A method for unmanned aerial vehicle identity authentication for a millimeter wave MIMO system

Abstract

The application discloses a kind of unmanned plane identity authentication methods for millimeter wave MIMO system, step 1: unmanned plane receives signal in communication system, wherein signal includes control signal from ground control station and the deception signal that antenna pair enemy disguises into base station sends to unmanned plane;Step 2: utilize Laplace prior modeling technique to accurately characterize the statistical model of angular domain millimeter wave MIMO channel;Step 3: based on maximum likelihood estimation / generalized approximation message passing algorithm extracts channel sparsity parameter;Step 4: establish theoretical model, and determine the threshold of identity authentication;Step 5: establish binary hypothesis testing model, build authentication framework, and carry out identity authentication based on threshold;The application utilizes efficient channel modeling and channel sparsity to develop a new physical layer authentication scheme for transmitter authentication in millimeter wave MIMO unmanned plane ground communication system.

Description

Technical Field

[0001] This invention relates to the field of unmanned aerial vehicle (UAV) technology, and in particular to a UAV authentication method for millimeter-wave MIMO systems. Background Technology

[0002] UAV (Unmanned Aerial Vehicle) ground communication systems have become highly attractive for overcoming geographical limitations in communication. In particular, UAV ground communication systems integrating millimeter-wave (mmWave) multiple-input multiple-output (MIMO) technology can offer ultra-high transmission rates and strong reliability, thus effectively supporting the high throughput and low latency requirements of some critical applications. To ensure the secure operation of millimeter-wave MIMO UAV ground systems, authentication of the ground control station (GCS) is a critical issue to prevent unauthorized access that could lead to the leakage of sensitive data. Currently, authentication of UAV ground systems is mainly addressed through upper-layer methods; however, recent research indicates that exploiting hardware vulnerabilities and / or wireless channel limitations can be problematic. Physical layer authentication (PLA), which utilizes inherent and unique physical layer characteristics to achieve identity verification, is promising for UAV ground systems. PLA offers advantages such as low communication overhead, reduced resource requirements, and improved compatibility. Therefore, it can serve as an effective supplement or enhancement to upper-layer authentication methods. PLA can be broadly categorized into hardware impairment-based methods and channel-based methods. Channel-based PLA is particularly interesting for millimeter-wave MIMO UAV ground systems because it offers better system protocol compatibility and lower feature extraction processing costs. Moreover, the structured channels in such systems possess rich intrinsic characteristics (e.g., spatial sparsity, unique non-Gaussianity), making them well-suited for high-performance authentication.

[0003] Although many channel-based authentication schemes have been developed to date, they cannot be directly applied to millimeter-wave MIMO UAV ground communication systems due to the following challenges: First, these schemes are mainly based on Gaussian channel model assumptions applicable to narrowband systems, while the large number of antennas and relatively few propagation paths in wideband millimeter-wave MIMO systems result in spatially sparse and inherently non-Gaussian channels. Second, traditional schemes typically utilize temporal channel correlation to distinguish transmitters, but the high UAV maneuverability in UAV ground communication systems significantly reduces channel correlation, making these schemes unsuitable for such systems. Furthermore, the sparse propagation environment in millimeter-wave MIMO systems leads to low spatial resolution of the channel in the antennas, so directly applying previous channel-based schemes to millimeter-wave MIMO UAV ground systems may result in significant performance losses. Summary of the Invention

[0004] The purpose of this invention is to solve the above-mentioned problems by designing a drone identity authentication method for millimeter-wave MIMO systems.

[0005] To achieve the above objectives, the technical solution of the present invention further includes, in the above-mentioned UAV identity authentication method for millimeter-wave MIMO systems, the physical layer authentication method includes the following steps:

[0006] Step 1: The drone receives signals from the communication system, including control signals from the ground control station and deceptive signals sent to the drone by the antenna opponent disguised as a base station;

[0007] Step 2: Utilize Laplace prior modeling techniques to accurately characterize the statistical model of the angular domain millimeter-wave MIMO channel;

[0008] Step 3: Extract channel sparsity parameters based on the expectation-maximization / generalized approximation message passing algorithm;

[0009] Step 4: Establish a theoretical model and determine the threshold for identity authentication;

[0010] Step 5: Establish a binary hypothesis testing model, build an authentication framework, and perform identity authentication based on thresholds.

[0011] Furthermore, in the aforementioned UAV authentication method for millimeter-wave MIMO systems, the communication system in step 1 is established by the following model:

[0012] Establish a millimeter-wave MIMO UAV ground communication system, which consists of three entities: a legitimate ground control station with an Nt antenna, a mobile UAV with an Nr antenna, and an adversary with an Nt antenna.

[0013] Establish a channel model, which has N C There are N spatial clusters, each cluster containing N... L A propagation path is used to characterize the ground-to-air millimeter wave propagation environment, and the millimeter wave channel matrix in the antenna domain. Represented as:

[0014]

[0015] in, It is the c-th propagation cluster. Path, These represent the c-th cluster's... A receiving and transmitting azimuth angle, and These are the normalized receiving and transmitting array steering vectors, respectively, expressed as:

[0016]

[0017]

[0018] The channel matrix is ​​transformed from the antenna domain to the angle domain using the spatial discrete Fourier transform, and its mathematical expression is as follows:

[0019]

[0020] in, and It is a DFT unitary matrix, H v It is a corner domain channel;

[0021] Using the Laplace distribution, a statistical model of the angular domain millimeter-wave channel is established. The mathematical expression for the zero-mean Laplace prior is:

[0022]

[0023] Among them, using σ v To characterize the sparsity of millimeter-wave channels;

[0024] Establish a communication model, where A, B, and E represent the ground control station, the UAV, and the antenna counterpart, respectively. The unknown ground control station X = {A, E} first sends a signal frame to the UAV for authentication. The received signal at time n of the k-th frame is represented as:

[0025]

[0026] in,

[0027] Indicates from N r The signal vector received by each antenna, where N is the number of symbols in a frame;

[0028] It is N t The training sequence for antenna transmission, with an average transmit power assumed to be...

[0029] It is composed of unknown variance The noise vector modeled by the zero-mean complex Gaussian distribution, i.e.

[0030] Stack all N symbols within a single frame and write the signal model into a matrix. Right now:

[0031]

[0032] in,

[0033] Leveraging the sparsity of millimeter-wave channels, the vectorized representation is as follows:

[0034]

[0035] in,

[0036]

[0037] The sparsity of millimeter-wave channels is characterized using the Laplace distribution. Assuming the Laplace distribution is defined only for real-valued random variables, the complex-valued model is transformed into an equivalent real-valued model:

[0038]

[0039] The linear model for obtaining the received signal of the k-th frame is:

[0040]

[0041] in, And M' = 2N r N, N' = 2N r N t .

[0042] Furthermore, in the aforementioned UAV authentication method for millimeter-wave MIMO systems, step 2, which utilizes Laplace's prior modeling technique to accurately characterize the statistical model of the angular domain millimeter-wave MIMO channel, includes:

[0043] After receiving signal frame y, the UAV obtains the angular domain channel estimate. Extracting σ from the corner domain channel estimate v The minimum mean square error estimator is used to obtain...

[0044]

[0045] Among them, h v (i) is h v The i-th element, the channel element Based on the zero-mean Laplace prior mathematical expression:

[0046]

[0047] Let the common prior distribution be independent and identically distributed (iid), σ v Therefore, h represents the sparsity of the millimeter-wave channel. v The marginal posterior probability of (i) is given by the following formula:

[0048]

[0049] Among them, h v \h v (i) indicates that, except for h v (i) other than h vThe integral of all elements;

[0050] Using Laplace's prior to define the diagonal domain millimeter-wave channel h v (k) is used for modeling. In the formula h v The marginal posterior distribution of (i) is:

[0051]

[0052] Where, ψ i (·) and ω i (·) is a parametric function They are represented as follows:

[0053]

[0054]

[0055] sgn(x) is a standard symbolic function, represented as:

[0056]

[0057] Factor After normalization, the result is:

[0058]

[0059] Where Q(·) represents the Gaussian Q-function, and It depends on the parameter The items are:

[0060]

[0061]

[0062] Derive h v The posterior mean and variance of (i) are:

[0063]

[0064]

[0065] Millimeter-wave channel estimates are obtained by using generalized approximate message-passing iteration. It follows a normal Laplace distribution, that is,

[0066] Furthermore, in the aforementioned method for UAV identity authentication for millimeter-wave MIMO systems, a normal Laplace variable is obtained. The probability density function:

[0067] Two random variables If z = x + w, then the sum of x and w is a random number following a normal Laplace distribution, i.e. The probability density function of z is expressed as:

[0068]

[0069] in, It is a data-related item.

[0070] Furthermore, in the aforementioned UAV authentication method for millimeter-wave MIMO systems, step 3, which extracts channel sparsity parameters based on the expectation-maximization / generalized approximation message passing algorithm, includes:

[0071] Extract σ using the expectation-maximization iterative method embedded in the t-th generalized approximation message passing iteration. v And estimate use Let represent the estimate of q during the l-th expectation maximization iteration, and then the E-step size for the (l+1)-th iteration is formulated as:

[0072]

[0073] Obtain the maximum likelihood (ML) method in the M-step. and

[0074]

[0075]

[0076] in, and They are represented as follows:

[0077]

[0078]

[0079] in, and Depends on the l-th expectation maximization iteration update

[0080] Furthermore, in the aforementioned UAV authentication method for millimeter-wave MIMO systems, step 3, which involves extracting channel sparsity parameters based on the expectation-maximization / generalized approximation message passing algorithm, further includes:

[0081] Use ∈ EM and T EMLet represent the error tolerance and the maximum number of iterations, respectively. The expectation maximization method terminates when the following condition is met:

[0082]

[0083] The result Used for the (t+1)th iteration of the generalized approximate message passing algorithm.

[0084] Furthermore, in the aforementioned drone authentication method for millimeter-wave MIMO systems, step 4 specifically includes:

[0085] The false alarm rate P is derived from the hypothesis testing and authentication framework based on binary hypothesis testing. f Theoretical model and detection probability P d The theoretical model is used to determine an optimal threshold using the Neyman-Pearson theorem and the Wilson-Hilferty theorem.

[0086] Furthermore, in the aforementioned UAV authentication method for millimeter-wave MIMO systems, the false alarm rate P is derived using a hypothesis testing authentication framework based on binary hypothesis testing. f Theoretical model and detection probability P d The theoretical models include:

[0087] False alarm rate P f Derivation: Hypothesis test results of the Laplace approximation method under assumption H0. Greater than a given threshold τ L Authentication is achieved by utilizing spatially relevant spatial features, within a given decision threshold τ. L Below, the false alarm rate P f Determined as:

[0088]

[0089] in, Let the right-tailed probability function represent a chi-square random variable with 2N' degrees of freedom:

[0090]

[0091] Detection probability P d Derivation: Authentication is achieved using spatially relevant spatial features, given a decision threshold τ. L In the case of P d It is estimated to be:

[0092]

[0093] Furthermore, in the aforementioned drone authentication method for millimeter-wave MIMO systems, determining an optimal threshold using the Neyman-Pearson theorem and the Wilson-Hilferty theorem includes:

[0094] According to the Neyman-Pearson theorem, Obtain the optimal threshold under constraints in This is the maximum false alarm rate allowed by the authentication protocol. An optimal threshold is calculated using the Wilson-Hilferty theorem.

[0095] For the chi-square variable x, for the threshold The small and large values ​​of the value, All follow a mean of μ WH The variance is Gaussian distribution, The probability density function (PDF) is expressed as:

[0096]

[0097] Where, μ WH and It can be represented as:

[0098]

[0099]

[0100] An approximate expression using the Wilson-Hilferty theorem:

[0101]

[0102] in, and The mean is μ WH The variance is σ WH Gaussian variables;

[0103] Under constraints Optimal threshold Written as:

[0104]

[0105] Substitute the derived optimal threshold into P d The expression, in Maximum detection probability under constraints It can be written as:

[0106]

[0107] Furthermore, in the aforementioned drone authentication method for millimeter-wave MIMO systems, step 5 specifically includes:

[0108] Based on millimeter-wave channel estimation and The drone will view the certification decision as:

[0109]

[0110] Among them, the null hypothesis The current signal comes from a legitimate ground control station, i.e., X = A. This indicates that the current signal originates from an antenna that is opposite to the phone's antenna, i.e., X = E;

[0111] based on Independent and identically distributed components The likelihood ratio test is expressed as:

[0112]

[0113] Using the Laplace approximation, we obtain the binary hypothesis test:

[0114]

[0115] Hypothesis tests using the Laplace approximation method are expressed as follows:

[0116]

[0117] in, This represents the likelihood ratio test, τ L Indicates the decision threshold. yes The function, Spatial related statistics, UAVs based on The results distinguish between ground control stations and antenna counterparts.

[0118] Its beneficial effect lies in proposing a physical layer authentication method based on channel sparsity for millimeter-wave MIMO UAV ground systems. The UAV collects control signals sent by the ground control station, uses Laplace prior modeling to model channel sparsity, and extracts channel sparsity parameters as device fingerprints using an expectation-maximization / generalized approximation message passing algorithm. Then, a hypothesis testing model is established as the identity authentication framework, and a discriminant model based on false alarm rate and false alarm rate is established. The discriminant model gives the threshold required for hypothesis testing. Finally, the UAV determines its identity by comparing the fingerprint difference with the threshold. Attached Figure Description

[0119] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, obtaining other drawings based on these drawings without creative effort still falls within the scope of the present invention.

[0120] Figure 1 This is a flowchart illustrating a drone authentication method for millimeter-wave MIMO systems according to an embodiment of the present invention.

[0121] Figure 2 This is a schematic diagram illustrating the Laplace prior feasibility of a drone identity authentication method for millimeter-wave MIMO systems in an embodiment of the present invention.

[0122] Figure 3 This is a performance diagram of a drone identity authentication method for millimeter-wave MIMO systems according to an embodiment of the present invention. Detailed Implementation

[0123] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0124] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and / or groups thereof.

[0125] The present invention will now be described in detail with reference to the accompanying drawings, such as... Figure 1 As shown, a physical layer authentication method for UAVs based on carrier frequency offset and phase noise is presented. The physical layer authentication method includes the following steps:

[0126] Step 1: The drone receives signals from the communication system, including control signals from the ground control station and deceptive signals sent to the drone by the antenna opponent disguised as a base station;

[0127] Establish a millimeter-wave MIMO UAV ground communication system, which consists of three entities: a legitimate ground control station with an Nt antenna, a mobile UAV with an Nr antenna, and an adversary with an Nt antenna.

[0128] Specifically, a device with an antenna: an N t Alice, a legally registered GCS (Ground Control Station) with an antenna, and an N r Bob, a mobile drone with an antenna, and an N t Antenna opponent Eve, which is a widely used three-body model.

[0129] Specifically, Alice transmits control signals to the intended drone Bob to perform a critical mission, while Eve attempts to inject false signals into the relevant network by impersonating Alice to perform unauthorized drone control. Due to the openness of the wireless transmission medium, the drone ground communication system is vulnerable to simulation attacks. If Eve successfully accesses the drone ground network by impersonating Alice, she may launch more aggressive attacks, such as man-in-the-middle attacks and physical collisions, causing serious damage. Therefore, it is crucial for Bob to verify the legitimacy of his current GCS identity by using a robust and effective authentication scheme.

[0130] In this embodiment, Bob authenticates GCS Alice to verify the source of the currently received signal frame.

[0131] A channel model is established. UAVs are typically used to perform tasks at relatively high altitudes with fewer reflecting objects in the vicinity, and millimeter-wave MIMO channels inherently have finite scattering paths. Therefore, this method employs a widely used geometric channel model with N... C There are N spatial clusters, each cluster containing N... L A propagation path is used to characterize the ground-to-air millimeter-wave propagation environment. Both the transmitter and receiver are considered as uniform linear arrays spaced half-waves apart. Under this model, the millimeter-wave channel matrix in the antenna domain is... Represented as

[0132]

[0133] in, It is the c-th propagation cluster. A path. These represent the c-th cluster's... The azimuth angles for receiving and transmitting. In addition, and These are the normalized receiving and transmitting array steering vectors, which can be further expressed as:

[0134]

[0135]

[0136] In the high-frequency millimeter-wave band, radio frequency signals propagate along several clusters, each containing a small number of sub-paths that exhibit narrow angular spread. Therefore, millimeter-wave channels are inherently sparse.

[0137] To better illustrate the sparsity of millimeter-wave channels, the spatial discrete Fourier transform (DFT) is used to transform the channel matrix from the antenna domain to the angle domain. Its mathematical expression is as follows:

[0138]

[0139] in, and It is a DFT unitary matrix, H v It is a angular domain channel.

[0140] Overview of conventional statistical models for narrowband channels: Due to the rich scattering environment in narrowband systems, the Gaussian distribution is often accurately applied to model channel elements in the antenna domain. Specifically, it is assumed that the variance of a single element h of the channel matrix H is... The zero-mean Gaussian distribution, i.e.

[0141]

[0142] Because U t and U r It is a unitary matrix, therefore H is equivalent to H v H v The elements in the model also follow a Gaussian distribution. However, due to the poor scattering environment of millimeter-wave communication, a Gaussian distribution is not suitable for modeling millimeter-wave channels. Therefore, it is necessary to find a more accurate statistical model to characterize H. v .

[0143] Statistical Models for Angular Domain Millimeter-Wave Channels with Laplace Distributions: Recently, some studies have described statistical models of the sparsity of millimeter-wave channels. They all propose using an M-order Gaussian mixture model (referred to as Gaussian for simplicity) to approximate the unknown prior distribution. The Gaussian model is as follows:

[0144]

[0145] in It is a scaling parameter vector.

[0146] While the methods described above offer feasible solutions, they require estimating a relatively large number of unknown parameters, leading to increased computational complexity and performance degradation. Inspired by the Discrete Cosine Transform (DCT) coefficient modeling method in image processing, and given the significant similarity between DCT elements and the sparsity of angular domain millimeter-wave channels, this embodiment utilizes more precise prior knowledge, namely the Laplace distribution, to model the angular domain millimeter-wave channel elements. If σ... v To represent the spatial correlation properties including average path loss and large fading effects, the mathematical expression for this zero-mean Laplace prior is:

[0147]

[0148] Using σ v To characterize the sparsity of the millimeter-wave channel, it is assumed that it is unknown for UAVBob. Compared to previous authentication schemes, the assumptions of this method are more feasible. To demonstrate the feasibility of the proposed Laplace channel modeling, as... Figure 2 As shown, this method presents the histograms and Laplace probability density functions of angular domain millimeter-wave MIMO channels corresponding to different geographical locations, from... Figure 2 The two figures above clearly show that the histograms of the angular domain millimeter-wave MIMO channels corresponding to different geographical locations fit the Laplace distribution curves well. Furthermore, the sparsity parameter σ related to Alice and Eve... v Significant differences were observed. The results validated the effectiveness of the new model and the parameter σ. v The discernibility of spatial sparsity.

[0149] Stability and distinguishability are fundamental criteria for the feasibility of fingerprint authentication. Recent research shows that the spatial statistics of a channel remain constant over the transmission bandwidth, changing much more slowly (approximately two orders of magnitude slower) than transient channel characteristics such as CIR and CFR, which exhibit long-term stability and hold promise for applications in highly mobile networks. Furthermore, long-term channel characteristics are related to the scattering environment around each transceiver, exhibiting different channel sparsity in different geographical locations; to further demonstrate these two properties, such as... Figure 2 As shown in the figure below, this paper extracts σ corresponding to Eve from four different geographical locations (x subscript = 0.6, 0.8, 1, 1.2). v And extracted the σ corresponding to Alice at two different spatial locations. v (x subscript = 0.5). It can be seen that the feature stability is reflected in two aspects: firstly, sparse parameters belonging to the same location are fixed within a certain range; secondly, although the UAV receiver moves at high speed along the trajectory, the σ associated with Alice... vIt still exhibits excellent stability. Furthermore, σ extracted from different locations... v It exhibits good distinguishability. Due to these two properties, the scale parameter σ, which includes large-scale fading coefficients, can be utilized. v To authenticate the currently unknown transmitter in the dynamic unmanned aerial vehicle ground system.

[0150] Establish a communication model. Let A, B, and E represent Alice, Bob, and Eve, respectively. The unknown GCS X = {A, E} first sends a signal frame to Bob for authentication. The received signal at time n of the k-th frame is represented as:

[0151]

[0152] in,

[0153] Indicates from N r The signal vector received by each antenna, where N is the number of symbols in a frame.

[0154] It is N t The training sequence for antenna transmission, with an average transmit power assumed to be...

[0155] It is composed of unknown variance The noise vector modeled by the zero-mean complex Gaussian distribution, i.e.

[0156] Stack all N symbols within a single frame and write the signal model into a matrix. Right now

[0157]

[0158] in,

[0159] To take advantage of the sparsity of millimeter-wave channels, the above equation can be vectorized as follows:

[0160]

[0161] in

[0162] This method uses the Laplace distribution to characterize the sparsity of millimeter-wave channels. Assuming that the Laplace distribution is defined only for real-valued random variables, the complex-valued model in the above equation is transformed into an equivalent real-valued model:

[0163]

[0164] Finally, the linear model of the received signal in the k-th frame is obtained as follows:

[0165]

[0166] in, And M' = 2N r N, N' = 2N r N t .

[0167] Based on the real-valued signal model obtained through the above process, channel sparsity parameters are extracted from the received signal frames, and it is determined whether the current GCS is Alice. To simplify the symbols, the frame index k and unit index X are omitted.

[0168] Step 2: Utilize Laplace prior modeling techniques to accurately characterize the statistical model of the angular domain millimeter-wave MIMO channel;

[0169] After receiving the signal frame y, Bob first needs to obtain the angular domain channel estimate. Then extract σ from that value. v The minimum mean square error (MMSE) estimator is used to obtain...

[0170]

[0171] Among them, h v (i) is h v The i-th element, the channel element Based on the zero-mean Laplace prior mathematical expression

[0172]

[0173] The common prior distribution in the matrix is ​​assumed to be independent and identically distributed (i.e., i.i.d.), where σ v Therefore, h represents the sparsity of the millimeter-wave channel. v The marginal posterior probability of (i) is given by the following formula:

[0174]

[0175] Among them, h v \h v (i) indicates that, except for h v (i) other than h v The integral of all elements. Due to the high-dimensional integrals involved in the above equation, deriving the analytical expression is significantly challenging and computationally difficult. Based on cyclic belief propagation, the sum-product GAMP algorithm can approximate the true marginal posterior distribution through an easily tractable expression, which is gradually refined during iteration. Furthermore, the definition... Given an unknown parameter vector, it will be learned in the EM algorithm embedded in the GAMP iteration. Therefore, the EM and GAMP methods are combined with a Laplace prior to obtain h. v (i) and sparsity parameters

[0176] GAMP is the first to model the relationship between the j-th observation y(j) and the corresponding noise-free output z(j) using p(y(j)|z(j); q), where express The j-th row. Then, z(j) and h v The true marginal posterior distribution of (i) can be approximated as follows:

[0177]

[0178]

[0179] in, and Let z(j) represent the mean and variance of the Gaussian variable z(j) at the t-th GAMP iteration, respectively. and Let h represent the Gaussian variables respectively. v (i) means and variance.

[0180] The marginal posterior distribution in the above equation is independent of the Laplace distribution; therefore, the posterior mean and variance of z(j) can be expressed as follows:

[0181]

[0182]

[0183] Unlike existing works based on Gaussian distributions, this embodiment specifies a Laplace prior for the diagonal domain millimeter-wave channel h. v (k) is used for modeling. In the formula h v The marginal posterior distribution of (i) is further expressed as

[0184]

[0185] Where, ψ i (·) and ω i (·) is a parametric function They are represented as follows:

[0186]

[0187]

[0188] sgn(x) is a standard symbolic function, which can be represented as:

[0189]

[0190] Factor After normalization, the result is:

[0191]

[0192] Here, Q(·) represents the Gaussian Q-function. Furthermore... and It depends on the parameter The term is defined as:

[0193]

[0194]

[0195] Derive h v The posterior mean (i.e., the MMSE estimate) and variance of (i) are as follows:

[0196]

[0197]

[0198] Based on the above steps, millimeter-wave channel estimates are obtained by using GAMP iteration. Imperfect estimation due to noise It can be further decomposed into actual values ​​h v (i) and Gaussian estimation error w h (i).

[0199] Due to h v (i) is a scaling parameter σ v The zero-mean symmetric Laplace variable, while w h (i) is a variance A zero-mean Gaussian variable. Therefore, It follows a normal Laplace distribution, that is,

[0200] To design an effective PHY layer authentication scheme using statistical signal processing techniques, it is necessary to obtain the normal Laplace variable. The probability density function (PDF).

[0201] If two random variables It has the following relationship:

[0202] z = x + w,

[0203] Then the sum of x and w is a random number distributed normally by a Laplace distribution, i.e.

[0204] Derive the probability density function between Gaussian and symmetric Laplace variables:

[0205]

[0206] make After some algebraic operations, we can obtain the following from the above formula:

[0207]

[0208] because Substituting it into the above formula, we get the final result.

[0209] The probability density function of z is expressed as:

[0210]

[0211] in, It is a data-related item.

[0212] Step 3: Extract channel sparsity parameters based on the expectation-maximization / generalized approximation message passing algorithm;

[0213] Extracting σ using the EM iteration method embedded in the t-th GAMP iteration v And estimate use Let represent the estimate of q in the l-th EM iteration, and then the E-step size of the (l+1)-th iteration is formulated as:

[0214]

[0215] Obtain the maximum likelihood (ML) method in the M-step. and

[0216]

[0217]

[0218] in, and They are represented as follows:

[0219]

[0220]

[0221] in, and Depends on the l-th EM iteration update Therefore, add the superscript 'l' to the four arguments of the expression. If using ∈ EM and T EM Let represent the error tolerance and the maximum number of iterations, respectively. The EM method terminates when the following condition is met:

[0222]

[0223] The result This is used for the (t+1)th iteration of the GAMP algorithm. Specifically, the proposed iterative EM method interacts with GAMP, where the latter's byproducts are used to progressively refine σ. v and The estimation is as follows, and vice versa. So far, the extraction of sparsity parameters (i.e., ...) from the currently received signal frames has been completed. This allows for effective authentication decisions and effectively defends against accidental attacks without requiring prior knowledge of Eve.

[0224] Step 4: Establish a theoretical model and determine the threshold for identity authentication;

[0225] Step 5: Establish a binary hypothesis testing model, build an authentication framework, and perform identity authentication based on thresholds.

[0226] LRT with unknown prior parameters: based on millimeter-wave channel estimation and Bob views the certification decision as being based on...

[0227]

[0228] The problem consists of a binary hypothesis testing problem, where the null hypothesis is... The indicator shows the signal frame source Alice, i.e., X = A. Conversely, This indicates that the current GCS transmitter is Eve, that is, X = E.

[0229] The proposed authentication scheme uses the inherent long-term statistical properties obtained from the estimated millimeter-wave channel to distinguish Alice and Eve. Next, an LRT framework is established for hypothesis testing to achieve authentication decision.

[0230] based on Independent and identically distributed components And based on the probability density function derived in step 2, the likelihood ratio test (LRT) for hypothesis testing can be expressed as:

[0231]

[0232] The Laplace approximation of the LRT: Since the likelihood ratio test for hypothesis testing has high computational complexity, it may reduce the efficiency of authentication and lead to potential communication delays. Due to the good accuracy of the extraction algorithm, the Laplace approximation can be used to address these issues. This is because when the signal-to-noise ratio is within a certain range (e.g., [-20, 20] dB), the channel estimation algorithm provides superior accuracy, causing the estimation error to gradually approach zero. Therefore, the Laplace distribution can approximate the normal Laplace distribution. Then, a simplified binary hypothesis test is given using the Laplace approximation:

[0233]

[0234] For the estimated millimeter-wave channel Assumption The elements in the array are independent and identically distributed. The probability density function under the two assumptions can be expressed as:

[0235]

[0236] Suppose that Λ(·) denotes the likelihood ratio test (LRT) decision operator, and τ L ' represents the decision threshold, and the LRT for hypothesis testing in (39) can be expressed as:

[0237]

[0238] in, It is the decision threshold that includes data independence items.

[0239] Therefore, the hypothesis test (LRT) with the Laplace approximation method is expressed as:

[0240]

[0241] in, This represents the likelihood ratio test, τ L This represents the decision threshold. yes The function, in essence, represents Spatial correlation statistics (sparse parameter σ) v Therefore, Bob can... The results effectively distinguished Alice and Eve.

[0242] The LRT authentication framework based on binary hypothesis testing derives the false alarm (using P) f (Representation) Theoretical model and detection probability (using P) dThe theoretical model of (represented by) is then presented. An optimal threshold selection scheme is then designed using the Neyman-Person criterion and the Wilson-Hilferty approximation.

[0243] False alarm rate P f The derivation of [the following is unclear and requires context: "False alarm" refers to a signal transmitted by a legitimate transmitter being incorrectly identified as an unauthenticated event. That is, under assumption H0, the LRT result...] Greater than a given threshold τ L .

[0244] Considering Figure 1 The image shows a millimeter-wave MIMO UAV ground system. A novel channel-based physical layer scheme is proposed, utilizing spatially correlated spatial features for authentication.

[0245] because It is approximated by a zero-mean symmetric Laplace variable; therefore, under the assumption H0, It is a chi-square random variable with 2N' degrees of freedom. According to P f Based on the definition and the above results, P under the LRT framework f It can be estimated as follows:

[0246]

[0247] Substituting the right-tailed probability function of the chi-square random variable into the equation, we can derive P. f The expression, at a given decision threshold τ L Below, the proposed scheme's P f Determined as

[0248]

[0249] in, The right-tailed probability function of a chi-square random variable with 2N' degrees of freedom can be further rewritten as follows:

[0250]

[0251] Detection probability P d The derivation suggests that detecting an event means that a signal originating from Eve has been successfully identified as originating from Alice; similarly, P... d The derivation process is as follows:

[0252] Similar to P f The derivation, under assumption H1, It is also a chi-square random variable with 2N' degrees of freedom. Therefore, P is obtained by following the same steps. d

[0253]

[0254] Substituting the right-tailed probability function of the chi-square random variable into the equation, we can derive P. d The expression for τ. Therefore, given the decision threshold τ. L In the case of P d It is estimated to be:

[0255]

[0256] For LRT-based authentication frameworks, P f and P d The value of P fully specifies the performance of the proposed scheme; therefore, to achieve better authentication performance, P should be optimized. f Make P as small as possible d As large as possible; according to the Neyman-Pearson theorem, it is usually within... Obtain the optimal threshold under constraints in It is the maximum false alarm probability allowed by the authentication protocol.

[0257] From P f In the derivation, it was found that τ L It exists in many terms and is difficult to derive directly. The analytical expression for this problem. To address this issue, previous researchers used a feasible method employing a log-normal approximation, which is only applicable to large degrees of freedom. Effective (e.g., Compared to previous methods, the Wilson-Hilferty approximation is used to calculate a more accurate optimal threshold, which... The value is relatively small.

[0258] For the chi-square variable x, for The smallest and largest values, All follow a mean of μ WH The variance is The Gaussian distribution. Therefore, The probability density function (PDF) can be expressed as:

[0259]

[0260] Where, μ WH and It can be represented as:

[0261]

[0262]

[0263] Using Wilson Hilferty's approximate expression,

[0264]

[0265] in, and The mean is μ WH The variance is σ WH Gaussian variables. Based on the above formula, it is easy to derive... The expression.

[0266] Based on the above approximation process, it is derived that The closed-form expression, for the proposed physical layer authentication scheme, under constraints Optimal threshold Written as

[0267]

[0268] Substitute the derived optimal threshold into P d The expression, in Maximum detection probability under constraints It can be written as

[0269]

[0270] Based on the discrimination criteria, a threshold for binary hypothesis testing is given. The difference between the fingerprints of the legitimate signal and the signal to be authenticated is compared with the threshold. If it is greater than the threshold, the drone is determined to be an illegal drone; otherwise, the drone is determined to be a legitimate user.

[0271] This embodiment evaluated the proposed method through simulation experiments, and the experimental results are as follows: Figure 3 As shown, using P d The size is used to assess the accuracy of certification performance. Figure 3 The two figures above show P under different hardware similarity parameters k and different numbers of subcarriers N. d With P f The changing ROC curve; Figure 3 The next two figures show P under different signal-to-noise ratios (SNR) and different antenna sizes. d With P f The changing ROC curve.

[0272] Those skilled in the art should understand that this invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples of the invention and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.

Claims

1. A method for unmanned aerial vehicle (UAV) authentication for millimeter-wave MIMO systems, characterized in that, Physical layer authentication methods include the following steps: Step 1: The drone receives signals from the communication system, including control signals from the ground control station and deceptive signals sent to the drone by the antenna opponent disguised as a base station; Step 2: Utilize Laplace prior modeling techniques to accurately characterize the statistical model of the angular domain millimeter-wave MIMO channel; Step 3: Extract channel sparsity parameters based on expectation maximization and generalized approximate message passing algorithms; Step 4: Establish a theoretical model and determine the threshold for identity authentication; Step 5: Establish a binary hypothesis testing model, build an authentication framework, and perform identity authentication based on thresholds; Step 4 specifically includes: deriving the false alarm rate based on the hypothesis testing and validation framework of binary hypothesis testing. Theoretical model and detection probability The theoretical model is used to determine an optimal threshold using the Neyman-Pearson theorem and the Wilson-Hilferty theorem; The false alarm rate is derived from the hypothesis testing and authentication framework based on binary hypothesis testing. Theoretical model and detection probability The theoretical models include: False alarm rate Derivation: Under the assumption Below are the hypothesis test results for the Laplace approximation method. Greater than a given threshold Authentication is achieved by utilizing spatially relevant spatial features, within a given decision threshold. Below, false alarm rate Determined as: ； in, Indicates having Right-tailed probability function of a chi-square random variable with degrees of freedom: ； Detection probability Derivation: Authentication is achieved using spatially relevant spatial features, given a decision threshold. In this case, It is estimated to be: ； Determining an optimal threshold using the Neyman-Pearson theorem and the Wilson-Hilferty theorem includes: According to the Neyman-Pearson theorem, Obtain the optimal threshold under constraints ,in This is the maximum false alarm rate allowed by the authentication protocol. An optimal threshold is calculated using the Wilson-Hilferty theorem. For chi-square variables For threshold The small and large values ​​of the value, All follow the mean. The variance is Gaussian distribution, The probability density function (PDF) is expressed as: ； in, and It can be represented as: ； An approximate expression using the Wilson-Hilferty theorem: ； in, and The mean is The variance is Gaussian variables; Under constraints Optimal threshold Written as: ； Substitute the derived optimal threshold into The expression, in Maximum detection probability under constraints It can be written as: ； Step 5 specifically includes: Based on millimeter-wave channel estimation and The drone will view the certification decision as: ； Among them, the null hypothesis The current signal comes from a legitimate ground control station, i.e. , This indicates that the ground control station transmitter of the current signal is the antenna counterpart, that is, ; based on Independent and identically distributed components The likelihood ratio test is expressed as: ； Using the Laplace approximation, we obtain the binary hypothesis test: ； Hypothesis tests using the Laplace approximation method are expressed as follows: ； in, This indicates the likelihood ratio test. Indicates the decision threshold. yes The function, Spatial related statistics, UAVs based on The results distinguish between ground control stations and antenna counterparts.

2. The UAV authentication method for millimeter-wave MIMO systems according to claim 1, characterized in that, The communication system in step 1 is established by the following model: Establish a millimeter-wave MIMO UAV ground communication system, which consists of three entities: a legitimate ground control station with an Nt antenna, a mobile UAV with an Nr antenna, and an adversary with an Nt antenna. Establish a channel model, which has There are spatial clusters, each cluster containing... A propagation path is used to characterize the ground-to-air millimeter wave propagation environment, and the millimeter wave channel matrix in the antenna domain. Represented as: ； in, It is the first The first propagation cluster Path, , They represent the first The first cluster A receiving and transmitting azimuth angle, and These are the normalized receiving and transmitting array steering vectors, respectively, expressed as: ； ； The channel matrix is ​​transformed from the antenna domain to the angle domain using the spatial discrete Fourier transform, and its mathematical expression is as follows: ； in, and It is a DFT unitary matrix. It is a corner domain channel; Using the Laplace distribution, a statistical model of the angular domain millimeter-wave channel is established. The mathematical expression for the zero-mean Laplace prior is: ； Among them, utilizing To characterize the sparsity of millimeter-wave channels; Establish a communication model, where A, B, and E represent the ground control station, the UAV, and the antenna counterpart, respectively. The unknown ground control station X = {A, E} first sends a signal frame to the UAV for authentication. The received signal at time n of the k-th frame is represented as: ； in, Indicates from The signal vector received by each antenna, where N is the number of symbols in a frame; It is by The training sequence for antenna transmission, with an average transmit power assumed to be... ; It is composed of unknown variance The noise vector modeled by the zero-mean complex Gaussian distribution, i.e. ; Stack all N symbols within a single frame and write the signal model into a matrix. ,Right now: ； in, , ; Leveraging the sparsity of millimeter-wave channels, the vectorized representation is as follows: ； in, ， ， ， ； The sparsity of millimeter-wave channels is characterized using the Laplace distribution. Assuming the Laplace distribution is defined only for real-valued random variables, the complex-valued model is transformed into an equivalent real-valued model: ； The linear model for obtaining the received signal of the k-th frame is: ； in, , , , ,and , .

3. The UAV authentication method for millimeter-wave MIMO systems according to claim 1, characterized in that, Step 2 utilizes Laplace prior modeling techniques to accurately characterize the statistical model of the angular domain millimeter-wave MIMO channel, including: Upon receiving the signal frame Subsequently, the UAV obtains the angular domain channel estimate. Extract from the angular domain channel estimate The minimum mean square error estimator is used to obtain : ； in, yes The Middle One element, channel element Based on the zero-mean Laplace prior mathematical expression: ; Let the common prior distribution be independent and identically distributed. Therefore, representing the sparsity of millimeter-wave channels, The marginal posterior probability is given by the following formula: ； in, Indicates except outside The integral of all elements; Using Laplace's prior for diagonal domain millimeter-wave channels Modeling, In the formula The marginal posterior distribution is: ； in, and It is a parametric function ( , , ), respectively represented as: ； It is a standard symbolic function, represented as: ； Factor After normalization, the result is: ； in, Represents the Gaussian Q-function. , , ,and It depends on the parameter ( , , The items are: ； Derivation The posterior mean and variance are: ； Millimeter-wave channel estimates are obtained by using generalized approximate message-passing iteration. , It follows a normal Laplace distribution, that is, .

4. The UAV authentication method for millimeter-wave MIMO systems according to claim 3, characterized in that, Obtain the normal Laplace variable The probability density function: Two random variables , It has the following relationship: but and The sum of these numbers is a random number distributed according to a normal Laplace distribution, i.e. , The probability density function is expressed as: ； in, It is a data-related item.

5. The UAV authentication method for millimeter-wave MIMO systems according to claim 1, characterized in that, Step 3, based on the expectation-maximization / generalized approximation message passing algorithm, extracts channel sparsity parameters, including: Using embedded first Extracting the Expectation-Maximization Iterative Method from the Sub-Generalized Approximate Message Passing Iteration And estimate ,use To indicate the first During the next expected value maximization iteration, The estimate, then the first The formula for the step size E in the next iteration is: ； Obtain the results in M ​​steps using the maximum likelihood method. and : ； in, and They are represented as follows: ； in, and Depends on the first Iterative updates with expectation maximization .

6. The UAV authentication method for millimeter-wave MIMO systems according to claim 1, characterized in that, Step 3, the extraction of channel sparsity parameters based on the expectation-maximization / generalized approximation message passing algorithm, also includes: use and Let represent the error tolerance and the maximum number of iterations, respectively. The expectation maximization method terminates when the following condition is met: ； The result The first generalized approximate message passing algorithm The next iteration.

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