Unmanned aerial vehicle-low earth orbit satellite uplink secure transmission performance evaluation method

Abstract

This application relates to a method for evaluating the uplink secure transmission performance of UAVs to low-Earth orbit satellites. The method includes: constructing a multi-orbit three-dimensional geometric model based on a three-dimensional coordinate system with the Earth's center as the origin, incorporating legitimate satellites, eavesdropping satellites, and UAVs, and obtaining geometric parameters; defining the probability density function of the squared propagation distance between the UAV and satellites in different orbital shells, and between the strongest eavesdropper and the UAV, and obtaining a statistical distribution model of the multi-orbit satellite propagation distance; modeling legitimate and eavesdropping links as shadowed Ricean fading, obtaining a multi-link channel model, and constructing an instantaneous signal-to-noise ratio model; constructing a preliminary lower bound form for the security interruption probability, and processing it to obtain a closed-form summation expression for the security interruption probability, and performing uplink security performance evaluation under multi-orbit threats. This application can accurately characterize the geometric and distance characteristics of multi-orbit systems, closely match actual channel modeling, achieve accurate uplink security performance evaluation, and provide a basis for risk assessment in multi-orbit eavesdropping scenarios.

Description

Technical Field

[0001] This application relates to the field of wireless communication security technology, and in particular to a method for evaluating the performance of secure uplink transmission between UAVs and low-Earth orbit satellites. Background Technology

[0002] With the large-scale deployment of low-Earth orbit (LEO) satellite constellations and the rapid development of UAV communication technology, space-air-ground integrated networks (SATN) have become core infrastructure supporting wide-area coverage, emergency communication, and remote monitoring. Among these, the UAV-LEO uplink serves as a critical signal backhaul channel, and its communication security is of paramount concern. Due to the inherent broadcast characteristics of radio frequency links, this uplink is vulnerable to eavesdropping threats from unauthorized satellites in adjacent or concentric orbits. In particular, the configuration of eavesdropping satellites in different orbital shells can significantly impact secure transmission performance.

[0003] In existing technologies, the evaluation of secure uplink transmission performance between UAVs and low-Earth orbit satellites typically involves constructing planar geometric or simplified 3D models to describe the positional relationships between the UAV, the legitimate satellite, and the eavesdropping satellite. Subsequent analysis is then conducted by setting fixed or simple distance parameters. However, this modeling approach fails to adequately consider the 3D geometric constraints of the legitimate satellite and the eavesdropping satellite being located in different orbital shells, and cannot accurately quantify the impact of different orbital altitude configurations on eavesdropping risks. This results in insufficiently accurate characterization of spatial geometric relationships and propagation distance statistical characteristics, leading to biases in subsequent performance evaluations. Furthermore, most methods employ Rayleigh or ordinary Rice fading models to characterize the link transmission... While simplifying the computational process, this model neglects the shadowing and multipath effects caused by atmospheric turbulence and cloud cover in satellite links. This results in a significant discrepancy between the channel and signal-to-noise ratio modeling and the actual propagation environment, affecting the authenticity and accuracy of the assessment results. Furthermore, existing technologies often use averaging or simple superposition to assess the impact of eavesdropping when dealing with multi-eavesdropper scenarios. Moreover, the derived security interruption probability is often in a complex integral form, lacking a concise closed-form summation expression. This makes it difficult to achieve efficient and accurate assessment of uplink secure transmission performance under multi-track threats, and fails to provide effective support for performance analysis and risk assessment in real-world scenarios.

[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 method for evaluating the performance of secure uplink transmission between unmanned aerial vehicles (UAVs) and low-Earth orbit satellites, thereby overcoming, to at least some extent, one or more problems caused by the limitations and defects of related technologies.

[0007] This application provides a method for evaluating the performance of secure uplink transmission between a UAV and a low-Earth orbit satellite, including: Based on a three-dimensional coordinate system with the Earth's center as the origin, a multi-orbit three-dimensional geometric model containing legitimate satellites, eavesdropping satellites, and drones is constructed to obtain geometric parameters; the geometric parameters include the orbital shell radius of the legitimate / eavesdropping satellites and the Earth's center radius of the drones. Define the probability density functions for the squared propagation distance between the UAV and satellites with different orbital shells, and the squared propagation distance between the strongest eavesdropper and the UAV. Define the piecewise probability density function for the ratio of the squared distance between the UAV and the legitimate satellite / the strongest eavesdropping satellite, and obtain the statistical distribution model of the propagation distance of multi-orbit satellites. The legitimate link and the eavesdropping link are modeled as shadowed Ricean fading to obtain a multi-link channel model. Based on the UAV's transmit power and the noise power of the legitimate satellite and the eavesdropping satellite, an instantaneous signal-to-noise ratio model of the legitimate satellite and the strongest eavesdropping satellite is constructed. The multi-link channel model includes the probability density function and cumulative distribution function of the power gain of the two link channels. A preliminary lower bound for the probability of security interruption is constructed. Substituting this into the instantaneous signal-to-noise ratio model and integrating the multi-link channel model and the distance square ratio, the final lower bound for the probability of security interruption is obtained. Then, substituting the piecewise probability density function of the distance square ratio between the UAV and the legitimate satellite / the strongest eavesdropping satellite and the multi-link channel model, a closed-form summation expression for the probability of security interruption is obtained, and uplink security performance is evaluated under multi-orbit threat conditions.

[0008] The technical solution provided in this application may include the following beneficial effects: This application presents a method for evaluating the uplink secure transmission performance of UAVs to low-Earth orbit satellites. By constructing a multi-orbit three-dimensional geometric model and establishing a statistical distribution model of the propagation distance of multi-orbit satellites, it accurately depicts the spatial geometric relationship between legitimate satellites, eavesdropping satellites, and UAVs, as well as the statistical characteristics of propagation distances under multi-orbit conditions. This lays a precise model foundation for evaluating uplink secure transmission performance. Furthermore, by modeling legitimate and eavesdropping links as shadowed Ricean fading and constructing an instantaneous signal-to-noise ratio (SNR) model, it closely matches the actual propagation characteristics of UAV-low-Earth orbit satellite links, improving the realism and accuracy of channel and SNR modeling. Simultaneously, by constructing a lower bound form of the secure interruption probability and deriving a closed-form summation expression through integration and substitution, it achieves a calculable and accurate evaluation of the uplink secure transmission performance of UAVs to low-Earth orbit satellites under multi-orbit threats, providing an effective basis for uplink secure transmission performance analysis and risk assessment in multi-orbit eavesdropping scenarios.

[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 the performance evaluation method for secure uplink transmission between a UAV and a low-Earth orbit satellite in an exemplary embodiment of this disclosure is shown. Figure 2 This diagram illustrates the uplink and satellite eavesdropper listening relationship in the UAV-Low Orbit Satellite Uplink Secure Transmission Performance Evaluation Method of the Exemplary Embodiment of this Disclosure. Figure 3 A detailed flowchart of step S100 of the UAV-Low Orbit Satellite Uplink Secure Transmission Performance Evaluation Method in an exemplary embodiment of this disclosure is shown. Figure 4 This diagram illustrates a multi-orbit three-dimensional geometric model of the UAV-Low-Earth Orbit satellite uplink secure transmission performance evaluation method in an exemplary embodiment of this disclosure. Figure 5 A detailed flowchart of step S200 of the UAV-Low Orbit Satellite Uplink Secure Transmission Performance Evaluation Method in an exemplary embodiment of this disclosure is shown. Figure 6 A detailed flowchart of step S300 of the UAV-Low Orbit Satellite Uplink Secure Transmission Performance Evaluation Method in an exemplary embodiment of this disclosure is shown. Figure 7 A detailed flowchart of step S400 of the UAV-Low Orbit Satellite Uplink Secure Transmission Performance Evaluation Method in an exemplary embodiment of this disclosure is shown. Figure 8 This illustrates the geocentric angle between the security breach probability and the line-of-sight power of different UAVs covering the satellite coverage area in an exemplary embodiment of this disclosure. The following is a simulation diagram; Figure 9 This illustrates the probability of security breach in an exemplary embodiment of the present disclosure, varying with line-of-sight power and the number of eavesdropping satellites. 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 method for evaluating the performance of secure uplink transmission between a UAV and a low-Earth orbit satellite. 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: Based on a three-dimensional coordinate system with the Earth's center as the origin, construct a multi-orbit three-dimensional geometric model containing legitimate satellites, eavesdropping satellites, and drones to obtain geometric parameters; the geometric parameters include the orbital shell radius of the legitimate / eavesdropping satellites and the Earth's center radius of the drones.

[0014] Step S200: Define the probability density function of the squared propagation distance between the UAV and satellites in different orbital shells, and the squared propagation distance between the strongest eavesdropper and the UAV. Define the piecewise probability density function of the ratio of the squared distance between the UAV and the legitimate satellite / the strongest eavesdropping satellite, and obtain the statistical distribution model of the propagation distance of multi-orbit satellites.

[0015] Step S300: Model the legitimate link and the eavesdropping link as shadowed Ricean fading to obtain a multi-link channel model, and construct an instantaneous signal-to-noise ratio model of the legitimate satellite and the strongest eavesdropping satellite based on the UAV's transmit power and the noise power of the legitimate satellite and the eavesdropping satellite; the multi-link channel model includes the probability density function and cumulative distribution function of the power gain of the two link channels.

[0016] Step S400: Construct a preliminary lower bound for the security interruption probability, substitute it into the instantaneous signal-to-noise ratio model, and integrate the multi-link channel model and the distance square ratio to obtain the final lower bound for the security interruption probability. Then, substitute it into the piecewise probability density function of the distance square ratio between the UAV and the legitimate satellite / the strongest eavesdropping satellite and the multi-link channel model to obtain the closed-form summation expression of the security interruption probability, and conduct an uplink security performance evaluation under multi-orbit threat.

[0017] The aforementioned method can accurately characterize the three-dimensional spatial geometric relationship and propagation distance statistical characteristics of legitimate satellites, eavesdropping satellites, and drones in multi-orbit scenarios, effectively quantifying the impact of different orbital shell configurations on uplink secure transmission. By adopting the shadowed Ricean fading model to fit the actual propagation environment of satellite links, and incorporating the modeling of the "strongest eavesdropping effect" of multiple eavesdroppers, the authenticity and accuracy of the security performance assessment are significantly improved. Finally, by deriving the closed-form summation expression of the security interruption probability, the computable and efficient assessment of uplink secure transmission performance under multi-orbit threats is achieved, providing reliable technical support for the security design, parameter optimization, and eavesdropping risk assessment of the drone-low-orbit satellite uplink in the space-air-ground integrated network.

[0018] Below, we will refer to Figures 2 to 7 The steps of the method described above in this example embodiment will be explained in more detail.

[0019] In step S100, a multi-orbit three-dimensional geometric model containing legitimate satellites, eavesdropping satellites, and drones is constructed based on a three-dimensional coordinate system with the Earth's center as the origin, and geometric parameters are obtained; the geometric parameters include the orbital shell radius of the legitimate / eavesdropping satellites and the Earth's center radius of the drones.

[0020] It should be noted that, as Figure 2 The diagram illustrates the uplink and satellite eavesdropping relationship. Network elements include: aerial drones. Legitimate satellite receivers ,as well as An independent satellite eavesdropper Among them, eavesdropping satellites The altitude of the orbit is Legitimate satellites The orbital altitude is and satisfy The core of the constructed multi-orbit 3D geometric model is to depict the spatial positional constraints between legitimate satellites, eavesdropping satellites, and drones. The orbital shell height of the eavesdropping satellites is always higher than that of the legitimate satellites, and all satellites are uniformly distributed within their respective orbital shells. The drones are located in the airspace below the orbital shells of the legitimate satellites. This modeling method closely matches the actual communication scenario between drones and low-Earth orbit satellites in the integrated space-air-ground network, providing a realistic spatial geometric basis for subsequent distance statistics and performance evaluation.

[0021] In one embodiment, such as Figure 3 As shown, step S100 may include the following sub-steps.

[0022] In step S110, a three-dimensional coordinate system with the Earth's center as the origin is constructed.

[0023] It should be noted that this three-dimensional coordinate system can be a spatial coordinate system combining spherical and Cartesian coordinate systems. By default, the origin is the Earth's center, the Earth's equatorial plane is the XY plane, and the Earth's rotation axis is the Z-axis. This coordinate system is a universal coordinate system used in the field of satellite communication to characterize the spatial positions of celestial bodies and nodes in the air. It is convenient for calculating the spatial propagation distance between nodes. Those skilled in the art can rotate and transform the coordinate system according to actual needs without affecting the final geometric parameter calculation results.

[0024] In step S120, the orbital shell radius of the legitimate satellite and the eavesdropping satellite and the geocentric radius of the UAV are determined based on the three-dimensional coordinate system to obtain geometric parameters.

[0025] It should be noted that the orbital shell radius of both legitimate satellites and eavesdropping satellites is the radial distance from the Earth's center to the corresponding orbital shell. The Earth's center radius of the UAV is the radial distance from the Earth's center to the UAV's communication operation location. The radius calculations for all three are in the form of Earth's radius and altitude, where altitude is the vertical height of each node relative to the Earth's surface. This calculation method is the conventional method for calculating the spatial distance between satellites and airborne nodes. The parameter values ​​can be determined based on the actual low-Earth orbit satellite constellation configuration and the UAV's operational mission.

[0026] Furthermore, the orbital shell radius of the legitimate satellite is: in, The radius of the orbital shell of a legitimate satellite. For the Earth's radius, This is the legal satellite orbital altitude; The orbital shell radius of the eavesdropping satellite is: in, To eavesdrop on the orbital shell radius of satellites, To eavesdrop on satellite orbital altitude; The geocentric radius of the drone is: in, Let the radius of the drone's center be . This refers to the drone's altitude.

[0027] In step S130, the geocentric angle between the UAV and the satellite coverage area is approximated as the coverage angle corresponding to the UAV beamwidth, and free space path loss is set as a geometric constraint.

[0028] It should be noted that, as Figure 4 The image shows a multi-orbit 3D geometric model. The geocentric angle between the UAV and the satellite coverage area is determined by... This indicates that the coverage angle is determined by the communication beamwidth of the UAV, which can be approximated by the beamwidth of the UAV, thus simplifying the definition of the geometric range. This approximation error is within an acceptable range for engineering applications; regarding free-space path loss... Under the assumption that the path loss index is typical for UAV-Low Orbit satellite links, which conforms to the propagation law of electromagnetic waves in free space, it provides a fixed parameter constraint for subsequent path loss and signal-to-noise ratio calculations.

[0029] In step S200, the probability density functions of the squared propagation distance between the UAV and satellites in different orbital shells and the squared propagation distance between the strongest eavesdropper and the UAV are defined, and the piecewise probability density function of the ratio of the squared distance between the UAV and the legitimate satellite / the strongest eavesdropping satellite is defined, thus obtaining the statistical distribution model of the propagation distance of multi-orbit satellites.

[0030] It should be noted that statistical modeling of the squared propagation distance, rather than directly modeling the propagation distance, is used to simplify the subsequent analytical solution process, eliminate the mathematical complexity caused by the square root of the distance, and ensure that the squared distance and the distance are monotonically increasing. Modeling the statistical distribution of the squared distance can accurately reflect the statistical characteristics of the distance and will not affect the final performance evaluation results.

[0031] In one embodiment, such as Figure 5 As shown, step S200 may include the following sub-steps.

[0032] In step S210, based on the propagation distance between the UAV and satellites in different orbital shells, a constant form probability density function of the square of the distance is defined, and the geometric range is delineated to obtain the probability density function of the square of the propagation distance between the UAV and satellites in different orbital shells.

[0033] It should be noted that defining the probability density function of the square of the propagation distance between the UAV and satellites in different orbital shells as a constant is based on the assumption that the satellites are uniformly distributed in the corresponding orbital shells. This assumption is a common assumption for low-Earth orbit satellite constellation modeling and fits the actual satellite constellation deployment. The definition of the geometric range is based on the three-dimensional geometric model in step S100 and the geocentric angle constraint to ensure that the value of the propagation distance conforms to the spatial position constraints of each node.

[0034] Furthermore, the probability density function of the squared propagation distance between the UAV and satellites in different orbital shells is: in, Let be the probability density of the squared propagation distance between the UAV and satellites with different orbital shells. For the radius of the orbital shell of a legitimate satellite / eavesdropping satellite, This refers to the geocentric angle between the drone and the satellite coverage area. For legitimate satellites, To eavesdrop on satellites, The geometric range is the distance between the drone and the legitimate / eavesdropping satellite. .

[0035] It should be noted that the denominator of the probability density function is the length of the range of values ​​for the square of the propagation distance, which ensures the normalization of the probability density function; the lower limit of the geometric range is the square of the closest propagation distance between the UAV and the satellite, and the upper limit is the square of the farthest propagation distance between the UAV and the satellite under the constraint of the geocentric angle. This range accurately describes the propagation distance constraint between the UAV and the satellite within the coverage area of ​​the UAV's communication beam.

[0036] In step S220, the eavesdropping satellite closest to the drone is taken as the strongest eavesdropper. The cumulative distribution function of the squared propagation distance between the strongest eavesdropper and the drone is defined, and the derivative and binomial expansion are performed to obtain the probability density function of the squared propagation distance between the strongest eavesdropper and the drone.

[0037] It should be noted that the cumulative distribution function is defined first and then the probability density function is obtained by differentiation in this step because the cumulative distribution function of the minimum distance between multiple independent and identically distributed eavesdroppers (i.e., the strongest eavesdropper) is easier to derive using probability theory methods. Differentiation is a conventional mathematical method in probability theory to obtain the probability density function from the cumulative distribution function. The binomial expansion is to transform the result of the differentiation of the cumulative distribution function into a closed form that is convenient for subsequent integral calculations. Those skilled in the art can use the conventional binomial theorem to complete the expansion calculation.

[0038] Furthermore, the probability density function of the squared distance between the strongest eavesdropper and the drone is: in, , The probability density of the squared distance between the strongest eavesdropper and the drone. To determine the transmission distance between drones and the most powerful eavesdropping satellites. To eavesdrop on the number of satellites, This is the index variable in the binomial expansion and summation. Let the values ​​of the random variable be the square of the distance between the strongest eavesdropper and the drone. The maximum value of the square of the propagation distance. This represents the minimum value of the square of the propagation distance.

[0039] It should be noted that the probability density function is derived based on the assumption that K eavesdropping satellites are independently and identically distributed, which is consistent with the scenario setting of non-collusive eavesdropping; the number of eavesdropping satellites K is a positive integer and can be selected according to the actual orbital eavesdropping threat situation. This function can accurately reflect the impact of changes in the number of eavesdropping satellites on the distance statistical characteristics of the strongest eavesdropper.

[0040] In step S230, the ratio of the squared distance between the UAV and the legitimate satellite and the strongest eavesdropping satellite is defined and expressed in a piecewise geometric boundary to obtain the piecewise probability density function of the ratio of the squared distance between the UAV and the legitimate satellite / the strongest eavesdropping satellite.

[0041] It should be noted that the distance-squared ratio variable In order to normalize the distance parameters between the legitimate link and the eavesdropping link and simplify the integral solution process for the probability of subsequent security interruption, the probability density function of the ratio is expressed piecewise according to the geometric boundary. This is because the range of the squared distance has upper and lower limits, which divides the range of the ratio variable into multiple intervals. The probability density function of each interval needs to be defined separately to ensure the accuracy of statistical modeling.

[0042] Furthermore, the piecewise probability density function of the ratio of the squared distance between the drone and the legitimate satellite / the most powerful eavesdropping satellite is: in, , , , , , , , , , , , , , , , , , ; Let the probability density function be a piecewise representation of the ratio of the squared distance between the drone and the legitimate satellite / the most powerful eavesdropping satellite. In order to be with the first Segment-related auxiliary coefficients, For segmented index variables, For summation index variables, Let the random variable be the ratio of the squared distance between the drone and the legitimate satellite / the most powerful eavesdropping satellite. , , and These are the coefficients of the piecewise probability density function after expansion. and Let be the exponent parameters of the power function terms of the piecewise probability density function, respectively. and The first The segmentation coefficients corresponding to the segments, , , and For the segmented interval boundaries, and These represent the range of values ​​for the squared propagation distance of the legitimate satellite link and the most powerful eavesdropping satellite link, respectively. and They are drones and the first Minimum and maximum values ​​of the squared propagation distance for satellite-like objects. , and These are the minimum and maximum values ​​of the squared distance between the drone and the legitimate satellite, respectively. and These are the minimum and maximum values ​​of the squared distance between the drone and the most powerful eavesdropping satellite, respectively.

[0043] It should be noted that the derivation of this piecewise probability density function is based on the distribution theorem of random variable functions in probability theory. The probability density function of the ratio variable is obtained by variable substitution. It has a non-zero value only in the preset interval, and the probability density is 0 in the other intervals, which conforms to the actual value constraints of the ratio variable.

[0044] In step S300, the legitimate link and the eavesdropping link are modeled as shadowed Ricean fading to obtain a multi-link channel model. Based on the UAV's transmission power and the noise power of the legitimate satellite and the eavesdropping satellite, an instantaneous signal-to-noise ratio model of the legitimate satellite and the strongest eavesdropping satellite is constructed. The multi-link channel model includes the probability density function and cumulative distribution function of the power gain of the two link channels.

[0045] It should be noted that the multi-link channel model is a statistical model, which describes the random distribution characteristics of channel power gain rather than a fixed channel gain value, and is consistent with the randomness of fading in wireless channels; the instantaneous signal-to-noise ratio model combines channel fading characteristics and path loss, and can accurately reflect the instantaneous communication quality of each link, providing core parameters for solving the subsequent probability of security interruption.

[0046] In one embodiment, such as Figure 6 As shown, step S300 may include the following sub-steps.

[0047] In step S310, both the legitimate link and the eavesdropping link are modeled as shadowed Ricean fading, and the channel power gain and the corresponding probability density function and cumulative distribution function are defined.

[0048] It should be noted that channel power gain is defined as... ( ),in The complex channel gain of the link is taken as the channel power gain, and the square of its modulus is the conventional definition in the field of wireless communication. The parameters in the probability density function and cumulative distribution function of shadowed Rice fading are all determined according to the actual propagation environment of the UAV-Low Orbit satellite link. Among them, the fading severity, line-of-sight power, and multipath power parameters can be obtained by fitting the channel measurement data of the actual link.

[0049] Furthermore, the probability density function of the power gain of the two link channels is: in, , , ; The probability density of the power gain of the two link channels. The normalization coefficients in the shadow Rice fading probability density function are... To indicate the severity of the fading, For the summation index variable in a finite series expansion, For the first The coefficients of the series expansion, The value of the random variable representing channel power gain. , It is a natural constant. The decay parameter corresponding to the exponential term. These are auxiliary parameters determined jointly by line-of-sight power and multipath power. For multipath power parameters, For line-of-sight power, It represents the decreasing factorial power.

[0050] The cumulative distribution function of the power gain of the two link channels is: in, This represents the cumulative distribution of power gain between the two link channels. This is the summation index variable in the finite-term expansion of the cumulative distribution function.

[0051] It should be noted that the probability density function and cumulative distribution function are the standard statistical expressions for shadowed Ricean fading. The gamma function, the confluence hypergeometric function, and the descent factorial power symbol are all standard special functions in the field of mathematics. Those skilled in the art can perform numerical calculations of these functions using numerical calculation libraries. The legitimate link and the eavesdropping link adopt the same form of statistical distribution, and the parameter values ​​can be adjusted according to the actual propagation environment.

[0052] In step S320, based on the UAV's transmission power, the noise power of the legitimate satellite and the eavesdropping satellite, and combined with the propagation distance between the UAV and the strongest eavesdropping satellite, the propagation distance between the UAV and the legitimate satellite, and the channel power gain, an instantaneous signal-to-noise ratio model of the legitimate satellite and the strongest eavesdropping satellite is constructed.

[0053] It should be noted that the instantaneous signal-to-noise ratio (SNR) modeling combines four core factors: transmit power, channel power gain, path loss, and noise power. This is a common form of SNR calculation in the field of wireless communication. The path loss is expressed as a power of η of the propagation distance, where η=2 is the free-space path loss exponent set in step S130, ensuring consistency with the geometric constraints mentioned above. The noise power is the thermal noise power of the receiver of the legitimate satellite and the eavesdropping satellite. It is a known equipment parameter and can be determined based on the actual performance of the satellite receiving equipment.

[0054] Furthermore, the instantaneous signal-to-noise ratio of the legitimate satellite is: in, For the instantaneous signal-to-noise ratio of legitimate satellites, To transmit power to the drone, For the channel power gain of the UAV and the legitimate satellite link, For the noise power of a legitimate satellite, The propagation distance between drones and legitimate satellites, This is the free space path loss index. .

[0055] The instantaneous signal-to-noise ratio of the high-powered eavesdropping satellite is: in, To enhance the instantaneous signal-to-noise ratio of eavesdropping satellites, Channel power gain for the link between the drone and the most powerful eavesdropping satellite. The noise power for eavesdropping on satellites.

[0056] It should be noted that the UAV transmission power is the output power of the UAV communication transmitter, which is a known engineering parameter and must comply with the power transmission specifications for wireless communication; the instantaneous signal-to-noise ratio is a random variable, and its randomness is jointly determined by the randomness of the channel power gain and the propagation distance. This model can accurately reflect the random variation characteristics of the signal-to-noise ratio in the actual link.

[0057] In step S400, a preliminary lower bound form of the security interruption probability is constructed. Substituting this into the instantaneous signal-to-noise ratio model and integrating the multi-link channel model and the distance square ratio, the final lower bound form of the security interruption probability is obtained. Then, substituting the piecewise probability density function of the distance square ratio between the UAV and the legitimate satellite / the strongest eavesdropping satellite and the multi-link channel model, a closed-form summation expression of the security interruption probability is obtained, and uplink security performance is evaluated under multi-orbit threat conditions.

[0058] It should be noted that the probability of security interruption is transformed into a directly calculable closed-form summation expression through analytical derivation. The entire derivation process is based on the integral transformation of probability theory and the assumption of independence of random variables. Among them, the channel fading of the legitimate link and the eavesdropping link are independent of each other, and the spatial position of the satellite is independent of the channel fading. This assumption is consistent with the actual wireless communication scenario and can effectively reduce the complexity of analytical solution.

[0059] In one embodiment, such as Figure 7 As shown, step S400 may include the following sub-steps.

[0060] In step S410, a preliminary lower bound for the security interruption probability is constructed.

[0061] It should be noted that the preliminary lower bound of the probability of security interruption is derived based on the definition of instantaneous security capacity. This lower bound applies when the instantaneous security capacity is less than the target security rate threshold. When a security breach occurs, an initial lower bound is obtained by transforming and approximating inequalities, expressed in terms of the signal-to-noise ratio. This derivation process is a conventional derivation method in the field of physical layer security, and the lower bound is a tight lower bound, which can accurately reflect the changing trend of the probability of a security breach.

[0062] Furthermore, the preliminary lower bound of the confidentiality interruption probability is as follows: in, To maintain the probability of interruption, , The target confidentiality rate threshold.

[0063] It should be noted that, , as a derived parameter of the target secrecy rate threshold, transforms the logarithmic secrecy capacity constraint into a linear signal-to-noise ratio constraint, simplifying the subsequent probability solution process; Target secrecy rate threshold These are pre-set engineering parameters, which can be set according to the uplink communication service requirements of UAVs and low-orbit satellites.

[0064] In step S420, the instantaneous signal-to-noise ratio model is substituted into the preliminary lower bound form of the security interruption probability, and the multi-link channel model and the distance squared ratio are integrated to obtain the final lower bound form of the security interruption probability.

[0065] It should be noted that after substituting the instantaneous signal-to-noise ratio model into the preliminary lower bound form, the probability constraint of the signal-to-noise ratio is transformed into the probability constraint of the ratio of channel power gain to the square of distance through variable substitution. Then, the channel power gain (multi-link channel model) and the ratio of the square of distance are double integrated to obtain the final lower bound form. In the integration process, the assumption of the independence of channel fading and distance is utilized to decompose the joint probability density function into the product of marginal probability density functions, thereby reducing the integration complexity.

[0066] Furthermore, the final lower bound of the secrecy interruption probability is in the form of: in, The distance-square ratio random variable The range of values, For legitimate link channel power gain The cumulative distribution function, For eavesdropping link channel power gain random variable The probability density function, The random variable representing the ratio of the squared distance between the drone and the legitimate satellite / the most powerful eavesdropping satellite. The probability density function.

[0067] It should be noted that the final lower bound is in integral form, where the inner integral is for the power gain of the legitimate link channel, and the outer integral is for the distance square ratio variable. The upper and lower bounds of the integral are determined by the constraint relationship of the signal-to-noise ratio and the actual range of values ​​of the variable.

[0068] In step S430, the piecewise probability density function of the ratio of the squared distance between the UAV and the legitimate satellite / the strongest eavesdropping satellite and the multi-link channel model are substituted into the final lower bound of the security interruption probability to obtain the closed-form summation expression of the security interruption probability, and the uplink security performance under multi-track threat is evaluated.

[0069] It should be noted that by substituting the piecewise probability density function and the probability density function and cumulative distribution function of the power gain of the two link channels into the final lower bound of the integral form, the integral form is transformed into a closed summation expression through piecewise integration and series expansion of special functions. This closed summation expression only contains conventional algebraic operations and standard special functions, and those skilled in the art can quickly complete the calculation using numerical calculation tools, which is convenient for performance evaluation and parameter optimization in engineering.

[0070] Furthermore, the closed-form summation expression for the secrecy interruption probability is as follows: in, , , , ; For legitimate link shadow Rice fading parameters, For the summation index variable in a finite term expansion, These are the combination coefficients in closed-form summation expressions. For interval Auxiliary integral function on, and These are auxiliary summation functions for different segmented intervals. and These are the normalized coefficients in the shadow Rice fading model for legitimate links and eavesdropping links, respectively. and These are the coefficients in the finite series expansions of the legitimate link and the eavesdropping link, respectively. This is an auxiliary parameter jointly determined by noise power and the target secrecy rate threshold. For gamma function, As an auxiliary index parameter, For the summation index variable in a finite term expansion, and For the boundaries of the piecewise integration interval, and These are expansion coefficients used to assist in summing functions.

[0071] Furthermore, such as Figure 8 The figure shown is a simulation diagram of the probability of security interruption as a function of line-of-sight power, under the geocentric angle corresponding to the satellite coverage area for different UAVs.

[0072] Performance monitoring: Using SOP as the core indicator, output is displayed at different geocentric angles. Under the given conditions, the curve of SOP (Standard Operating Position) versus line-of-sight power is presented, along with a comparison between theoretical calculations and Monte Carlo simulations. Specifically, when the line-of-sight power increases from -10 to 20, The corresponding SOP is approximately 8.3 × 10 - ¹Reduced to 5.3×10 -4 ; The corresponding SOP is approximately 8.5 × 10 - ¹Reduced to 3.2×10 - ³; The corresponding SOP is approximately 8.4 × 10 - ¹ Reduced to 6.5 × 10 - ³; The corresponding SOP is approximately 8.5 × 10 - ¹Reduced to 9.5×10 - ³. When the line-of-sight power is 10, Ψ DThe SOPs corresponding to π / 12, π / 6, π / 4, and π / 3 are approximately 6.6 × 10⁻⁶. - ², 1.2×10 - ¹、1.4×10 - ¹ and 1.5×10 - ¹; When the line-of-sight power is 15, the above-mentioned SOPs are approximately 8.2 × 10⁻⁶. - ³、2.6×10 - ², 3.8×10 - ² and 4.5×10 - ².

[0073] Results Analysis: As line-of-sight power increases, the probability of secure transmission interruption gradually decreases, indicating that enhancing the line-of-sight link component is beneficial for improving the quality of the legitimate uplink, thereby improving the secure transmission performance of the system; simultaneously, the geocentric angle... A larger value indicates a higher probability of security breach, suggesting that increasing the UAV's coverage area for satellites introduces more unfavorable propagation distance conditions, making the system more susceptible to security breaches. Furthermore, the theoretical calculation results are largely consistent with the Monte Carlo simulation results, verifying the effectiveness of the evaluation model and closed-form expression under different coverage geometries.

[0074] like Figure 9 The figure shown is a simulation graph of the probability of security breach as a function of line-of-sight power under different numbers of eavesdropping satellites.

[0075] Performance indicator monitoring: Using SOP as the core indicator, outputs data on different numbers of eavesdropping satellites. K Under the given conditions, the curve of SOP (Standard Operating Position) versus line-of-sight power is presented, along with a comparison between theoretical calculations and Monte Carlo simulations. Specifically, when the line-of-sight power increases from -10 to 20, K =1 corresponds to a SOP of approximately 7.3 × 10 - ¹Reduced to 2.1×10 -4 ; K =3 corresponds to a SOP of approximately 8.2 × 10 - ¹ Reduced to 5.0 × 10 -4 ; K =5 corresponds to a SOP of approximately 8.5 × 10 - ¹ Reduced to 7.0 × 10 -4 At a line-of-sight power of 10, K =1、 K =3 and K The SOP corresponding to =5 is approximately 3.1 × 10⁻⁵. - ²、6.2×10 - ² and 8.1×10 - ²; When the line-of-sight power is 15, the above SOPs are approximately 3.5 × 10⁻⁶. - ³、7.9×10- ³ and 1.1×10 - ².

[0076] Results Analysis: As line-of-sight power increases, the probability of security interruption gradually decreases, indicating that improved line-of-sight propagation conditions can enhance the reception quality of legitimate links, thereby reducing the probability of system security interruption; simultaneously, the number of eavesdropping satellites... K A higher number of satellites increases the probability of security breaches, indicating that an increase in the number of eavesdropping satellites raises the probability of strong eavesdropping links, enhancing the eavesdropping capabilities of the most powerful satellites and thus increasing the risk of system security breaches. Furthermore, the theoretical calculation results are largely consistent with the Monte Carlo simulation results, verifying the effectiveness of the evaluation model and closed-form expression in multi-eavesdropping satellite scenarios.

[0077] 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 evaluating performance of uplink secure transmission of UAV-low earth orbit satellite, characterized in that, include: Based on a three-dimensional coordinate system with the Earth's center as the origin, a multi-orbit three-dimensional geometric model containing legitimate satellites, eavesdropping satellites, and drones is constructed to obtain geometric parameters; The geometric parameters include the radius of the orbital shell of the legitimate / eavesdropping satellite and the geocentric radius of the UAV; Define the probability density functions for the squared propagation distance between the UAV and satellites with different orbital shells, and the squared propagation distance between the strongest eavesdropper and the UAV. Define the piecewise probability density function for the ratio of the squared distance between the UAV and the legitimate satellite / the strongest eavesdropping satellite, and obtain the statistical distribution model of the propagation distance of multi-orbit satellites. The legitimate link and the eavesdropping link are modeled as shadowed Ricean fading to obtain a multi-link channel model. Based on the UAV's transmit power and the noise power of the legitimate satellite and the eavesdropping satellite, an instantaneous signal-to-noise ratio model of the legitimate satellite and the strongest eavesdropping satellite is constructed. The multi-link channel model includes the probability density function and cumulative distribution function of the power gain of the two link channels. A preliminary lower bound for the probability of security interruption is constructed. Substituting this into the instantaneous signal-to-noise ratio model and integrating the multi-link channel model and the distance square ratio, the final lower bound for the probability of security interruption is obtained. Then, substituting the piecewise probability density function of the distance square ratio between the UAV and the legitimate satellite / the strongest eavesdropping satellite and the multi-link channel model, a closed-form summation expression for the probability of security interruption is obtained, and uplink security performance is evaluated under multi-orbit threat conditions.

2. The method of claim 1, wherein, The steps for constructing a multi-orbit 3D geometric model containing legitimate satellites, eavesdropping satellites, and drones based on a 3D coordinate system with the Earth's center as the origin, and obtaining geometric parameters, include: Construct a three-dimensional coordinate system with the Earth's center as the origin; Based on the three-dimensional coordinate system, the orbital shell radius of the legitimate satellite and the eavesdropping satellite, and the geocentric radius of the UAV are determined respectively, and the geometric parameters are obtained; The geocentric angle between the UAV and the satellite coverage area is approximated as the coverage angle corresponding to the UAV beamwidth, and free space path loss is set as a geometric constraint.

3. The method of claim 2, wherein, The orbital shell radius of the legitimate satellite is: in, The radius of the orbital shell of a legitimate satellite. For the Earth's radius, This is the legal satellite orbital altitude; The orbital shell radius of the eavesdropping satellite is: in, In order to eavesdrop on the orbital shell radius of satellites, To eavesdrop on satellite orbital altitude; The geocentric radius of the drone is: in, Let the radius of the drone's center be . This refers to the drone's altitude.

4. The method for evaluating the uplink secure transmission performance of UAV-Low Orbit satellite according to claim 1, characterized in that, The steps to define the probability density functions of the squared propagation distances between the UAV and satellites in different orbital shells, the squared propagation distance between the strongest eavesdropper and the UAV, and the piecewise probability density function of the ratio of the squared distances between the UAV and the legitimate satellite / the strongest eavesdropping satellite, to obtain the statistical distribution model of the propagation distances of multi-orbit satellites, include: Based on the propagation distance between the UAV and satellites with different orbital shells, a constant form probability density function of the square of the distance is defined, and the geometric range is delineated to obtain the probability density function of the square of the propagation distance between the UAV and satellites with different orbital shells. Taking the eavesdropping satellite closest to the drone as the strongest eavesdropper, we define the cumulative distribution function of the squared propagation distance between the strongest eavesdropper and the drone, and perform differentiation and binomial expansion to obtain the probability density function of the squared propagation distance between the strongest eavesdropper and the drone. Define the ratio of the squared distance between the UAV and the legitimate satellite and the most powerful eavesdropping satellite, and express it in a piecewise manner with geometric boundaries to obtain the piecewise probability density function of the ratio of the squared distance between the UAV and the legitimate satellite / the most powerful eavesdropping satellite.

5. The method for evaluating the uplink secure transmission performance of UAV-Low Orbit satellite according to claim 4, characterized in that, The probability density function of the squared propagation distance between the UAV and satellites with different orbital shells is: in, Let be the probability density of the squared propagation distance between the UAV and satellites with different orbital shells. For the radius of the orbital shell of a legitimate satellite / eavesdropping satellite, This refers to the geocentric angle between the drone and the satellite coverage area. For legitimate satellites, To eavesdrop on satellites, The geometric range is the distance between the drone and the legitimate / eavesdropping satellite. ; The probability density function of the squared distance between the strongest eavesdropper and the drone is: in, , The probability density of the squared distance between the strongest eavesdropper and the drone. The distance at which drones can communicate with the most powerful eavesdropping satellites. To eavesdrop on the number of satellites, This is the index variable in the binomial expansion and summation. Let the values ​​of the random variable be the square of the distance between the strongest eavesdropper and the drone. The maximum value of the square of the propagation distance. This represents the minimum value of the square of the propagation distance; The piecewise probability density function of the ratio of the squared distance between the drone and the legitimate satellite / the most powerful eavesdropping satellite is: in, , , ， ， ， ， ， ， ， ， ， ， ， ， ， ， ； Let the probability density function be a piecewise representation of the ratio of the squared distance between the drone and the legitimate satellite / the most powerful eavesdropping satellite. In order to be with the first Segment-related auxiliary coefficients, For segmented index variables, For summation index variables, Let the random variable be the ratio of the squared distance between the drone and the legitimate satellite / the most powerful eavesdropping satellite. , , and These are the coefficients of the piecewise probability density function after expansion. and Let be the exponent parameters of the power function terms of the piecewise probability density function, respectively. and The first The segmentation coefficients corresponding to the segments, , , and For the segmented interval boundaries, and These represent the range of values ​​for the squared propagation distance of the legitimate satellite link and the most powerful eavesdropping satellite link, respectively. and They are drones and the first Minimum and maximum values ​​of the squared propagation distance for satellite-like objects. , and These are the minimum and maximum values ​​of the squared distance between the drone and the legitimate satellite, respectively. and These are the minimum and maximum values ​​of the squared distance between the drone and the most powerful eavesdropping satellite, respectively.

6. The method for evaluating the uplink secure transmission performance of UAV-Low Orbit satellite according to claim 1, characterized in that, The steps of modeling the legitimate link and the eavesdropping link as shadowed Ricean fading to obtain a multi-link channel model, and constructing an instantaneous signal-to-noise ratio model of the legitimate satellite and the strongest eavesdropping satellite based on the UAV's transmit power and the noise power of the legitimate satellite and the eavesdropping satellite, include: Both legitimate links and eavesdropping links are modeled as shadowed Ricean fading, and the channel power gain and the corresponding probability density function and cumulative distribution function are defined. Based on the transmission power of the UAV, the noise power of the legitimate satellite and the eavesdropping satellite, and combined with the propagation distance of the UAV and the strongest eavesdropping satellite, the propagation distance of the UAV and the legitimate satellite and the channel power gain, an instantaneous signal-to-noise ratio model of the legitimate satellite and the strongest eavesdropping satellite is constructed.

7. The method for evaluating the uplink secure transmission performance of UAV-Low Orbit satellite according to claim 6, characterized in that, The probability density function of the power gain of the two link channels is: in, , , ; The probability density of the power gain of the two link channels. The normalization coefficients in the shadow Rice fading probability density function are... To indicate the severity of the fading, For the summation index variable in a finite series expansion, For the first The coefficients of the series expansion, The value of the random variable representing channel power gain. , It is a natural constant. The decay parameter corresponding to the exponential term. These are auxiliary parameters determined jointly by line-of-sight power and multipath power. For multipath power parameters, For line-of-sight power, It is a decreasing factorial power; The cumulative distribution function of the power gain of the two link channels is: in, This represents the cumulative distribution of power gain between the two link channels. This is the summation index variable in the finite-term expansion of the cumulative distribution function.

8. The method for evaluating the uplink secure transmission performance of UAV-Low Orbit satellite according to claim 6, characterized in that, The instantaneous signal-to-noise ratio of the legitimate satellite is: in, For the instantaneous signal-to-noise ratio of legitimate satellites, To transmit power to the drone, For the channel power gain of the UAV and the legitimate satellite link, For the noise power of a legitimate satellite, The propagation distance between drones and legitimate satellites, This is the free space path loss index. ; The instantaneous signal-to-noise ratio of the high-powered eavesdropping satellite is: in, To enhance the instantaneous signal-to-noise ratio of eavesdropping satellites, Channel power gain for the link between the drone and the most powerful eavesdropping satellite. The noise power for eavesdropping on satellites.

9. The method for evaluating the uplink secure transmission performance of UAV-Low Orbit satellite according to claim 1, characterized in that, The steps for constructing a preliminary lower bound for the security interruption probability, substituting it into the instantaneous signal-to-noise ratio model, integrating it with the multi-link channel model and the distance-squared ratio to obtain the final lower bound for the security interruption probability, and then substituting it into the piecewise probability density function of the distance-squared ratio between the UAV and the legitimate satellite / the strongest eavesdropping satellite and the multi-link channel model to obtain a closed-form summation expression for the security interruption probability, and conducting uplink security performance evaluation under multi-orbit threats, include: Construct a preliminary lower bound for the probability of security breach; Substituting the instantaneous signal-to-noise ratio model into the preliminary lower bound of the security interruption probability, and integrating the multi-link channel model and the distance square ratio, we obtain the final lower bound of the security interruption probability. Substituting the piecewise probability density function of the ratio of the squared distance between the UAV and the legitimate satellite / the most powerful eavesdropping satellite, along with the multi-link channel model, into the final lower bound of the security interruption probability, we obtain a closed-form summation expression for the security interruption probability, and use this expression to evaluate uplink security performance under multi-track threats.

10. The method for evaluating the uplink secure transmission performance of UAV-Low Orbit satellite according to claim 9, characterized in that, The preliminary lower bound of the security breach probability is as follows: in, To maintain the probability of interruption, , Set as the target security rate threshold; The final lower bound of the security breach probability is in the form of: in, The distance-square ratio random variable The range of values, For legitimate link channel power gain The cumulative distribution function, For eavesdropping link channel power gain random variable The probability density function, The random variable representing the ratio of the squared distance between the drone and the legitimate satellite / the most powerful eavesdropping satellite. The probability density function; The closed-form summation expression for the probability of security breach is: in, , ， ， ； For legitimate link shadow Rice fading parameters, For the summation index variable in a finite term expansion, These are the combination coefficients in closed-form summation expressions. For interval Auxiliary integral function on, and These are auxiliary summation functions for different segmented intervals. and These are the normalized coefficients in the shadow Rice fading model for legitimate links and eavesdropping links, respectively. and These are the coefficients in the finite series expansions of the legitimate link and the eavesdropping link, respectively. This is an auxiliary parameter jointly determined by noise power and the target secrecy rate threshold. For gamma function, As an auxiliary index parameter, For the summation index variable in a finite term expansion, and For the boundaries of the piecewise integration interval, and These are expansion coefficients used to assist in summing functions.

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