Lightweight physical layer authentication method based on real-time channel two-stage response

Abstract

A lightweight physical layer authentication method based on a two-stage response of a real-time channel belongs to the field of wireless communication technology. The present invention addresses the problem that existing physical layer authentication methods are not suitable for situations where computing resources and storage resources are limited, and lack robust methods for dealing with noisy observations. It includes two-stage authentication. The first stage uses a low-complexity channel tracking model to accurately model and track real-time channel changes, and uses historical data for online prediction without incurring significant computing or storage overhead; the second stage enhances the robustness of the authentication process by introducing power delay features. These features are inherently resistant to time fluctuations, thereby eliminating the need for additional feature extraction in noisy environments. The present invention can improve the security, robustness and online processing capabilities of physical layer authentication in dynamic time-varying channels.

Description

Technical Field

[0001] The invention relates to a lightweight physical layer authentication method based on a two-stage response of a real-time channel, and belongs to the technical field of wireless communications. Background Art

[0002] 5G technology has revolutionized the Internet of Things (IoT) by providing high-throughput, low-latency, and energy-efficient services, enabling seamless connectivity, sensing, and computing among millions of devices. However, the inherent broadcast and open nature of wireless communications makes them vulnerable to security threats such as eavesdropping, spoofing, and impersonation attacks, posing a significant challenge to IoT security. With the advancement of the vision of 6G network automation, innovative IoT applications are emerging, including wearable / implantable devices, augmented reality, and autonomous driving. The ever-increasing number of connections, expanding network coverage, and increasing heterogeneity highlight the urgent need for lightweight, low-complexity, and low-latency authentication mechanisms.

[0003] Traditionally, wireless network access authentication mechanisms rely on cryptographic security. This approach requires devices with sufficient computational resources to provide mathematical hardness. However, low-cost IoT devices often lack the ability to perform complex computations, and dynamic IoT applications cannot tolerate high latency. Therefore, physical layer authentication has emerged as a promising lightweight and fast authentication technique. The spatiotemporal uniqueness of channel responses makes them effective authentication features, providing information-theoretic security without requiring extensive computation. Existing channel prediction-based methods fail to consider the limited computational and storage resources of a large number of low-cost IoT devices, limiting their applicability. They also lack robustness to noisy observations, limiting their performance at low signal-to-noise ratios. Summary of the Invention

[0004] In view of the problem that existing physical layer identity authentication methods are not suitable for situations where computing resources and storage resources are limited and there is a lack of robust methods to deal with noise observations, the present invention provides a lightweight physical layer authentication method based on real-time channel two-stage response.

[0005] The present invention provides a lightweight physical layer authentication method based on a two-stage response of a real-time channel, comprising two-stage authentication:

[0006] First-stage authentication: A low-complexity channel tracking model is used to predict the channel frequency response of the selected subcarrier at the next moment; the low-complexity channel tracking model includes a low-complexity non-real-time model and a low-complexity real-time model; when the channel frequency response of the selected subcarrier at time t is predicted for the first time at time t, the low-complexity non-real-time model is trained using the historical observations of the channel frequency response of the selected subcarrier before time t+1, and the predicted value of the channel frequency response at time t+1 is predicted; the first-stage anomaly score at time t+1 is calculated using all the channel frequency response observations and corresponding prediction values ​​before time t+1, and the user whose first-stage anomaly score is less than the channel frequency response observation value corresponding to the first-stage anomaly score threshold is regarded as a legitimate user; the user whose first-stage anomaly score is greater than or equal to the channel frequency response observation value corresponding to the first-stage anomaly score threshold is regarded as an illegal user, and the request of the illegal user is rejected;

[0007] The low-complexity real-time model is updated based on the low-complexity non-real-time model, and the low-complexity real-time model is used to predict the channel frequency response of the selected subcarrier at time t+2 and later. The corresponding observation values ​​are then combined to perform real-time first-stage anomaly score calculation and user legitimacy authentication.

[0008] Phase II authentication: The Phase II anomaly score is calculated based on the power delay distribution of all channels at the previous time t. Users with a Phase II anomaly score below the Phase II anomaly score threshold are considered legitimate users. Otherwise, they are considered illegitimate users and their requests are rejected.

[0009] According to the lightweight physical layer authentication method based on the two-stage response of the real-time channel of the present invention, the training method of the low-complexity non-real-time model includes:

[0010] Set the channel frequency response history observation value before the selected subcarrier t+1 to h q :

[0011] h q =I n f+ε,

[0012] Where q represents the selected subcarrier, I n is the n-dimensional unit matrix, f is the Gaussian variable, ε is the noise, is a multivariate Gaussian distribution, η 2 is the noise variance, m T is the mean vector, K TT is the covariance matrix:

[0013]

[0014] represents the real number domain, n is the number of legal observations, KTTij is the covariance matrix K TT The element in row i and column j of i is time i, t j is the jth moment, k(t i ,t j ) is the kernel function;

[0015] To historical moments Sparsely take M r Induction points, M r =nM rate , M rate is the induction coefficient, and the induction point set Z is obtained:

[0016]

[0017] is the jth induction point z j The observation time;

[0018] The evidence lower bound ELBO for low-complexity non-real-time models is:

[0019]

[0020] Where β is the intermediate variable, Where K TZ is the covariance matrix between the observations at all historical moments and the observations in the induced point set Z, K ZZ is the covariance matrix between observations in the induced point set Z;

[0021] The gradient descent method is used to optimize the model parameters of the low-complexity non-real-time model, and the low-complexity non-real-time model is trained by minimizing the evidence lower bound ELBO.

[0022] According to the lightweight physical layer authentication method based on the two-stage response of the real-time channel of the present invention, the selected subcarrier q predicted by the low-complexity non-real-time model is * The channel frequency response prediction value at time for:

[0023]

[0024] Where μ * is the predicted mean of the channel frequency response, K t*Z is the covariance matrix between the observations at the prediction moment and the observations in the induction point set Z, m z For intermediate variables:

[0025]

[0026] S z is the intermediate variable; K ZTis the covariance matrix between the observations in the induced point set Z and the observations at all historical moments, which is equal to

[0027]

[0028] According to the lightweight physical layer authentication method based on the two-stage response of the real-time channel of the present invention, the method for updating the low-complexity real-time model based on the low-complexity non-real-time model is: updating the model parameters of the low-complexity real-time model to the model parameters of the trained low-complexity non-real-time model.

[0029] According to the lightweight physical layer authentication method based on the two-stage response of the real-time channel of the present invention, the evidence lower bound ELBO of the low-complexity real-time model is:

[0030]

[0031] Where Z2 is the induction point set corresponding to the low-complexity real-time model, is an intermediate variable, K is an intermediate variable, is the covariance matrix between the observations in the induced point set Z2 at the current moment, Σ is the intermediate variable, is the noise variance of the low-complexity real-time model at the current moment, is the covariance matrix between the observation values ​​of the low-complexity real-time model at the current moment that have been saved at the historical moment, is the moment of the saved historical moment, β2 is the intermediate variable, C is the intermediate variable,

[0032]

[0033] Where S z1 is the intermediate variable corresponding to the induction point set Z1 corresponding to the saved low-complexity non-real-time model, is the covariance matrix between observations corresponding to the low-complexity non-real-time model, γ is the intermediate variable, m z1 The intermediate variables corresponding to the induction point set Z1, is the covariance matrix corresponding to the low-complexity real-time model, is the intermediate variable corresponding to the induction point set Z1, is the saved historical observation value, n S For nth S Legal observations, is the covariance matrix between the historical observation set and the induced point set Z1 of the low-complexity real-time model at the current moment;

[0034] The gradient descent method is used to optimize the model parameters of the low-complexity real-time model, and the low-complexity real-time model is trained by minimizing ELBO (Z2).

[0035] According to the lightweight physical layer authentication method based on the real-time channel two-stage response of the present invention, the low-complexity real-time model predicts the selected subcarrier q at t * The channel frequency response prediction value at time for:

[0036]

[0037] Where μ * ′ is the predicted mean value of the channel frequency response corresponding to the complexity real-time model;

[0038]

[0039] According to the lightweight physical layer authentication method based on the two-stage response of the real-time channel of the present invention, the calculation method of the first-stage anomaly score is:

[0040] Constructing the first stage detection target for:

[0041]

[0042] Where t k Indicates time

[0043] First stage abnormality score for:

[0044]

[0045] Where k is the kth legal observation value, Δ is the smoothness control coefficient, and e is the exponential function.

[0046] According to the lightweight physical layer authentication method based on real-time channel two-stage response of the present invention, the channel power delay distribution PDP(t,τ) at time t is:

[0047]

[0048] Where τ is the path delay, IFFT is the inverse Fourier transform, L is the number of paths, and P t,l is the power of path l at time t, δ is the impulse function, τ l (t) represents the corresponding path delay.

[0049] According to the lightweight physical layer authentication method based on the two-stage response of the real-time channel of the present invention, the second stage abnormal classification S IIk for:

[0050]

[0051] x IIk =τl (t k )-τ l (t k-1 ).

[0052] Beneficial effects of the present invention: The method of the present invention provides a two-stage physical layer authentication scheme for a real-time channel that can achieve comprehensive guarantees of identity authentication security, complexity and robustness. It reduces the complexity of real-time channel tracking by reusing historical model information, improves the security of the real-time authentication scheme by utilizing the highly time-varying channel frequency response authentication in the first stage, and improves the robustness by utilizing the power delay distribution authentication that is robust to noise in the second stage.

[0053] The method of the present invention addresses current physical layer authentication schemes. Taking into account the limited computing and storage resources of low-power small devices and the low-latency requirements of real-time authentication in IoT applications, a new two-stage real-time physical layer authentication method is implemented within a channel feature-based physical layer authentication framework. This method combines channel prediction with power-delay properties to ensure superior performance in mobile and time-varying channel environments. The first stage uses a low-complexity channel tracking model to accurately model and track real-time channel changes, using historical data for online prediction without incurring significant computational or storage overhead. The second stage enhances the robustness of the authentication process by introducing power-delay features. These features are inherently resistant to time fluctuations, eliminating the need for additional feature extraction in noisy environments. Simulation experiments show that compared with existing technologies, the present invention can improve the security, robustness, and online processing capabilities of physical layer authentication in dynamic time-varying channels, reduce the computational and storage complexity of the authentication scheme, and is scalable to different channel scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 Schematic diagram of a real-time physical layer authentication scenario of the lightweight physical layer authentication method based on a two-stage response of a real-time channel according to the present invention;

[0055] Figure 2 Schematic diagram of the low-complexity channel tracking principle of the present invention;

[0056] Figure 3 It is a schematic diagram of channel tracking accuracy;

[0057] Figure 4 This is a schematic diagram of the real-time physical layer authentication effect under different signal-to-noise ratios;

[0058] Figure 5 This is a schematic diagram of the real-time physical layer authentication effect in different channel environments. DETAILED DESCRIPTION

[0059] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making any creative efforts shall fall within the scope of protection of the present invention.

[0060] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0061] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, but they are not intended to limit the present invention.

[0062] Specific implementation method 1. Combination Figure 1 and Figure 2 As shown, in a mobile IoT wireless communication scenario, the receiving end authenticates the user initiating the communication request. Because traditional encryption mechanisms rely on computational hardness, they occupy the already limited storage and computing resources of small IoT devices. Furthermore, upper-layer encryption mechanisms are difficult to defend against spoofing attacks from the physical layer. In contrast, the spatial uniqueness and rapid time-varying nature of channel characteristics make them information-theoretic secure. Currently, the difficulty in deploying physical layer authentication based on channel characteristics on small devices lies in the accuracy and complexity of real-time channel tracking, as well as the robustness to adapt to dynamic environments. To this end, the present invention provides a lightweight physical layer authentication method based on a two-stage response of a real-time channel.

[0063] Combine Figure 2 As shown, the method of the present invention includes two-stage authentication:

[0064] First-stage authentication: A low-complexity channel tracking model is used to predict the channel frequency response of the selected subcarrier at the next moment; the low-complexity channel tracking model includes a low-complexity non-real-time model and a low-complexity real-time model; when the channel frequency response of the selected subcarrier at time t is predicted for the first time at time t, the low-complexity non-real-time model is trained using the historical observations of the channel frequency response of the selected subcarrier before time t+1, and the predicted value of the channel frequency response at time t+1 is predicted; the first-stage anomaly score at time t+1 is calculated using all the channel frequency response observations and corresponding prediction values ​​before time t+1, and the user whose first-stage anomaly score is less than the channel frequency response observation value corresponding to the first-stage anomaly score threshold is regarded as a legitimate user; the user whose first-stage anomaly score is greater than or equal to the channel frequency response observation value corresponding to the first-stage anomaly score threshold is regarded as an illegal user, and the request of the illegal user is rejected;

[0065] The low-complexity real-time model is updated based on the low-complexity non-real-time model, and the low-complexity real-time model is used to predict the channel frequency response of the selected subcarrier at time t+2 and later. The corresponding observation values ​​are then combined to perform real-time first-stage anomaly score calculation and user legitimacy authentication.

[0066] Phase II authentication: The phase II anomaly score is calculated based on the power delay distribution of all channels at the previous time t. Users with a phase II anomaly score below the phase II anomaly score threshold are considered legitimate users and their requests are accepted. Otherwise, they are considered illegitimate users and their requests are rejected.

[0067] In this implementation, the first-stage anomaly score is calculated using kernel density nonparametric estimation. If the authentication is passed, the second stage is entered; otherwise, the request is rejected. When predicting the subcarrier channel frequency response for the first time, all valid historical observations are input and a low-complexity non-real-time model is selected. When predicting the subcarrier channel frequency response in real time, the historical model and visible observations are input and a low-complexity real-time model is selected.

[0068] After each authentication is completed, the historical model and part of the historical observations are saved, and the visible observations are updated using the current observations and part of the historical observations for the next authentication.

[0069] Furthermore, when predicting the subcarrier channel frequency response for the first time, all valid historical observations are input and a low-complexity non-real-time model is selected. The training method of the low-complexity non-real-time model includes:

[0070] The historical channel frequency response between the legitimate user and the receiver obtained by the upper layer authentication mechanism before the communication request is initiated, for example, t n The historical observation on subcarrier q at time is represented by h q =[h q (t1),h q (t2),...,h q (t n )] T , select some subcarriers from all M subcarriers for tracking and authentication, and the selected subcarrier set is expressed as Q = {q|1≤q≤M};

[0071] Set the channel frequency response history observation value before the selected subcarrier t+1 to h q :

[0072] h q =I n f+ε,

[0073] Where q represents the selected subcarrier, I n is the n-dimensional unit matrix, f is the Gaussian variable, ε is the noise, represents the degree to which the observation is affected by noise, is a multivariate Gaussian distribution, η 2 is the noise variance, Used to fit the time-varying law of channel frequency response, m T is the mean vector, which can be set to 0, K TT is the covariance matrix:

[0074]

[0075] represents the real number domain, n is the number of legal observations, K TTij is the covariance matrix K TT The element in row i and column j of i is time i, t j is the jth moment, k(t i ,t j ) is the kernel function;

[0076] Set up and train a low-complexity non-real-time model for historical moments Sparsely take M r Induction points, M r =nM rate , M rate is the induction coefficient, and the induction point set Z is obtained:

[0077]

[0078] is the jth induction point z j The observation time;

[0079] The evidence lower bound ELBO for low-complexity non-real-time models is:

[0080]

[0081] Where β is the intermediate variable, Where K TZ is the covariance matrix between the observations at all historical moments and the observations in the induced point set Z, K ZZ is the covariance matrix between observations in the induced point set Z;

[0082] The method for determining the optimal induction point set and model parameters is as follows:

[0083] initialization The working set is defined as Start optimizing, for each Find the union of Z in turn, expressed as If ELBO(Z + )>ELBO(Z), then update Z←Z +, recalculate the working set with the updated Z, and repeat the above steps until there is no Meet ELBO(Z + )>ELBO(Z).

[0084] The gradient descent method is used to optimize the model parameters of the low-complexity non-real-time model, and the low-complexity non-real-time model is trained by minimizing the evidence lower bound ELBO. Space complexity

[0085] In this embodiment, a low-complexity non-real-time model is used to predict the predicted value of the channel frequency response of the selected subcarrier at the next moment. The selected subcarrier q predicted by the low-complexity non-real-time model is * The channel frequency response prediction value at time for:

[0086]

[0087] Where μ * is the predicted mean of the channel frequency response, K t*Z is the covariance matrix between the observations at the prediction moment and the observations in the induction point set Z, m z For intermediate variables:

[0088]

[0089] S z is the intermediate variable; K ZT is the covariance matrix between the observations in the induced point set Z and the observations at all historical moments, which is equal to

[0090]

[0091] Predicting computational complexity Space complexity

[0092] The method for updating the low-complexity real-time model based on the low-complexity non-real-time model is to update the model parameters of the low-complexity real-time model to the model parameters of the trained low-complexity non-real-time model. When subsequently predicting the subcarrier channel frequency response in real time, the historical model and the observed observations are input and the low-complexity real-time model is selected.

[0093] Low-complexity real-time model at the current moment Parameters and input of low-complexity real-time / non-real-time model at the last moment The saved parameter comparison table is shown in Table 1:

[0094] Table 1

[0095]

[0096] In Table 1, the dot under K represents a variable, such as T, Z, and n. S .

[0097] Visible observations are made by the latest n S It consists of authenticated legal observations, represented by The evidence lower bound ELBO for the low-complexity real-time model is:

[0098]

[0099] Where Z2 is the induction point set corresponding to the low-complexity real-time model, is an intermediate variable, K is an intermediate variable, is the covariance matrix between the observations in the induced point set Z2 at the current moment, Σ is the intermediate variable, is the noise variance of the low-complexity real-time model at the current moment, is the covariance matrix between the observation values ​​of the low-complexity real-time model at the current moment that have been saved at the historical moment, For the saved historical moments, for example, in constituted β2 is the intermediate variable, C is the intermediate variable,

[0100]

[0101] Where S z1 is the intermediate variable corresponding to the induction point set Z1 corresponding to the saved low-complexity non-real-time model, is the covariance matrix between observations corresponding to the low-complexity non-real-time model, γ is the intermediate variable, m z1 The intermediate variables corresponding to the induction point set Z1, is the covariance matrix corresponding to the low-complexity real-time model, is the intermediate variable corresponding to the induction point set Z1, is the saved historical observation value, n S For nth S Legal observations, is the covariance matrix between the historical observation set and the induced point set Z1 of the low-complexity real-time model at the current moment;

[0102] The model parameters of the low-complexity real-time model are optimized using the gradient descent method, and the low-complexity real-time model is trained by minimizing ELBO (Z2). Space complexity

[0103] The low-complexity real-time model is used to predict the predicted value of the channel frequency response of the selected subcarrier at the next moment. The low-complexity real-time model predicts the selected subcarrier q at t * The channel frequency response prediction value at time for:

[0104]

[0105] Where μ′ * is the predicted mean value of the channel frequency response corresponding to the complexity real-time model;

[0106]

[0107] Predicting computational complexity Space complexity

[0108] subcarrier q on t * The calculation formula for the predicted channel frequency response variance at time is expressed as:

[0109]

[0110] Furthermore, in the first stage authentication, the observed and predicted channel frequency responses at the current moment are obtained, and the kernel density non-parametric estimation is used to calculate the first stage anomaly score and compare it with the threshold.

[0111] To determine whether the user who initiated the communication request is a legitimate user, a two-stage authentication is required. In the first stage, the channel characteristics with higher randomness are checked to see if they meet the security requirements of the overall authentication scheme. Taking the authentication of a subcarrier in Q as an example, the channel estimation is first performed on the current channel. Based on the channel frequency response on subcarrier q, the channel is estimated at the current time t k The observed values ​​and predicted values ​​are used to construct the first-stage detection target.

[0112] The calculation method of the first stage anomaly score is:

[0113] According to the channel frequency response on subcarrier q at the current time t k The observed and predicted values ​​construct the first stage detection target for:

[0114]

[0115] Where t k Indicates time

[0116] First stage abnormality score for:

[0117]

[0118] Where k is the kth legal observation value, Δ is the smoothness control coefficient, and e is the exponential function.

[0119] Calculate all selected The abnormal score of the detected target on the subcarriers and the acceptance threshold After comparison, if any anomaly score is higher than the threshold, the current observation is authenticated as coming from an illegal user and the user request is rejected. If all anomaly scores are lower than the threshold, the second stage of authentication begins.

[0120] In this implementation, the second phase infers the power delay distribution of the current and historical channels, calculates the second phase anomaly score and compares it with the threshold. If authentication passes, the user request is accepted; otherwise, the request is rejected. In the second phase, the validity of the power delay characteristics that are not strongly time-varying is verified to provide robustness assurance for the overall authentication scheme. After channel estimation, the power delay distribution of the current and historical channels is calculated by observing the channel frequency response. The channel power delay distribution PDP(t,τ) at time t is calculated using the channel frequency response obtained by channel estimation as follows:

[0121]

[0122] Where τ is the path delay, IFFT is the inverse Fourier transform, L is the number of paths, and P t,l is the power of path l at time t, δ is the impulse function, τ l (t) represents the corresponding path delay.

[0123] The second stage of abnormal score S IIk for:

[0124]

[0125] The second-stage detection target is constructed by the delay corresponding to the path at the current moment and the previous moment, and is defined as:

[0126] x IIk =τ l (t k )-τ l (t k-1 ).

[0127] Second stage anomaly score and acceptance threshold If the comparison is lower than the threshold, the current observation is authenticated as coming from a legitimate user and the user request is accepted. If the comparison is higher than the threshold, the current observation is authenticated as coming from an illegal user and the user request is rejected.

[0128] Next, save the historical model and some historical observations, use the current observations and some historical observations to update the visible observations, and then perform the next authentication. Specifically, the following steps are performed:

[0129] The storage resources occupied by the lightweight physical layer authentication method for real-time channel two-stage response include: after each low-complexity model training is completed, the induction point Z and model parameters are saved, and for each selected subcarrier, n S The channel frequency response of the channel estimation at the current moment and the previous moment is saved. After the two-stage authentication is completed, the current moment observed channel frequency response of the authenticated legitimate user is saved. For example, t n Save historical observations after training is completed Predicted t n+1 The channel frequency response at time t n+1 The received signal at time t passes the two-stage authentication, then n+1 The visible observation update is

[0130] This implementation can achieve physical layer authentication of real-time channel two-stage response under the premise of lightweight.

[0131] In order to verify the performance of the physical layer security authentication method proposed in this invention, the following simulation and analysis were performed:

[0132] Complexity analysis: Currently, the accurate Gaussian process (GP) provides a more reliable time-varying channel tracking. However, its computational complexity is proportional to the cubic relationship of the data volume, which is not suitable for deployment in real-time physical layer authentication applications of small-scale devices with limited resources. In order to verify the effectiveness of the method of the present invention in terms of low complexity and lightweight, the computational complexity and space complexity of the method of the present invention are compared with the accurate Gaussian model baseline, as shown in Table 2. From the simulation results in the table, it is found that due to M r <M r +n S <<n, the method of the present invention greatly reduces the computational complexity and space complexity in real-time and non-real-time channel tracking models, saving equipment resources.

[0133] Table 2

[0134]

[0135] Communication system simulation parameters: The propagation scenario adheres to the outdoor 3GPP TR 38.901 specification. The channel is generated by QuadRiGa, and the antenna is located at a height of 1.5 meters. The receiver is fixed, and legitimate users move around Bob at a speed of 20 km / h in a circular trajectory with a diameter of 30 meters. Illegal users have random trajectories. The center frequency is 3.5 GHz, the bandwidth is 100 MHz, and a 2048-point FFT / IFFT is used.

[0136] Simulation 1: Considering the induction coefficient M rateIt will affect the accuracy of the first stage authentication, thus affecting the security of the overall authentication method. At the same time, considering the computational burden brought by more induction points, the M rate The cases of 0.4, 0.5, and 0.6 are evaluated respectively, such as Figure 3 As shown in the figure, the lower normalized mean square error NMSE reflects the higher accuracy of the low-complexity real-time / non-real-time channel tracking model in predicting the channel frequency response. This accuracy directly affects the accuracy of the first-stage authentication and further reflects the security of the authentication method of the present invention. Figure 3 It can be seen that in the three cases, the real-time / non-real-time model achieved an NMSE lower than 0.005, which provides a theoretical guarantee for the security of the method of the present invention.

[0137] Simulation 2: Since the time-varying channel is subject to significant noise interference, the two-stage physical layer authentication scheme proposed by the present invention uses power delay response to improve the authentication ability to adapt to the noise environment. In order to verify the robustness of this method, simulations are performed under signal-to-noise ratio (SNR) of 5dB, 10dB and 20dB, and compared with the baseline accurate Gaussian process scheme. Figure 4 As shown in the figure, the closer the false alarm rate and miss detection rate curves are to the lower left of the first quadrant, the better the authentication performance is. Figure 4 The results show that under the same false alarm rate, the missed detection rate of the proposed method is always better than that of the GP method. The proposed method shows greater improvement in authentication performance under lower signal-to-noise ratio.

[0138] Simulation 3: To verify the scalability of the proposed method in different channel environments, simulations were performed in three common channel environments in time-varying IoT scenarios: 3GPP 38.901 InF LOS, Umi LOS, and Umi NLOS. When tracking two subcarrier channels and achieving a signal-to-noise ratio of 15 dB, the authentication performance in non-line-of-sight (NLoS) was slightly reduced compared to line-of-sight (LoS), but remained within an acceptable range. Overall, the proposed method maintained a high level of performance consistency across various channel models.

[0139] Therefore, in summary, compared with the existing technology, the method of the present invention can improve the security, robustness, and online processing capability of physical layer authentication in dynamic time-varying channels, reduce the computational and storage complexity of the authentication scheme, and is scalable to different channel scenarios.

[0140] The above describes in detail the lightweight physical layer authentication method for real-time channel two-stage response provided by the present invention. This article uses specific examples to illustrate the principles and implementation methods of the present invention. The description of the above examples is only intended to help understand the method and core concept of the present invention. The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included in the scope of protection of the present invention.

Claims

1. A lightweight physical layer authentication method based on real-time channel two-stage response, characterized in that: It includes two stages of authentication: Phase 1 authentication: A low-complexity channel tracking model is used to predict the channel frequency response of the selected subcarrier at the next moment; the low-complexity channel tracking model includes a low-complexity non-real-time model and a low-complexity real-time model; when the channel frequency response of the selected subcarrier at time t is predicted for the first time at time t, the low-complexity non-real-time model is trained using the historical observations of the channel frequency response of the selected subcarrier before time t+1 to obtain the predicted value of the channel frequency response at time t+1; all channel frequency response observations before time t+1 and the corresponding predicted values ​​are used to calculate the first-phase anomaly score at time t+1, and users whose first-phase anomaly score is less than the channel frequency response observation value corresponding to the first-phase anomaly score threshold are regarded as legitimate users; Users whose first-stage anomaly score is greater than or equal to the channel frequency response observation value corresponding to the first-stage anomaly score threshold are considered as illegal users, and their requests are rejected; The low-complexity real-time model is updated based on the low-complexity non-real-time model, and the low-complexity real-time model is used to predict the channel frequency response of the selected subcarrier at time t+2 and subsequent times; The corresponding observation values ​​are combined to perform real-time first-stage anomaly score calculation and user legitimacy authentication; Second-stage authentication: The second-stage anomaly score is calculated based on the power delay distribution of all channels at the previous time t. Users with a second-stage anomaly score below the second-stage anomaly score threshold are considered legitimate users. Otherwise, they are considered illegitimate users and their requests are rejected. Training methods for low-complexity, non-real-time models include: Set the channel frequency response history observation value before the selected subcarrier t+1 to h q : h q =I n f+ε, Where q represents the selected subcarrier, I n is the n-dimensional unit matrix, f is the Gaussian variable, ε is the noise, is a multivariate Gaussian distribution, η 2 is the noise variance, m T is the mean vector, K TT is the covariance matrix: represents the real number domain, n is the number of legal observations, K TTij is the covariance matrix K TT The element in row i and column j of i is time i, t j is the jth moment, k(t i ,t j ) is the kernel function; To historical moments Sparsely take M r Induction points, M r =nM rate , M rate is the induction coefficient, and the induction point set Z is obtained: is the jth induction point z j The observation time; The evidence lower bound ELBO for low-complexity non-real-time models is: Where β is the intermediate variable, Where K TZ is the covariance matrix between the observations at all historical moments and the observations in the induced point set Z, K ZZ is the covariance matrix between observations in the induced point set Z; The model parameters of the low-complexity non-real-time model are optimized using the gradient descent method, and the low-complexity non-real-time model is trained by minimizing the evidence lower bound ELBO; The selected subcarrier q predicted by the low-complexity non-real-time model is at t * The channel frequency response prediction value at time for: Where μ * is the predicted mean of the channel frequency response, K t*Z is the covariance matrix between the observations at the prediction moment and the observations in the induction point set Z, m z For intermediate variables: S z is the intermediate variable; K ZT is the covariance matrix between the observations in the induced point set Z and the observations at all historical moments, which is equal to The method for updating the low-complexity real-time model based on the low-complexity non-real-time model is: updating the model parameters of the low-complexity real-time model to the model parameters of the trained low-complexity non-real-time model; The evidence lower bound ELBO for the low-complexity real-time model is: Where Z2 is the induction point set corresponding to the low-complexity real-time model, is an intermediate variable, K is an intermediate variable, is the covariance matrix between the observations in the induced point set Z2 at the current moment, Σ is the intermediate variable, is the noise variance of the low-complexity real-time model at the current moment, is the covariance matrix between the observation values ​​of the low-complexity real-time model at the current moment that have been saved at the historical moment, is the moment of the saved historical moment, β2 is the intermediate variable, C is the intermediate variable, Where S z1 is the intermediate variable corresponding to the induction point set Z1 corresponding to the saved low-complexity non-real-time model, is the covariance matrix between observations corresponding to the low-complexity non-real-time model, γ is the intermediate variable, m z1 The intermediate variables corresponding to the induction point set Z1, is the covariance matrix corresponding to the low-complexity real-time model, is the intermediate variable corresponding to the induction point set Z1, is the saved historical observation value, n S For nth S Legal observations, is the covariance matrix between the historical observation set and the induced point set Z1 of the low-complexity real-time model at the current moment; The model parameters of the low-complexity real-time model are optimized using the gradient descent method, and the low-complexity real-time model is trained by minimizing ELBO(Z2); The low-complexity real-time model predicts the selected subcarrier q at t * The channel frequency response prediction value at time for: Where μ′ * is the predicted mean value of the channel frequency response corresponding to the complexity real-time model; The calculation method of the first stage anomaly score is: Constructing the first stage detection target for: Where t k Indicates time First stage abnormality score for: Where k is the kth legal observation value, Δ is the smoothing control coefficient, and e is the exponential function; The channel power delay profile PDP(t,τ) at time t is: Where τ is the path delay, IFFT is the inverse Fourier transform, L is the number of paths, and P t,l is the power of path l at time t, δ is the impulse function, τ l (t) represents the corresponding path delay; The second stage of abnormal score S IIk for: x IIk =t l (t k )-t l (t k-1 )。

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