Design method for realizing safety communication by combining communication and inductance integration with EKF waveform and unmanned aerial vehicle trajectory

Abstract

The invention discloses a waveform and unmanned aerial vehicle trajectory design method combining communication and inductance integration with an EKF (Extended Kalman Filter) for realizing secure communication, which is used for carrying out optimization design on the waveform and the unmanned aerial vehicle trajectory of the communication and inductance integration by taking maximization of the achievable rate of uplink communication as a target. According to the method, an optimization problem conforming to a scene is firstly constructed, then an original optimization problem of each time slot is decoupled into sub-problems about a same-inductance integrated waveform and a UAV flight path based on a BCD method, convex approximate fitting is carried out on each non-convex sub-problem, and finally, an iterative algorithm is adopted for solving, so that the algorithm is optimized. And finding a global suboptimal solution of the optimization problem, an optimal sensing integrated waveform and a UAV flight trajectory. The method mainly aims at mobile user and mobile eavesdropper scenes, communication perception integration is combined with extended Kalman filtering, waveform and unmanned aerial vehicle trajectory for design, the quality of wireless communication is ensured while communication safety is achieved, and the method has high innovativeness and uniqueness.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of communication and sensing integration, in particular to a method for realizing secure communication by combining EKF waveform and UAV trajectory design in communication and sensing integration. BACKGROUND

[0002] The statements in this section merely provide background information related to the present disclosure and can constitute the prior art. During the implementation of the present application, the inventors found at least the following problems in the prior art.

[0003] Wireless sensing performance is an important development direction of future 6G, and communication technology and sensing technology gradually move towards integration. EKF is a classic technology to predict the position of a moving target. Unmanned aerial vehicles (UAVs) are core nodes of future mobile communication networks, have a wide range of application forms and application prospects, and are attracting attention from all walks of life.

[0004] In the literature [J. Wu, W. Yuan, and L. Hanzo, "When UAVs meet ISAC: Real-Time trajectory design for secure communications," IEEE Transactions on Vehicular Technology, vol. 72, no. 12, pp. 16766-16771], it is proposed to use EKF to predict the state information of a legitimate mobile user, and to optimize the trajectory of the UAV using the predicted position information to maximize the throughput of the system. Compared with the model of setting a ground fixed user node in the past, the breakthrough of user target movement is realized.

[0005] In the literature [X. Pang, S. Guo, J. Tang, N. Zhao, and N. Al-Dhahir, "Dynamic ISAC beamforming design for UAV-Enabled vehicular networks," IEEE Transactions on Wireless Communications, vol. 23, no. 11, pp. 16852.], it is proposed that the UAV carries a ULA to sense the target, and a beamforming technology is newly added to further improve the throughput of the system.

[0006] In [W. Mao, Y. Lu, G. Pan, and B. Ai, "UAV-Assisted communications in SAGIN-ISAC: Mobile user tracking and robust beamforming," IEEE Journal on Selected Areas in Communications, vol. 43, no. 1, pp. 186-200, 2025.], it is further proposed that the unmanned aerial vehicle carries a planar array antenna (UPA) to perceive the target, which realizes the breakthrough of users moving arbitrarily on the ground under the mobile base station, and is not limited to straight-line movement.

[0007] However, the applicant found that the above solutions have the following problems:

[0008] 1. The problem of safe transmission is not considered in the scenario of unmanned aerial vehicle communication.

[0009] 2. Some documents do not consider trajectory optimization in the unmanned aerial vehicle communication system.

[0010] 3. In the scenario considering trajectory optimization, the optimization of vertical height is not considered.

[0011] In order to solve the problem of safe transmission, especially in the presence of mobile eavesdroppers, the patent with publication number CN114584235B and the patent name "Uplink communication security method for mobile aerial eavesdroppers based on perception" discloses an uplink communication security method for mobile aerial eavesdroppers based on perception. By establishing a communication and perception integrated model, in view of the characteristics of flexible and high mobility of mobile aerial eavesdroppers, the radar signal and the receiving beamformer are jointly designed and iteratively optimized, and the optimization between interference AE and user communication is balanced; under the condition of ensuring the communication between the base station BS and the user, the trajectory of the mobile AE and the channel state information CSI between the base station and the AE are predicted by using the extended Kalman filter method, the AE is accurately tracked, the accurate CSI between the base station and the AE is obtained in real time, the interference ability of the radar signal to the AE is further enhanced, and the confidentiality of reliable communication is improved; based on the alternating optimization algorithm, the optimization of the radar signal is converted into a series of semi-definite programming SDP problems by using the successive convex approximation SCA technology, and the radar signal and the receiving beam are jointly designed, and the communication confidentiality is further improved. However, since this method only considers fixed base stations and does not consider mobile communication scenarios, it has poor applicability in mobile wireless communication scenarios such as unmanned aerial vehicles, and does not design the trajectory of the unmanned aerial vehicle or accurately locate the eavesdropper.

[0012] In order to better apply in mobile wireless communication scenarios such as unmanned aerial vehicles, while improving reliability, the problem of solving the delay, the patent with the patent name "a physical layer security transmission method and system in a sensing integrated unmanned aerial vehicle network" with the publication number CN118042454A is adopted. Doppler processing is used to obtain sensing distance-doppler RD data, and then constant false alarm rate detection algorithm CFAR is used for target detection, and finally multiple signal classification MUSIC algorithm is used for angle estimation to obtain the coordinates of obstacles and eavesdroppers for safe trajectory planning. The secure communication process between the unmanned aerial vehicle and the ground user is modeled; the unmanned aerial vehicle communication performance constraint, sensing beam pattern constraint and transmit power constraint are modeled; the secure communication beam forming optimization target is established; and the semi-positive optimization algorithm based on the Dingkelbach algorithm is used to solve the established optimization target. This kind of scheme can realize the deep integration of sensing and communication sharing hardware and spectrum resources, maximize the sensing performance while ensuring the communication performance of the unmanned aerial vehicle, and assist the unmanned aerial vehicle in planning the obstacle avoidance path and optimizing the secure beam based on the sensing information. However, the improvement focus of this scheme is mainly on the planning of the obstacle avoidance route and the optimization of the secure beam of the unmanned aerial vehicle. The applicant found that the quality of wireless communication is not very ideal. Moreover, this kind of scheme ignores the scene that the eavesdropper can move, does not use technology to predict the state of the moving eavesdropper and include it in the optimization mathematical model. And when considering trajectory optimization, it does not consider the optimization of vertical height.

[0013] In the face of the need to handle time-sensitive tasks, how to ensure the quality of wireless communication while achieving the goal of secure communication in the scene of mobile users and mobile eavesdroppers is a problem that needs to be solved by this patent. SUMMARY

[0014] In view of the above problems, the purpose of the present application is to solve some problems in the prior art, or at least alleviate these problems.

[0015] A sensing integrated EKF waveform and unmanned aerial vehicle trajectory design method for realizing secure communication, comprising the following steps:

[0016] Constructing a communication system model: setting the unmanned aerial vehicle B as an air base station, setting the initial position and initial speed, making it serve a single mobile user on the ground, and considering that there is a mobile potential eavesdropper E; B transmits radar waves to predict E while interfering, realizing secure communication;

[0017] Constructing an optimization mathematical model: taking the maximum uplink communication rate as the target, constructing an optimization mathematical model with the eavesdropping threshold, sensing integrated waveform and unmanned aerial vehicle flight trajectory as constraints;

[0018] For the optimization mathematical model, based on BCD (Block Coordinate Descent) decoupling into only about the integrated waveform of common sense, unmanned aerial vehicle horizontal flight trajectory and unmanned aerial vehicle vertical flight trajectory sub-problems;

[0019] For each non-convex sub-problem, a convex approximation fitting method is used to convert it into a convex problem for solving; wherein, when solving the non-convex problem about the integrated waveform of common sense, SDR (Semidefinite Relaxation) is used to discard the rank-one constraint to convert the non-convex problem into a convex problem, and then CVX (Convex Optimization Toolbox) is used for solving, and then the obtained solution is obtained by Gaussian randomization to satisfy the rank-one constraint solution;

[0020] The integrated waveform of common sense, the horizontal flight trajectory of unmanned aerial vehicle and the vertical flight trajectory of unmanned aerial vehicle are solved by using an iterative algorithm to find the global suboptimal solution of the optimization problem and the optimal integrated waveform of common sense and the flight trajectory of unmanned aerial vehicle.

[0021] Further, the information about E in the optimization mathematical model is predicted by EKF (Extended Kalman Filter) technology.

[0022] The optimization mathematical model is:

[0023]

[0024] Wherein is the signal-to-interference-plus-noise ratio of E, γ p is the pre-set E signal-to-interference-plus-noise ratio threshold, P max represents the maximum value of the transmission power of each time slot of the radar signal, and are the maximum tolerable B horizontal flight speed threshold and acceleration threshold, respectively, and are the maximum tolerable B vertical flight speed threshold and acceleration threshold, respectively, Z min and Z max are the minimum and maximum altitudes of the unmanned aerial vehicle flight, P hor [n] and P ver [n] are the flight power of B in the horizontal and vertical directions in the nth time slot, and are the maximum tolerable unmanned aerial vehicle flight power threshold, q B [n] is the horizontal position of B, v B,xy [n] is the horizontal speed of B, z B [n] is the vertical position of B, v z [n] is the vertical speed of B, Tr represents the operation of taking the trace of a matrix, w B is the achievable speed of B, δ t represents the duration of a time slot.

[0025] The optimization mathematical model is solved Decoupling operation is performed to obtain sub-problems As shown below:

[0026]

[0027] Wherein, Tr represents the operation of finding the trace of a matrix;

[0028]

[0029] Further, for the sub-problems Introducing auxiliary variables And the relaxation variable η, the mathematical model is:

[0030]

[0031] Wherein, P U is the power of the signal transmitted by U, is the steering vector, is the variance of the noise received by B, β[n] is the reflection coefficient of the target, h U,B [n] is the channel from U to B, is the feasible point of X w1 [n] at the kth iteration;

[0032] When the rank-one constraint C4 is ignored, the entire convex optimization problem is an SDP (semidefinite programming) problem, which can be solved by SDR optimization method, and then the non-rank-one solution is processed by Gaussian randomization to obtain an approximate solution satisfying the rank-one condition.

[0033] Further, for the sub-problems The following steps are adopted:

[0034] Introducing the following four auxiliary variables u[n], λ B [n], H[n], I[n] that meet the needs:

[0035]

[0036] Wherein is the steering vector; ε represents the complex radar cross section (RCS); ρ0 represents the path loss at the reference distance d=1 meter; v0 is the average rotor induced speed in the forward flight state;

[0037] Rewritten by SCA as:

[0038]

[0039] Wherein a=P U |h U,E [n]2 ,

[0040]

[0041] where, qk[n] denotes the position of B obtained in the kth iteration, vk[n] denotes the horizontal velocity of B obtained in the kth iteration, Ik[n] denotes the relaxation variable of B obtained in the kth iteration;

[0042]

[0043] where, z B is the flight altitude of B, q U , q E are defined as the position of U and the position of E, respectively;

[0044] The turning vector involved in the arrival angle and the departure angle are approximated by the position of B q0[n] and z0[n] obtained in the previous iteration;

[0045] To ensure the optimization accuracy, constraints are set:

[0046]

[0047] where, ε1 denotes the threshold value for controlling the similarity between q B [n] and q0[n], and ε2 denotes the threshold value for controlling the similarity between z B [n] and z0[n];

[0048] For other non-convex constraints, the same method is adopted to obtain:

[0049]

[0050] where, I (k) [n] and H (k) [n] denote the relaxation variable obtained in the kth iteration;

[0051] Based on the above transformation, a new optimization problem is obtained, which is expressed as:

[0052]

[0053] where, P0 and P i are the profile power and induced power of B in the hovering state, respectively, and U tip denotes the tip speed of the rotor blade; d0, ρ, s and A are the fuselage drag ratio, air density, rotor solidity and rotor disc area, respectively; is the variance of the noise received by E.

[0054] Further, for the sub-problem Similar processing By using SCA (successive convex approximation), the relaxation variables H, I, u are expanded at and the right side is replaced by its convex lower bound:

[0055]

[0056] Based on the above transformation, a new optimization problem is obtained, expressed as:

[0057]

[0058] where, is the variance of the noise received by E, z0[n] is the iteration value of the last vertical position, is the kth iteration value, and ε2 represents the threshold for controlling the similarity between z B [n] and z0[n].

[0059] A system for realizing secure communication by integrating EKF waveform and UAV trajectory design method, comprising the following modules:

[0060] An initialization module: set the UAV B as an air base, set the initial position and initial speed of B at the same time, make B serve a single mobile user U existing on the ground, consider that there is a potential mobile eavesdropper E, in order to ensure the security of information transmission, B transmits radar waves to realize the perception and prediction of E while interfering, and realize secure communication;

[0061] A mathematical model module, which constructs a eavesdropping threshold, and constructs an optimization mathematical model with the integrated sensing and communication waveform and the UAV flight trajectory as constraints, with the goal of maximizing the uplink communication rate;

[0062] A mathematical model decoupling module, which is used for decoupling the optimization mathematical model into sub-problems only about the integrated sensing and communication waveform, the UAV horizontal flight trajectory and the UAV vertical flight trajectory based on the BCD method, and for each non-convex sub-problem, a convex approximation fitting method is used to convert it into a convex problem for solving; wherein, when solving the non-convex problem about the integrated sensing and communication waveform, the SDR method of discarding the rank one constraint is used to convert the non-convex problem into a convex problem, and then the CVX toolbox is used for solving, and then the obtained solution is obtained by Gaussian randomization to satisfy the solution of the rank one constraint;

[0063] A sub-problem solving module, which is used for solving the integrated sensing and communication waveform, the UAV horizontal flight trajectory and the UAV vertical flight trajectory by using an iterative algorithm.

[0064] A computer readable storage medium, which stores a computer program, the computer program is executed by a processor to implement the steps of the method for designing a sensing-integrated waveform and a UAV trajectory by using an EKF.

[0065] The present application has the following advantages:

[0066] The present application is aimed at scenarios that need to handle time-delay sensitive tasks for mobile users and mobile potential eavesdroppers, and optimizes the design of sensing-integrated waveform and UAV trajectory to maximize the uplink communication rate. The UAV uses extended Kalman filtering technology to predict the state of the eavesdropper in the next time slot, designs a beam to interfere with the eavesdropper according to the predicted state, and optimizes its own trajectory to fly to the best position for the overall communication quality of the system. The present application takes into account the scenario where the eavesdropper can move, and also considers the optimization of the vertical height of the UAV when optimizing the trajectory. It fully utilizes the flexible deployment characteristics of the UAV, and uses the sensing-integrated communication to combine extended Kalman filtering, waveform and UAV trajectory design, to achieve communication security while ensuring the quality of wireless communication, and has high innovation and uniqueness. BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 The communication system model of the present application;

[0068] Figure 2 The flowchart of the operation of the present application;

[0069] Figure 3 The communication rate and eavesdropping rate diagram for each time slot;

[0070] Figure 4 The iteration convergence diagram for any time slot DETAILED DESCRIPTION

[0071] The embodiments of the present application are used to illustrate the present application but not to limit the present application. Various substitutions and modifications can be made according to the ordinary knowledge and common practices in the art without departing from the technical idea of the present application, and all such substitutions and modifications shall be included in the scope of the present application.

[0072] In order to ensure the quality of wireless communication and achieve the goal of secure communication in the scenario of mobile users and mobile eavesdroppers, the present application designs a sensing-integrated waveform and UAV trajectory design method for secure communication by using EKF, which dynamically plans and designs the sensing-integrated waveform and 3D UAV trajectory to maximize the uplink communication rate.

[0073] The present application firstly constructs a system model, including a communication model and a perception model, and then proposes an optimization problem model, optimizes each time slot in sequence, and decouples the original optimization problem into sub-problems about integrated communication and perception waveforms and UAV flight trajectories by using a BCD method. Then, each non-convex sub-problem is fitted by convex approximation, and finally, an iterative algorithm is used to solve the global suboptimal solution and the optimal integrated communication and perception waveforms and UAV flight trajectories of the entire optimization problem.

[0074] The approximate steps are as follows:

[0075] Step one, firstly, according to the basic theory of wireless communication and physical layer security, a UAV-assisted wireless communication system model is constructed.

[0076] Steps two, three and four improve the mathematical theory derivation and problem solving analysis in the model building process. In view of the non-convexity and high coupling of the optimization problem corresponding to the system model, the original optimization problem is decoupled and converted by using the Block Coordinate Descent (BCD) algorithm and the continuous convex approximation fitting method.

[0077] Step five, based on the idea of iteration, when optimizing each time slot, the sub-problems obtained in steps two, three and four are iterated in a loop, so that the uplink communication rate constantly approaches a constant value, which is the maximum communication rate required by the present application.

[0078] The present application is mainly applied to the UAV-assisted wireless communication scene. Specifically, the characteristics of flexible maneuvering of UAV are combined with the characteristics of EKF predicting the position of a mobile eavesdropper, radar signal perception prediction is used, and the eavesdropper is interfered at the same time, a UAV-assisted integrated communication and perception communication system is constructed, and through theoretical derivation and simulation verification, the integrated communication and perception waveforms and the UAV flight trajectory are designed, and the maximum safety communication rate is realized.

[0079] The specific steps are as shown in Figure 2 .

[0080] S1, construction of a communication model.

[0081] The UAV B is set as an air base station, and the initial position and initial speed are set, so as to serve a single mobile user on the ground, and a mobile potential eavesdropper E is considered. In order to ensure the safety of information transmission, the UAV transmits radar waves to interfere with E while performing perception prediction, so as to realize safe communication.

[0082] Specifically as Figure 1As shown, consider a UAV system consisting of a full-duplex UAV base station (B) equipped with multiple antennas (ULA) and a single-antenna legitimate user (U). An unauthorized ground eavesdropper (E) with a single antenna attempts to eavesdrop on confidential signals transmitted by U. For ease of processing, the entire flight period T of B is discretized into N time slots, each time slot having a duration of δ. t =T / N. In the nth time slot, the horizontal and vertical positions of B are represented by q. B [n] = [x] B [n],0] T and z B [n], where the position of U is represented by q. U [n] = [x] U [n],y U [n] T The position E is represented as q E [n] = [x] E [n],0] T Assume that B and U are unaware of E's state. B is equipped with a ULA (Ultra-Ray) for detecting and tracking E. When B receives uplink signals, it also transmits radar signals to estimate E's position. Since radar signals are typically pointed at a target, they can also be used to jam E.

[0083] Array matrix of transmitting radar signal antennas and receiving signal antennas:

[0084]

[0085]

[0086] Where d represents the spacing between antennas, and λ represents the wavelength of the transmitted signal. Indicates the antenna guidance direction, N t and N r These represent the number of transmitting and receiving antennas, respectively, and j represents the imaginary unit.

[0087] Assuming the A2G (air-to-ground) channel between U and B is a Loso (line-of-sight) link, the channel from U to B is represented as follows:

[0088]

[0089] in, ρ is the distance between B and U, and ρ0 represents the path loss at the reference distance d = 1 meter.

[0090] The signal received by B can be represented as:

[0091]

[0092] Among them, P UThe power to transmit the signal to U, s(t) represents the uplink communication signal, κ represents the matched filter gain, μ[n] represents the Doppler shift of the signal, represents the measured value of the angle between B and E. represents the beamforming vector, and tr(w[n]w H [n]) = P[n], P[n] represents the total power transmitted by B per time slot, x(t - τ[n]) represents the time-delayed radar signal, the covariance matrix of the radar signal E[xx H ] = 1, represents the reflection coefficient of the target, ε represents the complex radar cross section (RCS), and it is assumed that the radar cross section is constant, represents the noise received by B, represents the variance of the noise received by B, d B,E [n] represents the distance between B and E.

[0093] Therefore, the signal-to-noise ratio (SNR) and the signal-to-interference-and-noise ratio (SINR) of the echo signal and the uplink signal received by B are respectively:

[0094]

[0095] The achievable rate of B is represented as:

[0096] R B = log2(1 + γ B The ground-to-ground (G2G) channel between U and E is characterized by a Rayleigh fading model, represented as:

[0097]

[0098] where d U,E [n] = ||q E [n] - q U [n]|| represents the distance between U and E.

[0099] The perception channel vector from B to E is represented as:

[0100]

[0101] where, represents the distance between B and E, and a(θ[n]) represents the steering vector of the transmit antenna.

[0102] The signal received by E can be represented as:

[0103]

[0104] where, is the noise received by E, is the variance of the noise signal received by E.

[0105] The signal-to-interference-plus-noise ratio of E is expressed as:

[0106]

[0107] A state prediction model of E is established.

[0108] All information about E in the optimization problem is predicted by the extended Kalman filter (EKF) technique, and the specific implementation steps are as follows:

[0109] a) Obtain a priori predicted state

[0110]

[0111] b) Linearize the state equation and the observation equation to solve the state transition matrix G[n-1] and the observation matrix H[n]:

[0112]

[0113] c) Prediction of the covariance matrix MSE[n|n-1]:

[0114] MSE[n|n-1] = G[n-1] MSE[n-1] G H [n-1] + Q s

[0115] d) Calculate the Kalman gain KAL:

[0116] KAL[n] = MSE[n|n-1] H H [n] (H[n] MSE[n|n-1] H H [n] + Q m ) -1

[0117] e) Update of the motion parameters, obtain the posteriori predicted state to calculate the priori predicted state of the next time slot:

[0118]

[0119] f) Update of the covariance matrix MSE, obtain the posteriori covariance matrix MSE[n] by the calculated KAL, to calculate the priori MSE of the next time slot:

[0120] MSE[n] = (I - KAL[n] H[n]) MSE[n|n-1]

[0121] Beam tracking and prediction: To linearize the non-linear model locally, the target motion parameters are expressed as e = [0, d, v] T where 0, d, v are the predicted elevation angle, range between B and E, and velocity of E through the state transition matrix, and the measurement signal parameters are expressed as where τ, μ are the extracted elevation angle between B and E, and time delay and Doppler shift of radar signal through echo signal. The established model can be simply rewritten as:

[0122]

[0123] where g(.), h(.) are defined by the motion state equation and measurement equation, respectively, and the state transition noise vector η[n] = [η θ , η d , η v ] T is independent of the state transition matrix g(e[n-1]), and the measurement noise vector is independent of the measurement matrix h(e[n]), η and z are subject to zero-mean Gaussian distribution, and the covariance matrix is:

[0124]

[0125] where η θ , η d , η v and z τ , z μ are the corresponding noises, which are assumed to be subject to Gaussian distribution with zero mean, and variances and These noise sources are due to approximation calculation and other system errors, and do not include thermal noise.

[0126] The Jacobian matrix of g(.) is derived as follows:

[0127]

[0128] The Jacobian matrix of h(.) is derived as follows:

[0129]

[0130] S2, a mathematical optimization model is constructed.

[0131] The optimization objective is to maximize the achievable rate of uplink communication, and the optimization variables are beamforming, 3D trajectory of UAV, etc.

[0132] The optimization mathematical model is:

[0133]

[0134] wherein is the signal-to-interference-plus-noise ratio of E, γ p is a pre-configured signal-to-interference-plus-noise ratio threshold of E, P max represents the maximum value of the transmission power of each time slot of the radar signal, and are respectively a maximum tolerable horizontal flight speed threshold and an acceleration threshold of B, and are respectively a maximum tolerable vertical flight speed threshold and an acceleration threshold of B, Z min and Z max are the minimum and maximum altitudes of the flight of the UAV, P hor [n] and P ver [n] are the flight powers of B in the horizontal and vertical directions at the nth time slot, and are maximum tolerable UAV flight power thresholds, q B [n] is the horizontal position of B, v B,xy [n] is the horizontal speed of B, z B [n] is the vertical position of B, v z [n] is the vertical speed of B, Tr represents the operation of taking the trace of a matrix, w[n] represents a beamforming vector, R B is the achievable speed of B, δ t represents the duration of a time slot.

[0135] wherein C1 is the maximum constraint on the signal-to-noise ratio of E, C2 is the constraint on the maximum transmission power of B at each time slot, C5-C10 are the constraints on the flight speed related to B, C11 is the constraint on the flight altitude of B, and C12 and C13 are the constraints on the flight power of B.

[0136] In view of the non-convexity and high coupling of the optimization problem corresponding to the system model, an approximate fitting method based on the Block Coordinate Descent (BCD) algorithm and continuous convex approximation is used to decouple and convert the original optimization problem.

[0137] The problem of the present application will be solved according to the following steps, and the specific steps are as follows:

[0138] S3, decoupling into sub-problems.

[0139] For the optimization mathematical model, the Block Coordinate Descent (BCD) algorithm is used to decouple the problem to obtain the sub-problem as follows:

[0140]

[0141] Where Tr represents the operation of finding the trace of a matrix;

[0142]

[0143]

[0144] S4, Subproblem Transformation.

[0145] For each non-convex subproblem, a convex approximation fitting method is used to transform it into a convex problem for solution.

[0146] S41, Transformation Subproblem

[0147] Regarding the sub-problems Introducing auxiliary variables And the slack variable η, the mathematical model is:

[0148]

[0149] Among them, P U The power of the signal transmitted by U. For steering vector, Let B be the variance of the noise received, β[n] be the reflection coefficient of the target, and h be the variance of the noise received. U,B [n] represents the channel from U to B. For X w1 [n] is a feasible point in the k-th iteration;

[0150] When the rank-one constraint C4 is ignored, the entire convex optimization problem is an SDP 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.

[0151] S42, Transformation Subproblem

[0152] Regarding the sub-problems By introducing the following four auxiliary variables u[n], λ, etc., we can meet the requirements. B [n], H[n], I[n]:

[0153]

[0154]

[0155] in ε represents the steering vector; ε represents the complex radar cross section (RCS); ρ0 represents the path loss at the reference distance d = 1 meter; v0 is the average rotor induced velocity in forward flight.

[0156] All of the above are non-convex constraints, which are rewritten by SCA as follows:

[0157]

[0158] where,

[0159]

[0160] where, qk[n] denotes the position of B obtained in the kth iteration, vk[n] denotes the horizontal velocity of B obtained in the kth iteration, rk[n] denotes the relaxation variable of B obtained in the kth iteration.

[0161]

[0162] where, z B is the flight altitude of B, q U , q E are defined as the position of U and E, respectively;

[0163] The turn vector The arrival and departure angles involved in the turn vector are approximated by the position of B q0[n] and z0[n] obtained in the previous iteration.

[0164] To ensure the accuracy of optimization, constraints are set as follows:

[0165]

[0166] where, ε1 denotes the threshold value for controlling the similarity between q B [n] and q0[n], and ε2 denotes the threshold value for controlling the similarity between z B [n] and z0[n].

[0167] The same method is taken for other non-convex constraints to obtain:

[0168]

[0169] where, I (k) [n] and H (k) [n] denote the relaxation variable obtained in the kth iteration;

[0170] Based on the above transformation, a new optimization problem can be obtained, which is expressed as:

[0171]

[0172] where, P0 and P iB is the power of the airfoil and induced power in hover, respectively, U tip is the tip speed of the rotor blade; d0, p, s and A are the fuselage drag ratio, air density, rotor solidity and rotor disc area, respectively; is the variance of the noise received by E.

[0173] Problem is a standard convex optimization problem, which is solved by using the convex optimization solver CVX.

[0174] S43, convert sub-problems

[0175] For sub-problems Similar processing By using SCA to expand the relaxation variables H, I, u at and replace the right side with its convex lower bound:

[0176]

[0177] Based on the above transformation, a new optimization problem can be obtained, which is expressed as:

[0178]

[0179] wherein, is the variance of the noise received by E, z0[n] is the iterative value of the last vertical position, is the kth iterative value, and e2 represents the threshold value for controlling the similarity between z B [n] and z0[n].

[0180] Problem is a standard convex optimization problem, which is solved by using the convex optimization solver CVX.

[0181] S5, iterative solution.

[0182] The integrated sensing waveform, the horizontal flight trajectory of the UAV and the vertical flight trajectory of the UAV are solved by using the iterative algorithm, so as to find the global suboptimal solution and the optimal integrated sensing waveform and UAV flight trajectory of the optimization problem.

[0183] The iterative algorithm process is designed, and the above convex optimization problems are connected in series, and the specific steps are shown in Table 1.

[0184] Table 1

[0185]

[0186] Figure 1 is the communication system model of the application;

[0187] Figure 2is a flow chart of the iterative algorithm proposed by the present application to solve the optimization problem. The detailed process corresponds to the specific solving steps of the above optimization problem.

[0188] Figure 3 is the flow of the simulation verification based on the proposed scheme, and Figure 2 the entire flight process as shown in Figure 3 the legal end reachable rate and the eavesdropping rate change with time.

[0189] Figure 4 The simulation verifies the convergence of the random selection of a time slot optimization in the scheme, and from the simulation graph, the effectiveness of the algorithm proposed in the scheme can be seen.

[0190] A system for realizing secure communication by integrating EKF waveform and UAV trajectory design method, comprising the following modules:

[0191] An initialization module: set the UAV B as an air base station, set the initial position and initial speed of S at the same time, make it serve a single mobile user existing on the ground, and consider that there is a potential mobile eavesdropper E. In order to ensure the security of information transmission, the UAV transmits radar waves to predict and interfere with E at the same time, so as to realize secure communication;

[0192] A mathematical model module, which constructs an eavesdropping threshold, an integrated sensing waveform and a UAV flight trajectory as constraints of an optimization mathematical model with the goal of maximizing the uplink communication reachable rate;

[0193] A mathematical model decoupling module, which is used for decoupling the optimization mathematical model into sub-problems only about the integrated sensing waveform, the UAV horizontal flight trajectory and the UAV vertical flight trajectory based on the BCD method, and for each non-convex sub-problem, a convex approximation fitting method is adopted to convert it into a convex problem for solving; wherein, when solving the non-convex problem about the integrated sensing waveform, the SDR method of discarding the rank-one constraint is adopted to convert the non-convex problem into a convex problem, and then the CVX toolbox is adopted to solve it, and then the obtained solution is obtained by Gaussian randomization to satisfy the solution of the rank-one constraint;

[0194] A sub-problem solving module, which is used for solving the integrated sensing waveform, the UAV horizontal flight trajectory and the UAV vertical flight trajectory by using an iterative algorithm.

[0195] A computer readable storage medium, which stores a computer program, the computer program is executed by a processor to realize the steps of the method for realizing secure communication by integrating EKF waveform and UAV trajectory design.

[0196] The present application is aimed at mobile users and potential eavesdroppers, and the scene needs to process time delay sensitive tasks, and the uplink communication reachable rate is maximized, and the sensing integrated waveform and unmanned aerial vehicle trajectory are optimized. The unmanned aerial vehicle uses the extended Kalman filter technology to predict the state of the next time slot of the eavesdropper, and designs the beam to interfere with the eavesdropper according to the predicted state, and optimizes the trajectory flight of the unmanned aerial vehicle to make the overall communication quality of the system best. The present application uses the characteristics of flexible deployment of unmanned aerial vehicle, and sends strong radar signal to interfere with potential eavesdroppers, and realizes the goal of safe communication. It involves the combination of communication sensing integration, extended Kalman filter, waveform and unmanned aerial vehicle trajectory design, realizes the communication safety, and has high innovation and uniqueness.

Claims

1. A method for achieving secure communication by integrating sensing and EKF waveforms and UAV trajectory design, characterized in that, Includes the following steps: Construct a communication system model: Set up UAV B as an airborne base station, and set its initial position and initial speed to serve a single mobile user on the ground, while considering the existence of a potential mobile eavesdropper E; B emits radar waves to sense and predict E while simultaneously interfering with it to achieve secure communication; Constructing an optimized mathematical model: With the goal of maximizing the uplink communication achievable rate, an optimized mathematical model is constructed with constraints such as the eavesdropping threshold, the integrated sensing waveform, and the UAV flight trajectory. For the aforementioned optimized mathematical model, it is decoupled into sub-problems based on BCD (block coordinate descent method) that concern only the integrated sensing waveform, the UAV's horizontal flight trajectory, and the UAV's vertical flight trajectory. For each non-convex subproblem, a convex approximation fitting method is used to transform it into a convex problem for solution. Specifically, when solving the non-convex problem concerning the synesthetic waveform, the SDR (semi-positive definite relaxation) method with rank-one constraints is used to transform the non-convex problem into a convex problem. Then, the CVX (convex optimization toolbox) is used to solve it, and the obtained solution is then randomized through Gaussian to obtain a solution that satisfies the rank-one constraints. An iterative algorithm is used to obtain the synesthetic waveform, the horizontal flight trajectory of the UAV, and the vertical flight trajectory of the UAV, in order to find the global suboptimal solution to the optimization problem and the optimal synesthetic waveform and UAV flight trajectory.

2. The method for achieving secure communication by integrating sensing and EKF waveforms and UAV trajectory design according to claim 1, characterized in that, The information about E in the optimized mathematical model is predicted by the Extended Kalman Filter (EKF) technique.

3. The method for achieving secure communication by integrating sensing and EKF waveforms and UAV trajectory design according to claim 1 or 2, characterized in that, The optimized mathematical model is as follows: in It is the signal-to-interference-plus-noise ratio of E, γ p It is the preset E-signal-to-noise ratio threshold, P max This represents the maximum transmit power of the radar signal in each time slot. and These are the maximum tolerable B-level flight speed threshold and acceleration threshold, respectively. and These are the maximum tolerable vertical flight speed threshold B and acceleration threshold Z, respectively. min and Z max These are the minimum and maximum altitudes of the drone's flight, P hor [n] and P ver [n] represents the horizontal and vertical flight power of B in the nth time slot. and It is the maximum tolerable drone flight power threshold, q B [n] represents the horizontal position of B, v B,xy [n] represents the horizontal velocity of B, z B [n] represents the vertical position of B, v z [n] represents the vertical velocity of B, Tr represents the operation of finding the matrix trace, w[n] represents the beamforming vector, and R B δ is the achievable rate of B. t This indicates the duration of a time slot.

4. The integrated sensing and sensing method for achieving secure communication combining EKF waveforms and UAV trajectory design according to claim 3, characterized in that, The optimized mathematical model Perform decoupling operations to obtain subproblems As shown below: Where Tr represents the operation of finding the trace of a matrix; 5. The integrated sensing and sensing method for secure communication combining EKF waveforms and UAV trajectory design as described in claim 4, characterized in that, Regarding the sub-problems Introducing auxiliary variables And the slack variable η, the mathematical model is: Among them, P U The power of the signal transmitted by U. For steering vector, Let B be the variance of the noise received, β[n] be the reflection coefficient of the target, and h be the variance of the noise received. U,B [n] represents the channel from U to B. For X w1 [n] is a feasible point in the k-th iteration; 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.

6. The integrated sensing and sensing method for achieving secure communication combining EKF waveforms and UAV trajectory design according to claim 4, characterized in that, Regarding the sub-problems The following steps are adopted: Introduce the following four auxiliary variables u[n], λ to meet the requirements. B [n], H[n], I[n]: in ε represents the steering vector; ε represents the complex radar cross section (RCS); ρ0 represents the path loss at the reference distance d = 1 meter; v0 is the average rotor induced velocity in forward flight. Rewritten using SCA as follows: Where a = P U |h U,E [n]| 2 , in, This represents the position obtained by B in the k-th iteration. This represents the horizontal velocity obtained by B in the k-th iteration. This represents the slack variable obtained by B in the k-th iteration; Among them, z B q is the flight altitude of B. U q E Define the positions of U and E respectively; Steering vector The arrival angle and departure angle involved are approximated by the positions q0[n] and z0[n] of B obtained in the previous iteration; To ensure optimization accuracy, the following constraints are set: Where ε1 represents the control q B The threshold for similarity between [n] and q0[n], ε2 represents the threshold used to control z B The threshold for similarity between [n] and z0[n]; For other non-convex constraints, the same method is used to obtain: Among them, I (k) [n]、H (k) [n] represents the slack variable obtained in the k-th iteration; Based on the above transformations, a new optimization problem is obtained, which can be expressed as: Among them, P0 and P i These represent the airfoil power and induced power in hovering state B, respectively, and U. tip The blade tip velocity is represented by d0, ρ, s, and A, which are the fuselage drag ratio, air density, rotor rigidity, and rotor disk area, respectively. It is the variance of the noise received by E.

7. The integrated sensing and sensing method for achieving secure communication combining EKF waveforms and UAV trajectory design according to claim 4, characterized in that, Regarding the sub-problems Similar processing By utilizing SCA (successive convex approximation), the slack variables H, I, and u are... Expand the area and replace the right side with its convex lower bound: Based on the above transformations, a new optimization problem is obtained, which can be expressed as: in, Let z0[n] be the variance of the noise received by E, and z0[n] be the iteration value of the previous vertical position. It is the value of the kth iteration, and ε2 represents the value used to control z. B The threshold for similarity between [n] and z0[n].

8. A system for achieving secure communication by integrating sensing and EKF waveforms and UAV trajectory design methods, characterized in that, Includes the following modules: Initialization module: Set up UAV B as an airborne base station, and set B's initial position and initial speed to serve a single mobile user U on the ground. At the same time, consider the existence of a potential mobile eavesdropper E. In order to ensure the security of information transmission, B emits radar waves to sense and predict E while interfering with it, so as to achieve secure communication. The mathematical model module aims to maximize the uplink communication achievable rate by constructing an optimized mathematical model with constraints such as the eavesdropping threshold, the integrated sensing waveform, and the UAV flight trajectory. The mathematical model decoupling module is used to decouple the optimized mathematical model based on the BCD method into subproblems concerning only the synesthetic waveform, the horizontal flight trajectory of the UAV, and the vertical flight trajectory of the UAV. For each non-convex subproblem, a convex approximation fitting method is used to convert it into a convex problem for solution. Specifically, when solving the non-convex problem concerning the synesthetic waveform, the SDR method, which discards the rank-one constraint, is used to convert the non-convex problem into a convex problem. Then, the CVX toolbox is used for solution, and the obtained solution is Gaussian randomized to obtain a solution that satisfies the rank-one constraint. The sub-problem solving module is used to solve the synesthetic waveform, the horizontal flight trajectory of the UAV, and the vertical flight trajectory of the UAV using iterative algorithms.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the method for designing secure communication by combining EKF waveforms and UAV trajectories with the integrated sensing of claims 1 to 7.

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