Ground-unmanned aerial vehicle uplink transmission safety analysis method based on directional beam antenna

Abstract

The application relates to a ground-unmanned aerial vehicle uplink transmission safety analysis method based on a directional beam antenna, which comprises the following steps: calculating a directional beam coverage volume formed by a source node, and modeling an active air eavesdropper as a homogeneous Poisson point process; constructing a fading channel model for a legal link and an eavesdropping link, obtaining a probability density function and a cumulative distribution function of channel power gain, defining an instantaneous receiving signal-to-noise ratio of a unmanned aerial vehicle relay end and a strongest eavesdropper end; defining a conditional secrecy outage probability lower bound form and a reliability outage probability, constructing a secrecy outage probability into a compound measurement form, and obtaining a secrecy outage probability expression; according to a change curve of the secrecy outage probability, system parameter selection basis can be provided for system designers according to actual requirements and system costs. The application can accurately depict low-altitude eavesdropping threats, realize computable evaluation of safety performance and beam width optimization, and provide engineering basis for related system design.

Description

Technical Field

[0001] This application relates to the field of wireless communication security technology, and in particular to a ground-to-UAV uplink transmission security analysis method based on a directional beam antenna. Background Technology

[0002] With the deep integration of space-air-ground integrated networks and low-altitude communication technologies, drones, with their advantages of flexible deployment and enhanced coverage, have become key aerial relay nodes for uplink access for ground users, and are widely used in scenarios such as emergency communication and remote monitoring. However, the characteristics of uplink transmission in open airspace make signals vulnerable to interception by unauthorized aerial nodes, leading to the risk of sensitive information leakage and service interruption. In particular, when the source node uses a directional antenna for uplink transmission, the beamwidth directly determines the effective radiation space of the signal and the reachable range of potential eavesdroppers, making its impact on security performance a core factor in assessing accuracy.

[0003] In existing technologies, the security performance analysis of ground-to-UAV uplink often adopts traditional modeling approaches. Some solutions rely on omnidirectional antennas to simplify the model, failing to incorporate the beamwidth and spatial coverage volume of directional antennas into a unified analysis framework. They estimate the eavesdropping exposure area based solely on empirical assumptions, leading to significant biases in the assessment of the probability of eavesdroppers appearing. Other solutions fix the location or pre-set the number of eavesdroppers, failing to characterize their actual random appearance and distribution within the beam coverage area, thus failing to reflect the "strongest eavesdropping effect" and underestimating security risks in dense threat environments. Meanwhile, although the use of maximum ratio combining (MRC) technology in UAV relay can significantly improve the signal-to-noise ratio of legitimate links, existing methods struggle to provide a directly calculable expression of the probability of security interruption under the combined effects of random geometry and fading channels.

[0004] Therefore, it is necessary to improve one or more of the problems existing in the above-mentioned related technical solutions.

[0005] It should be noted that the information disclosed in the background section above is only used to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this disclosure is to provide a ground-to-UAV uplink transmission security analysis method based on a directional beam antenna, thereby overcoming at least to some extent one or more problems caused by the limitations and defects of related technologies.

[0007] This application provides a ground-to-UAV uplink transmission security analysis method based on a directional beam antenna, including: The coverage volume of the directional beam formed by the source node is calculated based on the basic communication scenario, and the homogeneous Poisson point process model is performed on the active air eavesdroppers within the coverage volume of the directional beam to obtain the probability density function of the number of air eavesdroppers. A fading channel model is constructed for both legitimate and eavesdropping links to obtain the probability density function and cumulative distribution function of channel power gain. A multi-antenna maximum ratio combining reception model is also constructed for UAV relay terminals to identify the strongest eavesdropper in non-collusion scenarios and define the instantaneous received signal-to-noise ratio at the UAV relay terminal and the strongest eavesdropper terminal. Define the lower bound form of the conditional security interruption probability and the reliability interruption probability, transform them into closed expressions, and based on the hole probability and the conditional security interruption probability, construct the security interruption probability of the ground-UAV uplink transmission link into a composite metric form to obtain the security interruption probability expression. Based on the closed-form expression for the security interruption probability, the curve of the security interruption probability as a function of system parameters is obtained by Monte Carlo simulation.

[0008] The technical solution provided in this application may include the following beneficial effects: This application presents a ground-to-UAV uplink transmission security analysis method based on directional beam antennas. By combining directional beam coverage volume modeling with eavesdropper homogeneous Poisson point process distribution modeling, it accurately characterizes the spatial eavesdropping threat range in low-altitude communication scenarios. Simultaneously, it jointly constructs a fading channel model and a UAV multi-antenna MRC reception model to improve the channel characteristic analysis of legitimate and eavesdropping links, identify the strongest eavesdropper in non-collusion scenarios, and define the instantaneous received signal-to-noise ratio, making the security performance analysis model more closely resemble actual communication scenarios. Furthermore, by constructing closed-form expressions for conditional security interruption probability and reliability interruption probability, and combining them with void probability, it constructs a security... The composite metric of the probability of security interruption makes the system security performance evaluation index directly calculable, overcoming the limitations of traditional analysis methods that are difficult to quantify under the combined effects of random geometry and fading channels. At the same time, based on the closed-form expression of the security interruption probability, the curve of its variation with system parameters is calculated, and the security data analysis of ground-UAV uplink transmission based on directional beam antenna is completed. It can provide system designers with the basis for selecting system parameters according to actual needs and system costs, and can also complete the overall security energy assessment of the ground-UAV uplink transmission system. It provides scientific and direct engineering basis for parameter optimization and security design of related communication systems in the space-air-ground integrated network.

[0009] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Attached Figure Description

[0010] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure. It is obvious that the drawings described below are merely some embodiments of this disclosure, and those skilled in the art can obtain other drawings based on these drawings without any inventive effort.

[0011] Figure 1 A flowchart illustrating a ground-to-UAV uplink transmission security analysis method based on a directional beam antenna in an exemplary embodiment of this disclosure is shown. Figure 2 A detailed flowchart of step S100 of the ground-to-UAV uplink transmission security analysis method based on a directional beam antenna in an exemplary embodiment of this disclosure is shown. Figure 3 This illustration shows a system model of a ground source node, a UAV relay, and an aerial eavesdropper in a ground-to-UAV uplink transmission security analysis method based on a directional beam antenna, as shown in an exemplary embodiment of the present disclosure. Figure 4 A detailed flowchart of step S200 of the ground-to-UAV uplink transmission security analysis method based on a directional beam antenna in an exemplary embodiment of this disclosure is shown. Figure 5 This illustration shows a schematic diagram of the legitimate channels and eavesdropping channels of a ground-to-UAV uplink transmission security analysis method based on a directional beam antenna in an exemplary embodiment of this disclosure, for ground users, UAVs, and aerial eavesdroppers. Figure 6 A detailed flowchart of step S300 of the ground-to-UAV uplink transmission security analysis method based on a directional beam antenna in an exemplary embodiment of this disclosure is shown. Figure 7 This illustrates the security interruption probability as a function of the average channel power gain at different beam angles in an exemplary embodiment of this disclosure. Simulation plot of SOP versus transmit power Pr under different Eves eavesdroppers; Figure 8 This illustrates how the probability of security breach varies with average channel power gain at different eavesdropper densities in exemplary embodiments of this disclosure. The following is a simulation diagram. Detailed Implementation

[0012] Exemplary embodiments will now be described more fully with reference to the accompanying drawings. However, these exemplary embodiments can be implemented in many forms and should not be construed as limited to the examples set forth herein; rather, they are provided so that this disclosure will be more comprehensive and complete, and will fully convey the concept of the exemplary embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

[0013] This example implementation first provides a ground-to-UAV uplink transmission security analysis method based on a directional beam antenna. This method can be applied to a terminal device, such as a mobile terminal like a mobile phone, desktop computer, personal digital assistant, laptop, tablet, or smartwatch. (Reference) Figure 1 As shown, the method may include the following steps: Step S100: Calculate the coverage volume of the directional beam formed by the source node based on the basic communication scenario, and perform homogeneous Poisson point process modeling for active airborne eavesdroppers within the coverage volume of the directional beam to obtain the probability density function of the number of airborne eavesdroppers.

[0014] Step S200: Construct a fading channel model for both the legitimate link and the eavesdropping link, obtain the probability density function and cumulative distribution function of the channel power gain, and construct a multi-antenna maximum ratio combining reception model for the UAV relay end to determine the strongest eavesdropper in the non-collusion scenario, and define the instantaneous received signal-to-noise ratio of the UAV relay end and the strongest eavesdropper end.

[0015] Step S300: Define the lower bound form of the conditional security interruption probability and the reliability interruption probability, transform them into closed expressions, and based on the hole probability and the conditional security interruption probability, construct the security interruption probability of the ground-UAV uplink transmission link into a composite metric form to obtain the security interruption probability expression.

[0016] Step S400: Based on the closed-form expression for the security interruption probability, obtain the curve of the security interruption probability as a function of system parameters according to Monte Carlo simulation.

[0017] The aforementioned method, through the ground-to-UAV uplink transmission security analysis method based on directional beam antennas, can accurately combine the spatial radiation characteristics of directional beams with the random distribution characteristics of aerial eavesdroppers to complete the integrated security performance modeling of ground-to-UAV uplink transmission scenarios. This overcomes the technical limitations of traditional analysis methods, such as insufficient characterization of the impact of directional transmission and inconsistencies between eavesdropper distribution assumptions and the realities of low-altitude communication. This allows the system security performance evaluation results to better reflect the actual deployment scenarios of integrated space-air-ground networks. Furthermore, by deriving the closed-form expression for the probability of security interruption, it enables direct quantitative calculation of the security performance of the ground-to-UAV uplink transmission link, clearly reflecting the impact of key parameters such as directional beamwidth, the number of UAV receiving antennas, and eavesdropper density on system security performance, without requiring... Relying on extensive Monte Carlo simulations, the computational overhead for security performance assessment is significantly reduced, improving the efficiency of system parameter sensitivity analysis and optimization design. Simultaneously, based on the curve of the probability of confidentiality interruption changing with system parameters, it can complete the security data analysis of ground-to-UAV uplink transmission based on directional beam antennas. This provides system designers with a basis for selecting system parameters according to actual needs and system costs. Furthermore, it enables comprehensive and accurate security performance assessment of ground-to-UAV uplink transmission systems, providing direct and reliable theoretical basis for engineering practices such as beam design, UAV receiving antenna configuration, and transmit power control. This effectively guides system parameter optimization, improves the physical layer security performance of the ground-to-UAV uplink transmission link, and avoids the risks of sensitive information leakage and service interruption caused by aerial eavesdropping.

[0018] Below, we will refer to Figures 2 to 8 The steps of the method described above in this example embodiment will be explained in more detail.

[0019] In step S100, the directional beam coverage volume formed by the source node is calculated based on the basic communication scenario, and a homogeneous Poisson point process model is performed on the active air eavesdroppers within the directional beam coverage volume to obtain the probability density function of the number of air eavesdroppers.

[0020] It should be noted that this step is the foundational stage for the scenario and model construction of the entire security performance analysis method. The calculation of the directional beam coverage volume and the modeling of the homogeneous Poisson point process (PPP) for eavesdroppers are both based on the actual low-altitude communication scenario of the integrated space-air-ground network. All parameters adopt the general dimensions of physical layer security analysis in the field of wireless communication. The beam coverage volume is the effective radiation space of the source node's directional antenna for the relay transmission signal of the UAV in the air. The eavesdropper modeling only targets active airborne eavesdroppers within this radiation space, excluding invalid eavesdropping nodes outside the beam coverage.

[0021] In one embodiment, such as Figure 2 As shown, step S100 may include the following sub-steps.

[0022] In step S110, a ground-to-drone uplink communication scenario is constructed, in which the ground source node is the signal transmitter, the drone relay is the legitimate receiver, and an unknown number of aerial nodes are the eavesdroppers. This scenario serves as the basic communication scenario.

[0023] Optionally, all parameters are standard parameters for wireless communication system design and performance analysis, and the values ​​of each parameter follow the general range in this field: the transmit power can be 0.1~10W, the path loss index can be 2-4 for low-altitude wireless channels, the security threshold can be 0~5bps / Hz according to the security transmission rate requirements of the actual service, the hemispherical radius is the effective communication radius of the source node directional antenna, and the value can be 100~1000m, and the beamwidth is the horizontal / vertical beamwidth of the directional antenna, and the value can be 0°-180°; all parameters are input in numerical form and can be directly obtained through the simulation platform of the wireless communication system or the actual test equipment.

[0024] In step S120, the directional beam coverage volume formed by the source node is calculated based on the beamwidth and hemisphere radius, with the ground source node as the center of the hemisphere.

[0025] It should be noted that, as Figure 3 The diagram illustrates a system model of a ground source node, a drone relay, and an aerial eavesdropper. The source node is constructed as the center of a hemisphere, and the directional beam coverage volume is calculated using a hemispherical model. This aligns with the actual communication scenario where the drone acts as an aerial relay. The radiation space of the signal transmitted by the source node into the air is hemispherical, and there is no signal radiation in the ground direction. Therefore, the invalid ground area in the full-space model is excluded. The beamwidth is the beam angle of the directional antenna facing the drone relay direction, which directly determines the size of the beam coverage volume. The smaller the beamwidth, the smaller the coverage volume, and the narrower the distribution space of potential eavesdroppers.

[0026] The expression for the directional beam coverage volume is as follows: in, For the directional beam coverage volume, The radius of the hemisphere This refers to the beamwidth.

[0027] In step S130, a homogeneous Poisson point process model is performed on the active airborne eavesdroppers within the coverage volume of the directional beam to obtain the probability density function of the number of airborne eavesdroppers.

[0028] It should be noted that the homogeneous Poisson point process (PPP) is a general model in the field of wireless communication for characterizing the spatial distribution of random nodes. In this step, the spatial density of eavesdroppers represents the number of active aerial eavesdroppers per unit volume, and the value can be 0 to 0.001 per m³, which is consistent with the actual threat characteristics of eavesdroppers appearing randomly and in uncertain numbers in low-altitude communication. The mean is the expected number of eavesdroppers within the beam coverage volume, and its probability density function strictly follows the mathematical characteristics of the Poisson distribution, which can be directly calculated using conventional probability and statistics methods in this field.

[0029] The expression for the probability density function of the number of aerial eavesdroppers is as follows: in, , The number of aerial eavesdroppers is The probability density, The mean, The number of aerial eavesdroppers. It is a natural constant. For the density of aerial eavesdroppers, The volume covered by the directional beam.

[0030] In step S200, a fading channel model is constructed for the legitimate link and the eavesdropping link to obtain the probability density function and cumulative distribution function of the channel power gain. A multi-antenna maximum ratio combining reception model is also constructed for the UAV relay end to determine the strongest eavesdropper in the non-collusion scenario and to define the instantaneous received signal-to-noise ratio of the UAV relay end and the strongest eavesdropper end.

[0031] It should be noted that this step is the core modeling step for the channel and receiver. All channel and receiver models are based on the actual characteristics of the wireless channel with Nakagami-m fading. Furthermore, the modeling of the legitimate link (S→R) and the eavesdropping link (S→E) are independent of each other to avoid channel interference between links. Maximum ratio combining (MRC) at the UAV end is a classic combining technique for multi-antenna reception, which can maximize the received signal-to-noise ratio of the legitimate link. The mathematical expressions of all models in this step can be directly substituted into the parameters for calculation.

[0032] In one embodiment, such as Figure 4 As shown, step S200 may include the following sub-steps.

[0033] In step S210, the legitimate link and the eavesdropping link in the basic communication scenario are constructed as a Nakagami-m fading channel model with independent and identical distribution, and the channel power gain is modeled as a Gamma distribution. Based on the fading severity and the average channel power, the probability density function and cumulative distribution function of the channel power gain are obtained.

[0034] It should be noted that, as Figure 5 As shown, the channel between the ground user and the UAV relay (airborne relay) is a legitimate link (S→R), and the channel between the ground user and the eavesdropper (airborne eavesdropper) is an eavesdropping link (S→E). The two links are independent of each other. Nakagami-m fading is a general model for characterizing multipath fading in the field of wireless communication, which can be adapted to the channel characteristics of low-altitude communication. The fading severity is a positive real number. The greater the fading severity, the less severe the channel fading. When the fading severity = 1, Nakagami-m fading degenerates into Rayleigh fading. When the fading severity > 1, it is Ricean fading. In this application, the fading severity (m) R ), the severity of fading in the eavesdropping link (m) E All values ​​can be 1 to 5 to reflect the actual fading situation of low-altitude channels; average channel power Channel power gain g q The mathematical expectation, in dB, can be obtained through channel measurements or simulation platforms; gamma function It is a standard special function in the field of mathematics, and its value can be obtained by looking up a table or by numerical calculation method. Those skilled in the art can directly call mathematical calculation tools to solve it.

[0035] Furthermore, the expression for the probability density function of the channel power gain is as follows: in, , Let be the probability density of the channel power gain. To indicate the severity of the decline, For average channel power, Channel power gain random variable The values ​​of the independent variable, and , It is a natural constant. It is a gamma function; The expression for the cumulative distribution function of the channel power gain is: in, This represents the cumulative density of channel power gain.

[0036] In step S220, based on the fading channel model and the configuration of multiple receiving antennas for the UAV relay in the basic communication scenario, a multi-antenna maximum ratio combining receiving model is constructed at the UAV relay end to obtain the cumulative distribution function of the channel power gain at the UAV relay.

[0037] It should be noted that the number of receiving antennas L in the UAV relay configuration is a positive integer, ranging from 1 to 8, which is in line with the hardware capabilities of small UAVs. The core principle of maximum ratio combining (MRC) is to combine the signals of each receiving antenna by weighting them according to the channel power gain. Therefore, the combined channel power gain is the sum of the channel power gains of each antenna. Its cumulative distribution function (CDF) is derived from the Gamma distribution of a single antenna and strictly follows the mathematical characteristics of the additivity of the Gamma distribution. The channel power gain CDF obtained at the UAV relay in this step is used to calculate the signal-to-noise ratio and reliability interruption probability of the legitimate link reception in subsequent calculations.

[0038] Furthermore, the expression for the cumulative distribution function of the channel power gain at the UAV relay point is: in, , Let be the cumulative distribution function of the channel power gain. It is an incomplete gamma function. Number of receiving antennas This is a parameter representing the severity of fading in the legitimate link of the drone relay. This represents the average channel power.

[0039] In step S230, in a non-collusion scenario, the nearest eavesdropper is selected as the strongest eavesdropper within the coverage volume of the directional beam, and the instantaneous signal-to-noise ratio of the legitimate link received by the UAV relay end and the instantaneous signal-to-noise ratio of the eavesdropping link received by the strongest eavesdropper end are defined.

[0040] It should be noted that in non-collusive eavesdropping scenarios, each eavesdropper works independently without information exchange. Therefore, the system's security performance is dominated by the node with the strongest eavesdropping capability. The received signal-to-noise ratio (SNR) of the eavesdropping link is inversely proportional to the distance between the eavesdropper and the source node; the closer the distance, the smaller the path loss and the higher the SNR. Therefore, the eavesdropper closest to the source node is defined as the strongest eavesdropper. This judgment rule aligns with the path loss characteristics of wireless communication and is a common definition of the strongest non-colluding eavesdropper in physical layer security analysis. In the formula for calculating the instantaneous received signal-to-noise ratio, the path loss term can adopt the power-law path loss model, which is the standard path loss calculation form in the field of wireless communication and can be directly substituted into the distance and path loss exponent for calculation.

[0041] The expression for the instantaneous signal-to-noise ratio of the legitimate link at the UAV relay terminal is as follows: in, For the instantaneous received signal-to-noise ratio of a legitimate link, The source node transmit power, This represents the equivalent channel power gain after maximum ratio combining. The received noise power of the UAV relay terminal. This represents the distance between the drone relay and the source node. The path loss index; The expression for the instantaneous received signal-to-noise ratio of the eavesdropping link at the most powerful eavesdropper's end is: in, To eavesdrop on the instantaneous received signal-to-noise ratio of the link, Channel power gain corresponding to the most powerful eavesdropper. This represents the received noise power at the most powerful eavesdropper's end. This represents the distance between the strongest eavesdropper and the source node.

[0042] In step S300, the lower bound form of the conditional security interruption probability and the reliability interruption probability are defined and transformed into closed expressions. Based on the hole probability and the conditional security interruption probability, the security interruption probability of the ground-UAV uplink transmission link is constructed into a composite metric form, and the security interruption probability expression is obtained. This completes the theoretical derivation and analysis of the ground-UAV uplink transmission security based on the directional beam antenna.

[0043] It should be noted that this step is the core derivation of the secrecy interruption probability (SOP). All probability definitions and derivations are based on the law of total probability and the mathematical characteristics of stochastic processes. The derivations of the conditional secrecy interruption probability SOP1 and the reliability interruption probability OP are combined with the channel model, receiver model, and eavesdropper distribution model mentioned earlier. All closed-form expressions are derived through rigorous mathematical integration and variable substitution, without any empirical assumptions. Gaussian hypergeometric functions are also used. As a standard special function in the field of mathematics, its value can be obtained through numerical calculation tools or by looking up tables. Those skilled in the art can directly call relevant mathematical libraries to complete the calculation.

[0044] In one embodiment, such as Figure 6 As shown, step S300 may include the following sub-steps.

[0045] In step S310, the conditional security interruption probability is defined as the probability that the instantaneous security capacity is lower than the threshold when there is an active eavesdropper, thus obtaining the lower bound form of the conditional security interruption probability, and transforming it into a closed expression through a Gaussian hypergeometric function.

[0046] It should be noted that defining SOP1 as the lower probability bound of instantaneous security capacity falling below the threshold is to reduce the complexity of mathematical derivation while ensuring the accuracy requirements of engineering design. The error between this lower bound form and the precise value is within the allowable range of engineering, which can be less than 5%. Instantaneous security capacity adopts the general definition of physical layer security, which is the difference between the transmission rate of the legitimate link and the eavesdropping link. When this value is lower than the security threshold, it is determined that the system has experienced a security interruption. In this step, the closed-form expression of SOP1 integrates all core system parameters such as directional beam coverage volume, eavesdropper density, number of UAV antennas, and channel fading parameters. The coefficients and functional forms of each parameter are obtained through rigorous mathematical derivation and can be directly substituted into numerical calculations.

[0047] Furthermore, the closed-form expression for the conditional secrecy interruption probability is: in, For the first The coefficients of the series expansion, , This is the ratio of noise power to the rate parameter. , For auxiliary function difference terms, , For auxiliary functions, , , and These are the exponential or intermediate parameters introduced during the derivation of closed-form expressions. This represents the minimum altitude of the drone relay from the source node. , and In order to be with the first The combination coefficients related to the terms The parameters of the Gamma distribution corresponding to the legitimate link are... , The parameters of the Gamma distribution corresponding to the eavesdropping link are... , For eavesdropping links Nakagami- Fading parameters, As the independent variable of the auxiliary function, This refers to the upper limit parameter in the auxiliary function. As the second independent variable of the auxiliary function, It is a Gaussian hypergeometric function.

[0048] In step S320, the reliability interruption probability is defined as the probability of the UAV successfully decoding the signal, which is determined by the channel state information of the legitimate link. A threshold for the UAV to successfully decode the signal is set to obtain the reliability interruption probability, and the reliability interruption probability is transformed into a closed expression.

[0049] It should be noted that the reliability interruption probability OP is determined solely by the channel state information (CSI) of the legitimate link and is unrelated to eavesdroppers. This definition aligns with the system transmission reliability assessment requirements when there is no eavesdropping threat. The successful decoding threshold is the minimum received signal-to-noise ratio (SNR) for the UAV relay to correctly decode the source node signal. Its value can range from 0 to 10 dB and is determined by the performance of the UAV's receiving and demodulation equipment. It is a standard parameter in the field of wireless communication. The closed-form expression of OP is derived from the channel power gain (CDF) of the legitimate link. Its physical meaning is the probability that the received SNR of the legitimate link is lower than the successful decoding threshold, directly reflecting the transmission reliability of the legitimate link.

[0050] Furthermore, the closed-form expression for the reliability interruption probability is: in, For reliability outage probability, For each constant coefficient in the closed-form expression of the reliability outage probability, represents a constant coefficient. These are auxiliary integration terms or boundary terms introduced during the derivation of closed-form expressions. For auxiliary difference function, and The intermediate variable consists of valid link statistics, successful decoding threshold, and path loss parameters. This represents the minimum altitude of the drone relay from the source node.

[0051] In step S330, a void probability is introduced based on the void situation where there is no eavesdropper within the beam coverage volume. The ground-UAV uplink transmission link security interruption probability is defined as a weighted composite form of the reliability interruption probability when there is no eavesdropper and the conditional security interruption probability when there is at least one eavesdropper, thus obtaining the security interruption probability expression.

[0052] It should be noted that the hole probability is an inherent property of the homogeneous Poisson point process. Its physical meaning is the probability that there is no active eavesdropper within the beam coverage volume. This formula is the general calculation form of the hole probability in the Poisson point process. The security interruption probability is constructed as a weighted composite form of "reliable interruption probability without eavesdroppers" and "conditional security interruption probability with eavesdroppers". It strictly follows the mathematical rules of the total probability formula, where the weights are the hole probability and the non-hole probability, respectively. This composite metric form fits the two random scenarios of "with or without eavesdroppers" in actual communication scenarios, avoiding the bias in security performance assessment caused by fixing the eavesdropper.

[0053] The expression for the probability of confidentiality interruption is as follows: in, , , To maintain the probability of interruption, For the probability of a hole, For reliability outage probability, For non-hole probability, For conditional confidentiality, the probability of interruption For the density of aerial eavesdroppers, The volume covered by the directional beam.

[0054] In step S400, based on the closed-form expression of the security interruption probability, the change curve of the security interruption probability with system parameters is obtained according to Monte Carlo simulation. The analysis of the security data of ground-UAV uplink transmission based on directional beam antenna is completed. According to the change curve of the security interruption probability, the system designer can be provided with the basis for selecting system parameters based on actual needs and system costs.

[0055] It should be noted that the change curve of the confidentiality interruption probability in this step adopts the conventional simulation and plotting method in the field of wireless communication, which can be realized through the Matlab simulation platform. The horizontal axis represents the system parameters to be analyzed, and the vertical axis represents the confidentiality interruption probability value. The curve is plotted using a numerical iterative calculation method, with the number of iterations ranging from 1000 to 10000 to ensure the statistical accuracy of the calculation results. The principle for selecting system parameters is to minimize the confidentiality interruption probability while meeting the system reliability interruption probability requirements, such as OP < 0.1. The system security assessment takes the magnitude of the confidentiality interruption probability as the core indicator. The smaller the SOP value, the better the physical layer security performance of the system. Those skilled in the art can complete parameter optimization and security assessment according to the security requirements of actual business, such as SOP < 0.05.

[0056] Furthermore, to verify the correctness of the ground-UAV uplink transmission security analysis method based on directional beam antennas described in this application and the accuracy of the derived closed-form expression for the probability of security interruption, a Monte Carlo method was used for numerical simulation. Within the coverage volume of the directional beam, the location of the aerial eavesdropper was randomly generated according to a homogeneous Poisson point process, and the location was determined according to Nakagami- The fading model randomly generates the channel power gain for both legitimate and eavesdropping links. Under given system parameters, the probability of security breach is statistically analyzed through numerous repeated random experiments. The statistical results are then compared and verified with theoretical analysis results. Simulation results are as follows: Figure 7 and Figure 8 As shown. Figure 7 The curves showing the relationship between the probability of security breach and the average channel power gain under different aerial eavesdropper densities are presented. Figure 7It can be seen that as the average channel power gain increases, the probability of security interruption generally decreases; and the higher the density of airborne eavesdroppers, the higher the probability of security interruption, indicating that the denser the spatial distribution of eavesdroppers, the greater the physical layer security risk faced by the system. Figure 8 The curves showing the relationship between the probability of security breach and the average channel power gain are presented under different directional antenna beamwidths. Figure 8 It can be seen that, under the same average channel power gain, the smaller the beamwidth of the directional antenna, the lower the probability of security breach. This is because a smaller beamwidth can effectively compress the beam coverage space, reducing the probability of potential eavesdroppers falling into the beam coverage area, thereby weakening the impact of the strongest eavesdropper on the system's security performance. Furthermore, Figure 7 and Figure 8 The theoretical analysis curves and Monte Carlo simulation curves are in good agreement, which verifies that the confidentiality interruption probability model and its closed-form expression established in this application have high accuracy and can be used for security performance evaluation in the ground-UAV uplink transmission scenario.

[0057] Other embodiments of this disclosure will readily occur to those skilled in the art upon consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of this disclosure that follow the general principles of this disclosure and include common knowledge or customary techniques in the art not disclosed herein. The specification and examples are to be considered exemplary only, and the true scope and spirit of this disclosure are indicated by the appended claims.

Claims

1. A method for safety analysis of ground-unmanned aerial vehicle (UAV) uplink transmission based on directional beam antenna, characterized in that, include: The coverage volume of the directional beam formed by the source node is calculated based on the basic communication scenario, and the homogeneous Poisson point process model is performed on the active air eavesdroppers within the coverage volume of the directional beam to obtain the probability density function of the number of air eavesdroppers. A fading channel model is constructed for both legitimate and eavesdropping links to obtain the probability density function and cumulative distribution function of channel power gain. A multi-antenna maximum ratio combining reception model is also constructed for UAV relay terminals to identify the strongest eavesdropper in non-collusion scenarios and define the instantaneous received signal-to-noise ratio at the UAV relay terminal and the strongest eavesdropper terminal. Define the lower bound form of the conditional security interruption probability and the reliability interruption probability, transform them into closed expressions, and based on the hole probability and the conditional security interruption probability, construct the security interruption probability of the ground-UAV uplink transmission link into a composite metric form to obtain the security interruption probability expression. Based on the closed-form expression for the security interruption probability, the curve of the security interruption probability as a function of system parameters is obtained by Monte Carlo simulation.

2. The method of claim 1, wherein the method is based on a directional beam antenna for ground-UAV uplink transmission safety analysis. The steps of calculating the directional beam coverage volume formed by the source node based on the basic communication scenario, and modeling the active airborne eavesdroppers within the directional beam coverage volume using a homogeneous Poisson point process to obtain the probability density function of the number of airborne eavesdroppers, include: A ground-to-drone uplink communication scenario is constructed, with ground source nodes as signal transmitters, drone relays as legitimate receivers, and an unknown number of aerial nodes as eavesdroppers, serving as the basic communication scenario. Using the ground source node as the center of the hemisphere, the directional beam coverage volume formed by the source node is calculated based on the beamwidth and the radius of the hemisphere; A homogeneous Poisson point process model is performed on the active aerial eavesdroppers within the coverage volume of the directional beam to obtain the probability density function of the number of aerial eavesdroppers.

3. The ground-to-UAV uplink transmission security analysis method based on a directional beam antenna according to claim 2, characterized in that, The expression for the directional beam coverage volume is: in, For the directional beam coverage volume, The radius of the hemisphere This refers to the beamwidth.

4. The ground-to-UAV uplink transmission security analysis method based on a directional beam antenna according to claim 2, characterized in that, The expression for the probability density function of the number of aerial eavesdroppers is: in, , The number of aerial eavesdroppers is The probability density, The mean, The number of aerial eavesdroppers. It is a natural constant. For the density of aerial eavesdroppers, The volume covered by the directional beam.

5. The ground-to-UAV uplink transmission security analysis method based on a directional beam antenna according to claim 1, characterized in that, The steps of constructing a fading channel model for both legitimate and eavesdropping links, obtaining the probability density function and cumulative distribution function of channel power gain, constructing a multi-antenna maximum ratio combining reception model for the UAV relay end, determining the strongest eavesdropper in non-collusion scenarios, and defining the instantaneous received signal-to-noise ratio at the UAV relay end and the strongest eavesdropper end include: The legitimate link and the eavesdropping link in the basic communication scenario are constructed as a Nakagami-m fading channel model with independent and identical distribution, and the channel power gain is modeled as a Gamma distribution. Based on the fading severity and the average channel power, the probability density function and cumulative distribution function of the channel power gain are obtained. Based on the fading channel model and the configuration of multiple receiving antennas for UAV relay in the basic communication scenario, a multi-antenna maximum ratio combining receiving model is constructed at the UAV relay end to obtain the cumulative distribution function of channel power gain at the UAV relay point. In non-conspiracy scenarios, the nearest eavesdropper is selected as the strongest eavesdropper within the coverage volume of the directional beam, and the instantaneous received signal-to-noise ratio of the legitimate link at the UAV relay end and the instantaneous received signal-to-noise ratio of the eavesdropping link at the strongest eavesdropper end are defined.

6. The ground-to-UAV uplink transmission security analysis method based on a directional beam antenna according to claim 5, characterized in that, The expression for the probability density function of the channel power gain is: in, , Let be the probability density of the channel power gain. To indicate the severity of the decline, For average channel power, Channel power gain random variable The values ​​of the independent variable, and , It is a natural constant. It is a gamma function; The expression for the cumulative distribution function of the channel power gain is: in, The cumulative density of channel power gain; The expression for the cumulative distribution function of the channel power gain at the UAV relay point is: in, , Let be the cumulative distribution function of the channel power gain. It is an incomplete gamma function. Number of receiving antennas This is a parameter representing the severity of fading in the legitimate link of the drone relay. This represents the average channel power.

7. The ground-to-UAV uplink transmission security analysis method based on a directional beam antenna according to claim 5, characterized in that, The expression for the instantaneous received signal-to-noise ratio of the legitimate link at the UAV relay terminal is: in, For the instantaneous received signal-to-noise ratio of a legitimate link, The source node transmit power, This represents the equivalent channel power gain after maximum ratio combining. The received noise power of the UAV relay terminal. This represents the distance between the drone relay and the source node. The path loss index; The expression for the instantaneous received signal-to-noise ratio of the eavesdropping link at the most powerful eavesdropper's end is: in, To eavesdrop on the instantaneous received signal-to-noise ratio of the link, Channel power gain corresponding to the most powerful eavesdropper. This represents the received noise power at the most powerful eavesdropper's end. This represents the distance between the strongest eavesdropper and the source node.

8. The ground-to-UAV uplink transmission security analysis method based on a directional beam antenna according to claim 1, characterized in that, The steps of defining the lower bound of the conditional security interruption probability and the reliability interruption probability, transforming them into closed-form expressions, and constructing a composite metric form for the security interruption probability of the ground-UAV uplink transmission link based on the hole probability and the conditional security interruption probability, to obtain the security interruption probability expression, include: The conditional security interruption probability is defined as the probability that the instantaneous security capacity is lower than the threshold when there is an active eavesdropper. The lower bound form of the conditional security interruption probability is obtained and then transformed into a closed expression through a Gaussian hypergeometric function. The reliability interruption probability is defined as the probability of a UAV successfully decoding a signal, which is determined by the channel state information of the legitimate link. A threshold for successful UAV signal decoding is set to obtain the reliability interruption probability, which is then transformed into a closed-form expression. Based on the void probability introduced in the case where there is no eavesdropper within the beam coverage volume, the security interruption probability of the ground-UAV uplink transmission link is defined as a weighted composite form of the reliability interruption probability when there is no eavesdropper and the conditional security interruption probability when there is at least one eavesdropper, thus obtaining the security interruption probability expression.

9. The ground-to-UAV uplink transmission security analysis method based on a directional beam antenna according to claim 8, characterized in that, The expression for the probability of security interruption is: in, , , To maintain the probability of interruption, For the probability of a hole, For reliability outage probability, For non-hole probability, For conditional confidentiality, the probability of interruption For the density of aerial eavesdroppers, The volume covered by the directional beam.

10. The ground-to-UAV uplink transmission security analysis method based on a directional beam antenna according to claim 8, characterized in that, The closed-form expression for the probability of conditional secrecy interruption is: in, For the first The coefficients of the series expansion, , This is the ratio of noise power to the rate parameter. , For auxiliary function difference terms, , For auxiliary functions, , , and These are the exponential or intermediate parameters introduced during the derivation of closed-form expressions. This represents the minimum altitude of the drone relay from the source node. , and In order to be with the first The combination coefficients related to the terms The parameters of the Gamma distribution corresponding to the legitimate link are... , The parameters of the Gamma distribution corresponding to the eavesdropping link are... , For eavesdropping links Nakagami- Fading parameters, As the independent variable of the auxiliary function, This refers to the upper limit parameter in the auxiliary function. As the second independent variable of the auxiliary function, It is a Gaussian hypergeometry function; The closed-form expression for the reliability interruption probability is: in, For reliability outage probability, For each constant coefficient in the closed-form expression of the reliability outage probability, represents a constant coefficient. These are auxiliary integration terms or boundary terms introduced during the derivation of closed-form expressions. For auxiliary difference function, and The intermediate variable consists of valid link statistics, successful decoding threshold, and path loss parameters. This represents the minimum altitude of the drone relay from the source node.

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