A Physical Layer Key Generation Method and System Based on Polarization Reconfigurable Antenna

Abstract

This invention discloses a physical layer key generation method and system based on a polarization-reconfigurable antenna, belonging to the field of wireless communication technology. The method includes: establishing a polarization channel model jointly considering polarization correlation, spatial correlation, and channel depolarization effects, and deriving a closed-form expression for the key generation rate; constructing a joint optimization problem of beamforming vector and PRA phase shift vector under base station transmit power constraints and antenna phase modulation constraints, with the goal of maximizing the key generation rate; solving the problem using an alternating optimization method to obtain the optimal beamforming solution based on the Rayleigh quotient and the analytical closed-form solution for polarization phase modulation jointly determined by the polarization channel correlation coefficient, inverse cross-polarization discrimination, and receiver polarization vector. This invention requires no additional RF link, has low hardware complexity, effectively mitigates performance loss caused by polarization mismatch, and significantly improves key generation efficiency and system security in complex polarization environments.

Description

Technical Field

[0001] This invention relates to the field of wireless communication technology, and specifically to a physical layer key generation method and system based on a polarization reconfigurable antenna. Background Technology

[0002] Physical Layer Key Generation (PKG) is a lightweight and efficient wireless security mechanism. Its core principle lies in leveraging the reciprocity and inherent randomness of wireless channels to allow legitimate communicating parties to extract a shared symmetric key without explicit key exchange. This technology not only significantly reduces the system overhead of traditional key management, but its security also relies on the spatial decorrelation properties of the wireless channel. Specifically, when the distance between a passive eavesdropper and a legitimate receiver exceeds half a wavelength, it becomes difficult for the eavesdropper to obtain channel observation information relevant to the legitimate user.

[0003] However, the effectiveness of PKG is inherently limited by the availability of channel randomness and the correlation between legitimate parties' channel observations. In static or slowly changing propagation environments, insufficient channel dynamics will limit the achievable key capacity; simultaneously, a low signal-to-noise ratio (SNR) at the receiver will further reduce the key generation rate (KGR). To overcome these problems, existing research has extensively explored various enhancement techniques, including relay transmission, reconfigurable intelligent surfaces (RIS), and cooperative interference. However, existing literature largely focuses on spatial domain beamforming design and typically assumes ideal polarization matching conditions, employing fixed polarization antennas (FPA). In practical applications, electromagnetic waves often experience time-varying depolarization effects during propagation due to environmental changes and antenna mismatch, leading to severe degradation of received signal performance, and traditional FPAs often struggle to effectively address such issues.

[0004] In recent years, a novel polarization shaping technique—polarization-reconfigurable antennas (PRA) based on phase shifters (PS)—has been proposed to address the aforementioned challenges. PRA achieves dynamic and continuous adjustment of the polarization state through phase modulation and antenna rotation, effectively unlocking the polarization degree of freedom (DoF). Compared to dual-polarized antennas (DPA) and tri-polarized antennas (TPA)—which typically require two or three independent radio frequency (RF) links per antenna for independent amplitude and phase control—each PRA requires only a single RF link, significantly reducing hardware complexity and implementation costs. Currently, PRA is widely used in various communication scenarios. Some literature studies PRA-assisted multiple-input single-output (MISO) secure communication networks, maximizing the secure rate by jointly designing transmit beamforming and polarization shaping; other literature explores PRA-enabled movable antenna (MA) systems, proposing an optimization algorithm that combines antenna position and polarization shaping to maximize the achievable rate; still other studies target integrated sensing and communication (ISAC) systems, jointly optimizing transmit and receive polarization shaping vectors, antenna rotation angle, and antenna position to improve the system's average total rate.

[0005] While PRA has demonstrated advantages in communication scenarios such as beamforming and rate optimization, its application in the specific scenario of PKG is still lacking. Further research is needed to address the requirements of PKG by jointly considering the polarization mismatch, depolarization effects, and spatial correlation commonly found in actual channels, and to design corresponding beamforming and polarization state joint optimization schemes to improve key generation rate. Summary of the Invention

[0006] The purpose of this invention is to provide a physical layer key generation method and system based on polarization-reconfigurable antennas. It aims to solve the problem that existing fixed-polarization antenna schemes are limited in key generation rate due to neglecting the polarization signal dimension and difficulty in adapting to time-varying depolarization effects and polarization mismatch in actual channels. By establishing a joint polarization-spatial correlation channel model and designing a beamforming and polarization phase joint optimization algorithm aimed at maximizing the key generation rate, the invention effectively mines the polarization degree of freedom, thereby improving the key generation efficiency and robustness of the system in complex electromagnetic environments.

[0007] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A physical layer key generation method based on polarization reconfigurable antennas (PRA) is applied to a wireless communication system. The system includes a base station equipped with N PRAs, a single-antenna legitimate user, and a passive eavesdropper. The system operates in time-division duplex mode. The method comprises the following steps: Step S1: Establish a polarization channel model that jointly considers polarization correlation, spatial correlation and channel depolarization effect, and derive a closed-form expression for the key generation rate based on the mutual information of channel characteristic information of the legitimate communicating parties. Step S2: With the goal of maximizing the key generation rate, construct a joint optimization problem of beamforming vector and PRA phase shift vector under the constraints of base station transmit power and PRA phase shift. Step S3: The joint optimization problem is solved by using an alternating optimization method. In each iteration, the beamforming vector is optimized while the PRA phase shift vector is fixed, and the PRA phase shift vector is optimized while the beamforming vector is fixed, until convergence is achieved, and the optimal beamforming vector and the optimal PRA phase shift vector are obtained. Step S4: The base station configures the PRA based on the optimal beamforming vector and the optimal PRA phase shift vector, and sends pilot signals to each other with the legitimate user to perform channel estimation. Both parties extract channel feature information based on the channel estimation results, and quantize, negotiate information and amplify privacy of the channel feature information to generate a consistent physical layer key.

[0008] Furthermore, the process of establishing the polarization channel model in step S1 includes: The polarization formation vector of the nth PRA is defined as: in, For the first n The phase shift of each PRA, j It is the imaginary unit; The polarization channel matrix from the nth PRA to the legitimate user is represented as: in, For the polarization leakage matrix, The polarization correlation matrix, For inverse cross-polarization discrimination, This represents the correlation coefficient between the vertical and horizontal components at the base station and the legitimate user. The elements are independent and identically distributed circularly symmetric complex Gaussian random variables; The overall channel model from the base station to the legitimate user is as follows: in, This refers to path loss. Let be a Toeplitz matrix whose elements satisfy... , Representation matrix The Line number Column elements; , ,and Let g be the PRA phase shift vector, and g be the polarization vector of the legitimate user.

[0009] Furthermore, in step S1, the closed-form expression for the key generation rate is: , , , in, Indicates the key generation rate. Represents the channel characteristic information of the two parties in legitimate communication. and Mutual information between them; Represents the covariance parameter. This represents the autocovariance of the channel characteristic information at base station Alice. This represents the autocovariance of the channel characteristic information at the legitimate user Bob's location. This represents the joint covariance matrix of the channel characteristic information of both base station Alice and legitimate user Bob; , These are the channel feature information extracted from channel estimation by base station Alice and legitimate user Bob, respectively. express , The cross-variance between them yes The conjugate transpose of . This represents the determinant of the covariance matrix.

[0010] Furthermore, the joint optimization problem constructed in step S2 is expressed as: in, For beamforming vectors, The phase shift vector of PRA. This is the maximum transmit power of the base station. The key generation rate is represented by constraints C1 and C2, which represent the base station transmit power constraint and the PRA phase shift constraint, respectively.

[0011] Furthermore, in step S3, the PRA phase shift vector is fixed. At that time, beamforming vector The optimization subproblem is expressed as: Optimal solution of beamforming vector The following can be obtained by solving using Rayleigh's quotient: , in, Represents beamforming vector The conjugate transpose of; This indicates that the PRA phase shift vector is fixed. The channel covariance matrix under the given conditions integrates channel state information, polarization correlation, and channel depolarization effect. Representation matrix The eigenvector corresponding to the largest eigenvalue.

[0012] Furthermore, in step S3, the beamforming vector is fixed. At that time, the PRA phase shift vector The optimization subproblem is solved by reconstructing the objective function into a quadratic form in terms of the phase shift vector, PRA phase shift vector. The optimization subproblem is expressed as: in, , , , .

[0013] Given a block diagonal matrix, maximizing the objective function is equivalent to optimizing each PRA phase shift independently: in, It is a Hermitian matrix. Representation matrix The OK; Optimal phase shift Represented as: .

[0014] Furthermore, the optimal phase shift of each PRA has an analytical closed-form solution, the expression of which is jointly determined by the polarization channel correlation coefficient, the inverse cross-polarization discrimination, and the polarization vector of the legitimate user. The phase shift of each PRA... The optimal solution is the same as that of the beamforming vector. Irrelevant; The optimal phase shift Corresponding correlation quantity The explicit expression is: in, and The polarization channel correlation coefficient. denoted as inverse cross-polarization discrimination, and g is the polarization vector of the legitimate user.

[0015] Furthermore, when a legitimate user uses a linearly polarized antenna, i.e. Or, the legitimate user-end antenna is fully polarized and decorrelated. At that time, the optimal phase shift Directly When the base station antenna is fully polarized and decorrelated, that is... At that time, the optimal phase shift ; After obtaining the optimal PRA phase shift vector, the channel covariance matrix simplifies to: ; in It is a vector jointly determined by the optimal phase shift, the polarization channel matrix, and the polarization vector of the legitimate user. , This is the spatial correlation matrix of the PRA at the base station.

[0016] Further, the channel estimation in step S4 includes: obtaining the pilot signal sent by the base station from the legitimate user. The base station receives pilot signals sent by legitimate users and obtains... Both parties used the least squares method to perform channel estimation and obtained the channel estimates respectively. and The base station will Conjugate with the optimal beamforming vector Multiplication extracts the random components common to legitimate users, thereby obtaining highly correlated channel feature information.

[0017] A physical layer key generation system based on a polarization-reconfigurable antenna is provided for implementing the above method. The system includes: The base station is equipped with N polarization reconfigurable antennas (PRAs). Each PRA adjusts the phase difference between orthogonal polarization components through a phase shifter to achieve dynamic adjustment of the polarization state. It is used to configure the optimal beamforming vector and the optimal PRA phase shift vector based on statistical channel state information, transmit and receive pilot signals, and perform channel estimation. Legitimate users are equipped with a single fixed-polarization antenna to receive and transmit pilot signals, perform channel estimation, and generate a consistent physical layer key with the base station based on a highly correlated channel estimation value. A passive eavesdropper, whose distance from a legitimate user exceeds half a wavelength, has an eavesdropping channel that is statistically independent of the legitimate channel.

[0018] The beneficial effects of the above scheme are as follows: 1. Adaptable to complex wireless propagation scenarios, enhancing the versatility of the solution. This invention applies a polarization-reconfigurable antenna to physical layer key generation, systematically considering polarization correlation, spatial correlation, and channel depolarization effects, establishing a complete polarization channel model, and deriving a closed-form expression for the key generation rate. This model reveals the quantitative relationship between polarization channel parameters and the key generation rate, enabling this solution to accurately describe and effectively address the time-varying depolarization effects caused by environmental changes and antenna mismatch in real-world wireless channels, thus exhibiting stronger environmental adaptability and system robustness.

[0019] 2. Precise optimization and efficient solution for key generation are achieved. This invention constructs a joint optimization problem of beamforming vector and PRA phase shift vector with the objective of maximizing the key generation rate, and solves it using an alternating optimization method. In beamforming optimization, the optimal solution is obtained through the Rayleigh quotient, achieving effective utilization of spatial degrees of freedom; in polarization phase optimization, a concise analytical closed-form solution is derived. This algorithm requires minimal computational resources, has a fast solution speed and high accuracy, and can quickly obtain globally optimal control parameters, ensuring the efficiency and stability of key generation.

[0020] 3. Fully exploiting polarization degrees of freedom to effectively mitigate performance loss caused by polarization mismatch. This invention, through dynamic optimization and control of the polarization phase, enables the polarization state of the base station's transmitted signal to adaptively match channel characteristics and the receiver's polarization mode, effectively reducing the power loss of the received signal caused by polarization mismatch. Simulation results show that, under the same transmit power conditions, this scheme achieves a significant key generation rate gain compared to the fixed-polarization antenna scheme, especially when the channel depolarization effect is strong or when the receiver uses a linearly polarized antenna, the gain is even more significant, effectively improving the system's security performance in complex electromagnetic environments.

[0021] 4. Significantly reduces hardware complexity and implementation cost, offering strong engineering practicality. This invention employs a polarization-reconfigurable antenna based on a phase shifter. Each antenna element requires only a single RF link to achieve dynamic and continuous adjustment of the polarization state through phase modulation. Compared to traditional dual-polarization or multi-polarization antennas that require multiple independent RF links, this invention significantly reduces the number of RF components, lowering system hardware complexity, power consumption, and manufacturing costs. Furthermore, polarization reconfiguration is achieved through software control, eliminating the need for mechanical rotating parts, thus offering advantages such as fast response speed and high reliability for practical engineering applications. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the system model of the present invention; Figure 2 This is a schematic diagram of the alternating optimization solution process in beamforming optimization according to the present invention; Figure 3This is a schematic diagram of the process for obtaining the closed-form optimal solution in PRA phase shift optimization according to the present invention; Figure 4 The maximum transmit power of KGR and Alice in this embodiment of the invention. Relationship curve; Figure 5 The number of KGR and Alice antennas in this embodiment of the invention Relationship curve; Figure 6 The KGR and inverse cross-polarization function in this embodiment of the invention Relationship curve; Figure 7 The correlation coefficient between KGR and polarization channel in this embodiment of the invention. The relationship curve. Detailed Implementation

[0023] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0024] It should be noted that, unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0025] I. System Architecture Setup Reference Figure 1 This embodiment provides a physical layer key generation system based on polarization reconfigurable antennas (PRA), including a base station Alice equipped with N PRAs, a single-antenna legitimate user Bob, and a passive eavesdropper Eve. The system operates in time-division duplex mode and utilizes the reciprocity of the channel for key generation. Each PRA in base station Alice adjusts the phase difference between orthogonal polarization components through a phase shifter, achieving dynamic and continuous adjustment of the polarization state. Furthermore, each PRA only needs to be connected to one RF link, resulting in no additional RF resource overhead.

[0026] Legitimate users are equipped with a single fixed-polarization antenna, which has the signal processing capabilities related to pilot signal transmission and reception, channel estimation, and key generation. It can communicate bidirectionally with the base station and extract shared channel features.

[0027] Passive eavesdroppers are equipped with a single fixed-polarization antenna, and the distance between them and both the base station and the legitimate user exceeds half a wavelength. This makes the eavesdropping channel statistically independent of the legitimate communication channel, and it is impossible to obtain effective channel characteristics for key generation.

[0028] The following section details a physical layer key generation method based on polarization-reconfigurable antennas, which mainly addresses the problem that existing fixed-polarization antenna schemes suffer from limited key generation rates due to neglecting the polarization signal dimension and difficulty in adapting to time-varying depolarization effects and polarization mismatch in actual channels.

[0029] II. Establishment of Polarization Channel Model (a) Definition of PRA polarization formation vector Definition of the first The polarization formation vector of each PRA is: in, Let j be the phase shift of the nth PRA. By adjusting this phase shift, the antenna polarization state can be continuously changed. j is the imaginary unit.

[0030] (II) Construction of Polarization Channel Matrix The polarization channel matrix from the nth PRA to the legitimate user Bob is represented as follows: It is given by the following formula: in, The polarization leakage matrix at base station Alice. The polarization correlation matrix for the legitimate user Bob; The inverse cross-polarization discrimination value represents the degree of channel depolarization. Let be the correlation coefficient between the vertical and horizontal components at base station Alice and legitimate user Bob. The elements of are independent and identically distributed (iid) circularly symmetric complex Gaussian (CSCG) random variables with a mean of zero and a variance of 1.

[0031] (III) Overall Channel Modeling make Let Bob be the polarization vector of the legitimate user. Then the channel from Alice's polarization-reconfigurable antenna array to Bob can be modeled as follows: in, ,and Let represent the phase shift vector of the PRA, and g be the polarization vector of the legitimate user. To characterize spatial correlation, let This represents the spatial correlation matrix of the base station's PRA.

[0032] Therefore, the overall channel model from the base station to the legitimate user is as follows: in, This refers to path loss. Let be a Toeplitz matrix whose elements satisfy... , Representation matrix The Line number Column elements.

[0033] (iv) Derivation of the closed-form expression for the key generation rate First, Alice modifies the transmit beamforming vector based on statistical channel state information (CSI). and phase shift vector Configure it.

[0034] Secondly, the two parties in legitimate communication exchange pilot signals. The signals received by Bob and Alice are represented as follows: , in, and Let represent Alice's transmit beamforming vector and common pilot signal, respectively, and satisfy . . and They represent additive white Gaussian noise (AWGN), where , .

[0035] Subsequently, Bob and Alice used the least squares (LS) method to perform channel estimation, and the obtained channel estimate is expressed as follows: , in, .

[0036] To extract the reciprocal components of the channel, Alice will and Multiplying them together, we get: , in, It is important to note that the obtained channel characteristic information and The presence of common random components indicates that they can be used to generate a shared secret key.

[0037] Finally, Bob and Alice converted the collected channel feature information into two sets of raw bit sequences and eliminated inconsistencies through an information coordination process. Subsequently, privacy amplification techniques were employed to reduce information leakage and generate a consistent physical layer key.

[0038] Since it is assumed that the eavesdropper is located at least half a wavelength away from both Alice and Bob, their eavesdropping channel is statistically independent of the legitimate channel. Therefore, the key generation rate (KGR) can be defined as the mutual information between the channel characteristics of the two legitimate communicating parties, and its expression is: , in, , , in, Indicates the key generation rate. Represents the channel characteristic information of the two parties in legitimate communication. and Mutual information between them; Represents the covariance parameter. This represents the autocovariance of the channel characteristic information at base station Alice. This represents the autocovariance of the channel characteristic information at the legitimate user Bob's location. This represents the joint covariance matrix of the channel characteristic information of both base station Alice and legitimate user Bob; , These are the channel feature information extracted from channel estimation by base station Alice and legitimate user Bob, respectively. express , The cross-variance between them yes The conjugate transpose of . This represents the determinant of the covariance matrix.

[0039] III. Construction of Joint Optimization Problem With the goal of maximizing the key generation rate, a beamforming vector is constructed by combining base station transmit power constraints and PRA phase shift constraints. With PRA phase shift vector Joint optimization problem: in, This is the maximum transmit power of the base station. The key generation rate is represented by constraints C1 and C2, which represent the base station transmit power constraint and the PRA phase shift constraint, respectively.

[0040] IV. Alternating Optimization Solution Since the objective function of the above joint optimization problem is a non-concave function and the beamforming vector and the PRA phase shift vector are highly coupled, it is difficult to solve directly. In order to improve its tractability, the problem is first transformed into an equivalent function, and then the Alternating Optimization (AO) method is used to decouple the optimization variables.

[0041] Problem P1 can be equivalently transformed into the following form: Next, the beamforming vectors are optimized alternately. With PRA phase shift vector To solve problem P2, such as Figure 2 , Figure 3As shown.

[0042] (I) Optimization of beamforming vectors Fixed PRA phase shift vector Under the condition of beamforming vector The optimization subproblem is expressed as: Optimal solution of beamforming vector The following can be obtained by solving using Rayleigh's quotient: , in, Represents beamforming vector The conjugate transpose of; This indicates that the PRA phase shift vector is fixed. The channel covariance matrix under the given conditions integrates channel state information, polarization correlation, and channel depolarization effect. Representation matrix The eigenvector corresponding to the largest eigenvalue.

[0043] (II) Optimization of PRA Phase Shift Vector In a fixed beamforming vector Under the condition of PRA phase shift vector The optimization subproblem is solved by reconstructing the objective function into a quadratic form with respect to the phase shift vector.

[0044] First, the subproblem needs to be expressed as a function of the phase shift vector. In the form of.

[0045] Therefore, define as well as . It can be rewritten as: It can be rewritten as: in, , Representation matrix The OK, The variance is the additive white Gaussian noise.

[0046] Will Rewritten as: , , , .

[0047] Based on this, the phase shift vector of PRA can be... The subproblem is expressed as: Since it is a block diagonal matrix, we have: Therefore, maximize the objective function This is equivalent to optimizing the phase shift of each PRA independently.

[0048] Given a Hermitian matrix, the optimal phase shift is... It can be represented as .

[0049] each The optimal solution is the same as, and is the same as It is irrelevant. Through a series of mathematical derivations, it can be concluded that... Write it in the following explicit form: , in, and The polarization channel correlation coefficient. denoted as inverse cross-polarization discrimination, and g is the polarization vector of the legitimate user.

[0050] (III) Optimal phase shift simplification in special scenarios When a legitimate user uses a linearly polarized antenna, that is... Or, the legitimate user-end antenna is fully polarized and decorrelated. At that time, the optimal phase shift Directly .

[0051] When the base station antenna is fully polarized and decorrelation occurs, At that time, the optimal phase shift ; When the optimal PRA phase shift vector is obtained Then, the channel covariance matrix The expression can be further simplified to: in , It is a vector jointly determined by the optimal phase shift, the polarization channel matrix, and the polarization vector of the legitimate user. This is the spatial correlation matrix of the PRA at the base station.

[0052] It is important to note that the optimal beamforming direction is determined solely by the spatial correlation matrix. The eigenvector corresponding to the largest eigenvalue is determined by this. Under the assumptions of the iid channel model, i.e. The objective function of problem P3 can be simplified to .

[0053] Therefore, the optimal beamforming vector can be expressed as: ,in Let KGR be an independent and identically distributed random variable with zero mean. Accordingly, KGR can be expressed as... The results are consistent with Irrelevant.

[0054] (iv) Alternating Iteration Process The specific process of the alternating optimization algorithm is as follows: Step 1: Initialize the PRA phase shift vector, set the number of iterations and the convergence threshold.

[0055] Step 2: In the k-th iteration, fix the current PRA phase shift vector. Update the beamforming vector.

[0056] Step 3: Fix the updated beamforming vector The solution is directly calculated based on the analytical closed-form solution of the optimal phase shift. .

[0057] Step 4: Determine if the convergence condition is met. If it is, stop the iteration and output the optimal solution; otherwise, let k = k + 1 and return to step 2.

[0058] V. Key Generation Process The base station first configures the parameters of the polarization-reconfigurable antenna based on the optimal beamforming vector and optimal PRA phase shift vector obtained through alternating optimization. Then, it engages in bidirectional pilot signal exchange with legitimate users. The base station sends a common pilot signal to the legitimate user, who receives a mixed signal containing channel information and noise. Simultaneously, the legitimate user also sends the same pilot signal back to the base station, which also receives the signal. Because the system operates in time-division duplex mode, the uplink and downlink channels are reciprocal; therefore, the channel observations obtained by both parties contain a common random component.

[0059] Both parties use the least squares method to perform channel estimation on the received signal, obtaining corresponding channel estimates. The base station performs a calculation on its own channel estimate and the conjugate transpose of the optimal beamforming vector to obtain channel feature information highly correlated with legitimate users. Legitimate users then extract their corresponding channel feature information based on their own channel estimates. Thus, both parties obtain channel feature information containing common random components, providing a basis for generating a shared key.

[0060] Next, the base station and the authorized user quantize the extracted channel feature information, converting continuous channel feature values ​​into the original bit sequence. Due to factors such as noise interference, there may be slight inconsistencies in the initial bit sequences of both parties. Therefore, these differences are gradually corrected through an information negotiation process to obtain a consistent intermediate key sequence.

[0061] To further reduce the risk of information leakage, both parties perform privacy amplification on the intermediate key sequence. Privacy amplification typically uses a family of hash functions to map the longer negotiated bit sequence into a shorter final key sequence, ensuring that even if some information is leaked, the final key still has sufficient security. Finally, the base station and the legitimate user generate a consistent physical layer key, achieving secure communication.

[0062] VI. Simulation Results To verify the effectiveness of this invention, a simulation experiment was conducted. The simulation parameters were set as follows: Figures 4-7 Used to evaluate the system performance of the proposed solution in this invention. Figure 1 This is a three-dimensional coordinate diagram of the system model of the present invention, with units in meters. The large-scale path loss model is as follows: ,in , and These represent the path loss at 1 meter (m), the transmission distance, and the path loss exponent, respectively. Unless otherwise specified, the simulation parameters are set as follows: , , , , , as well as .

[0063] In the subsequent simulation results, the solid line represents the performance of the legitimate user Bob using a circularly polarized (CP) antenna configuration, and the dashed line represents the performance of Bob using a linearly polarized (LP) antenna configuration.

[0064] In addition to the polarization reconfigurable antenna (PRA) scheme proposed in this invention, two fixed polarization antenna (FPA) schemes are also introduced for comparison: (1) "CP" comparison scheme: the beamforming vector takes the optimal solution, and the polarization mode of the base station Alice is fixed as left-hand circular polarization. (2) "LP" comparison scheme: the beamforming vector takes the optimal solution, and the polarization mode of the base station Alice is fixed as vertical linear polarization. .

[0065] Simulation results show that, under different conditions such as maximum base station transmit power, number of antennas, inverse cross-polarization discrimination, and base station polarization channel correlation coefficient, the proposed scheme based on polarization reconfigurable antenna (PRA) consistently outperforms the two fixed polarization antenna (FPA) comparison schemes in terms of key generation rate (KGR). Furthermore, when the legitimate user Bob uses a circularly polarized (CP) antenna configuration, the overall key generation performance of the system is superior to that using a linearly polarized (LP) antenna configuration. This fully verifies that the present invention, by dynamically adjusting the PRA polarization state, can effectively alleviate the polarization mismatch problem, significantly improve the physical layer key generation rate and system security performance, and demonstrates good adaptability and stability in different application scenarios.

[0066] Finally, it should be noted that any parts of this invention not described in detail are prior art. Those skilled in the art will understand that the above descriptions are merely preferred embodiments of the invention and are not intended to limit the invention. Although the invention has been described in detail with reference to the foregoing examples, those skilled in the art can still modify the technical solutions described in the foregoing examples or make equivalent substitutions for some of the technical features. All modifications and equivalent substitutions made within the spirit and principles of the invention should be included within the scope of protection of the invention.

Claims

1. A physical layer key generation method based on polarization reconfigurable antennas (PRAs), applied to a wireless communication system, the system comprising a base station equipped with N PRAs, a single-antenna legitimate user, and a passive eavesdropper, the system operating in time-division duplex mode, characterized in that... The method includes the following steps: Step S1: Establish a polarization channel model that jointly considers polarization correlation, spatial correlation and channel depolarization effect, and derive a closed-form expression for the key generation rate based on the mutual information of channel characteristic information of the legitimate communicating parties. Step S2: With the goal of maximizing the key generation rate, construct a joint optimization problem of beamforming vector and PRA phase shift vector under the constraints of base station transmit power and PRA phase shift. Step S3: The joint optimization problem is solved by using an alternating optimization method. In each iteration, the beamforming vector is optimized while the PRA phase shift vector is fixed, and the PRA phase shift vector is optimized while the beamforming vector is fixed, until convergence is achieved, and the optimal beamforming vector and the optimal PRA phase shift vector are obtained. Step S4: The base station configures the PRA based on the optimal beamforming vector and the optimal PRA phase shift vector, and sends pilot signals to each other with the legitimate user to perform channel estimation. Both parties extract channel feature information based on the channel estimation results, and quantize, negotiate information and amplify privacy of the channel feature information to generate a consistent physical layer key.

2. The physical layer key generation method based on a polarization-reconfigurable antenna according to claim 1, characterized in that, The process of establishing the polarization channel model in step S1 includes: The polarization formation vector of the nth PRA is defined as: in, For the first n The phase shift of each PRA, j It is the imaginary unit; The polarization channel matrix from the nth PRA to the legitimate user is represented as: in, For the polarization leakage matrix, The polarization correlation matrix, For inverse cross-polarization discrimination, This represents the correlation coefficient between the vertical and horizontal components at the base station and the legitimate user. The elements are independent and identically distributed circularly symmetric complex Gaussian random variables; The overall channel model from the base station to the legitimate user is as follows: in, This refers to path loss. Let be a Toeplitz matrix whose elements satisfy... , Representation matrix The Line number Column elements; , ,and Let g be the PRA phase shift vector, and g be the polarization vector of the legitimate user.

3. The physical layer key generation method based on a polarization-reconfigurable antenna according to claim 1, characterized in that, In step S1, the closed-form expression for the key generation rate is: ， ， ， in, Indicates the key generation rate. Represents the channel characteristic information of the two parties in legitimate communication. and Mutual information between them; Represents the covariance parameter. This represents the autocovariance of the channel characteristic information at base station Alice. This represents the autocovariance of the channel characteristic information at the legitimate user Bob's location. This represents the joint covariance matrix of the channel characteristic information of both base station Alice and legitimate user Bob; , These are the channel feature information extracted from channel estimation by base station Alice and legitimate user Bob, respectively. express , The cross-variance between them yes The conjugate transpose of . This represents the determinant of the covariance matrix.

4. The physical layer key generation method based on a polarization-reconfigurable antenna according to claim 2, characterized in that, The joint optimization problem constructed in step S2 is expressed as: in, For beamforming vectors, The phase shift vector of PRA. This is the maximum transmit power of the base station. The key generation rate is represented by constraints C1 and C2, which represent the base station transmit power constraint and the PRA phase shift constraint, respectively.

5. The physical layer key generation method based on a polarization-reconfigurable antenna according to claim 4, characterized in that, In step S3, the PRA phase shift vector is fixed. At that time, beamforming vector The optimization subproblem is expressed as: Optimal solution of beamforming vector The following can be obtained by solving using Rayleigh's quotient: ， in, Represents beamforming vector The conjugate transpose of; This indicates that the PRA phase shift vector is fixed. The channel covariance matrix under the given conditions integrates channel state information, polarization correlation, and channel depolarization effect. Representation matrix The eigenvector corresponding to the largest eigenvalue.

6. The physical layer key generation method based on a polarization-reconfigurable antenna according to claim 4, characterized in that, In step S3, the beamforming vector is fixed. At that time, the PRA phase shift vector The optimization subproblem is solved by reconstructing the objective function into a quadratic form in terms of the phase shift vector, PRA phase shift vector. The optimization subproblem is expressed as: in, , , , ; Given a block diagonal matrix, maximizing the objective function is equivalent to optimizing each PRA phase shift independently: in, It is a Hermitian matrix. Representation matrix The OK; Optimal phase shift Represented as: .

7. The physical layer key generation method based on a polarization-reconfigurable antenna according to claim 6, characterized in that, The optimal phase shift of each PRA has an analytical closed-form solution, the expression of which is jointly determined by the polarization channel correlation coefficient, the inverse cross-polarization discrimination, and the polarization vector of the legitimate user. The optimal solution is the same as that of the beamforming vector. Irrelevant; The optimal phase shift Corresponding correlation quantity The explicit expression is: in, and The polarization channel correlation coefficient. denoted as inverse cross-polarization discrimination, and g is the polarization vector of the legitimate user.

8. The physical layer key generation method based on a polarization-reconfigurable antenna according to claim 7, characterized in that, When a legitimate user uses a linearly polarized antenna, that is... Or, the legitimate user-end antenna is fully polarized and decorrelated. At that time, the optimal phase shift Directly ; When the base station antenna is fully polarized and decorrelation occurs, At that time, the optimal phase shift ; After obtaining the optimal PRA phase shift vector, the channel covariance matrix simplifies to: ; in It is a vector jointly determined by the optimal phase shift, the polarization channel matrix, and the polarization vector of the legitimate user. , This is the spatial correlation matrix of the PRA at the base station.

9. The physical layer key generation method based on a polarization-reconfigurable antenna according to claim 1, characterized in that, The channel estimation in step S4 includes: obtaining the pilot signal sent by the base station from the legitimate user. The base station receives pilot signals sent by legitimate users and obtains... Both parties used the least squares method to perform channel estimation and obtained the channel estimates respectively. and The base station will Conjugate with the optimal beamforming vector Multiplication extracts the random components common to legitimate users, thereby obtaining highly correlated channel feature information.

10. A physical layer key generation system based on a polarization-reconfigurable antenna, used to implement the method according to any one of claims 1 to 9, characterized in that, The system includes: The base station is equipped with N polarization reconfigurable antennas (PRAs). Each PRA adjusts the phase difference between orthogonal polarization components through a phase shifter to achieve dynamic adjustment of the polarization state. It is used to configure the optimal beamforming vector and the optimal PRA phase shift vector based on statistical channel state information, transmit and receive pilot signals, and perform channel estimation. Legitimate users are equipped with a single fixed-polarization antenna to receive and transmit pilot signals, perform channel estimation, and generate a consistent physical layer key with the base station based on a highly correlated channel estimation value. A passive eavesdropper, whose distance from a legitimate user exceeds half a wavelength, has an eavesdropping channel that is statistically independent of the legitimate channel.

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