Physical layer security-oriented motion sensing integrated unmanned aerial vehicle track and wave beam joint optimization method

Abstract

The invention belongs to the field of communication sensing integration, and particularly relates to a physical layer security-oriented communication sensing integrated unmanned aerial vehicle track and beam joint optimization method. Comprising the following steps: constructing an unmanned aerial vehicle assisted wireless communication system model; with maximization of a secure communication reachable rate as an optimization target, constructing an unmanned aerial vehicle trajectory and beam joint optimization problem according to a transmitting power constraint, a beam matrix constraint, a flight speed constraint, a flight power constraint and a wide beam constraint; decoupling the unmanned aerial vehicle trajectory and wave beam joint optimization problem to obtain a common inductance integrated waveform sub-problem and an unmanned aerial vehicle flight trajectory sub-problem; iterative solution is carried out on the flux-inductance integrated waveform sub-problem and the unmanned aerial vehicle flight path sub-problem to obtain an optimal flux-inductance integrated waveform and an optimal unmanned aerial vehicle flight path; according to the method, communication perception integration is combined with extended Kalman filtering, waveform and unmanned aerial vehicle trajectory for design, so that the quality of wireless communication is ensured while communication security is realized.

Description

Technical Field

[0001] This invention belongs to the field of integrated communication and sensing, and specifically relates to a method for joint optimization of UAV trajectory and beam for physical layer security through integrated communication and sensing. Background Technology

[0002] Wireless sensing performance is a crucial development direction for future 6G, with communication and sensing technologies gradually converging. EKF (Extended Kalman Filter) is a classic technique for predicting the location of moving targets. As a core node in future mobile communication networks, drones have a wide range of applications and promising prospects, attracting significant attention from various industries.

[0003] Existing technologies offer various methods for optimizing UAV trajectories, but research has revealed numerous problems with these solutions, including: neglecting secure transmission in UAV communication scenarios; some existing technologies fail to consider trajectory optimization within UAV communication systems; and limitations such as restricting the target and UAV to movement to the same plane and allowing only one perceived target.

[0004] To address secure transmission issues, particularly in scenarios involving mobile eavesdroppers, patent CN114584235B, entitled "A Perception-Based Uplink Communication Security Method for Mobile Aerial Eavesdroppers," discloses a perception-based uplink communication security method for mobile aerial eavesdroppers. This method establishes an integrated communication and perception model. Considering the flexible deployment and high mobility of mobile aerial eavesdroppers, it jointly designs and iteratively optimizes radar signals and receiving beamformers, balancing interference with the active antenna (AE) and communication with the user. While ensuring communication between the base station (BS) and the user, it uses an extended Kalman filter to predict the trajectory of the mobile AE and the channel state information (CSI) between the base station and the AE, achieving accurate AE tracking and real-time accurate CSI between the base station and the AE. This further enhances the radar signal's ability to interfere with the AE and improves the confidentiality of reliable communication. Based on an alternating optimization algorithm, the optimization of the radar signal is transformed into a series of semidefinite programming (SDP) problems using continuous convex approximation (SCA) technology. This allows for the joint design of the radar signal and receiving beamform, further improving communication security. However, since this method only considers fixed base stations and not mobile communication scenarios, it has poor applicability in mobile wireless communication scenarios such as drones, and lacks drone trajectory design and high-precision positioning of eavesdroppers.

[0005] To better apply this technology in mobile wireless communication scenarios such as drones, and to address latency issues while improving reliability, patent CN118042454A, entitled "A Physical Layer Secure Transmission Method and System in an Integrated Sensing and Communication Drone Network," employs Doppler processing to obtain sensing distance-Doppler RD data, then uses the Constant False Alarm Rate (CFAR) algorithm for target detection, and finally uses the Multi-Signal Classification (MUSIC) algorithm for angle estimation to obtain the coordinates of obstacles and eavesdroppers for secure trajectory planning. It models the secure communication process between the drone and ground users, and models constraints on drone communication performance, sensing beammap, and transmit power. It establishes a secure communication beamforming optimization objective and uses a semi-definite optimization algorithm based on the Tinkerbach algorithm to solve the established optimization objective. This type of solution can achieve deep integration of sensing and communication sharing hardware and spectrum resources, maximizing sensing performance while ensuring drone communication performance, and assisting the drone in planning obstacle avoidance paths and optimizing secure beams based on sensing information. However, its main focus on improving drone obstacle avoidance routes and optimizing secure beams has revealed that its wireless communication quality is not entirely ideal, according to testing. Furthermore, this type of solution ignores scenarios where the eavesdropper can move, and fails to employ technology to predict the state of a moving eavesdropper and incorporate it into the optimization mathematical model. Moreover, it does not consider vertical height optimization when considering trajectory optimization.

[0006] In conclusion, for tasks requiring latency sensitivity, there is an urgent need for a new UAV trajectory optimization method that can ensure both the quality of wireless communication and the goal of secure communication in scenarios involving mobile users and mobile eavesdroppers. Summary of the Invention

[0007] To address the shortcomings of existing technologies, this invention proposes a sensor-integrated UAV trajectory and beam joint optimization method for physical layer security, which includes:

[0008] S1: Construct a model of a drone-assisted wireless communication system;

[0009] S2: A wireless communication system model based on unmanned aerial vehicles (UAVs) aims to maximize the achievable rate of secure communication. Based on constraints such as transmit power, beam matrix, flight speed, flight power, and wide beam, a joint optimization problem of UAV trajectory and beam is constructed.

[0010] S3: Decouple the joint optimization problem of UAV trajectory and beam to obtain the integrated sensing waveform sub-problem and the UAV flight trajectory sub-problem;

[0011] S4: Iteratively solve the synesthetic waveform subproblem and the UAV flight trajectory subproblem to obtain the optimal synesthetic waveform and UAV flight trajectory.

[0012] Preferred models of drone-assisted wireless communication systems include: a drone acting as a full-duplex airborne base station. A single-antenna legitimate mobile user A single-antenna ground mobile eavesdropper drones Equipped with two identical uniform planar arrays, one for transmitting radar signals and the other for receiving signals; UAV Transmitting radar signals and mobile users Conducting communication and targeting mobile eavesdroppers To interfere.

[0013] Preferably, the joint optimization problem of UAV trajectory and beam is expressed as:

[0014] ;

[0015] in, Indicates the first The achievable rate of secure communication within a time slot Represents the integrated waveform vector of the synesthesia. Represents the trajectory vector of the drone. Indicates the first Beamforming vectors for mobile users within a time slot Indicates the first Beamforming vector of a moving eavesdropper within a time slot This represents the maximum transmit power of the radar signal in each time slot. This represents the operation of finding the trace of a matrix. This indicates the rank-finding operation. Indicates the first The horizontal position of the drone within each time slot Indicates the first The horizontal position of the drone within each time slot Indicates the duration of a time slot. Indicates the first The horizontal speed of the drone within each time slot Indicates the first The horizontal speed of the drone within each time slot and These represent the maximum tolerable horizontal flight speed threshold and acceleration threshold for the drone, respectively. Indicates flight energy consumption. This represents the maximum tolerable drone flight power threshold. Indicates the first Beamforming matrix within each time slot , Indicates a mobile eavesdropper. Indicates mobile user; Indicates from arrive Antenna steering vector, and They represent the first Within a time slot arrive The azimuth departure angle and elevation departure angle, Indicates from arrive The set of values ​​for the azimuth angle departure angle coverage. Indicates from arrive The set of values ​​for the elevation angle and the departure angle. Indicates angular resolution. Represents a constant. Indicates from arrive The noise in the measured azimuth departure angle. Indicates from arrive The noise in the measured values ​​of the elevation angle and departure angle.

[0016] Preferably, the waveform problem of synesthesia integration is expressed as:

[0017] ;

[0018] in, Indicates the first The achievable rate of secure communication within a time slot Represents the integrated waveform vector of the synesthesia. Indicates the first Beamforming vectors for mobile users within a time slot Indicates the first Beamforming vector of a moving eavesdropper within a time slot This represents the maximum transmit power of the radar signal in each time slot. This represents the operation of finding the trace of a matrix. This indicates the rank-finding operation. Indicates the first Beamforming matrix within each time slot , Indicates a mobile eavesdropper. Indicates mobile user; Indicates from arrive Antenna steering vector, and They represent the first Within a time slot arrive The azimuth departure angle and elevation departure angle, Indicates from arrive The set of values ​​for the azimuth angle departure angle coverage. Indicates from arrive The set of values ​​for the elevation angle and the departure angle. Indicates angular resolution. Represents a constant. Indicates from arrive The noise in the measured azimuth departure angle. Indicates from arrive The noise in the measured values ​​of the elevation angle and departure angle.

[0019] Preferably, the UAV flight trajectory subproblem is represented as:

[0020]

[0021] in, Indicates the first The achievable rate of secure communication within a time slot Represents the trajectory vector of the drone. Indicates the first Beamforming vectors for mobile users within a time slot Indicates the first Beamforming vector of a moving eavesdropper within a time slot This represents the maximum transmit power of the radar signal in each time slot. This represents the operation of finding the trace of a matrix. This indicates the rank-finding operation. Indicates the first The horizontal position of the drone within each time slot Indicates the first The horizontal position of the drone within each time slot Indicates the duration of a time slot. Indicates the first The horizontal speed of the drone within each time slot Indicates the first The horizontal speed of the drone within each time slot and These represent the maximum tolerable horizontal flight speed threshold and acceleration threshold for the drone, respectively. Indicates flight energy consumption. This represents the maximum tolerable flight power threshold for drones.

[0022] Preferably, the iterative solution process for the synesthetic waveform subproblem and the UAV flight trajectory subproblem includes:

[0023] S41: By introducing slack variables, the synesthetic waveform subproblem is rewritten as a first convex optimization problem; by introducing auxiliary variables, the UAV flight trajectory subproblem is rewritten as a second convex optimization problem.

[0024] S42: For the current time slot, fix the current UAV flight trajectory, use the SDR optimization method and Gaussian randomization method to solve the first convex optimization problem, and obtain the new synesthetic integrated waveform;

[0025] S43: Fix the new integrated synesthesia waveform, use the convex optimization solution tool CVX to solve the second convex optimization problem, and obtain the new UAV flight trajectory;

[0026] S44: Determine whether the current secure communication reachable rate has converged. If it has converged, the output new synesthetic waveform and the new UAV flight trajectory are taken as the optimal solution for the current time slot, the next time slot is taken as the current time slot, and the process returns to step S42; otherwise, the new UAV flight trajectory is taken as the current UAV flight trajectory and the process returns to step S42.

[0027] Furthermore, the first convex optimization problem can be expressed as:

[0028]

[0029] in, Represents the integrated waveform vector of the synesthesia. Denotes the first slack variable. Indicates the first Beamforming vectors for mobile users within a time slot Indicates the first Beamforming vector of a moving eavesdropper within a time slot This represents the maximum transmit power of the radar signal in each time slot. This represents the operation of finding the trace of a matrix. This indicates the rank-finding operation. Indicates the first Beamforming matrix within each time slot , Indicates a mobile eavesdropper. Indicates mobile user; Indicates from arrive Antenna steering vector, and They represent the first Within a time slot arrive The azimuth departure angle and elevation departure angle, Indicates from arrive The set of values ​​for the azimuth angle departure angle coverage. Indicates from arrive The set of values ​​for the elevation angle and the departure angle. Indicates angular resolution. Represents a constant. Indicates from arrive The noise in the measured azimuth departure angle. Indicates from arrive The noise in the measured values ​​of elevation angle and departure angle. Represents the second slack variable. This represents the channel gain per unit distance. Indicates from arrive Antenna steering vector, and They represent from arrive The azimuth departure angle and elevation departure angle, express The noise variance at that location, Indicates the first Within each time slot and The distance between them Represents the fourth slack variable. Represents the third slack variable. Indicates from arrive Antenna steering vector, and They represent the first Within a time slot arrive The azimuth departure angle and elevation departure angle, express The noise variance at that location, Indicates the first Within each time slot and The distance between them Represents the fifth slack variable. This indicates the k-th iteration of the current time slot.

[0030] Furthermore, the second convex optimization problem can be expressed as:

[0031]

[0032] in, Denotes the first slack variable. Represents the trajectory vector of the drone. Indicates the first The horizontal position of the drone within each time slot Indicates the first The horizontal position of the drone within each time slot Indicates the duration of a time slot. Indicates the first The horizontal speed of the drone within each time slot Indicates the first The horizontal speed of the drone within each time slot and These represent the maximum tolerable horizontal flight speed threshold and acceleration threshold for the drone, respectively. Indicates the first The first auxiliary variable obtained by the UAV within each time slot and These are the blade shape power and induced power of the drone in hovering state, respectively. This indicates the tip velocity of the rotor blades; , , and These are the drone's airframe drag ratio, air density, rotor robustness, and rotor disk area, respectively. This represents the maximum tolerable drone flight power threshold. This is expressed as the average induced velocity of the rotor during hovering. Indicates the first The distance between the drone and the mobile user within each time slot This indicates the noise received by the user. Indicates the first The second auxiliary variable within each time slot, Indicates the first The third auxiliary variable within each time slot This indicates the k-th iteration of the current time slot. , and These represent the first, second, and third intermediate variables, respectively.

[0033] The beneficial effects of this invention are as follows:

[0034] This invention targets scenarios where the trajectories of mobile users and mobile eavesdroppers are unknown to UAVs, requiring latency-sensitive tasks. With the goal of maximizing the achievable rate of secure communication, it optimizes the design of integrated sensing waveforms and UAV trajectories. The UAV utilizes extended Kalman filtering technology to predict the state of the user and eavesdropper in the next time slot. Based on the predicted state, it designs beams to communicate with the user, intervenes in the eavesdropping, and simultaneously optimizes its own trajectory to achieve the best overall system communication quality. This invention considers scenarios where eavesdroppers can move, fully leveraging the flexible deployment capabilities of UAVs. By employing integrated communication and sensing combined with extended Kalman filtering, waveform analysis, and UAV trajectory design, it ensures both communication security and wireless communication quality, demonstrating promising application prospects. Attached Figure Description

[0035] Figure 1 This is a flowchart of the sensor-integrated UAV trajectory and beam joint optimization method for physical layer security in this invention;

[0036] Figure 2 This is a schematic diagram of the unmanned aerial vehicle-assisted wireless communication system model in this invention;

[0037] Figure 3 This is a test diagram of the EKF model in this invention. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] To address latency-sensitive tasks and ensure secure communication in scenarios involving mobile users and mobile eavesdroppers, this invention proposes a sensor-integrated UAV trajectory and beam joint optimization method for physical layer security. This method aims to maximize secure communication rate by dynamically planning and designing the sensor-integrated waveform and the UAV trajectory. The method includes the following:

[0040] This invention first constructs a system model, including a communication model and a sensing model. Then, it proposes an optimization problem model, optimizing each time slot sequentially and using the BCD method to decouple the original optimization problem into subproblems concerning the integrated sensing waveform and the UAV flight trajectory. Next, a convex approximation is performed on each non-convex subproblem. Finally, an iterative algorithm is used to find the global suboptimal solution to the entire optimization problem in this time slot, namely the optimal integrated sensing waveform and the UAV flight trajectory.

[0041] This invention is mainly applied to UAV-assisted wireless communication scenarios. Specifically, this invention combines the flexibility and maneuverability of UAVs with the ability of EKF (Electronic Keyframe Detection) to predict the location of moving targets. The UAV transmits radar signals to communicate with the user and interfere with eavesdroppers. At the same time, the UAV uses the received radar echo signals combined with EKF to predict the trajectories of the user and the eavesdropper, thus constructing a UAV-assisted, integrated communication and sensing system. Through theoretical derivation and simulation verification, the integrated communication and sensing waveform and UAV flight trajectory are designed to maximize the secure communication rate.

[0042] The general steps are as follows: First, based on the fundamental theories of wireless communication and physical layer security, a UAV-assisted wireless communication system model is constructed. Then, the mathematical derivation and problem-solving analysis in the model building process are refined. Addressing the non-convexity and high coupling of the optimization problem corresponding to this system model, an approximate fitting method based on the Block Coordinate Descent (BCD) algorithm and continuous convex approximation is used to decouple and transform the original optimization problem, obtaining two sub-problems. Finally, based on the iterative approach, when optimizing each time slot, the obtained sub-problems are iteratively applied to continuously approach a constant value for the secure communication rate. This constant value is the maximum communication rate required by this invention. Figure 1 As shown, the specific steps are as follows:

[0043] S1: Construct a model of a drone-assisted wireless communication system.

[0044] Drone B is set as an aerial base station, with its initial position and speed set to serve a single mobile user on the ground, while also considering the presence of a potential mobile eavesdropper E. To ensure the security of information transmission, the drone emits radar waves to sense and predict E while simultaneously jamming it, thus achieving secure communication. Specifically:

[0045] like Figure 2 As shown, the wireless communication system model constructed in this invention includes a full-duplex airborne base station ( It is equipped with two identical uniform planar arrays (UPAs), one for transmitting radar signals and the other for receiving signals. Each array contains... There are 1 antenna element, of which and They represent along shaft and The number of antenna elements arranged side-by-side on an axis, and the number of legal mobile users with a single antenna ( ), and a single-antenna ground mobile eavesdropper ( ), which attempted to intercept from The confidential signal. To ensure the processability of the analysis, The total flight time T is discretized into N time slots, and the duration of each time slot is... . and Moving on the ground along a specific trajectory, its coordinates are represented as follows: and Its speed is expressed as and Assuming Not available and The trajectory information. In the time slot. Inside, It obtains its own position through built-in sensors or an inertial navigation system (INS). and height . In the direction While sending downlink communication signals to achieve data transmission, the signal is also used to... To make predictions and track progress; in addition, It also actively transmits sensing signals to estimate The location, and thereby to To carry out interference.

[0046] In the Within each time slot, The downlink transmission signal can be represented as:

[0047]

[0048] in, Indicates sending to Information signals; This is artificial noise (AN) used for interference. Vector and They are the first Within each time slot Precoded vectors designed with artificial noise.

[0049] Assumption right and The link is a line-of-sight (LoS) channel, from arrive The channel coefficients are expressed as:

[0050]

[0051] in, This represents the path loss per unit distance. express and The distance between them. Angle. and They represent from arrive The azimuth departure angle (AOD) and elevation departure angle, From arrive The turning vector of the transmitting antenna, Indicates antenna spacing. Indicates wavelength.

[0052] Assumption Perfect time and frequency synchronization has been achieved. The received signal can be represented as:

[0053]

[0054] in, express Additive white Gaussian noise (AWGN) at the location. for The noise variance at that location.

[0055] The signal-to-interference-plus-noise ratio (SINR) of the received downlink signal can be expressed as:

[0056]

[0057] The achievable rate can be expressed as:

[0058]

[0059] from arrive The channel coefficients are expressed as:

[0060]

[0061] in, express and Distance and angle between and They represent from arrive The azimuth departure angle and elevation departure angle.

[0062] Similarly, suppose Perfect time and frequency synchronization has been achieved. The received signal can be represented as:

[0063]

[0064] in, This represents additive white Gaussian noise at point E. for The noise variance at that location.

[0065] The received signal-to-interference-plus-noise ratio can be expressed as:

[0066]

[0067] The achievable rate is expressed as:

[0068]

[0069] The secure rate, or the achievable rate for secure communication, is expressed as:

[0070]

[0071] The optimization problem in this invention is related to and All information is predicted using the Extended Kalman Filter (EKF) technique, and the specific implementation steps are as follows:

[0072] As the number of antennas increases, the steering vectors corresponding to different directions exhibit asymptotic orthogonality, a characteristic that typically effectively suppresses mutual interference between reflected echoes. If the target spacing is small, making the aforementioned asymptotic orthogonality insufficient to completely suppress interference, digital beamforming techniques can be further employed to reduce interference between echoes. Based on the above analysis, Directional phase reception echo It can be represented as:

[0073]

[0074] in, , Indicates the target reflectance coefficient. In this study, the radar cross section is assumed to be constant. and These represent the Doppler frequency shift and time delay of the sensed signal, respectively. This represents the turning vector of the receiving antenna. express Additive white Gaussian noise (AWGN) is present at this location. It should be noted that clutter reflected from other scatterers in the environment is ignored here—because such clutter has a unique reflection angle and Doppler frequency compared to the target echo, existing clutter suppression techniques can effectively suppress it.

[0075] The signal-to-noise ratio of the final radar echo signal can be described as follows:

[0076]

[0077] in, This represents the gain of the matched filter.

[0078] Using a matched filter, peak detection can be used to determine... , , and The values ​​represent the Doppler frequency shift, time delay, and frequency response of the echo signal, respectively. and The expressions for the azimuth and elevation angles are:

[0079]

[0080] The measurement model describes the relationship between observable target parameters and the hidden state, and is the core means of inferring the target state. Specifically, based on the positional relationship between the UAV and the target, the relevant measurement model can be described as follows:

[0081]

[0082] in, For carrier frequency, At the speed of light, , , and These represent a mean of zero and variances of zero, respectively. , , and Gaussian measurement noise. The variance of the measurement noise is inversely proportional to the echo signal-to-noise ratio, and can be expressed as... , , and ,in, It is a constant, and its characteristics are determined by the system configuration and the signal processing algorithm used. Furthermore, when... and When the value is small, it can be approximated by trigonometric identities. and .

[0083] To achieve accurate tracking, in addition to the measurement model, a suitable state evolution model for the target is also needed. Under the assumption of uniform motion, the state evolution of the target can be expressed as:

[0084]

[0085] in, , , and They represent State prediction noise in the x and y directions of displacement and The state prediction noise for velocities in the x and y directions is assumed to follow a zero-mean Gaussian distribution with variances of [missing information]. , , and .

[0086] To achieve local linearization of the nonlinear measurement model and the state evolution model, the established EKF model can be concisely rewritten as follows:

[0087]

[0088] in, and These represent the target state vector and the measurement vector, respectively. and Defined by the state transition equation and the measurement equation respectively; noise vector and Independent of and And they follow a zero-mean Gaussian distribution, with their covariance matrices being respectively and .

[0089] and The expression for the Jacobian matrix is ​​as follows:

[0090]

[0091]

[0092] in,

[0093] The process of state prediction and tracking can be summarized as follows:

[0094] Based on the state transition matrix, the expression for the prior prediction state is:

[0095]

[0096] By linearizing the state equations (measurement model) and observation equations (state evolution model), the expressions for the state transition Jacobian matrix and the measurement Jacobian matrix can be obtained as follows:

[0097]

[0098]

[0099] The covariance matrix of the posterior mean square error is expressed as follows:

[0100]

[0101] The expression for Kalman gain is as follows:

[0102]

[0103] The expression for the posterior state is as follows:

[0104]

[0105] like Figure 3 As shown in the figure, the actual trajectory and predicted trajectory of the user and the eavesdropper are compared, and it can be seen that the EKF filter has good convergence.

[0106] S2: A wireless communication system model based on unmanned aerial vehicles (UAVs) is proposed. With the optimization objective of maximizing the achievable rate of secure communication, a joint optimization problem of UAV trajectory and beam is constructed based on constraints of transmit power, beam matrix, flight speed, flight power, and wide beam.

[0107] To optimize the uplink achievable rate, we optimize beamforming and UAV flight trajectory, constructing a joint optimization problem of UAV trajectory and beamforming, which is expressed as:

[0108] ;

[0109] in, Represents the trajectory vector of the drone. Represents the integrated waveform vector of the synesthesia. This represents the maximum transmit power of the radar signal in each time slot. and These are the maximum tolerable values. Horizontal flight speed threshold and acceleration threshold It is the maximum tolerable drone flight power threshold. for Horizontal position, for The horizontal velocity, Tr represents the operation of finding the trace of a matrix. This indicates the rank-finding operation. Denotes the beamforming matrix, where , Indicates flight energy consumption. Indicates the duration of a time slot. Indicates from arrive The turning vector and angle of the transmitting antenna. and They represent from arrive azimuth departure angle and elevation departure angle, and Indicates the previous time slot from arrive Angle measurement noise, , They represent from arrive The set of coverage values ​​for azimuth and departure angles, from arrive The set of values ​​for the coverage of the elevation angle and departure angle satisfies the condition. , of arrive Angle set, For angular resolution, The value of this constant is usually 3.

[0110] Where C1 is the maximum transmit power constraint, i.e., the transmit power constraint; C2 and C3 are beam matrix constraints, where C2 is a positive semi-definite constraint on the beam matrix, and C3 is a rank-one constraint on the beam matrix; C4-C6 are... C7 is the flight speed constraint for B, C8 is the flight power constraint for B, and C8 is the wide beam constraint.

[0111] S3: Decouple the joint optimization problem of UAV trajectory and beam to obtain the integrated sensing waveform sub-problem and the UAV flight trajectory sub-problem.

[0112] Based on the Block Coordinate Descent (BCD) algorithm The problem is decoupled to obtain subproblems. , As shown below:

[0113]

[0114]

[0115] S4: Iteratively solve the synesthetic waveform subproblem and the UAV flight trajectory subproblem to obtain the optimal synesthetic waveform and UAV flight trajectory.

[0116] S41: By introducing slack variables, the synesthetic waveform subproblem is rewritten as a first convex optimization problem; by introducing auxiliary variables, the UAV flight trajectory subproblem is rewritten as a second convex optimization problem.

[0117] Regarding the sub-problems By introducing the first to fifth slack variables , , , and The synesthetic waveform problem can be rewritten as a first convex optimization problem:

[0118]

[0119] in, for right Steering vector, angle and They represent from arrive The azimuth departure angle and elevation departure angle, for right Steering vector, angle and They represent from arrive The azimuth departure angle and elevation departure angle, for The variance of the received noise, From arrive distance, for The variance of the received noise, From arrive distance, This represents the path loss per unit distance. This indicates the k-th iteration of the current time slot.

[0120] Regarding the sub-problems The following first, second, and third auxiliary variables are introduced: , and They respectively satisfy:

[0121]

[0122]

[0123]

[0124] in Indicates the reference distance Path loss at a distance of meters; The average induced velocity of the rotor during hovering.

[0125] Rewritten using Continuous Convex Approximation (SCA):

[0126]

[0127] in, express The position obtained in the k-th iteration. express The horizontal velocity obtained in the k-th iteration express The first auxiliary variable obtained in the k-th iteration.

[0128] in, Defined as height, This represents the second auxiliary variable obtained in the k-th iteration. (Steering vector) and The arrival and departure angles involved are obtained from the previous iteration. Location Approximate calculation.

[0129] For other non-convex constraints, the same method is used to obtain:

[0130]

[0131] in, express The third auxiliary variable obtained in the k-th iteration. Intermediate variable. ~ They respectively satisfy:

[0132]

[0133]

[0134]

[0135] Based on the above transformation, a new optimization problem is obtained, namely the second convex optimization problem, which is expressed as:

[0136]

[0137] in, and They are respectively Airfoil power and induced power in hovering state This indicates the tip velocity of the rotor blades; , , and These are the fuselage drag ratio, air density, rotor robustness, and rotor disk area, respectively.

[0138] S42: For the current time slot, fix the current UAV flight trajectory, use the SDR optimization method and Gaussian randomization method to solve the first convex optimization problem, and obtain the next integrated sensing waveform.

[0139] When the rank-one constraint C4 is ignored, the entire convex optimization problem is an SDP (semi-positive definite programming) problem, which can be solved using the SDR optimization method. Then, Gaussian randomization is used to process this non-rank-one solution to obtain an approximate solution that satisfies the rank-one condition, thus obtaining the new synesthetic integrated waveform.

[0140] S43: Fix the new integrated synesthetic waveform, use the convex optimization tool CVX to solve the second convex optimization problem, and obtain the new UAV flight trajectory.

[0141] question It is a standard convex optimization problem. By using the convex optimization solution tool CVX, the flight trajectory of the new UAV can be obtained.

[0142] S44: Determine whether the current secure communication reachable rate has converged. If it has converged, the output new integrated sensing waveform and the new UAV flight trajectory are used as the optimal solution for the current time slot. The next time slot is used as the current time slot and the process returns to step S42 to perform iterative optimization for the next time slot. Otherwise, the new UAV flight trajectory is used as the current UAV flight trajectory and the process returns to step S42 to perform the next iterative optimization for the current time slot.

[0143] This invention utilizes an iterative algorithm to obtain the integrated synesthetic waveform, the horizontal flight trajectory of the UAV, and the vertical flight trajectory of the UAV, in order to find the optimal integrated synesthetic waveform and UAV flight trajectory for the optimization problem. The steps of the iterative algorithm are shown in Table 1.

[0144] Table 1 Iterative Algorithm

[0145]

[0146] In summary, this invention addresses scenarios where the trajectories of mobile users and mobile eavesdroppers are unknown to UAVs, requiring latency-sensitive tasks. With the goal of maximizing the achievable rate of secure communication, it optimizes the design of integrated sensing waveforms and UAV trajectories. The UAV utilizes extended Kalman filtering technology to predict the state of the user and eavesdropper in the next time slot. Based on the predicted state, it designs beams to communicate with the user, intervenes in the eavesdropping, and simultaneously optimizes its own trajectory to achieve the best overall system communication quality. This invention considers scenarios where eavesdroppers can move, fully leveraging the flexible deployment capabilities of UAVs. By employing integrated communication and sensing combined with extended Kalman filtering, waveform analysis, and UAV trajectory design, it ensures both communication security and wireless communication quality, demonstrating high innovation and uniqueness.

[0147] The above-described embodiments further illustrate the purpose, technical solution, and advantages of the present invention. It should be understood that the above-described embodiments are merely preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made to the present invention within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A sensor-integrated UAV trajectory and beam joint optimization method for physical layer security, characterized in that, include: S1: Construct a model of a drone-assisted wireless communication system; S2: A wireless communication system model based on unmanned aerial vehicles (UAVs) aims to maximize the achievable rate of secure communication. Based on constraints such as transmit power, beam matrix, flight speed, flight power, and wide beam, a joint optimization problem of UAV trajectory and beam is constructed. S3: Decouple the joint optimization problem of UAV trajectory and beam to obtain the integrated sensing waveform sub-problem and the UAV flight trajectory sub-problem; S4: Iteratively solve the synesthetic waveform subproblem and the UAV flight trajectory subproblem to obtain the optimal synesthetic waveform and UAV flight trajectory.

2. The sensor-integrated UAV trajectory and beam joint optimization method for physical layer security as described in claim 1, characterized in that, The drone-assisted wireless communication system model includes: a drone acting as a full-duplex airborne base station. A single-antenna legitimate mobile user A single-antenna ground mobile eavesdropper drones Equipped with two identical uniform planar arrays, one for transmitting radar signals and the other for receiving signals; UAV Transmitting radar signals and mobile users Conducting communication and targeting mobile eavesdroppers To interfere.

3. The sensor-integrated UAV trajectory and beam joint optimization method for physical layer security according to claim 1, characterized in that, The joint optimization problem of UAV trajectory and beam is expressed as: ； in, Indicates the first The achievable rate of secure communication within a time slot Represents the integrated waveform vector of the synesthesia. Represents the trajectory vector of the drone. Indicates the first Beamforming vectors for mobile users within a time slot Indicates the first Beamforming vector of a moving eavesdropper within a time slot This represents the maximum transmit power of the radar signal in each time slot. This represents the operation of finding the trace of a matrix. This indicates the rank-finding operation. Indicates the first The horizontal position of the drone within each time slot Indicates the first The horizontal position of the drone within each time slot Indicates the duration of a time slot. Indicates the first The horizontal speed of the drone within each time slot Indicates the first The horizontal speed of the drone within each time slot and These represent the maximum tolerable horizontal flight speed threshold and acceleration threshold for the drone, respectively. Indicates flight energy consumption. This represents the maximum tolerable drone flight power threshold. Indicates the first Beamforming matrix within each time slot , Indicates a mobile eavesdropper. Indicates mobile user; Indicates from arrive Antenna steering vector, and They represent the first Within a time slot arrive The azimuth departure angle and elevation departure angle, Indicates from arrive The set of values ​​for the azimuth angle departure angle coverage. Indicates from arrive The set of values ​​for the elevation angle and the departure angle. Indicates angular resolution. Represents a constant. Indicates from arrive The noise in the measured azimuth departure angle. Indicates from arrive The noise in the measured values ​​of the elevation angle and departure angle.

4. The sensor-integrated UAV trajectory and beam joint optimization method for physical layer security according to claim 1, characterized in that, The integrated synesthetic waveform subproblem is expressed as: ； in, Indicates the first The achievable rate of secure communication within a time slot Represents the integrated waveform vector of the synesthesia. Indicates the first Beamforming vectors for mobile users within a time slot Indicates the first Beamforming vector of a moving eavesdropper within a time slot This represents the maximum transmit power of the radar signal in each time slot. This represents the operation of finding the trace of a matrix. This indicates the rank-finding operation. Indicates the first Beamforming matrix within each time slot , Indicates a mobile eavesdropper. Indicates mobile user; Indicates from arrive Antenna steering vector, and They represent the first Within a time slot arrive The azimuth departure angle and elevation departure angle, Indicates from arrive The set of values ​​for the azimuth angle departure angle coverage. Indicates from arrive The set of values ​​for the elevation angle and the departure angle. Indicates angular resolution. Represents a constant. Indicates from arrive The noise in the measured azimuth departure angle. Indicates from arrive The noise in the measured values ​​of the elevation angle and departure angle.

5. The sensor-integrated UAV trajectory and beam joint optimization method for physical layer security according to claim 1, characterized in that, The subproblem of the drone's flight trajectory is represented as follows: ； in, Indicates the first The achievable rate of secure communication within a time slot Represents the trajectory vector of the drone. Indicates the first Beamforming vectors for mobile users within a time slot Indicates the first Beamforming vector of a moving eavesdropper within a time slot This represents the maximum transmit power of the radar signal in each time slot. This represents the operation of finding the trace of a matrix. This indicates the rank-finding operation. Indicates the first The horizontal position of the drone within each time slot Indicates the first The horizontal position of the drone within each time slot Indicates the duration of a time slot. Indicates the first The horizontal speed of the drone within each time slot Indicates the first The horizontal speed of the drone within each time slot and These represent the maximum tolerable horizontal flight speed threshold and acceleration threshold for the drone, respectively. Indicates flight energy consumption. This represents the maximum tolerable flight power threshold for drones.

6. The sensor-integrated UAV trajectory and beam joint optimization method for physical layer security according to claim 1, characterized in that, The iterative solution process for the synesthetic waveform subproblem and the UAV flight trajectory subproblem includes: S41: By introducing slack variables, the synesthetic waveform subproblem is rewritten as a first convex optimization problem; by introducing auxiliary variables, the UAV flight trajectory subproblem is rewritten as a second convex optimization problem. S42: For the current time slot, fix the current UAV flight trajectory, use the SDR optimization method and Gaussian randomization method to solve the first convex optimization problem, and obtain the new synesthetic integrated waveform; S43: Fix the new integrated synesthesia waveform, use the convex optimization solution tool CVX to solve the second convex optimization problem, and obtain the new UAV flight trajectory; S44: Determine whether the current secure communication reachable rate has converged. If it has converged, the output new synesthetic waveform and the new UAV flight trajectory are taken as the optimal solution for the current time slot, the next time slot is taken as the current time slot, and the process returns to step S42; otherwise, the new UAV flight trajectory is taken as the current UAV flight trajectory and the process returns to step S42.

7. The sensor-integrated UAV trajectory and beam joint optimization method for physical layer security according to claim 6, characterized in that, The first convex optimization problem is expressed as: ； in, Represents the integrated waveform vector of the synesthesia. Denotes the first slack variable. Indicates the first Beamforming vectors for mobile users within a time slot Indicates the first Beamforming vector of a moving eavesdropper within a time slot This represents the maximum transmit power of the radar signal in each time slot. This represents the operation of finding the trace of a matrix. This indicates the rank-finding operation. Indicates the first Beamforming matrix within each time slot , Indicates a mobile eavesdropper. Indicates mobile user; Indicates from arrive Antenna steering vector, and They represent the first Within a time slot arrive The azimuth departure angle and elevation departure angle, Indicates from arrive The set of values ​​for the azimuth angle departure angle coverage. Indicates from arrive The set of values ​​for the elevation angle and the departure angle. Indicates angular resolution. Represents a constant. Indicates from arrive The noise in the measured azimuth departure angle. Indicates from arrive The noise in the measured values ​​of elevation angle and departure angle. Represents the second slack variable. This represents the channel gain per unit distance. Indicates from arrive Antenna steering vector, and They represent from arrive The azimuth departure angle and elevation departure angle, express The noise variance at that location Indicates the first Within each time slot and The distance between them Represents the fourth slack variable. Represents the third slack variable. Indicates from arrive Antenna steering vector, and They represent the first Within a time slot arrive The azimuth departure angle and elevation departure angle, express The noise variance at that location Indicates the first Within each time slot and The distance between them This represents the fifth slack variable. This indicates the k-th iteration of the current time slot.

8. The sensor-integrated UAV trajectory and beam joint optimization method for physical layer security according to claim 6, characterized in that, The second convex optimization problem is expressed as: ； in, Denotes the first slack variable. Represents the trajectory vector of the drone. Indicates the first The horizontal position of the drone within each time slot Indicates the first The horizontal position of the drone within each time slot Indicates the duration of a time slot. Indicates the first The horizontal speed of the drone within each time slot Indicates the first The horizontal speed of the drone within each time slot and These represent the maximum tolerable horizontal flight speed threshold and acceleration threshold for the drone, respectively. Indicates the first The first auxiliary variable obtained by the UAV within each time slot and These are the blade shape power and induced power of the drone in hovering state, respectively. This indicates the tip velocity of the rotor blades; , , and These are the drone's airframe drag ratio, air density, rotor robustness, and rotor disk area, respectively. This represents the maximum tolerable drone flight power threshold. This is expressed as the average induced velocity of the rotor during hovering. Indicates the first The distance between the drone and the mobile user within each time slot This indicates the noise received by the user. Indicates the first The second auxiliary variable within each time slot, Indicates the first The third auxiliary variable within each time slot This indicates the k-th iteration of the current time slot. , and These represent the first, second, and third intermediate variables, respectively.

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