for the large-scale path fading, and its expression is: ； Among them, is the reference distance at the path loss, is the distance corresponding to the path in the th time slot, is the path loss exponent corresponding to Based on this, the channel vector of the path in the th time slot is obtained as: ​ ； Among them, each item in , represents a random number between 3. The joint optimization method of beamforming and horizontal trajectory in UAV stealth communication according to claim 2, characterized in that Alice sends an ICAJ signal, which realizes covert communication while protecting the information content. Alice sends the ICAJ signal in the th time slot which is expressed by the formula: ； Among them, is the hypothesis that Alice does not send a signal, is the hypothesis that Alice sends a signal, is the communication beamforming vector for sending a signal in the nth time slot, and the signal sent is , is the interference beamforming vector for sending a spoofing signal in the nth time slot, and the spoofing signal sent is ; The signal received by the first Bob in the first time slot is expressed by the formula: ； Among them, represents the noise at Bob in the th time slot, ; The signal received by Willie in the nth time slot Is expressed by the formula as: ； Among them, represents the noise at Willie's location in the th time slot, ; The rate of Bob's covert communication in the th time slot is expressed by the formula: ​ ； ； Among them, represents the signal-to-noise ratio of the th Bob in the th time slot; Let denote the transmit power of Alice in the th time slot, we can obtain: ； The effective interference power at Willie for the first time slot is expressed as: ； The communication power at Willie for the first time slot is expressed as: ； Rather than actively transmitting signals, Willie determines whether Alice is transmitting signals by listening to the spatial channel, and can obtain and the likelihood functions of the signals received by Willie and respectively as follows: ； ； ； ； From Willie's perspective, its goal is to minimize the detection error to improve the monitoring performance. According to the Neyman-Pearson criterion, the likelihood ratio test can be obtained as: ； wherein, and are binary decisions corresponding to and respectively, indicating that Alice does not send a signal and that Alice sends a signal; Let denote the false alarm probability of Willie at the -th time slot. Let denote the miss detection probability of Willie at the -th time slot. Then the total detection error probability of Willie at the -th time slot is given by: ； Set The lower bound of: ； Among them, denotes to KL divergence; After calculation, it can be obtained that: ； Based on the basic concealment constraint , the defined strict concealment degree is as follows: ； Among them, is a small value used to define the concealment degree, and the concealment degree increases with decreasing; Continue the calculation to obtain: ； Let , we can get ; Since is monotonically increasing on, let be the unique solution of on, and it can be calculated that ; Based on this, the final covertness constraint is obtained as: 。 4. The joint optimization method of beamforming and horizontal trajectory in UAV stealth communication according to claim 3, wherein, The goal of the joint optimization problem of beamforming and horizontal trajectory in UAV covert communication is to balance the covert communication performance and interference performance. The constraint conditions include transmit power constraint, distance constraint, position constraint, interference constraint, and the final covertness constraint. The joint optimization problem of beamforming and horizontal trajectory in UAV covert communication is expressed by the formula as: ； ； Among them, the constraints from top to bottom are the transmit power constraint, the distance constraint of Alice in adjacent time slots, the initial and final horizontal position constraints of Alice, the effective interference power constraint at Willie, and the final concealment constraint, represents the beamforming of the signal transmitted by the UAV, represents the interference beamforming of the spoofing signal transmitted by the UAV, represents the horizontal trajectory of the UAV, , , , is a scaling factor used to make the dimensions of the covert communication performance and the interference performance consistent, represents the maximum transmit power of Alice in a single time slot.

5. The joint optimization method of beamforming and horizontal trajectory in UAV stealth communication according to claim 4, characterized in that Based on the joint optimization problem, fix the horizontal trajectory of the UAV and optimize the beamforming of the UAV transmitted signal to obtain an optimization sub-problem of the beamforming of the UAV transmitted signal, including: For the joint optimization problem, fix to solve and , and the first intermediate optimization sub-problem is obtained as follows: ； ； The zero-space method is adopted to remove the interference signal term in the first intermediate optimization sub-problem, and let be used as the new constraint condition, and we get , so that the objective function of the first intermediate optimization sub-problem is transformed into: ； Let , we can obtain . Next, let , we can obtain . Remove the constraint , and let , we get the following second intermediate optimization sub-problem: ； ； Next, let , , , , and , and , based on which the following can be obtained: ； ； ； ； ； The second intermediate optimization sub-problem is a multi-ratio fractional programming problem. The second intermediate optimization sub-problem is processed by using a quadratic transformation method, and an auxiliary variable set is introduced. , and is used to transform the objective function of the second intermediate optimization sub-problem. When is fixed, the objective function of the transformed second intermediate optimization sub-problem is a convex function, and the update formula of the -th is: ； When solving, first use the latest to obtain a solution, and then use the obtained solution to update . Iterate repeatedly until convergence, and the following third intermediate optimization sub-problem can be obtained: ； ； Introduce a penalty term and to solve the problem that the third intermediate optimization sub-problem is non-convex due to the constraint conditions, denotes the penalty factor, , denotes taking the sum of all singular values in denotes the upper bound of denotes taking the maximum value of all singular values in denotes taking the sum of all singular values in denotes the upper bound of denotes taking the maximum value of all singular values in, thus obtaining the optimization sub-problem of the beamforming of the UAV transmitted signal as follows: ； ； The optimization sub - problem of beamforming for the signals transmitted by the UAV is a convex problem, which can be solved by CVX, and then the eigenvalue decomposition is used to obtain and , which is obtained from to get.

6. The joint optimization method of beamforming and horizontal trajectory in UAV stealth communication according to claim 5, characterized in that Based on the joint optimization problem, fix the beamforming of the UAV transmitted signal and optimize the horizontal trajectory of the UAV to obtain an optimization sub-problem of the horizontal trajectory of the UAV, including: For the joint optimization problem, fix and to solve , and the following fourth intermediate optimization sub-problem is obtained: ； ； Let , and , and at the same time assume that , assume that the reference distance is , with the unit of meter, , based on this, we can obtain: ； ； ； ； ； ； Hypothesis Denote the horizontal position of Alice in the \(i\)-th iteration of the \(n\)-th time slot. Using the first-order Taylor expansion, we can obtain: ； Let ; Let ; Then ; Based on this, the fifth intermediate optimization sub-problem is obtained as follows: ； ； Hypothesis , it can be obtained that: ； ； Based on this, the objective function of the fifth intermediate optimization sub-problem is transformed into: ； Set a first slack variable , , corresponding to of the value is , let , , we can get: ； Set a second slack variable , , corresponding to of the value is , let , , we can get: ； Based on this, the optimization sub-problem of the horizontal trajectory of the UAV is obtained as follows: ； ； The optimization sub-problem of the horizontal trajectory of the UAV is a convex problem and can be solved by CVX.

7. A joint optimization method for beamforming and horizontal trajectory in UAV stealth communication according to claim 6, characterized in that Based on the two optimization sub-problems, perform alternating optimization to achieve the joint optimization of beamforming and horizontal trajectory in UAV covert communication under non-terrestrial networks, including: The input of the alternating optimization algorithm includes the initial feasible , the initial feasible horizontal trajectory of Alice , the threshold of the quadratic transformation is , the threshold of the alternating optimization algorithm is , the maximum number of iterations of the quadratic transformation is , the maximum number of iterations of the alternating optimization algorithm is ; Let the output of the alternating optimization algorithm be , and ; The alternating optimization algorithm includes the following steps: S1, let ; S2, if the number of iterations of the alternating optimization algorithm reaches or the absolute value of the difference between the objective function values of two adjacent iterations is less than or equal to , then go to S10, otherwise go to S3; S3, let ; S4, if the number of iterations of the second transformation reaches or the absolute value of the difference between the objective function values of two adjacent iterations is less than or equal to , then go to S7; otherwise, go to S5. S5, let , through using to solve the optimization sub - problem of beamforming of the UAV - transmitted signal, thereby obtaining and ; S6. Use to update , and enter S4; S7, via obtain , via and obtain ; S8 is used to and solve the optimization sub-problem of the horizontal trajectory of the UAV, thereby obtaining ; S9, make , enter S2; S10, output , , and .

8. A joint optimization system for beamforming and horizontal trajectory in UAV stealth communication, characterized in that, Applicable to integrated communication and interference signals, the system includes: A joint optimization problem establishment module, used to construct a joint optimization problem of beamforming and horizontal trajectory in UAV covert communication based on the integrated communication and interference signals; A beamforming optimization module, used to optimize the beamforming of the UAV transmitted signal by fixing the horizontal trajectory of the UAV based on the joint optimization problem to obtain an optimization sub-problem of the beamforming of the UAV transmitted signal; A horizontal trajectory optimization module, which is used to optimize the horizontal trajectory of the UAV based on the joint optimization problem by fixing the beamforming of the signal transmitted by the UAV, and obtain an optimization sub-problem of the horizontal trajectory of the UAV. An alternating optimization module, which is used to perform alternating optimization based on the two optimization sub-problems to achieve the joint optimization of the beamforming and the horizontal trajectory of the UAV for covert communication in a non-terrestrial network.

9. An electronic device, characterized in that, Comprising: At least one processor; And a memory communicatively connected to the at least one processor; Wherein, instructions executable by the at least one processor are stored in the memory, and when the instructions are executed by the at least one processor, the at least one processor is enabled to execute a method for joint optimization of beamforming and horizontal trajectory in UAV covert communication as described in any one of claims 1 to 7.

10. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it can implement a method for joint optimization of beamforming and horizontal trajectory in UAV covert communication as described in any one of claims 1 to 7.

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