High-reliability equipment authentication method based on antenna array error characteristics and dual-beam transmission

Abstract

The invention belongs to the technical field of wireless communication security and signal processing, and discloses a high-reliability equipment authentication method based on antenna array error characteristics and dual-beam transmission, which comprises the following steps of: 1, constructing dual beams, and transmitting a signal received by user equipment through the dual beams; 2, actively tracking the double beams, and adjusting the directions of the double beams in real time; 3, modeling the statistical analysis model of the radiation mode; 4, defining a radiation mode characteristic extraction target, completing characteristic extraction, and calculating a gain error value, a phase error value and a position error value; and step 5, calculating signal energy, comparing the signal energy as an energy detection statistic with a preset threshold value, judging the legality of a signal source, and completing the authentication of the equipment. The authentication scheme provided by the invention can effectively cope with the influence of array errors, so that a reliable and efficient authentication solution is provided for a millimeter wave communication system, and the security of a communication link is enhanced.

Description

Technical Field

[0001] The invention belongs to the technical field of wireless communication security and signal processing, and specifically is a high-reliability device authentication method based on antenna array error characteristics and dual-beam transmission. Background Art

[0002] Millimeter wave communication systems are an important part of the new generation of wireless communication technology. With the wide bandwidth characteristics brought by high frequency bands, they can meet the high data rate requirements of the fifth generation (5G) and future wireless networks. Millimeter wave communication significantly improves communication capacity and directivity through compact antenna array design and efficient beamforming, and has become an important technical foundation for promoting innovation in key areas such as industrial automation, autonomous driving, and precision agriculture. At the same time, millimeter wave communication systems are widely regarded as an important driving force for realizing future smart connectivity due to their high directivity, high speed, and high frequency.

[0003] However, the security of millimeter wave communication systems faces many challenges in an increasingly complex network environment. The high directionality and limited coverage of millimeter wave signals make their communication process vulnerable to identity spoofing attacks. By disguising themselves as legitimate users or devices, attackers can obtain unauthorized access rights, thereby destroying communication links and even carrying out malicious acts. Especially in critical scenarios with high security requirements such as autonomous driving and industrial automation, the potential harm of such attacks is more significant. Therefore, designing an efficient and reliable security mechanism for the identity authentication problem of millimeter wave communication systems has become an important task that needs to be solved urgently.

[0004] At present, physical layer authentication (PLA) is an emerging technology that implements identity authentication by utilizing the unique physical characteristics of wireless channels or hardware. Compared with traditional cryptography-based methods, physical layer authentication has significant advantages such as no need for key management, adaptability to dynamic networks and low computational overhead. However, existing physical layer authentication methods still have obvious shortcomings, mainly: First, many schemes rely on a single physical characteristic such as channel sparsity or hardware defects, resulting in insufficient differentiation of authentication features, making it difficult to achieve efficient and reliable identity authentication in complex dynamic scenarios; second, the single-beam transmission authentication method is sensitive to beam blocking and device movement, resulting in poor authentication stability and reliability; third, there is a lack of systematic statistical performance evaluation methods, making it difficult to fully quantify the actual effect of the authentication scheme.

[0005] Therefore, how to make full use of the multi-dimensional physical characteristics of millimeter wave communication systems to improve the accuracy and reliability of equipment authentication is an important direction of current research. Summary of the invention

[0006] In order to solve the above technical problems, the present invention provides a high-reliability device authentication method based on antenna array error characteristics and dual-beam transmission. By combining three random array error characteristics such as gain, phase and position, the distinguishability of radiation patterns is improved; two-beam transmission technology is adopted to enhance the reliability of authentication. By statistically modeling the radiation pattern and introducing composite hypothesis testing theory, the authentication scheme proposed in the present invention can effectively cope with the influence of array errors, thereby providing a reliable and efficient authentication solution for millimeter wave communication systems, which helps to enhance the security of communication links.

[0007] In order to achieve the above object, the present invention is achieved through the following technical solutions:

[0008] The present invention is a highly reliable device authentication method based on antenna array error characteristics and dual-beam transmission. The device authentication method is applied to a millimeter wave communication system. A user equipment (UE) needs to verify whether the signal it receives comes from a legitimate base station (Alice) rather than a disguised attacker (Eve). By extracting and analyzing the gain, phase and position error characteristics of the base station radiation pattern, the user equipment (UE) determines the source of the signal. The specific authentication method includes the following steps:

[0009] Step 1: construct a dual beam, transmit the signal received by the user equipment (UE) through the dual beam, calculate the parameters of the transmission path, and calculate the dual beam weight vector;

[0010] Step 2: Actively track the dual beams and adjust the dual beam directions in real time to ensure that the user equipment (UE) receives signals efficiently;

[0011] Step 3: Model the statistical analysis model of the radiation pattern, calculate the statistical characteristics of the mean, variance, and correlation of the real and imaginary parts of the radiation pattern, and describe the distribution of the radiation pattern through the statistical characteristics;

[0012] Step 4: define the radiation pattern characteristic extraction target, complete the characteristic extraction, and calculate the gain error value, phase error value and position error value according to the extracted characteristic parameters;

[0013] Step 5: Calculate the signal energy and compare it with the preset threshold as the energy detection statistic to determine the legitimacy of the signal source and complete the device authentication.

[0014] A further improvement of the present invention is that the step 1 specifically comprises the following steps:

[0015] Step 1.1, define the receiving signal as:

[0016] y(t)=hΓws(t)+ν(t)

[0017] Where Γ represents the gain-phase-position error matrix, s(t) is the transmitted signal of the legitimate base station (Alice) at time t, ν(t) represents the additive noise at the receiving antenna, and w = [W1,...,W M ] T Represents the component value of the beam weight vector, M represents the number of antennas, and the beam weight of each path It is expressed as: Indicates the path propagation angle of the antenna array The response vector on is the propagation angle of the path, The value of is 1 or 2;

[0018] Step 1.2: Assume that the millimeter wave propagation channel follows the geometry-based L-path model, and the channel expression is:

[0019]

[0020] in, Indicates The complex gain of the first scattering path, the channel of the second path is expressed as: h2 = h1δe jβ , represents relative attenuation, β∈[0, 2π] represents relative phase shift, and j is an imaginary unit;

[0021] Step 1.3, received signal update and weighted calculation: By combining the channel information of the two beam paths, the received signal is updated as follows:

[0022] y(t)=(α1b1+α1δe jβ b1)s(t)+ν(t)

[0023] Among them, α1 represents the complex gain of the first scattering path, and b1 is dependent on the propagation angle of the path. and the radiation pattern of frequency f;

[0024] Step 1.4, calculate the dual beam weights:

[0025]

[0026] Wherein, θ1 and θ2 represent the propagation angles of the first path and the second path, respectively, and w1 and w2 represent the beam weights of the first path and the second path, respectively;

[0027] Step 1.5, since the relative amplitude δ and relative phase shift β are expressed as channel ratios: Through additional channel detection, set the beam w(θ1,θ2,1,0) and w(θ1,θ2,1,π / 2) to estimate the channel strength respectively:

[0028]

[0029] And according to the values ​​of P3 and P4, the ratio of h2 to h1 is obtained, that is, the accurate values ​​of the relative amplitude δ and the relative phase shift β are calculated:

[0030]

[0031] in, represents the real part operation, Indicates the operation of taking the imaginary part, P1=||h1|| 2 ,P2=||h2|| 2 , indicating the channel strength.

[0032] A further improvement of the present invention is that in step 2, actively tracking the dual beams and adjusting the dual beam reflections in real time specifically include the following steps:

[0033] Step 2.1. In order to capture the change of beam direction, define the power measurement formula for each beam:

[0034] P i (t) = Ω T (θ i +φ i (t))+Ω R +P T -P c ,i=1,2;

[0035] Among them, θ i +φ i (t) represents the beam angle, Ω T (θ i +φ i (t)) represents the transmission gain of the beam, which changes with the beam angle, Ω R Represents the receiving gain, P T Represents the transmission power, P c Represents the power loss due to channel attenuation;

[0036] Step 2.2: Construct a uniform linear array (ULA) gain model. In a uniform linear array (ULA), the transmit gain is:

[0037]

[0038] Where M is the number of antennas. The offset angle φ is estimated from the measured beam power by inverse calculation. i (t0);

[0039] Step 2.3, beam power change differential calculation: By calculating the difference between the beam power at time t=t0 and the initial time t=0, the offset of the beam direction is obtained, which directly reflects the change trend of the beam direction and ensures continuous signal reception:

[0040] P i (t0)-P i (0) = Ω T (θ i +φ i (t0))-Ω T (θ i ).

[0041] A further improvement of the present invention is that step 3 specifically includes the following steps:

[0042] Step 3.1, build a statistical analysis model for the radiation pattern: statistically describe the gain error, phase error and position error, assuming that the gain error, phase error and position error are independent random variables and satisfy the following distribution:

[0043]

[0044] Among them, μ g is the mean value of the gain error, μ ψ is the mean value of the phase error, is the gain error variance, is the phase error variance, is the position error variance;

[0045] Step 3.2, the mean of the real part and the mean of the imaginary part of the statistical radiation pattern: define the following lemma: if the random variable θ obeys a normal distribution with mean μ and standard deviation σ, then the expectations of the cosine and sine are:

[0046]

[0047] Where a is a constant, σ is the standard deviation, and b is the real part of the radiation pattern. R and the imaginary part b I The definition of the mean of the real part of the radiation pattern and the mean of the imaginary parts They are:

[0048]

[0049] Using the differential formula of cosine and sine, we can further obtain:

[0050]

[0051] Assume phase Θ m The mean and variance of are:

[0052] μ Θ =μ ψ ,

[0053] Using the lemma we get:

[0054]

[0055] The mean of the real and imaginary parts of the radiation pattern is:

[0056]

[0057] Where c0 = 1 + μ g ;

[0058] Step 3.3: Calculate the variance of the real part and the imaginary part of the radiation pattern: The mean power of the radiation pattern consists of two parts: in,

[0059]

[0060] According to the above formula, calculate the real part b of the radiation pattern R and the imaginary part b I The squared power mean of is expressed as:

[0061]

[0062] in, and Represents the power contribution from the same antenna element:

[0063]

[0064] in represents the comprehensive statistical component of the gain error, Represents the power contribution from different antenna elements:

[0065]

[0066] in, represents the mean component of the gain error;

[0067] Using the square mean formula, the square mean formula of the real and imaginary parts of the radiation pattern is corrected:

[0068]

[0069] The variance of the real and imaginary parts of the radiation pattern is calculated by the relationship between the mean square of the power and the mean:

[0070]

[0071] Step 3.4: Statistical characteristics of the correlation between the real and imaginary parts of the statistical radiation pattern: Define the Pearson correlation coefficient between the real and imaginary parts of the radiation pattern as:

[0072]

[0073] Among them, Cov(b R ,b I ) represents the covariance, Expanding the covariance formula yields:

[0074]

[0075] Step 3.5: Describe the distribution of the radiation pattern by statistical characteristics: The real part b of the radiation pattern R and the imaginary part b I All obey Gaussian distribution, and their amplitude statistical distribution is derived according to the central limit theorem:

[0076] Beckmann distribution: The amplitude of the radiation pattern is described by a Beckmann distribution, whose probability density function (PDF) is:

[0077]

[0078] in,

[0079] The cumulative distribution function (CDF) is:

[0080] Rice distribution: Assuming that the variances of the real and imaginary parts are equal and uncorrelated, the amplitude distribution of the radiation pattern is approximately described by the Rice distribution, whose probability density function (PDF) is:

[0081]

[0082] in, It represents the ratio of the direct path power to the other path power. Indicates the total received power, represents the mean value of the amplitude, represents the variance of the amplitude, and I0 represents the zero-order modified Bessel function.

[0083] A further improvement of the present invention is that the step 4 specifically comprises the following steps:

[0084] According to the sample signal y(t), using the formula: Estimate the sample variance,

[0085] According to the formula Construct the tensor model χ, decompose the tensor model using COMFAC decomposition, jointly estimate the angle and error parameters to construct the matrix Q, estimate the gain-phase-position error, extract the beam direction, extract the error characteristics, and output the statistical parameter μ g ,

[0086] A further improvement of the present invention is that step 5 specifically includes the following steps:

[0087] Step 5.1: At the receiving end, the user equipment verifies whether the signal y(t) comes from the legitimate base station (Alice). The verification process is modeled as a composite hypothesis testing problem with the following assumptions:

[0088] Assumption H0: The signal comes from a legitimate base station (Alice), and its radiation pattern is

[0089] Alternative hypothesis H1: The signal comes from a disguised attacker (Eve), and its radiation pattern is

[0090] Step 5.2: Based on the hypothesis test, construct the energy detection statistic, i.e., the received signal energy Y, and compare it with the preset threshold λ t For comparison, the energy detection formula is:

[0091]

[0092] Among them, λ t Indicates the preset detection threshold, which is used to distinguish whether the signal comes from a legitimate user. is the noise power, y(t) is the received signal, if Y>λ t , then accept the null hypothesis H0, that is, the signal comes from a legitimate base station; if Y≤λ t , then accept the alternative hypothesis H1, that is, the signal comes from a disguised attacker (Eve). Through this method, the legitimacy of the signal source can be effectively determined.

[0093] The beneficial effects of the present invention are as follows: (1) The present invention establishes a statistical model of the radiation pattern and adopts the Rice distribution to approximate the radiation pattern modulus including gain, phase and position errors, proving that the distribution can accurately describe the cumulative distribution characteristics of the radiation pattern. This modeling method provides an accurate mathematical basis for the theoretical analysis of physical layer authentication. (2) The present invention effectively improves the discrimination of the radiation pattern by integrating multi-dimensional hardware features such as gain, phase and position errors, making the physical layer authentication more accurate and reliable; at the same time, combined with the dual-beam transmission technology, the authentication stability of the system in complex environments is further enhanced, especially in blocking scenarios. Higher robustness is shown. (3) The present invention adopts a single RF chain and phased array technology in the authentication process, and reduces the hardware implementation complexity and power consumption requirements by optimizing resource utilization. In addition, the closed expression of the detection probability and false alarm probability based on the statistical model provides accurate theoretical support for system performance evaluation. (4) The present invention uses the hardware characteristics of the device for physical layer authentication, gets rid of the dependence of traditional encryption technology on key management, can effectively resist identity-based camouflage attacks in dynamic networks and resource-constrained environments, and significantly improves the security and reliability of millimeter wave communication systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0094] Figure 1 It is a model diagram of the millimeter wave communication system.

[0095] Figure 2 It is a schematic diagram of the effects of gain error, phase error and position error on the antenna radiation pattern.

[0096] Figure 3 It is a graph of experimental results of the statistical analysis model of radiation pattern.

[0097] Figure 4 This is an experimental result diagram analyzing the impact of different direction angles (DoD) on the statistical characteristics of the radiation pattern.

[0098] Figure 5 This is an experimental diagram showing the impact of attacker characteristic parameters on authentication performance.

[0099] Figure 6 It is a graph of experimental results showing the impact of user equipment (UE) mobility on the authentication performance of the millimeter wave communication system.

[0100] Figure 7 This is an experimental result diagram showing how dual-beam transmission technology improves authentication performance.

[0101] Figure 8 It is an experimental result diagram comparing the authentication performance of millimeter wave communication system with different authentication feature combinations. DETAILED DESCRIPTION

[0102] The following will disclose the embodiments of the present invention with drawings. For the purpose of clear description, many practical details will be described together in the following description. However, it should be understood that these practical details should not be used to limit the present invention. That is to say, in some embodiments of the present invention, these practical details are not necessary.

[0103] like Figure 1 As shown, the present invention establishes a millimeter wave wireless communication system, including a legitimate base station (Alice): a uniform linear array (ULA) with M antennas, responsible for transmitting legitimate signals to user equipment; an attacker (Eve): attempts to impersonate a legitimate base station to send forged information; a user equipment (UE): a single antenna device, used to receive signals from the base station and verify the identity of the base station through radiation pattern characteristics.

[0104] Determine the attack scenario, Eve attempts to disguise as Alice to pass false information to the UE. The UE extracts radiation pattern characteristics such as gain error, phase error, antenna position error parameters through the beam training phase in millimeter wave standards such as 802.11ad, 802.11ay and 5G-NR, and uses these parameters for base station identity authentication.

[0105] Establish the frequency response model of the antenna array: define the complex frequency response of M antenna elements at the carrier frequency f as: in, Represents the nominal gain, which indicates the gain amplitude of the antenna unit.

[0106] Denotes the nominal phase, and denotes the phase offset of the antenna element. Establishing the actual frequency response model: Taking into account the errors in the actual manufacturing process, the actual frequency response can be defined as: Among them, ε g,m (f) represents the gain error, which describes the deviation between the actual gain and the nominal gain, 0<(1+ε g,m (f))<∞。ε ψ,m (f) represents the phase error, which describes the deviation between the actual phase and the nominal phase. Define the influence of the antenna unit position error, assuming that the nominal position of the mth antenna unit is p m , the actual position is offset ε p,m , then its actual position can be expressed as: p m +ε p,m . Define the beam weighting function: The beamforming weighting function in the far field direction θ is defined as:

[0107] Among them, w m (f) represents the beam weighting amplitude of the antenna element, represents the beam weighted phase. Based on the signal direction θ, the far-field radiation pattern is defined as: in, represents the product of the nominal gain and the beam weighting coefficient, c m (f) = 1 + ε g,m (f) represents the actual gain factor, including gain error.

[0108] Θ m (θ,f) represents the actual phase deviation, which is caused by phase error and position error: θ m (θ,f)=ε ψ,m (f)+kε p,m sinθ. represents the nominal phase and is defined as: in, represents the beam weighted phase, and θ0 represents the reference direction.

[0109] Decomposition of the radiation pattern, according to Euler's formula, decompose the radiation pattern into real and imaginary parts:

[0110]

[0111] Among them, b R (θ,f) represents the real part of the radiation pattern, which represents the cosine component of the pattern, b I (θ,f) represents the imaginary part of the radiation pattern, representing the sinusoidal component of the pattern.

[0112] Based on the above authentication background, the authentication objectives of the present invention are: 1. Verify whether the source of the signal is a legitimate base station (Alice); 2. Prevent malicious attackers (Eve) from committing identity fraud by disguising base stations; 3. Provide an efficient and reliable authentication mechanism to enhance the security of millimeter wave communications.

[0113] Based on the authentication target, the present invention provides a high-reliability device authentication method based on antenna array error characteristics and dual-beam transmission. The specific authentication method includes the following steps: Step 1, construct a dual beam, the signal received by the user equipment (UE) is transmitted through the dual beam, and the parameters of the transmission path are calculated, and the dual-beam weighting vector is calculated. In millimeter wave communications, the path loss increases due to the shorter wavelength and the sensitivity to obstacles is significantly enhanced. However, the propagation environment of millimeter wave signals usually exhibits sparsity, and only one or two significant paths are effective for communication. Therefore, by utilizing the sparse characteristics of multipath, the efficiency of the communication system can be improved. For the scenario of two paths, a two-beam weighting mechanism is designed to optimize the channel utilization efficiency. Specifically comprising the following steps: Step 1.1, define the received signal as:

[0114] y(t)=hΓws(t)+ν(t)

[0115] Where Γ represents the gain-phase-position error matrix, s(t) is the transmitted signal of the legitimate base station (Alice) at time t, and ν(t) represents the additive noise at the receiving antenna, which satisfies the zero mean and variance The complex circularly symmetric Gaussian distribution, w=[W1,...,W M ] T Represents the component value of the beam weight vector, M represents the number of antennas, and the beam weight of each path It is expressed as: Indicates the path propagation angle of the antenna array The response vector on is the propagation angle of the path, The value of is 1 or 2;

[0116] Step 1.2: Assume that the millimeter wave propagation channel follows the geometry-based L-path model, and the channel expression is:

[0117]

[0118] in, Indicates The complex gain of the first scattering path, the channel of the second path is expressed as: h2 = h1δe jβ , represents relative attenuation, β∈[0, 2π] represents relative phase shift, and j is an imaginary unit;

[0119] Step 1.3, received signal update and weighted calculation: By combining the channel information of the two beam paths, the received signal is updated as follows:

[0120] y(t)=(α1b1+α1δe jβ b1)s(t)+ν(t)

[0121] Among them, α1 represents the complex gain of the first scattering path, and b1 is dependent on the propagation angle of the path. and the radiation pattern of frequency f;

[0122] Step 1.4, calculate the dual beam weights:

[0123]

[0124] Wherein, θ1 and θ2 represent the propagation angles of the first path and the second path, respectively, and w1 and w2 represent the beam weights of the first path and the second path, respectively;

[0125] Step 1.5, since the relative amplitude δ and relative phase shift β are expressed as channel ratios: Through additional channel detection, set the beam w(θ1,θ2,1,0) and w(θ1,θ2,1,π / 2) to estimate the channel strength respectively:

[0126]

[0127] And according to the values ​​of P3 and P4, the ratio of h2 to h1 is obtained, that is, the accurate values ​​of the relative amplitude δ and the relative phase shift β are calculated:

[0128]

[0129] in, represents the real part operation, Indicates the operation of taking the imaginary part, P1=||h1|| 2 ,P2=||h2|| 2 , indicating the channel strength.

[0130] Step 2: Actively track the dual beams and adjust the dual beam directions in real time to ensure that the user equipment (UE) receives signals efficiently. In scenarios where the user equipment (UE) is moving, the initial dual beams may be offset. Even a small angle offset such as 14° can cause a 20dB drop in signal strength or even complete signal loss. Therefore, an active dual beam tracking method is proposed to adjust the beam direction in real time, which specifically includes the following steps:

[0131] Step 2.1. In order to capture the change of beam direction, define the power measurement formula for each beam:

[0132] P i (t) = Ω T (θ i +φ i (t))+Ω R +P T -P c ,i=1,2;

[0133] Among them, θ i +φ i (t) represents the beam angle, Ω T (θ i +φ i (t)) represents the transmission gain of the beam, which changes with the beam angle, Ω R Represents the receiving gain, P T Represents the transmission power, P c Represents the power loss due to channel attenuation, such as path loss or reflection loss;

[0134] Step 2.2: Construct a uniform linear array (ULA) gain model. In a uniform linear array (ULA), the transmit gain is:

[0135]

[0136] Where M is the number of antennas. The offset angle φ is estimated from the measured beam power by inverse calculation. i (t0);

[0137] Step 2.3, beam power change differential calculation: By calculating the difference between the beam power at time t=t0 and the initial time t=0, the offset of the beam direction is obtained, which directly reflects the change trend of the beam direction and ensures continuous signal reception:

[0138] P i (t0)-P i (0) = Ω T (θ i +φ i (t0))-Ω T (θ i ).

[0139] Step 3: Build a statistical analysis model of the radiation pattern, calculate the statistical characteristics of the mean, variance, and correlation of the real and imaginary parts of the radiation pattern, and describe the distribution of the radiation pattern through the statistical characteristics.

[0140] Figure 2 (a)-(d) respectively show the impact of gain error, phase error, position error and the combined effect of the three on the antenna radiation pattern, including changes in the beam shape.

[0141] The specific step 3 includes the following steps:

[0142] Step 3.1, build a statistical analysis model for the radiation pattern: statistically describe the gain error, phase error and position error, assuming that the gain error, phase error and position error are independent random variables and satisfy the following distribution:

[0143]

[0144] Among them, μ g is the mean value of the gain error, μ ψ is the mean value of the phase error, is the gain error variance, is the phase error variance, is the position error variance;

[0145] Step 3.2, the mean of the real part and the mean of the imaginary part of the statistical radiation pattern: define the following lemma: if the random variable θ obeys a normal distribution with mean μ and standard deviation σ, then the expectations of the cosine and sine are:

[0146]

[0147] Where a is a constant, σ is the standard deviation, and b is the real part of the radiation pattern. R and the imaginary part b I The definition of the mean of the real part of the radiation pattern and the mean of the imaginary parts They are:

[0148]

[0149] Using the differential formula of cosine and sine, we can further obtain:

[0150] Assume phase Θ m The mean and variance of are:

[0151] μ Θ =μ ψ , Using the lemma we get:

[0152]

[0153] The mean of the real and imaginary parts of the radiation pattern is:

[0154]

[0155] Where c0 = 1 + μ g ;

[0156] Step 3.3: Calculate the variance of the real part and the variance of the imaginary part of the radiation pattern: The mean power of the radiation pattern consists of two parts: in,

[0157]

[0158] According to the above formula, calculate the real part b of the radiation pattern R and the imaginary part b I The squared power mean of is expressed as:

[0159]

[0160] in, and Represents the power contribution from the same antenna element:

[0161]

[0162] in represents the comprehensive statistical component of the gain error, Represents the power contribution from different antenna elements:

[0163]

[0164] in, represents the mean component of the gain error;

[0165] Using the square mean formula, the square mean formula of the real and imaginary parts of the radiation pattern is corrected:

[0166]

[0167] The variance of the real and imaginary parts of the radiation pattern is calculated by the relationship between the mean square of the power and the mean:

[0168]

[0169] Step 3.4: Statistical characteristics of the correlation between the real and imaginary parts of the statistical radiation pattern: Define the Pearson correlation coefficient between the real and imaginary parts of the radiation pattern as:

[0170]

[0171] Among them, Cov(b R ,b I ) represents the covariance, Expanding the covariance formula yields:

[0172]

[0173] Step 3.5: Describe the distribution of the radiation pattern by statistical characteristics: The real part b of the radiation pattern R and the imaginary part b I All obey Gaussian distribution, and their amplitude statistical distribution is derived according to the central limit theorem:

[0174] Beckmann distribution: The amplitude of the radiation pattern is described by a Beckmann distribution, whose probability density function (PDF) is:

[0175]

[0176] in,

[0177] The cumulative distribution function (CDF) is:

[0178] Rice distribution: Assuming that the variances of the real and imaginary parts are equal and uncorrelated, the amplitude distribution of the radiation pattern is approximately described by the Rice distribution, whose probability density function (PDF) is:

[0179]

[0180] in, It represents the ratio of the direct path power to the other path power. Indicates the total received power, represents the mean value of the amplitude, represents the variance of the amplitude, and I0 represents the zero-order modified Bessel function.

[0181] Step 4: Define the radiation pattern feature extraction target, complete the feature extraction, and calculate the gain error value, phase error value, and position error value based on the extracted feature parameters. The specific steps include:

[0182] Step 4.1: Define the key parameter μ for the radiation pattern characteristic extraction target, i.e., the estimated direction b Key parameters on frequency These parameters are affected by array errors such as gain, phase, and position errors. By extracting these key characteristics, systematic errors can be effectively identified and corrected.

[0183] Step 4.2, define the gain-phase-position error matrix: Γ = diag(r)

[0184] in, M c represents the number of well-calibrated antenna elements, ρ m Parameters representing the combined gain, phase, and position errors;

[0185] Step 4.3: Establish a received signal model. The received signal considering the gain-phase-position error is expressed as:

[0186] y(t)=hΓws(t)+v(t)

[0187] =(ΓA) H ws(t)+ν(t)

[0188] Where Aα=A t , A t =[a(θ1),a(θ2)],α=[α1,α2] T represents the beam direction matrix, ν(t) represents additive noise, which obeys Gaussian distribution;

[0189] Step 4.4: Estimate sample variance using multiple snapshot data K:

[0190] in, Where K is the number of samples, y(t) is the signal received at time t, Γ is the error matrix containing gain, phase and position errors, A is the transmission matrix of the antenna array, and R s is the covariance matrix of the signal. By calculating the sample variance, the error level in the signal can be evaluated.

[0191] Step 4.5: Build a tensor model Decompose the tensor y(t) to obtain the estimated matrix Q of gain-phase-position error: According to the matrix Q, the gain-phase-position error is estimated:

[0192] Step 4.6: Correct the direction matrix to complete feature extraction:

[0193]

[0194] Step 4.7: Calculate the beam direction based on the estimated matrix in, Represents the relationship between the estimated direction matrix, A Γ,1 and A Γ,2 is the estimate of the direction matrix;

[0195] Step 4.8: Calculate the error value step by step by extracting characteristic parameters, where: Gain error calculation: Estimated gain error in, represents the parameters obtained from the joint estimation; the position error is calculated as: in, and They are the direction estimation values ​​of path 1 and path 2 respectively; phase error calculation: in, Represents the phase estimate, and finally obtains the statistical characteristics of gain, position and phase errors: μ g ,

[0196] Step 5: Calculate the signal energy and compare the signal energy with the preset threshold as the energy detection statistic to determine the legitimacy of the signal source and complete the device authentication, which specifically includes the following steps:

[0197] Step 5.1: At the receiving end, the user equipment verifies whether the signal y(t) comes from the legitimate base station (Alice). The verification process is modeled as a composite hypothesis testing problem with the following assumptions:

[0198] Assumption H0: The signal comes from a legitimate base station (Alice), and its radiation pattern is

[0199] Alternative hypothesis H1: The signal comes from a disguised attacker (Eve), and its radiation pattern is

[0200] Step 5.2: Based on the hypothesis test, construct the energy detection statistic, i.e., the received signal energy Y, and compare it with the preset threshold λ t For comparison, the energy detection formula is:

[0201]

[0202] Among them, λ t Indicates the preset detection threshold, which is used to distinguish whether the signal comes from a legitimate user. is the noise power, y(t) is the received signal, if Y>λ t , then accept the null hypothesis H0, that is, the signal comes from a legitimate base station; if Y≤λ t , then accept the alternative hypothesis H1, that is, the signal comes from a disguised attacker (Eve). Through this method, the legitimacy of the signal source can be effectively determined.

[0203] In order to evaluate the reliability and effectiveness of the authentication method in practical applications, two main indicators of detection performance are defined: detection probability P D,I : The probability of correct detection when the signal comes from the attacker Eve: P D,I =Pr(Y>λ t |H1). False alarm probability P F,I : The probability of false detection when the signal comes from the legitimate user Alice: P F,I =Pr(Y>λ t |H0).

[0204] The statistic Y is approximately the sum of squares of non-zero mean Gaussian random variables, and its probability density function (PDF) is:

[0205]

[0206] in, I K-1 (x) represents the modified Bessel function.

[0207] In the statistical distribution of energy detection, the generalized MarcumQ function Q is used n (a,b) describes the performance of energy detection. It is defined as follows: Where a represents the amplitude parameter of the non-zero mean Gaussian random variable, and b is the detection threshold parameter. n-1 (x) is the modified Bessel function. This function is used to quantify the detection and false alarm probability of a signal in hypothesis testing.

[0208] According to hypothesis H1, the detection probability P D,I It is expressed as: in, F Y (y|H1) represents the cumulative distribution function under assumption H1.

[0209] For hypothesis H0, the false alarm probability P F,I It is expressed as: in, λ t Indicates the detection threshold.

[0210] In order to more accurately describe the performance in the actual channel, the detection probability needs to be averaged. Assuming that there is path fading in the channel, the detection probability P D The expression is: Among them, f γ1 (x) represents the channel amplitude distribution under the assumption H1.

[0211] In millimeter wave communication systems, the uncertainty and randomness of the channel will cause the statistical characteristics of the received signal to change. Using the MarcumQ function modeling, we can accurately describe the detection performance of the signal under different assumptions and adjust the parameter λ t Optimize the performance of detection algorithms.

[0212] Further expand the performance analysis in random channels. In the case of path fading in the channel, the average behavior of the detection performance under different assumptions needs to be solved by integration. Specifically:

[0213] The detection probability P under the channel D :

[0214] The false alarm probability P in the channel F : By averaging the detection and false alarm probabilities, the system performance under random channels can be better described.

[0215] Define the detection probability P D and false alarm probability P F : Detection probability P D and false alarm probability P F It is a key indicator for evaluating system performance, and its mathematical formula is as follows:

[0216]

[0217]

[0218] Among them, Q n (a, b) represents the generalized MarcumQ function, which is used to describe the distribution characteristics of random variables. E and κ A are the shape parameters of the attack channel and the legitimate channel, respectively, indicating the power ratio of the direct path to the scattering path. and They represent the normalized signal-to-noise ratio, respectively, reflecting the impact of channel conditions on the performance.

[0219] The radiation pattern is described using Rice distribution. In order to accurately describe the distribution of the actual radiation pattern, it is assumed that The amplitude distribution of the radiation pattern obeys the non-central chi-square distribution and is based on the Rice distribution model. The amplitude distribution of the radiation pattern can be represented by the following probability density function (PDF):

[0220]

[0221] Where I0 is the zero-order modified Bessel function, is the parameter of the noncentral chi-square distribution, κ E is a parameter related to the error.

[0222] The integral formula for calculating the probability of detection is: and false alarm probability P F,I Substitute the detection probability P D , calculate the new detection probability P D To simplify the calculation, use variable substitution to convert the formula into standard form:

[0223] This integral form helps calculate the detection probability P D , and evaluate the performance of the authentication method in a practical communication system.

[0224] Define the detection probability P when K = 1 D When K = 1, the detection probability P D and false alarm probability P F This can be evaluated by using the change in the variable. Then the above formula becomes:

[0225]

[0226]

[0227] Then when K = 1, the detection probability P D It can be characterized as:

[0228]

[0229] The generalized integral formula is used for random channel analysis. To describe the performance under random channel conditions, the detection probability P D and false alarm probability P F Calculated by the following integral formula: in, represents the probability density function (PDF) of the attack channel gain. Represents the probability density function of the legal channel gain.

[0230] The randomness of the channel gain is modeled by the moment generating function (MGF), which is expressed as:

[0231]

[0232] in, and They represent the random characteristics of the attack channel and legitimate channel gains respectively. The introduction of MGF can simplify the integral calculation and is used to analyze the distribution of detection probability and false alarm probability.

[0233] Since many channel distributions are combined by adding or multiplying them, it is more convenient to use the moment generating function (MGF) than to calculate the average error probability on the channel PDF. The average detection probability PD is calculated using the moment generating function (MGF) by the contour integral representation of the MarcumQ function with the contour radius. Therefore, PD (similar to PF) can be expressed as:

[0234] Where o represents a circular contour with radius r∈[0,1], Φ(x) represents the MGF of x, which is given by Calculated.

[0235] When K>1, combining the MarcumQ function with the MGF of the channel gain, the detection probability can be expressed as the path integral formula:

[0236]

[0237] Among them, o means that the integral path is a closed path around the origin, z K represents the effect of the number of samples on performance, and ξ E,2 =κ E ξ E,1 (1-ξ E,1 ).

[0238] In order to verify whether the proposed statistical model is consistent with the characteristics of the actual signal, a comparison between numerical simulation and theoretical model is used. The cumulative distribution function (CDF) is calculated through Monte Carlo simulation and compared with the theoretical model of Beckmann distribution or Rice distribution to ensure that the statistical model can accurately describe the radiation pattern characteristics of the actual signal. Through this verification, the matching degree between the mathematical model of the certification process and the actual application is ensured, further guaranteeing the reliability of the certification method.

[0239] Specifically, set the system parameters and determine the key parameters that affect the reliable communication and authentication performance of millimeter waves. The characteristic parameters of the legitimate base station (Alice) and the attacker (Eve) are set as follows: Gain error μ A,g =0,σ A,g =0.1dB,σ A,ψ =10°,σ A,p=0.1λ, where λ represents the wavelength, the operating frequency f=30GHz, and the bandwidth is set to 1GHz. The communication distance is set between 50 and 100 meters, and the noise power spectral density is -174dBm / Hz. According to the ITU-RP.676-9 standard and the free space loss formula, the propagation loss is -124.6dB. The base station uses a 161×161 element uniform linear array (ULA), the antenna gain is 31.6dB, and the beam direction (DoD) is set to θ1=60°, θ2=40°, which are used to describe the LOS and NLOS link situations respectively.

[0240] In order to verify the statistical characteristics of the radiation pattern, the calculated CDF is compared with the Beckmann distribution and the Rice distribution. The LOS link is selected as an example for verification, and a 1×10 5 A radiation pattern is calculated, taking into account the three cases of gain, phase and position errors. Figure 3 The statistical model validation is presented, including the comparison with Beckmann distribution and Rice distribution. The results show that both are highly consistent with the Monte Carlo simulation results, verifying the accuracy of the proposed model. (a) shows the comparison between Beckmann distribution and Monte Carlo simulation results, and (b) shows the comparison between Rice distribution and Monte Carlo simulation results. According to the experimental result graph of the statistical analysis model of the radiation pattern, the validation results show that the theoretical models of Beckmann distribution and Rice distribution are highly consistent with the simulation data, verifying the excellent matching degree of the proposed model in the actual simulation.

[0241] In order to verify the effectiveness and superiority of the authentication scheme proposed in the present invention, a comparison is made with several existing identity authentication methods through numerical simulation, and multiple performance indicators are evaluated.

[0242] The changes in the variance and correlation coefficient between the real and imaginary parts of the radiation pattern under different direction angles (DoD) are analyzed. Figure 4 The variance and correlation coefficient between the real and imaginary parts of the radiation pattern are shown as a function of DoD (angle of arrival). Figure 4 (a) shows the variance of the real and imaginary parts of the radiation pattern. The results show that the variance is very small and the variation can be ignored. Figure 4 (b) shows the correlation coefficient between the real and imaginary parts of the radiation pattern. The results show that the correlation coefficient does not exceed 0.3, indicating that the correlation between them is negligible. This result proves that the CDF of the radiation pattern modulus can be effectively approximated by the Rice distribution, and at a specific steering angle, the Rice distribution has good overall accuracy and minimal deviation from the Monte Carlo simulation results.

[0243] Figure 5 The effect of different attacker characteristic parameters on the false alarm probability (P F) and detection probability (P D ). (a) shows the change of detection probability under different thresholds. A larger threshold leads to a lower detection probability. (b) shows the change of ROC curve under different feature parameters. The mean and variance of gain error have a significant impact on the authentication performance.

[0244] By analyzing the detection probability P D and false alarm probability P F It is found that when the threshold is small, the system can effectively identify the identity disguise attack launched by the attacker. However, if the threshold is set too large, the probability of false alarm will increase, which may cause the system to mistakenly identify the attacker as a legitimate user, thereby causing information leakage or malicious information injection.

[0245] By analyzing the changes in the radiation pattern power of LOS and NLOS links at different UE movement angles, Figure 6 The impact of UE movement on authentication performance is analyzed. (a) shows the impact of UE movement angle on radiation pattern power. As the movement angle increases, the power gradually decays, but the attenuation is less than 3dB; (b) shows the ROC curves under different movement angles. As the angle increases, the authentication performance decreases slightly. Further analysis shows that larger movement angles will lead to a slight performance degradation, mainly due to beam misalignment or blockage caused by UE mobility. However, the performance loss is relatively limited, indicating that the authentication system is highly robust to inherent hardware failures.

[0246] By comparing the receive operating characteristic (ROC) curve and overload probability (PO) under single-beam and dual-beam configurations, Figure 7 As shown in Figure 2, the results show that the authentication system using the dual-beam solution has a significant performance improvement compared to the single-beam solution. Figure 7 As shown in (a), the authentication success rate (ROC) is improved by about 5%, and the overload probability (PO) is reduced by about 1.5%. Figure 7 This improvement is attributed to the fact that dual-beam can effectively avoid the link blocking problem that single-beam solutions may face, thereby enhancing the system's robustness and anti-interference capabilities.

[0247] like Figure 8 As shown in Figure 1, the experiment compares the performance of the authentication method based on gain-phase-position error and the single gain error authentication method. The results show that the method combining three radiation pattern characteristics (gain, phase and position error) performs best in authentication performance. Figure 8 (a). In particular, the detection probability P DCompared with the method using only gain error, the detection accuracy is improved by about 10%. In addition, the authentication system using multi-dimensional radiation pattern characteristics can provide higher authentication reliability and make more accurate decisions from different signal angles and dimensions. The experiment analyzes the impact of beam alignment accuracy on authentication performance. The results show that accurate beam alignment can significantly improve authentication performance. On the contrary, Figure 8 As shown in (b), when there is a large error in beam alignment, such as Δ = 15°, the authentication performance will significantly degrade. At low signal-to-noise ratio (SNR), it becomes difficult to identify signal features, resulting in authentication failure. Therefore, maintaining beam alignment accuracy is critical to achieving the desired authentication performance.

[0248] The authentication method of the present invention can effectively cope with the movement changes of UE. The dual-beam scheme improves the authentication success rate (ROC) by about 5% and reduces the overload probability (PO) by about 1.5%. The authentication method combining gain, phase and position errors improves the detection accuracy by about 10% compared with the single gain error scheme, and precise beam alignment significantly improves the authentication performance, especially under low signal-to-noise ratio (SNR) conditions, where beam alignment errors will cause a significant decrease in authentication performance.

[0249] The above description is only an embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the scope of the claims of the present invention.

Claims

1. A highly reliable device authentication method based on antenna array error characteristics and dual-beam transmission, characterized in that: This device authentication method is applied to millimeter wave communication systems. The user equipment (UE) needs to verify whether the signal it receives comes from a legitimate base station (Alice) rather than a disguised attacker (Eve). By extracting and analyzing the gain, phase and antenna element position error characteristics of the base station radiation pattern, the user equipment (UE) determines the legitimacy of the signal source. The specific authentication method includes the following steps: Step 1: construct a dual beam, transmit the signal received by the user equipment (UE) through the dual beam, calculate the parameters of the transmission path, and calculate the dual beam weight vector; Step 2: Actively track the dual beams and adjust the dual beam directions in real time to ensure that the user equipment (UE) receives signals efficiently; Step 3: Model the statistical analysis model of the radiation pattern, calculate the statistical characteristics of the mean, variance, and correlation of the real and imaginary parts of the radiation pattern, and describe the distribution of the radiation pattern through the statistical characteristics; Step 4: define the radiation pattern characteristic extraction target, complete the characteristic extraction, and calculate the gain error value, phase error value and position error value according to the extracted characteristic parameters; Step 5: Calculate the signal energy and compare it with the preset threshold as the energy detection statistic to determine the legitimacy of the signal source and complete the device authentication.

2. The highly reliable device authentication method based on antenna array error characteristics and dual-beam transmission according to claim 1 is characterized in that: The step 1 specifically includes the following steps: Step 1.1, define the receiving signal as: y(t)=hΓws(t)+ν(t) Where Γ represents the gain-phase-position error matrix, s(t) is the transmitted signal of the legitimate base station (Alice) at time t, ν(t) represents the additive noise at the receiving antenna, and w = [W1,...,W M ] T represents the component value of the beam weight vector, M represents the number of antennas, and the beam weight w of each path l It is expressed as: Represents the antenna array in the path propagation angle θ l The response vector on θ l is the propagation angle of the path, and the value of l is 1 or 2; Step 1.2: Assume that the millimeter wave propagation channel follows the geometry-based L-path model, and the channel expression is: Among them, α l represents the complex gain of the lth scattering path, and the channel of the second path is expressed as: h2=h1δe jβ , represents relative attenuation, β∈[0, 2π] represents relative phase shift, and j is an imaginary unit; Step 1.3, received signal update and weighted calculation: By combining the channel information of the two beam paths, the received signal is updated as follows: y(t)=(α1b1+α1δe jβ b1)s(t)+ν(t) Where α1 represents the complex gain of the first scattering path, b1 is the radiation pattern that depends on the propagation angle θ and frequency f of the path; Step 1.4, calculate the dual beam weights: Wherein, θ1 and θ2 represent the propagation angles of the first path and the second path, respectively, and w1 and w2 represent the beam weights of the first path and the second path, respectively; Step 1.5, since the relative amplitude δ and relative phase shift β are expressed as channel ratios: Through additional channel detection, set the beam w(θ1,θ2,1,0) and w(θ1,θ2,1,π / 2) to estimate the channel strength respectively: And according to the values ​​of P3 and P4, the ratio of h2 to h1 is obtained, that is, the accurate values ​​of the relative amplitude δ and the relative phase shift β are calculated: in, represents the real part operation, Indicates the operation of taking the imaginary part, P1=||h1|| 2 ,P2=||h2|| 2 , indicating the channel strength.

3. The highly reliable device authentication method based on antenna array error characteristics and dual-beam transmission according to claim 1 is characterized in that: In step 2, actively tracking the dual beams and adjusting the dual beam reflections in real time specifically include the following steps: Step 2.

1. In order to capture the change of beam direction, define the power measurement formula for each beam: P i (t)=Ω T (i i +φ i (t))+Ω R +P T -P c ,i=1,2; Among them, θ i +φ i (t) represents the beam angle, Ω T (θ i +φ i (t)) represents the transmission gain of the beam, which changes with the beam angle, Ω R Represents the receiving gain, P T Represents the transmission power, P c Represents the power loss due to channel attenuation; Step 2.2: Construct a uniform linear array (ULA) gain model. In a uniform linear array (ULA), the transmit gain is: Where M is the number of antennas. The offset angle φ is estimated from the measured beam power by inverse calculation. i (t0); Step 2.3, beam power change differential calculation: By calculating the difference between the beam power at time t=t0 and the initial time t=0, the offset of the beam direction is obtained, which directly reflects the change trend of the beam direction and ensures continuous signal reception: P i (t0)-P i (0)=Ω T (i i +φ i (t0))-Ω T (i i )。 4. The highly reliable device authentication method based on antenna array error characteristics and dual-beam transmission according to claim 1 is characterized in that: Step 3 specifically includes the following steps: Step 3.1, build a statistical analysis model for the radiation pattern: statistically describe the gain error, phase error and position error, assuming that the gain error, phase error and position error are independent random variables and satisfy the following distribution: Among them, μ g is the mean value of the gain error, μ ψ is the mean value of the phase error, is the gain error variance, is the phase error variance, is the position error variance; Step 3.2, the mean of the real part and the mean of the imaginary part of the statistical radiation pattern: define the following lemma: if the random variable θ obeys a normal distribution with mean μ and standard deviation σ, then the expectations of the cosine and sine are: Where a is a constant, σ is the standard deviation, and b is the real part of the radiation pattern. R and the imaginary part b I The definition of the mean of the real part of the radiation pattern and the mean of the imaginary parts They are: Using the differential formula of cosine and sine, we can further obtain: Assume phase Θ m The mean and variance of are: m Θ =μ ψ , Using the lemma we get: The mean of the real and imaginary parts of the radiation pattern is: Where c0 = 1 + μ g ; Step 3.3: Calculate the variance of the real part and the imaginary part of the radiation pattern: The mean power of the radiation pattern consists of two parts: in, According to the above formula, calculate the real part b of the radiation pattern R and the imaginary part b I The squared power mean of is expressed as: in, and Represents the power contribution from the same antenna element: in represents the comprehensive statistical component of the gain error, Represents the power contribution from different antenna elements: in, represents the mean component of the gain error; Using the square mean formula, the square mean formula of the real and imaginary parts of the radiation pattern is corrected: The variance of the real and imaginary parts of the radiation pattern is calculated by the relationship between the mean square of the power and the mean: Step 3.4: Statistical characteristics of the correlation between the real and imaginary parts of the statistical radiation pattern: Define the Pearson correlation coefficient between the real and imaginary parts of the radiation pattern as: Among them, Cov(b R ,b I ) represents the covariance, Expanding the covariance formula yields: Step 3.5: Describe the distribution of the radiation pattern by statistical characteristics: The real part b of the radiation pattern R and the imaginary part b I All obey Gaussian distribution, and their amplitude statistical distribution is derived according to the central limit theorem: Beckmann distribution: The amplitude of the radiation pattern is described by a Beckmann distribution, whose probability density function (PDF) is: in, The cumulative distribution function (CDF) is: Rice distribution: Assuming that the variances of the real and imaginary parts are equal and uncorrelated, the amplitude distribution of the radiation pattern is approximately described by the Rice distribution, whose probability density function (PDF) is: in, It represents the ratio of the direct path power to the other path power. Indicates the total received power, represents the mean value of the amplitude, represents the variance of the amplitude, and I0 represents the zero-order modified Bessel function.

5. The highly reliable device authentication method based on antenna array error characteristics and dual-beam transmission according to claim 1 is characterized in that: The step 4 specifically includes the following steps: Step 4.1: Define the key parameter μ for the radiation pattern characteristic extraction target, i.e., the estimated direction b Key parameters on frequency Step 4.2: Define the gain-phase-position error matrix: Γ = diag(r). in, Θ m,l =ε ψ,m +kε x,m sinθ l , M c represents the number of well-calibrated antenna elements, ρ m Parameters representing the combined gain, phase, and position errors; Step 4.3: Establish a received signal model. The received signal considering the gain-phase-position error is expressed as: y(t)=hΓws(t)+v(t)=(ΓA) H ws(t)+ν(t) Where Aα=A t , A t =[a(θ1),a(θ2)],α=[α1,α2] T represents the beam direction matrix, ν(t) represents additive noise, which obeys Gaussian distribution; Step 4.4: Estimate sample variance using multiple snapshot data K: in, K is the number of samples, y(t) is the signal received at time t, Γ is the error matrix containing gain, phase and position errors, A is the transmission matrix of the antenna array, R s is the covariance matrix of the signal. By calculating the sample variance, the error level in the signal can be evaluated. Step 4.5: Build a tensor model Decompose the tensor y(t) to obtain the estimated matrix Q of gain-phase-position error: According to the matrix Q, the gain-phase-position error is estimated: Step 4.6: Correct the direction matrix to complete feature extraction: Step 4.7: Calculate the beam direction based on the estimated matrix in, Represents the relationship between the estimated direction matrix, A Γ,1 and A Γ,2 is the estimate of the direction matrix; Step 4.8: Calculate the error value step by step by extracting characteristic parameters, where: Gain Error Calculation: Estimating Gain Error in, denotes the parameters obtained from the joint estimation; Position error calculation: in, and are the estimated values ​​of the directions of path 1 and path 2 respectively; Phase error calculation: in, Represents the phase estimate, and finally obtains the statistical characteristics of gain, position and phase errors:

6. The highly reliable device authentication method based on antenna array error characteristics and dual-beam transmission according to claim 1 or 4, characterized in that: Step 5 specifically includes the following steps: Step 5.1: At the receiving end, the user equipment verifies whether the signal y(t) comes from the legitimate base station (Alice). The verification process is modeled as a composite hypothesis testing problem with the following assumptions: Assumption H0: The signal comes from a legitimate base station (Alice), and its radiation pattern is Alternative hypothesis H1: The signal comes from a disguised attacker (Eve), and its radiation pattern is Step 5.2: Based on the hypothesis test, construct the energy detection statistic, i.e., the received signal energy Y, and compare it with the preset threshold λ t For comparison, the energy detection formula is: Among them, λ t Indicates the preset detection threshold, which is used to distinguish whether the signal comes from a legitimate user. is the noise power, y(t) is the received signal, if Y>λ t , then accept the null hypothesis H0, that is, the signal comes from a legitimate base station; if Y≤λ t , then accept the alternative hypothesis H1, that is, the signal comes from a disguised attacker (Eve). Through this method, the legitimacy of the signal source can be effectively determined.

7. The high-reliability device authentication method based on antenna array error characteristics and dual-beam transmission according to any one of claims 1 to 6, characterized in that: The millimeter wave communication system includes: a legitimate base station (Alice): a uniform linear array (ULA) with M antennas, responsible for transmitting legitimate signals to user equipment; an attacker (Eve): attempting to impersonate a legitimate base station to send forged information; a user equipment (UE): a single-antenna device, used to receive signals from the base station and verify the identity of the base station through radiation pattern characteristics.

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