A UAV trajectory and scheduling design method and system for anti-collaborative detection

Abstract

The present invention proposes a method and system for designing drone trajectories and scheduling that are resistant to collaborative detection. The method comprises the following steps: first, deriving the expression and probability density function of the listener received signal under the multi-listener collaborative detection mechanism; then, deriving a closed-form expression for the lower bound of the minimum detection error rate for multi-listener collaborative detection based on likelihood ratio detection; then, establishing a drone trajectory and scheduling optimization problem that is resistant to collaborative detection based on the derived formula; and finally, iteratively solving the problem based on a continuous convex approximation algorithm to obtain the optimal drone trajectory and scheduling. The method proposed in the present invention is able to effectively resist collaborative detection between multiple illegal listeners, ensure the concealment of communication, and meet the communication security requirements of the future drone Internet of Things.

Description

Technical Field

[0001] The present invention belongs to the field of covert communication of unmanned aerial vehicles (UAVs), and in particular relates to a UAV trajectory and scheduling design method and system that is resistant to collaborative detection. Background Art

[0002] Compared with traditional terrestrial cellular networks, drones play an important role as a cutting-edge communication technology in the large-scale Internet of Things due to their high flexibility, controllability, and good air-to-ground line-of-sight channel. They can serve as aerial mobile base stations and mobile computing clouds, providing stable and reliable communication links for ground users, thereby significantly improving the performance of communication networks. In particular, the flexibility of drones introduces additional degrees of freedom to the network. Therefore, by properly designing the trajectory of drones, communication can be further improved.

[0003] However, while the good air-to-ground line-of-sight channel of drones improves communication performance, its open broadcast transmission characteristics also make it easier for illegal eavesdroppers to detect drone communication behavior and communication data through certain detection strategies, and the communication concealment is greatly challenged. In order to improve the communication concealment in networks where eavesdroppers exist, scholars in related fields at home and abroad have carried out a series of work. In 2021, considering the assistance of multi-antenna jammers, X. Zhou et al. studied the joint drone position and transmission power design to maximize the transmission rate while avoiding detection by multiple eavesdroppers. In addition, in 2024, J. Hu et al. developed a trajectory and resource allocation design for a drone-assisted battery-free covert communication, in which the drone provides power to legitimate devices while interfering with the detection of the eavesdropper. Based on the above work, Z. Tong et al. applied the emerging federated learning technology to construct a covert federated learning architecture to maximize network performance by jointly designing drone trajectories and resource allocation.

[0004] While a series of studies on drone communication systems in the presence of listeners, such as the aforementioned work, have contributed to improving the system's covert communication performance, these solutions only consider independent monitoring of drone communications by listeners in multi-listener communication networks, ignoring the collaborative nature of listeners. While information sharing and collaborative detection could improve overall drone communication detection performance, the system communication solutions involved still face significant security concerns. Therefore, further research is needed on trajectory and scheduling design methods and systems for collaborative multi-listener detection. Summary of the Invention

[0005] In view of the current situation that there is a lack of trajectory and scheduling design methods for drone covert communication networks under multi-listener collaborative detection, the present invention proposes a drone trajectory and scheduling design method and system that are resistant to collaborative detection, which is used to ensure communication concealment under multi-listener collaborative detection while improving covert communication performance.

[0006] In order to solve the above technical problems, the present invention provides the following technical solutions:

[0007] A method and system for designing drone trajectories and scheduling that resists collaborative detection includes the following steps:

[0008] Step 1: Based on the channel gain between the UAV and the listener, the background noise signal, the UAV transmission power, and the UAV transmission signal, the listener receiving signal is obtained in the multi-listener cooperative detection mechanism, and the probability density function of the received signal is derived;

[0009] Step 2: Based on the principle of multi-listener cooperative detection constructed by the probability density function of the received signal and likelihood ratio detection, we obtain the matrix expression of the minimum detection error rate lower bound of multi-listener cooperative detection, and derive the closed-form expression of the minimum detection error rate lower bound of multi-listener cooperative detection;

[0010] Step 3: Based on the closed-form expression for the minimum detection error rate lower bound and the covert communication requirements, a closed-form expression for the channel capacity between the UAV and the user that meets the covert communication requirements is derived and an objective function is constructed. Then, the mobility and scheduling constraints of the UAVs are set separately. Based on the objective function, mobility constraints, and scheduling constraints, a UAV trajectory and scheduling optimization problem that is resistant to cooperative detection is established.

[0011] Step 4: Based on the continuous convex approximation algorithm, the UAV trajectory and scheduling optimization problem resistant to collaborative detection is iteratively solved to obtain the optimal UAV trajectory and scheduling.

[0012] Furthermore, the probability density function of the received signal in step 1 is:

[0013]

[0014] in Representatives assume The probability density function of the received signal is: Representatives assume The probability density function of the received signal is: Represents the assumption that multiple listeners have no communication with the drone, represents the assumption by multiple listeners that the drone is communicating; r (l) [n] represents the lth signal vector received by multiple listeners in the nth time slot under the multi-listener cooperative detection mechanism, (·) Trepresents the matrix transpose operation; M is the number of listeners, Σ0 represents The covariance matrix of The covariance matrix of , (·) -1 represents the matrix inversion operation, |·| represents the determinant of the matrix; e is the natural base, and π is the pi.

[0015] Furthermore, the lth background noise signal vector received by multiple listeners in the nth time slot under the multi-listener cooperative detection mechanism described in step 1 is:

[0016]

[0017] Where l∈{1,...,L} represents the received signal sequence number, L is the total number of received signals in each time slot, represents the lth background noise signal received by the mth listener in the nth time slot, x (l) [n] represents the lth useful signal transmitted by the UAV in the nth time slot, P[n] represents the UAV transmission power; h m [n] represents the channel gain between the UAV and the mth listener in the nth time slot.

[0018] Furthermore, in step 1 The covariance matrix Σ0 and The covariance matrices Σ1 are:

[0019] Σ0=diag{σ 2 ,...,σ 2}∈R M×M

[0020]

[0021] where σ 2 represents the background noise power, diag{} represents the diagonal matrix, R M×M Represents an M×M dimensional matrix, h1[n], h2[n], h M [n] represents the channel gain between the UAV and the first listener, the second listener, and the Mth listener in the nth time slot, respectively.

[0022] Furthermore, the matrix expression of the minimum detection error rate lower bound of the multi-listener collaborative detection in step 2 is:

[0023]

[0024] Among them, ξ * [n] represents the lower bound of the minimum detection error rate of multi-listener cooperative detection in the nth time slot, and the expression is represent and The KL divergence between Representatives assume The probability density function of the received signal is multiplied, Representatives assume The probability density function of the received signal is multiplied together; tr(·) represents the trace of the matrix.

[0025] Furthermore, the closed-form expression for the lower bound of the minimum detection error rate of the multi-listener collaborative detection is:

[0026]

[0027] Among them, β0 represents the channel gain per unit distance, α represents the path attenuation exponent of the channel, q[n] represents the position of the UAV in the nth time slot, and w m represents the position of the mth listener, H represents the flight height of the drone, and ||·|| represents the 2-norm of the matrix.

[0028] Furthermore, the trajectory and scheduling optimization problem of the UAV against collaborative detection in step 3 is:

[0029]

[0030] in, is the objective function, ||q[n]-q[n-1]||≤VΔt is the mobility constraint, is the scheduling constraint; a u [n] represents the scheduling of the n-th time slot UAV and the u-th user, C u [n] represents the channel capacity between the UAV and the u-th user in the n-th time slot, Δt represents the time slot length, st represents the constraint condition, q[n] represents the position of the UAV in the n-th time slot, q[n-1] represents the position of the UAV in the n-1-th time slot, V represents the maximum speed of the UAV, A={a u [n]} represents the scheduling variable of the drone to the user, u∈{1,...,U} represents the user number, and U represents the total number of users.

[0031] Furthermore, the closed-form expression of the channel capacity between the UAV and the user that meets the covert communication requirements is:

[0032]

[0033] Among them, s u represents the u-th user position, P * [n] represents the optimal transmission power of the UAV in the nth time slot;

[0034] The covert communication requirements described in step 3 are:

[0035] ξ* [n]≥1-ρ,

[0036] Where ρ represents the maximum exposure probability allowed to be detected by multiple listeners in a collaborative manner; ξ * [n]About Monotonically decreasing, the closed-form expression of the optimal transmission power of the UAV that meets the covert communication requirements in step 3 is:

[0037]

[0038] Among them, P * [n] represents the optimal transmission power of the UAV in the nth time slot, P max represents the maximum transmission power of the UAV, and γ is ξ * [n]=1-ρ The value of .

[0039] Furthermore, the step 4 iteratively solves the UAV trajectory and scheduling optimization problem against collaborative detection based on a continuous convex approximation algorithm, including:

[0040] Step 4.1: Initialize the initial trajectory Q of the drone (0) and the initial scheduling variable A (0) , and the initial trajectory and initial scheduling variables of the UAV are used as the local points of iteration (Q (0) ,A (0) ), set iteration index r = 1;

[0041] Step 4.2: At the rth iteration, at the local point (Q (r-1) ,A (r-1) ) approximates the UAV trajectory and scheduling optimization problem against collaborative detection established in step 3 as a convex problem;

[0042] Step 4.3: Use the convex optimization algorithm to solve the convex problem obtained in step 4.2 and obtain the local optimal solution of this iteration (Q * ,A * );

[0043] Step 4.4: If the improvement of the objective function of this iteration compared to the previous objective function is less than the given threshold, the iteration is stopped, and the local optimal solution of this iteration is the optimal trajectory and scheduling of the UAV; otherwise, it will be used as the local point (Q (r) ,A (r) )=(Q * ,A * ), iterate index r=r+1, and return to step 4.2.

[0044] In another aspect, the present invention provides a UAV trajectory and scheduling design system resistant to collaborative detection, comprising:

[0045] Received signal probability density function acquisition module: It is used to obtain the listener's received signal in the multi-listener collaborative detection mechanism based on the channel gain between the drone and the listener, the background noise signal, the drone's transmit power, and the drone's transmission signal, and derive the received signal probability density function;

[0046] Minimum Detection Error Rate Acquisition Module: This module is used to obtain the matrix expression of the minimum detection error rate lower bound of multi-listener cooperative detection based on the principle of multi-listener cooperative detection constructed by the probability density function of the received signal and likelihood ratio detection, and derive the closed-form expression of the minimum detection error rate lower bound of multi-listener cooperative detection;

[0047] Optimization problem construction module: This module is used to derive a closed-form expression for the channel capacity between the UAV and the user that meets the covert communication requirements based on the closed-form expression for the minimum detection error rate lower bound and the covert communication requirements, and construct an objective function. Then, the mobility constraints and scheduling constraints of the UAV are set separately. Based on the objective function, mobility constraints, and scheduling constraints, a UAV trajectory and scheduling optimization problem that is resistant to collaborative detection is established.

[0048] Solution module: It is used to iteratively solve the UAV trajectory and scheduling optimization problem of anti-cooperative detection based on a continuous convex approximation algorithm to obtain the optimal UAV trajectory and scheduling.

[0049] Compared with the prior art, the present invention has the following beneficial effects:

[0050] This paper proposes a method and system for designing drone trajectories and scheduling to resist collaborative detection in networks with multiple listeners. This method maximizes the throughput of users with minimal throughput requirements for covert communication, subject to mobility and scheduling constraints. This method effectively combats collaborative eavesdropping in drone covert communication networks with multiple listeners, ensuring the confidentiality of communications and meeting the communication security requirements of future drone-based internet of things. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0052] Figure 1 Schematic diagram of a UAV covert communication network with multiple cooperative eavesdroppers according to an embodiment of the present invention;

[0053] Figure 2 A flow chart of the method for implementing the present invention;

[0054] Figure 3Designing an optimized drone trajectory map for embodiments of the present invention;

[0055] Figure 4 Schematic diagram comparing the communication concealment performance between the method proposed in the embodiment of the present invention and the traditional solution. DETAILED DESCRIPTION

[0056] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0057] Example 1

[0058] like Figure 1 As shown, this embodiment provides a method and system for designing drone trajectories and scheduling that is resistant to collaborative detection, including the following steps:

[0059] Step 1: Based on the channel gain between the UAV and the listener, the background noise signal, the UAV transmission power, and the UAV transmission signal, the listener receiving signal is obtained in the multi-listener cooperative detection mechanism, and the probability density function of the received signal is derived;

[0060] Step 2: Based on the principle of multi-listener cooperative detection constructed by the probability density function of the received signal and likelihood ratio detection, we obtain the matrix expression of the minimum detection error rate lower bound of multi-listener cooperative detection, and derive the closed-form expression of the minimum detection error rate lower bound of multi-listener cooperative detection;

[0061] Step 3: Based on the closed-form expression for the minimum detection error rate lower bound and the covert communication requirements, a closed-form expression for the channel capacity between the UAV and the user that meets the covert communication requirements is derived and an objective function is constructed. Then, the mobility and scheduling constraints of the UAVs are set separately. Based on the objective function, mobility constraints, and scheduling constraints, a UAV trajectory and scheduling optimization problem that is resistant to cooperative detection is established.

[0062] Step 4: Based on the continuous convex approximation algorithm, the UAV trajectory and scheduling optimization problem resistant to collaborative detection is iteratively solved to obtain the optimal UAV trajectory and scheduling.

[0063] Figure 2The specific embodiment of the present invention considers a drone covert communication network with multiple cooperative eavesdroppers. The network consists of a drone, U users, and M illicit eavesdroppers. The drone communicates with the users via downlink, and its communication with the users is subject to cooperative detection between the eavesdroppers. The drone's flight altitude is H and its maximum flight speed is V. To improve the performance of the drone covert communication network, it is necessary to jointly design the drone's trajectory and scheduling to maximize the system throughput while ensuring anti-eavesdropper cooperative detection. Solving this problem is very complex.

[0064] In this embodiment, Step 1: Derivation of the listener received signal expression and probability density function under a multi-listener collaborative detection mechanism. First, the channel gain between the drone and the listener is calculated based on the drone's position and the listener's position. Then, the expression for the listener received signal under a multi-listener collaborative detection mechanism is derived by combining the background noise signal, the drone's transmit power, and the drone's transmitted signal. Finally, the received signal probability density function is derived by combining the background noise signal and the drone's transmitted signal probability density function.

[0065] The channel gain between the drone and the listener in step 1 is:

[0066]

[0067] Where n∈{1,...,N} represents the time slot number, N is the total number of time slots, m∈{1,...,M} represents the listener number, h m [n] represents the channel gain between the UAV and the mth listener in the nth time slot; q[n] represents the position of the UAV in the nth time slot, w m represents the position of the mth listener, β0 represents the channel gain per unit distance, α represents the path attenuation exponent of the channel, and ||·|| represents the 2-norm of the matrix.

[0068] The expression of the listener receiving signal under the multi-listener cooperative detection mechanism described in step 1 is:

[0069]

[0070] Where l∈{1,...,L} represents the received signal sequence number, L is the total number of received signals in each time slot, r (l) [n] represents the lth signal vector received by multiple listeners in the nth time slot under the multi-listener cooperative detection mechanism. represents the lth background noise signal received by the mth listener in the nth time slot, x (l) [n] represents the lth useful signal transmitted by the UAV in the nth time slot, and P[n] represents the UAV transmission power; Represents the assumption that multiple listeners have no communication with the drone, Represents the assumption by multiple listeners that the drones are communicating.

[0071] Since the probability density function of the background noise signal is where σ 2 Represents the noise power, and the probability density function of the UAV transmission signal is The received signal probability density function described in step 1 is:

[0072]

[0073] in Representatives assume The probability density function of the received signal is: Representatives assume The probability density function of the received signal is: T represents the matrix transpose operation, (·) -1 represents the matrix inversion operation, |·| represents the determinant of the matrix; e is the natural base, π is the circumference of the circle; Σ0=diag{σ 2 ,...,σ 2}∈R M×M represent The covariance matrix of The covariance matrix of is expressed as:

[0074]

[0075] Step 2: Derive a closed-form expression for the minimum detection error rate lower bound for multi-listener cooperative detection. First, construct the principle process of multi-listener cooperative detection based on likelihood ratio detection. Then, use KL divergence to derive a matrix expression for the minimum detection error rate lower bound for multi-listener cooperative detection. Finally, based on the principles of matrix operations, a closed-form expression for the minimum detection error rate lower bound for multi-listener cooperative detection is obtained.

[0076] The principle process of multi-listener collaborative detection described in step 2 is as follows:

[0077]

[0078] in It means that multiple monitors have judged that there is no communication with the drone. Represents that multiple listeners judge that the drone is communicating. The above formula means: when the drone has no communication assumption Likelihood function under Greater than the assumption that drones are communicating Likelihood function under If the value is not set, it is determined that the drone is not communicating, otherwise it is determined that the drone is communicating.

[0079] According to the KL divergence property, the lower bound of the minimum detection error rate of multi-listener collaborative detection can be expressed as:

[0080]

[0081] where ξ * [n] represents the minimum detection error rate lower bound of multi-listener cooperative detection in the nth time slot,

[0082] represent and The KL divergence between , its value can be expressed as:

[0083]

[0084] for Its matrix expression is:

[0085]

[0086] where tr(·) represents the trace of the matrix; therefore, The matrix expression of is:

[0087]

[0088] In summary, the matrix expression of the minimum detection error rate lower bound of the multi-listener collaborative detection described in step 2 is:

[0089]

[0090] because

[0091] The closed-form expression for the lower bound of the minimum detection error rate of the multi-listener cooperative detection described in step 2 is:

[0092]

[0093] Step 3: Establish a collaborative detection-resistant UAV trajectory and scheduling optimization problem. First, based on the closed-form expression for the minimum detection error rate lower bound and the covert communication requirements, a closed-form expression for the optimal UAV transmit power that satisfies covert communication requirements is derived. Furthermore, a closed-form expression for the channel capacity between the UAV and the user that satisfies covert communication requirements is derived, and the optimization objective of the problem is constructed. Then, mobility constraints are defined for the optimization problem based on the position of the UAV in each time slot. The scheduling constraints of the optimization problem are defined based on the UAV's scheduling coefficient variables. Finally, based on the constructed objective and constraints, a collaborative detection-resistant UAV trajectory and scheduling optimization problem is established.

[0094] The covert communication requirements described in step 3 are:

[0095] ξ * [n]≥1-ρ,

[0096] Where ρ represents the maximum exposure probability allowed to be detected by multiple listeners in a collaborative manner; * [n]About is monotonically decreasing, so let ξ * [n]=1-ρ The value of is γ, then the closed-form expression of the optimal transmission power of the UAV that meets the covert communication requirements in step 3 is:

[0097]

[0098] Among them, P * [n] represents the optimal transmission power of the UAV in the nth time slot, P max Represents the maximum transmit power of the drone.

[0099] The closed-form expression for the channel capacity between the drone and the user that meets the covert communication requirements in step 3 is:

[0100]

[0101] Where u∈{1,...,U} represents the user number, C u [n] represents the channel capacity between the UAV and the u-th user in the n-th time slot, s u Represents the u-th user location.

[0102] Step 3 constructs the optimization problem with the following goal:

[0103]

[0104] Where Q = {q[n]} represents the trajectory of the UAV, A = {a u [n]} represents the scheduling variable of the drone to the user, a u [n] represents the scheduling of the n-th time slot UAV and the u-th user Δt represents the time slot length, represents the throughput of the u-th user that meets the covert communication requirements; the above objective means maximizing the throughput of the user with the minimum throughput that meets the covert communication requirements by optimizing the UAV trajectory and scheduling variables

[0105] The mobility constraint of the optimization problem described in step 3 is:

[0106] ||q[n]-q[n-1]||≤VΔt,

[0107] Where q[n-1] represents the position of the drone in the n-1th time slot. The above constraints mean that the speed of the drone should be less than the maximum speed.

[0108] The scheduling constraints of the optimization problem described in step 3 are:

[0109]

[0110] The above constraints mean that the value of the user scheduling variable A can only be 0 or 1, and the drone can only schedule one user in each time slot.

[0111] The UAV trajectory and scheduling optimization problem for anti-cooperative detection established in step 3 is:

[0112]

[0113] The meaning of the above design optimization problem is to maximize the throughput of users with the minimum throughput required for covert communication under mobility constraints and scheduling constraints by optimizing the UAV trajectory and scheduling variables.

[0114] Step 4: Iteratively solve the above problem based on the continuous convex approximation algorithm to obtain the optimal UAV trajectory and scheduling.

[0115] The iterative algorithm based on the continuous convex approximation algorithm described in step 4 is as follows:

[0116] Step 4.1: Initialize the initial trajectory Q of the drone (0) and the initial scheduling variable A (0) , and the initial trajectory and initial scheduling variables of the UAV are used as the local points of iteration (Q (0) ,A (0) ), set iteration index r = 1;

[0117] Step 4.2: At the rth iteration, at the local point (Q (r-1) ,A (r-1) ) approximates the UAV trajectory and scheduling optimization problem against collaborative detection established in step 3 as a convex problem;

[0118] Step 4.3: Use convex optimization algorithms such as interior point method to solve the convex problem obtained in step 4.2 and obtain the local optimal solution of this iteration (Q * ,A * );

[0119] Step 4.4: If the improvement of the objective function of this iteration compared to the previous objective function is less than the given threshold, the iteration is stopped, and the local optimal solution of this iteration is the optimal trajectory and scheduling of the UAV; otherwise, it will be used as the local point (Q (r) ,A (r) )=(Q * ,A * ), iterate index r=r+1, and return to step 4.2.

[0120] like Figure 3 As shown in FIG, the trajectory diagram of the UAV designed and optimized in the embodiment of the present invention, it can be seen that compared with the traditional comparison method based on independent detection, the trajectory of the proposed method is straighter and can make better use of the mission time. Figure 4 A comparison of the communication concealment performance of the method proposed in the embodiment of the present invention and a conventional method is presented, with a maximum permissible exposure probability of ρ = 0.05. It can be seen that the real-time exposure probability of the proposed method resistant to collaborative detection is always less than or equal to the maximum permissible exposure probability, meeting the communication concealment requirements. In contrast, the real-time exposure probability of the comparison method exceeds the maximum permissible exposure probability over a significant period of time, and the degree of excess increases with increasing maximum transmit power. This phenomenon demonstrates the necessity of considering anti-collaborative detection in the present invention.

[0121] The proposed method for designing drone trajectories and scheduling to resist collaborative detection in networks with multiple listeners can maximize the throughput of users with minimal throughput requirements for covert communication, subject to mobility and scheduling constraints. This method effectively combats collaborative eavesdropping in drone covert communication networks with multiple listeners, ensuring the confidentiality of communications and meeting the communication security requirements of future drone-based internet of things.

[0122] Example 2

[0123] This embodiment provides a UAV trajectory and scheduling design system that is resistant to collaborative detection, including:

[0124] Received signal probability density function acquisition module: It is used to obtain the listener's received signal in the multi-listener collaborative detection mechanism based on the channel gain between the drone and the listener, the background noise signal, the drone's transmit power, and the drone's transmission signal, and derive the received signal probability density function;

[0125] Minimum Detection Error Rate Acquisition Module: This module is used to obtain the matrix expression of the minimum detection error rate lower bound of multi-listener cooperative detection based on the principle of multi-listener cooperative detection constructed by the probability density function of the received signal and likelihood ratio detection, and derive the closed-form expression of the minimum detection error rate lower bound of multi-listener cooperative detection;

[0126] Optimization problem construction module: This module is used to derive a closed-form expression for the channel capacity between the UAV and the user that meets the covert communication requirements based on the closed-form expression for the minimum detection error rate lower bound and the covert communication requirements, and construct an objective function. Then, the mobility constraints and scheduling constraints of the UAV are set separately. Based on the objective function, mobility constraints, and scheduling constraints, a UAV trajectory and scheduling optimization problem that is resistant to collaborative detection is established.

[0127] Solution module: It is used to iteratively solve the UAV trajectory and scheduling optimization problem of anti-cooperative detection based on a continuous convex approximation algorithm to obtain the optimal UAV trajectory and scheduling.

[0128] It should be understood that parts not elaborated in detail in this specification belong to the prior art.

[0129] It should be understood that the above description of the preferred embodiments is relatively detailed and cannot be considered as limiting the scope of protection of the present invention. It is not necessary and impossible to list all embodiments here. Under the guidance of the present invention, ordinary technicians in this field can also make substitutions or modifications without departing from the scope of protection of the claims of the present invention, which fall within the scope of protection of the present invention. The scope of protection of the present invention shall be based on the attached claims.

Claims

1. A UAV trajectory and scheduling design method for anti-cooperative detection, characterized by: The following steps are involved: Step 1: Based on the channel gain between the UAV and the listener, the background noise signal, the UAV transmission power, and the UAV transmission signal, the listener receiving signal in the multi-listener cooperative detection mechanism is obtained, and the received signal probability density function is derived; the received signal probability density function is: in Representatives assume The probability density function of the received signal is: Representatives assume The probability density function of the received signal is: Represents the assumption that multiple listeners have no communication with the drone, represents the assumption by multiple listeners that the drone is communicating; Represents the multi-listener collaborative detection mechanism under the The time slot multiple listeners receive signal vectors, Represents the matrix transpose operation; is the number of listeners, represent The covariance matrix of represent The covariance matrix of represents the matrix inversion operation, represents the determinant of the matrix; is the natural base, is pi; Step 2: Based on the principle of multi-listener cooperative detection constructed by the probability density function of the received signal and likelihood ratio detection, we obtain the matrix expression of the minimum detection error rate lower bound of multi-listener cooperative detection, and derive the closed-form expression of the minimum detection error rate lower bound of multi-listener cooperative detection; Step 3: Based on the closed-form expression of the minimum detection error rate lower bound and the covert communication requirements, a closed-form expression for the channel capacity between the UAV and the user that meets the covert communication requirements is derived and an objective function is constructed. Then, the mobility constraints and scheduling constraints of the UAV are set respectively. Based on the objective function, mobility constraints, and scheduling constraints, a UAV trajectory and scheduling optimization problem that is resistant to cooperative detection is established. The UAV trajectory and scheduling optimization problem that is resistant to cooperative detection is: in, is the objective function, is the mobility constraint, is the scheduling constraint; Representative The time slot drone and Scheduling of users, Representative The time slot drone and The channel capacity between users, represents the time slot length, represents the constraints, Representative The position of the drone in each time slot, Representative The position of the drone in each time slot, Represents the maximum speed of the drone, Represents the scheduling variable of the drone to the user, Represents the user number, Represents the total number of users; Step 4: Based on the continuous convex approximation algorithm, the UAV trajectory and scheduling optimization problem resistant to collaborative detection is iteratively solved to obtain the optimal UAV trajectory and scheduling.

2. The method for designing UAV trajectories and scheduling to resist collaborative detection according to claim 1, characterized in that: Step 1 represents the multi-listener cooperative detection mechanism in the The time slot multiple listeners receive The signal vector is: in Represents the sequence number of the received signal, is the total number of received signals for each time slot, Representative Time slot The listener receives the background noise signal, Representative The first time slot that the drone transmits A useful signal, Represents the UAV transmission power; Representative The time slot drone and Channel gain between listeners.

3. The method for designing UAV trajectories and scheduling to resist collaborative detection according to claim 2, characterized in that: In step 1 The covariance matrix of and The covariance matrix of They are: in represents the background noise power, represents a diagonal matrix, express dimensional matrix, 、 、 Respectively represent The time slot drone and the first listener, the second listener, the Channel gain between listeners.

4. The method for designing UAV trajectories and scheduling to resist collaborative detection according to claim 2, characterized in that: The matrix expression of the minimum detection error rate lower bound of the multi-listener cooperative detection in step 2 is: in, Representative The minimum detection error rate lower bound of multi-listener cooperative detection in time slots, expression represent and The KL divergence between Representatives assume The probability density function of the received signal is multiplied, Representatives assume The probability density function of the received signal is multiplied; Represents the trace of the matrix.

5. The method for designing UAV trajectories and scheduling to resist collaborative detection according to claim 4, characterized in that: The closed-form expression for the lower bound of the minimum detection error rate of the multi-listener collaborative detection is: in, Represents the channel gain per unit distance, represents the path attenuation exponent of the channel, Representative The position of the drone in each time slot, Representative The location of the listener, Represents the flight altitude of the drone, Represents the 2-norm of the matrix.

6. The method for designing UAV trajectories and scheduling to resist collaborative detection according to claim 1, characterized in that: The closed-form expression of the channel capacity between the UAV and the user that meets the covert communication requirements is: in, Representative User locations, Representative The optimal transmission power of the drone in each time slot; The covert communication requirements described in step 3 are: in Represents the maximum exposure probability allowed for collaborative detection by multiple listeners; about Monotonically decreasing, the closed-form expression of the optimal transmission power of the UAV that meets the covert communication requirements in step 3 is: in Representative The optimal transmission power of the drone in each time slot is Represents the maximum transmission power of the drone, for hour The value of .

7. The method for designing UAV trajectories and scheduling to resist collaborative detection according to claim 6, characterized in that: The step 4 iteratively solves the anti-cooperative detection UAV trajectory and scheduling optimization problem based on the continuous convex approximation algorithm, including: Step 4.1: Initialize the initial trajectory of the drone and initial scheduling variables , and use the initial trajectory and initial scheduling variables of the UAV as the local points of iteration , set the iteration index ; Step 4.2: In iterations, at the local point of the iteration The trajectory and scheduling optimization problem of UAVs against cooperative detection established in step 3 is approximated as a convex problem; Step 4.3: Use the convex optimization algorithm to solve the convex problem obtained in step 4.2 and obtain the local optimal solution of this iteration ; Step 4.4: If the improvement of the objective function of this iteration compared to the previous objective function is less than the given threshold, the iteration is stopped, and the local optimal solution of this iteration is the optimal trajectory and scheduling of the UAV; otherwise, it will be used as the local point of the next iteration. , iterate index , return to step 4.

2.

8. A UAV trajectory and scheduling design system resistant to collaborative detection, characterized by: include: Received signal probability density function acquisition module: It is used to obtain the listener's received signal in the multi-listener collaborative detection mechanism based on the channel gain between the drone and the listener, the background noise signal, the drone's transmit power, and the drone's transmission signal, and derive the received signal probability density function; Minimum Detection Error Rate Acquisition Module: This module is used to obtain the matrix expression of the minimum detection error rate lower bound of multi-listener cooperative detection based on the principle of multi-listener cooperative detection constructed by the probability density function of the received signal and likelihood ratio detection, and derive the closed-form expression of the minimum detection error rate lower bound of multi-listener cooperative detection; Optimization problem construction module: This module is used to derive a closed-form expression for the channel capacity between the UAV and the user that meets the covert communication requirements based on the closed-form expression for the minimum detection error rate lower bound and the covert communication requirements, and construct an objective function. Then, the mobility constraints and scheduling constraints of the UAV are set separately. Based on the objective function, mobility constraints, and scheduling constraints, a UAV trajectory and scheduling optimization problem that is resistant to collaborative detection is established. Solution module: It is used to iteratively solve the UAV trajectory and scheduling optimization problem of anti-cooperative detection based on the continuous convex approximation algorithm to obtain the optimal UAV trajectory and scheduling; The UAV trajectory and scheduling design system for resisting collaborative detection is used to execute the steps in the UAV trajectory and scheduling design method for resisting collaborative detection as described in any one of claims 1-7.

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