Aviation ad hoc network survivability analysis method based on information timeliness

Abstract

The invention discloses an aviation ad hoc network survivability analysis method based on information timeliness, and belongs to the technical field of wireless communication. Firstly, network information is collected to establish an aviation ad hoc network system model; secondly, based on an aviation ad hoc network system model, the peak information age is split into end-to-end transmission delay and sensing interval time of continuous and successful transmission, the average peak information age is solved, and an information timeliness analytical expression is established; thirdly, performing performance evaluation on different system parameter combinations and transmission strategies and searching for optimal parameters and transmission strategies; and finally, implementing an information transmission scheme of the aviation aircraft according to an optimization result. The method can be used for quickly evaluating whether the network survivability requirement can be met or not under a certain aviation ad hoc network scene and system parameter configuration, and finding out the optimal system parameter enabling the information age to be minimum; and the method does not depend on large-scale system-level simulation. The method has the advantages of being simple, fast and universal, and the calculation complexity and the time consumption are remarkably reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless communication, and relates to a method for analyzing the survivability of an aviation ad hoc network, in particular to a method for analyzing the survivability of an aviation ad hoc network based on information timeliness. Background Art

[0002] According to the CMU / SEI technical report (see report: Ellison, RJ; Fisher, DA; Linger, RC et al. Survivable Network System: An Emerging Discipline Technical Report, CMU / SEI-97-TR-013, ESC-TR-97-013, 1999.), network survivability refers to the ability of the network to complete tasks in a timely manner when facing attacks, failures or accidents. This is a qualitative assessment of survivability and cannot be used as a quantitative indicator to objectively evaluate whether a technology can improve network survivability performance and how much it can improve. Although some scholars have given survivability evaluation indicators and quantitative methods for wired or wireless networks, such as the mean time between failures, reliability, availability and service life of network nodes (reference: Shi Qiong, Ding Yinghua, Qin Li, et al. Research on survivability evaluation of wireless sensor networks [J]. Journal of North University of China (Natural Science Edition), 2020, 41(05): 418-430+436.) and network downtime (reference: Pietrantuono R, Ficco M, and Palmieri F. Survivability Analysis of IoT Systems Under Resource Exhausting Attacks. IEEE Transactions on Information Forensics and Security [J]. 2023, 11: 3277-3288.). So far, there is still no unified standard. It is necessary to transform the general definition of network survivability into a quantifiable and analyzable evaluation indicator based on the specific functions of the target network. For aeronautical ad hoc networks, one of its main functions is to timely and reliably exchange information with the control end or other aircraft on the environmental data perceived by the aircraft for real-time decision-making. Generally, real-time decision-making pays more attention to the latest environmental status information. However, perception data packets face various challenges during wireless transmission, such as rapid changes in network connectivity caused by dynamic topology, channel fading, co-frequency interference, malicious attacks and other non-ideal transmission factors. When information transmission fails, a backlog will occur at the source or relay node, and the receiver will not be able to obtain the latest environmental status information in time to make decisions, resulting in decision deviations and making the aeronautical ad hoc network unable to complete key services. Therefore, analyzing the timeliness of the transmission of environmental perception data is the basic premise for studying the survivability of aeronautical ad hoc networks.

[0003] In order to enhance the timeliness of information transmission, most research work focuses on improving the effectiveness of information flow, such as increasing transmission rate and reliability or reducing transmission delay. However, for end-to-end complex information networks such as aviation ad hoc networks that integrate information perception, information transmission and information processing, the problem of information timeliness is not simply equivalent to the problem of information flow effectiveness. This is because the timeliness of information depends on the difference between the current environmental state and the environmental state information used for decision-making, and is strongly correlated with the speed of environmental state change, the frequency of perception and the transmission delay of perception data in wireless networks. Specifically, if the frequency of environmental perception is higher, the more perception data the aircraft needs to transmit, the longer the cache time in the source node or relay node, the longer the time interval between the environmental state information used for decision-making at the control end and the current environmental state, and the greater the difference may be. If the transmission efficiency of the aircraft is higher, the data transmission delay is shorter, and the perception information used by the receiver for current decision-making is closer to the current environmental state. The transmission efficiency is closely related to the characteristics of wireless transmission, including wireless fading, interference and wireless bandwidth resources. However, if the frequency of environmental perception of the aircraft is low, even if the transceiver system has high transmission efficiency, it is difficult to timely transmit the environmental status information required for correct decision-making. This means that the traditional wireless transmission optimization design with transmission effectiveness and reliability as the goal cannot solve the end-to-end information timeliness problem. In response to this problem, existing studies have proposed the concept of information age to characterize the timeliness of data in the network, where information age is defined as the survival time of the latest environmental status information used for decision-making in the network since its generation, and the wireless transmission method is optimized with information age as the goal (reference: Kaul S, Yates R and Gruteser M. Real-time status: How often should one update? [C] / / 2012 Proceedings IEEE INFOCOM, Orlando, 2012: 2731-2735.). Therefore, the survival time of the circulating information is used as a quantitative indicator of the network's survivability in the aeronautical ad hoc network, where the smaller the information age, the more timely the information transmission, and the closer the environmental status information used for decision-making is to the actual environment. If the information age is always greater than a certain threshold, it means that the AMANET cannot transmit the latest perceived environmental information to the control end in a timely manner, thus causing decision-making deviation. However, in the study of the impact of wireless transmission characteristics on information timeliness, most existing works use highly abstract transmission models, such as error-free channels, erasure channels, Markov channels, and information concurrency models based on "conflicts" to simply characterize, ignoring the important impact of key physical layer factors such as the topological change characteristics of AMANETs, ​​wireless channel propagation characteristics, and co-channel interference on information timeliness.

[0004] Based on this, the present invention proposes to use information age to characterize the end-to-end network survivability of information perception, transmission and processing in aeronautical ad hoc networks, and at the same time constructs an aeronautical ad hoc network survivability analysis method based on random geometry and queuing theory, which considers key factors such as the spatial topology of aeronautical ad hoc networks, the time-varying characteristics of environmental perception, the transmission characteristics of wireless channels, and co-frequency interference. The analytical method proposed in the present invention can be used to quickly evaluate whether a certain aeronautical ad hoc network scenario and system parameter configuration can meet the network survivability requirements, and find the optimal system parameters that minimize the information age.

[0005] This invention is supported by the Aeronautical Science Foundation of China (2022Z001063001). Summary of the invention

[0006] Most of the existing network survivability research focuses on the problem of effective transmission of information in the network, ignoring that the aeronautical ad hoc network is an end-to-end complex network that integrates information perception, transmission and processing decisions. In response to the above problems, the present invention proposes an aeronautical ad hoc network survivability analysis method based on information timeliness, where the information age is the survival time of the perception data that has been successfully received by the receiving end and used for decision-making to characterize the information timeliness. Specifically, random geometry and queuing theory are used to model the spatial topological characteristics of the aeronautical ad hoc network and the time-varying characteristics of the environment perception of the aircraft node, respectively, and the path loss model and small-scale fading model in the wireless channel model are introduced to establish a mapping relationship between the information age and the frequency of information perception, the quality of the transmission link, etc., and a theoretical analytical expression of the information age is given to evaluate the network survivability and optimize the system parameters.

[0007] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0008] A method for analyzing the survivability of an aeronautical ad hoc network based on information timeliness. The method first collects network information to establish an aeronautical ad hoc network system model, including an aeronautical ad hoc network spatial topology model, a transmitter's environmental information perception model, a data packet scheduling and transmission model, and a wireless channel model. Secondly, based on the established aeronautical ad hoc network system model, the peak information age is split into end-to-end transmission delay and the perception interval time of continuous successful transmission to solve the average peak information age and establish an information timeliness analytical expression. Thirdly, the performance of different system parameter combinations and transmission strategies is evaluated and the optimal parameters and transmission strategies are found. Finally, based on the optimization results, the information transmission plan for the aircraft is implemented. The following steps are included:

[0009] Step 1: Information collection and model building;

[0010] Step 1.1, collect information: Depending on the source of information, the information collection process mainly includes three steps:

[0011] (1) Aircraft configuration information, including communication time slot length T s , environmental information perception frequency ζ, perception data packet size K, communication bandwidth W, and scheduling probability p of data packet transmission.

[0012] (2) Aircraft transceiver interaction information, including the relative distance r0 between the aircraft transceivers.

[0013] (3) The aircraft obtains other system information through the network or the ground control center, including aircraft density λ, aircraft average altitude H, and earth radius R earth , normalized noise power σ n 2 And the path loss model of the air link. The path loss model of the air link is l(r)=r -α , where α is the path loss exponent and r is the propagation distance traveled by the wireless signal.

[0014] Step 1.2, establish the aviation ad hoc network system model, including the following five steps:

[0015] Step 1.2.1: Establish the spatial topology model of the aviation ad hoc network. Specifically, based on the collected aircraft density λ, the earth radius R earth and the aircraft height information H, the spatial position distribution of the aircraft node is modeled as distributed in a radius of R = R earth +H sphere Poisson point process model Φ, and the density of the Poisson point process is the same as the aircraft density λ.

[0016] Step 1.2.2: Establish a wireless channel model. Specifically, use the power rate function l(r)=r -α The path loss of the modeled signal, where α is the path loss exponent and r is the propagation distance of the wireless signal. Small-scale channel fading is modeled as Rayleigh fading, and the small-scale channel power fading factor follows an exponential distribution.

[0017] Step 1.2.3: Establish the transmitter's environmental information perception model. Specifically, based on the collected communication time slot length T s , environment sensing frequency ζ and sensing data packet size K bits, consider a discrete transmission system with equal time slots, where the time slot length is T s , the perception data process is modeled as an independent Bernoulli arrival process, where the arrival rate of the perception data packet is the same as the environment perception frequency ζ, that is, at the starting boundary of each time slot, the aircraft perceives the environment with probability ζ and generates a data packet with K information bits, and assigns a timestamp to each data packet and stores it in the cache queue.

[0018] Step 1.2.4, establish a data packet scheduling model. Specifically, each aircraft adopts the first-come-first-served principle to transmit the first data packet in the cache queue. If the aircraft's cache queue is not empty, the first data packet in the queue is sent at the starting boundary of the time slot with a scheduling probability p, that is, the sending probability of the data packet.

[0019] Step 1.2.5, establish a data packet transmission model. Specifically:

[0020] If the data packet is successfully transmitted, the receiver feeds back a confirmation signal, i.e., an ACK signal, to the transmitter. The transmitter then removes the successfully transmitted data packet from the cache queue, and the receiver makes a decision based on the most recently received perception data packet. The successfully transmitted data packet refers to the link capacity C = Wlog(1+SINR) from the transmitter x0 to the receiver y0 in a time slot length T s The size of the data packet is K bits, that is, C×T s >K, where represents the signal-to-interference-to-noise ratio of the link; r0 represents the relative distance of the aircraft transceiver; |x-y0| represents the distance from the interference transmitter x to the receiver y0; Φ represents the topological model of the aeronautical ad hoc network; Ω is the visible area formed by the earth blocking the receiver y0; and h x represent the small-scale channel power attenuation factors from transmitter x0 and interference transmitter x to receiver y0 respectively; l(r0) and l(|x-y0|) represent the path losses from transmitter x0 and interference transmitter x to receiver y0 respectively; B x Q is a Bernoulli random variable with probability p being 1 and probability 1-p being 0 indicating whether transmitter x sends data; x represents the number of packets in the buffer queue of transmitter x; represents the normalized noise power.

[0021] If the data packet transmission fails, C×T is not satisfied. s >K, the receiver feeds back a NACK signal to the transmitter and still makes decisions based on the last successfully received perception data packet, while the transmitter decides whether to remove the unsuccessfully transmitted data packet from the buffer queue based on the specific transmission strategy.

[0022] Furthermore, the transmission strategies include a no-retransmission strategy, an infinite retransmission strategy, and a retransmission strategy based on a maximum number of retransmissions, wherein when a no-retransmission strategy is adopted, a data packet is removed from the cache queue after a transmission failure; when an infinite retransmission strategy is adopted, a data packet is continuously retransmitted after a transmission failure until it is successfully transmitted and then removed from the cache queue; when a retransmission strategy based on a maximum number of retransmissions is adopted, a data packet is retransmitted after a transmission failure and the number of retransmissions is recorded, and if the number of retransmissions of the data packet is greater than the preset maximum number of retransmissions, it is removed from the cache queue.

[0023] Step 2: Establish an analytical expression for information timeliness;

[0024] Based on the aviation ad hoc network system model established in step 1.2, the analytical expression of information timeliness is established by solving the average peak information age, including solving the average end-to-end transmission delay and the average perception interval time of continuous successful transmission; the details are as follows:

[0025] In order to reflect the boundary characteristics of environmental information timeliness in the aeronautical ad hoc network, the present invention uses the Peak Age of Information (PAoI) to characterize the information timeliness in the worst case of the network, which is defined as the highest information age value that the current data packet can reach when the next data packet is successfully transmitted, that is, the maximum survival time of the data packet in the aeronautical ad hoc network (reference: Inoue Y, Masuyama H, Takine T, et al. A general formula for the stationary distribution of the age of information and its application to single-server queues [J]. IEEE Transactions on Information Theory, 2019, 65 (12): 8305-8324.). If the indexes n and m are two consecutive successfully transmitted data packets, based on the process that the data packet has gone through in the aeronautical ad hoc network, the PAoI can be split into two parts that are easy to analyze theoretically, as shown below:

[0026] A n =(d m -a m )+(a m -a n )

[0027] Among them, A n represents the peak information age of the nth packet, a n and a m represents the perception time of the nth and mth data packets of the aircraft; dn and d m They respectively represent the time points when the nth and mth data packets of the transmitter are successfully transmitted.

[0028] The expected peak information age PAoI is calculated to obtain the average peak information age, which is expressed as in, represents the expected operation of a random variable; D m =d m -a m represents the end-to-end transmission delay of a successfully transmitted data packet (data packet m), that is, the time period from the moment the data packet is sensed and generated until the data packet is successfully transmitted; X inter =a m -a n It indicates the perceived time difference between two consecutive successful transmissions of data packets (data packet n and data packet m) by the transmitter.

[0029] Therefore, the average peak information age can be converted into the average end-to-end transmission delay of the packet: and the average perceived interval between consecutive successful transmissions

[0030] Step 2.1: Calculate the average end-to-end transmission delay

[0031] The end-to-end transmission delay of a perceived data packet refers to the difference between the time it arrives at the transmitter and the time it is successfully transmitted to the receiver. It is related to the scheduling and transmission model of the transmitter. The present invention analyzes and solves it through queuing theory. The details are as follows:

[0032] Step 2.1.1, first, according to the environmental information perception model of the transmitter in step 1.2, the arrival process of the data packet obeys a Bernoulli random process.

[0033] Step 2.1.2, secondly, according to the scheduling and transmission model of the data packet in step 1.2, the service process of the data packet leaving the transmitter queue is related to the scheduling strategy of the transmitter, the transmission strategy of the data packet and the probability of successful transmission. At this time, the transmission process of the perception data can be modeled as a Geo / Geo / 1 queue model, where the arrival rate is ζ∈(0,1], that is, the environmental information perception frequency, and the service rate is pP del , where p∈(0,1] is the probability of sending a packet in each time slot, P del ∈(0,1] is the probability of a packet being removed from the queue in a time slot.

[0034] Step 2.1.3, finally, according to the queuing theory, the average end-to-end transmission delay is obtained as:

[0035] When pPdel >ζ, the average end-to-end transmission delay is When pP del When ≤ζ, then Where, ζ represents the frequency of environmental information perception; T s represents the length of the communication time slot; p represents the probability of sending a data packet in each time slot; P del is the probability of a packet being removed from the queue in a time slot; (Reference: Atencia I and Moreno P. A discrete-time GEO / G / 1 retrial queue with general retrial times [J]. Queueing Systems, 2004, 48: 5-21.)

[0036] Furthermore, the removal queue probability P del It is related to the specific transmission strategy, as follows:

[0037] When the transmitter adopts the no-retransmission strategy, the probability of packet removal from the queue is P del =1.

[0038] When the transmitter uses an infinite retransmission strategy, the probability of a packet being removed from the queue is P del , and the iterative method is used to solve it. Specifically, let the initial value of the probability of successful packet removal from the queue be M (0) =1, and use the following formula for iterative calculation:

[0039]

[0040] Until the condition is met|M (k+1) -M (k) |≤ε, where ε is the preset convergence threshold, for example, ε=10 -6 ; k = 0, 1, 2…; R earth is the radius of the earth; R is the radius of the sphere where the aviation is located; K represents the bit size of the data packet; W is the communication bandwidth; T s is the communication time slot length; r0 represents the relative distance of the aircraft transceiver; p represents the probability of data packet transmission of the transmitter; represents the normalized noise power; α represents the path loss index; λ represents the aircraft density. Let M ε It represents the convergence value of the removal probability calculated by the above iterative method, that is, P del =M ε .

[0041] When the transmitter adopts a retransmission strategy based on the maximum number of retransmissions, the probability of a packet being removed from the queue is Where Nmax is the maximum number of retransmissions, is the probability of successful transmission of a data packet, and is solved by an iterative method. Specifically, let the probability of successful transmission be The initial value is M (0) =1, and use the following formula for iterative calculation:

[0042]

[0043] Until |M (k+1) -M (k) |≤ε, where ε is the preset convergence threshold, for example, ε=10 -6 ; k = 0, 1, 2…; R earth is the radius of the earth; R is the radius of the sphere where the aircraft is located; K represents the bit size of the data packet; W is the communication bandwidth; T s is the communication time slot length; r0 represents the relative distance of the aircraft transceiver; p represents the probability of data packet transmission of the transmitter; represents the normalized noise power; α represents the path loss index; λ represents the aircraft density. Let M ε represents the convergence value of the successful transmission probability calculated by the above iterative method, that is, Solve the probability of removing the packet from the queue as P del =1 / N max +(N max -1) / N max M ε .

[0044] Step 2.2: Calculate the average perceived interval time of continuous successful transmission

[0045] The perception time interval for consecutive successful transmissions is X inter First, under the given aeronautical ad hoc network topology Φ, the perception time interval X of continuous successful transmission inter The conditional probability distribution of is a geometric distribution, and then the perception time interval X of consecutive successful transmissions inter The conditional mean of the expected operation on the topology Φ of the aeronautical ad hoc network is used to solve the average perception interval time of continuous successful transmission in Represents the expectation operation on a random variable.

[0046] Furthermore, the average perception interval time of the continuous successful transmission is related to the specific transmission strategy, which is as follows:

[0047] When the transmitter adopts a no-retransmission strategy, the solution is

[0048]

[0049] where F(·) is the Gaussian hypergeometric function (reference: Gradshteyn I and Ryzhik I. Table of integrals, series, and products seventh edition [M]. Academic Press, 2007); R earth is the radius of the earth; R is the radius of the sphere where the aircraft is located; K represents the bit size of the data packet; W is the communication bandwidth; T s is the communication time slot length; r0 represents the relative distance of the aircraft transceiver; represents the normalized noise power; α represents the road loss index; ζ represents the environmental information perception frequency; λ represents the aircraft density.

[0050] When the transmitter adopts an infinite retransmission strategy, the solution is

[0051] When the transmitter adopts a retransmission strategy based on the maximum number of retransmissions, the solution is

[0052]

[0053] in, Indicates from mN max The number of combinations of k elements taken from different elements; R earth is the radius of the earth; R is the radius of the sphere where the aircraft is located; K represents the bit size of the data packet; W is the communication bandwidth; T s is the length of the communication time slot; r0 represents the relative distance of the aircraft transceiver; P del represents the probability of removing the data packet from the queue obtained in step 2.1; represents the normalized noise power; α represents the road loss index; ζ represents the environmental information perception frequency; λ represents the aircraft density.

[0054] Step 3: Performance evaluation and optimization;

[0055] The overall process of performance evaluation and optimization is to evaluate the PAoI under the current system parameters based on a set of system parameter configurations (including aircraft density, flight altitude, communication time slot length, environmental information perception frequency, and maximum number of retransmissions) in a specific scenario based on the aviation ad hoc network system model established in step 1 and the information timeliness analysis method established in step 2. After evaluating multiple sets of parameter settings, the optimal communication time slot length, environmental information perception frequency, and maximum number of retransmissions are found by comparing the size of PAoI.

[0056] Step 4: Implement the information transmission plan for aviation aircraft;

[0057] Based on the optimal communication time slot length and environmental information perception frequency obtained by the evaluation in step 3, the aircraft transmitter and receiver system parameter configuration and scheme selection, information transmission is performed to minimize PAoI. The scheme selection refers to the transmission scheme corresponding to the PAoI minimization obtained according to the analytical method, including the no retransmission scheme, the unlimited retransmission scheme and the retransmission scheme with the maximum number of retransmissions in the specific implementation scheme of the present invention.

[0058] The beneficial effects of the present invention are:

[0059] (1) The survivability analysis method of an aeronautical ad hoc network based on information timeliness of the present invention adopts information age to characterize the end-to-end network survivability of information perception, transmission and processing in an aeronautical ad hoc network. At the same time, a survivability analysis method of an aeronautical ad hoc network based on random geometry and queuing theory is constructed, which takes into account key factors such as the spatial topology of the aeronautical ad hoc network, the time-varying characteristics of environmental perception, the transmission characteristics of the wireless channel and co-channel interference.

[0060] (2) The analytical method proposed in the present invention can be used to quickly evaluate whether a certain aviation ad hoc network scenario and system parameter configuration can meet the network survivability requirements, and to find the optimal system parameters that minimize the information age. In particular, the proposed analytical method is a statistical optimization of the entire network. This method does not rely on large-scale system-level simulations, and the information required to be collected is mostly relatively static, and does not require frequent measurements and reporting, thus avoiding the large amount of cumbersome calculations and resource consumption introduced by frequent decision-making.

[0061] In summary, the proposed aeronautical ad hoc network survivability analysis method has the advantages of being simple, fast, and universal, and can significantly reduce computational complexity and time consumption. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 It is a schematic diagram of the network topology of the aviation ad hoc network of the present invention.

[0063] Figure 2 It is the information age and time change curve of the present invention.

[0064] Figure 3 (a) is a flowchart of the transmitter side operation of the present invention.

[0065] Figure 3 (b) is a flowchart of the receiver side work flow of the present invention.

[0066] Figure 4 (a) is the relationship curve between PAoI and communication time slot length in step 3.

[0067] Figure 4 (b) is the relationship curve between PAoI and environmental information perception frequency in step three. DETAILED DESCRIPTION

[0068] The specific implementation of the present invention is described in detail below with reference to the accompanying drawings.

[0069] A method for analyzing the survivability of an aeronautical ad hoc network based on information timeliness comprises the following steps:

[0070] Step 1: Information collection and model building;

[0071] Step 1.1 Collect information: Depending on the source of information, the information collection process mainly includes three steps:

[0072] (1) Aircraft configuration information, including communication time slot length T s , environmental information perception frequency ζ, perception data packet size K, communication bandwidth W, and scheduling probability p of data packet transmission.

[0073] (2) Aircraft transceiver interaction information, including the relative distance r0 between the aircraft transceivers.

[0074] (3) The aircraft obtains other system information through the network or the ground control center, including aircraft density λ, aircraft average altitude H, and earth radius R earth , Normalized Noise Power And the path loss model of the air link. The path loss model of the air link is l(r)=r -α , where α is the path loss exponent and r is the propagation distance traveled by the wireless signal.

[0075] Step 1.2, establish the aviation ad hoc network system model, including the following five steps:

[0076] Step 1.2.1: Establish the spatial topology model of the aviation ad hoc network. Specifically, based on the collected aircraft density λ, the earth radius R earth and the aircraft height information H, the spatial position distribution of the aircraft node is modeled as distributed in a radius of R = R earth +H sphere Poisson point process model Φ, and the density of the Poisson point process is the same as the aircraft density λ. Figure 1 The spatial topology of the aeronautical ad hoc network is shown in the figure, where the typical receiver y0 = (0,0,R) is located at the zenith of the sphere, and its corresponding typical receiver is recorded as x0, and its relative distance is r0 = |x0-y0|. When the typical transceiver transmits information, it will receive interference from the concurrent transmitter with the same frequency.

[0077] Step 1.2.2: Establish a wireless channel model. Specifically, use the power rate function e(r) = r-α The path loss of the modeled signal, where α is the path loss exponent and r is the propagation distance of the wireless signal. Small-scale channel fading is modeled as Rayleigh fading, and the small-scale channel power fading factor follows an exponential distribution.

[0078] Step 1.2.3: Establish the transmitter's environmental information perception model. Specifically, based on the collected communication time slot length T s , environment sensing frequency ζ and sensing data packet size K bits, consider a discrete transmission system with equal time slots, where the time slot length is T s , the perception data process is modeled as an independent Bernoulli arrival process, where the arrival rate of the perception data packet is the same as the environment perception frequency ζ, that is, at the starting boundary of each time slot, the aircraft perceives the environment with probability ζ and generates a data packet with K information bits, and assigns a timestamp to each data packet and stores it in the cache queue.

[0079] Step 1.2.4, establish a data packet scheduling model. Specifically, each aircraft adopts the first-come-first-served principle to transmit the first data packet in the cache queue. If the cache queue of the aircraft is not empty, the data packet at the head of the queue is sent at the starting boundary of the time slot with a scheduling probability p, that is, the sending probability of the data packet. That is to say, the aviation ad hoc network adopts the commonly used ALOHA strategy for data packet scheduling, and only sends one data packet in a time slot.

[0080] Step 1.2.5, establish a data packet transmission model. Specifically:

[0081] If the data packet is successfully transmitted, the receiver feeds back a confirmation signal, i.e., an ACK signal, to the transmitter. The transmitter then removes the successfully transmitted data packet from the cache queue, and the receiver makes a decision based on the most recently received perception data packet. The successfully transmitted data packet refers to the link capacity C = Wlog(1+SINR) from the transmitter x0 to the receiver y0 in a time slot length T s The size of the data packet is K bits, that is, C×T s >K, where represents the signal-to-interference-to-noise ratio of the link; r0 represents the relative distance of the aircraft transceiver; |x-y0| represents the distance from the interference transmitter x to the receiver y0; Φ represents the topological model of the aeronautical ad hoc network; Ω is the visible area formed by the earth blocking the receiver y0; and h x represent the small-scale channel power fading factors from transmitter x0 and interference transmitter x to receiver y0 respectively; e(r0) and e(|x-y0|) represent the path losses from transmitter x0 and interference transmitter x to receiver y0 respectively; B x Q is a Bernoulli random variable with probability p being 1 and probability 1-p being 0 indicating whether transmitter x sends data;x represents the number of packets in the buffer queue of transmitter x; represents the normalized noise power.

[0082] If the data packet transmission fails, C×T is not satisfied. s >K, the receiver feeds back a NACK signal to the transmitter and still makes decisions based on the last successfully received perception data packet, while the transmitter decides whether to remove the unsuccessfully transmitted data packet from the buffer queue based on the specific transmission strategy.

[0083] The specific transmission strategies include a no-retransmission strategy, an infinite retransmission strategy, and a retransmission strategy based on a maximum number of retransmissions. When a no-retransmission strategy is adopted, a data packet is removed from the cache queue after a transmission failure. When an infinite retransmission strategy is adopted, a data packet is continuously retransmitted after a transmission failure until it is successfully transmitted and then removed from the cache queue. When a retransmission strategy based on a maximum number of retransmissions is adopted, a data packet is retransmitted after a transmission failure and the number of retransmissions is recorded. If the number of retransmissions of the data packet is greater than the preset maximum number of retransmissions, it is removed from the cache queue.

[0084] Step 2: Establish an analytical expression for information timeliness;

[0085] Based on the established aviation ad hoc network system model, an analytical expression for information timeliness is established by solving the average peak information age, including solving the average end-to-end transmission delay and the average perception interval time of continuous successful transmission; the details are as follows:

[0086] In order to reflect the boundary characteristics of environmental information timeliness in aviation ad hoc networks, the present invention uses Peak Age of Information (PAoI) to characterize the information timeliness of the network in the worst case, which is defined as the highest information age value that the current data packet can reach when the next data packet is successfully transmitted (reference: Inoue Y, Masuyama H, Takine T, et al. A general formula for the stationary distribution of the age of information and its application to single-server queues [J]. IEEE Transactions on Information Theory, 2019, 65 (12): 8305-8324.), and by solving the average PAoI, to quantitatively analyze the information timeliness of aviation ad hoc networks, and to evaluate and optimize the impact of each key system parameter on information timeliness. Figure 2As shown in Figure 1, PAoI represents the maximum survival time of a data packet in an aeronautical ad hoc network. At this time, if indexes n and m are two consecutive successfully transmitted data packets in the current typical transceiver link, the PAoI of the nth data packet can be expressed as

[0087] A n = sup{Δ(t):t∈[d n ,d m )}=d m -a n

[0088] Wherein, Δ(t)=tU(t) is the information age of the latest successfully received data packet at the receiving end, and U(t) is the timestamp of the latest successfully received data packet at the receiving end at time t (i.e., the perception time); a n represents the time point at which the aircraft perceives the nth data packet; d n and d m They respectively represent the time points when the nth and mth data packets of the transmitter are successfully transmitted.

[0089] When the receiver successfully receives the nth data packet, AoI equals d n -a n , then AoI will increase linearly with time variable t to a peak value until the next successful reception of the data packet. Based on the process that the data packet goes through in the aeronautical ad hoc network, PAoI can be split into two parts that are easy to analyze theoretically, as shown below:

[0090] A n =(d m -a m )+(a m -a n )

[0091] Among them A n represents the peak information age; X inter =a m -a n It represents the perceived time difference between two consecutive successful transmissions of data packets (data packet n and data packet m) by the transmitter; D m =d m -a m It represents the end-to-end transmission delay of a successfully transmitted data packet (data packet m), that is, the time period from the moment the data packet is perceived and generated until the data packet is successfully transmitted.

[0092] Based on this, the PAoI is expected to be averaged. Expressed as in, represents the expectation operation on random variables, It represents the average end-to-end transmission delay of a successfully transmitted data packet; It indicates the average perceived interval time between two consecutive successful data packet transmissions by the transmitter.

[0093] Therefore, the average PAoI can be converted into the average end-to-end transmission delay of the data packet and the average perceived interval time of continuous successful transmission.

[0094] Step 2.1, solving the average end-to-end transmission delay;

[0095] The end-to-end transmission delay of a perceived data packet refers to the difference between the time when it arrives at the transmitter and the time when it is successfully transmitted to the receiver. It is related to the scheduling and transmission strategy of the transmitter. The present invention analyzes and solves it through queuing theory.

[0096] Step 2.1.1, first, according to the environmental information perception model of the transmitter in step 1.2, the arrival process of the data packet obeys a Bernoulli random process.

[0097] Step 2.1.2, secondly, according to the data packet transmission model in step 1.2, the service process of the data packet leaving the transmitter queue is related to the transmitter scheduling strategy, the data packet transmission strategy and the probability of successful transmission. At this time, the transmission process of the perception data can be modeled as a Geo / Geo / 1 queue model, where the arrival rate is ζ∈(0,1], that is, the data packet perception frequency, and the service rate is pP del , where p∈(0,1] is the probability of sending a packet in each time slot, P del ∈(0,1] is the probability of a packet being removed from the queue in a time slot.

[0098] Step 2.1.3, finally, according to the queuing theory, the average end-to-end transmission delay can be obtained as:

[0099] When pP del >ζ, the average end-to-end transmission delay is When pP del When ≤ζ, then Where, ζ represents the frequency of environmental information perception; T s represents the length of the communication time slot; p represents the probability of sending a data packet in each time slot; P del is the probability of a packet being dequeued in a time slot; (Reference: Atencia I and Moreno PA discrete-time GEO / G / 1 retrial queue with general retrial times [J]. Queueing Systems, 2004, 48: 5-21.)

[0100] The probability of removing the queue in this embodiment is related to the specific transmission strategy, which is as follows:

[0101] When the transmitter adopts the no-retransmission strategy, the probability of packet removal from the queue is P del =1.

[0102] When the transmitter uses an infinite retransmission strategy, the probability of a packet being removed from the queue is P del , and the iterative method is used to solve it. Specifically, let the initial value of the probability of successful packet removal from the queue be M (0) =1, and use the following formula for iterative calculation:

[0103]

[0104] Until the condition is met|M (k+1) -M (k) |≤ε, where ε is the preset convergence threshold, for example, ε=10 -6 ;k=0,1,2...;θ=2arccos(R earth / R); R earth is the radius of the earth; R is the radius of the sphere where the aviation is located; K represents the bit size of the data packet; W is the communication bandwidth; T s is the communication time slot length; r0 represents the relative distance of the aircraft transceiver; p represents the probability of data packet transmission of the transmitter; represents the normalized noise power; α represents the path loss index; λ represents the aircraft density. Let M ε It represents the convergence value of the removal probability calculated by the above iterative method, that is, P del =M ε .

[0105] When the transmitter adopts a retransmission strategy based on the maximum number of retransmissions, the probability of a packet being removed from the queue is Where N max is the maximum number of retransmissions, P(CT s ≥K) is the probability of successful transmission of the data packet, and is solved by an iterative method. Specifically, let the probability of successful transmission be The initial value is M (0) =1, and use the following formula for iterative calculation:

[0106]

[0107]

[0108] Until |M (k+1) -M (k) |≤ε, where ε is the preset convergence threshold, for example, ε=10 -6 ; k = 0, 1, 2…; R earth is the radius of the earth; R is the radius of the sphere where the aircraft is located; K represents the bit size of the data packet; W is the communication bandwidth; T s is the communication time slot length; r0 represents the relative distance of the aircraft transceiver; p represents the probability of data packet transmission of the transmitter; represents the normalized noise power; α represents the path loss index; λ represents the aircraft density. Let M ε represents the convergence value of the successful transmission probability calculated by the above iterative method, that is, P(CT s ≥K)=M ε , solve the probability of removing the packet from the queue as P del =1 / N max +(N max -1) / N max M ε .

[0109] Step 2.2, solving the average perception interval time of continuous successful transmission;

[0110] The perception time interval for consecutive successful transmissions is X inter First, under the given aeronautical ad hoc network topology Φ, the probability of conditional successful transmission of data packets under the given aeronautical ad hoc network topology Φ is solved, and the perception time interval X of continuous successful transmission is obtained. inter The conditional probability distribution of is a geometric distribution, and then the perception time interval X of consecutive successful transmissions inter The conditional mean of the expected operation on the topology Φ of the aeronautical ad hoc network is used to solve the average perception interval time of continuous successful transmission in It represents the expectation operation of random variables. The details are as follows:

[0111] First, the conditional successful transmission probability of a data packet under a given aeronautical ad hoc network topology Φ is solved, that is, the conditional event ε Φ ={C×T s The probability of occurrence of ≥K|Φ} Where K represents the number of bits in the data packet; T s represents the length of the communication time slot; C is the capacity of the communication link in the time slot where the data packet is scheduled for transmission. According to the conditional successful transmission probability of the data packet and the environmental information perception model in step 1.2, the conditional probability distribution of the perception time interval of continuous successful transmission is obtained:

[0112]

[0113] Where n represents the number of communication time slots; T represents the length of the communication time slot; Φ represents the topological model of the aeronautical ad hoc network; ε ΦIt represents the successful transmission event of a data packet under the given aeronautical ad hoc network topology Φ; It represents the probability of successful transmission of a data packet under the given aeronautical ad hoc network topology Φ. The conditional probability of successful transmission of the data packet is related to the specific transmission strategy. Specifically, when the no-retransmission strategy is adopted, the conditional probability of successful transmission of the data packet is It is expressed as:

[0114]

[0115] Among them, Φ represents the topological model of the aeronautical ad hoc network, and Ω is the visible area formed by the receiver y0 being blocked by the earth. K represents the bit size of the data packet; W is the communication bandwidth; T s is the length of the communication time slot; r0 represents the relative distance of the aircraft transceiver; ζ represents the environmental information sensing frequency of the transmitter; represents the normalized noise power; α represents the path loss index; x and y0 represent the locations of the interference transmitter and receiver, respectively; e(|x-y0|) represents the path loss from the interference transmitter x to the receiver y0.

[0116] When the infinite retransmission strategy is adopted, the conditional successful transmission probability of the data packet

[0117] When the retransmission strategy based on the maximum number of retransmissions is adopted, the conditional successful transmission probability of the data packet is It is expressed as:

[0118]

[0119] Among them, Φ represents the topological model of the aeronautical ad hoc network, and Ω is the visible area formed by the receiver y0 being blocked by the earth. K represents the bit size of the data packet; W is the communication bandwidth; T s is the length of the communication time slot; r0 represents the relative distance of the aircraft transceiver; ζ represents the environmental information sensing frequency of the transmitter; represents the normalized noise power; α represents the path loss index; x and y0 represent the locations of the interference transmitter and receiver, respectively; e(|x-y0|) represents the path loss from the interference transmitter x to the receiver y0; P del represents the probability of removing the packet from the queue obtained in step 2.1, N max Indicates the maximum number of retransmissions.

[0120] Then, solve the perception time interval X of continuous successful transmission inter The conditional mean of The conditional mean is subjected to the expected operation of the aeronautical ad hoc network topology Φ, thereby solving the average perception interval time of continuous successful transmission. in It is the expected operation about the aeronautical ad hoc network topology Φ.

[0121] The results of the desired operation of the aeronautical ad hoc network topology Φ It is related to the specific transmission strategy, which is as follows:

[0122] When the transmitter adopts a no-retransmission strategy, the solution is:

[0123]

[0124] where F(·) is the Gaussian hypergeometric function (reference: Gradshteyn I and Ryzhik I. Table of integrals, series, and products seventh edition [M]. Academic Press, 2007); R earth is the radius of the earth; R is the radius of the sphere where the aircraft is located; K represents the bit size of the data packet; W is the communication bandwidth; T s is the communication time slot length; r0 represents the relative distance of the aircraft transceiver; represents the normalized noise power; α represents the road loss index; ζ represents the environmental information perception frequency; λ represents the aircraft density.

[0125] When the transmitter adopts an infinite retransmission strategy, the solution is

[0126] When the transmitter adopts a retransmission strategy based on the maximum number of retransmissions, the solution is:

[0127]

[0128] in, Indicates from mN max The number of combinations of k elements taken from different elements; R earth is the radius of the earth; R is the radius of the sphere where the aircraft is located; K represents the bit size of the data packet; W is the communication bandwidth; T s is the length of the communication time slot; r0 represents the relative distance of the aircraft transceiver; P del represents the probability of removing the data packet from the queue obtained in step 2.1; represents the normalized noise power; α represents the road loss index; ζ represents the environmental information perception frequency; λ represents the aircraft density.

[0129] Step 3: Performance evaluation and optimization

[0130] The overall process of performance evaluation and optimization is based on the aviation ad hoc network system model established in step 1 and the information timeliness analysis method established in step 2. The aircraft transmitter or ground control center evaluates the PAoI under the current system parameters according to a set of system parameter configurations in a specific scenario (including aircraft density, flight altitude, communication time slot length, environmental information perception frequency and maximum number of retransmissions), and after evaluating multiple sets of parameter settings, by comparing the size of PAoI, find the optimal communication time slot length, environmental information perception frequency or optimal transmission strategy. The transmission strategy refers to a no retransmission scheme, an unlimited retransmission scheme and a retransmission scheme with a maximum number of retransmissions.

[0131] An example is given as a reference, in which the aircraft can obtain some system parameters from its own configuration, transceiver interaction and network side as follows: Earth radius R earth =6371km, path loss index α=2.5, aircraft flight altitude H=40km, relative distance between aircraft transceiver r0=5km, communication bandwidth W=1MHz, data packet size K=1000, scheduling probability p=0.9. Figure 4 (a) Given a sensing frequency ζ = 0.4, the time slot length is changed from 0.1 ms to 1.0 ms, and a value is selected every 0.0001 ms to calculate the corresponding average PAoI, where two retransmission schemes, infinite retransmission and no retransmission, are considered, and the number of transmitters in the aircraft AMANET is N = 10. 4 and N = 10 6 Used to calculate the density of aviation transmitters λ = N / (4π(R earth +H) 2 ). Therefore, in this example, for example, when the system configuration is N=10 6 When the no-retransmission scheme is adopted and the time slot length is 0.4487ms, the minimum PAoI value is 2.949. Figure 4 (b) At a given time slot length T s =0.2ms, the sensing frequency is changed from 0.1 to 0.9, and a value is selected every 0.0001 to calculate the corresponding average PAoI, where two retransmission schemes, infinite retransmission and no retransmission, are considered. The number of transmitters in the aircraft aeronautical ad hoc network is N = 10 4 Used to calculate the density of aviation transmitters λ = N / (4π(R earth +H) 2 ), and different transceiver distances. Therefore, in this example, for example, when the system configuration is r0 = 4 km, the no retransmission scheme is adopted and the sensing frequency is 0.682, the minimum PAoI value can be obtained as 0.682.

[0132] Step 4: Implement the information transmission plan for aviation aircraft;

[0133] Based on the optimal communication time slot length, environmental information perception frequency or optimal transmission strategy evaluated in step 3, the aircraft transmitter and receiver perform system parameter configuration and transmission scheme selection to transmit information that minimizes PAoI. The scheme selection refers to the transmission scheme corresponding to the PAoI minimization obtained according to the analytical method, including the no retransmission scheme, the unlimited retransmission scheme and the retransmission scheme with the maximum number of retransmissions in the specific implementation scheme of the present invention. Specifically as follows:

[0134] If the performance evaluation and optimization steps are performed by the aircraft transmitter, the transmitter directly configures the optimal communication time slot length, environmental information perception frequency, and optimal transmission scheme. At the same time, the aircraft transmitter informs the receiver of the optimal communication time slot length and optimal transmission scheme through the control signaling link. After receiving the control information, the receiver configures the communication time slot length and transmission scheme.

[0135] If the ground control center performs the performance evaluation and optimization steps, the ground control center will inform the transmitter and receiver of the optimal communication time slot length, environmental information perception frequency, and optimal transmission scheme through the control signaling link. After receiving the control information, the transmitter configures the communication time slot length, environmental information perception frequency, and transmission scheme. After receiving the control information, the receiver configures the communication time slot length and transmission scheme.

[0136] From the above description, it can be seen that the network survivability analysis method of the present invention is significantly different from the existing network survivability evaluation method based on information transmission reliability or node survivability. The proposed analysis method directly evaluates network survivability based on the information timeliness of network circulation data, and provides a theoretical analytical formula for the average peak information age under different transmission schemes. The analysis method can directly obtain the mapping relationship between each system parameter and the information age, without relying on large-scale system simulation methods, and therefore does not need to occupy too much storage and computing resources.

[0137] The above-described embodiments merely express the implementation methods of the present invention, but they cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. A method for analyzing the survivability of an aeronautical ad hoc network based on information timeliness, characterized in that: The described aeronautical ad hoc network survivability analysis method first collects network information to establish an aeronautical ad hoc network system model, including an aeronautical ad hoc network spatial topology model, a transmitter's environmental information perception model, a data packet scheduling and transmission model, and a wireless channel model; secondly, based on the established aeronautical ad hoc network system model, the peak information age is split into end-to-end transmission delay and the perception interval time of continuous successful transmission, the average peak information age is solved, and an information timeliness analytical expression is established; thirdly, performance evaluation is performed on different system parameter combinations and transmission strategies, and the optimal parameters and transmission strategies are found; finally, according to the optimization results, an information transmission plan for the aircraft is implemented.

2. The method for analyzing the survivability of an aeronautical ad hoc network based on information timeliness according to claim 1, characterized in that: The following steps are involved: Step 1: Information collection and model building; Step 1.1, collect information: Depending on the source of information, the information collection process includes three steps: (1) Aircraft configuration information, including communication time slot length T s , environmental information perception frequency ζ, perception data packet size K, communication bandwidth W, and scheduling probability p of data packet transmission; (2) Aircraft transceiver interaction information, including the relative distance r0 between aircraft transceivers; (3) The aircraft obtains other system information through the network or the ground control center, including aircraft density λ, aircraft average altitude H, and earth radius R earth , Normalized Noise Power and path loss models for air links; Step 1.2, establish the aviation ad hoc network system model: Step 1.2.1, establish the spatial topology model of the aviation ad hoc network; specifically, based on the collected aircraft density λ, the earth radius R earth and the aircraft height information H, the spatial position distribution of the aircraft node is modeled as distributed in a radius of R = R earth +H sphere Poisson point process model Φ, the density of the Poisson point process is the same as the aircraft density λ; Step 1.2.2, establish a wireless channel model; specifically, use the power rate function l(r)=r -α represents the path loss of the modeled signal, where α is the path loss exponent and r is the propagation distance experienced by the wireless signal; Step 1.2.3, establish the transmitter's environmental information perception model; specifically, based on the collected communication time slot length T s , environment sensing frequency ζ and sensing data packet size K bits, consider a discrete transmission system with equal time slots, where the time slot length is T s , the sensing data process is modeled as an independent Bernoulli arrival process, where the arrival rate of the sensing data packet is the same as the environment sensing frequency ζ, that is, at the starting boundary of each time slot, the aircraft senses the environment with probability ζ and generates a data packet with K information bits, and assigns a timestamp to each data packet and stores it in the cache queue; Step 1.2.4, establish a data packet scheduling model; specifically, each aircraft adopts the first-come-first-served principle to transmit the first data packet in the cache queue; if the cache queue of the aircraft is not empty, the data packet at the head of the queue is sent at the starting boundary of the time slot with a scheduling probability p, that is, the sending probability of the data packet; Step 1.2.5, establish a data packet transmission model; specifically: If the data packet is successfully transmitted, the receiver feeds back a confirmation signal, i.e., an ACK signal, to the transmitter, and then the transmitter removes the successfully transmitted data packet from the cache queue, and the receiver will make a decision based on the currently most recently received perception data packet; If the data packet transmission fails, C×T is not satisfied. s >K, the receiver feeds back a NACK signal to the transmitter and still makes decisions based on the last successfully received perception data packet, while the transmitter decides whether to remove the unsuccessfully transmitted data packet from the buffer queue based on the transmission strategy; Step 2: Establish information timeliness analytical expression; Based on the aviation ad hoc network system model established in step 1.2, an analytical expression for information timeliness is established by solving the average peak information age, including solving the average end-to-end transmission delay and the average perception interval time of continuous successful transmission; The peak information age PAoI is used to characterize the information timeliness of the network in the worst case. It is defined as the maximum information age value that the current data packet can reach when the next data packet is successfully transmitted, that is, the maximum survival time of the data packet in the aeronautical ad hoc network. If indexes n and m are two consecutive successfully transmitted data packets, based on the process that the data packets have gone through in the aeronautical ad hoc network, the PAoI is split into two parts, as shown below: A n =(d m -a m )+(a m -a n ) Among them, A n represents the peak information age of the nth packet, a n and a m represents the perception time of the nth and mth data packets of the aircraft; d n and d m Respectively represent the time points when the nth and mth data packets of the transmitter are successfully transmitted; The expected peak information age PAoI is calculated to obtain the average peak information age, which is expressed as in, represents the expected operation of a random variable; D m =d m -a m represents the end-to-end transmission delay of a successfully transmitted data packet m, that is, the time period from the moment the data packet is sensed and generated until the data packet is successfully transmitted; X inter =a m -a n It indicates the perceived time difference between two consecutive successful data packet transmissions by the transmitter, where the two successfully transmitted data packets refer to data packet n and data packet m; The average peak information age is converted into the average end-to-end transmission delay of the data packet. and the average perceived interval between consecutive successful transmissions Step 2.1: Calculate the average end-to-end transmission delay The end-to-end transmission delay of a perception data packet refers to the difference between the time it arrives at the transmitter and the time it is successfully transmitted to the receiver. It is analyzed and solved through queuing theory; the details are as follows: Step 2.1.1, first, according to the transmitter's environmental information perception model in step 1.2, the arrival process of the data packet obeys a Bernoulli random process; Step 2.1.2, secondly, according to the scheduling and transmission model of the data packet in step 1.2, the service process of the data packet leaving the transmitter queue is related to the scheduling strategy of the transmitter, the transmission strategy of the data packet and the probability of successful transmission; at this time, the transmission process of the perception data is modeled as a Geo / Geo / 1 queue model, where the arrival rate is ζ∈(0,1], that is, the environmental information perception frequency, and the service rate is pP del , where p∈(0,1] is the probability of sending a packet in each time slot, P del ∈(0,1] is the probability of a packet being removed from the queue in a time slot; Step 2.1.3, finally, according to the queuing theory, the average end-to-end transmission delay is obtained as: When pP del >ζ, the average end-to-end transmission delay is When pP del When ≤ζ, then Where ζ represents the frequency of environmental information perception; T s represents the length of the communication time slot; p represents the probability of sending a data packet in each time slot; P del is the probability of a packet being removed from the queue in a time slot; Step 2.2: Calculate the average perceived interval time of consecutive successful transmissions The perception time interval for consecutive successful transmissions is X inter First, under the given aeronautical ad hoc network topology Φ, the perception time interval X of continuous successful transmission inter The conditional probability distribution of is a geometric distribution, and then the perception time interval X of consecutive successful transmissions inter The conditional mean of the expected operation on the topology Φ of the aeronautical ad hoc network is used to solve the average perception interval time of continuous successful transmission in It represents the expectation operation on random variables; Step 3: Performance evaluation and optimization; Based on the aviation ad hoc network system model established in step 1 and the information timeliness analysis method established in step 2, the PAoI under the current system parameters is evaluated according to a set of system parameter configurations in a specific scenario, and after evaluating multiple sets of parameter settings, the optimal communication time slot length, environmental information perception frequency and maximum number of retransmissions are found by comparing the size of PAoI; wherein the system parameter configuration includes aircraft density, flight altitude, communication time slot length, environmental information perception frequency and maximum number of retransmissions; Step 4: Implement the information transmission plan for aviation aircraft; Based on the optimal communication time slot length and environmental information perception frequency obtained in step 3, the aircraft transmitter and receiver system parameter configuration and solution selection are performed to minimize the PAoI information transmission.

3. The method for analyzing the survivability of an aeronautical ad hoc network based on information timeliness according to claim 2, characterized in that: In step 1.1, the path loss model of the air link is l(r)=r -α , where α is the path loss exponent and r is the propagation distance traveled by the wireless signal.

4. The method for analyzing the survivability of an aeronautical ad hoc network based on information timeliness according to claim 2, characterized in that: In the step 1.2.5, the successful transmission of the data packet refers to the link capacity C = Wlog(+1SIN in a time slot length T from the transmitter x0 to the receiver y0. s The size of the data packet is K bits, that is, C×T s >K, where represents the signal-to-interference-to-noise ratio of the link; r0 represents the relative distance of the aircraft transceiver; |x-y0| represents the distance from the interference transmitter x to the receiver y0; Φ represents the topological model of the aeronautical ad hoc network; Ω is the visible area formed by the earth blocking the receiver y0; and h x represent the small-scale channel power attenuation factors from transmitter x0 and interference transmitter x to receiver y0 respectively; l(r0) and l(|x-y0|) represent the path losses from transmitter x0 and interference transmitter x to receiver y0 respectively; B x Q is a Bernoulli random variable with probability p being 1 and probability 1-p being 0 indicating whether transmitter x sends data; x represents the number of packets in the buffer queue of transmitter x; represents the normalized noise power.

5. The method for analyzing the survivability of an aeronautical ad hoc network based on information timeliness according to claim 2, characterized in that: In the step 1.2.5, the transmission strategy includes a no-retransmission strategy, an infinite retransmission strategy and a retransmission strategy based on a maximum number of retransmissions, wherein when a no-retransmission strategy is adopted, a data packet is removed from the cache queue after a transmission failure; when an infinite retransmission strategy is adopted, a data packet is continuously retransmitted after a transmission failure until it is successfully transmitted and then removed from the cache queue; when a retransmission strategy based on a maximum number of retransmissions is adopted, a data packet is retransmitted after a transmission failure and the number of retransmissions is recorded. If the number of retransmissions of the data packet is greater than the preset maximum number of retransmissions, it is removed from the cache queue.

6. The method for analyzing the survivability of an aeronautical ad hoc network based on information timeliness according to claim 2, characterized in that: In step 2.1.3, the probability of removing the queue P del Related to the transmission strategy, as follows: When the transmitter adopts the no-retransmission strategy, the probability of packet removal from the queue is P del =1; When the transmitter uses an infinite retransmission strategy, the probability of a packet being removed from the queue is P del , using an iterative method to solve; specifically, let the initial value of the probability of successful packet removal from the queue be M (0) =1, and use the following formula for iterative calculation: Until the condition is met|M (k+1) -M (k) |≤ε, where ε is the preset convergence threshold; k=0,1,2…; R earth is the radius of the earth; R is the radius of the sphere where the aviation is located; K represents the bit size of the data packet; W is the communication bandwidth; T s is the communication time slot length; r0 represents the relative distance between the aircraft transceiver; p represents the probability of data packet transmission of the transmitter; represents the normalized noise power; α represents the road loss index; λ represents the aircraft density; Let M ε It represents the convergence value of the removal probability calculated by the above iterative method, that is, P del =M ε ; When the transmitter adopts a retransmission strategy based on the maximum number of retransmissions, the probability of a packet being removed from the queue is Where N max is the maximum number of retransmissions, is the probability of successful transmission of a data packet, and is solved by an iterative method; specifically, let the probability of successful transmission The initial value is M (0) =1, and use the following formula for iterative calculation: Until |M (k+1) -M (k) |≤ε, where ε is the preset convergence threshold; k=0,1,2…; R earth is the radius of the earth; R is the radius of the sphere where the aircraft is located; K represents the bit size of the data packet; W is the communication bandwidth; T s is the communication time slot length; r0 represents the relative distance between the aircraft transceiver; p represents the probability of data packet transmission of the transmitter; represents the normalized noise power; α represents the road loss index; λ represents the aircraft density; Let M ε represents the convergence value of the successful transmission probability calculated by the above iterative method, that is, Solve the probability of removing the packet from the queue as P del =1 / N max +(N max -1) / N mxa M ε .

7. The method for analyzing the survivability of an aeronautical ad hoc network based on information timeliness according to claim 2, characterized in that: In step 2.2, the average perception interval time of continuous successful transmission is related to the specific transmission strategy, which is as follows: When the transmitter adopts a no-retransmission strategy, the solution is: Where F(·) is the Gaussian hypergeometric function; R earth is the radius of the earth; R is the radius of the sphere where the aircraft is located; K represents the bit size of the data packet; W is the communication bandwidth; T s is the length of the communication time slot; r0 represents the relative distance of the aircraft transceiver; represents the normalized noise power; α represents the road loss index; ζ represents the environmental information perception frequency; λ represents the aircraft density; When the transmitter adopts an infinite retransmission strategy, the solution is When the transmitter adopts a retransmission strategy based on the maximum number of retransmissions, the solution is: in, Indicates from mN max The number of combinations of k elements taken from different elements; R earth is the radius of the earth; R is the radius of the sphere where the aircraft is located; K represents the bit size of the data packet; W is the communication bandwidth; T s is the length of the communication time slot; r0 represents the relative distance of the aircraft transceiver; P del represents the probability of removing the data packet from the queue obtained in step 2.1; represents the normalized noise power; α represents the road loss index; ζ represents the environmental information perception frequency; λ represents the aircraft density.

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