Unmanned aerial vehicle and reconfigurable intelligent surface joint optimization method for inter-sensing integration

Abstract

The application discloses a method for unmanned aerial vehicle and reconfigurable intelligent surface joint optimization oriented to integrated communication and sensing, which comprises the following steps: constructing a system model, wherein the system model comprises an unmanned aerial vehicle equipped with a dual-function antenna array, a ground reconfigurable intelligent surface, multiple users and sensing targets; constructing a joint optimization problem, wherein the joint optimization problem aims to maximize the average sum rate of the users, the optimization variables are unmanned aerial vehicle active beamforming, RIS passive reflection coefficient and unmanned aerial vehicle three-dimensional trajectory, and constraints such as communication service quality, sensing performance and SIC power ranking are set; the joint optimization problem is decomposed into three sub-problems of active beamforming, passive beamforming and unmanned aerial vehicle trajectory, and an alternating iteration algorithm is adopted for solving. Through deep collaborative optimization of three core degrees of freedom, the application realizes global resource efficiency maximization of the integrated communication and sensing system, and meets the high-precision sensing requirement while guaranteeing the communication quality.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, specifically to a joint optimization method for unmanned aerial vehicles (UAVs) and reconfigurable smart surfaces that integrate sensing and communication, and is particularly suitable for dynamic and complex environments employing non-orthogonal multiple access (NOMA) technology. Background Technology

[0002] 6G mobile communication aims to build an intelligent society where everything is interconnected. Its core requirement is to simultaneously achieve wide-area wireless communication and high-precision environmental perception in complex and dynamic physical environments. Sensor-Integrated Communication (ISAC), by sharing spectrum and resources on the same hardware platform, enables wireless networks to possess sensing capabilities while transmitting data, and is considered a key enabling technology for 6G. Non-Orthogonal Multiple Access (NOMA), due to its ability to reuse multiple users on the same resource block, highly aligns with the resource-sharing concept of ISAC. The combination of the two can effectively improve spectrum efficiency and access capacity, and has become a research hotspot.

[0003] To further enhance system performance, unmanned aerial vehicles (UAVs) and reconfigurable smart surfaces (RIS) have been introduced into ISAC systems. UAVs, with their maneuverability, can flexibly adjust their deployment locations to optimize communication links and improve sensing geometry, thereby mitigating occlusion effects. RIS, through active manipulation of the electromagnetic propagation environment, can reshape effective channels, enhance signal quality, and provide additional spatial degrees of freedom for sensing. Existing research has made some progress in UAV-assisted or RIS-assisted ISAC systems, for example, by jointly optimizing beamforming, power allocation, or UAV trajectories to improve system performance.

[0004] However, existing technologies still have the following shortcomings: (1) The performance of NOMA is highly dependent on superimposed channel differences between users to achieve effective serial interference cancellation. However, existing solutions fail to make full use of the mobility of UAVs and the reconfigurability of RIS to actively create or expand such differences, which limits the potential of NOMA in improving system capacity.

[0005] (2) In the ISAC system, communication and sensing functions share resources, which inevitably leads to competition. Existing research lacks a dynamic intelligent joint optimization mechanism, especially when the RIS serves multiple users and senses multiple targets at the same time. It is difficult to achieve the synergistic optimality of communication and sensing performance, which often results in the performance of one side improving at the expense of the performance of the other side declining.

[0006] (3) Most existing optimization methods only consider the joint design of some variables (such as beamforming and power allocation, or trajectory and beamforming), and fail to perform global collaborative optimization of the phase configuration of RIS, UAV trajectory and communication / sensing beamforming as a whole, thus limiting the overall performance limit of the system in terms of spectrum efficiency, energy efficiency and sensing accuracy. Summary of the Invention

[0007] To address the problems in existing technologies, this invention provides a joint optimization method for UAVs and reconfigurable smart surfaces for sensor-integrated systems. The method aims to solve the problem of maximizing the global resource efficiency of a sensor-integrated system by deeply co-optimizing the UAV mobile platform, reconfigurable smart surfaces, and non-orthogonal multiple access technology in dynamic and complex environments where direct links are blocked.

[0008] A joint optimization method for sensor-integrated unmanned aerial vehicles (UAVs) and reconfigurable smart surfaces includes the following steps: A system model is constructed, the system comprising: a UAV equipped with a dual-function antenna array for simultaneously transmitting communication signals and radar detection signals; and a reconfigurable smart surface deployed on the ground; Ground user equipment Index for users, ; and at least one perceived target; task duration Discretize into Each time slot For slot index The duration of each time slot is And define drones in the first The three-dimensional trajectory of each time slot is ,in, , , These represent the drones in the [number]th [month]. Each time slot axis, axis, Axis coordinates; Construct a joint optimization problem to maximize the average sum rate of all users over the task cycle. For the goal, among which For users In the Achievable data rates per time slot; using the UAV's active beamforming vector The passive reflection coefficient matrix of RIS and the three-dimensional trajectory To optimize the variables, constraints were set, including communication service quality constraints, perception performance constraints, serial interference cancellation power ordering constraints for non-orthogonal multiple access protocols, UAV kinematic constraints, and RIS unity mode constraints. The joint optimization problem is decomposed into three sub-problems: active beamforming optimization, passive beamforming optimization, and UAV trajectory optimization. An iterative algorithm is then used to solve these sub-problems.

[0009] Furthermore, the system model includes: The channel model adopts the generalized Ricean fading model, where any given link in a time slot... The channel vector or matrix model is as follows: in, Let be the Euclidean distance between the transmitter and receiver. This is the path loss index. The path loss is set at a reference distance of 1 meter; parameters , where is the Rice factor, representing the ratio of the deterministic line-of-sight component power to the random non-line-of-sight component power; The direction matrix for the line-of-sight component, and the non-line-of-sight component. It reflects the multipath scattering effect and follows the standard Rayleigh fading distribution; It is a non-line-of-sight component matrix, represented as the product of the array response vectors corresponding to the angle of arrival and the angle of departure; For a node equipped with a uniform planar array, the array response vector is: in Indicates the antenna spacing. For wavelength, It is the azimuth angle. The pitch angle, This is expressed as the number of antenna elements along the x and y axes. Represented as direction cosine; Signal transmission model, UAV in time slot The signal sent Composed of superimposed communication signals and radar detection signals, it is represented as: in and The first The information symbols of each user and their corresponding communication beamforming vectors and These are represented as radar detection signals and their corresponding sensing beamforming vectors, respectively, and satisfy the total transmit power constraint. , This is the maximum transmission power; set up For RIS to users The conjugate transpose of the channel vector. The channel matrix from the UAV to the RIS. For drones to users The conjugate transpose of the direct link channel vector, then the user The conjugate transpose of the equivalent synthesized channel vector is ,in This is the diagonal matrix of RIS reflection coefficients. For RIS phase shift vector, For the first Phase shift of each RIS unit; user The received signal is: in, It is additive white Gaussian noise. This represents noise power.

[0010] Furthermore, the serial interference cancellation power sorting constraint specifically refers to: Users are sorted in ascending order of equivalent channel strength, i.e. To ensure that users can successfully decode and eliminate interference in this order, according to the NOMA principle, the following must be satisfied: Among them radar detection signals Known at the transmitting end, the user end prioritizes decoding and elimination, and the conditions for successful elimination are: Under the premise of satisfying the above power ranking, the user The reachable signal-to-interference-plus-noise ratio (SINR) for decoding its own signal is: Corresponding achievable data rate .

[0011] Furthermore, the specific constraints on perception performance are as follows: set up Let be the channel vector from RIS to the sensing target. Let be the direct link channel vector from the UAV to the sensing target, then the equivalent one-way sensing channel vector is: ,in, express The conjugate transpose of the matrix; the effective round-trip sensing channel matrix is ​​approximately: ; The signal-to-interference-plus-noise ratio (SIR) of the radar echo signal must meet a preset threshold to ensure target detection performance. This constraint is expressed as: in This refers to the noise power of the radar receiver. To sense the signal-to-interference-plus-noise ratio threshold.

[0012] Furthermore, solving the active beamforming optimization sub-problem includes: Given a drone trajectory and RIS phase shift matrix Optimize the active beamforming vector under the given conditions. Introducing auxiliary rank-one positive definite matrix variables and And define the channel covariance matrix. and This transforms the original problem into a semidefinite programming problem. Introducing auxiliary variables Indicates user To determine the rate, apply a continuous convex approximation to the non-convex rate constraint, rewriting the rate expression as the difference between two concave functions. Then, perform a first-order Taylor expansion on the second term at the current iteration point to obtain the concave lower bound. ; For rank-one constraints, a penalty function-based approach is adopted, adding a penalty term to the objective function. ,in As a penalty factor, The nuclear norm is the sum of the singular values ​​of a matrix. This represents the spectral norm, which is the largest singular value of the matrix. Convex At the current iteration point Linearization to affine lower bound: in yes The eigenvector corresponding to the largest eigenvalue; This ultimately leads to a convex semidefinite programming subproblem: Constraints include: power constraints Perceived SINR constraints The trace form of SIC power ordering constraints, and the rate lower bound constraint. and semidefinite constraints .

[0013] Furthermore, solving the passive beamforming optimization sub-problem includes: Given an active beamforming vector and drone trajectory Optimize the RIS phase shift vector under the given conditions. ; First, a Lagrange dual transformation is used to process the non-convex sum-logarithm-ratio objective function, and auxiliary variables are introduced. and The result of the quadratic transformation is as follows: function ,in: in, , ; Introducing Dimensional Upgrade Variables sum matrix The objective function and all constraints are homogenized to be about The linear form; Define the sensing channel correlation matrix: , ; , , This is the transpose and conjugate of the channel vector from RIS to the target. This is the transpose and conjugate of the direct link channel vector from the UAV to the target; For non-convex trace product terms existing in perceptual constraints The continuous convex approximation method is used at the current iteration point. Performing a first-order Taylor expansion yields the linearized constraints: in Relax the rank constraint through semi-definite relaxation. The resulting convex semidefinite programming subproblem is solved using the CVX solver. If the solution is not rank-one, the Gaussian randomization method is used to recover the RIS phase vector that satisfies the unit modulus constraint. .

[0014] Furthermore, solving the UAV trajectory optimization sub-problem includes: With a fixed active beamforming vector Optimize UAV trajectory under RIS phase shift Θ conditions Introducing auxiliary slack variables , and These represent the drone to the user. Calculate the squared distance between RIS and the target, and apply convex constraints: in , , Representing users respectively Location, RIS location, target location; Channel gain Represented as a convex function of the distance variable: The coefficients are determined by a fixed beamforming and RIS phase shift: and It is a normalized line-of-sight direction vector. The path loss at the reference distance; Perceived gain Represented as: The coefficients are determined by the sensing beamforming matrix and the auxiliary channel matrix: in, and For non-convex SIC constraints , By linearizing the right-hand convex function at the current iteration point, we obtain the affine lower bound. ; For non-convex rate constraints, the rate expression is decomposed into two terms, and a concave lower bound is constructed using SCA: in , This is the value of the l-th iteration; For the sensing SINR constraint, the signal term Linearization is performed at the current iteration point to obtain the affine lower bound. This is transformed into a convex constraint: The final result is a convex second-order cone programming subproblem, which is solved using the CVX solver.

[0015] Furthermore, an iterative algorithm based on alternating optimization is used to solve the joint optimization problem: Initialize drone trajectory RIS phase shift Active beamforming vector Set the iteration index tolerance Calculate the initial target value ; In each iteration: Active beamforming update: based on current and Solve the corresponding convex semidefinite programming subproblem to obtain the optimal solution. , Indicates user The beam covariance matrix of the target and the beam covariance matrix of the target being sensed are obtained; the beam covariance matrix of the target is recovered through eigenvalue decomposition. ; Passive beamforming update: based on the updated and current Update fractional programming auxiliary variables and Solve the corresponding convex semidefinite programming subproblem to obtain... Recovery by Gaussian randomization ; Drone trajectory update: based on current and Update the SCA parameters, solve the convex second-order cone programming subproblem, and obtain... ; Calculate the current target value ; Repeat the above steps until the relative increment is reached. Or reach the maximum number of iterations Output the optimal solution .

[0016] The beneficial effects of this invention are: 1) By jointly optimizing active beamforming, RIS passive phase shifting, and UAV 3D trajectory, the system systematically utilizes UAV mobility and RIS reconfigurability to actively create and expand channel differences among NOMA users, significantly improving NOMA's spectral efficiency and multi-user access capability.

[0017] 2) A joint design and optimization framework for integrated communication and sensing was established. Under the premise of meeting the sensing performance threshold, energy and spatial degrees of freedom were dynamically and intelligently allocated between communication and sensing functions, achieving synergistic optimization of dual-function performance.

[0018] 3) By taking the phase configuration of RIS as a core degree of freedom, and performing global collaborative optimization with UAV trajectory and communication / sensing beamforming, it breaks through the limitation of existing solutions that optimize the three separately, and significantly improves the overall spectrum efficiency, energy efficiency and upper limit of sensing accuracy of the system. Attached Figure Description

[0019] Figure 1 Flowchart provided for embodiments of the present invention Figure 2 This is a schematic diagram of the operating mode of the UAV-RIS ISAC system provided in an embodiment of the present invention; Figure 3 Convergence curves of sum rate versus iteration number for different RIS sizes provided in embodiments of the present invention; Figure 4 An optimized 3D trajectory diagram of a drone provided for an embodiment of the present invention; Figure 5 The graph showing the variation of instantaneous speed and sensing signal-to-noise ratio with flight time slots is provided for embodiments of the present invention. Figure 6 A graph showing the change of power allocation ratio between communication and sensing over time, provided in an embodiment of the present invention; Figure 7 The graphs showing the instantaneous and rate variations over time at different RIS sizes are provided in this embodiment of the invention. Figure 8 This is a graph showing the variation of average sum and rate with the perceived signal-to-interference-plus-noise ratio threshold under different RIS sizes, provided in an embodiment of the present invention. Figure 9 A comparison chart of instantaneous and rate variations over time under different benchmark schemes provided in embodiments of the present invention; Figure 10 A comparison chart showing the instantaneous and rate variations with transmit power under different benchmark schemes provided in this embodiment of the invention. Detailed Implementation

[0020] The present invention will now be described in detail with reference to the accompanying drawings. Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. The directional terms such as left, center, right, top, and bottom in the embodiments of the present invention are only relative concepts or referenced to the normal use state of the product, and should not be considered restrictive.

[0021] A joint optimization method for drones and reconfigurable smart surfaces aimed at sensor-integrated communication, such as... Figure 1 As shown, it includes the following steps: Step 1: Constructing a system model Consider a 3D unmanned aerial vehicle (UAV) sensory integration system assisted by reconfigurable smart surfaces (RIS), such as Figure 2 As shown, the system includes a rotary-wing drone that serves as an airborne base station and a ground-reconfigurable smart surface (RIS) deployed on the exterior of a building. A single-antenna ground user equipment (UE) and a specific sensing target.

[0022] The drone is equipped with a... A uniform planar array composed of dual-function antennas is capable of simultaneous communication and radar sensing. Total mission duration. Discretized into Each time slot, indexed as The duration of each time slot is Furthermore, the drone's trajectory is determined by... It means that, among them, , , These represent the drones in the [number]th [month]. Each time slot axis , axis, Axis coordinates. To ensure safe operation, the drone's motion is affected by its initial position. Minimum flight altitude and maximum horizontal speed The constraints are specifically expressed as follows: .

[0023] RIS is located in a fixed position ,Depend on Composed of passive reflective units. Time slot The reflection coefficient matrix at a given location is defined as a diagonal matrix. The phase shift vector Explicitly defined as: here Indicates the first The phase shift of each unit is assumed to be 1, and the reflection amplitude is assumed to be 1 unit.

[0024] The location of the user equipment (UE) is used ,in A stationary sensing target is located at .

[0025] Step 1.1: Channel Model This embodiment employs a generalized Ricean fading model, explicitly considering both large-scale path loss and small-scale fading effects; for any given link in a time slot The channel vector or matrix model is as follows: in, Let be the Euclidean distance between the transmitter and receiver. This is the path loss index. The path loss is set at a reference distance of 1 meter; parameters , where is the Rice factor, representing the ratio of the deterministic line-of-sight component power to the random non-line-of-sight component power; The direction matrix for the line-of-sight component, and the non-line-of-sight component. It reflects the multipath scattering effect and follows the standard Rayleigh fading distribution; the Doppler frequency shift caused by UAV mobility is assumed to be constant in each time slot and can be fully compensated; Deterministic line-of-sight components This is expressed as the product of the array response vectors corresponding to the angle of arrival (AoA) and the departure angle (AoD). Let... and Let azimuth and elevation represent the azimuth and elevation angles respectively. Then the line-of-sight channel component is: Among them, subscript and These represent the arrival and departure directions, respectively. For equipment with a scale of... The nodes of a uniform planar array (e.g., drones or smart reflectors). , Let the array response vectors be the conjugate transposes of the receiver array response vector and the transmitter array response vector, respectively. Defined as the Kronecker product of the responses of two linear arrays: The specific expressions for the guide vectors along the x-axis and y-axis are as follows: Indicates the antenna spacing. For wavelength, It is the azimuth angle. The pitch angle; The number of antenna elements is expressed as the number of antenna elements along the x and y axes, with direction cosines. Depends on three-dimensional geometric relationships; Considering the high operating altitude of UAVs and the deployment of Intelligent Reflectors (RIS) on tall building facades, both the air-RIS link and the RIS-ground link primarily use line-of-sight (LoS) propagation. Therefore, the UAV-RIS channel... and RIS-related ground channels (i.e., RIS-user channels) With RIS-target channel The UAV is assigned a larger Rice factor and a smaller path loss exponent. In contrast, the direct link between the UAV and the ground node (i.e., the UAV-user channel) is... and UAV-target channel This assumes potential impact from shading and complex scattering environments. Therefore, these direct links have relatively small Rice factors (e.g., With a large path loss exponent, it actually degenerates into a Rayleigh fading channel.

[0026] Step 1.2: Signal Transmission Model Drones in time slots The signal sent Composed of superimposed communication signals and radar detection signals, it is represented as: in and The first The information symbols of each user and their corresponding communication beamforming vectors and Let these be the radar detection signal and its corresponding sensing beamforming vector, respectively, and satisfy the following conditions: and total transmit power constraints , This is the maximum transmission power; set up For RIS to users The conjugate transpose of the channel vector. The channel matrix from the UAV to the RIS. For drones to users The conjugate transpose of the direct link channel vector, then the user The conjugate transpose of the equivalent synthesized channel vector is ,in This is the diagonal matrix of RIS reflection coefficients. For RIS phase shift vector, For the first Phase shift of each RIS unit, and set the reflection amplitude to unit 1; user The received signal is: in, It is additive white Gaussian noise. Noise power; To effectively manage interference, this embodiment employs a two-stage interference cancellation strategy: Sensor interference cancellation: due to radar detection signals Known at the transmitting end and typically transmitted at high power, the communication user can decode and cancel the signal before decoding its own data; Serial interference cancellation: Without loss of generality, users are arranged in ascending order of equivalent channel strength, i.e. To ensure that users can successfully decode and eliminate interference in this order, according to the NOMA principle, the following must be satisfied: Among them radar detection signals Known at the transmitting end, the user end prioritizes decoding and elimination, and the conditions for successful elimination are: Under the premise of satisfying the above power ranking, the user The reachable signal-to-interference-plus-noise ratio (SINR) for decoding its own signal is: Corresponding achievable data rate ; For the perception component, the UAV performs single-station perception to detect target parameters. Let... Let be the channel vector from RIS to the sensing target. Let be the direct link channel vector from the UAV to the sensing target, then the equivalent one-way sensing channel vector is: ,in, express The conjugate transpose of the matrix; the effective round-trip sensing channel matrix is ​​approximately: ; The signal-to-interference-plus-noise ratio (SIR) of the radar echo signal must meet a preset threshold to ensure target detection performance. This constraint is expressed as: in This refers to the noise power of the radar receiver. To sense the signal-to-interference-plus-noise ratio threshold.

[0027] Step 2: Jointly optimize the active beamforming vector Passive RIS phase shift matrix and drone trajectories This maximizes the average sum and rate of all communication users throughout the entire task cycle. The mathematical formulation of this joint optimization problem is as follows: (1a) Constraints (st): Total transmit power constraint: (1b) UAV kinematic constraints: (1c) (1d) Communication service quality constraints: (1e) Perceived performance constraints: (1f) SIC power ranking constraint: (1g) RIS unity mode constraint: (1h) Among them, the constraints in problem P1 impose practical system limitations: (1b) limits the total transmit power, while (1c) and (1d) ensure kinematic feasibility. Constraints (1e) and (1f) impose constraints requiring the first... Each UE meets the minimum rate requirement. Meanwhile, the sensing receiver should meet the minimum SINR requirement. Crucially, (1g) applies strict receive power sequencing to ensure the serial interference cancellation process is effective, while (1h) reflects the pure phase characteristics of RIS.

[0028] in, Indicates the first Minimum demand rate per user This represents the minimum threshold for perceived SINR. Indicates the first The RIS unit in the first The reflection coefficient of the time slot.

[0029] Problem P1 is highly nonconvex due to the coupling of variables, the fractional SINR in the objective function, and nonconvex constraints (e.g., unity modulus constraints and quadratic forms). To address this problem, an alternating optimization (AO) algorithm is proposed, which handles the problem by iteratively solving three decomposed subproblems. Furthermore, since beamforming and phase shift design are independent across different time slots under a fixed trajectory, time indices are omitted in the subsequent analysis for simplicity. .

[0030] Step 3: Decomposition and Iterative Solution To address this issue, this embodiment proposes an alternating optimization (AO) algorithm, which iteratively solves three decomposed subproblems. Since beamforming and phase shift design are independent across different time slots under a fixed trajectory, time indexing is omitted in the subsequent analysis for simplicity. .

[0031] Step 3.1: Solving the active beamforming optimization subproblem Given a drone trajectory and RIS phase shift matrix Optimize the active beamforming vector under the given conditions. The subproblem can be expressed as: (1.1a) Constraints (st): (1.1b) (1.1c) (1.1d) (1.1f) question The problem becomes nonconvex due to the non-concave objective function and the coupled quadratic terms in constraints (1.1c), (1.1d), and (1.1e). To solve this problem, the semidefinite relaxation (SDR) method is employed.

[0032] Introducing auxiliary rank-1 positive definite matrix variables and and satisfy For simplicity, the channel covariance matrix is ​​defined as follows: and The original problem has been rephrased as: (1.2a) Constraints (st): (1.2b) (1.2c) (1.2d) (1.2e) (1.2f) (1.2g) (1.2h) in, It is an introduced auxiliary variable that represents the user. The rate; Indicates user Received expected signal power This indicates the source is a user with weaker power ( The interference power of ) Indicates noise power; and Both are traces of matrices, represented by users respectively. The transmission power and the transmission power of the sensed signal; Indicates the power of the sensed echo signal. This indicates the interference power of the communication signal to the sensing signal. Represents the trace of a matrix. Indicates the noise power of the sensing receiver; Indicates a rank-1 constraint; This indicates that the matrix is ​​positive semi-definite.

[0033] In the question In the equation, constraints (1.2b), (1.2d), (1.2e), (1.2f), and (1.2h) are convex because they are about the matrix variables. It is linear. However, the problem remains difficult to solve due to the non-convexity caused by the combined properties of the fractional SINR term in the rate constraint (1.2c) and the rank-1 constraint (1.2g). To address these challenges, a sequential optimization strategy is proposed: the Continuous Convex Approximation (SCA) method is used to convexize the rate constraint, while a penalty-based method is incorporated into the objective function to ensure that the solution satisfies the rank-1 constraint, thereby transforming the original problem into a tractable convex optimization form.

[0034] (1) Continuous convex approximation (SCA) for non-convex rate constraints: The rate constraint (1.2c) can be equivalently rewritten as the difference between two concave functions: Non-convexity originates from the second term To make it convex, a continuous convex approximation method is used. Specifically, in the previous iteration... Local points obtained to Apply a first-order Taylor expansion.

[0035] Since the concave function is bounded above by its first-order expansion, we have: in By using its linear upper bound replace A concave lower bound for the achievable rate was obtained: At this point, the constraints become This is now a convex constraint.

[0036] (2) Penalty-based approach for handling rank-one constraints: Discarding rank-one constraints (1.2g) often results in solutions with a rank greater than 1. While Gaussian randomization is a common technique for recovering rank-one solutions, it often leads to performance degradation or violation of strict constraints. To address this issue, a penalty-based approach is employed. This utilizes the following property: for any positive semi-definite matrix... Its nuclear norm (Sum of singular values) and its spectral norm The difference between (maximum singular values) is non-negative, i.e. If and only if When the equality holds, the equation is true.

[0037] Therefore, a penalty term is added to the objective function to strengthen the rank-one property: in This is a penalty factor. Since the goal is to maximize the objective function, this penalty term needs to be subtracted. Note that for a positive semi-definite matrix, we have... Therefore, the objective becomes maximizing However, the item It is convex, which makes the objective function after applying the penalty become a non-concave function. To solve this problem, in Convex term Linearization yields its affine lower bound: in yes The eigenvector corresponding to the largest eigenvalue. Let This represents the linearization term. Then, in the... In the next iteration, the final convex formulation of the active beamforming subproblem is: (1.3a) Constraints (st): (1.2b), (1.2d) - (1.2h) (1.3c) question This is a standard convex semidefinite programming problem, which can be solved efficiently using the CVX toolbox; Obtain the optimal solution Recovery through eigenvalue decomposition .

[0038] Step 3.2: Solving the passive beamforming optimization subproblem Given an active beamforming vector and drone trajectory In the case of optimizing the RIS phase shift vector The subproblem is described as follows: (2.1a) Constraints (st): (2.1b) (2.1c) (2.1d) (2.1e) Due to the fractional objective function, coupled variables in the constraints, and the unit modulus constraint, the problem... It is nonconvex. A solution based on fractional programming (FP), semidefinite relaxation (SDR), and continuous convex approximation (SCA) is proposed.

[0039] First, we use the Lagrange dual transformation to handle the non-convex sum-log-ratio objective function. This objective function is equivalent to: in These are auxiliary variables, with one auxiliary scalar corresponding to each user. For fixed... Optimal yes .when Given, by introducing auxiliary variables , and ,in, Indicates user Signal-to-interference-plus-noise ratio; Represents the combined channel matrix. This means converting a row vector into a diagonal matrix; Indicates user The transmitted signal passes through UAV→RIS→user Following this path, in the user The equivalent channel response formed at the location; Indicates user The transmitted signal reaches the user via a direct path. The signal components. The objective function can be expressed as: Next, a second transformation is applied, introducing auxiliary variables. In the second transformation, each user corresponds to one These are used to decouple the original fractional form. The objective function is transformed into: in, To denote the real part, for a fixed... and Optimal It is given by the following formula: Substitute these In the expression, the objective function includes The quadratic term. Introduce the following auxiliary matrix. ,vector and constant : Therefore, the objective function is rewritten as .in, Represents the coefficient matrix of the quadratic term. This represents the vector of coefficients for the first-order terms. This represents a constant term.

[0040] To homogenize the quadratic form, we introduce an up-dimensional variable. , Represent the boosted RIS phase vector and construct the matrix. , Representing the coefficient matrix of the objective function: make , The enhanced RIS phase matrix satisfies and At this point, the target becomes Similarly, the quadratic terms included in the quality of service constraint (2.1b) and the serial interference cancellation constraint (2.1d) It can also be equivalently expressed as about Linear constraints: in , Let represent the constraint coefficient matrix. Substituting the above results into constraints (2.1b) and (2.1d), these constraints can be rewritten as: Next, we address the non-convex perceptual signal-to-noise ratio constraint (2.1c). Definition and , This is the conjugate transpose of the channel vector from RIS to the target. The conjugate transpose of the direct link channel vector from the UAV to the target; the effective sensing channel component is represented as... and Therefore, the perception gain term becomes: in , , The coefficient matrix represents the squared norm of the sensing channel. Represents the combined sensing channel matrix. Indicates beam The perceptual projection matrix, This represents the enhanced sensing channel vector. The sensing constraint (2.1c) is therefore reformulated as: This inequality contains a nonconvex product term with trace. ,in and This represents a fixed coefficient matrix. Applying continuous convex approximation, at points... Linearization is achieved using a first-order Taylor expansion. : in , Representation function Regarding matrix variables The gradient. By defining a scalar and And substitute the expansion into This constraint is approximated by a convex linear matrix inequality: in, Indicates the first In the next iteration, the beam Projected power on the sensing channel Indicates the first In this iteration, the sensing channel energy and coefficient matrix are... and scalar It is given by the following formula: Finally, by relaxing the rank-one constraint, the optimization problem is formulated as the following semidefinite programming problem: Constraints (st): Except for the rank-one constraint, all other constraints are convex. Therefore, the positive semidefinite relaxation method transforms the original problem into a convex optimization problem by relaxing the rank-one constraint, which can then be solved using the CVX toolbox. If the optimal solution is obtained... If the vector is not rank-one, then Gaussian randomization is used to reconstruct a feasible vector. The overall algorithm is summarized in Algorithm 1.

[0041] Algorithm 1 proposes an iterative method based on fractional programming (FP) and continuous convex approximation (SCA) for solving the passive beamforming optimization problem of RIS. In each iteration, the algorithm first calculates the current solution... Update FP auxiliary variables and This is done to process the fractional form in the objective function; then the matrix required for the communication constraints is constructed. and And at the current point, calculate the gradient of the perceptual constraint to construct the convex constraint coefficients after SCA linearization. and constant Subsequently, the convex semidefinite programming problem with relaxed rank-1 constraints was solved using the CVX solver. A new matrix solution is obtained. Repeat the above steps until the target value converges or the maximum number of iterations is reached. Finally, the optimal solution is obtained through Gaussian randomization. The RIS phase vector satisfying the unit modulus constraint is recovered from the data. This algorithm transforms the original complex problem into a series of solvable convex subproblems by using FP to handle fractional objectives, SCA to handle non-convex perceptual constraints, and SDR to handle variable coupling.

[0042] Step 3.3: Solving the UAV trajectory optimization subproblem With a fixed active beamforming vector and RIS phase shift In this case, optimize the drone trajectory The optimization problem is described as follows: (3.1a) Constraints (st): (3.1b) (3.1c) (3.1d) (3.1e) (3.1f) in, Indicates the minimum flight altitude. Indicates the maximum flight speed. Indicates the time slot length.

[0043] question Due to the location of the drone It is highly non-convex due to the complex coupling relationship with channel gain.

[0044] To decouple the trajectory variable from the fractional term, an auxiliary slack variable is introduced. , and These represent the drone to the user. The squared distances to RIS and the target are given. The following constraints are applied: in, , , Representing users respectively The location of RIS, the location of the target.

[0045] Note that the above constraints are convex constraints. Based on the defined line-of-sight and Ricean channel model, the effective channel gain... It includes direct links and RIS reflection links. After expanding all terms, this gain can be expressed as a function of slack variables: in, This represents an approximate channel gain. The path loss at the reference distance is a non-negative coefficient. , and Relying solely on fixed beamforming and phase shift: in and It is the normalized line-of-sight direction vector. Here, the symbol... Representing vectors The normalized version. Due to the function and for It is a convex function, the reconstructed channel gain It's about variables. A convex function.

[0046] Similarly, effectively sensing channel gain It is also approximated. However, due to the two-way propagation characteristics of radar echoes, the sensing gain... It includes higher-order path loss terms (i.e.) ): The coefficients are determined by the sensing beamforming matrix and the auxiliary channel matrix: Here, the Greek letter matrix , and Let represent the normalized channel components of the target direct link, cross-link, and RIS reflection link, respectively, defined as follows: Please note, Represents communication channel components, , and And it is specifically used for target perception. Similar to the communication situation, The slack variable remains a convex function.

[0047] although and It has convexity, but the problem is... The constraints remain non-convex. A continuous convex approximation method is applied to handle serial interference cancellation (SIC), quality of service (QoS), and perception constraints, respectively.

[0048] The SIC constraint (3.1f) means that for ,have This is a constraint of the form of the difference of convex functions (convex ≤ convex). To make it convex, the convex function on the right-hand side (RHS) must be modified. Perform linearization. At local points from the previous iteration... Applying a first-order Taylor expansion, we obtain the affine lower bound: Where the partial derivatives The calculation formula is: in, Indicated as to The partial derivative of the first The value of the next iteration. Indicated as to The partial derivative of the first The value of the next iteration.

[0049] By replacing the right-hand side with its lower bound, the constraint becomes This is an effective convex constraint.

[0050] For constraint (3.1d), due to the effective channel gain Nonlinear coupling with trajectory variables, achievable rate expression It exhibits non-convexity. To address this issue, an auxiliary variable is introduced. Convert constraints Furthermore, the SCA method is used to construct a concave lower bound for the rate function.

[0051] Specifically, the rate expression can be decomposed into the difference between the signal term and the interference term: Where the interference power is defined as In order to obtain The concave lower boundary is then processed separately for these two items: For the first term: Utilizing the monotonicity of the logarithmic function, use a convex function at the iteration point. First-order linear lower bound Replace it. Since log (an affine function) is concave, this operation produces a concave lower bound for the first term.

[0052] Regarding the second item: because It is a convex function, which has local points The first-order Taylor expansion at a given point constitutes a global affine lower bound.

[0053] In summary, in the first In the next iteration SCA concave lower boundary Expressed as: Finally, the original non-convex constraint It is transformed into the following convex constraint: .

[0054] Regarding the perceived signal-to-noise ratio, constraint (3.1e) can be reformulated as follows: Define the signal term on the left as... .exist to Linearization is performed to obtain its affine lower bound. : in, , These represent the values ​​of the partial derivatives at the iteration points.

[0055] right Find the derivative of the expression, and the partial derivative. It is explicitly deduced as: The approximate convex constraint is Therefore, the original non-convex trajectory optimization problem is transformed into the following convex optimization problem: Constraints (st): question This is a standard convex optimization problem, which can be solved efficiently using the CVX toolbox. Detailed steps are summarized in Algorithm 2.

[0056] Algorithm 2 describes the UAV trajectory optimization process based on the Continuous Convex Approximation (SCA). First, initialization is performed, setting a feasible initial trajectory. Convergence tolerance and maximum number of iterations In each iteration, the auxiliary constants are first updated, i.e., based on the fixed beamforming vector. and RIS phase matrix Calculate the number of channel reconstructions and perception coefficient And based on the current trajectory Calculate the corresponding distance variables The SCA parameters are then updated, including calculating the gradient used for SIC-constrained linearization. Used for QoS constraint boundaries Parameters (around) ) and the gradient used for sensing SINR constraint linearization Next, the convex subproblem is solved using the CVX solver. To obtain the optimal trajectory Finally, update the current trajectory. and number of iterations Repeat the above process until the target value converges or the maximum number of iterations is reached. It outputs the optimized drone trajectory. .

[0057] Step 4: Overall Iterative Algorithm and Performance Analysis Step 4.1, Overall Alternating Optimization Algorithm Based on the solutions to the above three sub-problems, this embodiment proposes an iterative algorithm based on alternating optimization to solve the original problem. The detailed steps are summarized in Algorithm 3; Algorithm 3: Joint Trajectory and Beamforming Optimization Algorithm Based on AO 1. Initialization: Set a feasible initial trajectory for the drone. RIS initial phase shift and active beamforming initial vector and let the iterative index Tolerance Calculate the initial target value ; 2. Iteration: In each iteration, three update steps are executed sequentially: a. Active beamforming update: Based on the current... and Solve the subproblems To obtain the optimal solution , Indicates user The beam covariance matrix of the target and the beam covariance matrix of the target being sensed are obtained; the beam covariance matrix of the target is recovered through eigenvalue decomposition. ; b. Passive beamforming update: Based on the updated... and current Algorithm 1 is executed to obtain the optimal RIS phase shift. (Depend on The constructed rank-1 positive semi-definite matrix is ​​recovered by Gaussian randomization. ; c. Drone trajectory update: based on the current... and Algorithm 2 is executed to obtain the optimal UAV trajectory. ; Calculate the current target value ; Repeat the above steps until the relative increment is reached. Or reach the maximum number of iterations Output the optimal solution .

[0058] Step 4.2: Convergence Analysis By verifying the non-decreasing property of the objective function, the convergence of the proposed algorithm 3 is theoretically guaranteed. Let Let represent the objective function containing the rank-one penalty term. Since the total system speed is bounded by the physical power constraint, it suffices to prove that in each iteration... In the middle, there is Established.

[0059] For the active beamforming and UAV trajectory subproblems, a continuous convex approximation method is employed. Let For local points The surrogate function constructed at that point. Based on a first-order Taylor expansion, It is a global concave lower bound that satisfies: make To maximize The optimal solution. The following chain of inequalities exists: For passive beamforming optimization, a quadratic transformation fractional programming method ensures the equivalence of the auxiliary objective function with the original fractional objective function. Combined with continuous convex approximation applied to perception constraints, the feasible set of the approximation problem is a subset of the original feasible set. Monotonicity is preserved by employing a non-decreasing update strategy.

[0060] Therefore, the overall objective function value sequence satisfies This ensures that the algorithm converges to a stable point.

[0061] Step 4.3: Computational Complexity Analysis The computational complexity is analyzed based on the standard interior-point method. For a given... There are constraints and the variable matrix has a size of . The semidefinite programming problem has an approximate complexity of O(n log n) for each iteration. For a person with A second-order cone programming problem with n variables, with a complexity of O(n). .

[0062] Active beamforming (semidefinite programming): This subproblem involves dimensions of... The matrix variables, and the number of constraints varies with the number of users. Linear growth (i.e.) ).Will and Substituting into the semidefinite programming complexity formula and retaining the dominant term, the complexity is approximately... .

[0063] Passive beamforming (semidefinite programming): This subproblem optimizes a size of The upgraded RIS phase shift matrix is ​​subject to constraints. One constraint. Take and The complexity is mainly due to Dominant. This confirms that complexity is... It is a polynomial, not an exponential one.

[0064] Drone trajectory (second-order cone programming): The total number of trajectory and slack variables involved in trajectory optimization is approximately The time complexity of solving this second-order cone programming problem is approximately [missing information]. .

[0065] make This represents the number of iterations required for the alternating optimization algorithm to converge. To ensure accuracy, the total computational complexity is approximately: .

[0066] Step 5: Simulation Verification and Effect Analysis To verify the effectiveness of the proposed solution in this embodiment, a comparative analysis was conducted under the following simulation conditions: The simulation is set up based on a three-dimensional Cartesian coordinate system. The drone carries a... A uniform planar array of antenna elements, with a smart reflector consisting of... It consists of several reflective units. The drone starts from its initial position. Departing from [location] meters. Two ground users are located at [locations] respectively. Mihe Meters. The perceived target is located at The intelligent reflective surface is deployed on the building facade, and its location is... Meters. Total transmit power Noise power Minimum flight altitude Maximum speed of drone Minimum rate threshold Perceived signal-to-noise ratio threshold Number of time slots / time slot length : Reference path loss Path loss index Rice's K factor .

[0067] Comparison scheme: In order to fully evaluate the superiority of the proposed NOMA-ISAC framework, it is compared with five benchmark schemes; Unperceived constraints: Solving the problem without considering the perceived SINR constraint (1f), representing the theoretical upper bound of communication performance.

[0068] Fixed trajectory (straight flight): The drone flies at a constant speed from... Flying in a straight line to the destination, only beamforming and phase shift are optimized.

[0069] OMA scheme: The system uses time division multiple access instead of NOMA, that is, time slots are divided to serve users in an orthogonal manner.

[0070] Random phase: optimizes UAV trajectory and active beamforming, but RIS phase shift follows a uniform distribution. Randomly generated.

[0071] Two-dimensional trajectory: Optimizing the horizontal trajectory of drones At the same time, maintain a fixed height .

[0072] like Figure 3As shown, for all considered reconfigurable smart surface sizes, the objective function value monotonically increases with the number of iterations. It can be observed that the algorithm typically converges within a relatively small number of iterations (e.g., 5-8 iterations), validating the effectiveness and computational efficiency of the proposed alternating optimization method. Furthermore, the objective function value increases monotonically with the number of reconfigurable smart surface units. The increase in gain significantly improves system performance, which is attributed to enhanced passive beamforming gain and spatial diversity effect.

[0073] Figure 4 The optimized 3D trajectory of the UAV throughout the mission cycle is demonstrated. The visualization clearly shows that the UAV does not fly in a simple straight line. Instead, it adaptively adjusts its path, moving towards the RIS and the ground user cluster (UE1 and UE2). In the initial phase, the UAV descends from its initial altitude while simultaneously moving horizontally to shorten the distance to the communication nodes, thereby improving line-of-sight (LoS) channel conditions. As the mission progresses, the UAV hovers near the users to maximize communication and data rate while maintaining a geometric configuration that ensures the sensed targets are adequately illuminated to meet detection requirements. This dynamic adjustment confirms the necessity of joint motion planning in complex sensory integration scenarios.

[0074] Figure 5 This illustrates the variation of instantaneous sum and velocity with perceived signal-to-noise ratio (SNR) over flight time slots, where the left and right vertical axes represent communication sum and velocity with perceived SNR, respectively. The left axis shows that sum and velocity are highest during the initial flight phase (e.g., ...). The speed increased rapidly up to 20 bps / Hz. This improvement is attributed to trajectory optimization: the UAV maneuvers from its starting position toward the user and RIS, gradually shortening the communication link distance and increasing the line-of-sight probability. As the UAV reaches its optimal hovering position, the speed eventually saturates and stabilizes at approximately 49 bps / Hz. Meanwhile, the right axis reveals the dynamic behavior of the sensing performance. It can be seen that the sensing signal-to-noise ratio is strictly maintained at a preset threshold throughout the mission. Above dB, ensuring continuous and reliable target tracking. It is worth noting that, within time slots... A noticeable peak appeared nearby. By comparing it with the trajectory, this interval corresponds to the phase where the drone flew past the perceived target at the closest possible distance. Although the signal-to-noise ratio dropped slightly as the drone subsequently moved toward the communication user, the optimization algorithm ensured that it never violated the quality of service constraints.

[0075] Figure 6 This histogram illustrates the power distribution ratio between communication and sensing signals during flight. and The proportion. A clear two-stage trend can be observed from the simulation results. In the initial flight phase ( Up to 10), most of the transmit power (approximately 60%–65%) is allocated to the sensing beam. This phenomenon can be attributed to the initial geometric conditions: at this point, the UAV is relatively far from the sensing target. Under stringent sensing requirements (signal-to-interference-plus-noise ratio...), Under these conditions, the optimization algorithm is forced to allocate more power budget to the sensing function to compensate for higher path losses and ensure reliable target detection. This is achieved through... Figure 4 By comparing the trajectory with that of the aircraft, a deeper understanding can be gained. During the intermediate flight phase (approximately...) (Up to 15), the UAV maneuvers to a position closer to the sensing target and user 2. This improved geometry significantly enhances the channel gain, thereby lowering the threshold for meeting strict sensing signal-to-interference-plus-noise ratio (SINR). The minimum sensing power required is determined. Therefore, driven by the objective function, the remaining power budget is adaptively reallocated to maximize communication and rate, resulting in a sharp increase in the communication power allocation. Subsequently, the UAV begins to move slightly away from the sensing target to maintain proximity to User 2, eventually stabilizing at an optimal hovering position. At this stage, the system achieves resource balance between the two functional objectives, and the power allocation ratio tends to stabilize.

[0076] Figure 7 The number of RIS reflector units throughout the entire flight time was studied. The impact on system performance was compared. The instantaneous time and rate. Simulation results show that, due to the higher passive beamforming gain, the instantaneous time and rate are increased. Typically, the sum and rate increase. However, as flight progresses, the performance gap between the different curves tends to narrow. This convergence is attributed to the dominant role of the direct link. Specifically, as the UAV optimizes its trajectory to fly over the RIS and approach the user, the direct link between the UAV and the user is significantly enhanced. In this close-range scenario, the strong line-of-sight direct path plays a dominant role in determining channel capacity, making the additional gain from the RIS negligible. Therefore, the influence of the RIS size gradually diminishes, and in the final stable phase, the sum and rates tend to converge.

[0077] Figure 8 The average and rate are depicted as a function of the perceived signal-to-interference-plus-noise ratio threshold. The changes, among which The value ranges from -6 dB to 0 dB. Simulations were performed on different RIS sizes. The following steps were taken. The results show that, with increasing perceptual requirements... The requirements become more stringent, and the rate exhibits a decreasing trend. This confirms the inherent competition for limited space and power resources between dual-function tasks; specifically, to achieve a higher perceived signal-to-interference-plus-noise ratio (SINR), the beamforming vector must be more precisely aligned with the target, inevitably leading to a reduction in the power allocated to the communication user. However, a key finding is that increasing the size of the RIS can significantly alleviate this performance trade-off. Figure 7 As shown, for smaller RIS sizes, and with increasing speed... The rate decreases sharply with increasing speed. In contrast, for large-scale RIS, the rate decrease is negligible, and the curve remains almost flat. Therefore, deploying large-scale RIS effectively decouples sensing and communication functions, enabling the system to achieve high-resolution sensing while having a negligible impact on communication capacity.

[0078] Figure 9 The effectiveness of the proposed framework was verified, and the main findings are summarized as follows: First, the proposed scheme significantly outperforms baseline schemes such as OMA, random phase, and fixed trajectory. Notably, the NOMA-ISAC scheme significantly surpasses the OMA benchmark, confirming the significant spectral efficiency advantage brought by NOMA power domain multiplexing. Second, the advantage of three-dimensional mobility is evident. Compared with constrained two-dimensional trajectory and straight-line flight schemes, the proposed method utilizes vertical degrees of freedom to optimize flight altitude and establish a stronger line-of-sight link, thereby achieving a higher sum rate. Third, the comparison with the random phase scheme highlights the crucial role of RIS passive beamforming. The significant performance degradation caused by the lack of phase alignment emphasizes the necessity of jointly optimizing the trajectory and phase shift. Finally, the performance curve of the proposed scheme closely follows the theoretical upper bound of the unperceived constraints. The gap between the two indicates that the algorithm satisfies strict perception constraints while incurring only an acceptable communication cost, achieving an efficient dual-function integrated design.

[0079] Figure 10The effectiveness of the proposed framework under different transmit powers was verified, and the main findings are summarized as follows: First, the proposed scheme consistently outperforms baseline schemes such as OMA, random phase, and fixed trajectory at all power levels. The significant gap with the OMA benchmark confirms the spectral efficiency advantage of NOMA power domain multiplexing, especially at higher transmit powers. Second, the three-dimensional mobility demonstration is crucial: by optimizing altitude and horizontal position, the proposed method establishes a stronger line-of-sight link than constrained two-dimensional or straight-line flight schemes, achieving higher sum-rate gain, which expands with increasing power. Third, the comparison with random phase schemes highlights the necessity of RIS passive beamforming—without phase alignment, performance degrades sharply at high power, emphasizing the necessity of jointly optimizing trajectory and phase. Finally, the curves of the proposed scheme closely follow the theoretical upper bound of the unperceived constraint, indicating that the communication cost of the perceived constraint is minimal. This demonstrates an efficient dual-function design that can robustly scale with transmit power while maintaining near-optimal throughput.

[0080] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely illustrative of the principles of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A joint optimization method for UAVs and reconfigurable smart surfaces for sensory integration, characterized by: Includes the following steps: A system model is constructed, the system comprising: a UAV equipped with a dual-function antenna array for simultaneously transmitting communication signals and radar detection signals; and a reconfigurable smart surface deployed on the ground; Ground user equipment Index for users, ; and at least one perceived target; task duration Discretize into Each time slot For slot index The duration of each time slot is And define drones in the first The three-dimensional trajectory of each time slot is ,in, , , These represent the drones in the [number]th [month]. Each time slot axis, axis, Axis coordinates; Construct a joint optimization problem to maximize the average sum rate of all users over the task cycle. For the goal, among which For users In the Achievable data rates per time slot; using the UAV's active beamforming vector The passive reflection coefficient matrix of RIS and the three-dimensional trajectory To optimize the variables, constraints were set, including communication service quality constraints, perception performance constraints, serial interference cancellation power ordering constraints for non-orthogonal multiple access protocols, UAV kinematic constraints, and RIS unity mode constraints. The joint optimization problem is decomposed into three sub-problems: active beamforming optimization, passive beamforming optimization, and UAV trajectory optimization. An iterative algorithm is then used to solve these sub-problems.

2. The method for joint optimization of UAVs and reconfigurable smart surfaces for sensory integration as described in claim 1, characterized in that: The system model includes: The channel model adopts the generalized Ricean fading model, where any given link in a time slot... The channel vector or matrix model is as follows: in, Let be the Euclidean distance between the transmitter and receiver. This is the path loss index. The path loss is set at a reference distance of 1 meter; parameters , where is the Rice factor, representing the ratio of the deterministic line-of-sight component power to the random non-line-of-sight component power; The direction matrix for the line-of-sight component, and the non-line-of-sight component. It reflects the multipath scattering effect and follows the standard Rayleigh fading distribution; It is a non-line-of-sight component matrix, represented as the product of the array response vectors corresponding to the angle of arrival and the angle of departure; For a node equipped with a uniform planar array, the array response vector is: in Indicates the antenna spacing. For wavelength, It is the azimuth angle. The pitch angle, This is expressed as the number of antenna elements along the x and y axes. Represented as direction cosine; Signal transmission model, UAV in time slot The signal sent Composed of superimposed communication signals and radar detection signals, it is represented as: in and The first The information symbols of each user and their corresponding communication beamforming vectors and These are represented as radar detection signals and their corresponding sensing beamforming vectors, respectively, and satisfy the total transmit power constraint. , This is the maximum transmission power; set up For RIS to users The conjugate transpose of the channel vector. The channel matrix from the UAV to the RIS. For drones to users The conjugate transpose of the direct link channel vector, then the user The conjugate transpose of the equivalent synthesized channel vector is ,in This is the diagonal matrix of RIS reflection coefficients. For RIS phase shift vector, For the first Phase shift of each RIS unit, and set the reflection amplitude to unit 1; user The received signal is: in, It is additive white Gaussian noise. This represents noise power.

3. The method for joint optimization of UAVs and reconfigurable smart surfaces for sensory integration as described in claim 2, characterized in that: The specific serial interference cancellation power sorting constraint is as follows: Users are sorted in ascending order of equivalent channel strength, i.e. To ensure that users can successfully decode and eliminate interference in this order, according to the NOMA principle, the following must be satisfied: Among them radar detection signals Known at the transmitting end, the user end prioritizes decoding and elimination, and the conditions for successful elimination are: Under the premise of satisfying the above power ranking, the user The reachable signal-to-interference-plus-noise ratio (SINR) for decoding its own signal is: Corresponding achievable data rate .

4. The method for joint optimization of UAVs and reconfigurable smart surfaces for sensory integration according to claim 2, characterized in that: The specific constraints on perception performance are as follows: set up Let be the channel vector from RIS to the sensing target. Let be the direct link channel vector from the UAV to the sensing target, then the equivalent one-way sensing channel vector is: ,in, express The conjugate transpose of the matrix; the effective round-trip sensing channel matrix is ​​approximately: ; The signal-to-interference-plus-noise ratio (SIR) of the radar echo signal must meet a preset threshold to ensure target detection performance. This constraint is expressed as: in This refers to the noise power of the radar receiver. To sense the signal-to-interference-plus-noise ratio threshold.

5. The method for joint optimization of UAVs and reconfigurable smart surfaces for sensory integration according to claim 4, characterized in that: Solving the active beamforming optimization subproblem includes: Given a drone trajectory and RIS phase shift matrix Optimize the active beamforming vector under the given conditions. Introducing auxiliary rank-one positive definite matrix variables and And define the channel covariance matrix. and This transforms the original problem into a semidefinite programming problem. Introducing auxiliary variables Indicates user To determine the rate, apply a continuous convex approximation to the non-convex rate constraint, rewriting the rate expression as the difference between two concave functions. Then, perform a first-order Taylor expansion on the second term at the current iteration point to obtain the concave lower bound. ; For rank-one constraints, a penalty function-based approach is adopted, adding a penalty term to the objective function. ,in As a penalty factor, The nuclear norm is the sum of the singular values ​​of a matrix. This represents the spectral norm, which is the largest singular value of the matrix. Convex At the current iteration point Linearization to affine lower bound: in yes The eigenvector corresponding to the largest eigenvalue; This ultimately leads to a convex semidefinite programming subproblem: Constraints include: power constraints Perceived SINR constraints The trace form of SIC power ordering constraints, and the rate lower bound constraint. and semidefinite constraints .

6. The method for joint optimization of UAVs and reconfigurable smart surfaces for sensory integration according to claim 5, characterized in that: Solving the passive beamforming optimization subproblem includes: Given an active beamforming vector and drone trajectory Optimize the RIS phase shift vector under the given conditions. ; First, a Lagrange dual transformation is used to process the non-convex sum-logarithm-ratio objective function, and auxiliary variables are introduced. and The result of the quadratic transformation is as follows: function ,in: in, , ; Introducing Dimensional Upgrade Variables sum matrix The objective function and all constraints are homogenized to be about The linear form; Define the sensing channel correlation matrix: , ; , , This is the conjugate transpose of the channel vector from RIS to the target. This is the conjugate transpose of the direct link channel vector from the UAV to the target; For non-convex trace product terms existing in perceptual constraints The continuous convex approximation method is used at the current iteration point. Performing a first-order Taylor expansion yields the linearized constraints: in Relax the rank constraint through semi-definite relaxation. The resulting convex semidefinite programming subproblem is solved using the CVX solver. If the solution is not rank-one, the Gaussian randomization method is used to recover the RIS phase vector that satisfies the unit modulus constraint. .

7. The method for joint optimization of UAVs and reconfigurable smart surfaces for sensory integration as described in claim 6, characterized in that: Solving the UAV trajectory optimization subproblem includes: With a fixed active beamforming vector and RIS phase shift Optimize drone trajectory under the following conditions Introducing auxiliary slack variables , and These represent the drone to the user. Calculate the squared distance between RIS and the target, and apply convex constraints: in , , Representing users respectively Location, RIS location, target location; Channel gain Represented as a convex function of the distance variable: The coefficients are determined by a fixed beamforming and RIS phase shift: and It is a normalized line-of-sight direction vector. The path loss at the reference distance; Perceived gain Represented as: The coefficients are determined by the sensing beamforming matrix and the auxiliary channel matrix: in, and For non-convex SIC constraints , By linearizing the right-hand convex function at the current iteration point, we obtain the affine lower bound. ; For non-convex rate constraints, the rate expression is decomposed into two terms, and a concave lower bound is constructed using SCA: in , This is the value of the l-th iteration; For the sensing SINR constraint, the signal term Linearization is performed at the current iteration point to obtain the affine lower bound. This is transformed into a convex constraint: The final result is a convex second-order cone programming subproblem, which is solved using the CVX solver.

8. The method for joint optimization of UAVs and reconfigurable smart surfaces for sensory integration according to claim 7, characterized in that: The joint optimization problem is solved using an iterative algorithm based on alternating optimization: Initialize drone trajectory RIS phase shift Active beamforming vector Set the iteration index tolerance Calculate the initial target value ; In each iteration: Active beamforming update: based on current and Solve the convex subproblem as described in claim 5 to obtain the optimal solution. , Indicates user The beam covariance matrix of the target and the beam covariance matrix of the target being sensed are obtained; the beam covariance matrix of the target is recovered through eigenvalue decomposition. ; Passive beamforming update: based on the updated and current Update fractional programming auxiliary variables and Solving the convex subproblem as described in claim 6 yields the following results: Recovery by Gaussian randomization ; Drone trajectory update: based on current and Update the SCA parameters and solve the convex subproblem as described in claim 7 to obtain the following results. ; Calculate the current target value ; Repeat the above steps until the relative increment is reached. Or reach the maximum number of iterations Output the optimal solution .

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