Enhanced high-energy-efficiency cooperative covert communication method based on low-altitude economy

Abstract

The invention discloses an enhanced high-energy-efficiency cooperative covert communication method based on low-altitude economy, and relates to the technical field of wireless communication, and the method comprises the following specific steps: system model construction: constructing a basic framework of an air network ISAC system composed of M unmanned aerial vehicles, K ground users and mobile Willie, the unmanned aerial vehicles being capable of switching between a JUAV mode and an IUAV mode, by constructing a complex system model and combining a flexible interference framework and an optimization algorithm, accurate tracking and observation of a mobile monitor can be realized, and on this basis, by jointly optimizing the service role of the unmanned aerial vehicle, communication / interference power distribution and unmanned aerial vehicle trajectory design, the rate of covert communication can be maximized, and the communication efficiency can be improved. And meanwhile, the risk detected by an enemy or a potential threat person is reduced, not only is the concealment of communication improved, but also the security of communication content is ensured, and a more reliable guarantee is provided for wireless communication in low-altitude economy.

Description

Technical Field

[0001] The present invention relates to the field of wireless communication technology, and in particular to an enhanced high-energy-efficiency collaborative covert communication method based on low-altitude economy. Background Art

[0002] With the rapid development of the low-altitude economy, low-altitude flying equipment such as drones have been widely used in logistics, monitoring, communications and other fields. When performing tasks, these devices often need to communicate wirelessly with ground users or other drones to ensure real-time data transmission and effective execution of tasks. However, the security of wireless communications has always been an important issue in the field of low-altitude economy.

[0003] In the current wireless communication environment, covert communication has become an important means to ensure communication security. Covert communication aims to protect the communication content from being stolen or interfered with by reducing the probability of communication signals being detected by the enemy or potential threat actors. However, existing covert communication schemes face many challenges in their applications in the low-altitude economy. On the one hand, wireless communications in low-altitude environments are susceptible to a variety of interference factors, such as ground reflections, multipath effects, etc. These factors will reduce the signal-to-noise ratio of communication signals, thereby affecting the communication quality. On the other hand, existing covert communication schemes are often based on fixed communication modes and parameter settings, which are difficult to adapt to the complex and changeable communication needs in low-altitude environments. In addition, with the increase in the number of drones and the complexity of communication tasks, how to improve the energy efficiency and resource utilization of the system while ensuring the concealment of communications has also become an urgent problem to be solved in the low-altitude economy.

[0004] In response to the above problems, existing covert communication schemes have many limitations. Some schemes cover up communication signals by adding interference signals, but this method may reduce the receiving signal-to-noise ratio of legitimate users, thereby affecting the communication quality. Other schemes improve concealment by optimizing communication parameters, but because the communication requirements in low-altitude environments are more complex and changeable, these methods are often not directly applicable to covert communications in the low-altitude economy. Summary of the invention

[0005] The purpose of the present invention is to make up for the shortcomings of the existing technology and provide an enhanced high-energy-efficiency collaborative covert communication method based on low-altitude economy. It can achieve covert transmission of communication content by building an aerial network ISAC system, utilizing the flexibility of UAVs switching between jamming UAV (JUAV) and information UAV (IUAV) modes, and accurately tracking the position of the mobile monitor Willie. At the same time, by optimizing parameters such as the trajectory design, power allocation and jamming strategy selection of the UAV, the energy efficiency of the system is improved, meeting the requirements for communication concealment and security in the low-altitude economy.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions: an enhanced high-energy-efficiency cooperative covert communication method based on low-altitude economy, the method comprising the following specific steps:

[0007] System model construction: Construct the basic framework of the air network ISAC system consisting of M drones, K ground users and mobile Willie. The drone can switch between JUAV and IUAV modes, set the positions of the drone and ground users in the three-dimensional coordinate system, define the channel model from the drone to GU and Willie, introduce binary variables to describe the service and interference roles of the drone, as well as the communication and interference power parameters, and set the corresponding constraints;

[0008] Willie tracking and observation: By building a mobile state evolution model for Willie, the UKF method is used to calculate the sigma point, predict Willie's state and covariance matrix, and based on the echo reflected by Willie, the round-trip delay and Doppler frequency shift are calculated and an observation model is established to provide a basis for subsequent interference and communication decisions;

[0009] Energy consumption and performance indicators: Detailed analysis of the power consumption of drones, including signal transmission and motion-related power, and establishment of energy consumption models. At the same time, a series of constraints are set, including the distance between drones, position changes, and concealment requirements, to ensure that the system is optimized while meeting various actual needs;

[0010] Flexible jamming framework implementation: Given IUAV-GU scheduling, communication transmission power and UAV trajectory, the achievable rate is maximized by jointly optimizing JUAV selection strategy, IUAV-GU scheduling, communication / jamming power allocation and UAV trajectory design. For JUAV selection and jamming power optimization, the EE maximization problem is transformed into subproblems. Given other variables, the JUAV selection strategy and jamming power allocation are solved to maximize the achievable rate. For UAV-GU scheduling and communication transmission power optimization, for fixed jamming strategies, the IUAV-GU scheduling problem is solved by relaxing the constraints and converting the discrete α m,k The constraint is converted to continuous 0≤α m,k ≤1, and use the CVX tool to solve the problem as a linear programming problem. For the UAV trajectory design, when the jamming strategy and communication strategy are determined, the UAV trajectory design problem is transformed into a fractional programming problem. Through a series of transformations and approximations, the numerator in the objective function is converted into the difference between two logarithms, and a slack variable is introduced to approximate the problem as a convex problem. The algorithm is used to solve it, thereby obtaining the optimal trajectory.

[0011] Algorithm implementation and performance verification: Based on the UKF-AO algorithm, Willie’s position is predicted according to the state evolution model, and the jamming strategy, communication strategy and UAV trajectory are iteratively optimized. At the same time, the energy efficiency and stealth performance are verified by comparing with the benchmark solution.

[0012] Furthermore, in the system model building step, the fixed position of the ground user is set in the three-dimensional space. For the kth ground user (k∈G), its position q k =[x k ,y k ,0] T , where x k and k Represent the horizontal coordinates of the ground user, respectively, and determine the time-varying coordinates of the UAV in each time slot. The time-varying coordinates q of the mth UAV (m∈U) in the nth time slot are m [n] = [x m [n],y m [n],H] T , where H is a constant height, determined by the minimum height to avoid ground collisions, and defines the channel-related parameters, the channel gain from the drone to the ground user |h m,k [n]| 2 and the channel gain to Willie |h m,w [n]| 2 Determined according to the free space propagation model, that is Among them, ρ 0 represents the power gain of the channel at unit reference distance, q m [n] represents the position vector of the mth UAV in the nth time slot, q k [n] represents the position vector of the kth terrestrial user in the nth time slot, q w [n] represents the position vector of Willie moving in the nth time slot.

[0013] Furthermore, in the system model building step, in the variable definition and constraint setting part, define the binary variable α m,k [n] and β m [n], where α m,k [n] indicates whether UAV m serves ground user k as an IUAV in time slot n, β rn [n] indicates whether UAV m acts as a jammer in time slot n, and α m,k [n]∈{0,1},β m [n]∈{0,1}, by setting a variety of constraints, including that each ground user can only be served by one UAV, that is, For all k and n, each UAV serves at most one ground user in each time slot and considers the interference role, i.e. For all m and n, the non-negative constraints of communication power and interference power, and the limit of the total power, let the communication power of UAV m be The interference power is but For all m and n, where P m,max is the peak transmission power of drone m in each time slot. In addition, the received SINR formula is defined. For GU, the received SINR at k is set to Y m,k [n], in

[0014] Furthermore, in the Willie tracking and observation step, by establishing the Willie's mobile state evolution model, the UKF method is used to calculate the sigma point, and the where α u is a parameter that determines the spread of the sigma point around the mean value, then the sigma point x s The calculation of [n-1] is: when s=0, in is Willie's initial state estimate. When s=1,…,4, When s=5,…,8, And predict Willie's state and covariance matrix, state and the corresponding covariance matrix Predicted by: in Represents the predicted sigma point,

[0015] ω′ t is a scalar weight. When s=0, When s=1,…,8, in is a scalar weight. When s=0, β u =2 is optimal for Gaussian distribution when s=1,…,8 Q e is the covariance matrix of the state transition noise. At the same time, according to the echo reflected by Willie, the round-trip delay and Doppler frequency shift are calculated and an observation model is established to provide a basis for subsequent interference and communication decisions. The round-trip delay τ m [n] and Doppler shift ν m The calculation formula for [n] is: where c is the speed of light, is uncorrelated Gaussian noise, following and Gaussian distribution, where f c is the carrier frequency, is uncorrelated Gaussian noise.

[0016] Furthermore, in the energy consumption and performance index step, the energy consumption model is calculated, and the motion-related power of the nth UAV in the time slot is According to the formula Calculate, where U tip is the tip speed of the rotor blade, ρ is the air density, s is the rotor solidity, A is the rotor disk area, P 0 is the profile power of the blade in the hovering state, P 1 is the induced power in the hovering state, v 0 is the average rotor-induced velocity in forward flight, d 0 is the fuselage drag ratio. When the drone performs downlink transmission, the total power consumption When the drone acts as a jammer, the total power consumption The total power consumption of a time slot is And define the performance indicators, the energy efficiency EE[n] of the nth time slot is defined as: Where EE[n] represents the energy efficiency of the nth time slot, R k [n] represents the achievable rate of terrestrial user k in time slot n, E m,tot [n] represents the total power consumption of the mth UAV in time slot n, Δt represents the time slot length, where R k [n] = ∑ m∈U α m,k [n]R m,k [n], R m,k [n] = log 2 (1+γ m,k [n]), Its rate satisfies the distance constraint between drones |q m [n]-q m2 [n]|≥d m,m2 , UAV position change constraint |q m [n]-q m [n-1]|≤d max , hidden constraints Among them, the hidden constraints is the Kullback-Leibler divergence calculated from Willie's detection probability, and ε is a small constant determined by the required stealth.

[0017] Furthermore, in the implementation step of the flexible jamming framework, for JUAV selection and jamming power optimization, the EE maximization problem is transformed into sub-problems, and the JUAV selection strategy and jamming power allocation are solved by given other variables to maximize the achievable rate, where the achievable rate formula is R k [n] = ∑ m∈U α m,k [n]R m,k [n], R m,k [n] = log 2 (1+γ m,k [n]), signal-to-interference-noise ratio in And perform variable processing, using auxiliary variables Processing Beta rn [n] and The coupling of γ m,k [n], and the SCA method is used to iteratively solve the problem. The convex lower bound of the objective function is obtained through the first-order Taylor expansion. Let

[0018] get Finally, the big-M formula method is used to handle the constraints.

[0019] Furthermore, in the implementation steps of the flexible interference framework, the UAV-GU scheduling and communication transmission power optimization part is divided into two aspects: scheduling optimization and power optimization. In terms of scheduling optimization, for a fixed interference strategy, considering solving the IUAV-GU scheduling problem, the rate formula that can be achieved is R k [n] = ∑ m∈U α m,k [n]R m,k [n],R m,k [n] = log 2 (1+γ m,k [n]), signal-to-interference-noise ratio in Original constraint α m , k[n]∈{0,1} is an obstacle, which can be relaxed to 0≤α m,k [n]≤1Convert the problem into a linear programming problem, that is, max∑ k∈G ∑ m∈U α m,k [n]R m,k[n], and meet the constraints, use CVX tools to solve the optimal scheduling solution. In terms of power optimization, after determining the IUAV-GU association, optimize the communication transmission power set up And through the first-order Taylor expansion, we get the convex upper bound, is the given power of UAVi in the rth iteration, get Then, the approximate problem is solved to obtain the optimal communication transmission power allocation.

[0020] Furthermore, in the implementation step of the flexible interference framework, in the UAV trajectory design, the original problem is transformed and the achievable rate R is assumed to be k [n] = ∑ m∈U α m,k [n]R m,k [n], where R m,k [n] = log 2 (1+γ m,k [n]), signal-to-interference-noise ratio Then the original problem can be written as in There is a corresponding formula, the numerator of the objective function Convert to two logarithmic differences and derive the lower bound, i.e. in, In addition, two slack variables are used to m,k S [n] rewrite and obtain the constraints, by using replace The formula is estimated, and the auxiliary variable v[n] is introduced into the denominator through the first-order Taylor pair to obtain its convex form and convex subset. After all the slack variables are combined, the original problem is approximated as a standard concave convex single ratio fraction problem that can be effectively solved by the Dinkelbach method. After defining the auxiliary variable Z to update and substitute it into the original problem to replace the objective function, the optimal UAV trajectory is solved using the CVX tool.

[0021] Compared with the prior art, this enhanced high-energy-efficiency cooperative covert communication method based on low-altitude economy has the following beneficial effects:

[0022] 1. The present invention can accurately track and observe mobile monitors by constructing a complex system model and combining it with a flexible interference framework and optimization algorithm. On this basis, by jointly optimizing the service role of the drone, communication / interference power allocation and drone trajectory design, the rate of covert communication can be maximized while reducing the risk of being detected by the enemy or potential threat actors. This not only improves the concealment of communication, but also ensures the security of communication content, providing more reliable protection for wireless communications in the low-altitude economy.

[0023] 2. The present invention realizes accurate calculation and optimization of UAV power consumption through sophisticated energy consumption model and performance indicator design. During the optimization process, not only the power consumption related to signal transmission but also the power consumption related to UAV movement is considered. By jointly optimizing the service role, communication / interference power allocation and trajectory design of the UAV, the energy efficiency of the system can be maximized while ensuring the covert communication effect, which not only reduces the energy consumption of the UAV but also improves the utilization of resources.

[0024] Other advantages, objectives and features of the present invention will be set forth in part in the following description and, in part, will be apparent to those skilled in the art based on an examination of the following or may be taught from the practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the prior art descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention, and for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0026] Figure 1 A working schematic diagram of an enhanced high energy efficiency cooperative covert communication method based on low-altitude economy;

[0027] Figure 2 The flowchart of an enhanced high energy-efficiency cooperative covert communication method based on low-altitude economy is shown in FIG. DETAILED DESCRIPTION

[0028] The technical solutions in the embodiments of the present invention are described clearly and completely below. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0029] Example

[0030] This embodiment describes in detail a specific application of an enhanced high-energy-efficiency collaborative covert communication method based on low-altitude economy in a military covert communication scenario.

[0031] Assume that the ISAC system in the air network includes M = 5 drones and K = 10 ground users. The total flight period T is 100 seconds, which is evenly divided into N = 100 time slots. Each time slot Δt = 1 second. The position of the ground user q k =[x k ,y k ,0] T , where x k and k Randomly distributed in the range of 0-1000 meters, the drone's constant altitude H = 500 meters, and the time-varying coordinates q in each time slot m [n] = [x m [n],y m [n],H] T , for channel related parameter settings: according to the formula and Determine the channel gain, let ρ 0 =1, define binary variable α m ,k[n] and β m [n], satisfying α m ,k[n]∈{0,1},β m [n]∈{0,1}, with the constraint that each ground user can only be served by one UAV: Each UAV serves at most one ground user in each time slot (for all k and n) and considers the interference roles: (For all m and n), the non-negative constraints on communication power and interference power and the limit on the total power: Let the communication power of drone m be The interference power is but (For all m and n), let P m ,max=100W, for the received SINR at GUk, set in

[0032] Assume that Willie moves randomly in the region, and his initial position is estimated to be Covariance matrix For a given initial value, calculate the sigma point according to the UKF method: Assume When s = 0, When s=1,…,4, When s=5,…,8, For state and covariance forecasts: When s = 0, When s=1,…,8, in When s = 0, β u =2, when s = 1,…,8, Q e is the covariance matrix of the state transition noise, and the round-trip delay between the drone and Willie and Doppler shift Let c = 3 × 10 8 m / s, f c =10 9 hertz, and is the noise that conforms to the corresponding Gaussian distribution.

[0033] For energy consumption model calculation, its motion-related power Let P 0 =10 watts, U tip =10 m / s, d 0 =0.1,ρ s = 1.2 kg / m3, A = 1 m2, P 1 =5 watts, v 0 =5 m / s, when the drone performs downlink transmission, the total power consumption When the drone acts as a jammer, the total power consumption The total power consumption of a time slot is For performance indicators: Energy efficiency Where R k [n] = ∑ n∈U α m,k [n]R m,k [n], R m,k [n] = log 2 (1+γ m,k [n]), For constraint setting: distance constraint between drones |q m [n]-q m2 [n]|≥d m,m2 , let d m ,m2=100 meters, UAV position change constraint |q m [n]-q m [n-1]|≤d max , let d m ax=50m, concealment constraint Assume ε = 0.01 and calculate the detection probability by Willie

[0034] For JUAV selection and interference power optimization, the EE maximization problem is first transformed into sub-problems, and the JUAV selection strategy and interference power allocation are solved by given other variables to maximize the achievable rate, where the achievable rate formula is R k [n] = ∑ m∈U α m,k [n]R m,k [n], R m,k [n] = log 2 (1+γ m,k [n]), signal-to-interference-noise ratio Then proceed with variable processing, using auxiliary variables Processing Beta rn [n] and The coupling of γ m,k [n], the SCA method is used to iteratively solve the problem, and the convex lower bound of the objective function is obtained through the first-order Taylor expansion. Let get Finally, the big-M formula method is used to deal with constraints. In the UAV-GU scheduling and communication transmission power optimization part, it is divided into two aspects: scheduling optimization and power optimization. When scheduling optimization, for a fixed interference strategy, consider solving the IUAV-GU scheduling problem, and the rate formula that can be achieved is R k [n] = ∑ m∈U α m,k [n]R m,k [n], R m,k [n] = log 2 (1+γ m,k [n]), signal-to-interference-noise ratio Original constraint α m , k[n]∈{0,1} is an obstacle, which can be relaxed to 0≤α m,k [n]≤1Convert the problem into a linear programming problem, that is, max∑ k∈G ∑ m∈U α m,k [n]R m,k [n], meet a series of constraints, use CVX and other tools to solve the optimal scheduling solution, and optimize the communication transmission power after determining the IUAV-GU association. set up The first-order Taylor expansion gives a convex upper bound, let is the given power of UAVi in the rth iteration, get Then, the approximate problem is solved to obtain the optimal communication transmission power allocation. In the UAV trajectory design, the original problem is transformed and the achievable rate R is assumed. k [n] = ∑ m∈U α m,k [n]R m,k [n], where R m,k [n] = log 2 (1+γ m,k [n]), signal-to-interference-noise ratio The original problem can be written as in There is a corresponding formula, the numerator of the objective function Convert to two logarithmic differences and derive the lower bound, i.e. in, In addition, two slack variables are used to m,k S [n] rewrite and obtain the constraints, by using replace The formula is estimated, and a new numerator is used to make the numerator m [n] is concave, and the auxiliary variable v[n] is introduced into the denominator through the first-order Taylor pair to obtain its convex form and convex subset. After all the slack variables are combined, the original problem is approximated as a standard concave convex single ratio fraction problem that can be effectively solved by the Dinkelbach method. After defining the auxiliary variable Z to update and substitute it into the original problem to replace the objective function, the optimal UAV trajectory is solved using the CVX tool.

[0035] For algorithm implementation and performance verification, initialize the algorithm parameters, time slot index n = 0, number of iterations l = 0, Willie's initial position estimate The initial value of the system policy [0] ,P I[0] ,P J[0] ,Q [0]}, according to the state evolution model X w [n] = FX w [n-1]+e w [n], calculate the predicted position of Willie and the covariance matrix in The UKF method is used for prediction, as described in the previous Willie tracking and observation step to calculate the formula for sigma point, state and covariance prediction. In each iteration, the three sub-problems are solved in the order of determining the jamming strategy, updating the communication strategy, and designing the UAV trajectory. The jamming strategy is determined by solving the JUAV selection and jamming power optimization problems. [l+1] ,P J[l+1]} and a fixed communication strategy {A [l] ,P I[l]} and trajectory {Q [l] , involving formula R k [n] = ∑ m∈U α m,k [n]R m,k [n],R m,k [n] = log 2 (1+γ m,k [n]), According to the obtained {B [l+1] ,P J [l+1]} and {Q [l]}, update the communication strategy [l+1] ,P I[l+1]}, involving formula Optimize UAV trajectory Q based on jamming and communication strategies [l+1] , involving formula Update the number of iterations l = l + 1 and the time slot index n = n + 1 until the end condition is met, such as reaching the maximum number of iterations l max Or the score increase of the target value is less than the preset threshold θ 1 ,By selecting appropriate benchmark solutions for comparison, we can ensure the validity and reliability of the experiment, and conduct simulation experiments, set different scenarios and parameters, and set EE proposed [n] represents the energy efficiency EE of the method of the present invention in the nth time slot benchnark [n] represents the energy efficiency of the benchmark solution in the nth time slot, and records the performance indicators of the system, such as energy efficiency EE, concealment performance indicators (such as Calculations within hidden constraints, etc. By analyzing and processing experimental data, the performance difference between the method of the present invention and the benchmark solution is compared, and the performance improvement ratio, such as the energy efficiency improvement ratio, is calculated. Verify the advantages and innovations of the present invention.

[0036] To sum up, in this embodiment, after many experiments and data analysis, it is found that the method of the present invention has a significant improvement in energy efficiency compared with the benchmark solution, with an average improvement of about 30%. At the same time, it can better meet the requirements of military communications in terms of concealment performance, and the concealment index is always maintained within the set threshold range.

[0037] It will be apparent to those skilled in the art that the invention is not limited to the details of the exemplary embodiments described above and that the invention can be implemented in other specific forms without departing from the spirit or essential features of the invention. Therefore, the embodiments should be considered exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description, and it is intended that all variations falling within the meaning and scope of the equivalent elements of the claims be included in the invention. Any reference numeral in a claim should not be considered as limiting the claim to which it relates.

Claims

1. An enhanced high-energy-efficiency cooperative covert communication method based on low-altitude economy, characterized in that: The system includes the following specific steps: System model construction: Construct the basic framework of the air network ISAC system consisting of M drones, K ground users and mobile Willie. The drone can switch between JUAV and IUAV modes, set the positions of the drone and ground users in the three-dimensional coordinate system, define the channel model from the drone to GU and Willie, introduce binary variables to describe the service and interference roles of the drone, as well as the communication and interference power parameters, and set the corresponding constraints; Willie tracking and observation: By building a mobile state evolution model for Willie, the UKF method is used to calculate the sigma point, predict Willie's state and covariance matrix, and based on the echo reflected by Willie, the round-trip delay and Doppler frequency shift are calculated and an observation model is established to provide a basis for subsequent interference and communication decisions; Energy consumption and performance indicators: Detailed analysis of the power consumption of drones, including signal transmission and motion-related power, and establishment of energy consumption models. At the same time, a series of constraints are set, including the distance between drones, position changes, and concealment requirements, to ensure that the system is optimized while meeting various actual needs; Flexible jamming framework implementation: Given IUAV-GU scheduling, communication transmission power and UAV trajectory, the achievable rate is maximized by jointly optimizing JUAV selection strategy, IUAV-GU scheduling, communication / jamming power allocation and UAV trajectory design. For JUAV selection and jamming power optimization, the EE maximization problem is transformed into subproblems. Given other variables, the JUAV selection strategy and jamming power allocation are solved to maximize the achievable rate. For UAV-GU scheduling and communication transmission power optimization, for fixed jamming strategies, the IUAV-GU scheduling problem is solved by relaxing the constraints and converting the discrete α m,k The constraint is converted to continuous 0≤α m,k ≤1, and use the CVX tool to solve the problem as a linear programming problem. For the UAV trajectory design, when the jamming strategy and communication strategy are determined, the UAV trajectory design problem is transformed into a fractional programming problem. Through a series of transformations and approximations, the numerator in the objective function is converted into the difference between two logarithms, and a slack variable is introduced to approximate the problem as a convex problem. The algorithm is used to solve it, thereby obtaining the optimal trajectory. Algorithm implementation and performance verification: Based on the UKF-AO algorithm, Willie’s position is predicted according to the state evolution model, and the jamming strategy, communication strategy and UAV trajectory are iteratively optimized. At the same time, the energy efficiency and stealth performance are verified by comparing with the benchmark solution.

2. According to claim 1, an enhanced high-energy-efficiency cooperative covert communication method based on low-altitude economy is characterized in that: In the system model building step, the fixed position of the ground user is set in the three-dimensional space. For the kth ground user (k∈G), its position where x k and k Represent the horizontal coordinates of the ground user, respectively, and determine the time-varying coordinates of the UAV in each time slot. The time-varying coordinates q of the mth UAV (m∈U) in the nth time slot are m [n] = [x m [n], Where H is a constant height, determined by the minimum height to avoid ground collision, and defines the channel-related parameters, the channel gain from the drone to the ground user |h m，k [n]| 2 and the channel gain to Willie |h m，w [n]| 2 Determined according to the free space propagation model, that is, Where ρ0 represents the power gain of the channel at unit reference distance, q m [n] represents the position vector of the mth UAV in the nth time slot, q k [n] represents the position vector of the kth terrestrial user in the nth time slot, q w [n] represents the position vector of Willie moving in the nth time slot.

3. According to the enhanced high-energy-efficiency cooperative covert communication method based on low-altitude economy of claim 1, it is characterized in that: In the system model building step, in the variable definition and constraint setting part, define the binary variable α m，k [n] and β m [n], where α m，k [n] indicates whether UAV m serves ground user k as an IUAV in time slot n, β rn [n] indicates whether UAV m acts as a jammer in time slot n, and α m，k [n]∈{0, 1}, β m [n]∈{0, 1}, by setting multiple constraints, including that each ground user can only be served by one UAV, that is, For all k and n, each UAV serves at most one ground user in each time slot and considers the interference role, i.e. For all m and n, the non-negative constraints of communication power and interference power, and the limit of the total power, let the communication power of UAV m be The interference power is but For all m and n, where P m,max is the peak transmission power of drone m in each time slot. In addition, the received SINR formula is defined. For GU, the received SINR at k is set to Y m，k [n], in 4. According to the enhanced high-energy-efficiency cooperative covert communication method based on low-altitude economy according to claim 1, it is characterized in that: In the Willie tracking and observation step, the mobile state evolution model of Willie is established, and the sigma point is calculated using the UKF method. where α u is a parameter that determines the spread of the sigma point around the mean value, then the sigma point x s The calculation of [n-1] is: when s=0, in is Willie's initial state estimate. When s = 1, ..., 4, When s=5,…,8, And predict Willie's state and covariance matrix, state and the corresponding covariance matrix Predicted by: in Represents the predicted sigma point, ω′ t is a scalar weight. When s=0, When s=1,…,8, in is a scalar weight. When s=0, β u = 2 is optimal for Gaussian distribution when s = 1, ..., 8 Q e is the covariance matrix of the state transition noise. At the same time, according to the echo reflected by Willie, the round-trip delay and Doppler frequency shift are calculated and an observation model is established to provide a basis for subsequent interference and communication decisions. The round-trip delay τ m [n] and Doppler shift v m The calculation formula for [n] is: where c is the speed of light, is uncorrelated Gaussian noise, following and Gaussian distribution, where f c is the carrier frequency, is uncorrelated Gaussian noise.

5. According to the enhanced high-energy-efficiency cooperative covert communication method based on low-altitude economy of claim 1, it is characterized in that: In the energy consumption and performance index step, the energy consumption model is calculated, and the motion-related power of the nth UAV in the time slot is According to the formula Calculate, where U tip is the tip speed of the rotor blade, ρ is the air density, s is the rotor solidity, A is the rotor disk area, P 0 is the profile power of the blade in the hovering state, P 1 is the induced power in the hovering state, v0 is the average speed induced by the rotor in forward flight, d0 is the fuselage drag ratio, and when the drone performs downlink transmission, the total power consumption When the drone acts as a jammer, the total power consumption The total power consumption in one time slot is And define the performance indicators, the energy efficiency EE[n] of the nth time slot is defined as: Where EE[n] represents the energy efficiency of the nth time slot, R k [n] represents the achievable rate of terrestrial user k in time slot n, E m，tot [n] represents the total power consumption of the mth UAV in time slot n, Δt represents the time slot length, where R k [n] = ∑ m∈∪ α m，k [n]R m，k [n], R m，k [n] = log2(1 + γ m，k [n]), Its rate satisfies the distance constraint between drones |q m [n]-q m2 [n]|≥d m，m2 , UAV position change constraint |q m [n]-q m [n-1]|≤d max , hidden constraints Among them, the hidden constraints is the Kullback-Leibler divergence calculated from Willie's detection probability, and ε is a small constant determined by the required stealth.

6. According to the enhanced high-energy-efficiency cooperative covert communication method based on low-altitude economy of claim 1, it is characterized in that: In the implementation step of the flexible jamming framework, for JUAV selection and jamming power optimization, the EE maximization problem is transformed into sub-problems, and the JUAV selection strategy and jamming power allocation are solved by given other variables to maximize the achievable rate, where the achievable rate formula is R k [n] = ∑ m∈∪ α m，k [n]R m，k [n],R m,k [n] = log2(1 + γ m，k [n]), signal-to-interference-noise ratio in And perform variable processing, using auxiliary variables Processing Beta rn [n] and The coupling of γ m，k [n], and the SCA method is used to iteratively solve the problem. The convex lower bound of the objective function is obtained through the first-order Taylor expansion. Let get Finally, the big-M formula method is used to handle the constraints.

7. According to claim 1, an enhanced high-energy-efficiency cooperative covert communication method based on low-altitude economy is characterized in that: In the implementation steps of the flexible interference framework, the UAV-GU scheduling and communication transmission power optimization part is divided into two aspects: scheduling optimization and power optimization. In terms of scheduling optimization, for a fixed interference strategy, considering solving the IUAV-GU scheduling problem, the rate formula that can be achieved is R k [n] = ∑ m∈∪ α m，k [n]R m，k [n], R m,k [n] = log2(1 + γ m，k [n]), signal-to-interference-noise ratio in Original constraint α m , k[n]∈{0,1} is an obstacle, which can be relaxed to 0≤α m，k [n]≤1Convert the problem into a linear programming problem, that is, max∑ k∈G ∑ m∈∪ α m，k [n]R m,k [n], and meet the constraints, use CVX tools to solve the optimal scheduling solution. In terms of power optimization, after determining the IUAV-GU association, optimize the communication transmission power set up And the convex upper bound is obtained by first-order Taylor expansion, let is the given power of UAVi in the rth iteration, get Then, the approximate problem is solved to obtain the optimal communication transmission power allocation.

8. The enhanced high-energy-efficiency cooperative covert communication method based on low-altitude economy according to claim 1 is characterized in that: In the implementation steps of the flexible interference framework, in the UAV trajectory design, the original problem is transformed and the achievable rate R is assumed. k [n] = ∑ m∈∪ α m，k [n]R m,k [n], where R m,k [n] = log2(1 + γ m，k [n]), signal-to-interference-noise ratio Then the original problem can be written as in There is a corresponding formula, the numerator of the objective function Convert to two logarithmic differences and derive the lower bound, i.e. in, In addition, two slack variables are used to Rewrite and obtain the constraints by using replace The formula is estimated, and the auxiliary variable v[n] is introduced into the denominator through the first-order Taylor pair to obtain its convex form and convex subset. After all the slack variables are combined, the original problem is approximated as a standard concave convex single ratio fraction problem that can be effectively solved by the Dinkelbach method. After defining the auxiliary variable Z to update and substitute it into the original problem to replace the objective function, the optimal UAV trajectory is solved using the CVX tool.

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