Method for designing low-altitude information acquisition and transmission integrated secure waveform assisted by super-diagonal intelligent reflecting surface

Abstract

The application provides a low-altitude pass-through-sensing integrated secret waveform design method for an ultra-diagonal intelligent reflecting surface auxiliary, and belongs to the technical field of wireless communication.The method is applied to a low-altitude unmanned aerial vehicle auxiliary pass-through-sensing integrated system, and the method comprises the following steps: S1, constructing an optimization problem of maximizing the total secret rate of the system; S2, solving the optimization problem through two-layer circulation to obtain convergent global optimal configuration parameters; S3, a base station radio frequency processing unit reconfigures a digital transmission beamformer according to the optimal configuration parameters; an unmanned aerial vehicle flight control system controls the unmanned aerial vehicle to fly and hover to a three-dimensional high-altitude position corresponding to the optimal configuration parameters; a full-connection interconnection impedance network among 64 reflecting units on a backboard of the unmanned aerial vehicle is reconstructed; and through the cooperation of the three, an aerial intelligent security link for effectively suppressing eavesdropping and maximizing the secret rate of a legal user is constructed in a physical space.The application can break through the amplitude and phase regulation bottleneck and dynamically eliminate the spatial shielding blind area.

Description

Technical Field

[0001] This invention belongs to the field of wireless communication technology, and in particular relates to a method for designing a low-altitude integrated secure waveform for super-diagonal intelligent reflector-assisted low-altitude sensing. Background Technology

[0002] With the widespread application of drones in logistics delivery, low-altitude inspection, and other fields, the low-altitude economy is booming. To ensure the safe and orderly operation of massive numbers of drones, the system must possess both highly reliable communication and high-precision sensing capabilities. Integrated communication and sensing technology, through spectrum sharing and hardware reuse mechanisms, effectively overcomes the spectrum and energy efficiency bottlenecks of traditional architectures and has become a key enabling technology supporting the low-altitude economy.

[0003] However, due to the open nature of wireless channels, low-altitude integrated sensing systems face serious risks of information leakage. Physical layer security technologies, utilizing the inherent randomness of wireless channels and employing methods such as waveform design and artificial noise injection, have become a research hotspot for ensuring secure low-altitude transmission. Although existing defense measures can improve security to some extent, in the complex low-altitude environment, signals are easily and severely blocked by obstacles such as buildings, making it difficult for ground base stations to guarantee stable and secure transmission performance.

[0004] Intelligent reflectors, by dynamically reconstructing the electromagnetic environment, construct controllable virtual line-of-sight links for the system, becoming an effective means to solve occlusion problems. Currently, mounting intelligent reflectors on UAVs to build aerial nodes with dynamic deployment capabilities has become a research trend. However, most existing research is based on the traditional diagonal intelligent reflector architecture. The reflection coefficient matrix of this architecture is a diagonal matrix, assuming that each reflection unit is isolated from each other, ignoring the coupling effect between units, thus limiting the degrees of freedom of the reflection matrix and the spatial manipulation capability.

[0005] The recently proposed superdiagonal smart reflector breaks the sparse diagonal constraint of the traditional reflection matrix by introducing a reconfigurable interconnect impedance network between elements, extending it to a full-rank off-diagonal form and thus releasing additional degrees of freedom for amplitude and phase modulation. Although the superdiagonal smart reflector shows great potential in channel reconstruction, current research is mostly focused on fixed ground deployment scenarios. In complex low-altitude economic scenarios, how to combine the highly flexible superdiagonal smart reflector with a three-dimensional maneuverable UAV, and perform joint and collaborative optimization of waveform, reflection matrix, and UAV position to solve the non-convex secure transmission problem in integrated low-altitude sensing systems, remains a pressing technical challenge. Summary of the Invention

[0006] The purpose of this invention is to provide a secure waveform design method for low-altitude integrated sensing systems assisted by super-diagonal intelligent reflectors, in order to solve the technical problems of severe obstruction and security threats in low-altitude environments, the limited degrees of freedom of traditional intelligent reflectors, and non-convex secure transmission in low-altitude integrated sensing systems.

[0007] To solve the above-mentioned technical problems, the specific technical solution of the present invention is as follows:

[0008] A method for designing secure waveforms for low-altitude integrated sensing systems assisted by super-diagonal intelligent reflectors is proposed. This method is applied to a low-altitude unmanned aerial vehicle (UAV)-assisted integrated sensing system, which includes a... An integrated base station with a single antenna, equipped with A drone with a super-diagonal intelligent reflective surface of one reflective unit. The method includes the following steps: a single-antenna legitimate user and a single-antenna potential eavesdropper;

[0009] Step S1: Under the premise of satisfying the maximum transmission power of the base station, the minimum threshold required for sensing and detection performance, the hardware constraints of the super-diagonal intelligent reflector, and the deployment area limitations of the UAV, the transmission covariance matrix of the base station's confidential information is jointly optimized. The emission covariance matrix of artificial noise The reflection coefficient matrix of the super-diagonal smart reflector and the two-dimensional horizontal coordinates of the drone To maximize the overall security rate of the system, an optimization problem is constructed;

[0010] Step S2: Solve the optimization problem using two nested loops. The inner loop updates the variables by solving the optimization problem. The process continues until the inner convergence accuracy is reached. If the convergence judgment parameter is less than or equal to the constraint tolerance threshold, it indicates that the current solution has satisfied the constraints of the optimization problem. The outer loop executes the dual ascent method and updates the Lagrange multipliers. Otherwise, it indicates that the current penalty strength is insufficient. The penalty parameter is updated to apply a larger penalty weight to the objective function to enforce the constraints. The termination condition of the outer loop is that the convergence judgment parameter is less than or equal to the constraint violation threshold.

[0011] Step S3: After solving in step S2, the convergent globally optimal configuration parameters are obtained. The base station radio frequency processing unit is based on the latest... and Its digital transmit beamformer was reconfigured; the UAV flight control system received the UAV's two-dimensional horizontal coordinates. Then, combined with the drone's flight altitude The system controls the drone to fly and hover at the corresponding three-dimensional high-altitude position; simultaneously, it transmits the calculated reflection coefficient matrix of the super-diagonal smart reflector via a control link. The signal is sent to the super-diagonal intelligent reflector, and the fully connected interconnection impedance network between the 64 reflector units on its backplane is reconstructed. Through the coordinated execution of the three, an airborne intelligent security link is constructed in physical space to effectively suppress eavesdropping and maximize the confidentiality rate of legitimate users.

[0012] Furthermore, in step S2, the inner loop uses a block successive upper bound minimization method to update the variable parameters, thus dividing the highly coupled original non-convex problem into separate optimizations of the variables. , and The problem involves solving three smaller subproblems in an alternating loop, including the following steps:

[0013] Step S21: Update the emission covariance matrix of confidential information and artificial noise. ;

[0014] Step S22: Update the reflection coefficient matrix of the super-diagonal smart reflector. ;

[0015] Step S23: Update the UAV's two-dimensional horizontal coordinates .

[0016] Furthermore, in step S21, given the reflection coefficient matrix of the superdiagonal smart reflective surface... Two-dimensional horizontal coordinates of the drone Under the premise of optimization At that time, a linear compact convex substitution function is constructed, and a convex optimization problem is constructed based on the linear compact convex substitution function. The convex optimization problem is solved by calling the CVX interior point method solver toolbox.

[0017] Furthermore, in step S22, according to the Takagi decomposition theorem, the fully connected symmetric constraints are... and lossless hardware unitary constraints The reflection coefficient matrix of the superdiagonal smart reflector is equivalently decomposed into: In the form of, To meet The unitary matrix; through this variable substitution, regarding The strongly constrained subproblem is equivalently transformed into a problem concerning The problem is to construct the objective function. objective function The optimization problem was solved using the Manopt toolbox for manifold optimization.

[0018] Compared with the prior art, the present invention has the following beneficial technical effects:

[0019] This invention significantly improves the secure transmission performance of the low-altitude sensing integrated system by integrating a super-diagonal intelligent reflector with the maneuverability of UAVs. Its main advantages are as follows:

[0020] 1. Overcoming the bottleneck of amplitude and phase modulation: By utilizing the fully connected coupling mechanism of the super-diagonal smart reflector, the reflection matrix is ​​extended from a diagonal form to a full-rank off-diagonal form, significantly improving design freedom. Compared with traditional diagonal smart reflectors, this can effectively improve the security rate.

[0021] 2. Dynamically Eliminating Spatial Obstruction Blind Spots: By optimizing the three-dimensional spatial deployment of UAVs and proactively constructing dynamic virtual line-of-sight links, the signal obstruction problem in complex low-altitude environments is effectively solved. Compared to fixed-location deployment solutions, this significantly improves security and transmission rates.

[0022] 3. The algorithm is convergent, robust, and has low complexity: The proposed two-layer optimization algorithm utilizes high-tree decomposition and manifold optimization techniques to efficiently decouple highly coupled non-convex problems. The computational overhead increases polynomially with the system dimension, demonstrating good engineering applicability. Attached Figure Description

[0023] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0024] Figure 1 This is a schematic diagram of the low-altitude integrated sensing and security waveform design process for super-diagonal intelligent reflective surface assistance according to the present invention. Detailed Implementation

[0025] 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.

[0026] Consider a low-altitude drone-assisted sensing system, where the drone is equipped with a super-diagonal smart reflector to enhance communication and sensing performance. The system includes a... An integrated base station with a single antenna, equipped with A drone with a super-diagonal intelligent reflective surface of one reflective unit. There is one legitimate user with a single antenna and one potential eavesdropper with a single antenna. Specifically, the drone assists the base station in securely transmitting data to legitimate users while simultaneously detecting eavesdroppers using the transmitted waveform. Furthermore, considering that obstacles may render the direct line-of-sight link between the base station and legitimate users unavailable, the system utilizes the high-altitude line-of-sight advantage of the drone equipped with a super-diagonal intelligent reflector to establish a virtual reflective link. Consider a three-dimensional coordinate system, where the base station is located at the origin. , No. The coordinates of the legitimate users are The eavesdropper's coordinates are Drones equipped with super-diagonal intelligent reflectors can operate at a fixed altitude. Flight is achieved by adjusting the drone's two-dimensional horizontal coordinates. The auxiliary integrated base station corresponds to the three-dimensional coordinates of the UAV. .

[0027] A Ricean fading model is used to characterize all wireless channels in the system. The channel from the base station to the UAV equipped with a super-diagonal smart reflector... It can be modeled as:

[0028] (1)

[0029] in, This refers to path loss. The loss index; Rice factor; The distance between the base station and the drone; For non-line-of-sight transmission components that follow a complex Gaussian distribution, It is the identity matrix; Indicates the line-of-sight transmission component. Indicates the conjugate transpose; where:

[0030] (2)

[0031] and These are the guidance vectors at the drone equipped with a super-diagonal intelligent reflector and the base station, respectively. and These are the departure angle and arrival angle of the signal from the base station to the super-diagonal smart reflector, respectively. and Sure, This refers to the flight altitude of the drone.

[0032] Similarly, A ground node consists of a single-antenna legitimate user and a single-antenna potential eavesdropper. The drone equipped with a super-diagonal intelligent reflector has reached the first Channels of each ground node Represented as:

[0033] (3)

[0034] in, This refers to path loss. For the first The loss index of each node; For drones and the first The distance between each ground node For the first Three-dimensional coordinates of each ground node; For drones equipped with super-diagonal intelligent reflectors and the first The guide vector of each node, ; For the signal to travel from the super-diagonal smart reflector to the first The angle of arrival of each node. , For the first The height of each node; For Rayleigh channels that follow a complex Gaussian distribution.

[0035] To suppress potential eavesdroppers, base stations simultaneously send confidential information to legitimate users. and artificial noise Therefore, let Let represent the reflection coefficient matrix of the superdiagonal smart reflector, then the th Signals received by legitimate users and eavesdroppers and They can be modeled as follows:

[0036] (4)

[0037] (5)

[0038] in, In (3) when Time A channel for a legitimate user; In (3) when The eavesdropper's channel; and They represent the first Additive Gaussian white noise for legitimate users and eavesdroppers. Indicates the first Noise power at each legitimate user location; This indicates the noise power at the location of the eavesdropper.

[0039] It should be noted that in equations (4) and (5), this invention employs a super-diagonal intelligent reflector to enhance system performance. The super-diagonal intelligent reflector actively constructs coupling paths between arbitrary port pairs by introducing a reconfigurable interconnecting impedance network between the reflecting units, thereby achieving flexible redistribution of electromagnetic energy. Under purely reactive lossless conditions, the reflection coefficient matrix of the super-diagonal intelligent reflector... It can be modeled as:

[0040] (6)

[0041] This invention focuses on the second-order statistical properties of the transmitted signal to maximize the system's security rate. Specifically, let... and Let these represent the emission covariance matrices of confidential information and artificial noise, respectively. This represents the calculation of expectation. Assuming the signal flows of each legitimate user are independent, then... It can be further decomposed into ,in Indicates that it is sent to the first The covariance matrix of confidential information of each legitimate user. Under this definition, the maximum transmit power constraint of the base station can be expressed as: , This represents the computation of the trace of a matrix. This indicates the maximum transmit power at the base station. The confidentiality rate for a legitimate user is expressed as:

[0042] (7)

[0043] in, and They represent the first The achievable rate between a legitimate user and an eavesdropper is expressed as follows:

[0044] (8)

[0045] (9)

[0046] in, Indicates the first Joint channel matrix of legitimate users; Represents the joint channel matrix of the eavesdroppers; This represents the computation of the trace of a matrix; Indicates the first The covariance matrix of confidential information at each legitimate user location, where .

[0047] While performing secure transmission, the base station uses transmitted signals The eavesdropper is detected. To ensure the reliability of the detection, the signal-to-noise ratio (SNR) of the received echo at the eavesdropper's location must meet a specific threshold. Specifically, the detected SNR at the eavesdropper's location can be expressed as:

[0048] (10)

[0049] in, This represents the perceived signal-to-noise ratio at the eavesdropper's location.

[0050] In practical design, it is usually required ,in The minimum threshold required to meet the sensing and detection performance requirements.

[0051] The objective of this invention is to optimize the transmission covariance matrix of the base station's confidential information by jointly optimizing the base station's maximum transmit power, the minimum threshold required for sensing and detection performance, the hardware constraints of the super-diagonal intelligent reflector, and the deployment area limitations of UAVs, all while meeting the requirements of the base station's maximum transmit power, the minimum threshold required for sensing and detection performance, the hardware constraints of the super-diagonal intelligent reflector, and the limitations of the UAV deployment area. The emission covariance matrix of artificial noise The reflection coefficient matrix of the super-diagonal smart reflector and the two-dimensional horizontal coordinates of the drone To maximize the overall security rate of the system. For example... Figure 1 As shown, this joint optimization problem can be modeled in the following form:

[0052] (11a)

[0053] (11b)

[0054] (11c)

[0055] (11d)

[0056] (11e)

[0057] (11f)

[0058] in, This represents maximizing the overall security rate of the system; and These represent the movable ranges of the UAV equipped with a super-diagonal intelligent reflector along the x-axis and y-axis, respectively. In the optimization problem of equations (11a-11f), the perception performance constraint of equation (11f) exhibits high non-convexity and involves strong coupling between variables. Clearly, this coupling characteristic disrupts the separable structure between variable blocks. Therefore, an equivalent transformation is performed, combining the constraint (11f) with the objective function, and then solving it using an alternating optimization method. The perception performance constraint of equation (11f) is dualized and processed within the objective function (11a):

[0059] (12)

[0060] in, Represent the Lagrange function; For the Lagrange multipliers corresponding to the perceptual performance constraints in formula (11f), i.e., the dual variables; For penalty parameters; , indicating in 0 and Take the maximum value from the middle. Let (10) represent the signal-to-noise ratio perceived at the eavesdropper's location. Based on (12), construct the following optimization problem:

[0061] (13)

[0062] in, This indicates that by optimizing variables Minimize function ; The Lagrange function in expression (12) is represented.

[0063] Overall Algorithm:

[0064] The solution to the optimization problem of formula (13) is Algorithm 1, as shown in Table 1, which includes two nested loops. The process... This indicates that the inner loop updates the variables by solving problem (13). Until the inner layer convergence accuracy is reached. , This indicates an update and optimization operation; the specific convergence conditions for the inner loop are detailed in Algorithm 2 below. Furthermore, the convergence criteria parameters in Algorithm 1... Inequality constraints The maximum violation error. If , The constraint tolerance threshold indicates that the current solution satisfies the constraints of the optimization problem, and the outer algorithm executes the dual ascent method. Update Lagrange multipliers Otherwise, it indicates that the current penalty is insufficient, and the penalty parameters should be updated. (in (where the first scaling factor is used) to apply to the objective function A larger penalty weight is applied to enforce the constraint. The termination condition of the outer algorithm is the convergence criterion parameter. Less than or equal to constraint violation threshold ,Right now , This represents the constraint violation threshold. Additionally, a second scaling factor is set. Dynamically reduce the constraint tolerance threshold during outer iteration. .

[0065] Table 1. Two-level optimization algorithms for solving optimization problems.

[0066]

[0067] The inner algorithm uses a block successive upper bound minimization method to update variable parameters, breaking down the highly coupled original non-convex problem into separate optimizations of variables. , and The algorithm solves three smaller subproblems in an alternating loop. Next, the update process of the inner iterative algorithm will be shown, with the alternating optimization steps of the inner algorithm explained step by step for simplicity.

[0068] Step 1: Update the emission covariance matrix of confidential information and artificial noise. .

[0069] Given the reflection coefficient matrix of a superdiagonal smart reflector Two-dimensional horizontal coordinates of the drone Under the premise of and Treating it as a constant only optimizes The problem of time is due to the objective function The expression contains non-concave terms and remains non-convex. To achieve efficient solution, this invention utilizes the current iteration point... A first-order Taylor expansion is performed to construct a linear compact convex substitution function for the nonconvex term. As shown in equation (16), Representing variables The value in the previous iteration, express The value in the previous iteration. Based on this substitution function, the original subproblem concerning the waveform is equivalently transformed into the following convex optimization problem (standard positive semidefinite programming problem):

[0070] (14)

[0071] in:

[0072] (15a)

[0073] (16)

[0074] (17a)

[0075] (17b)

[0076] in, Indicates the first Risk of eavesdropping at individual users; Indicates the first The confidentiality capabilities of each user; Represents the intermediate equivalent matrix; Represents the judgment matrix; Indicates the first Covariance matrix of confidential information at each legitimate user The value in the previous iteration; The emission covariance matrix representing artificial noise The value in the previous iteration; Indicates the first Covariance matrix of confidential information at each legitimate user The value in the previous iteration.

[0077] Convex optimization problem (14) can be solved efficiently by calling the CVX interior point solver toolbox.

[0078] Step 2: Update the reflection coefficient matrix of the super-diagonal smart reflector .

[0079] Given the transmission covariance matrix of confidential information and artificial noise and the two-dimensional horizontal coordinates of the drone In this case, update the reflection coefficient matrix of the super-diagonal smart reflector. Faced with the need to simultaneously satisfy fully connected symmetric constraints and lossless hardware unitary constraints The dual coupling presents a challenge. To address this, this invention, based on Takagi's decomposition theorem, equivalently decomposes the reflection coefficient matrix of the super-diagonal smart reflector satisfying the aforementioned dual constraints into... In the form of, To meet The unitary matrix. Through this variable substitution, regarding... The strongly constrained subproblem is equivalently transformed into a problem concerning The problem, objective function It is expressed as follows:

[0080] (18)

[0081] in,

[0082] (19)

[0083] in, This indicates that by optimizing variables minimize The value; Represents the intermediate matrix; Representing variables The conjugate matrix; Represents the joint intermediate matrix of the eavesdroppers; Indicates a legitimate user The joint intermediate matrix; This indicates that legitimate users are not being considered. The intermediate matrix at that time.

[0084] because A complex Riemannian manifold is defined Problem (18) is reconstructed into an unconstrained optimization problem on the manifold space:

[0085] (20)

[0086] in, Represent the function value in problem (18), This indicates that through optimization in variables on Minimize function .

[0087] Such problems can be solved efficiently using the Manopt toolbox for manifold optimization. During the solution process, the Manopt toolbox requires an objective function. Relative to variables gradient The derivation of its expression is as follows:

[0088] (21a)

[0089] (21b)

[0090] in, express Relative to unitary matrix The gradient; This represents the solution matrix for the manifold.

[0091] Updating the unitary matrix using the Manopt toolbox for manifold optimization Afterwards, through You can get The updated value.

[0092] Step 3: Update the drone's 2D horizontal coordinates .

[0093] Two-dimensional horizontal coordinates of the drone The related subproblems are also nonconvex, and can be written as:

[0094] (twenty two)

[0095] in, This represents the function for optimizing UAV coordinates. This indicates that by optimizing variables minimize The value of .

[0096] This problem is difficult to solve directly. Therefore, this invention constructs a compact convex upper bound substitution function (23) for the UAV coordinate optimization function (22) at the current iteration point, and additionally introduces a quadratic regularization term to construct a soft trust region constraint. ,Right now:

[0097] (twenty three)

[0098] in, Represents the UAV coordinate optimization function The compact convex upper bound substitution function; Represents the two-dimensional horizontal coordinates of the UAV during the previous iteration. The value; This represents the function for optimizing UAV coordinates. Indicates the function In Replace with ; express Regarding variables The transpose of the Euclidean gradient; The step size factor that controls the magnitude of the position update; Representation function Regarding variables The transpose of the Euclidean gradient.

[0099] In equation (23) It can be represented as:

[0100] (twenty four)

[0101] in This represents the set of all nodes consisting of base stations, legitimate users, and eavesdroppers. This indicates the operation of taking the real part; The gradient matrix in expression (25b); Indicates the first The loss index of each node; Represents a node The complete Rice channel; Represents the node Height; Indicates the first The distance from each node to the drone; The node matrix in expression (25a); Represents a node The line-of-sight component; For nodes Two-dimensional horizontal coordinates, Represents a node 3D coordinates; and Representing nodes respectively The complete Rice channel and its line-of-sight components; in addition:

[0102] (25a)

[0103] (25b)

[0104] (25c)

[0105] (25d)

[0106] (25e)

[0107] in, The dimension is a diagonal matrix; The dimension is a diagonal matrix; Represents the joint channel matrix; Represents the joint position measurement matrix; Indicates the number of punitive interventions; Represents a node Position measurement vector; The vector representing the location of the eavesdropper; Indicates a legitimate user The channel; The channel representing the eavesdropper; Indicates a legitimate user The position measurement vector at the location; This represents the perceived signal-to-noise ratio at the eavesdropper's location.

[0108] Based on equations (22)-(25), the UAV horizontal coordinates in formula (22) The related subproblems can be transformed into:

[0109] (26)

[0110] UAV coordinates transformed by formula (26) The related subproblems are convex problems, and the following closed-form solutions exist:

[0111] (27)

[0112] in, and These represent the upper and lower boundaries of the drone's flight area, respectively. This indicates the maximum possible value of the drone's x-coordinate; This indicates the maximum possible value of the drone's ordinate. This indicates the minimum possible value of the drone's x-coordinate; This represents the minimum possible value of the drone's ordinate.

[0113] Thus, the block successive upper bound minimization method for solving problem (13) is summarized in Algorithm 2, as shown in Table 2. The complete algorithm for the original non-convex problem (11) is finally obtained by embedding Algorithm 2 into step 3 of Algorithm 1.

[0114] Table 2. Iterative optimization algorithm for the inner layer based on the block successive upper bound minimization method.

[0115]

[0116] Example 1

[0117] Network configuration: Consider a three-dimensional spatial region, where an integrated base station is deployed at location (0,0,0). The number of antennas... Maximum transmit power ;exist Each single-antenna legitimate user is located at... m and At point m; there exists a single-antenna eavesdropper, located at... At point m. Number of reflector units carried by the drone. The super-diagonal intelligent reflective surface, at a high Flying at m. Thermal noise power at the receiver for legitimate users and eavesdroppers. Path loss Loss index The Ricean channel model is adopted, and the Ricean factor is... The minimum threshold required to meet the sensing and detection performance requirements is... .

[0118] Define parameter: Covariance matrix of the confidential information waveform transmitted by the base station. Artificial noise covariance matrix The reflection coefficient matrix of the superdiagonal smart reflector ; Two-dimensional horizontal coordinates of the UAV ; the dual variable corresponding to the perception inequality constraint Penalty parameters Convergence criterion for measuring the degree of constraint violation Termination condition threshold of outer algorithm Inner Algorithm Termination Condition Threshold The first and second scaling factors of the outer layer .

[0119] Step 1: Initialize system variables , , and Initialize hyperparameters , , , , and .

[0120] Step 2: Start the outer loop of Algorithm 1, and record the current outer iteration number as... .

[0121] Step 3: Start the alternating optimization loop in the inner layer of Algorithm 2, and record the current inner layer iteration number as . .

[0122] Step 4: Update variables and The following convex problem was solved using the CVX Convex Optimization Toolbox for updating: (27)

[0123] Step 5: Update the reflection coefficient matrix parameters of the super-diagonal smart reflector First, we use the Manopt toolbox to solve the following unconstrained optimization problem on a Riemannian manifold to update... :

[0124] (28)

[0125] Update using Manopt Afterwards, through You can get The updated value.

[0126] Step 6: Update the drone's 2D horizontal coordinates , .

[0127] Step 7: Let Calculate the cost function value after the completion of this inner layer iteration. .

[0128] Step 8: Determine if the inner layer has converged. If If so, return to step 4 to continue inner-layer alternating optimization; This indicates that the inner algorithm has converged to a stationary point and exited the inner loop.

[0129] Step 9: Calculate the convergence criteria parameters .

[0130] Step 10: Determine convergence criteria Is it less than or equal to the current constraint tolerance threshold? .if Update the Lagrange multipliers using the dual ascent method. Otherwise, update the penalty parameters. To increase the severity of punishment.

[0131] Step 11: Update the constraint tolerance threshold for measuring constraint violations. ,make .

[0132] Step 12: If convergence is determined, check the parameters. If the algorithm succeeds, return to step 3 and proceed to the next outer iteration; otherwise, the outer algorithm stops executing, indicating that the globally optimal configuration parameters that satisfy both perception accuracy and security rate have been found. .

[0133] After completing the above optimization steps, the system extracts the converged globally optimal configuration parameters. The base station radio frequency processing unit is based on the latest... and Its digital transmit beamformer was reconfigured; the UAV flight control system received the UAV's two-dimensional horizontal coordinates. Then, combined with the drone's flight altitude The system controls the drone to fly and hover at the corresponding three-dimensional high-altitude position; simultaneously, it transmits the calculated reflection coefficient matrix of the super-diagonal smart reflector via a control link. The signal is sent to the super-diagonal intelligent reflector, reconstructing the fully connected interconnection impedance network between the 64 reflective units on its backplane. Through the coordinated execution of these three components, an airborne intelligent security link is constructed in physical space that effectively suppresses eavesdropping and maximizes the confidentiality rate for legitimate users.

[0134] This invention proposes a low-altitude integrated sensing and secure transmission method that combines a super-diagonal intelligent reflector with a UAV. This method not only breaks the sparse diagonal limitation of traditional intelligent reflectors to release higher degrees of freedom in amplitude and phase control, but also utilizes the three-dimensional maneuverability of UAVs to actively construct a high-altitude virtual line-of-sight link, effectively overcoming the ground obstruction problem in complex low-altitude environments.

[0135] In addition, a two-layer joint optimization algorithm is proposed, which effectively decouples strongly coupled non-convex variables such as waveform covariance, fully coupled reflection matrix and UAV position. The algorithm solves the problem alternately by manifold optimization and constructing a compact convex upper bound substitution function. Compared with traditional algorithms, this algorithm effectively reduces the difficulty of solving high-dimensional strongly coupled problems and ensures the robust convergence of the algorithm.

[0136] Furthermore, the joint optimization algorithm proposed in this invention can accurately suppress the eavesdropper channel and maximize the confidentiality rate of legitimate users while strictly meeting the radar's detection accuracy threshold for potential eavesdroppers. Compared with traditional diagonal intelligent reflectors or fixed UAV position schemes, it significantly improves the physical layer security performance of the system and achieves an efficient balance between communication and sensing.

[0137] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for designing a low-altitude integrated sensing and security waveform assisted by a super-diagonal intelligent reflector, characterized in that, The method is applied to a low-altitude unmanned aerial vehicle-assisted sensor-integrated system, the system comprising a An integrated base station with a single antenna, equipped with... A drone with a super-diagonal intelligent reflective surface of one reflective unit. The method includes the following steps: a single-antenna legitimate user and a single-antenna potential eavesdropper; Step S1: Under the premise of satisfying the maximum transmission power of the base station, the minimum threshold required for sensing and detection performance, the hardware constraints of the super-diagonal intelligent reflector, and the deployment area limitations of the UAV, the transmission covariance matrix of the base station's confidential information is jointly optimized. The emission covariance matrix of artificial noise The reflection coefficient matrix of the super-diagonal smart reflector and the two-dimensional horizontal coordinates of the drone To maximize the overall security rate of the system, an optimization problem is constructed; Step S2: Solve the optimization problem using two nested loops. The inner loop updates the variables by solving the optimization problem. The process continues until the inner convergence accuracy is reached. If the convergence judgment parameter is less than or equal to the constraint tolerance threshold, it indicates that the current solution has satisfied the constraints of the optimization problem. The outer loop executes the dual ascent method and updates the Lagrange multipliers. Otherwise, it indicates that the current penalty strength is insufficient. The penalty parameter is updated to apply a larger penalty weight to the objective function to enforce the constraints. The termination condition of the outer loop is that the convergence judgment parameter is less than or equal to the constraint violation threshold. Step S3: After solving in step S2, the convergent globally optimal configuration parameters are obtained. ; The base station radio frequency processing unit is based on the latest and Its digital transmit beamformer was reconfigured; the UAV flight control system received the UAV's two-dimensional horizontal coordinates. Then, combined with the drone's flight altitude The system controls the drone to fly and hover at the corresponding three-dimensional high-altitude position; simultaneously, it transmits the calculated reflection coefficient matrix of the super-diagonal smart reflector via a control link. The signal is sent to the super-diagonal intelligent reflector, and the fully connected interconnection impedance network between the 64 reflector units on its backplane is reconstructed. Through the coordinated execution of the three, an airborne intelligent security link is constructed in physical space to effectively suppress eavesdropping and maximize the confidentiality rate of legitimate users.

2. The low-altitude integrated sensing and security waveform design method for super-diagonal intelligent reflector-assisted design according to claim 1, characterized in that, In step S2, the inner loop uses a block successive upper bound minimization method to update the variable parameters, dividing the highly coupled original non-convex problem into separate optimizations of the variables. , and The problem involves solving three smaller subproblems in an alternating loop, including the following steps: Step S21: Update the emission covariance matrix of confidential information and artificial noise. ; Step S22: Update the reflection coefficient matrix of the super-diagonal smart reflector. ; Step S23: Update the UAV's two-dimensional horizontal coordinates .

3. The low-altitude integrated sensing and security waveform design method for super-diagonal intelligent reflector-assisted design according to claim 2, characterized in that, In step S21, given the reflection coefficient matrix of the super-diagonal smart reflector... Two-dimensional horizontal coordinates of the drone Under the premise of optimization At that time, a linear compact convex substitution function is constructed, and a convex optimization problem is constructed based on the linear compact convex substitution function. The convex optimization problem is solved by calling the CVX interior point method solver toolbox.

4. The low-altitude integrated sensing and security waveform design method for super-diagonal intelligent reflector-assisted design according to claim 2, characterized in that, In step S22, according to Takagi's decomposition theorem, the fully connected symmetric constraints are satisfied. and lossless hardware unitary constraints The reflection coefficient matrix of the superdiagonal smart reflector is equivalently decomposed into: In the form of, To meet unitary matrix; Through this variable substitution, regarding The strongly constrained subproblem is equivalently transformed into a problem concerning The problem is to construct the objective function. objective function The optimization problem was solved using the Manopt toolbox for manifold optimization.

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