A method for evaluating the probability of confidentiality interruption in communication systems based on intelligent reflective surfaces

Abstract

The present invention discloses a method for evaluating the probability of confidentiality interruption based on an intelligent reflective surface communication system, comprising: firstly, a legal user establishes a cumulative distribution function analysis model of the legal user according to a signal received from an intelligent reflective surface; then, an eavesdropping user establishes a probability density function analysis model of the eavesdropping user according to superimposed signals received from a base station and the intelligent reflective surface; finally, according to the cumulative distribution function of the legal user and the probability density function of the eavesdropping user, a confidentiality interruption probability analysis model of the intelligent reflective surface communication system is established, and an upper bound of the confidentiality interruption probability and an asymptotic expression under a high signal-to-noise ratio are calculated. The present invention is applicable to an actual phase-discrete intelligent reflective surface system, and the upper bound of the confidentiality interruption probability and the asymptotic expression under a high signal-to-noise ratio given by the present invention have low computational complexity, and are quite close to the actual simulation results, and can effectively evaluate the security performance of the intelligent reflective surface communication system.

Description

Technical Field

[0001] The invention relates to the technical field of wireless mobile communication, in particular to a method for evaluating the probability of confidentiality interruption based on an intelligent reflection surface communication system. Background Art

[0002] Smart reflective surfaces are a type of metasurface that consists of a large number of low-power passive reflective elements, each of which can individually control the reflection amplitude and phase, thereby achieving passive beamforming to improve the received signal quality of the target user. Therefore, smart reflective surfaces are used in various wireless communication systems to improve spectrum efficiency and energy efficiency.

[0003] In recent years, physical layer security has received extensive attention. As a supplement to traditional encryption technology, physical layer security can use the dynamic characteristics of the propagation channel to achieve secure communication. Since smart reflective surfaces have the ability to adjust the propagation channel, their deployment can give physical layer security an additional design dimension. Existing signal processing methods and security performance analysis results are usually not directly applicable to smart reflective surface systems, and related communication theories still need to be improved. Existing security performance analysis research is usually based on a phase-continuous smart reflective surface system, which has a high complexity in actual implementation. The present invention proposes a confidentiality interruption probability evaluation method based on a smart reflective surface communication system. The legal user establishes a cumulative distribution function distribution model of the legal user based on the signal received from the smart reflective surface; the eavesdropping user establishes a probability density function analysis model of the eavesdropping user based on the superimposed signal received from the base station and the smart reflective surface; based on the cumulative distribution function of the legal user and the probability density function of the eavesdropping user, a confidentiality interruption probability analysis model of the smart reflective surface communication system is established, and the upper bound of the confidentiality interruption probability and the asymptotic expression under high signal-to-noise ratio conditions are calculated. The present invention is applicable to a phase-discrete intelligent reflective surface system, and the upper bound of the confidentiality interruption probability and the asymptotic expression under a high signal-to-noise ratio condition provided by the present invention have low computational complexity and are quite close to actual simulation results. Summary of the invention

[0004] The technical problem to be solved by the present invention is the safety performance analysis problem of the intelligent reflecting surface system, and provides a confidentiality interruption probability evaluation method based on the intelligent reflecting surface communication system, which directly and effectively measures the safety performance of the system.

[0005] In order to solve the above technical problems, the present invention provides a method for evaluating the probability of confidentiality interruption based on an intelligent reflective surface communication system, comprising the following steps:

[0006] Step 1: Assume that the intelligent reflective surface communication system includes 1 base station, 1 intelligent reflective surface, 1 legitimate user and 1 eavesdropping user; the intelligent reflective surface is configured with N reflective elements, the number of phase quantization bits is b, and N and b are both integers greater than 1; the legitimate user receives a signal r from the intelligent reflective surface D ; The eavesdropping user receives the superimposed signal r from the base station and the smart reflective surface E ;

[0007] Step 2: The legitimate user receives the signal r from the smart reflective surface. D , establish the cumulative distribution function F of legitimate users γD ;

[0008] Step 3: The eavesdropping user receives the superimposed signal r from the base station and the smart reflective surface. E , establish the probability density function f of the eavesdropping user γE ;

[0009] Step 4: According to the cumulative distribution function of legitimate users and the probability density function of eavesdropping users, the confidentiality interruption probability SOP of the intelligent reflective surface communication system is established, and the upper bound of the confidentiality interruption probability is calculated. And the asymptotic expression for high signal-to-noise ratio

[0010] Preferably, in step 1, the received signal r of the legitimate user D It can be expressed as:

[0011]

[0012] Where x represents the signal sent by the base station. represents the expectation of the random variable, P represents the transmission power of the base station, η∈(0,1] represents the amplitude reflection coefficient of the smart reflective surface, d SR represents the distance from the base station to the smart reflective surface link, d RD represents the distance from the smart reflective surface to the legitimate user link, υ represents the path loss exponent, and h i represents the channel coefficient from the base station to the smart reflective surface, g i represents the channel coefficient from the smart reflective surface to the legitimate user, represents the phase shift of the i-th reflective element of the smart reflective surface, n D represents additive white Gaussian noise with zero mean and variance N0.

[0013] Eavesdrop on the user's received signal r E It can be expressed as:

[0014]

[0015] Among them, d RE represents the distance from the smart reflective surface to the eavesdropping user link, d SE represents the distance from the base station to the eavesdropping user link, p i represents the channel coefficient from the smart reflective surface to the eavesdropping user, h SE represents the channel coefficient from the base station to the eavesdropping user, n E It represents additive white Gaussian noise with zero mean and variance N0.

[0016] Preferably, in the above steps, the phase shift of the i-th reflective element of the smart reflective surface is The value formula is:

[0017]

[0018] Among them, the collection The operator ∠ represents the phase of a complex number, and the operator arg min x {y} represents the value of x that makes y reach its minimum value.

[0019] Preferably, in step 2, the cumulative distribution function F of legitimate users γD It can be expressed as:

[0020]

[0021] in, Г(·) represents the gamma function.

[0022] Preferably, in step 3, the probability density function f of the eavesdropping user is γE It can be expressed as:

[0023] f γE (x)=∈e -∈x

[0024] in,

[0025] Preferably, in step 4, the confidentiality interruption probability SOP of the intelligent reflective surface communication system can be expressed as:

[0026]

[0027] in, C th >0 indicates the target confidentiality rate.

[0028] Furthermore, we obtain the upper bound of the probability of confidentiality interruption: The expression is as follows:

[0029]

[0030] in,

[0031]

[0032]

[0033] in,

[0034] Furthermore, the asymptotic expression for high signal-to-noise ratio is obtained: The expression is as follows:

[0035]

[0036] The beneficial effects of the present invention are:

[0037] 1. The method of the present invention is applicable to the case of phase discreteness, which effectively reduces the implementation complexity of the smart reflective surface;

[0038] 2. The method of the present invention provides an upper bound expression for the probability of confidentiality interruption of the intelligent reflecting surface communication system and an asymptotic expression under high signal-to-noise ratio conditions. The method has low computational complexity and can effectively and clearly evaluate the security performance of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a block diagram of the intelligent reflective surface communication system on which the present invention is based.

[0040] Figure 2 This is a simulation curve diagram of the expression of confidentiality interruption probability given by the present invention. DETAILED DESCRIPTION

[0041] The present invention will be further described below with reference to the accompanying drawings and specific implementation examples:

[0042] like Figure 1 As shown in FIG. 1 , the intelligent reflective surface communication system includes a base station, a smart reflective surface, a legitimate user, and an eavesdropping user. The smart reflective surface is configured with N reflective elements, and the number of phase quantization bits is b, where N and b are both integers greater than 1. The legitimate user receives a signal r from the smart reflective surface. D ; The eavesdropping user receives the superimposed signal r from the base station and the smart reflective surface E .

[0043] (1) The received signal r of the legitimate user D It can be expressed as:

[0044]

[0045] Where x represents the signal sent by the base station. represents the expectation of the random variable, P represents the transmission power of the base station, η∈(0,1] represents the amplitude reflection coefficient of the smart reflective surface, d SR represents the distance from the base station to the smart reflective surface link, d RD represents the distance from the smart reflective surface to the legitimate user link, υ represents the path loss exponent, and h i represents the channel coefficient from the base station to the smart reflective surface, g i represents the channel coefficient from the smart reflective surface to the legitimate user, represents the phase shift of the i-th reflective element of the smart reflective surface, n D represents additive white Gaussian noise with zero mean and variance N0.

[0046] Eavesdrop on the user's received signal r E It can be expressed as:

[0047]

[0048] Among them, d RE represents the distance from the smart reflective surface to the eavesdropping user link, d SE represents the distance from the base station to the eavesdropping user link, p i represents the channel coefficient from the smart reflective surface to the eavesdropping user, h SE represents the channel coefficient from the base station to the eavesdropping user, n E It represents additive white Gaussian noise with zero mean and variance N0.

[0049] Preferably, in the above steps, the phase shift of the i-th reflective element of the smart reflective surface is The value formula is:

[0050]

[0051] Among them, the collection The operator ∠ represents the phase of a complex number, and the operator arg min x {y} represents the value of x that makes y reach its minimum value.

[0052] (2) In the above steps, the phase shift of the i-th reflective element of the smart reflective surface The value formula is:

[0053]

[0054] Among them, the collection The operator ∠ represents the phase of a complex number, and the operator arg min x {y} represents the value of x that makes y reach its minimum value.

[0055] (3) Cumulative distribution function F of legitimate users γDIt can be expressed as:

[0056]

[0057] in, Г(·) represents the gamma function.

[0058] (4) Probability density function f of eavesdropping users γE It can be expressed as:

[0059] f γE (x)=∈e -∈x

[0060] in,

[0061] Preferably, in step 4, the confidentiality interruption probability sop of the intelligent reflective surface communication system can be expressed as:

[0062]

[0063] in, C th >0 indicates the target confidentiality rate.

[0064] Furthermore, we obtain the upper bound of the probability of confidentiality interruption: The expression is as follows:

[0065]

[0066] in,

[0067]

[0068]

[0069] in,

[0070] Furthermore, the asymptotic expression for high signal-to-noise ratio is obtained: The expression is as follows:

[0071]

[0072] Figure 2 This is a simulation curve diagram of the expression of the confidentiality interruption probability given by the present invention. The simulation parameters are: N = 30, b = 1, C th=0.05. As can be seen from the figure, the present invention is applicable to the phase-discrete intelligent reflective surface system, and the upper bound of the confidentiality interruption probability and the asymptotic expression under high signal-to-noise ratio conditions given by the present invention are quite close to the actual simulation results, which can effectively measure the security performance of the intelligent reflective surface communication system.

[0073] The above is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principles of the present invention, and these improvements and modifications should also be considered as the protection scope of the present invention. All components not specified in this embodiment can be implemented using existing technologies.

Claims

1. A method for evaluating the probability of confidentiality interruption based on an intelligent reflective surface communication system, characterized in that: The method comprises the following steps: Step 1, assuming that the intelligent reflecting surface communication system includes 1 base station, 1 intelligent reflecting surface, 1 legitimate user and 1 eavesdropping user; the intelligent reflecting surface is configured with N reflecting elements, the number of phase quantization bits is b, and N and b are both integers greater than 1; Legitimate users receive signals from smart reflective surfaces D ; The eavesdropping user receives the superimposed signal r from the base station and the smart reflective surface E ; Step 2: The legitimate user receives the signal r from the smart reflective surface. D , establish the cumulative distribution function of legitimate users Step 3: The eavesdropping user receives the superimposed signal r from the base station and the smart reflective surface. E , establish the probability density function of the eavesdropping user Step 4: According to the cumulative distribution function of legitimate users and the probability density function of eavesdropping users, the confidentiality interruption probability SOP of the intelligent reflective surface communication system is established, and the upper bound of the confidentiality interruption probability is calculated. And the asymptotic expression for high signal-to-noise ratio The confidentiality interruption probability SOP of the intelligent reflective surface communication system is expressed as: in, C th >0 indicates the target confidentiality rate; Furthermore, we obtain the upper bound of the probability of confidentiality interruption: The expression is as follows: in, in, P represents the transmission power of the base station, η∈(0,1] represents the amplitude reflection coefficient of the smart reflective surface, and d SR represents the distance from the base station to the smart reflective surface link, d RD represents the distance from the smart reflective surface to the legitimate user link, N0 represents the zero mean variance, d RE represents the distance from the smart reflective surface to the eavesdropping user link, d SE Indicates the distance from the base station to the eavesdropping user link; Furthermore, the asymptotic expression for high signal-to-noise ratio is obtained: The expression is as follows:

2. According to claim 1, a method for evaluating the probability of confidentiality interruption based on an intelligent reflective surface communication system is characterized in that: In step 1, the received signal r of the legitimate user D It is expressed as: Where x represents the signal sent by the base station. represents the expectation of the random variable, v represents the path loss exponent, h i represents the channel coefficient from the base station to the smart reflective surface, g i represents the channel coefficient from the smart reflective surface to the legitimate user, represents the phase shift of the i-th reflective element of the smart reflective surface, n D represents additive white Gaussian noise with zero mean and variance N0; Eavesdrop on the user's receiving signal r E It is expressed as: Among them, p i represents the channel coefficient from the smart reflective surface to the eavesdropping user, h SE represents the channel coefficient from the base station to the eavesdropping user, n E It represents additive white Gaussian noise with zero mean and variance N0.

3. The method for evaluating the probability of confidentiality interruption based on an intelligent reflective surface communication system according to claim 2, characterized in that: Phase shift of the i-th reflective element of the smart reflective surface The value formula is: Among them, the collection The operator ∠ represents the phase of a complex number, and φ is used to calculate The intermediate parameter of the operator It represents the value of x that makes y reach its minimum value.

4. The method for evaluating the probability of confidentiality interruption based on an intelligent reflective surface communication system according to claim 1, characterized in that: In step 2, the cumulative distribution function of legitimate users It is expressed as: in, Γ(·) represents the gamma function, variable y∈(0,z), variable z>

0.

5. The method for evaluating the probability of confidentiality interruption based on an intelligent reflective surface communication system according to claim 1, characterized in that: In step 3, the probability density function of the eavesdropping user is It is expressed as: Among them, the variable x>0.

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