A physical layer authentication method based on RIS cascade channel signature

Abstract

This application belongs to the field of wireless communication security and signal processing technology, and discloses a physical layer authentication method based on RIS cascade channel signatures, including: Step 1: The target receiver Bob receives a signal from the transmitter, i.e., the potential attacker Eve or the legitimate sender Alice, and completes the received signal modeling; Step 2: Statistics are calculated for the cascaded channels from the transmitter to the smart reflective surface (RIS) and from the smart reflective surface (RIS) to the receiver, and the cascaded channels are equivalent to a point-to-point Nakagami fading channel model; Step 3: Channel estimation is performed on the received signal and statistical feature parameters are extracted; Step 4: After the target receiver Bob receives the signal from the transmitter, he performs identity authentication and makes an accurate judgment. This application effectively responds to identity impersonation attacks and other potential security threats, meeting the higher security and trustworthiness requirements of future communication systems.

Description

Technical Field

[0001] The present invention belongs to the technical field of wireless communication security and signal processing, and in particular relates to a physical layer authentication method based on RIS cascade channel signature. Background Art

[0002] Reconfigurable smart surfaces are a green and economical technology for future 5G / 6G communications. By programming them, they can dynamically adjust the propagation direction of incident electromagnetic waves with low energy consumption, thereby cleverly reconfiguring the wireless propagation environment.

[0003] To ensure the secure deployment of RIS technology in modern communication systems, there is an urgent need to design a robust and reliable security mechanism to safeguard the system's trustworthiness and integrity. Physical layer authentication (PLA) is considered a powerful complement to traditional upper-layer authentication mechanisms due to its advantages, including the lack of complex key management, low hardware dependency, and short authentication latency. Physical layer authentication leverages the inherent physical characteristics of wireless channels or hardware impairments. Physical layer authentication techniques can be categorized as channel-based authentication, hardware impairment-based authentication, and hybrid authentication. Physical layer authentication can effectively complement or enhance traditional upper-layer authentication methods, providing important insights for its application in RIS-assisted communication systems.

[0004] Recently, some preliminary research has focused on applying physical-layer authentication to RIS-assisted communication systems. One researcher proposed a tag-based physical-layer authentication scheme for RIS-assisted communication systems. This scheme extracts physical-layer characteristics such as channel gain and background noise, combines a random signal with the transmitter's private key to generate a robust tag signal, and uses asymmetric encryption to ensure the security of tag transmission. During the authentication process, the receiver recovers the tag signal through asymmetric decryption and verifies it using the Maximum A Posteriori Ratio (MAP) test method. Another study proposed a challenge-response physical-layer authentication mechanism based on a distributed reflective intelligent surface (DRIS). This mechanism transmits pilot signals (as challenges) by randomly selecting different reflective units and their configurations within a time slot and verifies the receiver's pre-shared channel characteristics (as responses), achieving identity authentication. Another study proposed a challenge-response physical-layer authentication (CR-PLA) mechanism based on RIS for cellular systems. This mechanism uses the base station to randomly configure the RIS (as a challenge) and verify the channel response of the received signal (as a response), effectively distinguishing legitimate users from attackers. Another study proposed a scheme that leverages the dual sparse structure of the RIS channel to improve authentication performance. By extracting features from the virtual angles of arrival and departure in the cascaded channel, a robust signature for authentication is constructed. During the training phase, reference signatures of legitimate users are stored; during the verification phase, authentication is performed by matching the extracted signatures in real time with the reference signatures.

[0005] The technical defects and deficiencies in the existing RIS-assisted communication system physical layer authentication technology mainly include the following issues:

[0006] First, existing work often considers the statistical characteristics of a single channel, but does not consider the overall statistical characteristics of the cascaded channels. Therefore, it is unclear how considering the statistical characteristics of the cascaded channels affects the design of physical layer authentication schemes.

[0007] Second, existing solutions mostly focus on instantaneous detection probability and false alarm probability. Their characterization capabilities are affected by channel fading and signal noise, resulting in instability.

[0008] 3. Existing solutions often focus on a single path, and no one has considered incorporating multipath effects, or multi-channel diversity effects, into solution design. The impact of multipath effects on RIS authentication performance has not been fully explored. Summary of the Invention

[0009] In order to solve the above technical problems, the present application provides a physical layer authentication method based on RIS cascade channel signature. This method overcomes the above technical bottlenecks and provides a physical layer authentication method with high reliability, high discrimination and quantifiable performance evaluation for RIS-assisted communication systems, so as to effectively deal with identity impersonation attacks and other potential security threats, and meet the higher requirements of future communication systems for security and credibility.

[0010] In order to achieve the above objectives, this application is implemented through the following technical solutions:

[0011] This application is a physical layer authentication method based on RIS cascade channel signatures. The physical layer authentication method is applied to a RIS-assisted communication system. The RIS-assisted communication system includes a legitimate sender Alice, a target receiver Bob, a potential attacker Eve, and a smart reflective surface (RIS). The legitimate sender Alice sends a data signal to the target receiver Bob via the smart reflective surface (RIS). The authentication method includes two stages: feature extraction and judgment, specifically including the following steps:

[0012] Step 1: In the feature extraction phase, the target receiver Bob receives a signal from the transmitter, i.e., the potential attacker Eve or the legitimate sender Alice. The received signal is modeled by considering the channel effects of the RIS-assisted communication system.

[0013] Step 2: Count the cascade channels from the transmitter to the smart reflecting surface (RIS) and from the smart reflecting surface (RIS) to the receiver, and equate the cascade channels to a point-to-point Nakagami fading channel model.

[0014] Step 3: Perform cascade channel estimation on the received signal of the target receiver Bob in step 1 to obtain a cascade channel estimation value, and extract the estimated value of the statistical characteristic parameter from the cascade channel estimation value, wherein the estimated value of the statistical characteristic parameter includes the estimated value of the scale parameter of the fading channel model obeying the Nakagami distribution. and the estimated value of the shape parameter of the fading channel model following the Nakagami distribution

[0015] Step 4: In the judgment stage, after the target receiver Bob receives the signal from the transmitter, the target receiver Bob performs identity authentication and makes an accurate judgment.

[0016] A further improvement of the present application is that in step 1, the target receiver Bob receives the signal from the transmitter, and considers the channel influence under the RIS-assisted communication system to complete the received signal modeling, which specifically includes the following steps:

[0017] Step 1.1: The smart reflection surface (RIS) in the RIS-assisted communication system consists of N reflection units. The complex fading channel vector from the transmitter to the reflection unit on the smart reflection surface is defined as , define the complex fading channel vector from the reflection unit on the smart reflection surface to the target receiver Bob as :

[0018] ,

[0019] Considering phase shift , the complex fading channel vector from the transmitter to the reflective unit on the smart reflective surface , the complex fading channel vector from the reflection unit on the smart reflection surface to the target receiver Bob Reflection loss is the multiplicative fading of two channels after the reflection surface is introduced. The initial received signal Modeled as:

[0020] ,

[0021] in, Represents the index identifier of the reflective unit on the smart reflective surface, satisfying , Indicates the distance from the transmitter to the smart reflective surface. The complex fading channel vector of the reflection unit, Indicates the first The complex fading channel vector from the reflection unit to the target receiver Bob, Indicates the first The phase shift introduced by the reflection unit, Indicates time The signal sent, represents additive Gaussian white noise, satisfying , represents a Gaussian distribution with a mean of 0 and a variance of 1. represents the average signal-to-noise ratio under a single reflection unit, represents the imaginary unit, is an exponential function, is a natural constant, and λ is the variable of the exponential part;

[0022] Step 1.2, the received signal is rewritten as:

[0023] ;

[0024] Among them, the channel coefficient , Represents the modulus of a complex number, the first The phase shift introduced by the reflection unit With smart reflective surface The deviation between the ideal compensation phases of the reflection units is modeled as Phase noise of a reflector unit :

[0025] in, Indicates the first The ideal compensation phase of each reflection unit, , is the argument operator, Phase noise of a reflector unit Randomly distributed in a circular pattern superior.

[0026] A further improvement of the present application is that: Step 2 performs statistics on the cascaded channels from the transmitter to the smart reflecting surface RIS and from the smart reflecting surface RIS to the receiver, and the cascaded channels are equivalent to a point-to-point Nakagami fading channel model, specifically comprising the following steps:

[0027] Step 2.1, define the transmitter to the smart reflective surface The complex fading channel vector of the reflection unit The expected value of the amplitude is , from the smart reflective surface The complex fading channel vector from the reflection unit to the target receiver Bob The expected value of the amplitude is :

[0028] in, Indicates the expectation operator, operator represents the modulus of a complex number, Represents the definition symbol, and the mean of the cascade channel is: , channel coefficient The real part of and the imaginary part are independent of each other and follow the following distributions:

[0029] ,

[0030] in, is the Gaussian distribution symbol, represents the real part operator of a complex number, The imaginary part operator of a complex number, the real part The mean statistical parameter of 、real part The variance statistical parameter of , imaginary part The variance statistical parameter of They are modeled as:

[0031]

[0032]

[0033] ;

[0034] The characteristic function is defined as , is the phase noise of The order characteristic function, is the order of the characteristic function, which is a non-zero integer. is the first-order characteristic function of phase noise, is the second-order characteristic function of phase noise;

[0035] Step 2.2: When it is large, according to the law of large numbers, the channel amplitude Modeled as a point-to-point Nakagami fading channel model, the channel amplitude The probability density function of is expressed as:

[0036] ;

[0037] in, Indicates that the fading channel model follows the shape parameter of the Nakagami distribution,

[0038] , Indicates that the fading channel model follows the scale parameter of the Nakagami distribution, , represents the gamma function, is the independent variable, representing the channel amplitude The value of .

[0039] A further improvement of the present application is that step 3 specifically includes the following steps:

[0040] Step 3.1: Least squares channel estimation to obtain the cascade channel estimation value: The equivalent channel gain of the RIS-assisted communication system is: , after discretization, At sampling points, the discrete received signal is: , is the sampling index, , To send discrete signals, is discrete additive white Gaussian noise, and the discrete received signal vector is: ,in, represents the pilot signal vector, represents the noise vector; the minimum residual norm is , is the conjugate transpose symbol, represents the Euclidean norm, for the equivalent channel gain Taking the derivative and setting it to zero, we get the optimal estimate of the equivalent channel gain: , thus obtaining the concatenated channel estimate: ;

[0041] In step 3.2, under the maximum likelihood (MLE) estimation method of the Nakagami fading channel model, the log-likelihood function is expressed as:

[0042] ,

[0043] in, is the amplitude of the concatenated channel estimate, represents the gamma function, Indicates that the fading channel model follows the shape parameter of the Nakagami distribution, Indicates that the fading channel model obeys the scale parameter of the Nakagami distribution, and the fading channel model obeys the scale parameter of the Nakagami distribution respectively by the log-likelihood function and the fading channel model follows the shape parameter of the Nakagami distribution Taking the derivative and setting it to zero, we can get the scale parameter of the fading channel model that follows the Nakagami distribution. Estimated value of: , the fading channel model follows the shape parameter of the Nakagami distribution Estimated value of The following equations are solved using numerical iteration method: ,in Represents the derivative of the natural logarithm of the gamma function.

[0044] A further improvement of the present application is that in step 4, the target recipient Bob performs identity authentication and makes an accurate decision, which specifically includes the following steps:

[0045] Step 4.1: Model the identity authentication problem as a binary hypothesis testing problem, that is, the target receiver Bob determines the current received signal Is it from the legitimate sender Alice or from the potential attacker Eve? The binary hypothesis test is written as:

[0046] in, is the null hypothesis, indicating that the current received signal comes from the legitimate sender Alice, is the alternative hypothesis, indicating that the current received signal comes from the potential attacker Eve, and denote the additive Gaussian white noise of the legitimate sender and potential attacker respectively, represents the channel coefficient of potential attacker Eve, represents the channel coefficient of the legitimate sender Alice;

[0047] Step 4.2: When the RF signal reaches the target receiver Bob, the target receiver Bob sends the received signal to the energy detector to obtain the test statistic value: , represents the scalar coefficient, Indicates the derivation of time and the test statistic value and the decision threshold of the energy detector Compare as a binary decision criterion: If , then the judgment is , the signal source is the legitimate sender Alice; if , then the judgment is , the signal originates from potential attacker Eve, and the RIS auxiliary communication system rejects the signal.

[0048] A further improvement of this application is to: Modeled as the sum of squares of several Gaussian random variables, under the null hypothesis The test statistic value under and the alternative hypothesis The test statistic value under All obey the non-central chi-square distribution. In the binary hypothesis testing framework, the judgment and certification performance indicators are divided into detection probability and false alarm probability :

[0049] ,

[0050] The order of use is in a broad sense function The detection probability is obtained respectively and false alarm probability The closed-form expression for :

[0051] in, Indicates that the alternative hypothesis Under these conditions, the test statistic Greater than the judgment threshold The probability of Indicates that the null hypothesis Under these conditions, the test statistic Greater than the judgment threshold The probability of channel fading and signal noise is taken into account. The authentication performance is analyzed in single fading cascade channel scenario and multipath fading cascade channel scenario. The single fading cascade channel scenario is analyzed in two cases: the signal-to-noise ratio has a clear probability density function (PDF) and the signal-to-noise ratio does not have a clear probability density function (PDF). The multipath fading cascade channel scenario is analyzed in two cases: the signal-to-noise ratio has a clear probability density function (PDF) and the signal-to-noise ratio does not have a clear probability density function (PDF).

[0052] The beneficial effects of this application are: (1) This application applies the Nakagami fading channel model distribution as the point-to-point Nakagami fading channel model of the RIS-assisted communication system, accurately characterizes it, and effectively describes its statistical characteristics under actual fading conditions. (2) Based on the statistical characteristics characterized by the established point-to-point Nakagami fading channel model, this application designs an authentication method based on an energy detector, and effectively analyzes the received signal through the energy detector to identify potential identity counterfeiting attacks. (3) Based on the statistical signal processing method, this application conducts an in-depth analysis of the false alarm probability and the detection probability in the authentication performance. In order to reduce the error, this application mathematically models the average false alarm probability and the average detection probability, and analyzes the performance under single-channel and multi-channel conditions respectively. This framework enables this application to accurately characterize the impact of the adopted characteristics on the identity authentication performance. (4) This application uses the system's cascade channel characteristics for physical layer authentication, gets rid of the traditional encryption technology's dependence on key management, and can effectively resist identity-based masquerade attacks in resource-constrained environments, significantly improving the security and reliability of the RIS-assisted communication system and enhancing the ability to resist impersonation attacks. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] Figure 1 This is a structural diagram of the RIS auxiliary communication system of this application

[0054] Figure 2 This is the verification experiment result of the point-to-point Nakagami fading channel model of this application.

[0055] Figure 3 This is a consistency verification diagram of the theoretical analysis and simulation results of this application.

[0056] Figure 4 This is an analysis chart of the authentication performance under different RIS-assisted communication system parameter settings for this application.

[0057] Figure 5 This is an experimental result diagram showing the impact of the change in the decision threshold of this application on the average false alarm probability of the system and the impact of the average false alarm probability on the average detection probability.

[0058] Figure 6 This is a diagram showing the impact of the signal-to-noise ratio on the detection probability under different Rice fading factors of illegal transmitters in this application.

[0059] Figure 7 This is a diagram showing the impact of the Ricean factor of an illegal transmitter on the average detection probability under different phase error concentrations in this application.

[0060] Figure 8 This is a graph showing the experimental results of this application studying the changing trend of authentication performance under different Nakagami shape parameters.

[0061] Figure 9 This is a performance comparison chart of the authentication scheme of this application and the existing channel gain-based authentication scheme.

[0062] Figure 10 This application is an experimental diagram of the impact of changes in the number of multi-channel branches on the performance of the maximum ratio combining authentication method. DETAILED DESCRIPTION

[0063] The following diagrams illustrate embodiments of the present invention. For clarity, many practical details are included in the following description. However, it should be understood that these practical details are not intended to limit the present invention. In other words, in some embodiments of this application, these practical details are not essential.

[0064] like Figure 1As shown, the present application is a physical layer authentication method based on RIS cascade channel signatures. The physical layer authentication method is applied to a RIS-assisted communication system, which includes a legitimate sender Alice, a target receiver Bob, a potential attacker Eve, and a smart reflective surface (RIS). In this system, Alice, Eve, and Bob are all single-antenna devices operating in an isotropic scattering environment. Due to obstacles in the communication path, there is no direct link between the legitimate sender and receiver. Therefore, communication relies entirely on the smart reflective surface (RIS) for signal reflection and transmission. In this scenario, the legitimate sender Alice sends a data signal to the target receiver Bob via the smart reflective surface (RIS). Suppose that a potential attacker Eve disguises herself as Alice, establishes a communication connection with Bob, and uses the smart reflective surface (RIS) to transmit a tampered malicious signal to Bob. Due to the high openness of the wireless channel, the RIS-assisted communication system is vulnerable to identity spoofing attacks. Once Eve successfully accesses the system through identity spoofing, she may launch more advanced attacks, such as man-in-the-middle attacks, to disrupt subsequent communications between Alice and Bob.

[0065] The physical layer authentication method based on RIS cascade channel signature includes two stages: feature extraction and judgment, and specifically includes the following steps:

[0066] Step 1: In the feature extraction phase, the target receiver Bob receives a signal from the transmitter, which is either the potential attacker Eve or the legitimate sender Alice. The received signal modeling is completed by considering the channel influence under the RIS-assisted communication system. The specific steps include:

[0067] Step 1.1: The intelligent reflective surface RIS in the RIS-assisted communication system consists of The complex fading channel vector from the transmitter to the reflection unit on the smart reflection surface is defined as , define the complex fading channel vector from the reflection unit on the smart reflection surface to the target receiver Bob as :

[0068]

[0069] Considering phase shift , the complex fading channel vector from the transmitter to the reflective unit on the smart reflective surface , the complex fading channel vector from the reflection unit on the smart reflection surface to the target receiver Bob With reflection loss, the initial received signal Modeled as: ,

[0070] in, Represents the index identifier of the reflective unit on the smart reflective surface, satisfying , It represents the transmission from the transmitter such as the legitimate sender Alice or the potential attacker Eve to the first The complex fading channel vector of the reflection unit, Indicates the first The complex fading channel vector from the reflection unit to the target receiver Bob, Indicates the first The phase shift introduced by the reflection unit, Indicates time The signal sent, represents additive Gaussian white noise, satisfying , represents a Gaussian distribution with a mean of 0 and a variance of 1. represents the average signal-to-noise ratio (SNR) under a single reflection unit, represents the imaginary unit, is an exponential function, is a natural constant, and λ is the variable of the exponential part;

[0071] Step 1.2, the received signal is rewritten as: ;

[0072] Among them, the channel coefficient , operator Represents the modulus of a complex number, the first Phase shift introduced by the reflection unit With smart reflective surface The deviation between the ideal compensation phases of the reflection units is modeled as Phase noise of a reflector unit :

[0073] in, Indicates the first The ideal compensation phase of each reflection unit, , phase noise Randomly distributed in a circular pattern superior, is the argument operator, Phase noise of a reflector unit are independent and identically distributed and have a common characteristic function ,in is an integer.

[0074] Step 2: Count the cascaded channels from the transmitter to the smart reflecting surface (RIS) and from the smart reflecting surface (RIS) to the receiver, and equate the cascaded channels to a point-to-point Nakagami fading channel model. This specifically includes the following steps:

[0075] Step 2.1, define the transmitter to the smart reflective surface The complex fading channel vector of the reflection unit The expected value of the amplitude is , from the smart reflective surface The complex fading channel vector from the reflection unit to the target receiver Bob The expected value of the amplitude is :

[0076] in, Indicates the expectation operator, operator represents the modulus of a complex number, Represents the definition symbol, and the mean of the cascade channel is: According to the central limit theorem, when the sample size is large enough, the sum of independent and identically distributed random variables approaches the normal distribution. In this modeling, when a large number of independent channel coefficients are considered, their linear combination can approximately obey the complex normal distribution. Therefore, when When it is large, the channel coefficient Obeying Gaussian distribution, channel coefficient The real part of and the imaginary part are independent of each other and follow the following distributions:

[0077] in, is the Gaussian distribution symbol, represents the real part operator of a complex number, The imaginary part operator of a complex number, the real part The mean statistical parameter of 、real part The variance statistical parameter of Imaginary part The variance statistical parameter of , are modeled as:

[0078]

[0079] The characteristic function is defined as , is the phase noise of The order characteristic function, is the order of the characteristic function, which is a non-zero integer. is the first-order characteristic function of phase noise, is the second-order characteristic function of phase noise;

[0080] Step 2.2: When the channel amplitude is large enough, The channel is modeled as a point-to-point Nakagami fading channel. Sufficiently large comes from the law of large numbers. This application is modeled using the law of large numbers. According to the law of large numbers, the channel amplitude The probability density function of is expressed as: ;

[0081] in, Indicates that the fading channel model follows the shape parameter of the Nakagami distribution, , Indicates that the fading channel model follows the scale parameter of the Nakagami distribution, , represents the gamma function, is the independent variable, representing the channel amplitude The value of .

[0082] Step 3: Perform cascade channel estimation on the received signal of the target receiver Bob in step 1 to obtain a cascade channel estimation value, and extract the estimated value of the statistical characteristic parameter from the cascade channel estimation value, wherein the statistical characteristic parameter includes the estimated value of the scale parameter of the fading channel model obeying the Nakagami distribution. and the estimated value of the shape parameter of the fading channel model following the Nakagami distribution The specific steps include:

[0083] Step 3.1: Least squares (LS) channel estimation to obtain the cascade channel estimation value: The equivalent channel gain of the RIS-assisted communication system is: , after discretization, At sampling points, the discrete received signal is: , is the sampling index, , For discrete received signals, To send discrete signals, is discrete additive white Gaussian noise, and the discrete received signal vector is: ,in, represents the pilot signal vector, represents the noise vector; the minimum residual norm is , the residual norm is expanded to: , is the conjugate transpose symbol, represents the Euclidean norm, for the equivalent channel gain Taking the derivative and setting it to zero, we get the optimal estimate of the equivalent channel gain: , thus obtaining the concatenated channel estimate: ;

[0084] Step 3.2, Nakagami fading channel model maximum likelihood (MLE) estimation, extract the estimated value of the statistical characteristic parameters: get the The concatenated channel estimate of samples , is the sample index, , represents the total number of samples collected for each received signal, and the amplitude of the cascaded channel estimate is , under the premise of keeping the communication parties and communication positions unchanged, the independent communications that send signals and do not interfere with each other are sampled to obtain A set of concatenated channel estimates , the amplitude of the concatenated channel estimate Considered as a group of independent samples in the channel fading channel model that obeys the Nakagami distribution, the log-likelihood function is expressed as follows under the maximum likelihood estimation method:

[0085]

[0086] in, represents the gamma function, Indicates that the fading channel model follows the shape parameter of the Nakagami distribution, Indicates that the fading channel model obeys the scale parameter of the Nakagami distribution, and the fading channel model obeys the scale parameter of the Nakagami distribution respectively by the log-likelihood function and the fading channel model follows the shape parameter of the Nakagami distribution Taking the derivative and setting it to zero, we can get the scale parameter of the fading channel model that follows the Nakagami distribution. Estimated value of: , the fading channel model follows the shape parameter of the Nakagami distribution Estimated value of The following equations are solved using numerical iteration method: ,in Represents the derivative of the natural logarithm of the gamma function.

[0087] Step 4: In the judgment phase, after the target receiver Bob receives the signal from the transmitter, he performs identity authentication and makes an accurate judgment. The specific steps include the following:

[0088] Step 4.1: Model the identity authentication problem as a binary hypothesis testing problem, that is, the target receiver Bob determines the current received signal Is it from the legitimate sender Alice or from the potential attacker Eve? The binary hypothesis test is written as:

[0089]

[0090] in, is the null hypothesis, indicating that the current received signal comes from the legitimate sender Alice, is the alternative hypothesis, indicating that the current received signal comes from the potential attacker Eve, represents the additive white Gaussian noise of the legitimate sender, represents the additive white Gaussian noise of potential attackers, represents the channel coefficient of potential attacker Eve, represents the channel coefficient of the legitimate sender Alice;

[0091] Step 4.2: When the RF signal reaches the target receiver Bob, the target receiver Bob sends the received signal to the energy detector. The energy detector first performs noise pre-filtering to suppress noise or interference within the filtering range; then squares the filtered output signal to calculate the energy of the filtered output signal. Finally, the integration operation is performed to calculate the energy of the filtered output signal through the integrator in the energy detector. Accumulate and get the test statistic value: , represents the scalar coefficient, Indicates the derivation of time and the test statistic value and the decision threshold of the energy detector Compare as a binary decision criterion: If , then the judgment is , the signal source is the legitimate sender Alice; if , then the judgment is , the signal originates from potential attacker Eve, and the RIS auxiliary communication system rejects the signal.

[0092] The test statistic value Modeled as the sum of squares of several Gaussian random variables, under the null hypothesis The test statistic value under and the alternative hypothesis The test statistic value under All obey the non-central chi-square distribution, and their probability density function (PDF) is:

[0093] in, is the modified Bessel function of the first kind, represents the order of the modified Bessel function of the first kind, is the degrees of freedom of the noncentral chi-square distribution, is the variable, is the test statistic The value of is the signal-to-noise ratio of the legitimate sender, For the signal-to-noise ratio of potential attackers, considering channel fading and signal noise, the authentication performance is analyzed in single fading cascade channel scenario and multipath fading cascade channel scenario. Among them, the single fading cascade channel scenario is analyzed under the two cases where the signal-to-noise ratio has a clear probability density function (PDF) and no clear probability density function (PDF). The multipath fading cascade channel scenario is analyzed under the two cases where the signal-to-noise ratio has a clear probability density function (PDF) and no clear probability density function (PDF). The judgment authentication performance indicators are divided into detection probability and false alarm probability :

[0094]

[0095] in, Indicates that the alternative hypothesis Under these conditions, the test statistic Greater than the judgment threshold The probability of Indicates that the null hypothesis Under these conditions, the test statistic Greater than the judgment threshold The probability of using the order is in a broad sense function The detection probability is obtained respectively and false alarm probability The closed-form expression for :

[0096]

[0097] In the single fading cascade channel scenario, the signal-to-noise ratio is analyzed in two cases: with a clear probability density function (PDF) and without a clear probability density function (PDF). In the RIS-assisted communication system, random factors such as channel fading and noise will significantly affect the accuracy of signal detection. In order to comprehensively evaluate the system performance, these fluctuation factors need to be modeled. Taking energy detection as an example, in order to reflect the channel characteristics, the channel fading is usually statistically averaged to ensure that the detector has stable performance under different channel conditions. This application uses the average detection probability and the average false alarm probability As the main performance indicators. Specifically:

[0098] Calculate the average detection probability in a single fading cascade channel scenario with a clear probability density function and the average false alarm probability :

[0099] Average detection probability The signal-to-noise ratio of the legitimate sender is The probability density function of Upper pair detection probability The integral calculation results in: , It obeys the Gamma distribution, and its probability density function is . Indicates the signal-to-noise ratio for legitimate senders Seek the derivative, represents the probability density function of the Gamma distribution, is the legitimate sender signal-to-noise ratio The shape parameter of the Gamma distribution is for The scale parameter of the Gamma distribution is is the scale parameter of the Nakagami distribution of the fading channel model corresponding to the legitimate sender, is the signal energy, is the unilateral noise power spectral density. This integral reflects the impact of the signal-to-noise ratio (SNR) change, comprehensively considering the impact of channel fading and signal noise, so that the detection performance can be fully evaluated. The series expansion form of the function and the signal-to-noise ratio of the legitimate sender obeying the Gamma distribution The probability density function of Integrate over , and we get the result:

[0100] in, is positive infinity, indicating that the upper limit of the sum is infinite, that is, this is an infinite series expansion. Based on The index of the summation term of the series expanded by the function, is an exponential function, is a natural constant, and λ is the variable of the exponential part;

[0101] By introducing the generalized hypergeometric function, the above formula is simplified to:

[0102]

[0103] in, is the generalized hypergeometric function, , combined with the generalized hypergeometric function and the legitimate sender binary hypergeometric function in a single fading cascade channel scenario Calculate the average detection probability under a single fading cascade channel scenario with a clear probability density function :

[0104]

[0105] Average false alarm probability is achieved by the signal-to-noise ratio of the potential attacker The probability density function of False alarm probability The integral calculation results in: , Represents the signal-to-noise ratio of potential attackers Derivative, potential attacker signal-to-noise ratio It obeys the Gamma distribution, and its probability density function is . represents the probability density function of the Gamma distribution, is the signal-to-noise ratio of a potential attacker The shape parameter of the Gamma distribution is Signal-to-noise ratio of potential attackers The scale parameter of the Gamma distribution is is the scale parameter of the channel amplitude corresponding to the potential attacker that follows the Nakagami distribution, using The series expansion form of the function, and in The signal-to-noise ratio of potential attackers following the Gamma distribution The probability density function of Integrate over , and we get the result:

[0106] By introducing the generalized hypergeometric function, the above formula is simplified to:

[0107]

[0108] Combined with generalized hypergeometric function and the potential attacker binary hypergeometric function Calculate the average false alarm probability in a single fading cascade channel scenario with a clear probability density function :

[0109]

[0110] Analyze and calculate the average detection probability in two cases in a single fading cascade channel scenario where the signal-to-noise ratio does not have a clear probability density function (PDF). and the average false alarm probability The traditional method is to calculate the average detection probability based on the probability density function (PDF) of SNR. ) and the average false alarm probability ( However, in complex channels, the PDF of SNR is often difficult to analyze or presents non-standard distribution, which makes calculation difficult. Therefore, this application converts the integral of SNR into Complex plane contour integral of a function can be solved without explicit PDF and This method is applicable to any integrable distribution, significantly reduces computational complexity, and is particularly suitable for real-time performance evaluation in dynamic channel environments.

[0111] Using broad Function, the detection probability Written as:

[0112] ,

[0113] in, is the integral variable, and its value path is a closed path. is a point with the origin as its center and a radius of A closed path where , represents the imaginary unit, and this path ensures that all poles in the integrand, in particular The poles at are all contained within the path, so the residue theorem can be easily applied to solve the integral. The moment generating function of ,in represents the expectation operator, is a real number parameter, and the detection probability exist The average detection probability is obtained by taking the average of the distribution of Written as: ;

[0114] For the legitimate sender Nakagami fading channel model, the moment generating function of the legitimate sender's signal-to-noise ratio is Expressed as:

[0115] ,

[0116] Will Substitution ,get:

[0117] ;

[0118] Among them, the characteristic coefficient , is the fading characteristic coefficient of the legitimate sender's channel. The above integral can be converted into the residue sum at the extreme point through the residue theorem, thus avoiding complex analytical integration. Let the integrand be: ,pole satisfy And the order , the integrand At the Pole The residue at Consider and analyze the following two situations respectively :

[0119] hour, ;

[0120] hour, ;

[0121] in, represents the integrand At the Pole = The residue at , where the order of the extreme point is the signal-to-noise ratio of the legitimate sender The shape parameter of the Gamma distribution , represents the integrand At the Pole =0, where the order of the extreme point is ;

[0122] Using broad Function, the false alarm probability Written as:

[0123] ,

[0124] Among them, by calculating the false alarm probability exist The average false alarm probability is obtained by taking the average of the distribution of Written as: in, Signal-to-noise ratio of potential attackers The general form of the moment generating function (MGF);

[0125] For the potential attacker Nakagami fading channel model, the moment generating function of the potential attacker's signal-to-noise ratio is Expressed as:

[0126] ,

[0127] Will Substitution ,get: ;

[0128] in, , is the potential attacker's channel fading characteristic coefficient, let the integrand: ,pole satisfy And the order , its residue , consider and analyze the following two cases respectively :

[0129] hour,

[0130] ;

[0131] hour,

[0132] in, represents the integrand At the Pole = The residue at , where the order of the extreme point is the signal-to-noise ratio of the potential attacker The shape parameter of the Gamma distribution , represents the integrand At the Pole =0, where the order of the extreme point is .

[0133] The multipath fading cascade channel scenario is analyzed in two cases: the signal-to-noise ratio has a clear probability density function (PDF) and the signal-to-noise ratio does not have a clear probability density function (PDF). In previous studies, the average detection probability of the system was calculated mainly for the single-path fading cascade channel. and the average false alarm probability . However, in actual RIS-assisted wireless communication systems, the channel structure is often more complex, and there are usually multiple cascaded channel paths. The impact of multi-channel diversity effect on system performance cannot be ignored. To this end, this application introduces the maximum ratio combining (MRC) technology: this technology is a classic multi-channel combining technology that can improve signal quality by performing optimal weighted combining of signals from different channels under multi-channel conditions, thereby significantly improving system performance. In addition, this application further explores the feasibility of applying identity authentication methods in multi-channel scenarios, and analyzes how the authentication mechanism can further improve the reliability and accuracy of the system under multi-channel conditions. Specifically:

[0134] Calculate the average detection probability of the system in a multipath fading cascade channel scenario with a clear PDF in the multipath fading cascade channel scenario Average false alarm probability of the system under multipath fading cascade channel scenario The method is:

[0135] for:

[0136] Average false alarm probability for:

[0137] in, is the binary hypergeometric function of the legitimate sender in the multipath fading cascade channel scenario, is the binary hypergeometric function of the potential attacker in the multipath fading cascade channel scenario, is the decision threshold, is the signal-to-noise ratio of the legitimate sender The shape parameter of the Gamma distribution is Signal-to-noise ratio of potential attackers The shape parameter of the Gamma distribution is is the average signal-to-noise ratio under a single reflection unit, is the scale parameter of the Nakagami distribution of the channel amplitude corresponding to the potential attacker, is the signal energy, is the unilateral noise power spectral density, is the degrees of freedom of the noncentral chi-square distribution, equal to the number of discrete sampling points, and is directly related to the time-bandwidth product. Indicates the number of channel branches of the multipath channel;

[0138] In the RIS-assisted communication system, the receiver uses the maximum ratio combining (MRC) technology to combine the The signal of the channel branch Perform optimal merging, where Indicates the The received signal on the channel branch, the number of channel branches The value range is 1 to , the optimal combined signal of the legitimate sender is expressed as: ,in, Indicates the legitimate sender Branch path channel coefficient The complex conjugate of Indicates the legitimate sender The received signal on the branch path is the square of the modulus of the legitimate sender's channel coefficient under the Nakagami fading channel model. Obeying the Gamma distribution, the legitimate sender optimally merges the signal Breaks down to:

[0139] in, Indicates time The signal sent, Indicates the legitimate sender The mean on the branch path is zero and the variance is Gaussian white noise, the signal-to-noise ratio expression of the legitimate sender after merger is derived: ,because Obey the Gamma distribution, It also obeys the Gamma distribution, specifically , the system detection probability in the multipath fading cascade channel scenario is expressed as the generalized function:

[0140] To obtain the average detection probability of the system in the multipath fading cascade channel scenario , need to The probability density function (PDF) of the system detection probability in the multipath fading cascade channel scenario is integrated, and the binary hypergeometric function of the legitimate sender in the multipath fading cascade channel scenario is introduced. Finally, the average detection probability of the system in the multipath fading cascade channel scenario is derived The analytical expression of , the analytical expression of , provides a theoretical basis for the performance evaluation of multipath communication systems.

[0141] The system false alarm probability in the multipath fading cascade channel scenario is expressed as the generalized function:

[0142]

[0143] The optimal combined signal of a potential attacker is expressed as: ,in, Indicates potential attacker Branch path channel coefficient The complex conjugate of Indicates potential attacker The received signal on the branch path is the square of the modulus of the potential attacker's channel coefficient under the Nakagami fading channel model. Following the Gamma distribution, the potential attacker's optimal combined signal Breaks down to:

[0144]

[0145] in, Indicates time The signal sent, Indicates potential attacker The mean on the branch path is zero and the variance is The additive Gaussian white noise of derives the signal-to-noise ratio expression after the potential attacker is combined: ,because Obey the Gamma distribution, Also obeys the Gamma distribution: , System false alarm probability in multipath fading cascade channel scenario Expressed as a generalized function:

[0146] To obtain the average false alarm probability of the system in the multipath fading cascade channel scenario , the signal-to-noise ratio after the potential attacker merges The probability density function of the system false alarm probability in the multipath fading cascade channel scenario is Perform integration, ,in For potential attackers The branch path channel coefficients are obtained by introducing the binary hypergeometric function of potential attackers in the multipath fading cascade channel scenario. Finally, the average false alarm probability of the system in the multipath fading cascade channel scenario is derived The analytical expression of provides a theoretical basis for the performance evaluation of multipath communication systems;

[0147] Calculate the average detection probability of the system in a multipath fading cascade channel scenario without a clear probability density function (PDF) in the absence of a clear signal-to-noise ratio (SNR) Average false alarm probability of the system under multipath fading cascade channel scenario :

[0148] For those with For a multi-channel scenario with multiple independent branches, the total signal-to-noise ratio of the moment generating function output of the legitimate sender is defined as the sum of the signal-to-noise ratios of each branch, that is: ,in, Indicates the legitimate sender The signal-to-noise ratio of the branch, under the premise that each channel is independent and identically distributed, the moment generating function of the signal-to-noise ratio of the Nakagami fading channel model of the legitimate sender is expressed as: ,

[0149] Moment Generating Function of Signal-to-Noise Ratio Based on the Nakagami Fading Channel Model with a Legal Sender , derive the average false alarm probability of the system in the multipath fading cascade channel scenario for:

[0150]

[0151] in, is the integration variable, is the fading characteristic coefficient of the legitimate sender channel in the multipath fading cascade channel scenario, and the integrand is: ,pole satisfy , consider and analyze the following two cases respectively :

[0152] when hour:

[0153] ;

[0154] when hour:

[0155] ;

[0156] in, represents the integrand At the Pole = The residue at , where the order of the extreme point is , represents the integrand At the Pole =0, where the order of the extreme point is ;

[0157] For those with In a multi-channel scenario with multiple independent branches, the total signal-to-noise ratio (SNR) of the moment generating function output of a potential attacker is defined as the sum of the SNRs of each branch: ,in, Indicates potential attacker The signal-to-noise ratio of the branch, under the premise that each channel is independent and identically distributed, the moment generating function of the signal-to-noise ratio of the Nakagami fading channel model of the potential attacker is expressed as:

[0158] Moment Generating Function Based on the Signal-to-Noise Ratio of Nakagami Fading Channel Model of Potential Attacker , derive the average false alarm probability of the system in the multipath fading cascade channel scenario for:

[0159]

[0160] in, is the fading characteristic coefficient of the potential attacker channel in the multipath fading cascade channel scenario, and the integrand is: ,pole satisfy , consider and analyze the following two cases respectively :

[0161] when When , the closed form expression of the system average false alarm probability in the multipath fading cascade channel scenario is:

[0162] ;

[0163] when When , the expression of the system average false alarm probability in the multipath fading cascade channel scenario is:

[0164] ;

[0165] in, represents the integrand At the Pole = The residue at , where the order of the extreme point is , represents the integrand At the Pole =0, where the order of the extreme point is .

[0166] To verify the effectiveness and superiority of the authentication scheme proposed in this application, numerical simulations were conducted to compare it with several existing identity verification methods and evaluate multiple performance metrics. This application first constructed a model of the cascade channel amplitude in the RIS-assisted communication system and fitted it using the Nakagami distribution. Comparison of the theoretical probability density function (PDF) with Monte Carlo simulation results showed a high degree of agreement between the fitted and simulated curves, validating the accuracy of the proposed channel model.

[0167] Figure 1 The schematic diagram of the system model structure of this application is shown. In this application, it is assumed that the phase error obeys the zero-mean vonMises distribution, and its concentration is determined by the parameter Characterization. Transmitter to reconfigurable smart reflective surface RIS The channel of a reflection unit experiences unit power Rice fading, and the Rice fading factor is recorded as ; The channel from the reflector to the receiver is subject to unit power Rayleigh fading. The Rice fading factors corresponding to the potential attacker and the legitimate sender channels are respectively denoted as and In order to quantify the difference in phase error concentration between the two types of transmitters, the von Mises distribution phase error difference parameter is introduced. ; The larger the value, the more significant the difference in phase error. Used to measure the difference in the Rice fading factor between the illegal and legal transmitter channels. The larger the value, the more obvious the difference between the two. In addition, the signal-to-noise ratio (SNR) is one of the key factors affecting system performance. Represents the difference in the shape parameter of the Nakagami distribution between illegal and legal senders. is the number of channel branches of the multipath channel, To evaluate the authentication performance under different parameter configurations, this application uses Monte Carlo simulation, and the number of experiments (nMCEvents) is set to 5000.

[0168] This application focuses on verifying the theoretical model of cascade channel amplitude Applicability in RIS-assisted communication systems. Figure 2 The probability density function of the cascade channel amplitude in this scenario and its fitting results with the Nakagami distribution are shown. Figure 2 Figure (a) shows the number of reflective units on the smart reflective surface RIS. The probability density function of the cascade channel amplitude when is consistent with the Nakagami distribution curve. Figure 2 Figure (b) shows that when the number of reflection units increases to The probability density function of , which fits the Nakagami distribution curve well. Figure 2 As shown, the probability density function of the cascade channel amplitude is highly consistent with the Nakagami distribution curve, verifying the effective characterization capability of the present application for equivalent channel characteristics.

[0169] like Figure 3 As shown in Figure (a), the receiver operating characteristic (ROC) curve obtained through simulation is highly consistent with the theoretical analysis results, effectively verifying the accuracy of the theoretical model of average detection probability and average false alarm probability in a single fading cascade channel scenario with a clear probability density function of the signal-to-noise ratio. Figure 3 Figure (a) shows that different signal-to-noise ratios (SNRs) have a significant impact on authentication performance. Specifically, authentication performance is optimal when the SNR is -5dB, while it is worst at -7dB. This trend indicates that a higher SNR generally indicates a better communication environment, thereby improving detection capabilities.

[0170] This application focuses on the number of reflective units in the reconfigurable smart reflective surface RIS The impact on the ROC curve under simulation and theoretical results. Figure 3 As shown in Figure (b), as the number of reflection units increases With the increase of , the authentication performance shows a trend of gradual improvement. Specifically, when When , the authentication performance reaches the best; When , the proposed authentication scheme performs the worst.

[0171] Based on the theoretical model of average detection probability and average false alarm probability in a single fading cascade channel scenario with a clear probability density function of the signal-to-noise ratio, this application deeply analyzes the system parameters such as the Rice factor difference. , Phase error concentration difference , Difference in Nakagami shape parameters between legitimate and potential attacker channels The mechanism of action for certification. First, we examine the difference in Rice factors. Impact on the performance of the authentication method of this application. Figure 4 The middle figure (a) shows the difference in Rice factor between a potential attacker and a legitimate sender. The effect on authentication performance, among which Pick .Depend on Figure 4 It can be seen that when When , the authentication method of this application achieves the highest authentication performance; and when The results show that the greater the difference in the Rice factor between the potential attacker and the legitimate sender, the better the detection performance of the system. Subsequently, this application investigates the difference in the concentration of phase errors in the zero-mean von Mises distribution. Impact on the performance of the authentication method used in this application. Figure 4 As shown in the middle figure (b), as the phase error concentration difference between the potential attacker and the legitimate sender increases The increase, for example , the authentication performance of the system is continuously improved. Specifically, when When is increased, the detection probability under the condition of a fixed false alarm probability is significantly increased, thereby improving the performance of the authentication method of the present application.

[0172] This application further studies the decision threshold Impact on the performance of the authentication method. Figure 5 As shown in the middle figure (a), the decision threshold The selection of has a significant effect on the system performance. Under the condition of The average false alarm probability will drop sharply, because the larger decision threshold The false alarm tolerance interval is expanded, thereby effectively reducing the average false alarm probability. Under the condition of , the average detection probability of the authentication scheme changes with the increase of SNR. Figure 5 As shown in the middle figure (b), all three curves increase significantly with the increase of SNR.

[0173] Next, in And the average false alarm probability Under fixed conditions, this application examines the signal-to-noise ratio Average detection probability The impact of Figure 6 As shown, when When all Take the value Both increase significantly with the improvement of SNR, indicating that a higher SNR can effectively enhance the system's ability to correctly authenticate the target signal. The performance is further improved. and The overall curve is higher than , and when k'=25, the system can make the detection probability quickly approach 1 under lower signal-to-noise ratio conditions. It helps to converge to the optimal detection performance faster. On the other hand, given And when the SNR is low, the average false alarm probability is small This often leads to a decrease in detection performance.

[0174] exist Figure 7 In this application, Under the setting of The Rice fading factor of the channel with potential attackers Here, represents the Rice fading factor of the potential attacker’s channel, while the Rice fading factor of the legitimate sender’s channel is fixed at 10. When it is close to 10, it means that the channel difference between the legitimate and potential attackers is small. area, larger Better performance can be achieved.

[0175] This paper investigates the difference in Nakagami shape parameters between legitimate and potential attacker channels in a single fading cascade channel scenario where an explicit expression of the SNR probability density function is not available. Impact on authentication performance. Figure 8 The results show that: when other parameters remain unchanged, When , the proposed scheme can achieve the best performance; and when It can be seen that the greater the difference in Nakagami shape parameters between the reference channel and the test channel, the better the authentication performance.

[0176] To further verify the superiority of the authentication method of this application, the experiment compares it with the existing authentication method that uses the time-varying characteristics of the channel gain to perform identity authentication and distinguishes the legitimate sender from the illegal sender by analyzing its change pattern. Figure 9 As shown in the figure, under the condition of maintaining SNR=-6dB, the proposed solution always outperforms the comparative solution in the ROC curve.

[0177] This application further combines MRC technology to improve the robustness and accuracy of authentication, and analyzes the channel branch number under multi-channel fading conditions. Impact on the performance of the MRC authentication method. Figure 10 The middle figure (a) shows the MRC certification performance calculated based on the PDF when the exact expression of the SNR PDF is available in the multipath fading cascade channel scenario; Figure 10 The middle figure (b) demonstrates the authentication performance evaluated using MGF technology for scenarios where the SNR PDF cannot be accurately obtained. The results show that, under the same false alarm probability, the detection probability increases significantly with the increase in the number of channel branches, fully demonstrating that increasing the number of channel branches can effectively enhance the overall reliability and robustness of the identity authentication process.

[0178] The experimental results fully verify the effectiveness, accuracy and robustness of the physical layer authentication method based on RIS cascade channel signature proposed in this application in complex wireless environments. It is significantly better than the existing mainstream authentication methods and has good engineering practical value and promotion prospects.

[0179] The foregoing is merely an embodiment of the present invention and is not intended to limit the present invention. It will be apparent to those skilled in the art that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention are intended to be included within the scope of the claims of the present invention.

Claims

1. A physical layer authentication method based on RIS cascade channel signatures, the physical layer authentication method being applied to a RIS-assisted communication system, the RIS-assisted communication system comprising a legitimate sender (Alice), a target receiver (Bob), a potential attacker (Eve), and a smart reflective surface (RIS). The legitimate sender (Alice) transmits a data signal to the target receiver (Bob) via the smart reflective surface (RIS), the method being characterized by: The physical layer authentication method based on RIS cascade channel signature includes two stages: feature extraction and judgment, and specifically includes the following steps: Step 1: In the feature extraction phase, the target receiver Bob receives a signal from the transmitter, i.e., the potential attacker Eve or the legitimate sender Alice. The received signal is modeled by considering the channel effects of the RIS-assisted communication system. Step 2: Count the cascade channels from the transmitter to the smart reflecting surface (RIS) and from the smart reflecting surface (RIS) to the receiver, and equate the cascade channels to a point-to-point Nakagami fading channel model. Step 3: Perform cascade channel estimation on the received signal of the target receiver Bob in step 1 to obtain a cascade channel estimation value, and extract the estimated value of the statistical characteristic parameter from the cascade channel estimation value, wherein the estimated value of the statistical characteristic parameter includes the estimated value of the scale parameter of the fading channel model obeying the Nakagami distribution. and the estimated value of the shape parameter of the fading channel model following the Nakagami distribution The specific steps include: Step 3.1: Least squares channel estimation to obtain the cascade channel estimation value: The equivalent channel gain of the RIS-assisted communication system is: N is the number of reflection units, represents the average signal-to-noise ratio under a single reflection unit. After discretization, at L sampling points, the discrete received signal is: is the sampling index, To send discrete signals, is discrete additive white Gaussian noise, and the discrete received signal vector is: y = c eff s+v, where s represents the pilot signal vector and v represents the noise vector. The minimized residual norm is The residual norm is expanded into: (·) H is the conjugate transpose symbol, ‖·‖2 represents the Euclidean norm, and the equivalent channel gain c eff Taking the derivative and setting it to zero, we get the optimal estimate of the equivalent channel gain: Thus, the concatenated channel estimate is obtained: Step 3.2, maximum likelihood estimation of the Nakagami fading channel model, extract the estimated value of the statistical characteristic parameters: obtain the cascade channel estimate of the wth sample w is the sample index, w=1,…,N s , N s represents the total number of samples collected for each received signal, and the amplitude of the cascaded channel estimate is Amplitude of the concatenated channel estimate Obeying the Nakagami distribution, under the premise of keeping the two communicating parties and the communication positions unchanged, the independent communications that send signals and do not interfere with each other are sampled to obtain N s A set of concatenated channel estimates Under the maximum likelihood estimation method, the log-likelihood function is expressed as: Where Γ(·) represents the gamma function. By taking the derivative of the scale parameter Ω and the shape parameter m of the Nakagami distribution of the fading channel model and setting the derivative to zero, we can obtain the estimated value of the scale parameter of the Nakagami distribution of the fading channel model: The estimated value of the shape parameter of the fading channel model following the Nakagami distribution The following equations are solved using numerical iteration method: in represents the derivative of the natural logarithm of the gamma function; Step 4: In the judgment stage, after the target receiver Bob receives the signal from the transmitter, the target receiver Bob performs identity authentication and makes an accurate judgment.

2. A physical layer authentication method based on RIS cascade channel signature according to claim 1, characterized in that: In step 1, the target receiver Bob receives the signal from the transmitter. Considering the channel influence in the RIS-assisted communication system, the received signal modeling is completed. Specifically, the following steps are included: Step 1.1: The smart reflecting surface (RIS) in the RIS-assisted communication system consists of N reflecting elements. Define the complex fading channel vector from the transmitter to the reflecting element on the smart reflecting surface as G, and define the complex fading channel vector from the reflecting element on the smart reflecting surface to the target receiver Bob as H: G=[G1,G2,…,G i …,G N ] H=[H1,H2,…,H i …,H N ] Considering the phase offset ψ, the complex fading channel vector G from the transmitter to the reflective element on the smart reflective surface, the complex fading channel vector H from the reflective element on the smart reflective surface to the target receiver Bob, and the reflection loss, the initial received signal y(t) is modeled as: Where i represents the index of the reflection unit on the smart reflection surface, i∈{1,2,…,N}, G i represents the complex fading channel vector from the transmitter to the i-th reflection unit on the smart reflection surface, H i represents the complex fading channel vector from the i-th reflective unit on the smart reflective surface to the target receiver Bob, ψ i represents the phase offset introduced by the i-th reflection unit on the smart reflection surface, s(t) represents the signal sent at time t, and v(t) represents the additive white Gaussian noise, satisfying represents a Gaussian distribution with a mean of 0 and a variance of 1. represents the average signal-to-noise ratio under a single reflection unit, j represents the imaginary unit, and e is a natural constant; Step 1.2, the received signal is rewritten as: Among them, the channel coefficient The operator |·| represents the modulus of the complex number, and the phase shift ψ introduced by the i-th reflection unit on the smart reflection surface is i The deviation from the ideal compensation phase of the i-th reflector unit on the smart reflective surface is modeled as the phase noise θ of the i-th reflector unit. i : in, represents the ideal compensation phase of the i-th reflection unit on the smart reflection surface, arg(·) is the argument operator, the phase noise θ of the i-th reflector unit i Randomly distributed in a circle on [-π,π).

3. The physical layer authentication method based on RIS cascade channel signature according to claim 2, characterized in that: The step 2 performs statistics on the cascade channels from the transmitter to the smart reflecting surface RIS and from the smart reflecting surface RIS to the receiver, and equates the cascade channels to a point-to-point Nakagami fading channel model, specifically comprising the following steps: Step 2.1: Define the complex fading channel vector G from the transmitter to the i-th reflection unit on the smart reflection surface i The expected value of the amplitude is m TR , the complex fading channel vector H from the i-th reflector unit of the smart reflector surface to the target receiver Bob i The expected value of the amplitude is m RB : Among them, E[·] represents the expectation operator, the operator |·| represents the modulus of the complex number, Represents the definition symbol, and the mean of the cascade channel is: The real part R = Re(h) and the imaginary part I = Im(h) of the channel coefficient h are independent of each other and obey the following distributions: in, is the Gaussian distribution symbol, Re(·) represents the real part operator of the complex number, Im(·) represents the imaginary part operator of the complex number, μ represents the mean statistical parameter of the real part R, represents the variance statistical parameter of the real part R, Represents the variance statistical parameter of the imaginary part I, the mean statistical parameter μ of the real part R, and the variance statistical parameter of the real part R Variance statistical parameter of the imaginary part I Modeled as: The characteristic function is defined as Ψ k =E[e jkθ ], is the k-order characteristic function of the phase noise θ, k is the order of the characteristic function, which is a non-zero integer, Ψ1 is the first-order characteristic function of the phase noise, and Ψ2 is the second-order characteristic function of the phase noise; Step 2.2: According to the law of large numbers, the channel amplitude |h| is modeled as a point-to-point Nakagami fading channel model. The probability density function of the channel amplitude |h| is expressed as: Where m represents the shape parameter of the fading channel model following the Nakagami distribution, Ω represents the scale parameter of the fading channel model following the Nakagami distribution, Γ(·) represents the gamma function, and x is the independent variable.

4. The physical layer authentication method based on RIS cascade channel signature according to claim 1, characterized in that: In step 4, the target recipient Bob performs identity authentication and makes an accurate decision, which specifically includes the following steps: Step 4.1: Model the identity authentication problem as a binary hypothesis test problem. The target receiver Bob determines whether the current received signal y'(t) comes from the legitimate sender Alice or from the potential attacker Eve. The binary hypothesis test is written as: in, is the null hypothesis, indicating that the current received signal comes from the legitimate sender Alice, is the alternative hypothesis, indicating that the current received signal comes from the potential attacker Eve, v0(t) represents the additive white Gaussian noise of the legitimate sender Alice, v1(t) represents the additive white Gaussian noise of the potential attacker, h1 is the channel coefficient of the potential attacker Eve, and h0 is the channel coefficient of the legitimate sender Alice; Step 4.2: When the RF signal reaches the target receiver Bob, the target receiver Bob will receive the signal y ′ (t) is sent to the energy detector, which first performs noise pre-filtering and then squares the filtered output signal to calculate the energy of the filtered output signal |y ′ (t)| 2 Finally, the integration operation is performed to calculate the energy of the filtered output signal |y ′ (t)| 2 Accumulate and get the test statistic value: a represents the scalar coefficient, dt represents the time derivative, and the test statistic value Y is compared with the decision threshold δ of the energy detector. If Y<δ, the decision is The signal source is the legitimate sender Alice; if Y≥δ, then the judgment is The signal originates from potential attacker Eve, and the RIS auxiliary communication system rejects the signal.

5. The physical layer authentication method based on RIS cascade channel signature according to claim 4, characterized in that: Model the test statistic value Y as the sum of squares of several Gaussian random variables. The test statistic value Y under the alternative hypothesis The test statistic values ​​Y under the null hypothesis all obey the non-central chi-square distribution. and the alternative hypothesis The probability density function f of the test statistic value Y under Y (y) is: Among them, I v (·) is the modified Bessel function of the first kind, represents the order of the first kind modified Bessel function, M D is the degree of freedom of the non-central chi-square distribution, y is the variable, γ0 is the signal-to-noise ratio of the legitimate sender, γ1 is the signal-to-noise ratio of the potential attacker, considering channel fading and signal noise, the authentication performance is analyzed in a single fading cascade channel scenario and a multipath fading cascade channel scenario. Among them, the single fading cascade channel scenario is analyzed in two cases where the signal-to-noise ratio has a clear probability density function and no clear probability density function, and the multipath fading cascade channel scenario is analyzed in two cases where the signal-to-noise ratio has a clear probability density function and no clear probability density function. The judgment authentication performance index is divided into the detection probability P d and false alarm probability P f : in, In the alternative hypothesis Under the condition, the probability that the test statistic Y is greater than the decision threshold δ is expressed as Indicates that the null hypothesis Under these conditions, the probability that the test statistic Y is greater than the decision threshold δ is calculated using the order M. D Generalized Marcum-Q function of / 2 The detection probability P is obtained respectively d and false alarm probability P f The closed-form expression for :

6. The physical layer authentication method based on RIS cascade channel signature according to claim 5, characterized in that: In a single fading cascade channel scenario, the analysis is done in two cases: the signal-to-noise ratio has a clear probability density function and the signal-to-noise ratio does not have a clear probability density function. Specifically: Calculate the average detection probability in a single fading cascade channel scenario with a clear probability density function and the average false alarm probability Average detection probability is the probability density function of the legitimate sender's signal-to-noise ratio γ0 Upper pair detection probability P d The integral calculation results in: The legitimate sender's signal-to-noise ratio γ0 follows the Gamma distribution, and the probability density function of the legitimate sender's signal-to-noise ratio γ0 is dγ0 represents the derivative of the legitimate sender's signal-to-noise ratio γ0, G(·,·) represents the probability density function of the Gamma distribution, and m0 is the shape parameter of the Gamma distribution to which the legitimate sender's signal-to-noise ratio γ0 obeys. is the scale parameter of the Gamma distribution obeyed by the legitimate sender’s signal-to-noise ratio γ0, where Ω0 is the scale parameter of the Nakagami distribution obeyed by the fading channel model corresponding to the legitimate sender, and E s is the signal energy, S0 is the unilateral noise power spectral density, and the series expansion form of the Marcum-Q function is used, and the probability density function of the signal-to-noise ratio γ0 of the legitimate sender obeys the Gamma distribution Integrate over , and we get the result: Where ∞ is positive infinity, n is the index of the summation term of the series expansion based on the Marcum-Q function, and e is a natural constant; By introducing the generalized hypergeometric function, the above formula is simplified to: Among them, 1F1(,;,;,) is the generalized hypergeometric function, n! represents the factorial function, Combining the generalized hypergeometric function 1F1(,;,;,) and the legitimate sender binary hypergeometric function in a single fading cascade channel scenario Calculate the average detection probability under a single fading cascade channel scenario with a clear probability density function Average false alarm probability is the probability density function of the potential attacker signal-to-noise ratio γ1 Upper false alarm probability P f The integral calculation results in: The potential attacker signal-to-noise ratio γ1 follows the Gamma distribution, dγ1 represents the derivative of the potential attacker signal-to-noise ratio γ1, and the probability density function of the potential attacker signal-to-noise ratio γ1 is: G(·,·) represents the probability density function of the Gamma distribution, m1 is the shape parameter of the Gamma distribution to which the potential attacker’s signal-to-noise ratio γ1 obeys, is the scale parameter of the Gamma distribution obeyed by the potential attacker's signal-to-noise ratio γ1, where Ω1 is the scale parameter of the Nakagami distribution obeyed by the channel amplitude corresponding to the potential attacker. The series expansion form of the Marcum-Q function is used, and the probability density function of the potential attacker's signal-to-noise ratio γ1 obeys the Gamma distribution is obtained. Integrate over , and we get the result: By introducing the generalized hypergeometric function 1F1(,;,;,), the above formula can be simplified to: Combining the generalized hypergeometric function 1F1(,;,;,) and the potential attacker binary hypergeometric function Calculate the average false alarm probability in a single fading cascade channel scenario with a clear probability density function Analyze and calculate the average detection probability in two cases in a single fading cascade channel scenario where the signal-to-noise ratio does not have a clear probability density function. and the average false alarm probability The method is: Using the generalized Marcum-Q function, the detection probability P d Written as: where \(z\) is the integration variable, and its path of integration is the closed path \(\Delta\). \(\Delta\) is a closed path centered at the origin with a radius \(r\), where \(0 < r < 1\), and \(j\) represents the imaginary unit. By averaging over the distribution of the legitimate sender's signal-to-noise ratio \(\gamma_0\), the average detection probability is obtained d and written as: where is the general form of the moment generating function of the legitimate sender's signal-to-noise ratio \(\gamma_0\), \(E[\cdot]\) represents the expectation operator, \(s\) is a real parameter, and \(\oint\) is the closed path integral; ​ For the legitimate sender Nakagami fading channel model, the moment generating function of the legitimate sender's signal-to-noise ratio is Expressed as: Will Substitution get: in, is the fading characteristic coefficient of the legitimate sender's channel, let the integrand be: The residue of the integrand f0(z) at the extreme point z0 is The pole z0 satisfies -1<z0<1, k0 is the order of the pole z0, k0≥1, and the following two cases are considered and analyzed respectively. M D When / 2>m0: M D When / 2≤m0: in, Indicates that the integrand f0(z) is at the extreme point z0=ξ 0,N The residue at , where the order of the extreme point is the shape parameter m0 of the Gamma distribution obeyed by the legitimate sender's signal-to-noise ratio γ0, It represents the residue of the integrand f0(z) at the extreme point z0=0, where the order of the extreme point is M D / 2-m0; Using the generalized Marcum-Q function, the false alarm probability P f Written as: By calculating the false alarm probability P f Average the distribution of potential attacker signal-to-noise ratio γ1 to obtain the average false alarm probability Written as: in, is the general form of the moment generating function of the potential attacker's signal-to-noise ratio γ1; For the potential attacker Nakagami fading channel model, the moment generating function of the potential attacker's signal-to-noise ratio is Expressed as: Will Substitution get: in, is the potential attacker's channel fading characteristic coefficient, let the integrand be: The pole z1 satisfies -1<z1<1 and the order k1≥1. The residue of the integrand f1(z) at the pole z1 is Consider and analyze the following two situations respectively M D When / 2>m1: M D When / 2≤m1: in, Indicates that the integrand f1(z) is at the extreme point z1=ξ 1,N The residue at , where the order of the extreme point is the shape parameter m1 of the Gamma distribution obeyed by the potential attacker's signal-to-noise ratio γ1, It represents the residue of the integrand f1(z) at the extreme point z1=0, where the order of the extreme point is M D / 2-m1.

7. The physical layer authentication method based on RIS cascade channel signature according to claim 5, characterized in that: In the multipath fading cascade channel scenario, the analysis is conducted in two cases: the signal-to-noise ratio has a clear probability density function and the signal-to-noise ratio does not have a clear probability density function. Specifically: Calculate the average detection probability of the system in a multipath fading cascade channel scenario with a clear probability density function in a multipath fading cascade channel scenario Average false alarm probability of the system under multipath fading cascade channel scenario The method is: for: for: in, is the binary hypergeometric function of the legitimate sender in the multipath fading cascade channel scenario, is the binary hypergeometric function of the potential attacker in the multipath fading cascade channel scenario, δ is the decision threshold, m0 is the shape parameter of the Gamma distribution obeyed by the signal-to-noise ratio of the legitimate sender, and m1 is the shape parameter of the Gamma distribution obeyed by the signal-to-noise ratio of the potential attacker. is the average signal-to-noise ratio under a single reflection unit, Ω0 is the scale parameter of the channel amplitude of the legitimate sender following the Nakagami distribution, Ω1 is the scale parameter of the channel amplitude corresponding to the potential attacker following the Nakagami distribution, γ0 is the signal-to-noise ratio of the legitimate sender, γ1 is the signal-to-noise ratio of the potential attacker, E s is the signal energy, S0 is the unilateral noise power spectrum density, M D is the degrees of freedom of the noncentral chi-square distribution, M B Indicates the number of channel branches of the multipath channel; In the RIS-assisted communication system, the receiver uses the maximum ratio combining technology to combine the M B The signal of the channel branch Perform optimal merging, where Indicates the Mth b The received signal on the channel branches, the number of channel branches is M B The value range of is 1 to N, and the optimal combined signal of the legitimate sender is expressed as: in, Indicates the legitimate sender M b Branch path channel coefficient The complex conjugate of Indicates the legitimate sender M b The received signal on the branch path is the square of the modulus of the legitimate sender's channel coefficient under the Nakagami fading channel model. Following the Gamma distribution, the legitimate sender's optimal combined signal y 0,MRC (t) is decomposed into: Among them, s(t) represents the signal sent at time t, Indicates the legitimate sender M b The additive white Gaussian noise with zero mean and variance S0W on the branch paths is used to derive the signal-to-noise ratio expression of the combined legitimate sender: because Obey Gamma distribution, γ 0,MRC Also obeys the Gamma distribution: System detection probability P in multipath fading cascade channel scenario d,MRC Expressed as a generalized Marcum-Q function: To obtain the average detection probability of the system in the multipath fading cascade channel scenario The signal-to-noise ratio after the legitimate sender is combined is γ 0,MRC The probability density function of the system detection probability P in the multipath fading cascade channel scenario is d,MRC Integrate and introduce the binary hypergeometric function of the legitimate sender in the multipath fading cascade channel scenario Finally, the average detection probability of the system in the multipath fading cascade channel scenario is derived The analytical expression of provides a theoretical basis for the performance evaluation of multipath communication systems; The optimal combined signal of a potential attacker is expressed as: in, Indicates the potential attacker M b Branch path channel coefficient The complex conjugate of Indicates the potential attacker M b The received signal on the branch path is the square of the modulus of the potential attacker's channel coefficient under the Nakagami fading channel model. Following the Gamma distribution, the potential attacker's optimal combined signal y 1,MRC (t) is decomposed into: Among them, s(t) represents the signal sent at time t, Indicates the potential attacker M b The additive Gaussian white noise with zero mean and variance S0W on the branch paths is used to derive the signal-to-noise ratio expression of the potential attacker after merger: because Obey Gamma distribution, γ 1,MRC Also obeys the Gamma distribution: System false alarm probability P in multipath fading cascade channel scenario f,MRC Expressed as a generalized Marcum-Q function: To obtain the average false alarm probability of the system in the multipath fading cascade channel scenario The signal-to-noise ratio γ after the potential attackers merge 1,MRC The probability density function of the system false alarm probability P in the multipath fading cascade channel scenario is f,MRC Integrate the binary hypergeometric function of potential attackers in the multipath fading cascade channel scenario Finally, the average false alarm probability of the system in the multipath fading cascade channel scenario is derived The analytical expression of provides a theoretical basis for the performance evaluation of multipath communication systems; Calculate the average detection probability of the system in a multipath fading cascade channel scenario without a clear probability density function for the signal-to-noise ratio Average false alarm probability of the system under multipath fading cascade channel scenario For the M B In a multi-channel scenario with multiple independent branches, the total signal-to-noise ratio (SNR) of the moment generating function output by the legitimate sender is defined as the sum of the SNRs of each branch: in, Indicates the legitimate sender M b The signal-to-noise ratio of the branches is output under the premise that each channel is independent and identically distributed, and the signal-to-noise ratio of the Nakagami fading channel model of the legitimate sender is output. The moment generating function M of the signal-to-noise ratio of the Nakagami fading channel model based on the legitimate sender 0,MRC (s), derive the average false alarm probability of the system in the multipath fading cascade channel scenario for: Where z is the integration variable, is the fading characteristic coefficient of the legitimate sender channel in the multipath fading cascade channel scenario, and the integrand is: pole satisfy Consider and analyze the following two situations respectively When M D / 2>M B At m0: When M D / 2≤M B At m0: in, represents the integrand At the Pole The residue at , where the order of the extreme point is M B m0, represents the integrand At the Pole The residue at the point where the order of the extreme point is M D / 2-M B m0; For the M B In a multi-channel scenario with multiple independent branches, the total signal-to-noise ratio (SNR) of the moment generating function output of a potential attacker is defined as the sum of the SNRs of each branch: in, Indicates the potential attacker M b The signal-to-noise ratio of the branch, under the premise that each channel is independent and identically distributed, the moment generating function of the signal-to-noise ratio of the Nakagami fading channel model of the potential attacker is expressed as: Moment generating function M based on the signal-to-noise ratio of the Nakagami fading channel model of potential attackers 1,MRC (s), derive the average false alarm probability of the system in the multipath fading cascade channel scenario for: in, is the fading characteristic coefficient of the potential attacker channel in the multipath fading cascade channel scenario, and the integrand is: pole satisfy Consider and analyze the following two situations respectively When M D / 2>M B When m1, the closed form expression of the system average false alarm probability in the multipath fading cascade channel scenario is: When M D / 2≤M B When m1, the expression of the system average false alarm probability in the multipath fading cascade channel scenario is: in, represents the integrand At the Pole The residue at , where the order of the extreme point is M B m1, represents the integrand At the Pole The residue at the point where the order of the extreme point is M D / 2-m1.

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