CN114339731A - Spatial interruption probability analysis method and device and electronic equipment - Google Patents
Spatial interruption probability analysis method and device and electronic equipment Download PDFInfo
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Abstract
The spatial interruption probability is used as a privacy performance measurement index of physical layer security, the spatial interruption probability is constructed by utilizing position information of legal equipment and a channel response function, and randomness of the position of the eavesdropping equipment is considered in the construction process of the spatial interruption probability by modeling the position information of the eavesdropping equipment, so that the spatial interruption probability under the condition that the eavesdropping equipment obeys uniform distribution can be defined. The influence of the antenna parameters on the spatial interruption probability can be obtained by solving a closed solution of the spatial interruption probability average value.
Description
Technical Field
The present application relates to the field of network security assessment technologies, and in particular, to a method and an apparatus for spatial outage probability analysis, and an electronic device.
Background
A Physical Layer Security (PLA) technology attracts attention as a new technology for improving information Security, and PLA is a way for performing data Security transmission by using channel characteristics such as fading, randomness, space-time uniqueness, reciprocity, and the like of a wireless channel, and realizes secure transmission of information through technologies such as precoding, beamforming, and artificial noise. Compared with the traditional encryption technology, the physical layer security does not depend on the computational complexity, and can be combined with the encryption technology of the upper layer to ensure the information security of the system. Many researchers analyze, using the security performance metric, a Secure Region (SR) or an Insecure Region (ISR) of the system, where a Secure Region refers to an eavesdropping apparatus located in the Region that cannot correctly decode received Secure information, and an Insecure Region refers to an eavesdropping apparatus located in the Region that can correctly decode received Secure information.
Device location information has gained much attention in wireless networks, however, this information is less utilized in physical layer security, and at the same time, the privacy performance metric does not take into account random fading of the channel and randomness of the device location.
Disclosure of Invention
In view of the above, an object of the present invention is to provide a method, an apparatus and an electronic device for spatial outage probability analysis, so as to solve or partially solve the above problems.
In view of the above, a first aspect of the present application provides a spatial outage probability analysis method, including:
acquiring the positions of the base station and legal equipment;
expressing the positions of the base station, the legal equipment and the eavesdropping equipment in a polar coordinate mode to obtain a position variable and a motion area;
acquiring an antenna parameter set of the base station;
modeling the position of the eavesdropping device to obtain an eavesdropping position model;
modeling legal channel response and wiretap channel response to obtain a channel response model, wherein the legal channel response and the wiretap channel response are random variables generated based on the position variables;
calculating the signal-to-noise ratio of the legal device and the eavesdropping device according to the position variable, the channel response model and the antenna parameter set, and calculating the channel capacity of the eavesdropping device according to the signal-to-noise ratio;
in response to the fact that the channel capacity is larger than a preset value, calculating according to the signal-to-noise ratio, the antenna parameter set and a motion region of the eavesdropping device to obtain an unsafe region expression, and calculating according to the unsafe region expression and the eavesdropping position model to obtain a space interruption probability expression;
and processing the spatial interruption probability expression, calculating to obtain a closed solution of the spatial interruption probability expression, and taking the closed solution as a spatial interruption probability analysis result.
A second aspect of the present application provides a spatial outage probability analysis apparatus, including:
a position obtaining module, configured to obtain positions of the base station and a legal device;
the position representation module is used for representing the positions of the base station, the legal device and the eavesdropping device in a polar coordinate mode to obtain a position variable and a motion area;
a parameter obtaining module, configured to obtain an antenna parameter set of the base station;
the position modeling module is used for modeling the position of the eavesdropping device to obtain an eavesdropping position model;
the channel response module is used for modeling legal channel response and wiretap channel response to obtain a channel response model, wherein the legal channel response and the wiretap channel response are random variables generated based on the position variables;
a capacity calculation module, configured to calculate signal-to-noise ratios of the legal device and the eavesdropping device according to the position variable, the channel response model, and the antenna parameter set, and calculate a channel capacity of the eavesdropping device according to the signal-to-noise ratios;
the probability calculation module is used for calculating to obtain an insecure area expression according to the signal-to-noise ratio, the antenna parameter set and the motion area of the eavesdropping device in response to the fact that the channel capacity is larger than a preset value, and calculating to obtain a spatial interruption probability expression according to the insecure area expression and the eavesdropping position model;
and the calculation closed-form solution module is used for processing the spatial interruption probability expression, calculating to obtain a closed-form solution of the spatial interruption probability expression, and taking the closed-form solution as a spatial interruption probability analysis result.
A third aspect of the application provides an electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the method of the first aspect when executing the program.
As can be seen from the above, according to the spatial interruption probability analysis method, the spatial interruption probability analysis device, and the electronic device provided by the present application, the spatial interruption probability is used as a security performance measurement index of physical layer security, the spatial interruption probability is constructed by using the position information of the legal device and a channel response function, and the randomness of the position of the eavesdropping device is considered in the construction process of the spatial interruption probability by modeling the position information of the eavesdropping device, so that the spatial interruption probability under the condition that the eavesdropping device obeys uniform distribution can be defined. The influence of the antenna parameters on the spatial interruption probability can be obtained by solving a closed solution of the spatial interruption probability average value.
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In order to more clearly illustrate the technical solutions in the present application or the related art, the drawings needed to be used in the description of the embodiments or the related art will be briefly introduced below, and it is obvious that the drawings in the following description are only embodiments of the present application, and it is obvious for those skilled in the art that other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a flow chart of a spatial outage probability analysis method according to an embodiment of the present application;
FIG. 2 is a flowchart of obtaining a polar position variable according to an embodiment of the present disclosure;
FIG. 3 is a flowchart of acquiring a model of an eavesdropping location according to an embodiment of the present application;
FIG. 4 is a flowchart of obtaining a channel response model according to an embodiment of the present application;
FIG. 5 is a flow chart of calculating a signal-to-noise ratio according to an embodiment of the present application;
FIG. 6 is a flow chart of calculating an unsafe zone in an embodiment of the present application;
FIG. 7 is a flowchart of computing spatial outage probabilities according to an embodiment of the present application;
FIG. 8 is a flow chart of a closed-form solution to compute spatial outage probability according to an embodiment of the present application;
fig. 9 is a block diagram of a spatial outage probability analysis apparatus according to an embodiment of the present application;
fig. 10 is a block diagram of an electronic device according to an embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the present application is further described in detail below with reference to the accompanying drawings in combination with specific embodiments.
It should be noted that technical terms or scientific terms used in the embodiments of the present application should have a general meaning as understood by those having ordinary skill in the art to which the present application belongs, unless otherwise defined. The use of "first," "second," and similar terms in the embodiments of the present application do not denote any order, quantity, or importance, but rather the terms are used to distinguish one element from another. The word "comprising" or "comprises", and the like, means that the element or item listed before the word covers the element or item listed after the word and its equivalents, but does not exclude other elements or items. The terms "connected" or "coupled" and the like are not restricted to physical or mechanical connections, but may include electrical connections, whether direct or indirect.
In wireless communication, due to the openness of spectrum resources, a malicious user in an effective transmission range can interfere or eavesdrop on secret information of a legitimate user, so that information security is a problem to be solved urgently in the field of wireless communication. The traditional solution is to adopt a key-based encryption technology, and a transmitting end encrypts the secret information through a key, so that even if an eavesdropping user intercepts the secret information, the intercepted information cannot be decrypted because the eavesdropping user cannot know the key. Key-based encryption techniques rely on the computational complexity of the encryption algorithm, and with the development of computer technology, especially the advent of quantum computers, keys are at risk of being deciphered.
In recent years, a Physical Layer Security (PLA) technology has attracted attention as a new technology for improving information Security, and PLA is a method for performing data Security transmission by using channel characteristics such as fading, randomness, space-time uniqueness, and reciprocity of a wireless channel, and realizes secure transmission of information by using techniques such as precoding, beamforming, and artificial noise. Compared with the traditional encryption technology, the physical layer security does not depend on the computational complexity, and can be combined with the encryption technology of the upper layer to ensure the information security of the system.
In the MISO system, the transmitting end improves the security performance of the communication system by using the beam forming technology, and the basic principle of the MISO system is to transmit the security Information to the legal user by using the multi-antenna technology under the condition that the Channel State Information (CSI) of the legal Channel is known, and simultaneously reduce the receiving signal-to-noise ratio of the eavesdropping user (the ratio of useful signal to noise is larger, and the larger the value is, the better the quality of the signal is, the smaller the noise is). The transmitting terminal (Alice) obtains the CSI or the position information of the legal user (Bob) through channel estimation, so that Alice can improve the signal-to-noise ratio of signals received by the Bob terminal by using a beam forming technology, and the probability of information leaked to the eavesdropping user (Eve) is reduced. Since Eve uses a passive eavesdropping mode in most cases, Alice cannot know the CSI or location information of Eve. Therefore, many researchers analyze, using the security performance metric, a Secure Region (SR) in which an eavesdropping user located in the Region cannot correctly decode the received Secure information, or an Insecure Region (ISR) in which an eavesdropping user located in the Region can correctly decode the received Secure information. The user position information has gained wide attention in wireless networks, but the information is less utilized in the physical layer security, the privacy performance measurement index of the patent not only considers the random fading of a channel, but also considers the randomness of the user position, and the Spatial correlation output Probability (SSOP) of the system is constructed by utilizing the position information of the user, so as to measure the privacy performance of the system.
In the physical layer security research, a transmitting end Alice generally assumes that CSI of a legal channel (a channel between Alice and Bob) and an eavesdropping channel (a channel between Alice and Eve) are known, but for a passively eavesdropping user Eve, Alice cannot acquire position information or CSI thereof, so in order to measure the security performance of the system, the patent analyzes a secure area and an insecure area of the system by using a secret performance measurement index (such as secret capacity), defines an SSOP according to the insecure area of the system, and deduces a closed solution of an upper boundary thereof.
As shown in fig. 1, the method of the present embodiment includes:
In this step, the base station may be a multi-antenna transmitting end, and the legitimate device may be a single-antenna user. For example, the transmitting end (Alice) is located at the origin of coordinates and is configured with ntAccording to the uniformly distributed antenna array, the antenna spacing delta d is half wavelength delta d which is lambda/2. Both the legal device (Bob) and the eavesdropping device (Eve) are equipped with a single antenna.
In the scheme, by acquiring the positions of the base station and the legal equipment, a data basis is provided for the subsequent representation of the positions of the base station and the legal equipment in a polar coordinate form.
And 102, representing the positions of the base station, the legal device and the eavesdropping device in a polar coordinate mode to obtain a position variable and a motion area.
In this step, polar coordinates refer to taking a fixed point O in the plane, called pole, and a ray Ox, called polar axis, and selecting a length unit and the positive direction of the angle (usually counterclockwise). For any point M in the plane, ρ represents the length of a line segment OM (sometimes r), θ represents the angle from Ox to OM, ρ is the polar diameter of point M, θ is the polar angle of point M, and the ordered pair of numbers (ρ, θ) is the polar coordinate of point M.
In the above scheme, the positions of the base station, the legal device and the eavesdropping device are expressed in a polar coordinate form, and the position information of the base station, the legal device and the eavesdropping device is converted into a variable that can be applied in the security performance measurement index.
In some embodiments, as shown in fig. 2, step 102 specifically includes:
In this step, the angle information refers to an included angle between a line segment formed by the legal device and the base station and the polar axis in the counterclockwise direction, and an included angle between a line segment formed by the eavesdropping device and the base station and the polar axis in the counterclockwise direction. The amplitude information refers to the length of a line segment formed by a legitimate device and a base station, and the length of a line segment formed by a wiretapping device and a base station.
And 202, representing the angle variable and the amplitude variable in a polar coordinate mode, and taking a representation result as the position variable.
Through the scheme, although the position of the wiretapping device adopting the passive wiretapping mode is unknown, the position information of the wiretapping device is expressed into the position variable which can be processed by constructing the position variables of the base station, the legal device and the wiretapping device, so that a variable basis is provided for the subsequent position modeling of the wiretapping device.
And 103, acquiring an antenna parameter set of the base station.
In this step, the antenna parameter set refers to transmission power, antenna array parameters, noise information, and privacy rate.
In the scheme, a data basis is provided for the subsequent calculation of the signal-to-noise ratio by acquiring the antenna parameter set of the base station.
And 104, modeling the position of the eavesdropping device to obtain an eavesdropping position model.
In this step, the wiretap location model means that the wiretap devices obey a uniform distribution in a circular area.
In the scheme, the unknown position information of the wiretapping device is added into the subsequent spatial interruption probability analysis process in the form of random variables by establishing the wiretapping position model.
In some embodiments, as shown in fig. 3, step 104 specifically includes:
In this step, the first predetermined probability distribution function refers to a uniform distribution function.
In this step, the bit is eavesdroppedAngle of incidence θ in the phantomeCompliance thetaeU (0,2 pi) distribution, eavesdropping distance D in position modeleCompliance
The distribution, U (: means that uniform distribution is obeyed,
representing the square of the farthest transmission distance of the base station.
By the scheme, the eavesdropping equipment is modeled in a uniformly distributed mode in the circular area, and the unknown location information of the eavesdropping equipment is added into the subsequent spatial interruption probability analysis process in a random variable mode.
And 105, modeling the legal channel response and the wiretap channel response to obtain a channel response model, wherein the legal channel response and the wiretap channel response are random variables generated based on the position variables.
In this step, the channel response model refers to a model obtained by modeling the channel responses of a legitimate device and an eavesdropping device using flat rayleigh fading.
In some embodiments, as shown in fig. 4, step 105 specifically includes:
In this step, the second predetermined probability distribution function refers to a flat rayleigh fading function. Both the legitimate channel and the eavesdropped channel are subject to flat Rayleigh fading with a path loss exponent of alpha, and the legitimate channel response function is expressed as
The eavesdropping channel response function is expressed as
Wherein
Representing the directional vector of the antenna array of a legitimate device,
representing the direction vector of the antenna array of a legitimate device, DeIndicating the distance of the eavesdropping device from the base station, DbIndicating the distance, theta, of legitimate devices from the base stationb∈(0，2π)，θeE (0,2 π). Wherein h iseAn eavesdropping channel response, h, representing an eavesdropping devicebIndicating the legitimate channel response of the legitimate device,
representing a complex gaussian distribution.
By adopting the scheme, a legal channel response model and an interception channel response model are established by adopting flat Rayleigh fading, so that a data basis is provided for the calculation of the subsequent signal-to-noise ratio.
And 106, calculating the signal-to-noise ratios of the legal device and the eavesdropping device according to the position variable, the channel response model and the antenna parameter set, and calculating the channel capacity of the eavesdropping device according to the signal-to-noise ratios.
In this step, when the base station transmits signals to the legal device and the eavesdropping device by using the beam forming technology, the information y received by the legal devicebAnd information y received by the eavesdropping deviceeComprises the following steps:
where P represents transmit power, beamforming vector
s denotes a transmission signal, ntWhich indicates the number of antennas of the base station,
indicating a desire; n isbAnd neRespectively representing that the mean value and the variance received by the legal device and the eavesdropping device are respectively 0 and 0
And
complex gaussian noise. The received signal-to-noise ratios of the legitimate device and the eavesdropping device are respectively expressed as
Wherein,
Deindicating the distance of the eavesdropping device from the base station, DbIndicating the distance, G (theta), of a legitimate device from the base statione,θb) Representing the angle function of the eavesdropping device to the legitimate device.
In some embodiments, as shown in fig. 5, step 106 specifically includes:
In this step, Ce＝log2(1+γe) Wherein, CeFor eavesdropping on the channel capacity of the channel, log2Is a logarithmic function.
By the scheme, the channel capacity of the wiretap equipment is obtained, and a data basis is provided for the calculation of the subsequent non-secure area expression.
And 107, in response to the fact that the channel capacity is larger than a preset value, calculating to obtain an unsafe area expression according to the signal-to-noise ratio, the antenna parameter set and the motion area of the eavesdropping device, and calculating to obtain a spatial interruption probability expression according to the unsafe area expression and the eavesdropping position model.
In this step, the predetermined value is the difference between the legitimate channel rate and the secret rate.
In some embodiments, as shown in fig. 6, step 107 specifically includes:
in this step, the channel rate R of the eavesdropping channeleGreater than the channel capacity C of the eavesdropping channeleThe eavesdropping device may receive and decode the secret information, which is leaked to the eavesdropping device, referred to as a secret outlet.
Defining the insecure area as the area where the privacy interruption event occurs, i.e. the insecure area Θ, has the preliminary expression:
Θ＝{z:Ce＞Rb-Rs}
wherein R isbIndicating the legal channel rate, RsIndicating the system security rate and z indicating the eavesdropping device coordinates.
In this step, the signal-to-noise ratio γ of the eavesdropping device is estimated according to the preliminary expression of the insecure area ΘeChannel rate R of eavesdropping deviceeSecret rate RsSubstituting the preliminary expression to obtain a further expression of the non-secure area: Θ ═ { z ═ D (D)e,θe):De＜D(θe) And (c) the step of (c) in which,
calculating the area of the unsafe zone, taking the area of the unsafe zone as an expression A of the unsafe zone:
where P denotes a transmission power.
By the scheme, the relation between the expression of the nonsecure region and the position variable of the wiretapping equipment and the relationship between the expression of the wiretapping channels are obtained, so that the expression of the space interruption probability can be obtained in the following process.
In some embodiments, as shown in fig. 7, step 107 specifically further includes.
In this step, the process is carried out,
wherein D ismaxDenotes the radius of the circular area, pssopDependent on a random variable | he|2，pssopIs the spatial outage probability.
By the scheme, the probability expression of the confidentiality performance measurement index is obtained by converting the nonsecure region expression into the spatial interruption probability expression, so that the confidentiality performance measurement index can be solved subsequently.
And 108, processing the spatial interruption probability expression, calculating to obtain a closed solution of the spatial interruption probability expression, and taking the closed solution as a spatial interruption probability analysis result.
In this step, closed-form solution means that a strict formula is used, and the dependent variable can be obtained by giving any independent variable, namely the solution of the problem. The independent variables include an antenna parameter set of the base station, a position variable of the wiretap device, a path loss index of flat rayleigh fading, and the like.
In some embodiments, as shown in fig. 8, step 108 specifically includes:
In this step, the process is carried out,
The jensen inequality is expressed as:
wherein X is a random variable, and alpha is more than or equal to 2. For any random variable X, the equation holds if and only if α is 2.
Available according to the Jansen inequality
Wherein J0(x) Representing a first type of bessel function,
thus, it is possible to provide
The closed-form solution of (c) is:
when α is 2, the equation holds.
In the scheme, a closed-form solution of the average value of the spatial interruption probability is obtained through calculation by adopting a Jensen inequality, so that the average value of the spatial interruption probability can be obtained by substituting an antenna parameter set of a base station, a position variable of eavesdropping equipment and a path loss index of flat Rayleigh fading into the closed-form solution, and the relation between the spatial interruption probability and the antenna parameter is obtained.
According to the scheme, the spatial interruption probability is used as a privacy performance measurement index of physical layer security, the spatial interruption probability is constructed by utilizing the position information of legal equipment and a channel response function, the randomness of the position of the eavesdropping equipment is considered in the construction process of the spatial interruption probability by modeling the position information of the eavesdropping equipment, and thus the spatial interruption probability under the condition that the eavesdropping equipment obeys uniform distribution can be defined. The influence of the antenna parameters on the spatial interruption probability can be obtained by solving a closed solution of the spatial interruption probability average value.
It should be noted that the method of the embodiment of the present application may be executed by a single device, such as a computer or a server. The method of the embodiment can also be applied to a distributed scene and completed by the mutual cooperation of a plurality of devices. In such a distributed scenario, one of the multiple devices may only perform one or more steps of the method of the embodiment, and the multiple devices interact with each other to complete the method.
It should be noted that the above describes some embodiments of the present application. Other embodiments are within the scope of the following claims. In some cases, the actions or steps recited in the claims may be performed in a different order than in the embodiments described above and still achieve desirable results. In addition, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve desirable results. In some embodiments, multitasking and parallel processing may also be possible or may be advantageous.
Based on the same inventive concept, the application also provides a spatial interruption probability analysis device corresponding to the method of any embodiment.
Referring to fig. 9, the spatial interruption probability analysis apparatus includes:
a location obtaining module 901, configured to obtain locations of the base station and the legal device.
A position representing module 902, configured to represent the positions of the base station, the legal device, and the eavesdropping device in a polar coordinate manner, so as to obtain a position variable and a motion area.
In some embodiments, the location representation module 902 is further configured to:
acquiring an angle variable and an amplitude variable of the position;
and expressing the angle variable and the amplitude variable in a polar coordinate form, and taking the expression result as the position variable.
A parameter obtaining module 903, configured to obtain an antenna parameter set of the base station.
And the position modeling module 904 is configured to model the position of the eavesdropping device to obtain an eavesdropping position model.
In some embodiments, the location modeling module 904 is further configured to:
acquiring a position variable of the eavesdropping device;
processing the position variable of the eavesdropping device by adopting a first preset probability distribution function to obtain a first preset probability distribution model related to the second position variable;
using the first predetermined probability distribution model as a wiretap position model, wherein the incidence angle theta in the wiretap position modeleCompliance thetaeU (0,2 pi) distribution, eavesdropping distance D in position modeleCompliance
The distribution, U (: means that uniform distribution is obeyed,
representing the square of the farthest transmission distance of the base station.
The channel response module 905 is configured to model a legal channel response and an eavesdropping channel response to obtain a channel response model, where the legal channel response and the eavesdropping channel response are random variables generated based on the position variable.
In some embodiments, the channel response module 905 is further configured to:
acquiring the position variables, wherein the position variables comprise the position variables of the legal equipment and the position variables of the eavesdropping equipment;
acquiring the legal channel response and the eavesdropping channel response;
processing the position variable of the legal device, the position variable of the wiretapping device, the legal channel response and the wiretapping channel response by adopting a second predetermined probability distribution function to obtain a second predetermined probability distribution model;
using the second predetermined probability distribution model as a channel response model, wherein the channel response model comprises a legal channel response function and an eavesdropping channel response function, and the legal channel response function is expressed as
The eavesdropping channel response function is expressed as
Wherein
Representing the directional vector of the antenna array of a legitimate device,
representing the direction vector of the antenna array of a legitimate device, DeIndicating the distance of the eavesdropping device from the base station, DbIndicating the distance, theta, of legitimate devices from the base stationbIndicating angle of incidence, theta, of legitimate devicesb∈(0，2π)，θeIndicating angle of incidence theta of eavesdropping apparatuseE (0,2 π). Wherein h iseAn eavesdropping channel response, h, representing an eavesdropping devicebIndicating the legitimate channel response of the legitimate device,
representing a complex gaussian distribution, and α is the path loss exponent of flat rayleigh fading.
A capacity calculating module 906, configured to calculate signal-to-noise ratios of the legal device and the eavesdropping device according to the location variable, the channel response model, and the antenna parameter set, and calculate a channel capacity of the eavesdropping device according to the signal-to-noise ratio.
A probability calculation module 907, configured to calculate, in response to determining that the channel capacity is greater than a predetermined value, an insecure area expression according to the signal-to-noise ratio, the antenna parameter set, and the motion area of the eavesdropping device, and calculate a spatial outage probability expression according to the insecure area expression and the eavesdropping position model.
In some embodiments, the probability calculation module 907 is further configured to:
the antenna parameter set comprises a secret rate and a channel rate;
in response to determining that the channel capacity is greater than the difference between the channel rate and the secret rate, an insecure area exists;
calculating to obtain the expression of the nonsecure region according to the signal-to-noise ratio, the channel rate, the privacy rate and the motion region of the eavesdropping device, wherein the expression of the nonsecure region is
P represents the transmit power, heIndicating an eavesdropping channel response of an eavesdropping device,
variance, R, representing complex Gaussian noise of eavesdropping equipmentbIndicating the legal channel rate, RsWhich represents the rate at which the system is kept secret,
ntindicating the number of antennas of the base station.
In some embodiments, the probability calculation module 907 is further configured to:
acquiring the nonsecure region expression and the eavesdropping position model;
dividing the nonsecure region expression by a circular region in the eavesdropping position model to obtain a random variable expression;
taking the random variable expression as the spatial interruption probability expression, wherein,
Dmaxdenotes the radius of the circular area, pssopDependent on a random variable | he|2，pssopIs the spatial outage probability.
And a closed-form solution calculation module 908, configured to process the spatial interruption probability expression, calculate a closed-form solution of the spatial interruption probability expression, and use the closed-form solution as a spatial interruption probability analysis result.
In some embodiments, the calculate closed form solution module 908 is further to:
arranging the spatial interruption probability expression into a function model about eavesdropping channel response;
calculating an average value expression of the function model;
processing the average value expression by adopting a Zhansen inequality to obtain a relational expression of the average value and the position variable, wherein the Zhansen inequality is expressed as
X is a random variable, and alpha is more than or equal to 2;
taking the relational expression as a closed-form solution of the spatial interruption probability expression, wherein the closed-form solution is
When α is 2, the equation holds.
For convenience of description, the above devices are described as being divided into various modules by functions, and are described separately. Of course, the functionality of the various modules may be implemented in the same one or more software and/or hardware implementations as the present application.
The apparatus of the foregoing embodiment is used to implement the corresponding spatial outage probability analysis method in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiment, which are not described herein again.
Based on the same inventive concept, corresponding to the method of any embodiment described above, the present application further provides an electronic device, which includes a memory, a processor, and a computer program stored on the memory and running on the processor, and when the processor executes the program, the spatial interrupt probability analysis method described in any embodiment above is implemented.
Fig. 10 is a schematic diagram illustrating a more specific hardware structure of an electronic device according to this embodiment, where the electronic device may include: a processor 1010, a memory 1020, an input/output interface 1030, a communication interface 1040, and a bus 1050. Wherein the processor 1010, memory 1020, input/output interface 1030, and communication interface 1040 are communicatively coupled to each other within the device via bus 1050.
The processor 1010 may be implemented by a general-purpose CPU (Central Processing Unit), a microprocessor, an Application Specific Integrated Circuit (ASIC), or one or more Integrated circuits, and is configured to execute related programs to implement the technical solutions provided in the embodiments of the present disclosure.
The Memory 1020 may be implemented in the form of a ROM (Read Only Memory), a RAM (Random Access Memory), a static storage device, a dynamic storage device, or the like. The memory 1020 may store an operating system and other application programs, and when the technical solution provided by the embodiments of the present specification is implemented by software or firmware, the relevant program codes are stored in the memory 1020 and called to be executed by the processor 1010.
The input/output interface 1030 is used for connecting an input/output module to input and output information. The i/o module may be configured as a component in a device (not shown) or may be external to the device to provide a corresponding function. The input devices may include a keyboard, a mouse, a touch screen, a microphone, various sensors, etc., and the output devices may include a display, a speaker, a vibrator, an indicator light, etc.
The communication interface 1040 is used for connecting a communication module (not shown in the drawings) to implement communication interaction between the present apparatus and other apparatuses. The communication module can realize communication in a wired mode (such as USB, network cable and the like) and also can realize communication in a wireless mode (such as mobile network, WIFI, Bluetooth and the like).
It should be noted that although the above-mentioned device only shows the processor 1010, the memory 1020, the input/output interface 1030, the communication interface 1040 and the bus 1050, in a specific implementation, the device may also include other components necessary for normal operation. In addition, those skilled in the art will appreciate that the above-described apparatus may also include only those components necessary to implement the embodiments of the present description, and not necessarily all of the components shown in the figures.
The electronic device of the above embodiment is used to implement the corresponding spatial outage probability analysis method in any of the foregoing embodiments, and has the beneficial effects of the corresponding method embodiment, which are not described herein again.
Based on the same inventive concept, corresponding to any of the above-described embodiment methods, the present application further provides a non-transitory computer-readable storage medium storing computer instructions for causing the computer to perform the spatial outage probability analysis method according to any of the above embodiments.
Computer-readable media of the present embodiments, including both non-transitory and non-transitory, removable and non-removable media, may implement information storage by any method or technology. The information may be computer readable instructions, data structures, modules of a program, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), Static Random Access Memory (SRAM), Dynamic Random Access Memory (DRAM), other types of Random Access Memory (RAM), Read Only Memory (ROM), Electrically Erasable Programmable Read Only Memory (EEPROM), flash memory or other memory technology, compact disc read only memory (CD-ROM), Digital Versatile Discs (DVD) or other optical storage, magnetic cassettes, magnetic tape magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device.
The computer instructions stored in the storage medium of the foregoing embodiment are used to enable the computer to execute the spatial interruption probability analysis method according to any one of the foregoing embodiments, and have the beneficial effects of the corresponding method embodiments, which are not described herein again.
Those of ordinary skill in the art will understand that: the discussion of any embodiment above is meant to be exemplary only, and is not intended to intimate that the scope of the disclosure, including the claims, is limited to these examples; within the context of the present application, features from the above embodiments or from different embodiments may also be combined, steps may be implemented in any order, and there are many other variations of the different aspects of the embodiments of the present application as described above, which are not provided in detail for the sake of brevity.
In addition, well-known power/ground connections to Integrated Circuit (IC) chips and other components may or may not be shown in the provided figures for simplicity of illustration and discussion, and so as not to obscure the embodiments of the application. Furthermore, devices may be shown in block diagram form in order to avoid obscuring embodiments of the application, and this also takes into account the fact that specifics with respect to implementation of such block diagram devices are highly dependent upon the platform within which the embodiments of the application are to be implemented (i.e., specifics should be well within purview of one skilled in the art). Where specific details (e.g., circuits) are set forth in order to describe example embodiments of the application, it should be apparent to one skilled in the art that the embodiments of the application can be practiced without, or with variation of, these specific details. Accordingly, the description is to be regarded as illustrative instead of restrictive.
While the present application has been described in conjunction with specific embodiments thereof, many alternatives, modifications, and variations of these embodiments will be apparent to those of ordinary skill in the art in light of the foregoing description. For example, other memory architectures (e.g., dynamic ram (dram)) may use the discussed embodiments.
The present embodiments are intended to embrace all such alternatives, modifications and variances which fall within the broad scope of the appended claims. Therefore, any omissions, modifications, substitutions, improvements, and the like that may be made without departing from the spirit and principles of the embodiments of the present application are intended to be included within the scope of the present application.
Claims (10)
1. A spatial interruption probability analysis method is characterized in that the method is applied to a base station; the method comprises the following steps:
acquiring the positions of the base station and legal equipment;
expressing the positions of the base station, the legal equipment and the eavesdropping equipment in a polar coordinate mode to obtain a position variable and a motion area;
acquiring an antenna parameter set of the base station;
modeling the position of the eavesdropping device to obtain an eavesdropping position model;
modeling legal channel response and wiretap channel response to obtain a channel response model, wherein the legal channel response and the wiretap channel response are random variables generated based on the position variables;
calculating the signal-to-noise ratio of the legal device and the eavesdropping device according to the position variable, the channel response model and the antenna parameter set, and calculating the channel capacity of the eavesdropping device according to the signal-to-noise ratio;
in response to the fact that the channel capacity is larger than a preset value, calculating according to the signal-to-noise ratio, the antenna parameter set and a motion region of the eavesdropping device to obtain an unsafe region expression, and calculating according to the unsafe region expression and the eavesdropping position model to obtain a space interruption probability expression;
and processing the spatial interruption probability expression, calculating to obtain a closed solution of the spatial interruption probability expression, and taking the closed solution as a spatial interruption probability analysis result.
2. The method according to claim 1, wherein said modeling the location of said eavesdropping device comprises:
acquiring a position variable of the eavesdropping device;
processing the position variable of the eavesdropping device by adopting a first preset probability distribution function to obtain a first preset probability distribution model related to the second position variable;
using the first predetermined probability distribution model as a wiretap position model, wherein the incidence angle theta in the wiretap position modeleCompliance thetaeU (0,2 pi) distribution, eavesdropping distance D in position modeleCompliance
The distribution, U (: means that uniform distribution is obeyed,
representing the square of the farthest transmission distance of the base station.
3. The method of claim 1, wherein modeling the legitimate channel response and the eavesdropping channel response comprises:
acquiring the position variables, wherein the position variables comprise the position variables of the legal equipment and the position variables of the eavesdropping equipment;
acquiring the legal channel response and the eavesdropping channel response;
processing the position variable of the legal device, the position variable of the wiretapping device, the legal channel response and the wiretapping channel response by adopting a second predetermined probability distribution function to obtain a second predetermined probability distribution model;
using the second predetermined probability distribution model as a channel response model, wherein the channel response model comprises a legal channel response function and an eavesdropping channel response function, and the legal channel response function is expressed as
The eavesdropping channel response function is expressed as
Wherein
Representing the directional vector of the antenna array of a legitimate device,
representing the direction vector of the antenna array of a legitimate device, DeIndicating the distance of the eavesdropping device from the base station, DbIndicating the distance, theta, of legitimate devices from the base stationbIndicating angle of incidence, theta, of legitimate devicesb∈(0，2π)，θeIndicating angle of incidence theta of eavesdropping apparatuseE (0,2 π). Wherein h iseAn eavesdropping channel response, h, representing an eavesdropping devicebIndicating the legitimate channel response of the legitimate device,
representing a complex gaussian distribution, and α is the path loss exponent of flat rayleigh fading.
4. The method according to claim 1, wherein said calculating an insecure area representation of the system from the signal-to-noise ratio, the set of antenna parameters, and the area of motion of the eavesdropping device in response to determining that the channel capacity is greater than a predetermined value comprises:
the antenna parameter set comprises a secret rate and a channel rate;
in response to determining that the channel capacity is greater than the difference between the channel rate and the secret rate, an insecure area exists;
calculating to obtain the expression of the nonsecure region according to the signal-to-noise ratio, the channel rate, the privacy rate and the motion region of the eavesdropping device, wherein the expression of the nonsecure region is
P represents the transmit power, heIndicating an eavesdropping channel response of an eavesdropping device,
variance, R, representing complex Gaussian noise of eavesdropping equipmentbIndicating the legal channel rate, RsWhich represents the rate at which the system is kept secret,
ntindicating the number of antennas of the base station.
5. The method according to claim 1, wherein said calculating a spatial outage probability expression for the system based on the nonsecure region expression and the eavesdropping location model comprises:
acquiring the nonsecure region expression and the eavesdropping position model;
dividing the nonsecure region expression by a circular region in the eavesdropping position model to obtain a random variable expression;
taking the random variable expression as the spatial interruption probability expression, wherein,
Dmaxdenotes the radius of the circular area, pssopDependent on a random variable | he|2，pssopIs emptyInter-break probability.
6. The method of claim 1, wherein the processing the spatial outage probability expression to compute a closed-form solution to the spatial outage probability expression comprises:
arranging the spatial interruption probability expression into a function model about eavesdropping channel response;
calculating an average value expression of the function model;
processing the average value expression by adopting a Zhansen inequality to obtain a relational expression of the average value and the position variable, wherein the Zhansen inequality is expressed as
X is a random variable, and alpha is more than or equal to 2;
taking the relational expression as a closed-form solution of the spatial interruption probability expression, wherein the closed-form solution is
When α is 2, the equation holds.
7. The method according to claim 1, wherein said representing the locations of the base station, the legitimate device and the eavesdropping device in polar coordinate form comprises:
acquiring an angle variable and an amplitude variable of the position;
and expressing the angle variable and the amplitude variable in a polar coordinate form, and taking the expression result as the position variable.
8. The method according to claim 1, wherein said calculating a channel capacity of the eavesdropping device according to the signal-to-noise ratio comprises:
substituting the signal-to-noise ratio into a logarithmic function to obtain a function output quantity, wherein the expression of the logarithmic function is Ce＝log2(1+γe) Wherein，CeFor eavesdropping on the channel capacity of the channel, gammaeIs the signal-to-noise ratio of the eavesdropping device;
taking the function output as the channel capacity of the eavesdropping device.
9. A spatial outage probability analysis apparatus, comprising:
a position obtaining module, configured to obtain positions of the base station and a legal device;
the position representation module is used for representing the positions of the base station, the legal device and the eavesdropping device in a polar coordinate mode to obtain a position variable and a motion area;
a parameter obtaining module, configured to obtain an antenna parameter set of the base station;
the position modeling module is used for modeling the position of the eavesdropping device to obtain an eavesdropping position model;
the channel response module is used for modeling legal channel response and wiretap channel response to obtain a channel response model, wherein the legal channel response and the wiretap channel response are random variables generated based on the position variables;
a capacity calculation module, configured to calculate signal-to-noise ratios of the legal device and the eavesdropping device according to the position variable and the antenna parameter set, and calculate a channel capacity of the eavesdropping device according to the signal-to-noise ratios;
the probability calculation module is used for calculating to obtain an insecure area expression according to the signal-to-noise ratio, the antenna parameter set and the motion area of the eavesdropping device in response to the fact that the channel capacity is larger than a preset value, and calculating to obtain a spatial interruption probability expression according to the insecure area expression and the eavesdropping position model;
and the calculation closed-form solution module is used for processing the spatial interruption probability expression, calculating to obtain a closed-form solution of the spatial interruption probability expression, and taking the closed-form solution as a spatial interruption probability analysis result.
10. An electronic device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, characterized in that the processor implements the method according to any of claims 1 to 8 when executing the program.
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