Environment backscattering covert communication method and system assisted by unmanned aerial vehicle

Abstract

The invention relates to an environment backscattering covert communication method and system assisted by an unmanned aerial vehicle. The method comprises the following steps: constructing a system model; the probability of error detection and missing detection is supervised and calculated by an eavesdropper, and the minimum detection error probability is deduced to evaluate the concealment of the system; the signal to interference plus noise ratio is calculated from the aspect of a receiving end, and an expression of an effective transmission rate is obtained to evaluate the covert communication rate; by jointly optimizing the hovering position of the unmanned aerial vehicle and the reflection coefficient of the ground reflection equipment, the constructed optimization problem of the maximum covert communication rate is solved in a mode of alternately optimizing sub-problems under the condition that the concealment constraint condition is met, and the maximum covert communication rate assisted by the unmanned aerial vehicle is achieved. According to the method, the security and privacy protection capability of the Internet of Things equipment are improved, the development of low-power-consumption Internet of Things application is promoted, and the method is suitable for low-power-consumption equipment deployed on a large scale and shows remarkable advantages in complex application scenes such as emergency response, smart cities and industrial automation.

Description

Technical Field

[0001] This invention relates to the fields of wireless communication and secure communication technology, and in particular to a UAV-assisted environmental backscatter covert communication method and system. Background Technology

[0002] As an extremely low-power communication method, ambient backscatter communication (APR) utilizes ambient radio frequency (RF) signals from existing infrastructure such as TV towers, WiFi access points, and base stations to achieve wireless transmission, eliminating the need for a dedicated RF source to power the backscatter tags. Specifically, in an APR system, the transmitter modulates the reflected ambient RF signal to send data to its corresponding receiver. The receiver can then decode and obtain the desired data. Therefore, APR is considered a promising solution for supporting future low-power IoT applications. However, in environments without terrestrial infrastructure, finding a suitable RF source for backscattering is challenging.

[0003] Compared to traditional ground platforms, unmanned aerial vehicles (UAVs) offer better transmission conditions due to their short-range line-of-sight (LoS) links, making them excellent aerial platforms for supplementing wireless transmission. Furthermore, UAVs can help extend wireless coverage in remote areas with limited or lacking communication infrastructure. Specifically, in disaster areas or emergencies where ground communication facilities are damaged, UAVs can serve as flying base stations, effectively enhancing the coverage and capacity of wireless networks. In addition, UAV relay is an emerging technology for connecting isolated ground nodes, especially when there is congestion between them. Existing literature shows that the connectivity of UAV relay systems can be significantly enhanced through carefully designed UAV deployments and resource optimization.

[0004] Covert communication has garnered significant attention as a new model for ensuring wireless security. Unlike information encryption and physical layer security technologies, covert communication aims to achieve low-probability detection by the other party (unauthorized users) through various means, thereby concealing the communication behavior or process. Information encryption and physical layer security technologies focus on protecting the transmitted content; however, the communication behavior can still be detected by eavesdroppers, leading to privacy leaks. Even the leakage of communication behavior alone can cause significant losses; for example, the wireless transmission itself may expose the source node's location information, and transmission modes and traffic can also be exploited to obtain critical information. Covert communication technology provides the first line of defense for drone communication networks, offering new possibilities for solving the privacy protection problems faced by drone communication networks. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides a UAV-assisted environmental backscattering covert communication method and system, solving the problems existing in the prior art. This invention constructs a UAV hovering point set that meets the minimum communication requirements of ground users; calculates the probability of false detection and missed detection from the perspective of eavesdropper supervision, deriving the minimum detection error probability to evaluate the system's covertness; calculates the signal-to-interference-plus-noise ratio from the receiver's perspective, obtaining an expression for the effective transmission rate to evaluate the covert communication rate; and solves the optimization problem of maximizing the constructed covert communication rate by jointly optimizing the UAV hovering position and the reflection coefficient of the ground reflecting device, under the condition of satisfying covertness constraints, through alternating optimization of sub-problems.

[0006] To achieve the above objectives, the present invention provides the following technical solution: a UAV-assisted environmental backscattering covert communication method, comprising: A drone-assisted environmental backscatter covert communication system is established and a system model is constructed. The drone-assisted environmental backscatter covert communication system includes a drone flying at a fixed altitude and ground equipment. The ground equipment includes a ground user, a ground reflector (BD), a ground receiver (BR), and an eavesdropper (Willie). By setting a detection threshold, the false alarm probability and false negative probability of the eavesdropper Willie are obtained based on the received signal and detection strategy of the eavesdropper Willie, and then the total detection error probability is obtained to measure the detection performance of the eavesdropper Willie. Based on the relationship between the total detection error probability of the eavesdropper Willie and the detection threshold, the optimal detection threshold and the minimum detection error probability of the eavesdropper Willie are derived. Calculate the received signal and signal-to-interference-plus-noise ratio of the ground receiver BR. Based on the target transmission rate of the backscatter receiver, construct the probability formula for signal transmission interruption of the ground reflector BD to the ground receiver BR, and then calculate the effective transmission rate of the ground reflector BD to the ground receiver BR. The hovering position of the UAV that meets the minimum communication requirements of ground users is calculated, and a set of UAV hovering points is constructed. By optimizing the reflection coefficient of the ground reflector (BD) and the UAV hovering position, an optimization problem to maximize the covert communication rate is constructed under the covert constraint. The monotonicity of the effective transmission rate with respect to the reflection coefficient is solved, and the range of values ​​for the reflection coefficient is narrowed to simplify the optimization problem. The covert communication rate is quantified by the effective transmission rate. The covert constraint is constructed based on the minimum detection error probability. The simplified optimization problem is decomposed into two sub-problems: one for the reflection coefficient and the other for the hovering position of the UAV. The two sub-problems are optimized alternately to solve the optimization problem, thereby realizing UAV-assisted environmental backscattering covert communication.

[0007] Optionally, the drone communicates with the ground user, while the ground reflector BD reflects signals from the drone to communicate with the ground receiver BR. Optionally, the eavesdropper Willie monitors whether the ground reflector BD reflects signals to communicate with the ground receiver BR; Optionally, the UAV-assisted environmental backscatter covert communication system includes an air-to-ground channel dominated by short line-of-sight (LoS) between the UAV and various ground devices, and a ground channel dominated by Rayleigh fading between various ground devices. Optionally, there is an uncertainty regarding ambient noise at the location of the eavesdropper Willie.

[0008] Optionally, the setting of the detection threshold, based on the received signal of the eavesdropper Willie and its detection strategy, to obtain the false alarm probability and false negative probability of the eavesdropper Willie, and thus to obtain its total detection error probability, includes: Based on the system model, the location of the eavesdropper Willie in the time slot was obtained. The received signal within; the eavesdropper Willie in the time slot The received signals include two cases: signals from the UAV reflected by the ground-based reflector (BD) and signals from the UAV that are not reflected. Set a detection threshold and construct a detection strategy; the detection strategy includes two decision-making processes: whether the eavesdropper Willie conducts reflective communication with the ground reflective device BD or not. Based on the eavesdropper Willie's time slot The system calculates the average power received by the eavesdropper Willie from the received signal. If the average power is greater than or equal to the detection threshold, the detection strategy determines that the ground reflector BD will perform reflective communication. If the average power is less than the detection threshold, the detection strategy determines that the ground reflector BD will not perform reflective communication. The average power includes two cases: the ground reflector BD reflects the signal of the UAV and the ground reflector BD does not reflect the signal of the UAV. Based on the decision-making of the detection strategy, the false alarm probability and the missed detection probability of the eavesdropper Willie are calculated, and the two are added together to obtain the total detection error probability of the eavesdropper Willie.

[0009] Optionally, the minimum detection error probability is the total detection error probability of the eavesdropper Willie under the optimal detection threshold.

[0010] Optionally, the calculation of the received signal and signal-to-interference-plus-noise ratio of the ground receiver BR includes: calculating the ground receiver BR in the time slot based on the system model. The received signal is then used to calculate its signal-to-interference-plus-noise ratio. The ground receiver BR in the time slot The received signals include two cases: signals from the UAV reflected by the ground-based reflector (BD) and signals from the UAV that are not reflected. Optionally, the formula for constructing the signal transmission interruption probability formula from the ground reflector device BD to the ground receiver BR based on the target transmission rate of the backscatter receiver includes: first, based on the signal-to-interference-plus-noise ratio... Calculate channel capacity Then, based on the target transmission rate of the backscatter receiver With channel capacity Obtain the probability of signal transmission interruption Therefore, a formula for the probability of signal transmission interruption is constructed; the probability of signal transmission interruption... If the channel capacity Less than the target transmission rate of the backscatter receiver If the signal transmission is interrupted, then the signal transmission interruption is considered to be interrupted; the constructed probability formula for signal transmission interruption is as follows: ; In the formula, Expressing the request The probability of; Optionally, calculating the effective transmission rate of the ground reflector BD to the ground receiver BR includes: setting a tolerable interruption probability. An interruption constraint is constructed, and the target transmission rate under the interruption constraint is calculated using the signal transmission interruption probability formula, which is the effective transmission rate; the interruption constraint is mathematically expressed as follows: .

[0011] Optionally, the calculation of the UAV hovering position that meets the minimum communication requirements of the ground user and the construction of the UAV hovering point set includes: calculating the minimum communication signal-to-interference-plus-noise ratio of the ground user based on the communication requirements of the ground user, and deriving the UAV hovering point set that meets the requirements; Optionally, the optimization problem of maximizing the covert communication rate is defined as follows: ; in, Indicates the need to make Maximize , ; This represents the effective transmission rate from the ground reflector BD to the ground receiver BR, used to quantify the rate of covert communication. For drone hovering point set The hovering position of the drone in the image; The concealment threshold is set within the range of (0, 0.5). This represents the minimum detection error probability of the eavesdropper Willie. These are hidden constraints; This represents the reflectivity of the ground-based reflector BD. It is a range constraint on the reflection coefficient; It indicates that it is subject to restrictions.

[0012] Optionally, the simplified optimization problem is decomposed into two sub-problems: one for the reflection coefficient and the other for the drone hovering position. This includes: optimizing the reflection coefficient to maximize the effective transmission rate while keeping the drone hovering position fixed; and calculating the effective transmission rate for each drone hovering position while keeping the reflection coefficient fixed, finding the drone hovering position index that maximizes the effective transmission rate, and using it as the optimal drone hovering position index. Optionally, the alternating optimization of the two sub-problems to solve the optimization problem includes: first, fixing the drone hovering position and updating the reflection coefficient; then, fixing the updated reflection coefficient and updating the optimal drone hovering position index; repeating the above process until the increase in effective transmission rate is lower than a preset threshold, or the number of repetitions reaches a preset maximum value.

[0013] Optionally, optimizing the reflection coefficient to maximize the effective transmission rate when the UAV is hovering at a fixed position includes: based on the functional relationship between the reflection coefficient and the effective transmission rate when the UAV is hovering at a fixed position, finding the optimal solution of the reflection coefficient that maximizes the effective transmission rate through boundary analysis of the reflection coefficient.

[0014] The present invention also provides a drone-assisted environmental backscatter covert communication system for applying the drone-assisted environmental backscatter covert communication method, comprising: a drone flying at a fixed altitude and ground equipment; The ground equipment includes: a ground user, a ground reflector (BD), a ground receiver (BR), and an eavesdropper (Willie).

[0015] Optionally, the drone communicates with the ground user, while the ground reflector BD reflects signals from the drone to communicate with the ground receiver BR. Optionally, the eavesdropper Willie monitors whether the ground reflector BD reflects signals to communicate with the ground receiver BR; Optionally, the UAV-assisted environmental backscatter covert communication system includes an air-to-ground channel dominated by short line-of-sight (LoS) between the UAV and various ground devices, and a ground channel dominated by Rayleigh fading between various ground devices. Optionally, there is an uncertainty regarding ambient noise at the location of the eavesdropper Willie.

[0016] By employing the above technical solution, the present invention provides a UAV-assisted environmental backscattering covert communication method and system, which has at least the following beneficial effects: (1) This invention is aimed at the backscatter communication scenario assisted by UAVs, and introduces eavesdropper detection modeling and joint optimization strategy to realize the covert control of communication behavior; (2) Compared with traditional systems that only focus on communication efficiency or encryption mechanisms, this invention focuses on ensuring the undetectability of communication behavior. By optimizing the hovering position and reflection coefficient of the UAV while meeting the communication needs of multiple users, the covert communication rate and anti-detection capability are significantly improved. (3) The system constructed by the present invention has the advantages of low power consumption, flexible deployment and high concealment, and is particularly suitable for application scenarios with extremely high requirements for the concealment of communication behavior, such as military surveillance and border reconnaissance; (4) This invention considers an environment backscattering scenario assisted by a drone. By replacing the traditional fixed radio frequency source with a drone, and taking advantage of its flexibility, the concealed communication rate of the reflection system is improved by optimizing the reflection coefficient and the position of the drone. On the one hand, it improves the security and privacy protection capabilities of IoT devices, especially in dealing with malicious attacks such as eavesdropping, interference and deception. On the other hand, it promotes the development of low-power IoT applications, is suitable for large-scale deployment of low-power devices, and shows significant advantages in complex application scenarios such as emergency response, smart cities and industrial automation. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, illustrate exemplary embodiments and are used to explain this application, but do not constitute an undue limitation of this application. In the drawings: Figure 1 This is a flowchart of an unmanned aerial vehicle (UAV)-assisted environmental backscattering covert communication method according to the present invention. Figure 2 This is a diagram showing the hovering positions (effective hovering points) of the UAVs that meet the requirements in this embodiment of the invention, and the distribution of nodes in the UAV covert communication system. Figure 3 This is a schematic diagram of the UAV-assisted environmental backscatter covert communication system constructed according to the present invention; Figure 4 This is a graph showing the trend of covert communication rate changes under different covertness thresholds in an embodiment of the present invention. Figure 5 This is a graph showing the trend of covert communication rate variation under different UAV transmission powers when the covertness threshold is fixed in an embodiment of the present invention. Detailed Implementation

[0018] To make the above-mentioned objects, features, and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. This will allow for a full understanding of how the present application uses technical means to solve technical problems and achieve technical effects, and to facilitate its implementation.

[0019] Those skilled in the art will understand that all or part of the steps in the implementation of the methods of the embodiments can be implemented by a program instructing related hardware. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Moreover, this application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0020] Please refer to Figures 1-5 This paper illustrates a specific implementation of this embodiment. This embodiment constructs a system model, derives the total detection error probability of the eavesdropper Willie to measure its detection performance, and then derives its minimum detection error probability. It constructs a formula for the signal transmission interruption probability of the ground reflector BD to the ground receiver BR, thereby calculating the effective transmission rate, quantifying the covert communication rate, constructing an optimization problem, and alternately optimizing the reflection coefficient and the UAV hovering position to solve the optimization problem, thus maximizing the UAV-assisted covert communication rate. Numerical simulation results show that this invention can effectively improve the covert communication performance of the system in different scenarios, verifying the superiority of the proposed method. This invention is of great significance for the development and application of covert communication technology.

[0021] Please refer to Figure 1 This embodiment proposes a UAV-assisted environmental backscattering covert communication method, which includes the following steps: S1. Establish an unmanned aerial vehicle (UAV)-assisted environmental backscatter covert communication system and construct a system model; the UAV-assisted environmental backscatter covert communication system includes a UAV flying at a fixed altitude, a ground user, a ground reflector (BD), a ground receiver (BR), and an eavesdropper (Willie).

[0022] As a preferred embodiment of step S1, it specifically includes: The established UAV-assisted environmental backscatter covert communication system includes: a UAV at a fixed altitude Flying drones The system consists of one ground user, one ground reflector (BD), one ground receiver (BR), and one eavesdropper (Willie). The drone, acting as the sole radio frequency (RF) source, continuously transmits stable RF signals to the ground, serving not only for communication with the laser reflector but also meeting the channel coverage and communication quality requirements of each ground user. Due to its mobility, the drone can hover at an optimal location among several preset hovering positions. The BD passively reflects signals from the drone and transmits information to the BR by modulating the reflected waves. The BD does not actively transmit signals, resulting in extremely low energy consumption, making it suitable for deployment in resource-constrained or high-concealment scenarios. The eavesdropper, Willie, is deployed at a fixed location on the ground. Its objective is to use energy detection technology to determine whether the BD is transmitting information, thereby threatening the system's concealment.

[0023] If the drone is deployed high enough, the probability of a short line-of-sight (LoS) signal in the air-to-ground channel is typically approximately 1. Therefore, for simplicity, from the drone to... The channels are dominated by short line-of-sight (LoS), so for links from UAVs to various ground devices, the channel gain... It can be represented as: ; in, Indicates the air-to-ground channel gain at a unit reference distance; The horizontal coordinates of the drone; These are the coordinates of the ground equipment. Indicates the type of ground equipment, where This represents the k-th ground user. BD represents the ground reflector. Indicates ground receiver BR, Willie, the eavesdropper, The altitude of the drone.

[0024] Considering the fast fading due to multipath propagation and the slow fading due to blockage in the ground detection channel, the channel fading from the ground reflector BD to the ground receiver BR and from the ground reflector BD to the eavesdropper Willie is as follows. , It can be represented as: ; in This represents the ground channel gain corresponding to 1 meter; , These represent the distances from the ground reflector BD to the ground receiver BR and the eavesdropper Willie, respectively. It is the path loss exponent of the backscatter link, and Slow fading gain This indicates a small-scale decline that follows an exponential distribution with a parameter of 1.

[0025] In a preferred embodiment of the present invention, due to the influence of the dynamic environment, the noise power of the eavesdropper Willie cannot be accurately obtained. It is assumed that the noise power is a random variable with a known distribution. Specifically, there is uncertainty regarding the environmental noise at the location of the eavesdropper Willie, and the noise power at Willie's location... probability density function It is given by the following formula: ; in This is the nominal noise power. This represents the detection threshold parameter, i.e., the noise uncertainty coefficient. Indicates noise power Possible values ​​for .

[0026] S2. Set the detection threshold, obtain the false alarm probability and false negative probability of the eavesdropper Willie based on the received signal of the eavesdropper Willie and its detection strategy, and then obtain its total detection error probability to measure the detection performance of the eavesdropper Willie.

[0027] As a preferred embodiment of step S2, it specifically includes: Based on the system model constructed in step S1, the location of the eavesdropper Willie in the time slot is obtained. Internal received signal for: ; in, This refers to the drone's transmission power. This indicates that the ground-based reflector (BD) does not reflect the drone's signals; This indicates that the ground-based reflector (BD) is reflecting the signals of the drone. This represents the reflectivity of the ground-based reflector BD. It is complex Gaussian noise at the location of the eavesdropper Willie ( This indicates that it follows a mean of 0 and a variance of . Gaussian normal distribution); This represents the channel gain of the air-to-ground channel from the drone to the eavesdropper Willie; This represents the channel gain of the air-to-ground channel from the UAV to the ground-based reflector (BD). This indicates the channel fading of the ground channel from the ground reflecting device BD to the eavesdropper Willie; For transmitting signals for drones; This is the signal transmitted when the ground-based reflector BD reflects the signal.

[0028] Based on the eavesdropper Willie's time slot Internal received signal Willie's detection strategy was as follows: ; in, This represents the average power received by the eavesdropper Willie. Indicates the detection threshold. and These represent the binary decision made by the eavesdropper Willie regarding whether to conduct reflected communication with the ground-based reflective device BD. This indicates that reflective communication will not be performed. Indicates reflection communication; subchannel index , The total number of sub-channels in each time slot. Assuming the eavesdropper Willie can observe an infinite number of samples, this invention applies the law of large numbers to calculate the average power. for: .

[0029] The detection performance of the eavesdropper Willie was measured using the probability of detection errors. and Under the assumption of uniform prior probability, the total detection error probability Defined as false alarm probability With the probability of missed detection sum: ; in, Willie was deemed the eavesdropper. The actual situation of the ground reflector BD is... The probability of.

[0030] To obtain the total detection error probability First, calculate the false alarm probability. : ; Calculating the intermediate value .

[0031] Next, we calculate the probability of missed detection. : ; Calculating the intermediate value .

[0032] This leads to the total detection error probability of the eavesdropper Willie. for: ; in, .

[0033] It should be noted that this invention incorporates a special design for the derivation of false alarm and false detection probabilities in the context of UAV-assisted environmental backscattering, unlike traditional energy detection methods. This invention simultaneously considers the direct link from the UAV to the eavesdropper (Willie) and the reflected link from the UAV to the ground-based reflector (BD) to the eavesdropper (Willie), resulting in a dual-path detection statistic for the eavesdropper (Willie). Furthermore, this invention introduces a noise uncertainty model when subsequently deriving the optimal detection threshold for the eavesdropper (Willie), making the optimal detection threshold susceptible to noise fluctuations and increasing detection difficulty. Since the UAV's position is controllable, the channel gain varies significantly with the UAV's location, further impacting the eavesdropper's detection performance. Through these designs, this invention effectively improves the false detection probability of the eavesdropper, thereby enhancing the overall system's covert communication capabilities.

[0034] S3. Based on the relationship between the total detection error probability of the eavesdropper Willie and the detection threshold, derive the optimal detection threshold and the minimum detection error probability of the eavesdropper Willie.

[0035] As a preferred embodiment of step S3, it specifically includes: Based on the results derived from step S2, it can be observed that when or At that time, the total detection error probability A value of 1 is the worst-case scenario for an eavesdropper. Meanwhile, [the value will be...]. right Find the partial derivative: ; It can be seen about It is monotonically decreasing. about Since it is monotonically increasing, the optimal detection threshold can be determined. for: ; Accordingly, the minimum detection error probability is calculated. for: ; in This represents the coordinates of the eavesdropper Willie.

[0036] S4. Calculate the received signal and signal-to-interference-plus-noise ratio of the ground receiver BR. Based on the target transmission rate of the backscatter receiver, construct the signal transmission interruption probability formula of the ground reflector BD to the ground receiver BR, and then calculate the effective transmission rate of the ground reflector BD to the ground receiver BR.

[0037] As a preferred embodiment of step S4, it specifically includes: Based on the system model, the BR of the ground receiver is calculated in the time slot. Internal received signal : ; In the formula, This represents the channel gain from the UAV to the ground receiver BR; This indicates the channel fading from the ground reflecting device BD to the ground receiver BR; This represents the Gaussian white noise received by the ground receiver BR. This indicates that it follows a mean of 0 and a variance of . Gaussian normal distribution (This represents the noise power of the ground receiver BR).

[0038] For an environmental backscatter link, the ground-based reflector (BD) modulates its own information from the UAV and then reflects it with a specific reflection coefficient to the modulated signal of its corresponding ground receiver (BR). It is feasible to reduce RF source interference by 50 dB by deviating the backscatter frequency from the UAV's signal frequency. In this way, only a small fraction of the interference power will carry the interference factor. The backscattering receiver leaves behind the signal. Therefore, the signal-to-interference-plus-noise ratio (SIR) of the received signal at the ground receiver BR can be calculated. for: ; The probability of signal transmission interruption from ground reflector BD to ground receiver BR. It can be represented as: ; in, Expressing the request The probability of; Indicates channel capacity; Indicates the target transmission rate of the backscatter receiver; Indicates the coordinates of the ground receiver BR; Represents the coordinates of the ground reflector BD; slow fading gain. It follows an exponential distribution with a parameter of 1.

[0039] Set the tolerable interruption probability Therefore, in the interruption constraint The effective transmission rate of backscattering that can be achieved can be calculated as follows: ; in, This represents the effective transmission rate, i.e., the target transmission rate under interruption constraints.

[0040] It should be noted that the calculation of signal-to-interference-plus-noise ratio (SIR) and interruption probability is not a simple application of existing models, but rather involves key design considerations for the unique structure of the UAV-assisted backscattering link. Specifically, the constructed SIR model... This system simultaneously incorporates both the cascaded reflected useful signal from the "drone-reflector-receiver" link and the direct link interference from the "drone-receiver" link, precisely characterizing the unique interference properties of this hybrid system. More importantly, it derives the effective transmission rate from this. Minimum detection error probability compared to the eavesdropper's side By reflectance coefficient A deep coupling relationship has been formed: increasing the speed requires increasing... However, ensuring concealment requires restrictions. This inherent contradiction forms the core of the joint optimization problem, making S4 computation a key bridge connecting and unifying the two dimensions of system communication performance and stealth. This drives subsequent alternating optimization of UAV position and reflection coefficient, thereby achieving system-level maximization of stealth communication rate.

[0041] S5. Calculate the hovering position of the UAV that meets the minimum communication requirements of ground users, construct a UAV hovering point set, and construct an optimization problem to maximize the covert communication rate under the covert constraint by optimizing the reflection coefficient of the ground reflection device BD and the UAV hovering position. Solve the monotonicity of the effective transmission rate with respect to the reflection coefficient, and narrow the range of values ​​of the reflection coefficient to simplify the optimization problem.

[0042] As a preferred embodiment of step S5, it specifically includes: Assume the communication needs of ground users are ,ground The lowest possible signal-to-noise ratio for a single user is: ; in, This function represents the signal-to-interference-plus-noise ratio (SIR) for the k-th ground user. This indicates that among K ground users, those meeting the condition... In the case of The minimum value; This represents the horizontal coordinate of the k-th ground user. This represents the noise power at the k-th ground user. This represents the channel gain from the UAV to the k-th ground user.

[0043] Based on the above formula, points on the plane can be input, and points that meet the communication needs of all ground users can be selected as candidate points to obtain a set of drone hovering points that meet the requirements. That is, the following formula: ; In the formula, This represents the condition "" for K ground users. "of The maximum value in.

[0044] Figure 2 This demonstrates the qualified drone hovering positions (effective hovering points) and the distribution of drone covert communication system nodes, as well as the drone hovering point set composed of effective hovering points. like Figure 2 The green dot is shown in the middle.

[0045] The objective of this invention is to maximize the covert communication rate, i.e., maximize the effective transmission rate, by jointly optimizing the reflection coefficient of the ground-based reflector (BD) and the hovering position of the UAV. At the same time, it is necessary to ensure normal communication between ground users and drones. Therefore, the optimization problem can be defined as: ; in, Indicates the need to make Maximize , ; This represents the effective transmission rate from the ground reflector BD to the ground receiver BR, used to quantify the rate of covert communication. For drone hovering point set The hovering position of the drone in the image; The concealment threshold is set within the range of (0, 0.5). This represents the minimum detection error probability of the eavesdropper Willie. These are hidden constraints; This represents the reflectivity of the ground-based reflector BD. It is a range constraint on the reflection coefficient; It indicates that it is subject to restrictions.

[0046] Find the effective transmission rate Regarding the reflectance coefficient The monotonicity of can be calculated. Possible values; based on the drone hovering point set The effective transmission rate at each drone hovering position can be calculated. Ultimately, the effective transmission rate is given. The reflection coefficient is related to the drone's hovering position.

[0047] First, the effective transmission rate Regarding the reflectance coefficient Find the partial derivative: ; in, express right Find the partial derivative.

[0048] Based on the above formula, we can derive... about It is monotonically increasing, and then based on the concealment constraint... Seeking The upper realm : .

[0049] S6. Decompose the simplified optimization problem into two sub-problems: one for the reflection coefficient and the other for the hovering position of the UAV. Alternately optimize the two sub-problems to solve the optimization problem and realize UAV-assisted environmental backscattering covert communication.

[0050] As a preferred embodiment of step S6, it specifically includes: In step S5, the hovering position of the UAV and the reflection coefficient of the ground reflector BD have been compared. The joint optimization problem was formally modeled. Although the objective function of this optimization problem has a clear monotonicity, the coupling between the optimization variables makes direct solution computationally complex and impractical for engineering applications. Therefore, this invention proposes a problem decomposition strategy, transforming the original optimization problem into two more easily solvable subproblems: Sub-problem 1: At a fixed drone hovering position In this case, optimize the reflection coefficient Maximize the effective transmission rate ;because Follow Monotonically increasing, while hidden constraints will affect Given an upper bound, and because Therefore, the optimal solution for the reflection coefficient By adjusting the reflection coefficient The boundary analysis yields the following result: .

[0051] In this way, the optimal solution for the reflection coefficient at each drone hovering position can be quickly obtained through closed-form solutions.

[0052] Sub-problem 2: Traversing the set of UAV hovering points under a fixed reflection coefficient. Calculate the hovering position index for each drone. Effective transmission rate : ; Find the drone hovering position index that maximizes the effective transmission rate. This yields the optimal drone hovering position index. (This is because the drone hovering point set...) Since the scale is limited, this process can be efficiently achieved through exhaustive search.

[0053] Through the above decomposition, this invention resolves the complex joint optimization problem into two independent sub-problems, thereby significantly reducing the optimization complexity and providing a foundation for subsequent iterative optimization.

[0054] After completing the problem decomposition, this invention proposes to solve the constructed optimization problem using an alternating optimization algorithm, with the following steps: Initialization phase: Select an initial hover position index And calculate the corresponding initial value of the reflection coefficient. This ensures that it meets the concealment constraints and the communication needs of ground users.

[0055] Alternating Iteration Phase: in the first In the next iteration, the hover position index is first fixed. Update the reflection coefficients based on the closed-form solution of subproblem one: ; Then fix the updated reflection coefficient The new optimal hovering position for the drone is selected based on the search method for subproblem two: ; in This represents a function that finds the index of the maximum value.

[0056] Convergence Criterion: Repeat the above process until the increase in effective transmission rate is lower than a preset threshold. Or the number of repetitions reaches the preset maximum value. .

[0057] Final output: After the algorithm converges, the optimal solution with the highest reflection coefficient is obtained. Index of optimal drone hovering position This represents the optimal solution to the optimization problem. At this point, the system maximizes the covert communication rate while ensuring user communication needs and concealment constraints.

[0058] It should be noted that while breaking down complex optimization problems into two sub-problems and employing alternating optimization is a common approach, this invention specifically designs the problem modeling and decomposition method for a drone-assisted backscattering covert communication scenario. The unique design in step S6 of this invention lies in constructing a deep physical coupling and closed-loop feedback mechanism between the reflection coefficient and the drone's hovering position. Unlike existing methods that treat covertness as a static constraint, this invention dynamically embeds covertness into the optimization variables: when optimizing the reflection coefficient, its upper bound is dynamically determined by the real-time geometric relationship between the drone and the eavesdropper; when optimizing the position, the drone must simultaneously act as both a "service provider" and an "interference agent"—both enhancing the legitimate link and actively worsening the eavesdropping environment. This design achieves a synergistic shaping of covertness and communication performance, enabling the system to adaptively balance the inherent contradiction between "high speed" and "low detection," thereby achieving dynamic optimization in complex environments that is difficult to achieve with existing methods.

[0059] Furthermore, unlike existing methods that only maximize secure communication rates or reflection link capacity, the optimization objective of this invention is based on a unique structure of "jointly improving effective reflection gain and UAV geometric gain under covert communication constraints." This invention incorporates the eavesdropper detection model, the cascaded channel characteristics of the UAV-reflection device, and time-varying geometric relationships into the optimization process. This ensures that reflection coefficient optimization affects not only the legitimate link gain but also the probability of eavesdropper detection; while UAV position optimization affects not only communication quality but also directly controls the concealment index. Through this joint design, this invention achieves a functional coupling between reflection coefficient control and UAV trajectory planning, thereby significantly improving covert communication performance under weak reflection link conditions—a feature not considered in existing technologies.

[0060] This application also provides a UAV-assisted environmental backscatter covert communication system for applying the aforementioned UAV-assisted environmental backscatter covert communication method, including: at a fixed altitude Flying unmanned aerial vehicles (UAVs) and ground equipment; the ground equipment includes: The system comprises one ground user (User 1, User 2, ..., User K), one ground reflector (BD), one ground receiver (BR), and one eavesdropper (Willie). The structure of this UAV-assisted environmental backscattering covert communication system can be referenced from [reference needed]. Figure 3 .

[0061] Specifically, the drone communicates with the ground user, while the ground reflector BD reflects signals from the drone to communicate with the ground receiver BR. The eavesdropper Willie was monitoring whether the ground reflector BD was reflecting signals to communicate with the ground receiver BR. The UAV-assisted environmental backscatter covert communication system includes an air-to-ground channel dominated by short line-of-sight (LoS) between the UAV and various ground devices, and a ground channel dominated by Rayleigh fading between various ground devices. There is an uncertainty regarding the ambient noise at the location of the eavesdropper, Willie.

[0062] To facilitate understanding of the specific implementation of the invention by those skilled in the art, the following examples, simulation parameters, and numerical results are provided. Regarding the selection of simulation parameters, without loss of generality, consider an environmental backscattering scenario, which includes an environmental reflector UAV, ground users (User 1, User 2, ..., User K), an eavesdropper Willie, and ground reflector BD and ground receiver BR. Simulation is performed using MATLAB, and the simulation parameters are shown in Table 1.

[0063] Table 1. System Simulation Parameters

[0064] The simulation results will be explained next.

[0065] Figure 4 Different concealment thresholds are given. The covert communication rate (bps / Hz) is specified. When covertness constraints are strict (i.e.... When the reflection coefficient is relatively small, in order to ensure that the detection error probability of the eavesdropper Willie is close to 1, the system must significantly reduce the reflection coefficient. This leads to a decrease in signal power at the receiving end, resulting in a lower rate of covert communication. With With the relaxation of restrictions, the requirements for concealment gradually become looser, allowing the system to choose a wider range of options. This effectively improves the received signal-to-interference-plus-noise ratio, causing the covert communication rate to increase monotonically. When When the value is large enough, the concealment constraint becomes essentially ineffective, and the concealed communication rate approaches the maximum value under the unconstrained condition, verifying the constraint relationship between concealment and communication performance.

[0066] Figure 5 Demonstrates concealment threshold When fixed at 0.20, the transmit power of different drones The trend of covert communication rate (bps / Hz) under the following conditions. It can be seen that when... When the value is small, the useful signal power received by the backscatter link increases with... The increase is rapid, resulting in a significant rise in the rate of covert communication. However, with... As the number of devices increases, Willie's detection capabilities also improve. To meet the concealment constraints, the reflection coefficient... It must be reduced, and its upper bound is approximately the same as... This is inversely proportional to the effective received power, thus keeping it at a limited level. Therefore, in a wider range of transmit power, the covert communication rate gradually saturates, exhibiting a "first increase, then stability" characteristic, reflecting the trade-off between increasing transmit power and covert constraints.

[0067] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of this application. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0068] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus or device (such as a computer-based system, a processor-included system or other system that can fetch and execute instructions from, an instruction execution system, apparatus or device).

[0069] The above embodiments provide a detailed description of the present invention. Specific examples have been used to illustrate the principles and implementation methods of the present invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of the present invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of the present invention. Therefore, the content of this specification should not be construed as a limitation of the present invention.

Claims

1. A UAV-assisted environmental backscattering covert communication method, characterized in that, include: A drone-assisted environmental backscatter covert communication system is established and a system model is constructed. The drone-assisted environmental backscatter covert communication system includes a drone flying at a fixed altitude and ground equipment. The ground equipment includes a ground user, a ground reflector (BD), a ground receiver (BR), and an eavesdropper (Willie). By setting a detection threshold, the false alarm probability and false negative probability of the eavesdropper Willie are obtained based on the received signal and detection strategy of the eavesdropper Willie, and then the total detection error probability is obtained to measure the detection performance of the eavesdropper Willie. Based on the relationship between the total detection error probability of the eavesdropper Willie and the detection threshold, the optimal detection threshold and the minimum detection error probability of the eavesdropper Willie are derived. Calculate the received signal and signal-to-interference-plus-noise ratio of the ground receiver BR. Based on the target transmission rate of the backscatter receiver, construct the probability formula for signal transmission interruption of the ground reflector BD to the ground receiver BR, and then calculate the effective transmission rate of the ground reflector BD to the ground receiver BR. The hovering position of the UAV that meets the minimum communication requirements of ground users is calculated, and a set of UAV hovering points is constructed. By optimizing the reflection coefficient of the ground reflector (BD) and the UAV hovering position, an optimization problem to maximize the covert communication rate is constructed under the covert constraint. The monotonicity of the effective transmission rate with respect to the reflection coefficient is solved, and the range of values ​​for the reflection coefficient is narrowed to simplify the optimization problem. The covert communication rate is quantified by the effective transmission rate. The covert constraint is constructed based on the minimum detection error probability. The simplified optimization problem is decomposed into two sub-problems: one for the reflection coefficient and the other for the hovering position of the UAV. The two sub-problems are optimized alternately to solve the optimization problem, thereby realizing UAV-assisted environmental backscattering covert communication.

2. The UAV-assisted environmental backscattering covert communication method according to claim 1, characterized in that: The drone communicates with the ground user, and at the same time, the ground reflector BD reflects the signal from the drone and communicates with the ground receiver BR. The eavesdropper Willie was monitoring whether the ground reflector BD was reflecting signals to communicate with the ground receiver BR. The UAV-assisted environmental backscatter covert communication system includes an air-to-ground channel dominated by short line-of-sight (LoS) between the UAV and various ground devices, and a ground channel dominated by Rayleigh fading between various ground devices. There is an uncertainty regarding the ambient noise at the location of the eavesdropper, Willie.

3. The UAV-assisted environmental backscatter covert communication method according to claim 1, characterized in that: The set detection threshold, based on the eavesdropper Willie's received signal and detection strategy, yields the false alarm probability and false negative probability of Willie, and thus the total detection error probability, including: Based on the system model, the location of the eavesdropper Willie in the time slot was obtained. The received signal within; the eavesdropper Willie in the time slot The received signals include two cases: signals from the UAV reflected by the ground-based reflector (BD) and signals from the UAV that are not reflected. Set a detection threshold and construct a detection strategy; the detection strategy includes two decision-making processes: whether the eavesdropper Willie conducts reflective communication with the ground reflective device BD or not. Based on the eavesdropper Willie's time slot The system calculates the average power received by the eavesdropper Willie from the received signal. If the average power is greater than or equal to the detection threshold, the detection strategy determines that the ground reflector BD will perform reflective communication. If the average power is less than the detection threshold, the detection strategy determines that the ground reflector BD will not perform reflective communication. The average power includes two cases: the ground reflector BD reflects the signal of the UAV and the ground reflector BD does not reflect the signal of the UAV. Based on the decision-making of the detection strategy, the false alarm probability and the missed detection probability of the eavesdropper Willie are calculated, and the two are added together to obtain the total detection error probability of the eavesdropper Willie.

4. The UAV-assisted environmental backscatter covert communication method according to claim 1, characterized in that: The minimum detection error probability is the total detection error probability of the eavesdropper Willie under the optimal detection threshold.

5. The UAV-assisted environmental backscatter covert communication method according to claim 1, characterized in that: The calculation of the received signal and signal-to-interference-plus-noise ratio (SINNR) of the ground receiver (BR) includes: calculating the BR's received signal and SINNR in the time slot based on the system model. The received signal is then used to calculate its signal-to-interference-plus-noise ratio. The ground receiver BR in the time slot The received signals include two cases: signals from the UAV reflected by the ground-based reflector (BD) and signals from the UAV that are not reflected. The formula for constructing the signal transmission interruption probability formula from the ground reflector (BD) to the ground receiver (BR) based on the target transmission rate of the backscatter receiver includes: first, based on the signal-to-interference-plus-noise ratio (SINR). Calculate channel capacity Then, based on the target transmission rate of the backscatter receiver With channel capacity Obtain the probability of signal transmission interruption Therefore, a formula for the probability of signal transmission interruption is constructed; the probability of signal transmission interruption... If the channel capacity Less than the target transmission rate of the backscatter receiver If the signal transmission is interrupted, then the signal transmission interruption is considered to be interrupted; the constructed probability formula for signal transmission interruption is as follows: ； In the formula, Expressing the request The probability of; The calculation of the effective transmission rate from the ground reflector BD to the ground receiver BR includes: setting the tolerable interruption probability. An interruption constraint is constructed, and the target transmission rate under the interruption constraint is calculated using the signal transmission interruption probability formula, which is the effective transmission rate; the interruption constraint is mathematically expressed as follows: .

6. The UAV-assisted environmental backscatter covert communication method according to claim 1, characterized in that: The calculation of the drone hovering position that meets the minimum communication requirements of ground users and the construction of the drone hovering point set include: calculating the minimum communication signal-to-interference-plus-noise ratio of ground users based on their communication requirements and deriving the drone hovering point set that meets the requirements. The optimization problem of maximizing the rate of covert communication is defined as follows: ； in, Indicates the need to make Maximize , ; This represents the effective transmission rate from the ground reflector BD to the ground receiver BR, used to quantify the rate of covert communication. For drone hovering point set The hovering position of the drone in the image; The concealment threshold is set within the range of (0, 0.5). This represents the minimum detection error probability of the eavesdropper Willie. These are hidden constraints; This represents the reflectivity of the ground-based reflector BD. It is a range constraint on the reflection coefficient; It indicates that it is subject to restrictions.

7. The UAV-assisted environmental backscatter covert communication method according to claim 1, characterized in that: The simplified optimization problem is decomposed into two sub-problems: one for the reflection coefficient and the other for the drone hovering position. The sub-problems include: optimizing the reflection coefficient to maximize the effective transmission rate while keeping the drone hovering position fixed; and calculating the effective transmission rate for each drone hovering position while keeping the reflection coefficient fixed, finding the drone hovering position index that maximizes the effective transmission rate, and using it as the optimal drone hovering position index. The alternating optimization of the two sub-problems, and the solution of the optimization problem, includes: first, fixing the hovering position of the UAV and updating the reflection coefficient; then, fixing the updated reflection coefficient and updating the index of the optimal UAV hovering position; repeating the above process until the increase in effective transmission rate is lower than a preset threshold, or the number of repetitions reaches a preset maximum value.

8. The UAV-assisted environmental backscatter covert communication method according to claim 7, characterized in that: The step of optimizing the reflection coefficient and maximizing the effective transmission rate when the UAV is hovering at a fixed position includes: based on the functional relationship between the reflection coefficient and the effective transmission rate when the UAV is hovering at a fixed position, finding the optimal solution of the reflection coefficient that maximizes the effective transmission rate through boundary analysis of the reflection coefficient.

9. A UAV-assisted environmental backscattering covert communication system, used to apply the UAV-assisted environmental backscattering covert communication method as described in any one of claims 1-8, characterized in that, include: Unmanned aerial vehicles (UAVs) and ground equipment that fly at a fixed altitude; The ground equipment includes: a ground user, a ground reflector (BD), a ground receiver (BR), and an eavesdropper (Willie).

10. The UAV-assisted environmental backscatter covert communication system according to claim 9, characterized in that: The drone communicates with the ground user, and at the same time, the ground reflector BD reflects the signal from the drone and communicates with the ground receiver BR. The eavesdropper Willie was monitoring whether the ground reflector BD was reflecting signals to communicate with the ground receiver BR. The UAV-assisted environmental backscatter covert communication system includes an air-to-ground channel dominated by short line-of-sight (LoS) between the UAV and various ground devices, and a ground channel dominated by Rayleigh fading between various ground devices. There is an uncertainty regarding the ambient noise at the location of the eavesdropper, Willie.

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