A method for device identity authentication of a millimeter wave communication system based on multipath time delay
Patent Information
- Application Number
- CN202611111757.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-24
- Publication Date
- 2026-10-30
AI Technical Summary
当噪声水平上升时，传统基于信道状态信息的方法容易出现明显性能退化，难以保持可靠的检测率
[0038]本申请利用毫米波传播固有的稀疏性，将多径时延作为物理层指纹。与传统的瞬时信道状态信息或相位特征相比，多径时延具有极强的空间几何依赖性和卓越的时间稳定性，能够有效克服环境微小时间波动带来的干扰，提升了指纹特征的唯一性和身份认证的可靠性。
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Figure CN123021152A_ABST
Abstract
Description
Technical Field
[0001] This application belongs to the field of wireless communication security technology, specifically relating to a device authentication method for millimeter-wave communication systems based on multipath delay. Background Technology
[0002] The rapid development of fifth-generation (5G) and future networks heavily relies on the integration of millimeter-wave frequency bands with multi-antenna technology. Millimeter-wave technology, with its abundant bandwidth resources and extremely short wavelengths, makes it possible to integrate massive MIMO antenna arrays in compact devices, thereby supporting multiple-input multiple-output (MIMO) architectures to achieve ultra-high data rates and ultra-low latency. However, the inherently open and broadcast nature of wireless transmission media makes millimeter-wave communication systems highly vulnerable to malicious spoofing attacks. Unauthorized attackers can easily impersonate authorized, legitimate transmitters to deceive receivers, leading to serious security threats such as man-in-the-middle attacks and denial-of-service attacks.
[0003] While traditional high-layer cryptographic protocols are effective against the aforementioned threats, they often come with high computational and communication overhead. Therefore, physical layer authentication has emerged as a crucial supplementary line of defense. It leverages the unique and non-clonable physical characteristics of wireless links to verify device identity, offering significant advantages such as information-theoretical security, low computational complexity, and compatibility with existing standards.
[0004] Currently, traditional schemes mainly rely on raw channel state information or phase characteristics. These characteristics are highly sensitive to small time fluctuations and lack necessary time stability. When noise levels rise, traditional channel state information-based methods are prone to significant performance degradation, making it difficult to maintain a reliable detection rate. Furthermore, existing technologies generally lack analysis of the theoretical performance boundaries of the accuracy of underlying parameter estimation, failing to establish quantitative benchmarks and theoretical evaluation systems for authentication performance. Therefore, developing a secure device authentication scheme with high noise resistance, high time stability, and strict theoretical performance boundaries is an important direction for current research. Summary of the Invention
[0005] To address the shortcomings of existing technologies, this application provides a device authentication method for millimeter-wave communication systems based on multipath delay, combining the inherent sparse propagation characteristics of millimeter-wave channels with high-precision multipath delay fingerprints. This method effectively overcomes the sensitivity of traditional channel state information to environmental fluctuations and performance degradation under low signal-to-noise ratios, thereby enhancing the security of communication links.
[0006] To achieve the above objectives, this application employs the following technical solution:
[0007] This application discloses a device authentication method for a millimeter-wave communication system based on multipath delay, applied to millimeter-wave communication scenarios. The method includes a base station Bob as the receiver, a legitimate device Alice equipped with a single antenna as the legitimate transmitter, and a potential attacker Eve equipped with a single antenna. The base station Bob is equipped with… A uniform cylindrical array of antennas, the authentication method specifically includes the following steps:
[0008] Step 1: Determine the attack scenario and threat assumptions: The legitimate device Alice sends a data frame to the base station Bob. Assume that base station Bob is... The system has verified the identity of the legitimate device Alice through the upper-layer cryptographic mechanism and extracted and stored the multipath delay features of the legitimate device Alice as a legitimate fingerprint template. At any given moment, a potential attacker, Eve, attempts to impersonate the legitimate device Alice to communicate with base station Bob in order to gain unauthorized access. Due to the spatial decorrelation between legitimate and illegitimate channels, base station Bob needs to use a legitimate fingerprint template to distinguish the source of the currently received millimeter-wave communication signal.
[0009] Step 2: Establishing a millimeter-wave channel and signal model: After receiving the millimeter-wave communication signal, base station Bob establishes a model containing the number of multipath propagation paths based on the sparse multipath propagation characteristics of the millimeter-wave communication system. Complex path gain Path propagation delay azimuth of arrival Reaching the angle of elevation The frequency domain channel vector is obtained; based on the frequency domain channel vector, additive white Gaussian noise is introduced and the received signal model corresponding to each subcarrier is constructed; and based on the propagation delay difference between adjacent multipath paths, a first-order Gaussian-Markov statistical evolution model of multipath delay as a function of continuous data frames is established, providing a model basis for extracting stable multipath delay fingerprints from the received signal.
[0010] Step 3: Extracting Multipath Delay Fingerprints: Base station Bob vectorizes the multiple subcarriers of the received signal obtained in Step 2, constructs a joint spatiotemporal response matrix containing multipath delay information, and obtains the signal subspace through covariance matrix eigenvalue decomposition; then, using the phase rotation relationship between adjacent subcarriers caused by multipath delay, a delay-related submatrix is constructed to estimate the propagation delay of each multipath path; finally, the delay difference between adjacent multipath paths is calculated to form the structured multipath delay fingerprint of the current data frame.
[0011] Step 4: Secure physical layer authentication based on binary hypothesis testing: Base station Bob accumulates the deviation between the structured multipath delay fingerprint of the current sender to be authenticated obtained in Step 3 and the multipath delay fingerprint of the legitimate device Alice stored in Step 1 at the previous authenticated moment, and obtains the test statistic. The test statistic is compared with the decision threshold. When the test statistic is not greater than the decision threshold, the current sender is determined to be the legitimate device Alice, and the authentication is successful. When the test statistic is greater than the decision threshold, the current sender is determined to be the potential attacker Eve, the authentication fails, and the current signal is discarded.
[0012] A further improvement in this application is that step 2 specifically includes the following steps:
[0013] Step 2.1, Calculate the frequency domain channel vector: Due to the sparse scattering characteristics of millimeter-wave channels, the first... Subcarriers and time frequency domain channel vector Represented as:
[0014]
[0015] in, It is the number of distinguishable multipaths. It is the complex path gain. It is the path propagation delay. It is an array steering vector that includes the azimuth and elevation angles. It is the first The multipath at time The azimuth of arrival, No. The multipath at time The angle of elevation at which it arrives;
[0016] Step 2.2: Construct a statistical model for time delay evolution: Model the arrival of multipath components as a Poisson process, and the time delay difference between different propagation paths. Following an independent and identically distributed exponential distribution, reflecting the slow changes in the physical environment between consecutive data frames, the evolution of the time delay difference components between adjacent multipath propagation paths over consecutive moments is modeled as a first-order Gaussian-Markov process:
[0017]
[0018]
[0019] in, and For the first Time delay difference between paths Gaussian components, To control the correlation coefficient of time delay stability, Let Variance be the variance of the Gaussian components. and This is an independent and identically distributed Gaussian random perturbation term with zero mean; where the multipath components are the signal components of the same transmitted signal that arrive at the base station after passing through different propagation paths. Each multipath component corresponds to a set of parameters, including the complex path gain. Path propagation delay azimuth of arrival and the angle of elevation .
[0020] Step 2.3: Construct the received signal model: Within the observation window, the receiver operates on subcarriers... Received signal vector at the location Represented as:
[0021]
[0022] in, This is due to phase rotation caused by time delay. It is additive white Gaussian noise.
[0023] A further improvement in this application is that step 3 specifically includes the following steps:
[0024] Step 3.1, Extract the signal subspace: Extract all... Vectorize the aggregated received signal matrix on each subcarrier to obtain the observed signal model. :
[0025]
[0026] in, Represents the Khatri-Rao product. This represents the joint spatiotemporal response matrix that incorporates multipath delay information. The subcarrier phase rotation matrix is caused by multipath propagation delay. For the receiver array manifold matrix, This is the multipath gain vector. For the received noise matrix The vectorized form, based on the obtained observed signal model Calculate the covariance matrix of the observed signal: And for the covariance matrix Perform eigenvalue decomposition Separate and extract the signal subspace matrix orthogonal noise subspace matrix ;
[0027] Step 3.2: Construct the time-delay correlated submatrix: Use the delay selection matrix to construct the signal subspace matrix. Extracting the frequency of each subcarrier Related delay submatrix Based on the frequency characteristics between adjacent subcarriers, a model satisfying the phase rotation relationship is established: ,in It is a rotation operator matrix that contains multipath delay information;
[0028] Step 3.3: Use the TLS-ESPRIT algorithm to solve for the delay difference between adjacent multipath paths, and divide the delay submatrix of adjacent subcarriers. Stacking creates two overlapping block matrices. and : , ;
[0029] For composite matrices Perform singular value decomposition and use total least squares to suppress noise: The right singular matrix Divided into sub-blocks The optimal rotation operator matrix is estimated as follows: ;
[0030] Step 3.4: Construct a structured multipath delay fingerprint: for the rotation operator matrix Perform eigenvalue decomposition and extract the rotation operator matrix. Complex eigenvalues The multipath delay values for each path were calculated:
[0031]
[0032] in, Given the subcarrier spacing, the inter-path delay difference between adjacent multipath components is then calculated: This is used to construct the structured multipath delay fingerprint features of the current frame, where For the first Multiple path propagation at time The estimated propagation delay.
[0033] A further improvement in this application is that step 4 specifically includes the following steps:
[0034] Step 4.1: Construct the test statistic: Extract... Reference fingerprint that has been verified at all times ,Will Unknown fingerprints extracted at any time With reference fingerprint Accumulate biases and construct test statistics. :
[0035] ;
[0036] Step 4.2: Establish the binary hypothesis test criteria: Define the null hypothesis. That is, the transmitter is the legitimate user Alice and the alternative assumptions. That is, the transmitter is the attacker Eve, and the test statistic is... With the decision threshold Comparison: If Then accept If the signal is determined to originate from a legitimate device, authentication is successful; if Then accept The system determines that the signal originated from an unauthorized, spoofed device, fails authentication, and discards the signal.
[0037] The beneficial effects of this application are:
[0038] This application utilizes the inherent sparsity of millimeter-wave propagation to use multipath delay as a physical layer fingerprint. Compared with traditional instantaneous channel state information or phase features, multipath delay has extremely strong spatial geometric dependence and excellent temporal stability, which can effectively overcome the interference caused by small temporal fluctuations in the environment, thereby improving the uniqueness of fingerprint features and the reliability of identity authentication.
[0039] This application utilizes a rotation-invariant subspace technique based on total least squares to extract multipath delay features in millimeter-wave communication systems. This method effectively overcomes the resolution limitations of existing delay estimation methods, mitigates noise impact by deeply mining the spatial and frequency coherence of the signal, and still exhibits superior noise immunity and detection success rate compared to traditional channel state information schemes even under low signal-to-noise ratio conditions.
[0040] This application utilizes the time consistency of the delay difference between paths between consecutive data frames to rigorously formulate physical layer authentication into a binary hypothesis testing problem, deriving closed-form analytical expressions for false alarm probability and detection probability, providing accurate and easily processed statistical theoretical support for quantitative evaluation of system security performance and dynamic adjustment of decision thresholds.
[0041] This application derives the performance boundaries for multipath delay estimation, mathematically linking the accuracy of lower-level parameter estimation with the performance of upper-level authentication. Analysis and simulation results confirm that the performance of this application approaches these theoretical optimal boundaries, providing a quantitative benchmark and theoretical guidance for the design of next-generation millimeter-wave secure communication systems. Attached Figure Description
[0042] Figure 1 This is a flowchart illustrating the process of this application.
[0043] Figure 2 This is a schematic diagram of device authentication in a millimeter-wave communication system.
[0044] Figure 3 It is a frequency distribution histogram of decision statistics.
[0045] Figure 4 This is a schematic diagram comparing the positioning performance of the traditional solution with that of this application.
[0046] Figure 5 This is a graph showing the experimental results of the performance boundary of this application.
[0047] Figure 6 This is a graph showing the experimental results of the impact of signal-to-noise ratio on authentication performance.
[0048] Figure 7 This is a graph showing the experimental results regarding the impact of the number of paths on authentication performance. Detailed Implementation
[0049] The embodiments of the present invention will be disclosed below with reference to the drawings. For clarity, many practical details will be described in the following description. However, it should be understood that these practical details are not intended to limit the present invention. That is, in some embodiments of the present invention, these practical details are not essential. In addition, for the sake of simplicity, some conventional structures and components will be shown in the drawings in a simple schematic manner.
[0050] like Figure 1-2 As shown, this application discloses a device authentication method for a millimeter-wave communication system based on multipath delay, applied to a millimeter-wave communication scenario. The method includes a base station Bob as the receiver, a legitimate device Alice equipped with a single antenna as the legitimate transmitter, and a potential attacker Eve equipped with a single antenna. The base station Bob is equipped with… A uniform cylindrical array of antennas, the authentication method specifically includes the following steps:
[0051] Step 1: Determine the attack scenario and threat assumptions: The legitimate device Alice sends a data frame to the base station Bob. Assume that base station Bob is... The system has verified the identity of the legitimate device Alice through the upper-layer cryptographic mechanism and extracted and stored the multipath delay features of the legitimate device Alice as a legitimate fingerprint template. At any given moment, a potential attacker, Eve, attempts to impersonate the legitimate device Alice to communicate with base station Bob in order to gain unauthorized access. Due to the spatial decorrelation between legitimate and illegitimate channels, base station Bob needs to use a legitimate fingerprint template to distinguish the source of the currently received millimeter-wave communication signal.
[0052] Step 2: Establishing a millimeter-wave channel and signal model: After receiving the millimeter-wave communication signal, base station Bob establishes a model containing the number of multipath propagation paths based on the sparse multipath propagation characteristics of the millimeter-wave communication system. Complex path gain Path propagation delay azimuth of arrival Reaching the angle of elevation The frequency domain channel vector is obtained; based on the frequency domain channel vector, additive white Gaussian noise is introduced and a received signal model corresponding to each subcarrier is constructed; and based on the propagation delay difference between adjacent multipath paths, a first-order Gaussian-Markov statistical evolution model of multipath delay variation with continuous data frames is established, providing a model basis for subsequently extracting stable multipath delay fingerprints from the received signal. Specifically, the steps include:
[0053] Step 2.1, Calculate the frequency domain channel vector: Due to the sparse scattering characteristics of millimeter-wave channels, the first... Subcarriers and time frequency domain channel vector Represented as:
[0054]
[0055] in, It is the number of distinguishable multipaths. It is the complex path gain. It is the path propagation delay. It is an array steering vector that includes the azimuth and elevation angles. It is the first The multipath at time The azimuth of arrival, No. The multipath at time The angle of elevation at which it arrives;
[0056] Step 2.2: Construct a statistical model for time delay evolution: Model the arrival of multipath components as a Poisson process, and the time delay difference between different propagation paths. Following an independent and identically distributed exponential distribution, reflecting the slow changes in the physical environment between consecutive data frames, the evolution of the time delay difference components between adjacent multipath propagation paths over consecutive moments is modeled as a first-order Gaussian-Markov process:
[0057]
[0058]
[0059] in, and For the first Time delay difference between paths Gaussian components, To control the correlation coefficient of time delay stability, Let Variance be the variance of the Gaussian components. and This is an independent and identically distributed Gaussian random perturbation term with zero mean; where the multipath components are the signal components of the same transmitted signal that arrive at the base station after passing through different propagation paths. Each multipath component corresponds to a set of parameters, including the complex path gain. Path propagation delay azimuth of arrival and the angle of elevation .
[0060] Step 2.3: Construct the received signal model: Within the observation window, the receiver operates on subcarriers... Received signal vector at the location Represented as:
[0061]
[0062] in, This is due to phase rotation caused by time delay. It is additive white Gaussian noise.
[0063] Step 3: Extract Multipath Delay Fingerprint: Base station Bob vectorizes the multiple subcarriers of the received signal obtained in Step 2, constructs a joint spatiotemporal response matrix containing multipath delay information, and obtains the signal subspace through covariance matrix eigenvalue decomposition. Then, using the phase rotation relationship between adjacent subcarriers caused by multipath delay, a delay-related submatrix is constructed to estimate the propagation delay of each multipath path. Finally, the delay difference between adjacent multipath paths is calculated to form the structured multipath delay fingerprint of the current data frame. Specifically, this includes the following steps:
[0064] Step 3.1, Extract the signal subspace: Extract all... Vectorize the aggregated received signal matrix on each subcarrier to obtain the observed signal model. :
[0065]
[0066] in, Represents the Khatri-Rao product. This represents the joint spatiotemporal response matrix that incorporates multipath delay information. The subcarrier phase rotation matrix is caused by multipath propagation delay. For the receiver array manifold matrix, This is the multipath gain vector. For the received noise matrix The vectorized form, based on the obtained observed signal model Calculate the covariance matrix of the observed signal: And for the covariance matrix Perform eigenvalue decomposition Separate and extract the signal subspace matrix orthogonal noise subspace matrix ;
[0067] Step 3.2: Construct the time-delay correlated submatrix: Use the delay selection matrix to construct the signal subspace matrix. Extracting the frequency of each subcarrier Related delay submatrix Based on the frequency characteristics between adjacent subcarriers, a model satisfying the phase rotation relationship is established: ,in It is a rotation operator matrix that contains multipath delay information;
[0068] Step 3.3: Use the TLS-ESPRIT algorithm to solve for the delay difference between adjacent multipath paths, and divide the delay submatrix of adjacent subcarriers. Stacking creates two overlapping block matrices. and : , ;
[0069] For composite matrices Perform singular value decomposition and use total least squares to suppress noise: The right singular matrix Divided into sub-blocks The optimal rotation operator matrix is estimated as follows: ;
[0070] Step 3.4: Construct a structured multipath delay fingerprint: for the rotation operator matrix Perform eigenvalue decomposition and extract the rotation operator matrix. Complex eigenvalues The multipath delay values for each path were calculated:
[0071]
[0072] in, Given the subcarrier spacing, the inter-path delay difference between adjacent multipath components is then calculated: This is used to construct the structured multipath delay fingerprint features of the current frame, where For the first Multiple path propagation at time The estimated propagation delay.
[0073] Step 4: Secure physical layer authentication based on binary hypothesis testing: Base station Bob accumulates the deviation between the structured multipath delay fingerprint of the current sender to be authenticated obtained in Step 3 and the multipath delay fingerprint of the legitimate device Alice stored in Step 1 at the previous authenticated moment, obtaining a test statistic. The test statistic is compared with a decision threshold. When the test statistic is not greater than the decision threshold, the current sender is determined to be the legitimate device Alice, and authentication is successful. When the test statistic is greater than the decision threshold, the current sender is determined to be the potential attacker Eve, authentication fails, and the current signal is discarded. Specifically, this includes the following steps:
[0074] Step 4.1: Construct the test statistic: Extract... Reference fingerprint that has been verified at all times ,Will Unknown fingerprints extracted at any time With reference fingerprint Accumulate biases and construct test statistics. :
[0075] ;
[0076] Step 4.2: Establish the binary hypothesis test criteria: Define the null hypothesis. That is, the transmitter is the legitimate user Alice and the alternative assumptions. That is, the transmitter is the attacker Eve, and the test statistic is... With the decision threshold Comparison: If Then accept If the signal is determined to originate from a legitimate device, authentication is successful; if Then accept The system determines that the signal originated from an unauthorized, spoofed device, fails authentication, and discards the signal.
[0077] The following section presents the verification and performance analysis of this application.
[0078] Statistical analysis and modeling of identity authentication performance includes the following steps:
[0079] Step 5.1, Derivation of the False Alarm Probability Model: Under the null hypothesis Below, we analyze the fingerprint differences extracted between two consecutive frames from the same legitimate channel, and define the first... Delay difference variable for each path interval By combining the first-order Gaussian-Markov evolution process of multipath delay and the additive estimation noise of the system, it is derived and proved that the delay difference variable It follows a Laplace distribution with a mean of zero;
[0080] Step 5.2, Determining the distribution of the test statistic under the null hypothesis: Take the absolute value of the above Laplace distribution variable to prove the absolute deviation. It follows an exponential distribution, due to the test statistic for The sum of independent and identically distributed exponential variables, thus deriving the... Under the given assumptions, the test statistic Obeying shape parameters Scale parameters are The Erlang distribution is used to derive a closed-form analytical expression for the false alarm probability: ,in The subscript for summation indicates the index of the term to be summed. It is a natural constant, approximately equal to 2.71828;
[0081] Step 5.3, Derivation of the Detection Probability Model: Based on the alternative hypothesis Under these circumstances, due to the physical spatial decorrelation between legitimate and illegitimate channels, the attacker's current characteristics... Historical reference features of legitimate users Statistically, they are independent of each other; the time delay difference variable is defined. ,
[0082] Its scale parameter is The Laplace distribution of the absolute value follows an exponential distribution. ,in , This represents the variance of the Gaussian component of the time delay difference between the attacker's channel paths. The variance of the Gaussian component representing the time delay difference between legitimate device channel paths. This represents the variance of the multipath delay estimation error;
[0083] Step 5.4, Determining the distribution of the test statistic under the alternative hypothesis: deriving the distribution under the alternative hypothesis. Under the given assumptions, the test statistic Obeying shape parameters Scale parameters are The Erlang distribution is used to derive a closed-form analytical expression for the detection probability: ;
[0084] Step 5.5, Optimal setting of the decision threshold: Based on the derived test statistic... and The property of the false alarm probability is obtained by using the closed-form analytical expression of the Erlang distribution that the false alarm probability follows. The closed-form analytical expression for the detection probability Based on the security constraints set by the system, the optimal decision threshold is calculated and determined. .
[0085] Performance boundary analysis of multipath estimation error
[0086] Step 6.1: Establish the underlying error analysis signal model: Considering a bandwidth of Total energy is broadband waveform In the transmission of a dispersive multipath channel, the bandpass signal is represented as: ,in For unit energy baseband signal, For carrier frequency, This indicates taking the real part. The receiver is at the... The noiseless response signal at each subcarrier is represented as: ,in The sampling interval is... and They represent the first The in-phase and quadrature components of a multipath tap. Define the first... The average power delay distribution of the multipath taps is as follows: And the channel coefficients are combined into a vector. This establishes the signal space basis for the derivation of the theoretical error lower bound.
[0087] Step 6.2, Derivation of the Cramer-Rao lower bound: For the high signal-to-noise ratio region, the Fisher information matrix is constructed based on the log-likelihood function of the received signal, yielding the conditional Cramer-Rao lower bound under given channel implementation conditions: For an additive white Gaussian noise channel, the conditional Cramer-Rao lower bound is expressed as: ,in To obtain the effective bandwidth for receiving noiseless response signals, For signal-to-noise ratio, The noise variance is represented by the received noiseless response signal expanded into a channel coefficient vector. The quadratic form is obtained. ,in Let be the curvature matrix formed by the autocorrelation function of the baseband signal and its derivatives. To eliminate the influence of specific random channel implementations, the random channel parameters are averaged using Jensen's inequality to obtain the modified Cramer-Rhodes lower bound: ,in The effective bandwidth of the baseband signal. The channel coefficient covariance matrix is... This is the mean vector of the channel coefficients.
[0088] Step 6.3: Conditional Probability Evaluation of the Zif-Zake Lower Bound: Given that the Cramer-Rhodes lower bound may be overly optimistic at low signal-to-noise ratios, the Zif-Zake lower bound is introduced. Two specific time delay assumptions are constructed: , ,in Let's assume a test baseline delay value. This represents the time delay offset between the two hypotheses. Based on the likelihood ratio test. Calculation implemented in a given channel Minimum error probability under the given conditions ,in For Gauss function, This is a parameterized autocorrelation function for receiving a noiseless response signal under a given channel implementation. The parameterized autocorrelation function is... ,in Due to time delay offset Subcarrier frequency The autocorrelation matrix is determined by the correlation matrix of the baseband signal.
[0089] Step 6.4: Calculate the unconditional theoretical Ziff-Zake bound: Implemented in a given channel Under the given conditions, the Ziv-Zakae lower bound is represented as ,in Let be the length of the observation interval for the time delay parameter. To obtain an unconditional Ziv-Zakae lower bound independent of a specific channel implementation, the random channel parameters are... Take an average: , ,in Channel coefficient vector The probability density function, This represents the minimum error probability after averaging the random channel parameters. To reduce the computational complexity of high-dimensional integrals, the Q-function is expressed using the Craig formula: Thus we obtain ,in Let be the moment generating function of the Gaussian quadratic vector form. Then the moment generating function is ,in This is the mean vector of the channel coefficients. To expand the covariance matrix, for An identity matrix of order 1. For integration variables And the average minimum error probability of the closed form is obtained using the moment generating function of the Gaussian vector. Finally, the high-dimensional expectation calculation is reduced to a two-dimensional continuous integral with respect to time and the integration angle, yielding the unconditional Ziff-Zakay bound. By comparing the variance extracted by the actual algorithm with the theoretical value of the Ziv-Zake bound, the accuracy and robustness of the identity authentication algorithm in harsh environments with low signal-to-noise ratios were verified.
[0090] Step 7: Performance Evaluation
[0091] Step 7.1, System Parameter Settings. In the simulation, key system parameters are set to evaluate the performance of the physical layer authentication method. The signal-to-noise ratio is defined. , Indicates the number of resolvable multipaths. Indicates the number of subcarriers. Indicates the first The center frequency of each subcarrier This represents the time autocorrelation coefficient between continuous multipath delay components. During the simulation, two consecutive data frames are generated. The first frame undergoes legality verification using an upper-layer encryption authentication method, and its features are extracted as a reference template. Subsequently, the physical layer authentication method proposed in this invention is used to verify the legality of the unknown identity in the second frame.
[0092] Step 7.2: Distribution analysis and model validation of test statistics. The system parameters are set to the number of subcarriers. Number of receiving antennas , the number of multipaths Correlation coefficient and Under these conditions, decision statistics are obtained through Monte Carlo simulation. The probability distribution histogram. For example... Figure 3 As shown, the theoretically derived distribution curve and the simulated histogram are in high agreement. Under the null hypothesis... Down, The distribution is tightly concentrated in the low-value region, showing strong time correlation; while in the alternative hypothesis... Below, due to the decorrelation of spatial location, The distribution center is significantly higher and the distribution is wider. The distribution regions under the two assumptions hardly overlap, proving that the proposed bimodal fingerprint has extremely high discriminative power and stability.
[0093] Step 7.3: Performance Comparison with Existing Channel State Information-Based Authentication Methods. The multipath delay fingerprint-based authentication method proposed in this invention is compared with traditional authentication methods based on raw channel state information. The false alarm probability is set to a fixed value. The detection probabilities were compared under different signal-to-noise ratios and multipath numbers. For example... Figure 4 As shown, in rich scattering environments and low signal-to-noise ratio ranges, the time-delay structured features extracted by the super-resolution algorithm in this invention have significant noise resistance advantages compared to directly using the original channel state information, greatly improving the detection probability under adverse channel conditions.
[0094] Step 7.4, Basic Theoretical Performance Boundary Benchmark Test. To rigorously evaluate the theoretical optimality of the proposed scheme, the ROC curve obtained from the simulation of this scheme is compared with the theoretical performance limits derived based on the Cramer-Rhodes lower bound and the Ziv-Zakhe lower bound. Figure 5 As shown, the actual detection performance of the present invention closely matches the theoretical curves of the Cramer-Rhodes bound and the Ziv-Zakke bound, confirming that the time delay estimation algorithm used has extremely high statistical efficiency and its operational performance is close to the theoretical optimal state allowed by physical channel conditions.
[0095] Step 7.5: Analysis of the impact of key system parameters on certification performance.
[0096] 1. Signal-to-noise ratio (SNR) impact analysis: Analyze the ROC curves of the system at different SNRs (0dB, 5dB, 10dB, and 15dB). For example... Figure 6 As shown, when At that time, the extracted multipath delay features tend to be deterministic fingerprints. Even when Even under extremely limited conditions, thanks to the noise resistance of processing gain and subspace algorithms, a clear boundary of discrimination capability can still be maintained.
[0097] 2. Number of transmission paths Impact analysis: Evaluating the impact of different multipath numbers on detection performance. For example... Figure 7 As shown, authentication performance varies with The increase in propagation paths leads to a monotonic increase in the number of propagation paths. More propagation paths effectively increase the independent degrees of freedom in the fingerprint feature space, increasing the KL divergence between legitimate and illegitimate channel distributions. This indicates that the highly complex millimeter-wave multipath scattering environment can actually serve as a physical fingerprint, significantly increasing the difficulty for malicious attackers to mimic legitimate channel distributions.
[0098] The above description is merely an embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of the present invention should be included within the scope of the claims of the present invention.
Claims
1. A device authentication method for a millimeter-wave communication system based on multipath delay, applied to a millimeter-wave communication scenario, comprising a base station Bob as the receiving end, a legitimate device Alice equipped with a single antenna as the legitimate transmitting end, and a potential attacker Eve equipped with a single antenna, wherein the base station Bob is equipped with... A uniform cylindrical array of antennas, characterized in that: The authentication method specifically includes the following steps: Step 1: Determine the attack scenario and threat assumptions: The legitimate device Alice sends a data frame to the base station Bob. Assume that base station Bob is... The system has verified the identity of the legitimate device Alice through the upper-layer cryptographic mechanism and extracted and stored the multipath delay features of the legitimate device Alice as a legitimate fingerprint template. At any given moment, a potential attacker, Eve, attempts to impersonate the legitimate device Alice to communicate with base station Bob in order to gain unauthorized access. Due to the spatial decorrelation between legitimate and illegitimate channels, base station Bob needs to use a legitimate fingerprint template to distinguish the source of the currently received millimeter-wave communication signal. Step 2: Establishing a millimeter-wave channel and signal model: After receiving the millimeter-wave communication signal, base station Bob establishes a model containing multipath signals. Complex path gain Path propagation delay Arrival azimuth Reaching the angle of elevation The frequency domain channel vector is obtained; based on the frequency domain channel vector, additive white Gaussian noise is introduced and the received signal model corresponding to each subcarrier is constructed; and based on the propagation delay difference between adjacent multipath paths, a first-order Gaussian-Markov statistical evolution model of multipath delay as a function of continuous data frames is established, providing a basis for extracting multipath delay fingerprints from the received signal. Step 3: Extracting Multipath Delay Fingerprints: Base station Bob vectorizes the multiple subcarriers of the received signal obtained in Step 2, constructs a joint spatiotemporal response matrix containing multipath delay information, and obtains the signal subspace through covariance matrix eigenvalue decomposition; then, using the phase rotation relationship between adjacent subcarriers caused by multipath delay, a delay correlation submatrix is constructed to estimate the propagation delay of each multipath path; finally, the delay difference between adjacent multipath paths is calculated to form the structured multipath delay fingerprint of the current data frame. Step 4, Secure physical layer identity authentication based on binary hypothesis testing: Base station Bob accumulates the deviation between the structured multipath delay fingerprint of the current unauthenticated sender obtained in step 3 and the multipath delay fingerprint of the legitimate device Alice stored in step 1 at the previous authenticated time, and obtains the test statistic. The test statistic is compared with the decision threshold. If the test statistic is not greater than the decision threshold, the current sender is determined to be the legitimate device Alice, and the authentication is successful. If the test statistic is greater than the decision threshold, the current sender is determined to be the potential attacker Eve, the authentication fails, and the current signal is discarded.
2. The method for device authentication in a millimeter-wave communication system based on multipath delay according to claim 1, characterized in that: Step 2 specifically includes the following steps: Step 2.1, Calculate the frequency domain channel vector: Due to the sparse scattering characteristics of millimeter-wave channels, the first... Subcarriers and time Frequency domain channel vector Represented as: in, It is the number of multipaths. It is the complex path gain. It is the path propagation delay. It is an array steering vector that includes the azimuth and elevation angles. It is the first The multipath at time The azimuth of arrival, No. The multipath at time The angle of elevation at which it arrives; Step 2.2: Construct a statistical model for time delay evolution: Model the arrival of multipath components as a Poisson process, and the time delay difference between different propagation paths. Following an independent and identically distributed exponential distribution, the evolution of the time delay difference components between adjacent multipath propagation paths over consecutive time intervals is modeled as a first-order Gaussian-Markov process: in, and For the first The time delay difference between each path Gaussian components, To control the time delay stability coefficient, Let Variance be the variance of the Gaussian components. and It is an independent and identically distributed Gaussian random perturbation term with zero mean; Step 2.3: Construct the received signal model: Within the observation window, the receiver operates on subcarriers... Received signal vector at the location Represented as: in, This is due to phase rotation caused by time delay. It is additive white Gaussian noise.
3. The device authentication method for a millimeter-wave communication system based on multipath delay according to claim 1, characterized in that: Step 3 specifically includes the following steps: Step 3.1, Extract the signal subspace: Extract all... Vectorize the aggregated received signal matrix on each subcarrier to obtain the observed signal model. : in, Represents the Khatri-Rao product. This represents the joint spatiotemporal response matrix that incorporates multipath delay information. The subcarrier phase rotation matrix is caused by multipath propagation delay. For the receiver array manifold matrix, This is the multipath gain vector. For the received noise matrix The vectorized form, based on the obtained observed signal model Calculate the covariance matrix of the observed signal: And for the covariance matrix Perform eigenvalue decomposition Separate and extract the signal subspace matrix orthogonal noise subspace matrix ; Step 3.2: Construct the time-delay correlated submatrix: Use the delay selection matrix to construct the signal subspace matrix. Extracting the frequency of each subcarrier Related delay submatrix Based on the frequency characteristics between adjacent subcarriers, a model satisfying the phase rotation relationship is established: ,in It is a rotation operator matrix that contains multipath delay information; Step 3.3: Use the TLS-ESPRIT algorithm to solve for the delay difference between adjacent multipath paths, and divide the delay submatrix of adjacent subcarriers. Stacking creates two overlapping block matrices. and : , ; For composite matrices Perform singular value decomposition and use total least squares to suppress noise: The right singular matrix Divided into sub-blocks The optimal rotation operator matrix is estimated as follows: ; Step 3.4: Construct a structured multipath delay fingerprint: for the rotation operator matrix Perform eigenvalue decomposition and extract the rotation operator matrix. Complex eigenvalues The multipath delay values for each path were calculated: in, Given the subcarrier spacing, the inter-path delay difference between adjacent multipath components is then calculated: This is used to construct the structured multipath delay fingerprint features of the current frame, where For the first Multiple path propagation at time The estimated propagation delay.
4. The device authentication method for a millimeter-wave communication system based on multipath delay according to claim 1, characterized in that: Step 4 specifically includes the following steps: Step 4.1: Construct the test statistic: Extract... Reference fingerprint that has been verified at all times ,Will Unknown fingerprints extracted at any time With reference fingerprint Accumulate biases and construct test statistics. : ； Step 4.2: Establish the binary hypothesis test criteria: Define the null hypothesis. That is, the transmitter is the legitimate user Alice and the alternative assumptions. That is, the transmitter is the attacker Eve, and the test statistic is... With the decision threshold Comparison: If Then accept If the signal is determined to originate from a legitimate device, authentication is successful; if Then accept The system determines that the signal originated from an unauthorized, spoofed device, fails authentication, and discards the signal.