A satellite-ground fusion network physical layer security transmission method based on AN technology

Abstract

The application discloses a kind of based on AN technology's star-ground fusion network physical layer security transmission method, comprising the following steps: step one, a plurality of parameters in star-ground fusion network are collected;Step two, U-R ground link signal power, R-S air link signal power, satellite's contact angle distribution probability density function, service relay distance distribution's probability density function, satellite network's visibility probability and ground relay network's visibility probability are calculated;Step three, according to the visibility probability, the signal-to-noise ratio received by U-R ground link service relay RB and the signal-to-jamming noise ratio received by air R-S link terminal LS and eavesdropping satellite ES are determined, and Laplace transformation is carried out;Step four, according to security transmission probability maximization, the data to be transmitted is transmitted.The application has the characteristics of improving security transmission performance and solving cumulative interference.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of satellite-ground integrated network security transmission, and more particularly, to a satellite-ground integrated network physical layer security transmission method based on AN technology. BACKGROUND

[0002] The widespread deployment of low earth orbit (LEO) satellites brings significant security challenges to the communication security problem in satellite-ground integrated networks. As more and more satellites can act as eavesdroppers, it becomes increasingly important to integrate physical layer security (PLS) into satellite communications. However, the security performance of satellite communication networks faces the following technical difficulties: processing of dynamic topology, cumulative interference analysis, and high complexity of performance evaluation. In order to solve these challenges, an analytical framework of stochastic geometry is used in satellite communications, and the benefits brought by artificial noise (AN) technology to network security transmission are evaluated.

[0003] Artificial noise (AN) technology is a physical layer security enhancement method mainly used in wireless communications to resist eavesdropping. Its basic principle is to inject a specially designed noise signal into the channel at the same time as the legitimate signal, so that the legitimate receiver can correctly demodulate, while the eavesdropper is difficult to obtain effective information due to noise interference, thereby improving the confidentiality of communication. However, AN technology also faces many challenges: first, the design of artificial noise depends on accurate channel state information (CSI), and in dynamic or complex environments, it is difficult and prone to error to obtain CSI, thereby affecting the accuracy of interference positioning; second, how to maximize the interference of eavesdroppers without interfering with the communication of legitimate users requires delicate power allocation and beamforming strategies; third, in multi-user or large-scale antenna systems, the computational complexity of artificial noise design increases significantly, requiring higher real-time processing capabilities. In addition, in the face of adaptive attacks by intelligent eavesdroppers, traditional AN strategies may fail, and it is urgent to introduce more intelligent and dynamically adjusted mechanisms.

[0004] Among them, the beamforming strategy needs to obtain the accurate CSI of the legitimate user and the eavesdropper in real time. However, due to the long propagation distance, Doppler shift and atmospheric attenuation of satellite channels, it is difficult to obtain and update the CSI in real time, especially in dynamic scenarios (such as low-orbit satellite movement and high-speed user movement), the error is significant, and in multi-user satellite networks, beamforming needs to optimize the beam direction for each user independently, resulting in an exponential increase in computational complexity. Beamforming suppresses a single eavesdropper through spatial isolation, but it is difficult to effectively deal with multiple eavesdroppers distributed widely (such as scattered attackers under the wide coverage of satellites), and beamforming also requires multiple antenna arrays and high-speed signal processors, resulting in a sharp increase in satellite payload cost and power consumption.

[0005] The prior art also prevents eavesdropping through time compression technology, which artificially introduces controllable inter-symbol interference, and the legal user can effectively eliminate the interference through a pre-defined pulse shape and overlapping mode (such as a raised cosine filter), while the eavesdropper cannot accurately estimate the overlapping parameters, and the decoding capability is significantly weakened. However, the pulse overlapping parameters (such as overlap degree and symbol interval) are fixed, and it is difficult to adjust them in real time according to the behavior of the eavesdropper or the dynamic change of the channel. Once the parameters are cracked by the eavesdropper, the system needs to redesign the signal format, and the flexibility is insufficient. Moreover, in high-speed movement or strong Doppler effect (such as LEO satellite scene), channel estimation error will reduce the interference effect, and even cause the bit error rate of the legal user to rise; time compression improves the interference strength by sacrificing the symbol interval (increasing tau), but it will cause the inter-symbol interference to intensify, and complex equalization algorithm is needed to compensate, which increases the processing complexity of the receiving end. In addition, high overlap degree may reduce the spectral efficiency, limiting the application of high data rate scenarios; time compression technology is more suitable for short packet and low rate IoT transmission, but in wideband high-speed satellite communication (such as high-definition video transmission), high overlap pulse will cause the equalization complexity to explode, and it is difficult to expand.

[0006] The artificial noise technology also brings some adverse effects: although it can improve the physical layer security, it will also reduce the SNR and throughput of the legal link, increase the transmission power consumption and system hardware complexity, and in high-speed movement or multipath environment, it is easy to cause noise leakage due to CSI error, affecting stability, and may cause spectrum pollution and protocol incompatibility, and also brings the security illusion of over-reliance. SUMMARY

[0007] The purpose of the present application is to design and develop a satellite-ground integrated network physical layer security transmission method based on AN technology, which can obtain the maximum security transmission probability by adjusting the information carrying ratio, improve the security and solve the cumulative interference.

[0008] The technical scheme provided by the present application is as follows:

[0009] A satellite-ground integrated network physical layer security transmission method based on AN technology, comprising the following steps:

[0010] Step 1, collect the number of eavesdropping satellites, the number of legal satellites, the maximum distance of communication between the relay and the service user, the height of the satellite from the ground, the power of the service user's transmitted signal, and the fading index of the satellite-to-ground link channel;

[0011] Step 2, according to the channel model and the homogeneous Poisson point process, calculate the U-R ground link signal power, the R-S air link signal power, the contact angle distribution probability density function of the satellite, the probability density function of the service relay distance distribution, the visibility probability of the satellite network and the visibility probability of the ground relay network;

[0012] Step three, determine the signal-to-noise ratio received by the U-R ground link service relay RBs and the signal-to-interference noise ratio received by the R-S air link terminal LS and eavesdropping satellite ES according to the U-R ground link signal power, R-S air link signal power and visibility probability, and perform Laplace transform;

[0013] Step four, transmit the data to be transmitted according to the maximum security transmission probability;

[0014] The security transmission probability satisfies:

[0015]

[0016] In the formula, The security transmission probability Ρ s,suc The successful transmission probability of the satellite network Ρ out The security interruption probability of the satellite network.

[0017] Preferably, the U-R ground link signal power satisfies:

[0018]

[0019] In the formula, (R i ) -ν The path loss gain of the ground channel v is the path loss exponent of the ground channel, The square of the Nakagami-m fading index;

[0020] The R-S air link signal power satisfies:

[0021]

[0022]

[0023] In the formula, ρ tj,0 The signal power received by the jth satellite in the tth layer to the service relay RBs, β U-R The threshold value of the SNR at the ground RBs, φ(β U-R ) indicates whether the service relay RBs can decode the signal of the service UE, P R The constant power transmitted by each ground relay, G s The receiving antenna gain, The square of the fading index of the satellite-to-ground link channel, L(R tj,0 ) is the path loss gain of the jth satellite in the tth layer to the service relay RBs, ρ tj,i / i≠0 The signal power received by the jth satellite in the tth layer to the other ground interference relay RBs except the service relay RBs, L(R tj,i / i≠0) is the path loss gain of the jth satellite in the tth layer to other ground interfering relay RBs.

[0024] Preferably, the contact angle distribution probability density function of the satellite is:

[0025]

[0026] The probability density function of the service relay distance distribution is:

[0027]

[0028] where r is the distance of the service UE to the nearest relay node RBs, λ R is the density of the point process Φ R of the location distribution of the relay RBs.

[0029] Preferably, the visibility probability of the satellite network satisfies:

[0030]

[0031] where P s,vis is the visibility probability of the legal satellite terminal LS, R s is the spherical radius in which the terminal LS is distributed, λ s is the density of the point process Φ s of the location distribution of the legal layer LS;

[0032] The visibility probability of the ground relay network satisfies:

[0033]

[0034] where P 0,vis is the visibility probability of the service relay RBs, P[Φ R | B(0, R Z ) > 0] is the probability that there is no other relay node RBs within the range B(0, R Z ) > 0 with a distance less than R Z .

[0035] Preferably, the signal-to-noise ratio received by the U-R ground link service relay RBs satisfies:

[0036]

[0037] where ρ0 is the signal power of the service relay RBs, is the noise power generated by the service relay RBs device.

[0038] Preferably, the signal-to-interference-and-noise ratio received by the air R-S link terminal LS satisfies:

[0039]

[0040] In the formula, I LS This represents the aggregated interference power generated by ground-based interference relays (RBs) on terminal LS. The noise power generated by satellite equipment;

[0041] The signal-to-interference-plus-noise ratio received by the airborne RS link eavesdropping satellite ES satisfies:

[0042]

[0043] In the formula, ρ k,0 In order to eavesdrop on the power signals received by the Serving Relays (RBs) from the ES satellite, I ES The aggregate interference power generated by the interference RBs on the ES.

[0044] Preferably, the Laplace transform includes:

[0045]

[0046] In the formula, For those containing random variables The average of the formulas is calculated. For those containing random variables The average of the formulas is calculated. For LTs subjected to aggregation interference by legitimate satellite LS, LTs for eavesdropping on the aggregated interference of the ES satellite.

[0047] Preferably, the success rate of the satellite network transmission is:

[0048]

[0049] In the formula, The probability of successful transmission on the UR link. This represents the probability of successful transmission on the RS link.

[0050] Preferably, the successful transmission probability of the UR link satisfies:

[0051]

[0052] In the formula, P(SNR) RU ≥β U-R The probability that the SNR at the serving relay RBs is higher than the SNR at the ground RBs is given by the given SNR value. RU The signal-to-noise ratio received by the serving relay RBs;

[0053] The successful transmission probability of the RS link satisfies:

[0054]

[0055] where P(SINR LS ≥ β LS ) is the probability that the SINR at the terminal LS is higher than the threshold of the SINR at the aerial LS, SINR LS is the received SINR at the terminal LS, and β LS is the threshold of the SINR at the aerial LS.

[0056] Preferably, the secrecy outage probability of the satellite network is:

[0057]

[0058] where P(SINR ES < β ES ) is the probability that the SINR at the eavesdropping satellite ES is lower than the threshold of the SINR at the eavesdropping satellite ES, SINR ES is the received SINR at the eavesdropping satellite ES, and β ES is the threshold of the SINR at the eavesdropping satellite ES.

[0059] The beneficial effects of the present application are:

[0060] (1) The satellite-ground integrated network physical layer secure transmission method based on AN technology designed and developed by the present application uses the random geometry theory to derive the visibility probability, contact angle and contact distance distribution, and further derives the successful transmission probability at the legal satellite and the secrecy outage probability at the eavesdropping satellite, and finally obtains the closed expression of the secure transmission probability of the network uplink. In the case where other parameters (such as the height, density and beam width of the satellite antenna) remain unchanged, by adjusting the appropriate information carrying ratio, the maximum value of the secure transmission probability can be obtained, and the secure transmission probability is improved.

[0061] (2) The satellite-ground integrated network physical layer secure transmission method based on AN technology designed and developed by the present application integrates the random geometry (SG) analysis framework and the advanced physical layer security (PLS) technology. This novel combination can comprehensively analyze the dynamic topology and interference, and provides a low complexity solution for evaluating the network security performance based on the multi-layer LEO satellite constellation. BRIEF DESCRIPTION OF DRAWINGS

[0062] Figure 1 FIG. 1 is a schematic diagram of the satellite-ground integrated network system model based on the artificial noise technology according to the present application.

[0063] Figure 2 FIG. 2 is a schematic diagram of the aerial link model according to the present application.

[0064] Figure 3A graph of the change of the secure transmission probability with the AN information carrying ratio for the application.

[0065] Figure 4 A graph of the change of the secure transmission probability with the AN information carrying ratio for the application with different numbers of satellites. DETAILED DESCRIPTION

[0066] The application will be further described in detail below with reference to the accompanying drawings of the specification, so that those skilled in the art can implement the application according to the description of the specification.

[0067] As shown in the figure, the application provides a satellite-ground fusion network physical layer secure transmission method based on AN technology, which is implemented through an artificial noise (AN) technology system model. Figure 1

[0068] Among them, the artificial noise technology system model is obtained by considering the uplink satellite-ground fusion relay network secure transmission performance analysis framework of the eavesdropping satellite, and modeling the system. When the line-of-sight link between the satellite and the user is severely blocked, the user communicates with the satellite through the relay, all nodes are fixed points, the user is the source node UE, the satellite is the terminal node S (divided into eavesdropping satellite ES and legal satellite LS), and the ground relay node is RBs. The ground DF protocol relay RBs use artificial noise (AN) technology. This model considers the case of mixed channel conditions. The air channel model uses the shadow Rician (SR) fading model, and the ground channel model uses the Nakagami-m fading. If all ES are non-colluding eavesdropping satellites, that is, they do not cooperate with each other, therefore, the signals they receive are not combined, but are decoded separately, and when the CSI of ES is known, directional beam design can be performed according to the channel state information of the eavesdropper to maximize the interference to the signal reception of the eavesdropper. Assuming that the satellite uses a single antenna with directional beamforming technology, a simplified model is considered in which the transmit and receive antenna gains of the serving relay RBs and the serving UE are 1. The ground link uses the enhanced interference coordination technology (eICIC) conforming to the 3GPP standard. It is assumed that each UE is dynamically allocated spectrum resources so that it uses different frequency bands to avoid interference to the relay node RBs.

[0069] The uplink HSTRN communication process is specifically divided into two transmission links: the first link is the U-R ground link, that is, the link between the user node UE and the relay node RBs. The user first needs to establish a communication connection with the nearest relay for communication to the satellite. The user node (service) UE sends the signal to the nearest RBs within the coverage range A0. This RBs is the serving relay RBs, which forwards the decoded nearly distortionless signal to the terminal LS to establish the communication connection of the entire network. Among them, the user coverage range A0 = Β(0,R Z ) represents the origin of the service user, R​Z A circular region with radius R Z This refers to the maximum distance at which the relay can communicate with the serving user; such as... Figure 2 As shown, the second link is the RS air link. After completing the communication of the first link, the serving relays (RBs) decode the signal and forward it to the nearest terminal (LS). During this period, multiple ESs may pose a threat to the terminal LS. The relay devices all use AN technology to send redundant interference signals to the ESs, reducing the communication quality of the eavesdropping link and thus improving network security. There are N t The satellites are evenly distributed around a point with the Earth's center (0,0,0) as the origin and a radius of R. t =R e +a t spherical D t Above, where t∈{s,k}, t is s, representing satellite LS, t is k, representing satellite ES, a t R is the altitude of the satellite above the ground. e The sphere on which the satellite lies, with a radius of Earth (approximately 6371 km), is represented in spherical coordinates as: Where ρ, θ and Let represent the radial distance, geocentric angle, and azimuth angle, respectively. When t is s, D s It is a sphere on which LS is distributed, with radius R. s The height above the ground is a s When t is k, it represents D. k It is the sphere on which ES is distributed, with radius R. k The height above the ground is a k The locations of the satellite, ground relay nodes (RBs), and user nodes (UEs) are modeled as three independent homogeneous Poisson point processes, denoted as Φ. t Φ R and Φ U Its spatial density is λ. t , λ R and λ U And satellite and ground relay x i The location follows a homogeneous Poisson point process (HPPP) with a Ф t ∈{s tj} and Ф R ∈{x i} point process, where s tj Let j be the j-th satellite within the legal or eavesdropping sphere, where j = 0, 1, ..., N. t i = {0, 1, ...} and their densities are λ. t and λ R When i = 0, the ground relay nodes RBs are serving relay nodes RBs.

[0070] The AN technology-based satellite-ground fusion network physical layer secure transmission method based on the satellite-ground fusion network system model based on artificial noise technology comprises the following steps:

[0071] Step one, collect multiple parameters in the satellite-ground fusion network, specifically including the number of eavesdropping satellites, the number of legal satellites, the maximum distance of relaying and serving user communication, the height of satellite from the ground, the power of service user signal transmission, the fading index of satellite-to-ground link channel, etc.

[0072] Step two, construct a channel model, and determine the U-R ground link signal power and the R-S air link signal power according to the channel model, calculate the surface area of any spherical cap according to the model geometric relationship, and then combine the HPPP theorem to derive the satellite contact angle distribution function, the service relay distance distribution, the satellite network visibility probability and the ground relay network visibility probability.

[0073] 1. The signal is sent by the service UE to the service relay RBs, and then forwarded to the terminal satellite by the service relay RBs. The signal power expression received at the service relay RBs and the terminal LS is determined by the wireless channel model, and the wireless channel model is composed of path loss gain, small-scale fading model and antenna gain. When considering the small-scale fading model of the ground link channel, Nakagami-m fading is often used as the small-scale fading model of the ground link because Nakagami-m fading can flexibly describe the characteristics of different fading environments. When m = 1, the Nakagami-m channel is equivalent to the Rayleigh channel, and the greater the m represents the more serious the fading degree. The cumulative probability distribution function (CDF) and the probability density function (PDF) of the square of the fading index are as follows:

[0074]

[0075]

[0076] In the formula, CDF is the cumulative probability distribution function (CDF) of the square of the fading index, m is the fading parameter and is an integer, and σ is the average channel power gain, which is generally set to σ = 1. 2 PDF is the probability density function (PDF) of the square of the fading index, and Γ(m) is the Gamma function. 2

[0077] ​​​​In the S-R air link, considering shadowed Rician fading as the small-scale fading model of the air link satellite transmission channel, which is widely applicable to the research and analysis of satellite communication, through the simulation of multipath propagation and other complex environments, the performance of satellite communication can be comprehensively understood, represents the channel fading exponent square of RBs and satellite S, if the channel adopts shadowed Rician fading model, The CDF of is:

[0078]

[0079] Where b0, m, ξ are SR fading coefficients, Γ(·) is the gamma function, (m)n=Γ(m+n) / Γ(m) is the Pochhammer symbol, and Υ(·) is the incomplete gamma function.

[0080] The receiving antenna gain of the service relay RBs and the transmitting antenna gain of the service UE are both simplified to 1, and all user UEs transmit signals with the same constant power P U The service relay RBs antenna adopts interference coordination technology to approximately eliminate the interference of other users, therefore, the signal power received by the service relay RBs from the service UE, i.e. the U-R ground link signal power, satisfies:

[0081]

[0082] In the formula, ρ i is the signal power received by the i-th relay node RBs from the service UE, (R i ) -ν is the path loss gain of the ground channel, v is the path loss exponent of the ground channel, is the Nakagami-m fading exponent square.

[0083] The service relay RBs adopts a threshold-based DF decoding and forwarding protocol, when the SNR of the U-R link is greater than a set threshold β U-R , it indicates that the service UE can successfully transmit the signal to the service RBs, therefore, the signal power received by the satellite from the service relay RBs, i.e. the R-S air link signal power, satisfies:

[0084]

[0085] In the formula, ρ tj,0 is the signal power received by the j-th satellite at the t-th layer from the service relay RBs, β U-R is the threshold of the SNR at the ground RBs, and φ(β U-R) indicates whether the serving relay RBs can decode the signal of the serving UE, φ(β U-R ) = 1 if the serving UE can successfully transmit the signal to the serving relay RBs and then forward to the satellite after successfully decoding at the serving relay RBs; otherwise, φ(β U-R ) = 0 if the signal fails to decode at the relay; P R is the constant power transmitted by each ground relay, G s is the receive antenna gain, is the square of the fading exponent of the satellite-to-ground link channel, L(R tj,0 ) is the path loss gain from the jth satellite in the tth tier to the serving relay RBs;

[0086] The signal power received by the satellite from the ground interfering relay RBs is expressed as:

[0087]

[0088] where ρ tj,i / i≠0 is the signal power received by the jth satellite in the tth tier from other ground interfering relay RBs except the serving relay RBs, L(R tj,i / i≠0 ) is the path loss gain from the jth satellite in the tth tier to the other ground interfering relay RBs;

[0089] The relationship between the central angle and the distance R tj,i between the jth satellite in the tth tier and the ith relay can be obtained by the cosine law:

[0090]

[0091] where R t is the spherical radius of the satellite t distribution, R e is the radius of the earth, and θ is the central angle.

[0092] 2. Surface area of any spherical cap

[0093] The area of any satellite spherical cap D θ of the R-S air link can be obtained as:

[0094]

[0095] 3. Contact angle distribution function of the satellite

[0096] The cumulative probability distribution function (CDF) of the contact angle distribution of the serving relay RBs and the terminal LS is:

[0097]

[0098] where P[θ t,0P [0 < Θ ≤ θ] is the probability that the geodetic angle Θ is greater than or equal to the geodetic angle between satellite t and the serving RBs, P [Φ(S(D θ )) = 0] is the probability that the number of satellites inside the spherical cap D θ is 0, Φ(S(D θ )) is the number of satellites inside the spherical cap D θ that follow a point process;

[0099] The CDF is differentiated to get its probability density function (PDF):

[0100]

[0101] where λ t is the satellite distribution density of the satellite sphere of any layer, and satisfies:

[0102]

[0103] where N t is the number of satellites t;

[0104] 4. Distance distribution of serving RBs

[0105] If the distance from the serving UE to the nearest RBs is r, according to the empty probability theorem of HPPP, the probability that there is no other RBs within the range whose distance is less than r is:

[0106] P [Φ R | B(0, r) = 0] = exp(-λ R πr 2 );

[0107] Therefore, when the distance from the serving UE to the nearest RBs is R b , the CDF of R b is:

[0108]

[0109] where P [R b ≤ r] is the probability that the distance from the serving UE to the nearest RBs is less than or equal to the distance from the serving UE to the nearest RBs, and P [R b > r] is the probability that the distance from the serving UE to the nearest RBs is greater than the distance from the serving UE to the nearest RBs;

[0110] The derivative of the formula is:

[0111]

[0112] 5、For data transmission and secure communication, neither the satellite's visibility can be achieved, therefore, the satellite's visibility probability is defined as the probability that at least one satellite can communicate with the service RBs in the visible area of the service RBs, since s Subject to homogeneous Poisson point process HPPP, the probability of the legal satellite LS visibility can be obtained by using its theorem:

[0113]

[0114] In the formula, Ρ s,vis is the visibility probability of the legal satellite terminal LS, R s is the spherical radius of the terminal LS distribution, λ s is the density of the point process Φ s which the legal layer LS position distribution is subject to.

[0115] Since the relay node RBs is subject to uniform Poisson point process Φ R , the number of RBs in the A0 area is λ R A0, the probability that at least one relay node RBs can communicate with the service UE in the visible area of the service UE:

[0116]

[0117] In the formula, Ρ 0,vis is the visibility probability of the service relay RBs, Ρ[Φ R |B(0,R Z )>0] is the probability that there is no other relay node RBs within the range B(0, R Z )>0 with a distance less than R Z , λ R is the density of the point process Φ R which the relay RBs position distribution is subject to.

[0118] Step three, according to the U-R ground link signal power, R-S air link signal power, visibility probability to determine the U-R ground link user equipment received signal to noise ratio (SNR) and air R-S link relay RBs at the signal to interference noise ratio (SINR), and according to the satellite's contact angle distribution function and the distance distribution of the service relay to Laplace transform;

[0119] 1、U-R ground link SNR performance

[0120] In the communication system of the uplink satellite ground fusion relay network, first, the service UE establishes a link with the nearest relay RBs (i.e. service RBs) for communication, and the receiving antenna of the relay RBs uses interference coordination technology to approximately eliminate the interference of other UEs to the relay, then the signal to noise ratio SNR received by the service RBs is expressed as follows:

[0121]

[0122] where ρ0is the signal power of serving RBs, N0is the noise power generated by serving RBs devices;

[0123] 2. R-S air link SINR performance

[0124] The SINR performance of two satellite communication links, i.e., the terminal LS and the eavesdropping satellite ES, is considered, and the AN technique is adopted by the ground relay nodes RBs to improve the security of the network, i.e., the CSI of the eavesdropping satellite ES is known, and the relay nodes RBs transmit the secret effective information to the LS accurately by using the directional beamforming technique, and the transmit power of the relay nodes RBs is Ρ R is divided into two parts: one part ΥΡ R is allocated to transmit the secret effective information, and (1 - Υ)Ρ R is used to transmit the (artificial noise) AN information, Υ is called the information-bearing ratio, Υ ∈ (0, 1), and when Υ = 1, it means that the AN technique is not used, and all the transmit power of the relay nodes RBs is used for effective signal transmission.

[0125] For the serving relay, only the terminal LS is connected in the legal layer to communicate, and then ρ tj,i in the formula can be directly omitted, because the terminal LS only receives the effective secret information, and the terminal LS will automatically filter out the AN artificial noise part, and therefore the SINR received by the terminal LS is:

[0126]

[0127] where I LS is the aggregate interference power generated by the ground interfering relay nodes RBs to the terminal LS, N0is the noise power generated by the satellite devices;

[0128] where the aggregate interference power generated by the ground interfering relay nodes RBs to the terminal LS is:

[0129]

[0130] where ρ s,i is the signal power of the ground interfering relay nodes RBs received by the terminal LS.

[0131] Since the eavesdropping satellite ES not only receives the effective information but also receives the AN noise part, the eavesdropping satellite ES cannot filter out the AN noise part, and therefore the SINR received by the eavesdropping satellite ES is represented as:

[0132]

[0133] where ρ k,0 is the power signal of the service RBs received by the eavesdropping satellite ES, I ES is the aggregate interference power generated by the interfering RBs to the ES, and satisfies:

[0134]

[0135] where ρ k,i is the signal power of the ground interfering RBs received by the eavesdropping satellite ES.

[0136] 3. Laplace transform

[0137] The randomness caused by the aggregate interference is described by the Laplace transform (LT) of the interference, which helps to analyze the network performance and lay a theoretical foundation for the subsequent derivation of the security performance of the satellite network. Given that the spatial location distribution of the relay devices follows HPPP, the LT of the aggregate interference suffered by the terminal LS is derived in combination with the network model as follows:

[0138]

[0139] where is the mean value of the formula containing the random variable , and thus the CDF of and the density function of the point process Φ R to which the relay RBs are subjected will be used in the subsequent derivation of the formula.

[0140] Similarly, the LT of the aggregate interference obtained by the eavesdropping satellite ES is transformed as follows:

[0141]

[0142] where is the mean value of the formula containing the random variable , and thus the CDF of and the density function of the point process Φ R to which the relay RBs are subjected will be used in the subsequent derivation of the formula, θ k,max is the maximum central angle of the sphere in which the eavesdropping layer ES satellite is located, n is the variable of the Laplace transform, κ and β are the Gamma parameters after the SR fading distribution is approximated as a Gamma distribution, and l0 is the path loss coefficient, which is expressed as:

[0143] The replacement formula is as follows:

[0144]

[0145] l0 = (c / 4πf c )2 ;

[0146] wherein c is the speed of light, f c is the carrier frequency.

[0147] Step four, transmitting the data to be transmitted according to the maximum security transmission probability;

[0148] The security transmission probability of the uplink HSTRN system is the success transmission probability of the LS and the confidentiality interrupt probability of the ES:

[0149] 1. Success transmission probability

[0150] When the signal-to-noise ratio SNR at the U-R ground link service relay is greater than the threshold β U-R of the SNR at the ground RBs, it means that the signal can be successfully transmitted from the serving UE to the ground service relay, and after successful decoding at the service relay RBs, the information is retransmitted to the terminal LS, and the R-S air link also needs to meet certain communication channel conditions, that is, the SINR received by the terminal LS is greater than the threshold β LS of the SINR at the air LS, so that the signal can be successfully transmitted between the serving UE and the terminal LS. Therefore, the success transmission probability is defined as the successful establishment of communication between the serving user equipment and the nearest terminal LS, that is, the visibility of the relay and the satellite in the R-U link and the R-S link and the channel quality of the link are met at the same time, and the table is shown as follows:

[0151]

[0152] wherein P s,suc is the success transmission probability, is the success transmission probability of the U-R link, is the success transmission probability of the R-S link;

[0153] The success transmission probability of the U-R link needs to meet the following conditions: ① There is at least one relay node RBs in the visibility range of the serving user UE; ② The SNR at the service relay RBs is higher than the set threshold β U-R , which is expressed as:

[0154]

[0155] wherein P(SNR RU ≥β U-R ) is the probability that the SNR at the service relay RBs is higher than the set threshold β U-R , SNR RU is the signal-to-noise ratio received by the service relay RBs;

[0156] The SNR at the service relay RBs is higher than the set threshold β U-RThe expression of the probability that

[0157]

[0158] where, is the expression of the PDF of the random variable R b , the PDF function of R b will be substituted in the following formula derivation, λ R is the spatial density of the point process Φ R that the serving relay RBs obey, r is the distance from the serving UE to the nearest serving relay RBs, R Z is the coverage radius of the serving UE, P U is the transmission power of the serving UE, and g is an intermediate parameter, g! is the factorial of g.

[0159] The success transmission probability of the R-S link needs to satisfy the following conditions: ① there is at least one LS in the visible range of the serving relay RBs; ② the SINR at the terminal LS is higher than the set threshold β LS , which is expressed as:

[0160]

[0161] where, P(SINR LS ≥ β LS ) is the probability that the SINR at the legal LS is higher than the set threshold β LS , SINR LS is the SINR received by the terminal LS, and β LS is the threshold of the SINR at the air LS;

[0162] The expression of the probability that the SINR at the legal LS is higher than the set threshold β LS

[0163]

[0164] where, is the expression of the PDF of the random variable I LS , θ s,0 , the Laplace transform of I LS and the PDF function of θ s,0 will be substituted in the following formula derivation, κ is the Gamma parameter after the SR fading distribution is approximated as a Gamma distribution, and the SR fading parameter is replaced, and the following is the replacement formula: l is an intermediate variable, which is only a variable of the cumulative symbol, and is added from l = 1 to κ, and the following derivation will not have this symbol after l is removed, θ s,max is the maximum geodetic angle of the terminal LS, is a first intermediate variable,​ Laplace transform LTs of the aggregate interference experienced by the terminal LS, probability density function of the contact angle distribution of the terminal LS;

[0165] The satellite antenna adopts the directional beam forming technology of fixed beam, the satellite beam points to the center of the earth, and the width angle of the receiving beam is represented as 2Ψ max , assuming that only the satellite with line-of-sight link established with the relay node RBs device can communicate, the maximum geocentric angle θ t,max can be represented by the half angle of the satellite beam width Ψ max :

[0166]

[0167] In the formula, θ t,max is the maximum geocentric angle of the satellite t, and Ψ max is the half beam width angle of the satellite;

[0168] The first intermediate variable satisfies:

[0169]

[0170] In the formula, β is the Gamma parameter after the SR fading distribution is approximated as a Gamma distribution, and the SR fading parameter is replaced as follows: l0 is the path loss coefficient, and is represented as: l0=(c / 4πf c ) 2 , where c is the speed of light, f c is the carrier frequency, Y is the information carrying ratio, and Y∈(0,1), (R s,0 ) -υ (θ) is the-υ power of the distance between the terminal LS and the serving RBs.

[0171] Based on the AN technology, in the uplink satellite-ground fusion relay network communication scenario, the successful transmission probability of the satellite network is:

[0172]

[0173] 2. The probability of secret interruption

[0174] In addition to ensuring the successful transmission of communication, the calculation of the secret interruption probability is crucial in analyzing the security performance of the network. The secret interruption probability is the probability that the serving relay successfully receives the signal from the service user and successfully forwards the signal to the eavesdropping satellite ES, that is, it satisfies the successful transmission of the U-R ground link. Secondly, the SINR of any potential eavesdropping satellite ES is lower than the threshold value β ESTherefore, the secrecy outage probability of uplink HSTRN can be expressed as

[0175]

[0176] where P(SINR ES <β ES ) is the probability that the SINR at the eavesdropper ES is lower than a given threshold β ES , SINR ES is the received SINR at the eavesdropper ES, and β ES is the threshold of SINR at the eavesdropper ES.

[0177] The expression of the probability that the SINR at the eavesdropper ES is lower than a given threshold β ES is given by

[0178]

[0179] where θ k,max is the maximum geocentric angle of the eavesdropper ES, R is the second intermediate variable, is the Laplace transform LTs of the aggregate interference at the eavesdropper ES, f is the probability density function of the contact angle distribution of the eavesdropper ES, and R k is the spherical radius of the eavesdropper distribution.

[0180] The second intermediate variable satisfies

[0181]

[0182] where (R k,0 ) -υ (θ) is the -vth power of the distance between the terminal ES and the serving RBs.

[0183] Based on the AN technique, the closed-form expression of the secrecy outage probability of satellite networks in the uplink satellite-ground hybrid relay network is given by

[0184]

[0185] 3. Secure transmission probability

[0186] The secure transmission probability is expressed by the product of two key probabilities:

[0187]

[0188] From the above equations, we have

[0189]

[0190] In the formula, The probability of secure transmission is used to characterize the physical layer security performance of satellite networks; P s,suc To determine the probability that the UE will successfully transmit the signal to the terminal node LS, P out The probability that valid information is interrupted at all eavesdropping satellites (ES);

[0191] In this embodiment, the threshold β of SNR at the ground RBs U-R The threshold β of SINR at the air LS is -20dB. LS The threshold β of SINR at the eavesdropping satellite ES ES The values ​​are -30dB and -10dB respectively, and the receiving antenna gain is a fixed value of 41.9dBi.

[0192] The secure transmission performance of the model established in this invention was simulated using Matlab, with the relay device distribution density λ. R 10 -6 km -2 The radius R of the relay visible area disk Z The satellite beamwidth is 2km, and the half-angle ψ max The number of satellites is π / 3, N t The user transmits at a constant power P of 500. U It is 23 dBi.

[0193] like Figure 3 As shown, compared to other altitudes of legitimate satellites and eavesdropping satellites, when the altitude of a legitimate satellite (a s When the altitude is 500km, the altitude of the eavesdropping satellite (a) k When the distance is 800km and the signal-to-carrier ratio Y is constant, what is the probability of secure transmission? The larger Υ is. When Υ approaches 0, It can approach the maximum when Υ increases to 1. It also decreases to near 0. However, Υ cannot be 0, which strictly means that no information is sent. The probability of secure transmission can be considered to be the highest "in form," but at this point, the communication system does not transmit any valid data. Therefore, by Figure 3 It can be seen that selecting a signal-to-carrier ratio (Y) in the range of 0-0.1 can achieve a secure transmission probability of nearly 90%, providing guidance for real-world scenarios.

[0194] like Figure 4 As shown, with different numbers of satellites (N) t Under the condition that the AN information carrying ratio (Y) affects the probability of secure transmission ( The influence of the number of satellites on the security transmission probability is analyzed. The results show that the security transmission probability can reach the maximum value when the number of satellites is 500, the signal-to-interference ratio is in the range of 0-0.1, and the height of the legal satellite is 500 km.

[0195] The application discloses a satellite-ground fusion network physical layer security transmission method based on AN technology, which comprises the following steps: firstly, the surface area of an arbitrary spherical cap is calculated according to the geometric relationship of the model, and then the contact angle distribution function of the satellite and the distance distribution of the service relay are derived by combining the HPPP theorem; secondly, the visible probability of the satellite network and the visible probability of the ground relay network are derived according to the random geometry theory, and the signal-to-noise ratio (SNR) received by the user equipment of the U-R ground link, the signal-to-interference noise ratio (SINR) at the relay RBs of the R-S air link and the Laplace transform of the aggregate interference of the S-R air link are analyzed; finally, the closed expression of the successful transmission probability, the security interruption probability and the final security transmission probability of the network are derived, and the maximum value of the security transmission probability can be obtained by adjusting the appropriate information carrying ratio under the condition that other parameters (for example, the height, density and beam width of the satellite antenna) remain unchanged, so that the high complexity of the dynamic topology processing, the cumulative interference analysis and the performance evaluation is solved.

[0196] Although the embodiments of the application have been disclosed as above, they are not limited to the application listed in the specification and the embodiments, and can be fully applied to various fields suitable for the application, and other modifications can be easily realized by those skilled in the art, therefore, the application is not limited to the specific details and the embodiments shown and described herein, and the application is not limited to the specific details and the embodiments shown and described herein.

Claims

1. A secure transmission method for the physical layer of a satellite-ground fusion network based on artificial noise (AN) technology, characterized in that, Includes the following steps: Step 1: Collect data on the number of eavesdropping satellites, the number of legitimate satellites, the maximum distance between relay and service users, the altitude of satellites above the ground, the power of signals transmitted by service users, and the fading index of the satellite-to-ground link channel; Step 2: Based on the channel model and homogeneous Poisson point process, calculate the UR ground link signal power, RS air link signal power, satellite contact angle distribution probability density function, serving relay distance distribution probability density function, satellite network visibility probability, and ground relay network visibility probability. Wherein, UR refers to the transmission between the user as the source node UE and the serving relay RBs, and RS refers to the transmission between the serving relay RBs and the satellite as the terminal node S; Step 3: Determine the signal-to-noise ratio (SNR) received by the UR ground link service relay RBs and the signal-to-interference-plus-noise ratio (SIR) received by the legitimate satellite LS and the eavesdropping satellite ES in the RS air link based on the UR ground link signal power, RS air link signal power, and visibility probability, and then perform a Laplace transform. Step 4: Transmit the data to be transmitted based on maximizing the probability of secure transmission. Wherein, the secure transmission probability satisfies: In the formula, For secure transmission probability, P s,suc P represents the probability of successful transmission in a satellite network. out This represents the probability of a security breach in a satellite network.

2. The secure transmission method for the physical layer of a satellite-to-ground fusion network based on artificial noise (AN) technology as described in claim 1, characterized in that, The UR ground link signal power satisfies: In the formula, P U To serve the UE's transmit power, (R i ) -ν Let v be the path loss gain of the ground channel, and v be the path loss exponent of the ground channel. The square of the Nakagami-m fading exponent; The RS air link signal power satisfies: In the formula, ρ tj,0 Let β be the signal power received by the j-th satellite in layer t from the serving relay RBs. U-R The threshold for SNR at ground RBs is φ(β). U-R This indicates whether the serving relay (RBs) can decode the signal of the serving UE. R For each ground relay transmission, the constant power, G s For receiving antenna gain, L(R) is the square of the fading exponent of the satellite-to-ground link channel. tj,0 ρ is the path loss gain from the j-th satellite in layer t to the serving relay RBs. tj,i / i≠0 Let L(R) be the signal power received by the j-th satellite at layer t from other ground interference relay RBs besides the serving relay RBs. tj,i / i≠0 ) represents the path loss gain from the j-th satellite in layer t to other ground-based interference relays RBs.

3. The secure transmission method for the physical layer of a satellite-to-ground fusion network based on artificial noise (AN) technology as described in claim 2, characterized in that, The contact angle distribution probability density function of the satellite is: In the formula, λ t The point process Φ follows the position distribution of satellite t. t The density, R t N is the origin of the Earth. t The sphere radius of the evenly distributed satellites, t∈{s,k} means that t=s represents a legitimate satellite LS, t=k represents a listening satellite ES, and θ represents the geocentric angle; The probability density function of the service relay distance distribution is: f Rb (r)=2pl R exp(-pl R r 2 ); In the formula, r is the distance from the serving UE to the nearest relay node RBs, and λ R The location distribution of relay RBs follows a point process Φ R The density.

4. The secure transmission method for the physical layer of a satellite-ground fusion network based on artificial noise (AN) technology as described in claim 3, characterized in that, The visibility probability of the satellite network satisfies: In the formula, Ρ s,vis R is the visibility probability of a legitimate satellite LS. s Let λ be the radius of the sphere on which the legitimate satellite LS is distributed. s The point process Φ is the position distribution of legal satellite LS. s density, cosθ s,max The cosine of the maximum geocentric angle of the legitimate satellite LS; The visibility probability of the ground relay network satisfies: In the formula, Ρ 0,vis For the visibility probability of service relay RBs, Ρ[Φ R |B(0,R Z [)>0] is the range B(0,R) Z There is no distance less than R within 0. Z The probability of other relay nodes (RBs).

5. The secure transmission method for the physical layer of a satellite-ground fusion network based on artificial noise (AN) technology as described in claim 4, characterized in that, The signal-to-noise ratio received by the relay RBs in the UR ground link service meets the following requirements: In the formula, ρ0 is the signal power of the serving relay RBs. The noise power generated by the service relay RBs equipment.

6. The secure transmission method for the physical layer of a satellite-ground fusion network based on artificial noise (AN) technology as described in claim 5, characterized in that, The signal-to-interference-plus-noise ratio (SIN / N) received by the legitimate satellite LS via the RS air link satisfies: In the formula, Υ represents the information carrying ratio, and ρ represents the information carrying capacity ratio. s,0 For the signal power received by a legitimate satellite LS from a serving relay RBs, I LS This represents the aggregated interference power generated by ground-based jamming relays (RBs) against legitimate satellites (LS). The noise power generated by satellite equipment; The signal-to-interference-plus-noise ratio received by the RS air link eavesdropping satellite ES satisfies: In the formula, ρ k,0 In order to eavesdrop on the power signals received by the Serving Relays (RBs) from the ES satellite, I ES The aggregate interference power generated by the interference RBs on the ES.

7. The secure transmission method for the physical layer of a satellite-ground fusion network based on artificial noise (AN) technology as described in claim 6, characterized in that, The Laplace transform includes: In the formula, For those containing random variables The average of the formulas is calculated. For those containing random variables The average of the formulas is calculated. The Laplace transform (LTs) of the aggregation interference experienced by legitimate satellites (LS). The Laplace transform (LTs) of the aggregated interference experienced by the eavesdropping satellite ES.

8. The secure transmission method for the physical layer of a satellite-ground fusion network based on artificial noise (AN) technology as described in claim 7, characterized in that, The probability of successful transmission by the satellite network: In the formula, The probability of successful transmission on the UR link. This represents the probability of successful transmission over the RS air link.

9. The secure transmission method for the physical layer of a satellite-ground fusion network based on artificial noise (AN) technology as described in claim 8, characterized in that, The successful transmission probability of the UR ground link satisfies: In the formula, P(SNR) RU ≥β U-R The probability that the SNR at the serving relay RBs is higher than the SNR at the ground RBs is given by the given SNR value. RU The signal-to-noise ratio received by the serving relay RBs; The successful transmission probability of the RS air link satisfies: In the formula, P(SINR) LS ≥β LS SINR is the probability that the SINR at a legitimate satellite LS is higher than the threshold of the SINR at a legitimate satellite LS. LS For the SINR received by a legitimate satellite LS, β LS The threshold for SINR at the legitimate satellite LS.

10. The secure transmission method for the physical layer of a satellite-ground fusion network based on artificial noise (AN) technology as described in claim 9, characterized in that, The probability of the satellite network's security being disrupted: In the formula, P(SINR) ES <β ES The probability that the SINR at the eavesdropping satellite ES is lower than the threshold of the SINR at the eavesdropping satellite ES is given by SINR. ES For the SINR received by the eavesdropping satellite ES, β ES The threshold for SINR at the eavesdropping satellite ES.

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