Unmanned aerial vehicle-based sensing integrated beam forming and trajectory optimization method

Abstract

The invention provides an unmanned aerial vehicle (UAV)-based flux-inductance integrated beam forming and trajectory optimization method, on one hand, an FP-AROS method is proposed based on fractional programming and semi-definite relaxation technologies in combination with approximate rank-one solution construction to carry out optimization design on ISAC beams, the Cramer-Rao bound of AoD is adopted as a sensing performance evaluation index, and the FP-AROS method is adopted to carry out optimization design on the ISAC beams; target estimation performance can be reflected more directly, so that a collaborative optimization effect of communication and sensing performance is realized; on the other hand, the invention provides an improved continuous convex approximation method based on a trust domain, and the method is used for optimization design of a UAV track. The ITRSCA method obtains a local trend approximate solution of an original objective function by calculating a second derivative, and introduces a dynamic trust domain mechanism to control approximate precision, so as to ensure global convergence of an output solution; in addition, the method is combined with a penalty function method to process non-convex constraints, and the limitation of a trust domain method in a constrained optimization problem is effectively overcome.

Description

Technical Field

[0001] The present invention relates to the technical field of Integrated Sensing and Communication (ISAC), and more specifically, to a method for integrated sensing and communication beamforming and trajectory optimization based on an unmanned aerial vehicle (UAV). Background Art

[0002] With the rapid development of 5G-A / 6G communication technologies, ISAC, as an emerging wireless technology, has shown significant advantages in simultaneously meeting the requirements of high-rate communication and high-precision sensing. Multiple-Input-Multiple-Output (MIMO) technology, as one of the core supports of modern wireless communication systems, plays a key role in both communication and radar systems. In an ISAC system, MIMO beamforming design has become a current research hotspot. Existing research shows that by optimizing the beam design in an ISAC system, both communication performance improvement and sensing accuracy improvement can be achieved simultaneously.

[0003] However, existing ISAC research mainly focuses on traditional ground network scenarios and is not suitable for low-altitude scenarios, and it has the following technical limitations: 1) The sensing performance highly depends on the Line-of-Sight (LOS) transmission condition between the sensing target and the transceiver. For sensing targets far from the base station or blocked by obstacles, the sensing performance drops sharply; 2) The coverage range of ground base stations is limited, making it difficult to meet the requirements of wide-area communication and wide-area sensing.

[0004] To address the above problems, researchers have introduced unmanned aerial vehicles (UAVs) as a new type of aerial ISAC platform, which has the following technical advantages: 1) The high-altitude deployment characteristic of UAVs can ensure strong LOS paths in the Air-to-Ground (A2G) channel, thus significantly improving the sensing performance; 2) UAVs have flexible mobility and can be deployed as quasi-stationary air access points (APs), or as mobile APs close to the target area, which can effectively reduce the sensing power requirement; 3) The UAV platform can expand the coverage range of the ISAC system and significantly improve the overall system performance.

[0005] Currently, researchers have made certain progress in both the fields of UAV communication and sensing, forming various technologies and system solutions such as UAV relay communication, energy-efficient communication, interference network optimization, and synthetic aperture radar. However, the research on UAV-assisted ISAC systems is still in its infancy. Different from traditional independently designed systems, due to the mobile characteristics of UAVs, the communication and sensing performance of UAV-based ISAC systems are affected by more complex factor couplings than in traditional scenarios, including beamforming design, communication and sensing resource allocation, and UAV trajectory optimization. These all bring new technical challenges to the performance optimization of UAV-ISAC systems.

[0006] The existing patent document with the publication number "CN119628698A" provides a method for joint optimization of UAV communication and sensing trajectory and beamforming. This method first constructs the UAV communication and sensing environment. In this environment, the UAV uses non-orthogonal multiple access technology to send superimposed signals, and then establishes a bit rate model and a sensing power model, and constructs an objective function based on these two models. Finally, the UAV flight parameter constraints are set, and under this constraint, an improved particle swarm algorithm is used to solve the optimal solution of the objective function. However, this method focuses on maximizing the weighted sum of the communication user throughput and the effective target sensing power, with a relatively high algorithm complexity, and the overall communication spectrum efficiency and adaptability to complex constraint problems still need to be improved. Summary of the Invention

[0007] To overcome the deficiencies of the low overall communication spectrum efficiency and adaptability to complex constraint problems in the above-mentioned existing technologies, combined with the mobile characteristics of UAVs, the present invention provides a method for integrated communication and sensing beamforming and trajectory optimization based on UAVs, which can reduce the computational complexity, while improving the adaptability to complex constraint problems while ensuring global convergence, and finally achieves the goal of maximizing the overall communication spectrum efficiency of the system on the premise of ensuring that the sensing performance meets the preset requirements.

[0008] To solve the above technical problems, the technical solution of the present invention is as follows:

[0009] A method for integrated communication and sensing beamforming and trajectory optimization based on UAVs, comprising the following steps:

[0010] S1: Build an integrated communication and sensing system including at least one UAV, multiple ground users, and multiple ground sensing targets. Among them, the UAV serves as an aerial access point to provide downlink communication services for ground users, and at the same time performs radar sensing on ground sensing targets.

[0011] S2: Construct a communication model of the integrated communication and sensing system, calculate the communication spectrum efficiency between the UAV and each ground user according to the communication model, and estimate the Cramer-Rao bound of the departure angle between the UAV and each ground sensing target.

[0012] S3: Introduce sensing constraints according to the Cramer-Rao lower bound of the departure angles between the UAV and each ground sensing target, and construct a beamforming optimization problem with the goal of maximizing the communication spectral efficiency between the UAV and each ground user;

[0013] S4: Solve the beamforming optimization problem based on fractional programming and semidefinite relaxation techniques to obtain the optimized beam vector results between the UAV and each ground user;

[0014] S5: Construct a UAV trajectory optimization problem based on the optimized beam vector results between the UAV and each ground user;

[0015] S6: Transform the sensing constraints into penalty terms to reconstruct the UAV trajectory optimization problem, and use the trust-region-based Successive Convex Approximation (SCA) algorithm to iteratively solve the reconstructed UAV trajectory optimization problem to obtain the optimized results of the UAV trajectory vector;

[0016] S7: Repeat steps S3 - S6 several times to perform several rounds of alternating optimization on the beam vectors and UAV trajectory vectors between the UAV and each ground user, and solve to obtain the optimal beam vectors between the UAV and each ground user by combining the construction of an approximate rank-one solution, and obtain the optimal trajectory vector of the UAV.

[0017] Preferably, in step S1, the integrated communication and sensing system includes at least one UAV, K single-antenna ground users, and J ground sensing targets; the UAV is equipped with a uniform linear array of M antennas and flies from a preset initial position to a target position within the mission period T;

[0018] Use the UAV as an aerial access point to provide downlink communication services for ground users and simultaneously perform radar sensing on ground targets;

[0019] Represent the index sets of ground users and ground sensing targets as and Denote the planar position of ground user as u k =(u k,x , u k,y ), and the planar position of ground sensing target as v j =(v j,x , v j,y );

[0020] Decompose the mission period T into N time slots, with the duration of each time slot being The time slot index is Denote the planar position of the UAV as q[n]=(q x [n], q y[n]), and assume that the UAV flies at a fixed altitude H that meets air traffic control regulations;

[0021] The UAV transmits a signal matrix in time slot n where L is the signal frame length; the signal matrix X[n] satisfies X[n]=W[n]S[n], where contains data streams sent to K ground users. Assume that the data streams are independent of each other, that is (·) H is the conjugate transpose operator; is the beamforming matrix, which is used to simultaneously realize communication and sensing functions.

[0022] Preferably, in step S2, the communication model of the communication and sensing integrated system includes: a communication received signal sub-model and a sensing received signal sub-model;

[0023] The communication received signal sub-model is constructed based on the LOS channel model. Assume that the Doppler effect caused by the movement of the UAV has been fully compensated at the ground user end; the channel vector h of the UAV to ground user k in time slot n k is expressed as:

[0024]

[0025] where β0 represents the channel power gain corresponding to the reference distance d0, represents the distance between the UAV and ground user k, a k [n] represents the antenna steering vector pointing to ground user k, satisfying d is the antenna spacing, λ is the wavelength, θ k [n] is the departure angle between the UAV and ground user k, (·) T is the transpose operator;

[0026] The signal y received by ground user k in time slot n k is expressed as:

[0027]

[0028] where, is the desired signal, represents the interference between users, represents the additive Gaussian white noise received by ground user k, is the noise power;

[0029] The communication spectral efficiency R of ground user k in time slot n k is expressed as:

[0030]

[0031] The described sensing received signal sub-model includes:

[0032] Assume that the Doppler frequency shift caused by the ground sensing target and the UAV movement has been fully compensated, and the ground sensing target is modeled as an unstructured point target. Then, the sensing channel G j [n] of the ground sensing target j is expressed as:

[0033]

[0034] where is the complex reflection coefficient, ∈ j represents the radar cross-section of the ground sensing target j, e j [n] is the distance between the UAV and the ground sensing target j; in a monostatic radar setup, θ j [n] is the departure angle between the UAV and the ground sensing target j;

[0035] The Cramer-Rao lower bound C(θ j [n]) for estimating the departure angle θ j [n] between the UAV and each ground sensing target is expressed as:

[0036]

[0037] where represents the derivative of A j [n]| θ with respect to θ j [n], is the magnitude of the sensing noise.

[0038] Preferably, in the step S3, the constructed beamforming optimization problem is specifically:

[0039]

[0040] where η k represents the weight coefficient of the ground user k, and the larger η k is, the higher the priority of the ground user k in the spectrum efficiency optimization; the constraint C1 is the sensing constraint, indicating that the value of the Cramer-Rao lower bound is less than a given threshold ξ to ensure that the sensing performance meets the preset requirements; the constraint C2 indicates that the transmission power of the UAV cannot exceed the maximum power P max .

[0041] Preferably, the step S4 includes:

[0042] Converting the problem P1 into a semidefinite programming problem based on the semidefinite relaxation technique, and further equivalently converting this semidefinite programming problem into the problem P2 by applying the Lagrangian dual transformation method:

[0043]

[0044] Among them, is an introduced auxiliary variable, where and is the first set of auxiliary variables;

[0045]

[0046] Use the quadratic transformation method to transform problem P2 into problem P3:

[0047]

[0048] Among them, is the second set of auxiliary variables;

[0049] Alternately optimize Z, Δ, and until the maximum number of iterations l 1,max is reached, then terminate the iteration and obtain the optimal solution of problem P3, denoted as which represents the beam vector optimization results between the UAV and each ground user.

[0050] Preferably, when alternately optimizing Z, Δ, and until the maximum number of iterations l 1,max is reached, terminating the iteration and obtaining the optimal solution of problem P3 includes:

[0051] Set the initial value of, and sequentially execute the following l 1,max alternate optimization steps:

[0052] Fix Set the derivative of problem P2 with respect to ζ k,n to zero to obtain the optimal solution of Z which is expressed as:

[0053]

[0054] According to Fix Z, set the derivative of problem P3 with respect to δ k,n to zero to obtain the optimal solution of Δ which is expressed as:

[0055]

[0056] According to Fix Z, and according to fix Δ, use the CVX tool to solve problem P3 to obtain the solution result of problem P3;

[0057] When the maximum number of iterations l is reached1,max Terminate the iteration to obtain the optimal solution to problem P3

[0058] Preferably, in the step S5, the constructed UAV trajectory optimization problem is specifically:

[0059]

[0060] C7: q[1] = q I , q[N] = q F

[0061] where:

[0062]

[0063] represents the distance between the ground user k and the UAV, represents the matrix the element in the p-th row and p-th column of, represents the matrix the phase angle of the element in the p-th row and q-th column of; the constraint C6 represents that the maximum flight speed of the UAV is limited to V max ; the constraint C7 represents that the initial horizontal position and the final horizontal position of the UAV are q I and q F respectively.

[0064] Preferably, the step S6 includes:

[0065] Denote the total number of alternating optimization rounds of the beam vector between the UAV and each ground user and the UAV trajectory vector as E;

[0066] Use the UAV trajectory vector q (ε-1) [n] obtained in the (ε - 1)-th round of iteration to approximately replace the UAV trajectory vector q (ε) [n] in the ε-th round for calculating the which is expressed as:

[0067]

[0068] where,

[0069] Approximate Ω k (q[n]) further as:

[0070]

[0071] where, g k,n is the first-order derivative at the point q (ε-1) [n];

[0072] Transform the perception constraint C1 into a penalty term to reconstruct the UAV trajectory optimization problem P4, obtaining problem P5, which is expressed as:

[0073]

[0074] where μ(q[n]) is a penalty function, defined as:

[0075]

[0076] For the l-th iteration process in the ε-th round, approximate C(θ j [n]) in the penalty function μ(q[n]) in problem P5 by a second-order Taylor expansion to obtain the approximated penalty function The approximation of C(θ j [n]) is expressed as:

[0077]

[0078] where f j (l) [n], and are respectively the function value, the first-order derivative, and the second-order partial derivative matrix of C(θ j [n]) at the point q (l) [n];

[0079] Decompose into where is a positive semi-definite matrix, and further approximate the second-order term, expressed as:

[0080]

[0081] Introduce a trust region constraint to transform problem P5 into problem P6:

[0082]

[0083] where ψ (l) is the size of the trust region radius at the l-th iteration;

[0084] Use the CVX tool to iteratively solve problem P6. In the l-th iteration process, obtain the local optimal solution of the current problem P5 by iteratively solving problem P6. If the objective function value does not increase after substituting this local optimal solution into problem P5, then reduce the radius of the trust region to ψ (l) = ψ (l) / 2, and continue the iterative optimization; until ψ (l) is lower than the given threshold χ or reaches the given maximum number of iterations l 2,maxWhen this happens, the iterative process is terminated, and at this time, the optimal solution q of problem P5 in the ε-th round is obtained. (ε) [n], as the optimization result of the UAV trajectory vector in the ε-th round.

[0085] Preferably, in step S7, after the E-round alternating optimization of the beam vectors and UAV trajectory vectors between the UAV and each ground user, the results obtained from the E-round alternating optimization are obtained. Solve the rank-one matrix respectively according to the following formula and the auxiliary matrix W′ n :

[0086]

[0087] After Gaussian randomization of the auxiliary matrix W n ′, combined with the rank-one matrix to obtain the optimal beam vectors between the UAV and each ground user

[0088] Preferably, in step S7, after the E-round alternating optimization of the beam vectors and UAV trajectory vectors between the UAV and each ground user, the optimal solution q of problem P5 in the E-th round is obtained. (E) [n], and take q (E) [n] as the optimal trajectory vector q * [n] of the UAV.

[0089] Compared with the prior art, the beneficial effects of the technical solution of the present invention are:

[0090] The present invention provides an integrated communication and sensing beamforming and trajectory optimization method based on UAVs, which realizes the alternating optimization of ISAC beamforming and UAV trajectories;

[0091] On the one hand, based on Fractional Programming (FP) and Semi-Definite Relaxation (SDR) techniques, the present invention proposes a Fractional Programming with Approximate Rank-One Solution (FP-AROS) method for the optimal design of ISAC beams; the FP-AROS method can achieve a higher communication rate compared to traditional methods such as Gaussian Randomization (GR) by designing an efficient rank-one solution approximation scheme; at the same time, the Cramér-Rao Bound (CRB) of the Angle of Departure (AoD) is used as the sensing performance evaluation index, which can more directly reflect the target estimation performance compared to the traditional beam pattern gain index, thus achieving the co-optimization effect of communication and sensing performance;

[0092] On the other hand, the present invention proposes an Improved Trust-Region based Successive Convex Approximation (ITRSCA) method for the optimal design of UAV trajectories; the ITRSCA method obtains a local trend approximation solution of the original objective function by calculating the second derivative, and introduces a dynamic trust-region mechanism to control the approximation accuracy to ensure the global convergence of the output solution; in addition, it combines the penalty function method to handle non-convex constraints, effectively overcoming the limitations of the trust-region method in constrained optimization problems; compared with traditional benchmark methods such as SCA, the ITRSCA method has significant performance advantages and provides an efficient solution for the trajectory design of UAVs;

[0093] Overall, the above alternating optimization method for ISAC beamforming and UAV trajectories can be called the FP-AROS-and-ITRSCA-based Alternating Optimization (FIAO) method, which can reduce the computational complexity, improve the adaptability to complex constraint problems while ensuring global convergence, and finally achieve the goal of maximizing the overall communication spectrum efficiency of the system on the premise of ensuring that the sensing performance meets the preset requirements. Description of the Drawings

[0094] Figure 1 It is a flowchart of a method for integrated communication and sensing beamforming and trajectory optimization based on an unmanned aerial vehicle provided in Embodiment 1.

[0095] Figure 2 It is a flowchart of an integrated communication and sensing beamforming and trajectory optimization method based on an unmanned aerial vehicle provided in Embodiment 2.

[0096] Figure 3 It is a graph showing the variation of the average spectral efficiency of different methods provided in Embodiment 3 with the number of antennas.

[0097] Figure 4 It is a graph showing the variation trend of the average spectral efficiency of different methods provided in Embodiment 3 with the CRB threshold.

[0098] Figure 5 It is a comparison graph of the UAV trajectories of the ITRSCA method and the existing method provided in Embodiment 3.

[0099] Figure 6 It is a graph of the average spectral efficiency of different trajectory optimization methods provided in Embodiment 3. Detailed implementation manners

[0100] The accompanying drawings are only for illustrative purposes and should not be construed as limitations to this application;

[0101] To better illustrate this embodiment, some components in the accompanying drawings are omitted, enlarged or reduced, which do not represent the dimensions of the actual product;

[0102] For those skilled in the art, it is understandable that some well-known structures and their descriptions in the accompanying drawings may be omitted.

[0103] The technical solutions of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0104] Embodiment 1

[0105] As Figure 1 shown, this embodiment provides an integrated communication and sensing beamforming and trajectory optimization method based on an unmanned aerial vehicle, including the following steps:

[0106] S1: Build an integrated communication and sensing system including at least one unmanned aerial vehicle, multiple ground users and multiple ground sensing targets. Among them, the unmanned aerial vehicle serves as an aerial access point to provide downlink communication services for ground users, and at the same time performs radar sensing on ground sensing targets;

[0107] S2: Construct a communication model of the integrated communication and sensing system, calculate the communication spectral efficiency between the unmanned aerial vehicle and each ground user according to the communication model, and estimate the Cramer-Rao bound of the angle of departure between the unmanned aerial vehicle and each ground sensing target;

[0108] S3: According to the Cramér-Rao bound (CRB) of the departure angle between the UAV and each ground sensing target, introduce sensing constraints, and construct a beamforming optimization problem with the goal of maximizing the communication spectral efficiency between the UAV and each ground user;

[0109] S4: Solve the beamforming optimization problem based on fractional programming and semidefinite relaxation techniques to obtain the optimized beam vector results between the UAV and each ground user;

[0110] S5: Based on the optimized beam vector results between the UAV and each ground user, construct a UAV trajectory optimization problem;

[0111] S6: Transform the sensing constraints into penalty terms to reconstruct the UAV trajectory optimization problem, and use the trust-region-based Successive Convex Approximation (SCA) algorithm to iteratively solve the reconstructed UAV trajectory optimization problem to obtain the optimized results of the UAV trajectory vector;

[0112] S7: Repeat steps S3 - S6 several times to perform several rounds of alternating optimization on the beam vectors and UAV trajectory vectors between the UAV and each ground user, and combine the construction of an approximate rank-one solution to solve for the optimal beam vectors between the UAV and each ground user, and obtain the optimal trajectory vector of the UAV.

[0113] In the specific implementation process, first build a communication and sensing integrated system, which includes at least one UAV, multiple ground users, and multiple ground sensing targets. Among them, the UAV serves as an aerial access point to provide downlink communication services for ground users, and at the same time performs radar sensing on ground sensing targets;

[0114] Then construct a communication model of the communication and sensing integrated system, calculate the communication spectral efficiency between the UAV and each ground user according to the communication model, and estimate the Cramér-Rao bound of the departure angle between the UAV and each ground sensing target;

[0115] Different from the existing solutions that generally use the beam pattern gain to measure the target estimation performance, this solution introduces the CRB as a sensing performance evaluation index; the CRB is the theoretical lower bound of the mean squared error (MSE) of parameter estimation, and its value directly reflects the minimum estimable error of the AoD; in addition, in a multi-target sensing scenario, it can effectively characterize the coupling effect between targets, so as to achieve the collaborative optimization effect of communication and sensing performance; in contrast, the traditional beam pattern gain can only reflect the power concentration degree of the beam in the target direction, while ignoring the influence of factors such as noise magnitude and channel model on the sensing performance, and there is no direct mathematical correlation with the parameter estimation accuracy. Therefore, the beam pattern gain may not be able to fully reflect the sensing performance in practical applications;

[0116] After that, first optimize the beamforming. According to the Cramér-Rao bound of the departure angle between the UAV and each ground sensing target, introduce sensing constraints, and construct a beamforming optimization problem with the goal of maximizing the communication spectral efficiency between the UAV and each ground user; solve the beamforming optimization problem based on fractional programming and semidefinite relaxation techniques to obtain the optimized beam vector results between the UAV and each ground user;

[0117] Then optimize the UAV trajectory. Based on the optimized beam vector results between the UAV and each ground user, construct a UAV trajectory optimization problem; transform the sensing constraints into penalty terms to reconstruct the UAV trajectory optimization problem, and use the trust-region-based SCA algorithm to iteratively solve the reconstructed UAV trajectory optimization problem to obtain the optimized results of the UAV trajectory vector;

[0118] During the optimization process of the UAV trajectory, this method introduces a dynamic trust-region mechanism to control the approximation accuracy and ensure the global convergence of the output solution; at the same time, combines the penalty function method to handle non-convex constraints, effectively overcoming the limitations of the trust-region method in constrained optimization problems;

[0119] Finally, repeat the steps of beamforming and trajectory optimization several times, perform alternating optimization on the beam vector and the UAV trajectory vector between the UAV and each ground user for several rounds, and combine the construction of an approximate rank-one solution to solve and obtain the optimal beam vector between the UAV and each ground user, and obtain the optimal trajectory vector of the UAV;

[0120] For the solution of the optimal beam vector between the UAV and each ground user, compared with using traditional eigenvalue decomposition or Gaussian randomization methods to obtain feasible solutions, this method proposes a new method for constructing an approximate rank-one solution, which can significantly improve the system performance and reduce the computational complexity at the same time;

[0121] This method can reduce the computational complexity, and at the same time improve the adaptability to complex constraint problems while ensuring global convergence, and finally achieves the goal of maximizing the overall communication spectral efficiency of the system on the premise of ensuring that the sensing performance meets the preset requirements.

[0122] Embodiment 2

[0123] As Figure 2 shown, this embodiment provides a communication and sensing integrated beamforming and trajectory optimization method based on a UAV, including the following steps:

[0124] S1: Build a communication and sensing integrated system including at least one UAV, multiple ground users and multiple ground sensing targets. Among them, the UAV serves as an air access point to provide downlink communication services for ground users, and at the same time performs radar sensing on ground sensing targets;

[0125] S2: Construct the communication model of the integrated communication and sensing system, calculate the communication spectral efficiency between the UAV and each ground user according to the communication model, and estimate the Cramer-Rao bound of the departure angle between the UAV and each ground sensing target;

[0126] S3: According to the Cramer-Rao bound of the departure angle between the UAV and each ground sensing target, introduce sensing constraints, and construct a beamforming optimization problem with the goal of maximizing the communication spectral efficiency between the UAV and each ground user;

[0127] S4: Solve the beamforming optimization problem based on fractional programming and semidefinite relaxation techniques to obtain the optimized beam vector results between the UAV and each ground user;

[0128] S5: Based on the optimized beam vector results between the UAV and each ground user, construct a UAV trajectory optimization problem;

[0129] S6: Transform the sensing constraints into penalty terms to reconstruct the UAV trajectory optimization problem, and use the trust-region-based SCA algorithm to iteratively solve the reconstructed UAV trajectory optimization problem to obtain the optimized results of the UAV trajectory vector;

[0130] S7: Repeat steps S3 - S6 several times to perform several rounds of alternating optimization on the beam vector and the UAV trajectory vector between the UAV and each ground user, and combine the construction of an approximate rank-one solution to solve for the optimal beam vector between the UAV and each ground user, and obtain the optimal trajectory vector of the UAV.

[0131] In the specific implementation process, the application scenario of this method is a typical ISAC scenario based on UAVs. The technical solution is elaborated in detail below;

[0132] First, build an integrated communication and sensing system, which includes a UAV, K ground single-antenna users, and J ground sensing targets; the UAV is equipped with a uniform linear array (ULA) containing M antennas and flies from a preset initial position to the target position within the mission period T; the UAV serves as an aerial AP to provide downlink communication services for ground users and simultaneously performs radar sensing on ground targets; the user index set and the sensing target index set are respectively represented as and Let the planar position of user be denoted as u k =(u k,x , u k,y ), which can be obtained through uplink signal estimation or the Global Positioning System (GPS); the planar position of the sensing target is denoted as v j =(vj,x , v j,y ), and its value is usually determined by the specific sensing task; for example, v j can be set to the uniform sampling position of the region of interest in the object detection task, or can be set to the estimated position of the previous frame in the object tracking task; for the convenience of system optimization, in this embodiment, the entire task cycle T is decomposed into N time slots, and the duration of each time slot is The time slot index is The planar position of the UAV is denoted as q[n] = (q x [n], q y [n]), and it is assumed that it flies at a fixed altitude H that meets the air traffic control specifications;

[0133] At the transmitter, the UAV transmits the signal matrix at time slot n, where L is the signal frame length; more specifically, the signal matrix can be expressed as X[n] = W[n]S[n], where contains the data streams sent to K users; without loss of generality, in this embodiment, it is assumed that the data streams are independent of each other, that is where (·) H is the conjugate transpose operator; this assumption holds asymptotically when the frame length L is large enough; in addition, is the beamforming matrix, which is used to simultaneously achieve communication and sensing functions and is one of the core design goals of this method;

[0134] Next, a communication model of the integrated communication and sensing system is constructed, and the communication spectral efficiency between the UAV and each ground user is calculated according to the communication model, and the Cramér-Rao bound of the departure angle between the UAV and each ground sensing target is estimated;

[0135] In this embodiment, the communication model of the integrated communication and sensing system includes: a communication received signal sub-model and a sensing received signal sub-model;

[0136] 1) Communication received signal sub-model:

[0137] Since there is generally a strong LOS path in the A2G scenario, in this embodiment, a communication received signal sub-model is constructed based on the LOS channel model. In addition, for the convenience of analysis, it is assumed that the Doppler effect caused by the UAV mobility has been fully compensated at the communication user end through means such as frequency offset estimation; based on the above assumptions, the channel vector h k from the UAV to the ground user k at time slot n is expressed as:

[0138]

[0139] where β0 represents the channel power gain corresponding to the reference distance d0 = 1m, represents the distance between the UAV and the ground user k, ak [n] represents the antenna steering vector pointing to the ground user k, satisfying d is the antenna spacing, λ is the wavelength, and θ k [n] is the departure angle between the UAV and the ground user k, and (·) T is the transpose operator;

[0140] The signal y received by the ground user k at time slot n k [n] is expressed as:

[0141]

[0142] where is the desired signal, represents the interference between users, represents the additive white Gaussian noise (AWGN) received by the ground user k, is the noise power;

[0143] Therefore, the communication spectral efficiency R of the ground user k at time slot n k [n] is expressed as:

[0144]

[0145] 2) The received signal sensing sub-model includes:

[0146] For the radar sensing task of the target in the mission area, assuming that the Doppler frequency shift caused by the ground sensing target and the UAV movement has been fully compensated, and the ground sensing target is modeled as an unstructured point target, then the sensing channel G of the ground sensing target j j [n] is expressed as:

[0147]

[0148] where is the complex reflection coefficient, ∈ j represents the radar cross-section (RCS) of the ground sensing target j, e j [n] is the distance between the UAV and the ground sensing target j; in a monostatic radar setup, θ j [n] is the departure angle between the UAV and the ground sensing target j;

[0149] Different from the existing solutions that generally use beam pattern gain to measure target estimation performance, this solution introduces the CRB as a perception performance evaluation metric; the CRB is the theoretical lower bound of the mean squared error (MSE) of parameter estimation, and its value directly reflects the minimum estimable error of AoD; in addition, in the multi-target perception scenario, it can effectively characterize the coupling effect between targets, thus achieving the co-optimization effect of communication and perception performance; in contrast, the traditional beam pattern gain can only reflect the power concentration degree of the beam in the target direction, while ignoring the influence of factors such as noise magnitude and channel model on perception performance, and there is no direct mathematical correlation with parameter estimation accuracy. Therefore, the beam pattern gain may not be able to fully reflect perception performance in practical applications;

[0150] For the point target scenario, when other target directions are given, estimate the departure angle θ between the UAV and each ground perception target j The Cramér-Rao bound C(θ j [n]) of [n], which is expressed as:

[0151]

[0152] where denotes A j [n]| θ the derivative of θ j [n], is the magnitude of the perception noise;

[0153] Based on the above communication model, the design goal of this method is to maximize the overall communication spectrum efficiency of the system on the premise of ensuring that the perception performance meets the preset requirements; specifically, when the perception performance measurement index C(θ j [n]) meets the specified constraints, by jointly optimizing the ISAC beam vector {w k [n]} and the UAV trajectory vector {q[n]}, to achieve the maximization of R k [n];

[0154] Due to the tight coupling relationship between the UAV trajectory vector and the beamforming vector, and involving complex perception constraint conditions, it is difficult to directly solve the ISAC beam vector {w k [n]} and the UAV trajectory vector {q[n]}; aiming at the above technical difficulties, this embodiment designs a new alternating optimization scheme, by decoupling the optimization variables and adopting an iterative solution strategy to obtain a high-quality local optimal solution;

[0155] The alternating optimization scheme mainly includes two parts: 1) Beamforming optimization based on FP-AROS; 2) UAV trajectory optimization based on ITRSCA;

[0156] 1) Beamforming Optimization Based on FP-AROS:

[0157] According to the alternating optimization strategy, first, optimize the ISAC beam vector {w k [n]} under the assumption of any given UAV trajectory vector, which corresponds to solving the following optimization problem:

[0158]

[0159] where η k represents the weight coefficient of the ground user k. The larger η k is, the higher the priority of the ground user k in spectrum efficiency optimization; the constraint C1 is the sensing constraint, indicating that the value of the Cramér-Rao bound is less than the given threshold ξ to ensure that the sensing performance meets the preset requirements; the constraint C2 means that the transmission power of the UAV cannot exceed the maximum power P max ;

[0160] For the non-convex characteristic of the objective function in Problem P1, this method first converts it into a semi-definite programming problem (SDP) based on the SDR technique, that is, introduce auxiliary variables where and

[0161] After relaxing the rank constraint, since the converted objective function is still non-convex, further apply the Lagrangian dual transformation method to equivalently convert it into the following problem:

[0162]

[0163] where, is the first set of auxiliary variables,

[0164] The optimization variables and the variable {ζ k,n} in Problem P2 can be iteratively optimized; when fixing , set the derivative of the objective function with respect to ζ k,n to zero to obtain the optimal solution Specifically expressed as:

[0165]

[0166] After fixing the set of auxiliary variables Z according to Equation (8), Problem P2 is still a non-convex problem. For this, this method equivalently converts it into the following problem by using the quadratic transformation method:

[0167]

[0168] Among them, is the second auxiliary variable set; in P3, when the auxiliary variables Z and Δ are fixed, the objective function with respect to the variable is concave, and thus the CVX tool can be used to solve it; similarly, when and Z are fixed, the optimal solution can be obtained by setting the derivative of the objective function with respect to δ k,n to zero Specifically expressed as:

[0169]

[0170] In summary, by alternately optimizing Z and Δ, reaching the maximum number of iterations l 1,max when the iteration is terminated, problem P3 can be solved to obtain the optimal solution of problem P3

[0171] Specifically, first set the initial value, and successively execute the following l 1,max alternate optimization steps:

[0172] a) Fix According to Equation (8), set the derivative of problem P2 with respect to ζ k,n to zero to obtain the optimal solution of Z

[0173] b) According to Fix Z, and according to Equation (10), set the derivative of problem P3 with respect to δ k,n to zero to obtain the optimal solution of Δ Expressed as:

[0174]

[0175] c) According to Fix Z, and according to fix Δ, and according to Equation (9), use the CVX tool to solve problem P3 to obtain the solution result of problem P3;

[0176] After the above transformation, the relaxed problem P3 can be solved, but the non-convex rank constraint still needs to be processed By analyzing the Karush-Kuhn-Tucker (KKT) optimal conditions of P3, it is found that due to the existence of the sensing constraint C3, the system does not have a rank-one optimal solution; compared with using the traditional eigenvalue decomposition or Gaussian randomization method to obtain a feasible solution, this embodiment proposes a new construction method for an approximate rank-one solution, which can significantly improve the system performance and reduce the computational complexity at the same time; the specific construction process of this method is as follows:

[0177] a) First, find the optimal solution of problem P3, denoted as

[0178] b) Solve separately according to the following formula and W′ n :

[0179]

[0180] where and z ∈ κ;

[0181] It can be proved that is also the solution of problem P3; in the above method of constructing a rank-one solution, the core idea is to replace the matrix with a rank-one matrix while keeping the useful signal power of user k unchanged, and by constructing an auxiliary matrix W′ n , making the sets and equivalent under constraints C3 and C4; in this way, it can be ensured that while the original objective function and constraints remain unchanged, the rank constraint on is simplified to the rank constraint on W′ n ;

[0182] Therefore, the first K - 1 rank-one matrices can be obtained through equations (11) and (12), that is, the first two steps have obtained Then, after calculating the auxiliary matrix W′ n through equation (13), performing Gaussian randomization on the auxiliary matrix W′ n can obtain the complete K rank-one matrices, that is, obtain the complete optimal beam vector This step can effectively reduce the computational complexity;

[0183] In addition, the beam-related variable actually used in the trajectory optimization of this embodiment is instead of w k [n], so the obtained from the previous round of optimization can be directly substituted for calculation; but for beam optimization, the ultimate goal is to obtain So, equations (11) to (13) are used to obtain from To avoid introducing errors into the intermediate beam-trajectory alternating optimization iteration process, the calculations of equations (11) to (13) are only performed after the E-th iteration;

[0184] 2) UAV trajectory optimization based on ITRSCA:

[0185] After obtaining the ISAC beam according to the FP-AROS method, the UAV trajectory vector {q[n]} can be further optimized; at this time, the optimization problem can be simplified as:

[0186]

[0187] wherein:

[0188]

[0189] wherein: represents the distance between user k and the UAV, represents the matrix the element in the p-th row and p-th column of, represents the matrix the phase angle of the element in the p-th row and q-th column of; the constraint C6 describes that the maximum flight speed is limited to V max ; the constraint C7 indicates that the initial horizontal position and the final horizontal position of the UAV are q I , q F ;

[0190] Due to the highly non-linear relationship between the trajectory variables and the channel vectors, the objective function in problem P4 is difficult to solve; to simplify the calculation, the UAV trajectory vector q (ε-1) [n] obtained in the (ε - 1)-th iteration can be approximately used to replace the UAV trajectory vector q (ε) [n] in the ε-th iteration for calculating wherein, the iteration number ε represents the number of rounds of the process of alternately optimizing the beam vector and the trajectory vector; the specific approximation expression is as follows

[0191]

[0192] wherein:

[0193] Since the relevant formulas in the following text all refer to the ε-th iteration, for the sake of simplicity of description, unless otherwise specified, the following relevant variables omit the superscript (·) (ε) ;

[0194] Using Equation (17), the objective function of Equation (15) can be approximately expressed as:

[0195]

[0196] wherein, g k,n is the first-order derivative at the point q (ε-1) [n]; it can be proved that g k,n < 0, and the global lower bound of Equation (18) is a concave function;

[0197] After the above transformation, the objective function of problem P4 has been transformed into a concave function. However, due to the complexity of the sensing performance constraint conditions, it is still difficult to solve directly. The existing popular SCA solution methods use linear approximations of the first-order Taylor expansion, but there are problems such as insufficient approximation accuracy caused by ignoring high-order curvature information. Different from this, in this embodiment, first, the second-order Taylor expansion of constraint C3 is strictly derived, and a trust region mechanism is introduced to more accurately approximate the local trend of the original function while ensuring the convergence of the method. Second, to solve the limitations of the trust region scheme in constrained problems, this embodiment further proposes a hybrid strategy combining penalty functions, converting the constraints into penalty terms of the objective function, so that the constraint violation amount can be flexibly adjusted, improving the adaptability to complex constraint problems while ensuring global convergence. The new solution method adopted in this embodiment is elaborated in detail below;

[0198] First, convert the sensing constraint C1 into a penalty term, thereby reconstructing problem P4 as:

[0199]

[0200] where the penalty function is defined as:

[0201]

[0202] According to the definition of the penalty function, when the sensing constraint conditions are satisfied, the value of the penalty function is zero, and at this time, no penalty is imposed on the original objective function. When the sensing constraint conditions are not satisfied, the value of the penalty function is determined by the current CRB value. The larger C(θ j [n]) is, the stronger the penalty. This design mechanism can effectively control the sensing constraints. When solving problem P5, due to the high complexity of the penalty function, this embodiment applies the trust-region-based SCA method to solve it iteratively. Specifically, in the l-th iteration process, for the local trajectory vector q (l) [n], the non-concave part of the objective function can be approximated as the second-order Taylor expansion, which is specifically expressed as follows:

[0203]

[0204] where, f j (l) [n], and are the function value, the first-order derivative, and the second-order partial derivative matrix of C(θ j [n]) at the point q (l) [n] respectively. Since the second-order partial derivative matrix is not positive semi-definite, the convexity of equation (21) cannot be guaranteed. Therefore, can be decomposed into where is a positive semi - definite matrix; the second - order term in Equation (21) can be approximated as:

[0205]

[0206] When \(v > - v\) min the approximated second - order term in Equation (22) is convex, where \(v\) min is the minimum eigenvalue of the matrix After the approximation in Equations (21) - (22), the penalty function can be converted into a concave function, denoted as To ensure the accuracy of the approximation, a trust - region constraint mechanism can be further introduced, that is, in each iteration process, the selection range of the approximate point is restricted within the trust - region; after imposing the trust - region constraint, Problem P5 can be converted into an iterative solution form of Problem P6, and thus can be efficiently solved by the CVX tool:

[0207]

[0208] where \(\psi\) (l) is the size of the trust - region at the \(l\) - th iteration; theoretically, when setting a sufficiently small trust - region radius, the convergence of Equation (23) can be ensured;

[0209] In an actual system, in the \(l\) - th iteration process, by iteratively solving Problem P6 to obtain the local optimal solution of the current P5. If the objective function value does not increase after substituting this local optimal solution into P5, then the radius of the trust - region is reduced to \(\psi\) (l) =\(\psi\) (l) / 2, and continue the iterative optimization; when \(\psi\) (l) is lower than the given threshold \(x\) or reaches the given maximum number of iterations \(l\) 2,max the iterative process can be terminated, and the obtained \(\{q[n]\}\) is the optimal solution at this time;

[0210] Due to the non - positive definiteness of the second - order partial derivative matrix the iterative process of P6 is to handle the non - convexity of the penalty function; "after the \(l\) - th iteration of solving Problem P6" can be understood as: the \(l\) - th iteration (for P5) of solving Problem P6 (each iteration makes an internal iteration for P6 to obtain the solution of P5 at this time), that is, an internal iteration for P6 is required during iteration to obtain a stable solution, and then substitute this stable solution into P5 and determine the size of the trust - region according to the change of the objective function value of P5;

[0211] Finally, repeat the steps of FP - AROS and ITRSCA several times, perform several rounds of alternating optimization on the beam vector and the UAV trajectory vector, and combine Equations (11) - (13) to solve for the optimal beam vector between the UAV and each ground user, and obtain the optimal trajectory vector of the UAV;

[0212] Based on the above analysis, for the convenience of reading, the alternating optimization solution designed in this embodiment is summarized in Table 1, where E is the maximum number of alternating optimizations;

[0213] Table 1 FIAO method proposed in this embodiment

[0214]

[0215] This method (FIAO) can reduce the computational complexity, and at the same time improve the adaptability to complex constraint problems while ensuring global convergence. Finally, the goal of maximizing the overall communication spectrum efficiency of the system is achieved on the premise that the sensing performance meets the preset requirements.

[0216] Embodiment 3

[0217] This embodiment provides a simulation experiment to verify the effectiveness of a drone-based integrated communication and sensing beamforming and trajectory optimization method proposed in Embodiment 2.

[0218] In the specific implementation process, the simulation parameters of the integrated communication and sensing system constructed in this embodiment are shown in Table 2:

[0219] Table 2 System simulation parameter table

[0220]

[0221] First, the performance of the FP-AROS beam optimization method is verified and compared with the following test schemes:

[0222] 1) Successive Convex Approximation with Gaussian Randomization (SCA-GR) method: This scheme uses the SCA method to iteratively solve the problem P1 converted into a convex problem, and uses the GR scheme to handle the rank-1 constraint;

[0223] 2) Successive Convex Approximation with Approximate Rank-One Solution (SCA-AROS) method: The SCA method is used to iteratively solve the problem P1 converted into a convex problem, and the AROS scheme proposed by the present invention is applied to handle the rank-1 constraint;

[0224] 3) Fractional Programming with Gaussian Randomization (FP-GR) method: The FP method described in this scheme is used to solve P1, and the GR scheme is used to handle the rank-1 constraint;

[0225] As Figure 3 shown Figure 3 it verifies the average spectral efficiency of the FP-AROS beam optimization method under different numbers of antennas which is defined as: As Figure 3 shown, the average spectral efficiency achieved by the proposed AROS scheme approximately increases linearly with the increase in the number of antennas, indicating that more antennas provide higher beamforming gain; while the GR scheme does not show a similar growth trend, indicating that direct Gaussian randomization is not an effective beam optimization scheme, and the FP scheme applied in Example 2 exhibits significant performance advantages compared with the traditional SCA method, further demonstrating the effectiveness of the proposed method;

[0226] As Figure 4 shown Figure 4 it shows the average spectral efficiency that can be obtained under different CRB threshold conditions of AoD estimation; it can be seen from the figure that as the threshold ζ increases, the average spectral efficiency shows an upward trend; this is because when the sensing requirement decreases, more power can be allocated for communication, thus optimizing the spectral efficiency; at the same time, this result indicates that under the same threshold requirement, the AROS method proposed in Example 2 can effectively improve the spectral efficiency, and the FP method also has better performance than the traditional SCA method; as the threshold increases, the FP-AROS method proposed in Example 2 can obtain more performance advantages;

[0227] Next, the performance of the integrated FIAO method in Example 2 is evaluated;

[0228] This example considers trajectory optimization schemes such as Straight Flight (SF), Fly-Hover-Fly (FHF), and Trust-Region based Successive Convex Approximation (TRSCA) as comparisons; for fair comparison, all schemes use the FP-AROS method proposed in Example 2 to optimize the beam;

[0229] As Figure 5 shown Figure 5In (a) and (b), the UAV trajectory results optimized by the proposed ITRSCA method and the TRSCA method are compared respectively. When only performing the sensing task, the flight trajectory generated by the ITRSCA method significantly biases towards the target sensing area, thus effectively meeting the specific sensing task requirements. However, the trajectory result generated by the TRSCA method is close to the SF and cannot achieve the optimization of sensing performance. In addition, when the CRB threshold ξ gradually increases, the UAV flight trajectory optimized by the ITRSCA method shows an obvious user approach tendency to provide a higher data rate communication service, while the trajectory optimized by the TRSCA method does not show a similar trend. The above experimental results show that the ITRSCA method has significant adaptive advantages compared with the TRSCA method, can be dynamically adjusted according to different sensing task requirements, and effectively improves the communication rate while meeting the sensing performance requirements.

[0230] Finally, as Figure 6 shown, Figure 6 the communication and sensing performance under different trajectory optimization methods is compared. Figure 6 In (a), it shows that the average spectral efficiency of each method increases with the increase of the number of antennas, and the proposed ITRSCA method can achieve a higher spectral efficiency, which fully shows that its UAV trajectory has been more fully optimized, making the UAV closer to the communication user area on the premise of meeting the sensing requirements, thus improving the communication performance. Figure 6 In (b), the relationship between the average spectral efficiency and the CRB threshold is analyzed. The proposed ITRSCA method is significantly better than the SF, FHF, and TRSCA schemes. In addition, when the CRB threshold is small, the performance gap between the four design schemes is small, because to ensure the sensing requirements, the flightable area of the UAV is more restricted, thus restricting the design freedom of the trajectory optimization. In addition, when the CRB threshold is large enough, the average spectral efficiency gradually reaches the upper bound. At this time, most of the transmit power is allocated to maximize the communication rate, and the sensing requirements can be met by reusing the communication signal.

[0231] The same or similar reference numerals correspond to the same or similar components.

[0232] The terms describing the positional relationship in the drawings are only for illustrative purposes and should not be construed as a limitation to this application.

[0233] Obviously, the above embodiments of the present invention are only examples for clearly illustrating the present invention, and are not limitations to the implementation manners of the present invention. For those of ordinary skill in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to enumerate all the implementation manners here. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. A method for integrated communication and sensing beamforming and trajectory optimization based on an unmanned aerial vehicle, characterized in that It includes the following steps: S1: Build a communication and sensing integrated system including at least one unmanned aerial vehicle (UAV), multiple ground users, and multiple ground sensing targets. Among them, the UAV serves as an aerial access point to provide downlink communication services for ground users, and at the same time performs radar sensing on ground sensing targets; S2: Construct a communication model of the communication and sensing integrated system, calculate the communication spectral efficiency between the UAV and each ground user according to the communication model, and estimate the Cramér-Rao bound of the departure angle between the UAV and each ground sensing target; S3: According to the Cramér-Rao bound of the departure angle between the UAV and each ground sensing target, introduce sensing constraints, and construct a beamforming optimization problem with the goal of maximizing the communication spectral efficiency between the UAV and each ground user; S4: Solve the beamforming optimization problem based on fractional programming and semidefinite relaxation techniques to obtain the optimized result of the beam vector between the UAV and each ground user; S5: Based on the optimized result of the beam vector between the UAV and each ground user, construct a UAV trajectory optimization problem; S6: Transform the sensing constraint into a penalty term to reconstruct the UAV trajectory optimization problem, and use the trust-region-based Successive Convex Approximation (SCA) algorithm to iteratively solve the reconstructed UAV trajectory optimization problem to obtain the optimized result of the UAV trajectory vector; S7: Repeat steps S3 - S6 several times, perform several rounds of alternating optimization on the beam vector and the UAV trajectory vector between the UAV and each ground user, and combine the construction of an approximate rank-one solution to solve for the optimal beam vector between the UAV and each ground user, and obtain the optimal trajectory vector of the UAV.

2. The integrated communication and sensing beamforming and trajectory optimization method based on an unmanned aerial vehicle according to claim 1, wherein In step S1, the communication and sensing integrated system includes at least one UAV, K single-antenna ground users, and J ground sensing targets; the UAV is equipped with a uniform linear array of M antennas and flies from a preset initial position to a target position within a mission period T; Take the UAV as an aerial access point to provide downlink communication services for ground users, and at the same time perform radar sensing on ground targets; Denote the index sets of ground users and ground sensing targets as and Denote the planar position of the ground user as u k =(u k,x , u k,y ), and denote the planar position of the ground sensing target as v j =(v j,x , v j,y ); Decompose the task cycle T into N time slots, and the duration of each time slot is The time slot index is Denote the planar position of the UAV as q[n] = (q x [n], q y [n]), and assume that the UAV flies at a fixed altitude H that meets air traffic control regulations; The UAV transmits a signal matrix in time slot n where L is the length of the signal frame; the signal matrix X[n] satisfies X[n]=W[n]S[n], where contains data streams sent to K ground users. It is assumed that the data streams are independent of each other, that is (·) H is the conjugate transpose operator; is the beamforming matrix, which is used to simultaneously implement communication and sensing functions.

3. The integrated communication and sensing beamforming and trajectory optimization method based on an unmanned aerial vehicle according to claim 2, wherein In step S2, the communication model of the communication and sensing integrated system includes: a communication received signal sub-model and a sensing received signal sub-model; Construct the communication received signal sub-model based on the LOS channel model, assuming that the Doppler effect caused by the movement of the UAV has been fully compensated at the ground user end; the channel vector h k at the UAV to the ground user k at time slot n is expressed as: Among them, β0 represents the channel power gain corresponding to the reference distance d0, represents the distance between the UAV and the ground user k, a k [n] represents the antenna steering vector pointing to the ground user k, satisfying d is the antenna spacing, λ is the wavelength, θ k [n] is the departure angle between the UAV and the ground user k, (·) T is the transpose operator; The signal y received by the ground user k at time slot n k is expressed as Among them, is the desired signal, represents the interference between users, represents the additive white Gaussian noise received by the ground user k, is the noise power; The communication spectral efficiency R of the ground user k in time slot n k is expressed as: The sensing received signal sub-model includes: Assume that the Doppler frequency shift caused by ground sensing targets and UAV movement has been fully compensated, and the ground sensing targets are modeled as unstructured point targets. Then, the sensing channel \(G\) j [n] of the ground sensing target \(j\) is expressed as: Among them, is the complex reflection coefficient, ∈ j represents the radar reflection surface of the ground sensing target j, e j [n] is the distance between the UAV and the ground sensing target j; in the case of a monostatic radar setting, θ j [n] is the departure angle between the UAV and the ground sensing target j; Estimate the departure angle θ between the UAV and each ground sensing target j The Cramér-Rao lower bound C(θ j [n]) of [n], which is expressed as: Among them, represents A j [n]| θ the derivative of θ j [n], is the perceived noise level.

4. The integrated communication and sensing beamforming and trajectory optimization method based on an unmanned aerial vehicle according to claim 3, wherein In step S3, the specifically constructed beamforming optimization problem is: Among them, η k represents the weight coefficient of the ground user k. The larger η k is, the higher the priority of the ground user k in spectrum efficiency optimization. The constraint C1 is the sensing constraint, indicating that the value of the Cramer-Rao bound is less than the given threshold ξ to ensure that the sensing performance meets the preset requirements. The constraint C2 means that the transmission power of the UAV cannot exceed the maximum power P max .

5. A method for integrated communication and sensing beamforming and trajectory optimization based on an unmanned aerial vehicle, characterized in that, Step S4 includes: Based on the semidefinite relaxation technique, convert problem P1 into a semidefinite programming problem, and further apply the Lagrangian dual transformation method to equivalently convert this semidefinite programming problem into problem P2: Among them, is the introduced auxiliary variable, where and is the first set of auxiliary variables; Use the quadratic transformation method to convert problem P2 into problem P3: s.t. C3 - C5 Among them, is the second auxiliary variable set; Alternately optimize Z, Δ, and terminate the iteration when reaching the maximum number of iterations l 1,max to obtain the optimal solution of problem P3, denoted as indicating the beam vector optimization results between the UAV and each ground user.

6. The integrated communication and sensing beamforming and trajectory optimization method based on an unmanned aerial vehicle according to claim 5, wherein The alternating optimization of Z, Δ, and reaches the maximum number of iterations l 1,max terminates the iteration, and obtaining the optimal solution to problem P3 includes: Set the initial value, and sequentially execute l 1,max times of the following alternating optimization steps: Fixed Set the derivative of problem P2 with respect to ζ k,n to zero to obtain the optimal solution of Z which is expressed as: According to Fix Z, and set the derivative of problem P3 with respect to δ k,n to zero to obtain the optimal solution of Δ which is expressed as: According to Fix Z, according to Fix Δ, use the CVX tool to solve problem P3, and obtain the solution result of problem P3; Terminate the iteration when the maximum number of iterations \(l\) is reached 1,max and obtain the optimal solution to problem \(P3\) 7. A joint sensing and communication beamforming and trajectory optimization method based on an unmanned aerial vehicle according to claim 6, wherein In step S5, the specifically constructed UAV trajectory optimization problem is: s.t. C1 C7: q[1] = q I , q[N] = q F Where: denotes the distance between the ground user k and the UAV denotes the matrix and is the element in the p-th row and p-th column of the matrix denotes the matrix and is the phase angle of the element in the p-th row and q-th column of the matrix; the constraint C6 represents that the maximum flight speed of the UAV is limited to V max ; the constraint C7 represents that the initial horizontal position and the final horizontal position of the UAV are q I and q F respectively.

8. A method for integrated communication and sensing beamforming and trajectory optimization based on an unmanned aerial vehicle, characterized in that, Step S6 includes: Denote the total number of alternating optimization rounds of the beam vector and the UAV trajectory vector between the UAV and each ground user as E; Using the UAV trajectory vector q (ε-1) [n] obtained from the (ε - 1)-th round of iteration to approximately replace the UAV trajectory vector q (ε) [n] in the ε-th round for calculating which is expressed as: Among them, Denote Ω k (q[n]) is further approximated as: where g k,n is the first derivative at point q (ε-1) [n]; Convert the sensing constraint C1 into a penalty term to reconstruct the UAV trajectory optimization problem P4 to obtain problem P5, expressed as: s.t. C6, C7 Where, μ(q[n]) is a penalty function, defined as: For the $l$-th iteration process in the $\epsilon$-th round, approximate $C(\theta j [n])$ in the penalty function $\mu(q[n])$ in problem P5 by a second-order Taylor expansion to obtain the penalty function after approximation processing The approximation processing of $C(\theta j [n])$ is expressed as: wherein, and are the function value, the first-order derivative, and the second-order partial derivative matrix of C(θ j [n]) at the point q (l) [n], respectively; Decompose into where is a positive semi - definite matrix, and further approximate the second - order term, which is expressed as: Introduce a trust-region constraint to convert problem P5 into problem P6: s.t. C6, C7 where ψ (l) is the trust region radius size at the l-th iteration; Use the CVX tool to iteratively solve problem P6. During the l-th iteration, obtain the local optimal solution of the current problem P5 by iteratively solving problem P6. If the objective function value does not increase after substituting this local optimal solution into problem P5, then reduce the radius of the trust region to ψ (l) = ψ (l) / 2, and continue with iterative optimization; until ψ (l) is lower than the given threshold χ or reaches the given maximum number of iterations l 2,max at which point, terminate the iterative process. At this time, obtain the optimal solution q (ε) [n] of problem P5 in the ε-th round, as the optimization result of the UAV trajectory vector in the ε-th round.

9. A method for integrated communication and sensing beamforming and trajectory optimization based on an unmanned aerial vehicle, characterized in that, In step S7, after the E-round alternating optimization of the beam vectors between the UAV and each ground user and the UAV trajectory vector, the results obtained from the E-round alternating optimization are obtained. Solve the rank-one matrix respectively according to the following formula and the auxiliary matrix W' n : For the auxiliary matrix W′ n After performing Gaussian randomization and combining it with a rank-one matrix The optimal beam vectors between the UAV and each ground user are obtained 10. A method for integrated communication and sensing beamforming and trajectory optimization based on an unmanned aerial vehicle according to claim 8, characterized in that In the step S7, after the E-round alternating optimization of the beam vectors between the UAV and each ground user and the UAV trajectory vector, the optimal solution q (E) [n] of the problem P5 in the E-th round is obtained, and q (E) [n] is used as the optimal trajectory vector q * [n] of the UAV.

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